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Isaac Hewisn, 
 
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 V /rr/s/Ss’ ' Sr? i 
 
THE 
 
 ARTISAN; 
 
 OR, 
 
 MECHANICS INSTRUCTOR: 
 
 CONTAINING 
 
 A POPULAR, COMPREHENSIVE, AND SYSTEMATIC VIEW OF THE FOLLOWING 
 
 SCIENCES : 
 
 GEOMETRY, 
 
 MECHANICS, 
 
 HYDRODYNAMICS, 
 
 PNEUMATICS, 
 
 OPTICS, 
 
 CHEMISTRY, 
 
 ASTRONOMY, 
 
 ARCHITECTURE, 
 
 PERSPECTIVE, 
 
 ELECTRICITY, 
 
 MAGNETISM, 
 
 ALGEBRA. 
 
 biographical Notice# of eminent Scientific Jtten, 
 
 ENRICHED BY PORTRAITS: 
 
 WITH MAttY INTERESTING AND VALUABLE ARTICLES 
 
 RELATING TO 
 
 THE MECHANICAL AND USEFUL ARTS. 
 
 THE WHOLE INTENDED AS A 
 
 COMPANION TO THE INSTITUTES. 
 
 VOL. I. 
 
 LONDON : 
 
 PRINTED FOR WILLIAM COLE, 
 
 (LATE HODGSON AND CO.) 
 
 10, NEWGATE-STREET. 
 
PREFACE 
 
 Nothing tends so much to the successful cultivation of scientific 
 knowledge, as forming clear and accurate ideas of the Elements, or first 
 principles, of those sciences which form the basis of all physical know- 
 ledge. Convinced of the truth of this observation, and of the value of 
 scientific knowledge to the Artisans and Mechanics of this commercial 
 and manufacturing country, the Editor of the following work has endea- 
 voured to render the various subjects contained in it as plain and as 
 easily understood as the nature of them would permit. 
 
 In pure Geometry, it is scarcely possible to abridge the steps of a 
 demonstration, without rendering the truth of the proposition less appa- 
 rent; it has therefore been deemed more advantageous to the Geome- 
 trical student, to present him with the Propositions of Euclid’s Elements, 
 without attempting any abridgement or alteration of them. He will, 
 however, find many observations and useful remarks, on a number of 
 the propositions, that are not to be found in the common editions of the 
 Elements. 
 
 The science of Mechanics, though more intricate and complex than 
 Geometry, may nevertheless be very much simplified in many of its 
 most useful and practical branches, by explaining the laws and prin- 
 ciples upon which they rest, in common language , instead of expressing 
 them in mathematical and algebraical symbols. This has been particu- 
 larly attended to, in delivering the general doctrines of this science in 
 the following work, as well as in treating of the power and effects of 
 particular machines-. 
 
 The same rule has been observed in treating of Hydrodynamics, 
 Pneumatics, Optics, and Astronomy, though they are strictly mixed 
 mathematical sciences, and have hitherto been treated in the most 
 abstract and mathematical manner, even in works pretending to be 
 purely elementary. 
 
IV 
 
 PREFACE. 
 
 The science of Chemistry is also rendered as simple and amusing as 
 it is possible to make it; and the most accurate and modern improve- 
 ments which have been introduced into that science have been noticed. 
 
 To render the work useful and amusing, not only to the scientific 
 student, but to the general reader, an extensive miscellaneous depart- 
 ment has been added, including memoirs of the lives of men who have 
 distinguished themselves, either by the improvements they have made 
 in the Sciences, or the discoveries they have made in the Arts. Another 
 important feature of this department of the work is, a comprehensive 
 and popular view of the beautiful and elegant science of Architecture, 
 illustrated by neatly engraved specimens of the various orders of build- 
 ing, both ancient and modern. 
 
 The other subjects introduced into the Miscellaneous part of the 
 work, are perhaps as numerous as in some other works, which are 
 appropriated solely to subjects of this nature. And, upon examination, 
 they will be found not only interesting and useful at the 'present time, 
 but to be of such a nature, as to render them equally useful at any 
 future period. 
 
 The mathematical and philosophical questions contained in the work 
 may, perhaps, be considered by some as of too abstruse and intricate a 
 nature to be generally understood; but the reason for devoting a small 
 portion of the work to subjects of this kind, was to render it interesting, 
 and, if possible, valuable to the mathematician, and the philosopher, 
 as well as the tradesman and the mechanic. 
 
 The Copper-plate portraits which are given along with the work, are 
 of the very first order in point of execution; the same may be said 
 of the numerous Wood engravings interspersed through it. But a care- 
 ful perusal of the whole, and a comparison with other works that treat 
 of the same subjects, will afford the best criteria , for determining both 
 the comparative and real value of the work now offered to the public. 
 
INDEX 
 
 GEOMETRY. 
 
 
 Friction of Wheels - Page 245 
 
 Angles, various kinds of - 
 
 - 
 
 Page 5 
 
 , Method of diminishing 
 
 
 245 
 
 — , exterior, Property of 
 
 - 
 
 - 83 
 
 Fulcrum, what - 
 
 
 55 
 
 - — — , vertical, ditto 
 
 - 
 
 - 82 
 
 Gravity, what 
 
 - 
 
 7 
 
 Axioms - 
 
 - 
 
 - 17 
 
 ■ , centre of - 
 
 
 53 
 
 Book 1st. 
 
 - 
 
 - 4 
 
 Hook's Universal Joint - 
 
 
 278 
 
 Book 2d. 
 
 - 
 
 - 273 
 
 Inclined Plane, of the 
 
 
 ns 
 
 Book 3d. 
 
 - 
 
 - 369 
 
 Lever, of the - - 
 
 54. 84 
 
 Circle - 
 
 - 
 
 - 5 
 
 of Lagaroust 
 
 _ 
 
 277 
 
 Contrary Propositions, what 
 
 - 
 
 - 18 
 
 Machine in which all the Mechanical 
 
 
 Corollary, what 
 
 
 - 17 
 
 Powers are united 
 
 _ 
 
 279 
 
 Converse Propositions, what 
 
 - 
 
 - 17 
 
 Machine for trying the Strength 
 
 of 
 
 
 Definitions - - - 
 
 
 - 4 
 
 Materials - 
 
 _ 
 
 342 
 
 Demonstration, Direct and Indirect - 17 
 
 Machinery, Regulation of 
 
 _ 
 
 307 
 
 Enunciation, what 
 
 
 - 18 
 
 Matter, what - 
 
 _ 
 
 6 
 
 Geometry, Definition of - 
 
 
 - 4 
 
 Mechanics 6, 21, 51, 84, 115, 148, 
 
 
 Lemma, what 
 
 - 
 
 - 17 
 
 179, 212, 243, 276, 307, 
 
 340 
 
 Parallelogram, Definition of 
 
 " 
 
 - 177 
 
 Mechanical Agents - - ' 
 
 - 
 
 276 
 
 • , Properties of 
 
 
 - 178 
 
 Contrivances 
 
 
 277 
 
 Parallel Lines, what 
 
 - 
 
 - 6 
 
 Powers 
 
 
 54 
 
 Properties of 
 
 * 
 
 - 146 
 
 Mobility, what 
 
 . 
 
 7 
 
 Pons Asinorum 
 
 - 
 
 - 20 
 
 Motion, various kinds of - 
 
 
 8 
 
 Postulates - 
 
 - 
 
 - 17 
 
 , 1st. Law of - 
 
 
 21 
 
 Problem, what 
 
 * 
 
 - 17 
 
 2d ditto - 
 
 
 22 
 
 Proposition, Definition of 
 
 - 
 
 - 17 
 
 , 3d ditto - 
 
 
 23 
 
 Propositions, Book 1st. 18, 49, 
 
 81, 
 
 Pinion, what - 
 
 
 86 
 
 113, 145, 177, 
 
 209, 241 
 
 Pulley, of the - - 
 
 
 115 
 
 Propositions, Book 2d. 273, 
 
 305, 337 
 
 Screw, of the - 
 
 - 
 
 149 
 
 Propositions, Book 3d. 
 
 - 
 
 - 369 
 
 Smeaton's Machine for Experiments 
 
 
 Rectangle, what 
 
 - 
 
 - 273 
 
 on Rotatory Motion 
 
 _ 
 
 341 
 
 Reductio ad Absurdum - 
 
 - 
 
 - 17 
 
 Specific Gravity, what 
 
 _ 
 
 8 
 
 Square, Definition of 
 
 - 
 
 - 6 
 
 Steelyard, what - 
 
 _ 
 
 181 
 
 Superficies, what 
 
 
 - 4 
 
 Time, how expressed 
 
 
 8 
 
 — — Plane, ditto - 
 
 - 
 
 - 4 
 
 Velocity, various rates of - 
 
 _ 
 
 21 
 
 Theorem, what 
 
 - 
 
 - 17 
 
 Vis Inertia - 
 
 
 7 
 
 Triangles, various kinds of 
 
 - 
 
 - 5 
 
 Wedge, of the - 
 
 . 
 
 148 
 
 MECHANICS. 
 
 
 
 Weight, what - 
 
 _ 
 
 7 
 
 Animals, Strength of 
 
 _ 
 
 - 276 
 
 Wheel and Axle, of the - 
 
 - 
 
 85 
 
 Atwood's Machine, Description of - 309 
 
 Windlass - 
 
 - 
 
 86 
 
 Balance, of the 
 
 - 
 
 - 179 
 
 HYDRODYNAMICS. 
 
 
 
 — — - Fraudulent - 
 
 _ 
 
 - 181 
 
 Archimedes’s Screw 
 
 _ 
 
 151 
 
 Ball and Socket 
 
 - 
 
 - 278 
 
 Barker’s Mill - 
 
 _ 
 
 312 
 
 Belts or Bands 
 
 - 
 
 - 277 
 
 Capillary Tubes, effects of 
 
 _ 
 
 56 
 
 Capstan - 
 
 
 - 86 
 
 Suspension 
 
 _ 
 
 57 
 
 Crank, various kinds of . 
 
 - 
 
 - 278 
 
 Columnaria, what 
 
 
 87 
 
 Density, what 
 
 - 
 
 - 8 
 
 Equilibrium of Indifference 
 
 
 26 
 
 Divisibility, what 
 
 - 
 
 - 7 
 
 Stable — Unstable - 
 
 „ 
 
 27 
 
 Dynamics, Definition of - 
 
 - 
 
 - 6 
 
 Fluids, Bodies floating in 
 
 _ 
 
 26 
 
 Extension, Definition of - 
 
 - 
 
 - 76 
 
 — issuing through Apertures 
 
 _ 
 
 57 
 
 Falling Bodies * 
 
 
 - 51 
 
 pressure of - 
 
 - 
 
 87 
 
 Figure, what 
 
 - 
 
 - 6 
 
 how conveyed in Pipes 
 
 - 
 
 87 
 
 Forces, various kinds of 
 
 - 
 
 - 21 
 
 percussion and resistance of 
 
 
 119 
 
 Composition and Resolution of 24 
 
 Fountain, Hungarian 
 
 _ 
 
 217 
 
 Friction, account of, 
 
 - 
 
 - 212 
 
 — of Schemnitz and Hiero 217, 
 
 218 
 
 of Surfaces 
 
 - 
 
 - 212 
 
 Hydraulics 87, 118, 151, 183, 216, 
 
 
 — of Axles - 
 
 > 
 
 - 214 
 
 247, 280, 311, 
 
 343 
 
 of Wheel Carriages 
 
 _ 
 
 - 215 
 
 Hydraulic Ram - 
 
 - 
 
 216 
 
 of Ropes - 
 
 - 
 
 - 243 
 
 Hydrostatics - - - 9, 
 
 25 
 
 , 56 
 
 — of Pivots - 
 
 - 
 
 - 244 
 
 Hydrostatical Balance and Paradox 
 
 9 
 
 nn 
 
INDEX. 
 
 Montgolfier’s Ram - - Page 
 
 Pump Chain ..... 
 
 • — — Cellular .... 
 Pump, Paternoster - 
 
 ■ Rope - 
 
 Pump, Spiral 
 
 Shower Bellows .... 
 
 Spanish Noria - 
 
 Specific Gravity defined ... 
 
 — method of Determining - 
 
 — Table of ... 
 
 Stopcock, compound - 
 
 Syphon - 
 
 Floating - 
 
 Tantalus’s Cup - - - - 
 
 Valves, various kinds of - 
 Water discharged by Pipes 
 
 effective head of - 
 
 form of the dead 
 
 Machines for discharging 
 
 ■ Machines moved by the re- 
 
 action of ... 
 
 Machines for measuring the 
 
 velocity of - 
 
 Machine for raising 
 
 Machines raised by changes in 
 
 the air - 
 
 running in Canals - 
 
 Screw ..... 
 
 Snail 
 
 — Velocity of - 
 
 Wheels, comparative effects of 
 
 Waves, formation and Extent of ; 
 
 Velocity of - 
 
 Wheels, Breast ----- 
 
 Chain - 
 
 Horizontal - 
 
 Persian - 
 
 Scoop - 
 
 Overshot - 
 
 Smeaton’s - 
 
 Undershot .... 
 
 at right angles to the Stream 
 
 Besant’s - ... 
 
 Bossut’s ... 
 
 Pitot’s .... 
 
 • Smeaton’s - 
 
 with Spiral float-boards 
 
 Whitehurst’s Engine - 
 
 Zurich Machine - 
 
 PNEUMATICS. 
 
 Air, Condensed - 
 
 — — Effects of on bodies in motion - 
 
 Elasticity of 
 
 Experiments Avith - 
 
 Gun described - 
 
 Properties of - 
 
 . Pressure of ~ 
 
 Pump described 
 
 Resistance of - 
 
 Temperature of 
 
 Weight of - 
 
 Anemoscope - - - 
 
 Barometer, Mensuration of heights by 
 
 Bellows, wind - - - 
 
 Diving Bell - 
 
 Experiments with Air Pump - 
 
 Experiments on the weight of the Air 67 
 
 * on Resistance of ditto - 97 
 
 — on Elasticity of Air - 98 
 
 _ Miscellaneous on ditto - 99 
 
 Lift-tenter described ... 226 
 Parallel Motion described - - 259 
 
 Pistons of Pumps - - - 133 
 
 of Steam Engines - - 195 
 
 Pneumatics 10, 33, 67, 97, 131, 161, 
 
 195, 225, 259, 289, 321, 
 
 353, 
 
 385 
 
 Pump Valves, of 
 
 - 
 
 - 
 
 133 
 
 — Lifting - - - 
 
 - 
 
 
 161 
 
 Forcing 
 
 - 
 
 - 
 
 166 
 
 Centrifugal 
 
 - 
 
 - 
 
 162 
 
 Steam Engine 
 
 _ 
 
 - 
 
 195 
 
 Maudslay’s 
 
 - 
 
 289, 
 
 322 
 
 Newcomen’s 
 
 - 
 
 - 
 
 195 
 
 Savery’s 
 
 Watt’s 
 
 - 
 
 - 
 
 195 
 
 _ 
 
 . 
 
 196 
 
 Worcester’s 
 
 . 
 
 . 
 
 165 
 
 Steam Gauge 
 
 . 
 
 - 
 
 228 
 
 Navigation 
 
 - 
 
 - 
 
 322 
 
 Sun and Planet wheels 
 
 . 
 
 - 
 
 227 
 
 Symington’s Boat 
 
 
 . 
 
 323 
 
 Vacuum Gas Engine 
 
 - 
 
 _ 
 
 259 
 
 Valve, Safety ... 
 
 - 
 
 
 353 
 
 Throttle 
 
 _ 
 
 . 
 
 226 
 
 Wind Mill 
 
 . 
 
 
 354 
 
 Chariot 
 
 _ 
 
 - 
 
 385 
 
 Waggon 
 
 - 
 
 - 
 
 386 
 
 OPTICS. 
 
 
 
 
 Camera Lucida 
 
 . 
 
 
 264 
 
 Obscura 
 
 . 
 
 - 
 
 228 
 
 Catoptrics - - 
 
 _ 
 
 - 
 
 11 
 
 Colour, what 
 
 - 
 
 - 
 
 102 
 
 of Natural Bodies 
 
 - 
 
 _ 
 
 136 
 
 of the Atmosphere 
 
 - 
 
 - 
 
 199 
 
 Concave Glass, what 
 
 . 
 
 - 
 
 13 
 
 Properties, of 
 
 - 
 
 - 
 
 39 
 
 Mirrors, of 
 
 - 
 
 - 
 
 72 
 
 Convex Glass, what - 
 
 . 
 
 - 
 
 13 
 
 — Properties of 
 
 - 
 
 - 
 
 37 
 
 Dioptrics 
 
 - 
 
 - 
 
 11 
 
 Eye, Description of the 
 
 - 
 
 - 
 
 39 
 
 Defects of the - 
 
 . 
 
 . 
 
 70 
 
 Focus, what - - - 
 
 - 
 
 . 
 
 37 
 
 Glasses, various kinds of 
 
 _ 
 
 . 
 
 13 
 
 Incidence, angle of - 
 
 . 
 
 - 
 
 12 
 
 Light, opinions respecting 
 
 - 
 
 - 
 
 21 
 
 of various colours of 
 
 - 
 
 - 
 
 102 
 
 Polarization of - 
 
 . 
 
 - 
 
 163 
 
 Magic Lantern - - 
 
 . 
 
 
 229 
 
 Medium, what 
 
 _ 
 
 _ 
 
 12 
 
 Megascope ... 
 
 
 _ 
 
 229 
 
 Meniscus Glass, what 
 
 - 
 
 - 
 
 13 
 
 Microscopes, various kinds of - - 70 
 
 — — Magnifying power of - 71 
 
 Mirror, Cylindrical - - 199 
 
 Multiplying Glass 
 
 
 - 101 
 
 Optics, 36, 70, 101, 134, 163, 
 
 197. 
 
 ,228, 
 
 263, 291, 
 
 324, 
 
 357, 388 
 
 Optics, Division of 
 
 
 - 11 
 
 Optigraph, Description of 
 
 
 - 386 
 
 Phantasmagoria, what 
 
 
 - 263 
 
 Phatometry, what 
 
 
 - 388 
 
 Plano Concave Glass, what 
 
 
 - 13 
 
 — - — Convex Glass, what 
 
 - 
 
 - 13 
 
 216 
 
 183 
 
 184 
 
 184 
 
 153 
 
 152 
 
 343 
 
 153 
 
 10 
 
 10 
 
 25 
 
 89 
 
 34 
 
 343 
 
 59 
 
 89 
 
 88 
 
 59 
 
 121 
 
 343 
 
 311 
 
 313 
 
 151 
 
 218 
 
 89 
 
 152 
 
 151 
 
 89 
 
 311 
 
 118 
 
 119 
 
 153 
 
 250 
 
 284 
 
 183 
 
 183 
 
 247 
 
 249 
 
 280 
 
 283 
 
 281 
 
 281 
 
 281 
 
 281 
 
 284 
 
 184 
 
 152 
 
 131 
 
 34 
 
 95 
 
 67 
 
 131 
 
 10 
 
 67 
 
 34 
 
 97 
 
 11 
 
 10 
 
 386 
 
 33 
 
 • 387 
 
 132 
 
 67 
 
INDEX; 
 
 Prism, Description of - Page 
 Rainbow, account of - 
 
 Lunar, ditto - 
 
 Rays, Parallel - 
 
 Coloured - 
 
 Diverging - - - 
 
 Homogeneous - 
 
 Reflected — Refracted 
 
 Reading Glasses - 
 
 Refraction, Angle of - 
 
 Double - 
 
 unusual, of the Atmos- 
 phere - 
 
 Refractive Power of Substances 
 Solar Spectrum - 
 
 Telescope, of the - - 
 
 Achromatic - 
 
 Astronomical - 
 
 — Brewster’s ... 
 
 Cassegrainian - 
 
 Dolland’s - 
 
 Galilean ... 
 
 ■ Gregorian ... 
 
 Herschel’s - 
 
 ■ Newtonian - 
 
 Reflecting kind 
 
 Refracting ditto 
 
 — Tremors of 
 
 CHEMISTRY. 
 
 Affinity, what - 
 
 Elective - 
 
 Alloys, what - 
 
 Amalgam, what - 
 
 Azote, what - ... 
 
 how procured 
 
 Combinations of 
 
 ■ Properties of - 
 
 Carbon, what — How procured - 
 
 Properties and Combinations 
 
 Carburetted Hydrogen Gas 
 Charcoal, Preparation of - 
 
 Properties of - 
 
 Chemistry IB, 40, 73, 103, 138, 166, 
 
 200, 230, 267, 294, 327, 359, 
 
 Etymology of - _ ; - 
 
 — - History of 
 
 Chlorine, how obtained - - 
 
 — Combinations of 
 
 Properties of - 
 
 Uses of 
 
 Compound Bodies - 
 
 Diamond, nature and Properties of - 
 
 Gold ..... 361, 
 
 Oxides and Properties of 361, 
 
 Hydrogen Gas - 
 
 — — how procured 
 
 — — — Combinations of 
 
 — . Properties of 
 
 Iodine, Combinations of - 
 
 — Discovery of - - 
 
 how procured ... 
 
 — Properties of - 
 
 Lutes, their use - 
 
 Metals, account of - 
 
 Calces of ... 
 
 Classification of 
 
 - — ____ General Properties of - 
 
 Metals, History of - Page 227 
 
 Imperfect ... 3G0 
 
 Oxides of ... 229 
 
 Perfect .... 3 go 
 
 Table of 361 
 
 • Uses of .... 327 
 
 Muffle, what .... 105 
 
 Muriatic Acid .... 230 
 
 absorbed by Water - 232 
 
 how procured - - 231 
 
 • Properties of - 231 
 
 Oxygen Gas, how obtained - 41 
 
 — its Properties - - 42 
 
 Phosphorus, Description of 105 
 
 how procured - - 105 
 
 Properties of - - 139 
 
 Phosphoric acid .... 139 
 
 Phosphuretted Hydrogen - - 139 
 
 Platina, history of ... 391 
 
 Simple Bodies, what - - - 40 
 
 Sulphur, account of - - 166 
 
 — • — Combinations of - 166 
 
 Combustion of - - - 167 
 
 Properties and Purification of 166 
 
 Wolf’s Apparatus, representation of - 232 
 
 ASTRONOMY. 
 
 Astronomical definitions - - - 78 
 
 Astronomy 16, 27, 44, 76, 106, 140, 169, 
 
 202, 233, 270, 296, 330, 362, 394 
 
 History of - - - 16 
 
 — various systems of - 46 
 
 Atmosphere - - - - 364 
 
 — refraction of the - - 364 
 
 Ceres, description of ... 169 
 Cirrus ...... 395 
 
 Clouds, formation of ... 394 
 Comets, account of - - -169 
 
 Copernican system - - - 47 
 
 Cumulus ----- 396 
 
 Earth, of the - - - - 108 
 
 Eclipses, how produced - - 330 
 
 ■ of the Sun ... 331 
 
 of the Moon - - - 331 
 
 of Jupiter’s Satellites - 233 
 
 Jupiter, description of - 109,. 140 
 
 Light, an account of ... 362 
 Mars, description of 108 
 
 Mercury, description of - - - 107 
 
 Moon, description of ... 203 
 
 apparent size of 234 
 
 Harvest - 233 
 
 Motions >of - 204 
 
 Mountains of, &c. - - - 270 
 
 — Phases of 203 
 
 New Planets - - - - 169 
 
 Pallas described F - - - - 169 
 
 Planets, inferior— -primary - - 77 
 
 secondary — superior - - 77 
 
 Ptolemaic system - - - - 46 
 
 Saturn, description of - - 141 
 
 Solar System 76 
 
 Stars, fixed ..... 296 
 
 their distance and number - 297 
 
 Sun, of the ----- 78 
 
 heat of - - - 106 
 
 Sun, light of - - - - - 79 
 
 Tychonic System - - - - 47 
 
 102 
 
 134 
 
 135 
 
 13 
 
 103 
 
 13 
 
 103 
 
 12 
 
 70 
 
 12 
 
 165 
 
 197 
 
 165 
 
 102 
 
 265 
 
 357 
 
 266 
 
 325 
 
 292 
 
 357 
 
 266 
 
 291 
 
 324 
 
 293 
 
 291 
 
 365 
 
 357 
 
 40 
 
 43 
 
 330 
 
 330 
 
 209 
 
 200 
 
 201 
 
 200 
 
 75 
 
 104 
 
 104 
 
 75 
 
 76 
 
 390 
 
 40 
 
 13 
 
 267 
 
 268 
 
 268 
 
 269 
 
 40 
 
 105 
 
 390 
 
 362 
 
 73 
 
 74 
 
 75 
 
 74 
 
 295 
 
 294 
 
 294 
 
 294 
 
 42 
 
 327 
 
 229 
 
 360 
 
 328 
 
INDEX. 
 
 Uranus, or Georgium Sidus 
 
 
 Page 141 
 
 Venus, description of 
 
 
 - 107 
 
 transit of - - 
 
 - - 
 
 - 108 
 
 Vesta described - 
 
 - 
 
 - 166 
 
 ARCHITECTURE. 
 
 
 Arches, Construction of 
 
 
 - 317 
 
 — Catanarian 
 
 
 - 317 
 
 Various kinds of 
 
 - 
 
 - 317 
 
 Architecture, Civil 
 
 - 
 
 - 253 
 
 Definitions 
 
 
 - 175 
 
 — Division of 
 
 - 
 
 - 154 
 
 — Gothic 
 
 - 
 
 - 253 
 
 History of 
 
 - 
 
 - 154 
 
 — Military and Naval - 154 
 
 Architecture 154, 174, 188, 
 
 205, 
 
 221, 
 
 236, 
 
 253, 
 
 286, 317 
 
 Architrave, what 
 
 - 
 
 - 175 
 
 Astragal, what 
 
 - 
 
 - 175 
 
 Base - - - 
 
 - 
 
 - 175 
 
 Bridge, Blackfriars’ 
 
 
 - 318 
 
 Capital, and Cornice, what 
 
 - 
 
 - 175 
 
 Entablature 
 
 ■ - 
 
 - 175 
 
 Facades, what — Frieze 
 
 - 
 
 - 175 
 
 King’s Chapel, Cambridge, view 
 
 of - 254 
 
 Mouldings, various kinds of 
 
 - 
 
 - 286 
 
 Order, what 
 
 - 
 
 •• 175 
 
 Composite 
 
 - 
 
 - 236 
 
 Corinthian 
 
 - 
 
 - 221 
 
 Doric 
 
 
 - 188 
 
 Ionic 
 
 - 
 
 - 205 
 
 Tuscan 
 
 - 
 
 - 188 
 
 Pedestal, what — Plinth - 
 
 - 
 
 - 175 
 
 Shaft - 
 
 - 
 
 - 175 
 
 Tri glyph, what 
 
 - 
 
 - 205 
 
 Volute, what 
 
 - 
 
 175 
 
 BIOGRAPHY. 
 
 
 
 Life of Agnesi, M. - 
 
 - 
 
 - 154 
 
 Archimedes 
 
 - 
 
 - 30 
 
 Bacon, Lord Francis 
 
 - 
 
 - 193 
 
 — Bacon, Roger - 
 
 - 
 
 - 314 
 
 Copernicus 
 
 - 
 
 - 122 
 
 Davy, Sir H. 
 
 - 
 
 - 65 
 
 — Emerson, W. 
 
 - 
 
 - 251 
 
 Euclid 
 
 _ 
 
 - 59 
 
 — - — - Euler, Leonard 
 
 - 
 
 - 345 
 
 Ferguson, James 
 
 - 
 
 - 235 
 
 Franklin, Dr. 
 
 - 
 
 - 366 
 
 Galileo 
 
 - 
 
 - 172 
 
 Hutton, Dr. 
 
 Hypatia 
 
 - 
 
 - 257 
 
 - 
 
 - 333 
 
 Mayer, J. Tobias v 
 
 - 
 
 - 397 
 
 Newton, Sir I. 
 
 - 
 
 - 3 
 
 Playfair, Professor 
 
 - 
 
 - 218 
 
 Ramsden, Mr. 
 
 - 
 
 - 185 
 
 Saunderson, Nicholas 
 
 - 298 
 
 Simpson, Thomas 
 
 - 
 
 - 90 
 
 Watt, James 
 
 - 
 
 - 129 
 
 Questions and Solutions 32, 
 
 , 48, 
 
 63, 
 
 80, 95, 112, 127, 144, 1G0, 175, 191, 
 207, 223, 240, 256, 272, 288, 304, 
 320, 336, 352, 368, 384, 399 
 
 END OF 
 
 MISCELLANEOUS. 
 
 Alcohol, quantity in Porter Page 23S 
 Apartments, method of warming - 302 
 Aquatinta Engraving - - - 32 
 
 Balloons, construction of - 238 
 
 improvement of - » 351 
 
 Bell’s Apparatus, description of - 301 
 Bridges, suspension - 159 
 
 Carey’s Arithmetic reviewed - - 318 
 
 Celestial Atlas, account of 235 
 
 Chinese Year, on the - - ■■ 143 
 
 Clocks, oil for 94 
 
 Cloth, how embroidered - 303 
 
 Columns, strongest form of 189 
 
 Congelation, line of - - - - 110 
 
 Electro-magnetic experiments - - 352 
 
 Fire, how to extinguish - 384 
 
 Fixed Stars, pamphlet on the - - 303 
 
 Galvanism and Fermentation, on - 237 
 Gases, correction for temperature - 126 
 Gilding with Gold - 206 
 
 - — — on Brass, &c. - 207 
 
 on Leather - • - 238 
 
 Glass, to etch designs on - - 191 
 
 — to stain .... 206 
 
 Gunter’s Scale, description of - 347, 380 
 Heat, singular application of - - 63 
 
 Hydraulic Ram, of the - 335. 
 
 Inks, sympathetic - 252 
 
 Longitude Scale - - - - 31 
 
 Machine for making bread - - 94 
 
 Magnetism-electro, on - 157 
 
 effects of - - 158 
 
 Medical pump - 286 
 
 Moon, conjectures respecting the - 94 
 
 Mosaic, manufacture of - 239 
 
 Mountains, heights of - - - 61 
 
 Nautical eye tube - 158 
 
 Nitre, preparation of - - - 157 
 
 Optics, on the study of - - 62 
 
 Pendulum, Kater on the - 142 
 
 application of - - 155 
 
 Perpetual motion impossible - - 222 
 
 Printing, on Lithographic - - 159 
 
 Queries, answers to - - - 111 
 
 Query, Philosophical - - - 32 
 
 Rain, the cause of ... 207 
 
 Refraction of the atmosphere - - 156 
 
 Safety Lamp ----- 125 
 
 Seamen, apparatus for saving - - 349 
 
 Sea, temperature of the - - 158 
 
 Starch, preparation of - - - 191 
 
 Stars, change in the place of - - 157 
 
 Steam, force of - 159 
 
 Sulphur, action of on Iron - -158 
 
 Trees, representation of - - - 287 
 
 Trigonometrical Survey, on the - 80 
 
 Vernier Scale described - - 205 
 
 Water, electric effects of - 319 
 
 Weights, new French - - - 111 
 
 Weights, &c., uniformity of - 281, 398 
 Wind, intensity of - 190 
 
 VOL. I. 
 
 Printed by W\ Cole , in, Newgatc-street. 
 
Stye artisan; 
 
 OR, 
 
 MECHANIC’S INSTRUCTOR: 
 
 BEING 
 
 A COMPANION TO THE INSTITUTES. 
 
 INTRODUCTION. 
 
 The value of scientific knowledge is now so generally known and appre- 
 ciated in this country, that any attempt to point out the advantages 
 resulting from an acquaintance with it, would be quite superfluous. It 
 must, however, be admitted, that the value of this species of knowledge is 
 more generally understood than the principles upon which it is founded. 
 The effects produced by it are seen and acknowledged by all; but com- 
 paratively few are acquainted with the mode of producing them. Every 
 one has seen and must admire both the structure and powerful effects of 
 the Steam-engine ; but few are acquainted either with the scientific prin- 
 ciples upon which its construction depends, or with the nature of the 
 extraordinary fluid by which its surprising effects are produced. Being 
 fully convinced of the truth of these observations, and of the great 
 importance of scientific knowledge to every individual engaged in the 
 cultivation of the Arts, the Conductors of the present Publication have 
 resolved to devote the greater part of the work to the developement and 
 explanation of the fundamental principles of those Sciences which form 
 the basis of the Mechanical Arts. Particular care will, therefore, be 
 taken to give a comprehensive and connected view of the most useful 
 branches of Mathematics, Mechanics, Hydrostatics, Pneumatics, Optics, 
 Astronomy, and Chemistry. 
 
 In treating of these sciences, the greatest pains will be taken to render 
 them as plain and easily understood as their nature will admit ; — and in 
 order to render the work of permanent utility, not only to those who are 
 beginning the study of these sciences, but to those who are already well 
 acquainted with them, a regular and systematic arrangement of the 
 various parts of each will be preserved, and no part omitted which can 
 be considered of real value. 
 
 Mathematical knowledge being the foundation of all physical science, 
 as well as most of the mechanical arts, has certainly the first claim to 
 attentive observation; a portion of “ Euclid's Elements" will therefore 
 be given in each Number of the “ Artisan," in a more simple and popular 
 form than that celebrated work has ever yet assumed : for although we 
 are perfectly aware that “ there is no Royal Road to Geometry," yet we 
 do think that many of the Propositions in that work may be made more 
 intelligible to mathematical Students than they are, as they stand in the 
 most popular editions of the Elements. It will, therefore, be the parti- 
 
 Yol. I. B 
 
2 
 
 INTRODUCTION. 
 
 cular care of the Conductors of the “ Artisan,” to make this part of the 
 work as easily understood as possible, knowing that little progress can he 
 made in any of the physical sciences without possessing a tolerable share 
 of mathematical knowledge. This is a fact so well knowh to those who 
 have made those sciences their particular study, that no arguments can be 
 employed to give additional weight to it. And though it may be impos- 
 sible to give an adequate idea of the usefulness of mathematical know- 
 ledge to those who are wholly unacquainted with it, yet it may atford 
 some satisfaction to those who are about to commence the study to 
 observe, that mathematical knowledge supplies most of the means by 
 which, the business of society is carried on, and its comfort secured. To 
 mathematical principles the skilful Architect necessarily resorts for the 
 means of contriving and executing his plans ; and to them every building, 
 from the cottage to the palace, owes its existence. By mathematical 
 knowledge the mariner shapes his course through the wide and pathless 
 ocean, the intrepid soldier plans his operations for the protection of his 
 country, the skilful miner contrives his subterraneous excavations, and 
 procures for our use most of the substances employed in the arts of 
 civilized life. 
 
 Having here stated, in general terms, some of the uses of mathematical 
 science, it is unnecessary to make any observations on the other sciences 
 to be introduced in the present publication, because the utility of these 
 are much more apparent to the generality of mankind, than the science 
 upon which they immediately depend. But though this be the case, the 
 sciences themselves are necessarily as little known as the elementary 
 branches of mathematics. It will, therefore, be the study of the Conductors 
 of the “ Artisan v to present their readers with a regular and comprehen- 
 sive view of the various branches of Natural Philosophy, as far as they 
 are known at the present day. And to render their work of general 
 interest, part of each Number will be devoted to giving an account of any 
 discovery or improvement that may be made in the Arts ; with biogra- 
 phical notices of men who have contributed to the advancement either of 
 the Arts or Sciences. 
 
 The Editors will therefore receive with gratitude short and authentic 
 communications relative to every species of useful knowledge ; but they 
 have resolved to exclude every thing of a speculative nature, and to con- 
 fine their work entirely to the promulgation of facts founded on experi- 
 ment and observation. By thus selecting and condensing their materials, 
 and by endeavouring to give a popular form to the various subjects that 
 come under their notice, the Conductors of the “ Artisan” trust that they 
 may, in some degree, advance the interest of science, by promoting its 
 general diffusion, at a time when there is so much anxiety shown 
 by every class of the community to acquire a knowledge of the accurate 
 sciences. 
 
 The Editors also trust that the plan here adopted, of giving a clear and 
 connected view of each of the Sciences contained in the present Number, 
 will be considered the most effectual mode of aiding the laudable exertions 
 now making by the operative Mechanics of this Country, to acquire a 
 knowledge of the principles upon which their respective arts depend. 
 They are, therefore, not without hopes that their exertions may suc- 
 cessfully contribute to the diffusion of scientific knowledge, as well as to 
 the advancement of the useful Arts. 
 
3 
 
 BIOGRAPHICAL MEMOIR 
 
 OF 
 
 SIR ISAAC NEWTON, 
 
 Sir Isaac Newton, one of the greatest mathematicians and philosophers that ever 
 lived, was born in Lincolnshire, in 1642. Having made some proficiency in the clas- 
 sics, &c. at the grammar school at Grantham, he (being an only child) was taken 
 home by his mother (who was a widow) to be her companion, and to learn the manage- 
 ment of his paternal estate : bnt the love of books and study occasioned his farming 
 concerns to be neglected. In 1660 he was sent to Trinity College, Cambridge : here 
 he began with the study of Euclid, but the propositions of that book being too easy to 
 arrest his attention long, he passed rapidly on to the Analysis of Des Cartes, Kepler’s 
 Optics, &c. making occasional improvements on his author, and entering his ob- 
 servations, &c. on the margin. His genius and attention soon attracted the favourable 
 notice of Dr. Barrow, at* that time one of the most eminent mathematicians in 
 England, who soon became his steady patron and friend. In 1664 he took his 
 degree of B.A. and employed himself in speculations and experiments on the na- 
 ture of light and colours, grinding and polishing optic glasses, and opening the way 
 for his new method of fluxions and infinite series. The next year, the plague which 
 raged at Cambridge obliged him to retire into the country ; here he laid the foundation 
 of his universal system of gravitation, the first hint of which he received from 
 seeing an apple fall from a tree ; and subsequent reasoning induced him to conclude, 
 that the same force which brought down the apple might possibly extend to the 
 moon, and retain her in her orbit. He afterwards extended the doctrine to all the 
 bodies which compose the solar system, and demonstrated the same in the most 
 evident manner, confirming the laws which Kepler had discovered, by a laborious 
 train of observation and reasoning ; namely, that u the planets move in elliptical orbits,” 
 that “ they describe equal areas in equal times and that the squares of their 
 periodic times are as the cubes of their distances. Every part of natural philo- 
 sophy not only received improvement by his inimitable touch, but became c new 
 science under his hands : his system of gravitation, as we have observed, confirmed 
 the discoveries of Kepler, explained the immutable laws of nature, changed the 
 system of Copernicus from a probable hypothesis to a plain and demonstrated truth, 
 and effectually overturned the vortices and other imaginary machinery of Des Cartes, 
 with all the improbable epicycles, deferents, and clumsy apparatus, with which the 
 ancients and some of the moderns had encumbered the universe. In fact, his Phi- 
 losophies Naturalis Principia Mathematica contains an entirely new system of philo- 
 sophy, built on the solid basis of experiment and observation, and demonstrated 
 by the most sublime Geometry ; and his treatises and papers on optics supply a new 
 theory of light and colours. The invention of the reflecting telescope, which is due to 
 Mr. James Gregory, would in all probability have been lost, had not Newton inter- 
 posed, and by his great improvements brought it forward into public notice 
 
 In 1667, Newton was chosen fellow of his College, and took his degree of M.A. 
 Two years after, his friend Dr. Barrow resigned to him the mathematical chair ; he 
 became a member of parliament in 1688 ; and through the interest of Mr. Montagu, 
 Chancellor of the Exchequer, who had been educated with him at Trinity College, 
 our author obtained in 1696 the appointment of Warden, and three years after that 
 of Master, of the Mint : he was elected in 1699 member of the Royal Academy of 
 Sciences at Paris ; and in 1703 President of the Royal Society, a situation which he 
 filled during the remainder of his life, with no less honour to himself than benefit 
 to the interests of science. 
 
 In 1705, in consideration of his superior merit, Queen Anne conferred on him the 
 honour of knighthood : he died on March 20th, 1727, in the 85th year of his age. 
 His works, collected in 5 volumes, 4to. with a valuable Commentary by Dr. Horsley, 
 were published in 1784, 
 
 b 2 
 
4 
 
 THE ARTISAN. 
 
 GZSOMZSTZt'Sr. 
 
 Geometry is that branch of the Mathema- 
 tics which treats of figure and extension ; 
 and is divided* into Plane and Solid.* 
 
 Plane Geometry being the foundation, 
 not only of solid Geometry, but of most 
 of the other branches of the Mathematics, 
 it naturally falls to be considered before 
 any of the other branches ; — and as Euclid’s 
 Elements is generally allowed to be the 
 best system of Geometry that has yet made 
 its appearance in the world, we shall adopt 
 that celebrated work as our text-book in 
 treating of Geometry, in this and the suc- 
 ceeding Numbers of the Artisan. 
 
 In attempting to illustrate, or explain, 
 the following definitions and propositions, 
 we are perfectly aware that many of our 
 expressions and illustrations will be ob- 
 jected to by the speculative and rigid 
 mathematician ; but, as we have already 
 stated elsewhere, our object is simplicity ; 
 and to convey a knowledge of the sciences 
 to those who are wholly unacquainted 
 with them. 
 
 DEFINITIONS.! 
 
 1. A Mathematical point is that which 
 hath no parts nor magnitude. 
 
 2. A line is length without breadth. 
 
 3. The extremities of a line are points. 
 
 It is evident that there is nothing in na- 
 ture agreeing with, or corresponding to, a 
 point or a line taken in the sense of the 
 first and second definition ; but still they 
 may be comprehended by the mind, for they 
 may be conceived to mark the position 
 where a real point or a line may be 
 formed. In the case of a real distance 
 between two places, which is certainly a 
 line, no enquiry is ever made about the 
 breadth of that distance. 
 
 4. A straight line joining any two points 
 upon a plane, or surface, lies wholly on 
 that surface. 
 
 5. A superficies is a space which has only 
 length and breadth, or it is a surface, with- 
 out thickness. 
 
 In speaking of the superficies, or surface, 
 of a table, a wall, or a field, the thickness 
 is laid out of the question. 
 
 6. The extremities or boundaries of a 
 superficies are lines, which may be either 
 straight or curved.— A circle is bounded 
 only by one line. 
 
 * The word Geometry is formed from two Greek 
 words; and literally signifies to measure tta earth. 
 
 t Though some of Euclid’s definitions are omitted, 
 as being unnecessary, yet those which are intro- 
 duced here are numbered as in Dr. Simpson’s 
 Euclid, which is the one we intend to use in the 
 present work. 
 
 7. A plane superficies is that in which 
 any two points being taken, the straight 
 line joining them lies wholly in that super- 
 ficies. 
 
 This will perhaps be better understood 
 by considering the nature of a curved su- 
 perficies; as the surface of a globe, for 
 example. If two points be taken on its 
 surface, the straight line that joins them 
 does not lie wholly in that superficies, and 
 therefore, the surface of a globe is not a 
 plane superficies. 
 
 9, A plane rectilineal angle is the incli- 
 nation of two straight lines to each other, 
 meeting in a point. Or, it is the opening, 
 or diverging, of two straight lines from a 
 point. 
 
 If there be only one angle at a point, as 
 at A, then it may be expressed by one 
 letter placed at the angular point. But 
 when several angles are formed at the 
 same point, it is necessary to employ three 
 letters, to express any one of these angles; 
 and the letter which is at the angular 
 point is put between the other two letters.* 
 Thus the angles at the point B, which is 
 formed by the lines B C and B D, is named 
 the angle CBD or DBG; and the angle 
 formed by the lines B D and B E, is named 
 the angle DBEorEBD. 
 
 When two angles are separated from 
 each other only by a straight line, as the 
 angles CBD and DBE, they are called 
 adjacent angles. 
 
 10. When a straight line standing on 
 another straight line makes the adjacent 
 angles equal to one another, each of these 
 angles is called a right angle; and the 
 
 * A straight line is usually expressed by placing a 
 letter at each end of it. 
 
THE ARTISAN. 
 
 line which stands on the other is called a 
 perpendicular to it. 
 
 11. An obtuse angle is that which is 
 greater than a right angle. 
 
 12. An acute angle is that which is less 
 than a right angle. 
 
 13. A circle is a plane figure contained 
 by one line, which is called the circum- 
 ference ; and is such, that all straight lines 
 drawn from the centre to the circumference 
 are equal to one another.* 
 
 14. A diameter of a circle is a straight 
 line drawn through the centre, and termi- 
 nated both ways by the circumference. 
 
 15. A semi-circle is that part of a circle 
 contained between the diameter and cir- 
 cumference. 
 
 * A plane surface included by one or more lin 
 is called a mathematical figure, as a triangle , 
 square, &c. 
 
 16. A segment of a circle is that part of 
 the circle contained between part of the 
 circumference, and a straight line which 
 cuts off that part of the circumference. 
 
 17. Rectilineal figures are those which 
 are contained by straight lines. 
 
 18. Trilateral figures, or triangles, are 
 
 contained by three straight lines, . 
 
 19. Quadrilateral figures by four straight 
 lines. 
 
 20. Multilateral figures, or polygons, 
 by more than four straight lines. 
 
 21. An equilateral triangle is that which 
 has three equal sides. 
 
 22. An isosceles triangle, is that which 
 has two sides equal. 
 
 23. A scalene triangle, is that which has 
 three unequal sides. 
 
 24. A right angled triangle, is that which 
 has a right angle in it. 
 
THE ARTISAN. 
 
 25. An obtuse angled triangle, is that 
 which has an obtuse angle in it. 
 
 26. An acute angled triangle, is that 
 which has three angles acute. 
 
 30. A rhomboid, is that which has its 
 opposite sides equal to one another, but 
 none of its angles are right angles 
 
 All other four - sided figures besides these 
 are called trapeziums. 
 
 Parallel straight lines, are such as are 
 in the same plane, and though produced 
 ever so far both ways, do not meet. 
 
 27. Of four-sided figures,— a square is 
 that which has all its sides equal, and all 
 its angles right angles. 
 
 28. An oblong, or rectangle, is that 
 which has all its angles right angles, but 
 not all its sides equal. 
 
 29. A rhombus, is that which has all its 
 sides equal, but none of its angles are 
 
 right angles. 
 
 MECEAH€S- a 
 
 Mechanics, is a mixed mathematical sci- 
 ence, which treats of the nature, produc- 
 tion, and change of motion. 
 
 When bodies are free to obey the im- 
 pulses communicated to them, that branch 
 of Mechanics which treats of their motion 
 is called Dynamics. 
 
 Dynamics is the most elementary branch 
 of the doctfine of motion, and is also the 
 most general in its principles. 
 
 Previous to entering upon the explana- 
 tion of the general laws of motion, or what 
 is termed the composition and resolution of 
 forces , it will be necessary to state a few of 
 the general properties of matter, as well 
 as to explain a few terms which frequently 
 occur in treating of philosophical subjects. 
 
 Matter is a substance, the object of 
 our senses, in which are always united the 
 following properties : extension, figure, 
 
 solidity, mobility, divisibility, gravity, 
 and inactivity. 
 
 Extension may be considered in three 
 points of view : 1st. As simply denoting 
 the part of space which lies between two 
 points, in which case it is called distance. 
 2d. As implying both length and breadth, 
 w hen it is denominated surface or area. 
 3d. As comprising three dimensions, length, 
 breadth, and thickness ; in which case it 
 may be called bulk, solidity, or content. 
 When considered as a property of matter, 
 it is used in the last of these senses. 
 
 Figure , is the boundary of extension : 
 for all bodies are included by one or 
 
THE ARTISAN. 
 
 7 
 
 more boundaries, and consequently possess 
 figure ; they have also the capacity of 
 receiving an indefinite variety of figures. 
 Some bodies receive new figures with diffi- 
 culty, but maintain them easily ; such are 
 the bodies usually called solid. Others 
 receive any figure easily, but cannot main- 
 tain it without the assistance of other bo- 
 dies ; fluid bodies are of this kind. 
 
 Many bodies have figures that are pecu- 
 liar to them in their natural state. This is 
 the case not only with plants and animals, 
 but with certain mineral productions called 
 crystals, which are usually bounded by 
 plane surfaces. 
 
 Mobility , or a capacity of being moved 
 from one place to another, is a quality 
 found to belong to all bodies upon which 
 we can make suitable experiments ; hence 
 we conclude that it belongs to all bodies. 
 
 Divisibility signifies a capacity'of being 
 separated into parts. 
 
 That matter is thus divisible, our daily 
 experience convinces us. How far the divi- 
 sion can actually be carried is not so easily 
 ascertained : we are., however, certain that 
 many bodies can be divided into very mi- 
 nute parts. Of this we have examples in 
 the gilding of silver wire, in the propaga- 
 tion of odours, ^and in the colours produced 
 by chemical solutions, &c. These, and 
 other considerations, lead us to conclude 
 that the division of matter is carried to a 
 degree of minuteness far exceeding the 
 bounds of our comprehension ; and it seems 
 not unreasonable to suppose, that this 
 capability of division is without limit, or as 
 it is usually expressed, ad infinitum . 
 
 That any portion of extension is divisible 
 into parts which become less and less 
 without end, may easily be perceived, by 
 a moment’s consideration of the following 
 figure. 
 
 Suppose the line AB is to be divided 
 into as minute parts as possible. It will 
 soon be perceived, that if the line A C be 
 extended indefinitely, and that an unli- 
 mited number of points, as E, F, G, &c. 
 may be taken in it ; and if straight lines 
 be drawn from these points to the point D, 
 the line A B will be divided into an inde- 
 finite number of parts. Hence it appears 
 that the division of the line A B may be 
 continued ad infinitum. 
 
 Gravity is the tendency which all bodies 
 have to the centre of the earth. 
 
 That all bodies have this tendency expe- 
 rience convinces us ; for we see that when 
 a body is supported, its pressure is exerted 
 in that direction ; and when every impe- 
 diment is removed, it always descends in 
 that direction. 
 
 The weight of a body is its tendency to 
 the earth, compared with the like tendency 
 of some other body, which is considered as 
 a standard. The weight of a given body 
 may, therefore, be employed to measure 
 the weights of all other bodies. 
 
 From these definitions it appears, that 
 gravity must be distinguished from weight ; 
 for the force of gravity is the same in all 
 bodies ; that is, all bodies have an equal 
 tendency to the earth, and would fall at 
 the same rate to the ground were the 
 resistance of the air removed ; but it is 
 well known that the weight of all bodies 
 are not the same. 
 
 As gravity is a property belonging to 
 every particle of matter, however minute, 
 the weight of a body is the sum of the 
 gravities of all its particles ; or it is the 
 product of all its particles, multiplied by a 
 single particle. Inactivity may be consi- 
 dered in two lights : 1st. As an inability 
 in matter to change its state, whether it be 
 at rest or in motion. 2d. As that quality 
 by which it resists any such change. In 
 this latter sense it is usually called the 
 force of inactivity , the inertia, or the vis 
 inertice. 
 
 That a body resists any change in its 
 state of rest, or uniform rectilinear motion, 
 is known from constant experience. We 
 cannot move the least particle of matter 
 without some exertion ; nor can we destroy 
 any motion without perceiving some re- 
 sistance.* 
 
 Thus we see, in general, that inertia is a 
 property inherent in all bodies with which 
 we are acquainted ; different indeed in 
 different cases, but existing, in a greater 
 or less degree, in all. 
 
 These properties, which are always 
 found to exist together in the same sub- 
 stance, have sometimes been said to be 
 essential to matter. Whether they are or 
 are not necessarily united in the same sub- 
 stance, it is impossible to decide, nor does 
 it concern ns to inquire. Our business is 
 not to find out what might have been the 
 constitution of nature, but to examine what 
 it is in fact, and to account for the pheno- 
 mena, or appearances, which fall under 
 our observation, from those properties of 
 
 * This resistance is quite distinct from, and inde- 
 pendent of , gravity ; because it is perceived where 
 gravity produces no effect : as when a: wheel is 
 turned round its- axis, or a body moved along a 
 horizontal plane. 
 
THE ARTISAN. 
 
 8 
 
 matter which we know by experience that 
 it possesses. 
 
 The density of a body is measured by 
 the quantity of matter it contains in a given 
 bulk; and the quantity of matter in any 
 body is always proportional to its weight. 
 That is, a body which is double the weight 
 of another body contains double the quan- 
 tity of matter. 
 
 The specific gravity of a body is the 
 weight of a given bulk of it, compared with 
 an equal bulk of another body, which is 
 assumed as a standard of comparison.— 
 Water has been generally assumed as this 
 standard ; hence it is said that the specific 
 gravity of gold is 19, which signifies that 
 any given bulk of gold is as many times 
 the weight of an equal bulk of water. 
 
 By motion we understand the act of a 
 body constantly changing its place ; and is 
 generally considered of two kinds, absolute 
 and relative. 
 
 A body is said to be in absolute motion, 
 when it is actually transferred from one 
 place to another ; and to be relatively in 
 motion , when its situation is changing with 
 respect to the bodies around it. 
 
 These two kinds of motion often coin- 
 cide ; as for example, when a person walks 
 from any given place to another, he changes 
 his place both absolutely and relatively 
 with respect to the first place ; but if another 
 person walks by his side all the time, he 
 has no relative motion with respect to him. 
 
 When a body passes over equal parts of 
 space, in equal portions of time, its motion 
 is said to be uniform. When its motion 
 continually increases, it is said to be acce- 
 lerated ; and when it continually decreases, 
 to be retarded. If it increases or decreases 
 uniformly, it is said to be equally accele- 
 rated, or retarded. 
 
 When a body falls from any considerable 
 height, its motion is uniformly accelerated, 
 or its velocity increases proportionally to 
 the time ; but if a body be projected directly 
 upwards, its motion will be uniformly re- 
 tarded, or its velocity will decrease pro- 
 portionally to the time it has been in 
 motion. 
 
 In measuring the velocity of bodies, it is 
 necessary to take a certain portion of time 
 as the unit, or standard, to which all other 
 portions of time may be referred. The unit 
 generally employed for this purpose is one 
 second. 
 
 The space passed over in any time, by a 
 body moving with a uniform velocity, is 
 obtained by multiplying the time by the 
 Telocity ; that is, by multiplying the space 
 passed over in one second by the number 
 of seconds that the body has been in mo- 
 tion. Hence, if any two of these three 
 things, viz. the time, velocity, and the 
 space passed over, be known, the third is 
 easily obtained : for the velocity is equal to 
 
 the space passed over divided by. the time 
 that the body has been in motion ; and the 
 time is equal to the space divided by the 
 velocity. 
 
 The time is here supposed to be expressed 
 in seconds, the velocity in some known 
 measure of length, and the space in the 
 same kind of measure. 
 
 If two bodies move uniformly on the 
 same line in opposite directions, their rela- 
 tive velocity is equal to the sum of their 
 absolute velocities ; but when they move 
 in the same direction, their relative velocity 
 is eqnal to the difference of their absolute 
 velocities. Thus, if two vessels saii from 
 the same port, the one steering straight 
 north, at the rate of ten miles per hour, and 
 the other straight south, at the rate of six; 
 miles per hour, their relative velocity is 
 sixteen miles per hour; that is, they are 
 moving from each other at the rate of six- 
 teen miles per hour. But if both vessels 
 were to sail in the same direction, their 
 relative velocity would be four miles per 
 hour ; that is, the one would gain four 
 miles per hour upon the other. 
 
 niTBIkOSTATSCS. 
 
 The science which applies the principles 
 of Dynamics (see page 6.) to fluid bodies, 
 is called Hydrodynamics, and is divided 
 into four parts, according as fluids are in- 
 compressible or elastic , and according as 
 their equilibrium or their motion is con- 
 sidered. * 
 
 When fluids are incompressible like 
 water, the science which explains their 
 equilibrium is called Hydrostatics, and 
 that which explains the laws of their 
 motion *js called Hydraulics. When they 
 are compressible and elastic, like air, 
 the science which treats of the laws of 
 their equilibrium is called Aerostatics , 
 and that which treats of their motion 
 Pneumatics. 
 
 The surface of every fluid, when at rest, 
 is horizontal, or level ; but if it be per- 
 mitted to flow freely from one vessel to 
 another, it will never be at rest till it be 
 the lowest possible. 
 
 If a communication, by means of a tube 
 or pipe, either straight or crooked, be 
 made between the water in one vessel and 
 that in another, the surfaces of both will 
 come to be at the same level before the 
 water is at rest ; and if there is not water 
 
 * A fluid is a body so constituted as to yield 
 to any degree of pressure, however small, in any 
 direction. 
 
THE ARTISAN. 
 
 9 
 
 sufficient to bring both to a level, the whole 
 will be accumulated in the lowest. This 
 singular fact is easily proved, by procur- 
 ing a vessel of the following form, and 
 
 A B C 
 
 pouring water into it, either by the large 
 aperture A, or the small one B ; for the 
 water will, in both cases, stand at the same 
 level in each of the tubes ; and this will 
 be the case, however small the one be in 
 proportion to the other. The same thing 
 would take place, if the small tube were 
 made longer and inclined, like the one C. 
 This shows that a small quantity of water 
 may be made to balance a very large 
 quantity. 
 
 If the liquid in any vessel be perfectly 
 at rest, the pressure on the bottom and 
 sides of the vessel is equal to the weight 
 of a vertical column of the liquid having 
 the same base as the vessel, and reaching 
 to the surface of the water ; that is, having 
 its altitude equal to the perpendicular 
 depth of the water. Hence, the pressure 
 on any part of the bottom or sides of a ves- 
 sel, depends entirely on the depth of the 
 liquid at that part, and not at all on the 
 extent of the liquid in a horizontal direc- 
 tion. If the figure of a vessel be as is here 
 represented, the pressure on every point of 
 the bottom is the same as if it were filled 
 with liquid every where to the height of 
 the line, F, E, G. 
 
 It is, therefore, evident that the pressure 
 of a liquid on the bottom of a vessel may 
 
 be very great, while the weight of the liquid 
 is very small ; it is also evident, that the 
 addition of a small quantity of water, in 
 the neck or tube H E, may increase the 
 pressure on the bottom, CD, in a very 
 great proportion. This is called the Hy- 
 drostatic Paradox: and it certainly does 
 appear incredible, although the fact is be- 
 yond dispute, that all vessels, whatever 
 their shape or size may be, having equal 
 heights, and equal areas of bottom, sustain 
 equal pressure on their bottoms, when filled 
 with water, even though the quantity in 
 each should be very different. 
 
 When a body is immersed in a fluid, it 
 is pressed upwards by a force equal to the 
 weight of the fluid which it displaces, and 
 the direction of that force passes through 
 the centre of gravity of the part immersed. 
 This holds good, whether the body sink in 
 the fluid or float on its surface : when it 
 floats, the weight of the fluid displaced is 
 equal to the weight of the body. 
 
 The difference between the absolute 
 weight of a body, and its weight when 
 entirely immersed in a fluid, is the same 
 with the weight of a quantity of the fluid 
 equal in bulk to the body. 
 
 Hence, the specific gravities of bodies 
 are found by weighing them, first in air, 
 and then in water, by means of an instru- 
 ment called the Hydrostatic Balance, which 
 so nearly resembles a common balance, that 
 it is quite unnecessary to give any repre- 
 sentation of it here. The method of deter- 
 mining the specific gravity of any sub- 
 stance by this instrument is exceedingly 
 simple. 
 
 Suppose it were required to determine 
 the specific gravity of a body so light as 
 not to sink in water, by means of the Hy- 
 drostatic Balance. 
 
 Weigh the body first in aif, and then by a 
 slender thread attach to it a heavier body, 
 that the two together may sink in water, 
 the weight of the heavier body being previ- 
 ously ascertained, both in air and water. Let 
 the compound body thus formed be weighed 
 in water; then, from the weight lost by it, 
 subtract the weight lost by the heavier body, 
 when weighed alone ; the remainder is the 
 weight lost by the lighter body : by which, 
 its weight in air being divided, will give 
 its specific gravity. 
 
 If it were required to determine the 
 specific gravity of a body heavier than 
 water, the process is still more simple : 
 for it is only to weigh the body first in air, 
 and then in water, and to divide its weight 
 in air by the weight it has lost when 
 weighed in water, — the quotient is its 
 specific gravity. 
 
 An example in each of these cases will 
 render the method of determining the speci- 
 fic gravity of any substance quite plain. 
 
 Suppose a, piece of elm wood to weigh 
 
10 
 
 THE ARTISAN. 
 
 15 grains in air, and that a piece of copper, 
 weighing 18 grains in air, when attached 
 to the wood, is just sufficient to sink it. 
 The sum of these weights, or the weight of 
 the compound, is SB grains. Now, sup- 
 pose the weight of the copper alone, when 
 weighed in water, to be 16 grains, and the 
 weight of the compound 6 grains. The loss 
 of the compound is therefore 27 grains; 
 from which the 2 grains, lost by the copper, 
 being subtracted leaves 25 grains ; now the 
 weight of the wood, in air (15 grains), 
 being divided by this number, quotes '6, or 
 3-fifths for the specific gravity of the 
 elm. 
 
 Let it now be required to determine the 
 specific gravity of a substance which sinks 
 in water. 
 
 Suppose a piece of gold weighs 130 
 grains in air, but in water only 123 grains, 
 the difference of these weights, or the 
 weight lost in water is 7 grains. Now the 
 weight in air, or 130 grains divided by 7, 
 quotes 18 and 4-sevenths, the specific gra- 
 vity of the gold, in this instance. * 
 
 If the same body be weighed in two 
 different fluids, such as oil and water, 
 the weights lost will be to one ano- 
 ther as the specific gravities of the flu- 
 ids ; that is, the lighter the fluid is, in 
 which any body is weighed, the greater 
 will be the difference between the weight 
 of the body weighed in air and in that fluid. 
 
 The knowledge of this circumstance 
 affords the means of comparing the speci- 
 fic gravities of different fluids with eacjx 
 other. 
 
 Thus : suppose a piece of copper lost 4 
 grains by weighing it in water, and 3| in 
 spirits ; required the specific gravity of the 
 spirits, that of water being considered 1000;? 
 As 4 ; 3| : : 1000 : *875, the specific gravity 
 of the spirits. 
 
 The specific gravities of different fluids 
 may also be found, by weighing equal 
 bulks of them. 
 
 If a body float on different fluids, the 
 bulks of the part immersed will be the 
 greater, the lighter the fluid is in which it 
 is immersed ; because a light fluid is less 
 able to support it than a heavy fluid. It is 
 on this principle that the Hydrometer, 
 Aerometer, &c. are constructed, t 
 
 In the foregoing directions, for determin- 
 ing the specific gravity of any body, no 
 notice has been taken of the weight of the 
 
 * As Tables of the specific gravities of bodies are 
 of great use, a very extensive and accurate Table of 
 this kind will be given in a future Number of the 
 “ Artisan.” 
 
 t The Hydrometer is an instrument used for ascer- 
 taining the specific gravities of liquids, and the 
 Aerometer for . ascertaining the specific gravity of 
 air. These instruments will be described in a future 
 Number. 
 
 air ; because the weight of a body, when 
 weighed in vacuo, or in a vessel from which 
 the air lias been extracted, and when 
 weighed in air will be so nearly equal, 
 that the difference is scarcely deserving of 
 notice. 
 
 PNEUMATICS. 
 
 That branch of Natural Philosophy which 
 treats of the nature, properties, and effect 
 of the atmosphere, or body of aii encom- 
 passing the earth, is called Pneumatics, 
 from the Greek word for wind or breath. 
 
 The air is that thin transparent fluid in 
 which we live and move. It encompasses 
 the whole earth to a considerable height, 
 and together with the clouds and vapours 
 which float in it, is called the atmosphere. 
 The air is justly reckoned among the num- 
 ber of fluids, because it has all the proper- 
 ties by which a fluid is distinguished ; for 
 it yields to the least pressure, its parts are 
 easily moved among themselves, it presses 
 according to its perpendicular altitude, 
 and its pressure is every where equal. 
 
 The air differs from all other fluids in 
 the three following particulars : — 1st. It 
 can be compressed into much less space 
 than it naturally occupies, which no other 
 fluid can be, except the gasses, which will 
 be treated of under the head of Chemistry. 
 2d. It cannot be congealed or fixed like 
 other fluids. 3d. It is of a different den- 
 sity at different heights from the earth’s 
 surface, decreasing the higher it rises ; for 
 each stratum is compressed only by the 
 weight of those above it ; the upper strata 
 are therefore less compressed, and of course 
 less dense, than those below them. 
 
 That the air is a real substance, or body, 
 is evident, from its excluding all other bo- 
 dies from the space which it occupies. : for 
 if a glass jar be plunged into a, vessel of 
 water, with its mouth downwards, very 
 little water will get into the jar, the air in 
 it keeping the water out. 
 
 As the air is a real substance, it must 
 necessarily have weight ; and that this is 
 the case, is easily demonstrated by experi- 
 ment. For if the air be extracted from a 
 vessel by means of the air pump, and the 
 vessel afterwards weighed, it will be con- 
 siderably lighter than it was before the 
 air was extracted; or which amounts to 
 the same thing, it will be considerably 
 heavier after the air is again let into it. 
 Thus a bottle that contains a wine quart 
 will be found to be 18 grains heavier when 
 full of air, than when the air is extracted 
 from it. 
 
 The weight of the air is also known by 
 the Torricellian experiment, or that of the 
 
THE ARTISAN. 
 
 11 . 
 
 barometer. For the air presses on the 
 orifice of the invented tube with a force 
 just equal to the weight of the column of 
 mercury sustained by it. 
 
 The pressure or weight of the atmos- 
 phere is about 14 pounds on every square 
 inch of the earth’s surface. Hence the 
 total pressure on the whole convex surface 
 of the earth is 10,686,000,000,090,000,000 
 pounds. 
 
 The air being of an elastic or springy 
 nature, it is plain that it must be more 
 dense or pressed at the earth’s surface 
 than at any .considerable height above it ; 
 and that the greater the height the less 
 must be the density. The law by which 
 the density and elasticity diminish has 
 been determined by several philosophers, 
 and may be stated thus : if altitudes be 
 taken from the earth’s surface in arithme- 
 tical progression, the densities of the strata 
 of air will decrease in geometrical pro- 
 gression. For example, at 3§ miles height 
 the density or weight of the air will be 
 only half what if is at the earth’s surface ; 
 at 7 miles height, one-fourth of the den- 
 sity ; at 10| miles, one-eighth of the den- 
 sity; at 14 miles, one-sixteenth part of 
 the density, and so on. 
 
 From the effect of this law it is easy to 
 perceive that a small quantity of air, a cubic 
 inch, for example, at the earth’s surface, 
 would be so much rarefied at the altitude 
 of 500 miles, as to occupy a most extraordi- 
 nary space. It must also be evident that 
 no person could breathe or live for a mo- 
 ment at so small a height as 20 miles, or 
 even at the top of some of the mountains 
 on the earth, none of which exceed five 
 miles in height. 
 
 When the end of a tube, or pipe, is im- 
 mersed in water, and the air extracted 
 from the tube, the water will rise in it to 
 the height of about 33 feet above the sur- 
 face of the water in which it is immersed, 
 but will rise no higher ; and this is the 
 greatest height to which water can be 
 raised above the surface of a well by the 
 common pump : therefore, unless the piston 
 or bucket goes within 33 feet of the sur- 
 face of the water in a well, it will never 
 rise above the piston. Now as it is the 
 pressure of the atmosphere on the surface 
 of the water in the well which causes the 
 water to ascend in the pump, and follow 
 the piston or bucket when the air above it 
 is lifted up, it is evident that a column of 
 water 33 feet high is equal in weight to a 
 column of quicksilver of the same base, 
 29 1 inches high, and to a column of air 
 having the same base, and reaching to the 
 top of the atmosphere. 
 
 In calm serene weather the air is capa- 
 ble of supporting a column of quicksilver 
 31 inches high ; but- in rainy or stormy 
 weather often not above 28 inches. Hence 
 
 the rising and falling of the quicksilver in 
 the tube of a'barometer is an excellent indi- 
 cator of the changes which take place in 
 the weight of the atmosphere. 
 
 In all that has been said of the weight 
 of the air, its temperature is supposed to 
 remain unchanged; but it is well known 
 that this is not the case for any length of 
 time, and that its density is very much 
 diminished by heat. 
 
 The temperature of the air diminishes on 
 ascending into the atmosphere, both on 
 account of the greater distance from the 
 earth, the principal source of its heat, and 
 the greater power of absorbing heat, which 
 air acquires by being less compressed. 
 
 The heat, however, appears not to de- 
 crease in the same ratio that the distance 
 increases. That is, the temperature at any 
 particular height from the earth is not 
 double what it is at twice that height. 
 
 M. de Saussure found, that by ascending 
 from Geneva to Chamouni, a height of 
 347 toises, or about 2220 feet, Fahrenheit’s 
 thermometer fell 9| degrees ; and that on 
 ascending from thence to the top of Mont 
 Blanc, 1941 toises more, or about 12,500 
 feet, it fell 46§ degrees. The first of these 
 gives a diminution of 1 degree for 221 
 feet f and the second 1 degree for 268 feet. 
 However, it may be inferred that the de- 
 crease of temperature, for the greatest 
 heights which we can reach, is not far 
 from uniform ; and the average in our cli- 
 mate may be taken at 1 degree for 90 
 yprds, or 270 feet of perpendicular height. 
 But philosophers are not agreed respecting 
 the rate at which the heat of the atmosphere 
 diminishes in ascending from the earth’s 
 surface. La Grange thinks that the hypo- 
 thesis of a uniform decrease of heat is the 
 most conformable to appearances ; while 
 Euler considers a harmonical progression 
 as the most probable. 
 
 ©fTICS. 
 
 Optics is divided into two parts : — 
 
 1. Catoptrics , which treats of vision by 
 reflection. 
 
 2. Dioptrics, which treats of direct vision. 
 
 Some philosophers regard light as con- 
 sisting of particles of inconceivable minute- 
 ness, flowing from some luminous body, in 
 straight lines in all directions. 
 
 Others conceive that it consists in cer- 
 tain undulations, or waves, communicated 
 by luminous bodies to an etherial fluid 
 which fills all space. With these specula- 
 tions, Optics has no more to do than 
 Astronomy has with speculations concern- 
 ing the nature of gravitation. 
 
 That the rays of light move in straight 
 lines is proved beyond the possibility of 
 doubt, from the fact that no body can be 
 
12 
 
 THE ARTISAN. 
 
 seen through the bore of a bended tube or 
 pipe, where there is nothing to refract or 
 turn them out of their rectilineal course. 
 
 When the rays of light fall upon the 
 surface of bodies, they are in part reflected, 
 from those surfaces, and in part imbibed 
 by them, or pass through them. The rays 
 that are reflected always return or pass off 
 from those surfaces at an angle equal to 
 that at which they fell upon them ; which 
 is usually expressed by saying that the 
 angle of incidence is equal to the angle of 
 reflection. 
 
 This will be eastly understood by a mo- 
 ment’s observation of the following figure. 
 
 If A B be supposed to be the surface of 
 a plain mirror, DC a ray of light falling 
 on it at C, then will the ray DC be re- 
 flected in the direction CF, making the 
 angle D C E (called the angle of incidence ), 
 equal to the angle E C F, or angle of re- 
 flection. 
 
 It has already been stated that the rays 
 of light pass from luminous bodies in 
 straight lines ; but they continue only in 
 this direction while the medium in which 
 they are moving remains of the same den- 
 sity ; but when they pass obliquely out of 
 •ne medium into another of a different den- 
 sity, whether denser or rarer, they are 
 refracted towards the denser medium : and 
 this refraction is the greater the more 
 obliquely the rays fall on the refracting 
 surface.* 
 
 This is very easily proved by experiment 
 in the following manner : 
 
 which permits the rays of light to pass through it, 
 such as air, water, glass, &c. 
 
 Words which have once been explained in any 
 part of this work, will uot again be explained in 
 any other part. 
 
 Let the vessel A B C D be placed in any 
 situation where the sun shines obliquely 
 upon it in the direction EF, and let the 
 rays enter it at the top of the side A D, 
 they will fall on the bottom at F. Let the 
 vessel now be filled with water, and the 
 rays EA will not proceed through the 
 water to F as before, but will be turned 
 downward in the direction A G, which is 
 therefore termed the refracted ray ; the 
 angle DAG is also called the angle of 
 refraction ; and the angle D A F the angle 
 of incidence. 
 
 These angles bear the same proportion 
 to each other as the straight lines I and 
 L, which are called the sines of these 
 angles ; and are to each other as 3 to 4 
 nearly in water, 2 to 3 in glass, and 2 to 5 
 in diamond. 
 
 If a stick be laid over the above vessel, 
 and the rays be refracted by means of a 
 glass so as to fall upon it perpendicularly, 
 the shadow of the stick will fall upon the 
 same part of the bottom when the vessel is 
 full of water, as when it is empty ; which 
 shews that the rays of light are not re- 
 fracted when they fall perpendicularly on 
 the surface of any medium. 
 
 Another very amusing method of proving 
 that the rays of light are refracted in 
 passing out of air into water is the follow- 
 ing : — Place a piece of money in a cup or 
 basin, and let a person stand at such a dis- 
 tance from it as barely not to see the mo- 
 ney ; then fill the basin with water, and 
 the money will appear to be raised up to 
 a considerable height in the basin, and be- 
 come distinctly visible to the person who 
 could not perceive it before the water was 
 poured into the basin. 
 
 In consequence of the atmosphere being 
 much denser at the surface of the earth 
 than at considerable altitudes, (see Pneu- 
 matics) the rays of light which proceed 
 from any celestial body are refracted from 
 their rectilineal course, and enter the eye 
 in a direction somewhat different from that 
 in which the object really is. This refrac- 
 tive power of the atmosphere has the 
 effect of making all the heavenly bodies 
 appear higher than they really are. Hence 
 the moon has been seen eclipsed when 
 she was actually under the horizon of the 
 place. This is also the cause of twilight ; 
 and of the light of the sun being seen, in 
 high latitudes, when he is several degrees 
 below the horizon. 
 
 Rays of light are usually divided into 
 three kinds ; namely, parallel, converging 
 and diverging rays. Parallel rays are such 
 as keep always at the same distance in 
 passing from a luminous body to any other 
 body, such as the rays of the sun, or any 
 body at an immense distance. Converging 
 rays are such as approach nearer to each 
 other in their progress. Diverging rays 
 
THE ARTISAN. 
 
 HI 
 
 are such as recede or separate from each 
 other as they proceed from any luminous 
 body. That point where the rays are con- 
 densed or collected is called the focus, or 
 burning point. 
 
 Glasses, for optical purposes, are ground 
 into eight different forms, which are all 
 exhibited in the following figure : — 
 
 A. B C T> E 
 
 1. The one marked A is a plane glass , 
 which is flat on both sides, and of equal 
 thickness in all parts. 
 
 2. A plano-convex is flat on one side, and 
 convex or raised on the other, as B. 
 
 3. A double-convex, is convex on both 
 sides, as C. 
 
 4. A plano-concave , is flat on one side, 
 and concave or hollow on the other, as D. 
 
 5. A double-concave, is concave on both 
 sides, as E. 
 
 6. A meniscus, is concave on one side, 
 and convex on the other, as F. 
 
 7. A flat plano-convex, is plane on one 
 side, and its convex side is ground into 
 several little flat surfaces, as G. 
 
 8. A prism has three flat sides, and 
 when viewed endwise, appears like an 
 equilateral triangle, as H. 
 
 Glasses ground in any of the shapes 
 B, C, D, E, F, are generally called lenses. 
 
 A right line going perpendicularly 
 through the middle of a lens, as L I, is 
 called the axis of the lens. 
 
 When a ray of light falls perpendicularly 
 on a plane glass, it passes through the 
 glass without changing its direction. 
 
 If a ray fall obliquely upon a plane glass, 
 it will be refracted on entering the glass ; 
 but on passing out of the glass it will then 
 proceed in the original direction, but not in 
 the same right line ; that is, it will proceed 
 in a line parallel to the one in which it 
 moved previous to entering the glass. 
 This change proceeds from the refraction 
 occasioned by the glass. 
 
 CHEMISTRY, 
 
 HISTORY OF CHEMISTRY. 
 Chemistry, considered as an Art, is of the 
 earliest origin ; but, considered as a Sci- 
 ence, it may be said to be of very modem 
 date. The method of kind ling fires, baking 
 bread , moulding clays into various forms, 
 extracting metals from their ores and work- 
 ing them into different shapes, as well as 
 several other chemical processes, were 
 certainly known to the Antediluvians. 
 
 Tubal Cain, who is mentioned in Scrip- 
 ture, and whom the Pagans made their 
 Vulcan, is the first person on record who 
 knew any thing of this art. 
 
 It is said, “ he was a worker in Iron and 
 Brass:” he must, therefore, have known 
 something of Chemistry before he could 
 have extracted metals from their ores, and 
 rendered them malleable. 
 
 It appears that, soon after the Deluge, 
 the family of Ham made great progress in 
 the Art. For the Egyptians, whose coun- 
 try is called Ham in Scripture, and who 
 are said to be the descendants of Ham , 
 applied themselves very much to this 
 branch of study, and made many discove- 
 ries ; such as Embalming the bodies of the 
 dead, making Vases , fabricating a kind of 
 Nitre, making common Salt, and even 
 Wine ; and, it is said, they knew the art of 
 distillation. 
 
 It was in Egypt that the famous Hermes 
 Trismegistus lived, who has been regarded 
 by many heathen nations as the inventor of 
 all the arts. He is said to be the Author of 
 all the learning of the Egyptians, and be- 
 lieved by many to have been Chanaan, son 
 of Ham, or Abraham, or Joseph. 
 
 From this person the Science of Chemis- 
 try derived the name of the hermetical Art ; 
 a name which it was long known by, and 
 is often called so in old books. 
 
 It was in Egypt that Moses learned the 
 properties of Metals, the method of ex- 
 tracting Oils, the preparation of Gums 
 and Perfumes, the solution of Gold, the 
 dying of Linen, the art of Gilding, the 
 making of Pottery, Soap, & c. 
 
 The Ph(enicians were the first who 
 applied themselves to the examination of 
 the chemical effects of different bodies 
 upon each other ; and it is said the Grecians 
 derived their arts which depend on che- 
 mical principles from the Phienicians. 
 
 The Romans being mostly engaged in 
 war, were not distinguished among the 
 ancient nations for discoveries in the art 
 or inventors in science. They, however, 
 understood the art of making excellent 
 Wines and Spirits, and knew the appli- 
 cation of manures; and the remains of 
 their works of Architecture evince the 
 incomparable perfection of their Cement. 
 
 But all the Arts , Sciences , and Lite - 
 
14 
 
 THE ARTISAN. 
 
 rature, of the Greeks and Romans, were 
 destined to sink into oblivion. Hosts of bar- 
 barian conquerors descended upon them 
 from the North, and completely destroyed 
 the principles of civilization, and gave a 
 death-blow both to science and literature. 
 
 Driven as it were from Europe, the arts 
 obtained an asylum among the Arabians. 
 The attachment of this nation to magic, 
 and their predilection for the marvellous, 
 soon increased the mysteries in which the 
 arts were then involved ; hence Alchymy, 
 or the art of transmuting the various metals 
 into gold, took its rise. This happened 
 about the beginning of the fourth century. 
 As this delusive dream of the imagination 
 held out a bait to' avarice, it soon acquired 
 a numerous train of followers. 
 
 Those who professed this Art , gradually 
 assumed the form of a Sect, under the 
 name of Alchymists ; a term which is sup- 
 posed to be merely the word Chemist with 
 the Arabian article al prefixed. 
 
 The Alchymists laid it down as a first 
 principle, that all metals are composed of 
 the same ingredients ; or, that the princi- 
 ples (at least) which compose gold exist 
 in all metals , and were capable of being 
 brought to a perfect state by purification. 
 
 The substance which possessed this 
 wonderful property, they called lapis phi- 
 losophorum, or the “ Philosopher’s Stone 
 and many of them boasted that they were 
 in possession of that grand instrument. 
 
 The fortunate few who were acquainted 
 with the philosopher’s stone, called them- 
 selves adepti, or adepts ; that is, persons 
 who had got possession of the secret. 
 
 This secret, they pretended, they were 
 not at liberty to disclose, and that ven- 
 geance would fall on the man’s head who 
 should venture to publish it. 
 
 In consequence of these notions, the 
 Alchymists kept themselves as private as 
 possible ; and concealed with the greatest 
 care, their opinions , their knowledge, and 
 their pursuits. 
 
 The 'Alchymists seem to have been 
 established in the West of Europe as early 
 as the ninth century. 
 
 Between the eleventh and fifteenth cen- 
 turies , Alchymy was in its most flourishing 
 state. The writers who' appeared during 
 that period were very numerous ; but their 
 books are altogether unintelligible, and 
 bear a stronger resemblance to the reveries 
 of madmen, than to the sober investigations 
 of philosophers. 
 
 The principal Alchymists who flourished 
 during the dark ages were Albertus Mag- 
 nus, Roger* Bacon, Raymond Lully, and 
 the two Isaacs of Holland. It was against 
 this sect that' Erasmus directed his well- 
 known Satire, entitled the Alchymist. 
 
 Chemists had for many ages hinted at 
 the importance of discovering a universal 
 
 remedy for all diseases, and several of 
 them had asserted that this remedy was to 
 be found in the philosopher’s stone. This 
 notion gradually gained ground ; and the 
 word Chemistry, in consequence, at length, 
 acquired a more extensive signification, 
 and implied, not only the art of making 
 gold, but also of preparing the universal 
 Medicine. The first person who formally 
 applied Chemistry to medicine, was Basil 
 Valentine, who was said to be borne in 
 1394, at Erfurd, in Germany. 
 
 Just about the time that the first of 
 these branches was sinking into discredit, 
 the second, and with it the study of Che- 
 mistry , acquired an unparalleled degree of 
 celebrity, and attracted the attention of all 
 Europe. This was owing to the appear- 
 ance of Theophrastus Paracelsus, who was 
 born in 1493, near Zurich, in Switzerland, 
 and was, in the thirty- fourth year of his 
 age, appointed to read lectures on Chemis- 
 try in the city of Basil. He was the first 
 professor of Chemistry in Europe. 
 
 Van Helmont, who was born in 1577, is 
 considered as the last of the Alcyhmists. His 
 death completed both the disgrace of the 
 philosopher’s stone and the universal medi- 
 cine. 
 
 The foundation of the alchymical sys- 
 tem being thus shaken, the facts which had 
 been collected soon became a mere chaos, 
 and Chemistry was left without any fixed 
 principles, and destitute of any object. 
 But, fortunately, about this time, arose a 
 person completely acquainted with the 
 whole of these facts, and rescued this 
 branch of science from the oblivion into 
 which it would soon have fallen. This 
 person was the celebrated Beecher. He 
 accomplished the arduous task in a work 
 entitled Pigysica Subterranea, published at 
 Frankfort in 1669. The publication of this 
 book forms a very important aera in the 
 history of Chemistry, as it contains the 
 rudiments of the science as taught at the 
 present day. After the death of Beecher, 
 Ernest Stahl, the editor of the Physica 
 Subterranea, adopted and taught the theory 
 of his master : but he simplified and im- 
 proved it so much, that he made it entirely 
 his own : and accordingly it has been 
 known ever since by the name of the 
 Stahlian Theory , 
 
 Ever since the days of Stahl, Chemistry, 
 has been cultivated with ardour in Ger- 
 many and the North of Europe. The most 
 celebrated men which these countries have 
 produced are, Margraf, Bergman, Slieel, 
 and Klaproth. 
 
 In France, soon after the establishment 
 of the Academy of Sciences in 1666, Hom- 
 berg, Geoffrey, and Lemery, acquired great 
 celebrity by their chemical experiments 
 and discoveries. 
 
 From that time Chemistry became the 
 
THE ARTISAN. 
 
 15 
 
 fashionable study in France, and men of 
 eminence appeared every where; disco- 
 veries multiplied ; the spirit for chemical 
 research pervaded the whole of that king- 
 dom, and extended itself over the continent 
 of Europe. After the death of Boyle, and 
 some of the other early members of the 
 Royal Society of London, little attention 
 was paid to Chemistry in Britain, except 
 by a few individuals. But when Dr. Cul- 
 len was appointed Professor of Chemistry 
 in the University of Edinburgh, in 1T56, he 
 kindled a flame of enthusiasm among the 
 students, which soon spread through the 
 kingdom ; and, after this, soon followed 
 the important discoveries of Dr. Black , 
 Cavendash, and Priestly, which, joined to 
 the discoveries made in France, Germany, 
 and Sweden, made the science of Chemistry 
 burst forth at once with unexampled lustre. 
 Hence, the rapid progress it has made dur- 
 ing the last thirty years ; the universal 
 attention which it has excited, and the un- 
 expected light it has thrown on almost 
 every useful art. 
 
 Having thus given a .short but compre- 
 hensive view of the history of Chemistry 
 down to our own times, we shall conclude 
 this article by taking a retrospective view 
 of some of the most distinguished theories 
 of the ancients, the various modifications 
 which they have undergone at different 
 times, and the steps by which chemists 
 have been led to the opinions which they 
 hold at present. 
 
 It seems to have been an opinion estab- 
 lished among the most ancient philoso- 
 phers, that there are only four simple 
 bodies, out of which all others are formed, 
 or to which all others may be reduced; 
 viz. fire, air , water, and earth. To these 
 they gave the name of Elements. 
 
 This opinion variously modified was 
 maintained by all the ancient philosophers. 
 It is, however, well known now that all 
 these supposed elements are compounds 
 if we except fire. 
 
 Air is a compound of oxygen and nitro- 
 gen ; water, of oxygen and hydrogen ; and 
 earth, of many different substances. 
 
 The doctrine of the four elements seems 
 to have continued undisputed till the time 
 of the Alchymists. 
 
 This class of men having made them- 
 selves much better acquainted with the 
 analysis of bodies than the ancient philo- 
 sophers were, soon perceived that the 
 common doctrine was insufficient to ex- 
 plain all the appearances which were 
 familiar to them. They therefore substi- 
 tuted a theory of their own in its place. 
 According to them there are three elements 
 of which all bodies are composed ; namely, 
 salt, sulphur , and mercury , which they dis- 
 tinguished by the appellation of the tria 
 prima. These principles were adopted by 
 succeeding writers, particularly by Para- 
 
 celsus, who added two more to their num- 
 ber, namely, phlegm and caput mortuum. 
 
 It is not easy to say what the alchymists 
 meant by salt, sulphur, and mercury ; it is 
 probable they had affixed no precise mean- 
 ing to the words. 
 
 Every thing fixed in the fire (i.e.) on 
 which the fire had little or no effect, they 
 called salt ; every inflammable substance 
 they called sulphur ; and every substance 
 which flies off without burning was mer- 
 cury. Accordingly they tell us, that all 
 bodies may be decomposed by fire, into 
 these three principles; the salt remains 
 behind fixed, the sulphur takes fire, and 
 the mercury flies off in the form of smoke. 
 The phlegm and caput mortuum of Para- 
 celsus were the water and earth of the 
 ancient philosophers. 
 
 Mr. Boyle attacked this hypothesis in 
 his Sceptical Chemist , and in several 
 other of his publications, and proved that 
 the Chemists comprehended under each of 
 the terms salt, sulphur, mercury, phlegm, 
 and earth, substances possessed of very 
 different properties ; and that these prin- 
 ciples themselves are not elements but 
 compounds. 
 
 Mr. Boyle’s refutation was so complete, 
 that the hypothesis of the tria prima seems 
 to have been almost immediately aban- 
 doned by all parties. About this time a 
 very different hypothesis was proposed by 
 Beecher, in his Pysica Subterranea, which 
 has been already mentioned. 
 
 To this hypothesis we are indebted for 
 the present state of the science, because he 
 first pointed out chemical analysis, as the 
 true method of ascertaining the elements of 
 bodies. 
 
 According to him all terrestrial bodies 
 are composed of water, air, and three 
 earths ; viz. the fusible, the inflammable, or 
 sulphurous earth, and the mercurial. The 
 different combinations of these, with a 
 universal acid (which he believed to be 
 composed of fusible earth and water), com- 
 posed all the different substances which 
 are to be met with in nature. 
 
 Stahl modified the theory of Beecher 
 considerably. He seems to have admitted 
 the universal acid as an element ; the mer- 
 curial earth he at last discarded altogether, 
 and to the sulphurous earth he sometimes 
 gave the name of ether. 
 
 Earths he considered as of different 
 kinds, but all of them as containing a cer- 
 tain element called earth. So that accord- 
 ing to him there are five elements ; air, 
 water, phlogiston, earth, and the universal 
 acid. He speaks too of heat and light; 
 but it is not clear what his opinion was 
 respecting them. 
 
 Stahl’s theory was gradually modified 
 by succeeding chemists. 
 
 The universal acid was tacitly discarded, 
 and the different knoivn acids were con- 
 
10 
 
 THE ARTISAN. 
 
 side red as distinct, undscomposed, or philosopher, who lived 551 years B.C. has 
 simple substances : the different earths recorded 36 eclipses ; but be this as it may, 
 were distinguished from each other, and all the Chinese are allowed to have had a very 
 the metalic calces were considered as dis- early knowledge of Astronomy, 
 tinct substances. Some authors say it had its origin among 
 
 For these important changes Chemistry the Chaldeans, others among the Hindoos, 
 was chiefly indebted to Bergman. While and some, with more probability, among 
 the French and German chemists were the Egyptians. Professor Playfair has 
 occupied with theories about the universal given a learned and ingenious dissertation 
 acid, that illustrious philosopher and im- on the Astronomy of the Brahmins, in the 
 mortal friend of Bergman’s (Scheele of 2d volume of the Transactions of the Royal 
 Sweden) loudly proclaimed the necessity Society of Edinburgh, in which he shews 
 of considering every undecomposed body the great accuracy and high antiquity of 
 as simple, till it has been decomposed, the science among them ; and he also shows 
 and of distinguishing all those substances that it is extremely probable that the Hin~ 
 from each other which possess distinct doos were among the first Astronomers in 
 properties. the world. 
 
 Thus the elements of Stahl were, in fact, 
 banished from the science of Chemistry, 
 and in place of them were substituted a 
 great number of bodies, which were con- 
 sidered as simple , because they had not 
 been analyzed. These were phlogiston, 
 acids, alkalies, earths, metalic calces, 
 water, and oxygen. 
 
 The rules established by Bergman 
 and Scheele are still followed ; but subse- 
 quent discoveries have shewn, that most 
 of the bodies which they considered as 
 simple , are really compounds ; while 
 several of their compounds are now placed 
 among simple bodies, because the doctrine 
 of phlogiston (in which they believed) is 
 now entirely abandoned. 
 
 ASTRONOMY. 
 
 HISTORY OF ASTRONOMY. 
 
 No science in the world is of more value, 
 or of higher antiquity, than Astronomy. 
 Its antiquity may be learned from what 
 was spoken by God himself at the creation 
 of the world ; for He said — “ Let the sun 
 and the moon be for signs and for sea- 
 sons,” &c. 
 
 By this it is thought the human race 
 never existed without some knowledge of 
 Astronomy among them. It is said by some 
 Jewish Rabbins, that Adam was endowed 
 with a knowledge of the nature, influence, 
 and uses of the heavenly bodies; and 
 Josephus ascribes to Seth and his posterity 
 an extensive knowledge of Astronomy. 
 
 It is supposed, by some writers, that 
 Noah retired after the flood to the north- 
 east part of Asia, where his descendants 
 peopled the vast empire of China. “ This,” 
 says Dr. Long, “ may account for the Chi- 
 nese having so early cultivated the study 
 of Astronomy.” But the vanity of the 
 Chinese has prompted them to pretend to 
 a knowledge of this science almost as early 
 as the flood itself. 
 
 To the emperor Hoang-ti, the grand-son 
 of Noah, they attribute the discovery of 
 the Pole star and the mariner’s compass. 
 They also say, that Confucius, their great 
 
 But Thales of Miletus is considered as 
 the first person that propagated any truly 
 scientific knowledge of Astronomy ; and it 
 is said he acquired his knowledge of the 
 subject in Egypt. 
 
 Thales taught his countrymen the cause 
 of the inequality of the days and nights ; 
 explained to them the theory of eclipses, 
 and the manner of predicting them ; and gave 
 them an example of his art in an eclipse 
 of the sun, which happened soon after: he 
 was born about 640 years B. C. Anaxi- 
 mander was a pupil of Thales, and suc- 
 ceeded him as head of the school of Mile- 
 tus. It is said he had some idea of the 
 spherical shape of the earth; he is also 
 said to have been the inventor of celestial 
 globes, and of the orthographic projection 
 of maps. He constructed a gnomon at 
 Sparta, by which he ascertained the obli- 
 quity of the ecliptic, with the solstices and 
 equinoxes. 
 
 Pythagoras was the next person who im- 
 proved the science. He founded a school 
 in Italy for that very purpose. Seconded 
 by his earliest scholars, he clearly demon- 
 strated the spherical shape of the earth, 
 which Anaximander had only conjectured. 
 Pythagoras taught that the sun was fixed 
 in the centre of the planetary orbits, and 
 that the earth moved round it with the 
 other planets — the very system which is 
 taught at this day. This opinion he com- 
 municated only to his pupils in secret ; for 
 being repugnant to the received opinions 
 of that time, (and even appearances,) he 
 did not wish to expose himself to the de- 
 rision and persecution of ignorance and 
 fanaticism, which would have been the 
 inevitable consequence. For about 100 
 years after his time, Anaxagoras was con- 
 demned to banishment for saying that the 
 sun was a mass of fiery matter. The mea- 
 suring of time being a principal object in 
 Astronomy, many efforts were made by the 
 ancients to determine accurately, and to 
 compare with each other, the motions of 
 the sun and moon, on which this measure 
 universally depends. 
 
 [To be continued .] 
 
THE ARTISAN. 
 
 17 
 
 t&EOMETSilr. 
 
 POSTULATES.* 
 
 A Postulate is a self-evident practical 
 Proposition. 
 
 The Postulates are, however, not to be 
 so understood, as if Euclid required a 
 practical dexterity in managing a ruler 
 and pencil, or a pair of compasses. They 
 are inserted at the beginning of the Ele- 
 ments, that his readers may admit the pos- 
 sibility of what he may hereafter require 
 to be done. He therefore enumerates all 
 the operations required in his future de- 
 monstrations and problems, requiring their 
 possibility to be acknowledged in order 
 to avoid all future objections on this head. 
 The Postulates are three in number ; viz. 
 
 1. Let it be granted that a straight line 
 may be drawn from any one point to any 
 other point. 
 
 2. That a terminated straight line may 
 be produced to any length in a straight 
 line. 
 
 3. That a circle may be described from 
 any centre, at any distance from that 
 centre. 
 
 AXIOMS. 
 
 An Axiom is a self-evident theoretical 
 proposition, which neither admits of nor 
 requires proof : it may require to be ex- 
 plained in order to be made intelligible ; 
 but as soon as understood, it should be 
 what all immediately assent to. 
 
 Axioms evidently depend, in the first 
 instance, on particular observation, from 
 whence the mind intuitively perceives their 
 truth in general : like the postulates, after 
 they have been once laid down and ac- 
 knowledged, they are applied to the proof 
 of the demonstrable propositions which 
 follow in the Elements. 
 
 The axioms laid down by Euclid are the 
 following :» — 
 
 1. Things which are equal to the same 
 thing, are equal to one another. 
 
 2. If equals be added to equals, the 
 wholes are equal. 
 
 3. If equals be taken from equals the 
 remainders are equal. 
 
 4. If Equals be added to unequals, the 
 wholes are unequal. 
 
 5. If equals be taken from unequals, the 
 remainders are unequal. 
 
 6. Things which are double of the same, 
 are equal to one another. 
 
 7. Things which are halves of the same, 
 are equal to one another. 
 
 8. Magnitudes which coincide with one 
 another, that is, which exactly fill the same 
 space, are equal to one another. 
 
 # The word postulate literally means a petition, 
 or request. 
 
 VOL. I. 
 
 9. The whole is greater than its greatest 
 part. 
 
 10. Two straight lines cannot enclose a 
 space. 
 
 11. All right angles are equal to ona 
 another. 
 
 12. If a straight line meets two straight 
 lines, so as to make the two interior angles 
 on the same side of it taken together less 
 than two right angles, these straight lines 
 being continually produced, shall at leng th 
 meet upon that side on which are the 
 angles which are less than two right 
 angles. 
 
 The first ten axioms are too plain to re- 
 quire illustration ; the eleventh is what is 
 usually called an identical proposition, 
 for it amounts to no more than this, “ all 
 right angles are right angles.” 
 
 The 12th axiom is not properly an axiom, 
 but a proposition which requires proof; 
 therefore, if the reader does not fully com- 
 prehend its import, he may substitute the 
 following simple proposition in its stead. 
 
 Two straight lines meeting in a point, 
 are not both parallel to a third line. 
 
 PROPOSITIONS. 
 
 In a geometrical proposition, something 
 is either proposed to be done , or some truth 
 is to be demonstrated*. 
 
 In the former case the proposition is 
 called a Problem ; in the latter, it is a 
 Theorem. 
 
 Euclid, in his Elements, employs two 
 methods of demonstrating his propositions; 
 namely, direct and indirect. 
 
 A direct demonstration is that which pro- 
 ceeds from acknowledged truths, by a 
 chain of successive inferences, the last of 
 which is the thing to be proved. 
 
 An indirect demonstration, or, as it is often 
 termed, Reductio ad Absurdum, consists in 
 assuming as true, a proposition which di- 
 rectly contradicts the one which is intended 
 to be p.roved; and by proceeding on this 
 assumption, in the same manner as in the 
 direct method, we at length deduce an in- 
 ference which contradicts some self-evident 
 or previously demonstrated truth ; the as- 
 sumption is therefore absurd and false ; — 
 consequently the proposition we intended 
 to prove must be true, since two contrary 
 propositions cannot be both true or both 
 false at the same time. 
 
 As the converse of some propositions are 
 true, and of others not, it may be proper 
 
 * A subordinate property included in a demon- 
 stration, is sometimes stated in a detached torm, 
 and is t en called a f.emma. 
 
 An obvious consequence that results from a pro- 
 position is called a Corollary . 
 
 An excursive remark on the nature and applica- 
 tion of a demonstrated proposition is called a 
 Scholium. 
 
 C 
 
THE ARTISAN. 
 
 18 
 
 to inform the reader that the converse of a 
 proposition is not necessarily true, — there 
 fore, when it is so, it requires demonstra- 
 tion ; and accordingly Euclid demonstrates 
 such as he has occasion for.* The con- 
 verse of the 5th is true, and it is demon- 
 strated to be so in the 6th. But the con- 
 verse of the 8th proposition, for example, 
 is not true. For though all triangles having 
 their sides respectively equal, have their 
 angles also equal; yet all triangles which 
 have their angles equal have not their sides 
 equal. 
 
 It may also be of use to inform the stu- 
 dent of Geometry, that every proposition 
 consists of three distinct particulars ; viz. 
 the Enunciation, the Construction, and the 
 Demonstration . The enunciation declares 
 in general terms what is intended to be 
 done or proved. The construction teaches 
 how to draw the necessary lines, circles, 
 &c. and applies the enunciation to the 
 figure thus constructed. The demonstra- 
 tion is the chain of reasoning that follows, 
 whereby what was enunciated is clearly 
 and fully proved. { 
 
 Before the demonstration of any propo- 
 sition is attempted, the enunciation should 
 be well understood, and even got by heart. 
 The figure should then be constructed 
 solely by the directions which immedi- 
 ately follow the enunciation ; and the more 
 accurately this is done, the better will it 
 assist the recollection : compasses, &c. 
 may be employed for this purpose, but 
 they are not absolutely necessary, for the 
 truth of any proposition does not in the 
 least depend on the accuracy of the con- 
 struction. 
 
 Previous to beginning with the proposi- 
 tions, of Euclid’s Elements, we may remark, 
 for the information of those who are unac- 
 quainted with that valuable work, that we 
 shall endeavour to render these proposi- 
 tions as simple as it is possible to make 
 them ; but we must also remark, that there 
 are many of these which it is impossible 
 to render more simple ; and that there are 
 certain principles or mathematical truths 
 that do not admit of being rendered more 
 clear or more intelligible than they appear 
 by merely enunciating them. 
 
 The greatest assistance we can give the 
 student in this branch of science, will be 
 found in the observations and notes upon 
 the propositions to which they are sub- 
 joined. 
 
 * Converse and contrary propositions are not to 
 be confounded, as is often done : the contrary pro- 
 position is, when what is affirmed in the former 
 proposition is denied in the latter. Thus the con- 
 trary of proposition 5th is this, that the angles at 
 the base of an isosceles triangle are not equai : 
 now the converse of this proposition is demon- 
 strated to be true in the 6th proposition. 
 
 PROPOSITION I. 
 
 Problem : — To describe an equilateral tri- 
 angle upon a given straight line. 
 
 Let A B be the given straight line ; it is 
 required to describe an equilateral triangle 
 upon it. 
 
 From the centre A, at the distance A B, 
 describe the circle BCE; and from the 
 centre B, at the distance B A, describe the 
 circle A C D; and from the point C, in 
 which the circles cut one another, draw 
 the straight lines C A, C B, to the points 
 A and B ; A B C shall be an equilateral 
 triangle.* 
 
 Because the point A is the centre of the 
 circle B C E, A C is equal to A B ; and 
 because the point B is the centre of the 
 circle A C D,B C is equal to B A. But it 
 has been proved that C A is equal to A B ; 
 therefore C A, C B, are each of them equal 
 to A B : but things which are equal to the 
 same are equal to one another ; therefore 
 C A is equal to C B ; wherefore C A, A B, 
 B C, are equal to one another; and the 
 triangle A B C is therefore equilateral, — 
 and it is described upon the given 
 straight line A B, which was required to 
 be done. 
 
 PROPOSITION II. 
 
 Problem : — From a given point to draw a 
 straight line equal to a given straight 
 line. 
 
 Let A be the given point, and B C the 
 given straight line; it is required to draw 
 from the point A a straight line equal to 
 B C. 
 
 From the point A to B draw the straight 
 line A B ; and upon it describe the equi- 
 lateral triangle DAB, and produce the 
 straight line DA, D B, to E and F ; from 
 the centre B, at the distance B C, describe 
 the circle C G H, and from the centre D, 
 
 * It may be proper to remark, that in the follow- 
 ing propositions a comma is often used for the word 
 and, to prevent its repetition, as in most editions of 
 Euclid. 
 
THE ARTISAN* 
 
 19 
 
 at the distance D G, describe the circle 
 GKL, A L shall be equal to B C. 
 
 Because the point B is the centre of the 
 circle C G H, B C is equal to B G ; and 
 because D is the centre of the circle GKL, 
 X> L is equal to D G, and D A, D B, parts 
 of them, are equal ; therefore the re- 
 mainder A L is equal to the remainder 
 B G. But it has been shown, that B C is 
 equal to B G ; wherefore A L and B C are 
 each of them equal to B G; and things 
 that are equal to the same, are equal to one 
 another ; therefore the straight line A L is 
 equal to B C. Wherefore, from the given 
 point A a straight line A L has been drawn 
 equal to the given straight line B C. — 
 Which was to be done. 
 
 PROPOSITION III. 
 
 Problem : — From the greater of two given 
 straight lines to cut off a part equal to 
 the less. 
 
 Let A B and C be the less given straight 
 lines, whereof A B is the greater. It is 
 required to cut olf from A B, the greater, 
 a part equal to C, the less. 
 
 From the point A draw the straight line 
 A D equal to C, and from the centre A, 
 and at the distance A D, describe the 
 circle DEF. 
 
 DEF, A E is equal to A D ; but the straight 
 line C is likewise equal to A D ; whence 
 A E and C are each of them equal to 
 A I) ; wherefore the straight line A E is 
 equal to C, and from A B, the greater of 
 the two straight lines, a part A E has been 
 
 cut off equal to C, the less. Which was 
 to be done. 
 
 The three foregoing propositions may 
 appear to some as very trifling — because 
 any person who knows what a rule, and 
 compasses are, can set off 1 a straight line 
 of' a given length from a given point. 
 But Euclid’s design is not solely to teach 
 the practical delineation of figures, but to 
 derive the possibility of doing so in idea 
 from the postulates and axioms before 
 laid down without regard to their being 
 easy or difficult. 
 
 If these propositions, simple as they 
 are, be well understood, and readily de- 
 monstrated by the student of geometry, it 
 Will be the means of giving him a habit of 
 strict and accurate reasoning, of strength- 
 ening and enlarging the powers of his 
 mind, and of enabling him to demonstrate, 
 with ease and facility, the most difficult 
 propositions in the Elements. 
 
 PROPOSITION IV. 
 
 Theorem. — If two triangles have two sides 
 and the included angle of the one, equal 
 to two sides and the included angle of the 
 other, the triangles are equal in every 
 respect. 
 
 Let A B C, and D E F, be two triangles, 
 which have the two sides, A B and A C, 
 equal to the two sides D E and D F, each 
 to each ; viz. A B to DE, and A C to D F ; 
 and the angle BAC equal to the angle 
 E D F, the base B C shall be equal to the 
 baseEF; and the whole triangle ABC 
 to the whole triangle DEF; and the other 
 angles, to which the equal sides are oppo- 
 site, shall be equal to each other ; viz. the 
 angle A B C to the angle DEF, and the 
 angle ACBtoDFE* 
 
 A X> 
 
 For if the triangle A B C be applied to 
 D E F, so that the point A may be on D, and 
 the straight line A B upon D E, the point 
 B shall coincide with the point E ; because 
 AB is equal to DE, and AB coinciding 
 
 * As every triangle has three shies and three angles, 
 each angle must have a side opposite to it, and 
 each side an angle opposite to it. Thus, in the tri- 
 angle ABC, the side A C is opposite to the angle 
 at B ; ami the angle at C is opposite to the side 
 A B. This, though simple, must be carefully attend- 
 ed to, and if this is done, it will tend very much to 
 render the demonstration of the next proposition 
 more easily understood- 
 
 c 2 
 
THE ARTISAN. 
 
 with DE, AC shall coincide with DF, 
 because the angle BAC is equal to the 
 angle EDF; wherefore the point C shall 
 coincide with the point F, because the 
 stright line A C is equal to D F : but the 
 point B coincides with the point E; 
 wherefore the base B C shall coincide 
 with the base E F, because the point B co- 
 inciding with E, and C with F, if the base 
 BC does not coincide with EF, two 
 straight lines would inclose a space; which 
 is impossible, (see Ax. 10.) Therefore, as 
 the base B C coincides with the base E F, 
 the whole triangle ABC shall coincide 
 with the whole triangle DEF, and be 
 equal to it ; and the other angles of the 
 one shall coincide with the remaining an- 
 gles of the other, and be equal to them ; 
 viz. the angle A B C to the angle DEF, 
 and the angle A C B to D F E. Q. E. D.* 
 This and the eighth are important pro- 
 positions, for on them depends the whole 
 doctrine of triangles ; they are both proved 
 by superposition — a mode of demonstra- 
 tion which has been objected to by some 
 celebrated mathematicians ; not from any 
 want of evidence, but because they consi- 
 dered it not strictly geometrical, as it de- 
 pends upon no postulate. 
 
 PROPOSITION V. 
 
 Theorem. — The angles at the base of an Isos- 
 celes Triangle are equal to one another; 
 and , if the equal sides be produced, the 
 angles upon the other side of the base 
 shall be equal. 
 
 Let A B C be an isosceles triangle, of 
 which the side A B is equal to A C, and 
 let the straight lines A B and A C be pro- 
 duced to D and E, the angle ABC shall 
 be equal to the angle A C B, and the angle 
 C B D to the angle BCE. 
 
 A 
 
 words quod erat demonstrandum , which was to 
 He demonstrated. 
 
 In B D take any point F, and make A G 
 equal to A F, and join F C and G B. 
 
 Because A F is equal to A G, and A B 
 to A C, the two sides F A and A C are 
 equal to the two sides G A and A B, each 
 to each ; and they contain the angle FAG, 
 which is common to the two triangles 
 AFC and A G B ; therefore (by the 4th 
 prop.) the base F C is equal to the base 
 G B, and the whole triangle A F C to the 
 whole triangle A G B ; and the remaining 
 angles of the one to the remaining angles 
 of the other, each to each, to which the 
 equal sides are opposite ; viz. the angle 
 A C F to the angle A B G, and the angle 
 A F C to the angle A G B : and because the 
 whole A F is equal to the whole A G, of 
 which the parts A B and A C, are equal ; 
 the remainder B F shall be equal to the re- 
 mainder C G ; and F C was proved to be 
 equal to G B ; therefore the two sides B F 
 and F C are equal to the two C G and G B, 
 each to each; and the angle B F C is equal 
 to the angle CGB; therefore the triangles 
 are equal (by prop. 4th), and the remain- 
 ing angles of the one to the remaining an- 
 gles of the other; viz. the angle F B C to 
 G C B, and the angle B C F to CBG: and 
 since it has been demonstrated that the 
 whole angle A B G is equal to the whole 
 AC F, and that the angles C B G and B CF, 
 which are parts of these, are also equal ; 
 the remaining angle ABC is therefore 
 equal to the remaining angle A C B, which 
 are the angles at the base of the triangle 
 ABC: and it has also been proved, that 
 the angle F B C is equal to the angle G C B, 
 which are the angles upon the other side 
 of the base. Q. E. D. 
 
 Corollary. — From the demonstration of 
 this proposition it is evident, that every 
 equilateral triangle is also equiangular; 
 that is, it has all its angles equal to each 
 other. 
 
 For all equilateral triangles are also 
 lisosceles triangles; but all isosceles tri- 
 angles are not equilateral ones ; therefore, 
 when a triangle has only two of its sides 
 equal, it has only two of its angles equal; 
 but when it has all its sides equal it has 
 also all its angles equal. 
 
 The intricacy of this proposition, and its 
 being placed near the beginning of the 
 Elements, has procured it the name of the 
 Pons Asinorum , or Bridge of Asses. The 
 difficulty in the demonstration arises from 
 proving the angles upon the other side of 
 the base equal to each other 
 
THE ARTISAN. 
 
 21 
 
 'Ji 
 
 MECHANICS. 
 
 The quantity of motion, or, as it is often 
 termed, the momentum of a body, is mea- 
 sured by the velocity and quantity of mat- 
 ter jointly; that is, the quantity of matter 
 in any body, multiplied by its velocity, is 
 considered as its momentum , at least in 
 comparing the quantity of motion in one 
 body with that in another. 
 
 Thus, if the quantity of matter in one 
 body be represented by the number 8, and 
 its velocity by 3 ; and the quantity of mat- 
 ter in another body by 6, and its velocity 
 by 4, the momentum* or quantity of motion 
 in each of these bodies is equal. For 8 
 multiplied by 3 is equal to 6 multiplied 
 by 4. 
 
 The cause of motion is denominated 
 force, and a force is always measured by 
 its effect ; that is, by the motion which it 
 produces in a given time. 
 
 Forces are often represented by lines, 
 as well as by numbers . lines are employed 
 when the motions which they produce are 
 in any particular direction, with respect 
 to another line. 
 
 Forces have received different names 
 according to the manner in which they 
 act, as impact or percussion, gravity, pres- 
 sure, &c. 
 
 When a force produces its effect instan- 
 taneously, it is said to be impulsive, or to 
 act by impulse. 
 
 When it acts incessantly, it is called 
 constant , or a continued force. 
 
 Constant forces are of two kinds, uni- 
 ! orm and variable. A force is said to be 
 uniform , when it always produces equal 
 effects in equal successive portions of time ; 
 and variable, when the effects produced 
 in equal times are unequal. 
 
 As the velocity of a body is sometimes 
 estimated in a direction different from that 
 in which it actually moves, we shall here 
 shew how its place may be determined at 
 any time, in a direction making any given 
 angle with the one in which it is actually 
 moving. 
 
 Thus suppose a body to move along the 
 line A C, and that when it has reached the 
 point IJ, it is required to find its place in 
 the line A E, which makes with A C a given 
 angle. 
 
 from the body, or point B, at right angles, 
 to the line A E, that is, by letting fall a 
 perpendicular from the point B upon the 
 line A E. 
 
 The velocity of a body moving in a given 
 direction, is to its velocity estimated in any 
 other direction, as radius to the cosine of 
 the angle which the two directions make 
 with one another : or the velocity of the 
 body multiplied by the cosine of the angle 
 which the directions make with each other, 
 is the velocity of the body reduced to the 
 direction of that line. And the space de- 
 scribed by the body in its own path, multi- 
 plied by the cosine of the angle, is the 
 space described by the peipendicular in 
 the other line. Hence, if the velocity of 
 the body in its ow n path be uniform, it 
 will be uniform when reduced to any other 
 direction. 
 
 As the performance of this operation re- 
 quires a slight knowledge of trigonometry, 
 we shall here illustrate it by an example. 
 
 Suppose a body to move in the direction 
 A C, with a velocity of 50 feet per second, 
 and that its velocity is required in the di- 
 rection A E,* which make with A C an an- 
 gle of 30 degrees. The cosine of 30 de- 
 grees is *866, which, multiplied by 50, is 
 43’3, the velocity per second in the direc- 
 tion A E. 
 
 Again, let the space passed over in the 
 direction AC in any given time, be 500 
 feet, required the space passed over in the 
 direction A E in the same time. Here *866 
 multiplied by 500, is 433, the number of 
 feet passed over in the direction A E.f 
 
 ON THE LAWS OF MOTION. 
 
 1st Law. If a body be at rest, it will con- 
 tinue at rest ; and if in motion , it will 
 continue to move uniformly forward in a 
 right line , if it be not disturbed by the ac- 
 tion of some external cause. 
 
 The truth of this law is perfectly evi- 
 dent, for if there be no action of another 
 body, there can be nothing to determine it 
 to move in one direction more than another 
 when it is at rest ; and if it be in motion, 
 it must continue to go on in the same di- 
 rection, if there be nothing to turn it out 
 of that direction. 
 
 It is likewise impossible to change its 
 velocity without some cause, for there is 
 no tendency in matter itself either to in- 
 crease or diminish any motion impressed 
 upon it. I 
 
 t The cosine here employed is the natural cosine 
 of the angle, radius or the sine of 90 degrees being 
 unity, or — 1. These are the sines generally alluded 
 to in Works on Natural Philosophy; tables of na- 
 tural sines are to be found in all the common works 
 which contain mathematical tables. 
 
 i The resistance which a body makes to any 
 change in its state, whether at rest or in a state of 
 rectilineal motion, is called the inertia , or vis in 
 ertia, as has already been remarked, at page 7. 
 
 The plural of this word is momenta. 
 
22 
 
 THE ARTISAN. 
 
 The causes which retard a body in 
 motion are, collision, gravity, friction, 
 and the resistance of the air ; and it will 
 readily appear, by the following expe- 
 riments, that when these causes are re- 
 moved, or due allowance made for their 
 known effects, we are necessarily led 
 to infer the truth of tho law stated 
 above. 
 
 1st. If a ball be thrown along a rough 
 pavement, its motion, on account of the 
 many obstacles it meets with, will be very 
 irregular, and soon cease ; but if it be bowl- 
 ed upon a smooth bowling green, its mo- 
 tion will continue longer, and be more 
 rectilineal : and if it be thrown along a 
 smooth sheet of ice, it will preserve both 
 its direction and its motion for a still longer 
 time. 
 
 In these cases the gravity, which acts in 
 a direction perpendicular to the plane of 
 the horizon, neither accelerates nor retards 
 the motion ; the causes which produce the 
 latter effect are collision, friction, and the 
 air’s resistance ; and in proportion as the 
 two former of these are lessened, the mo- 
 tion becomes more nearly uniform and 
 rectilineal. 
 
 2nd. When a wheel is accurately con- 
 structed, and a rotatory motion about its 
 axis communicated to it, if the axis, and 
 the grooves in which it rests, be well po- 
 lished, the motion will continue a consi- 
 derable time ; if the axis be placed upon 
 friction wheels, the motion will continue 
 longer ; and if the apparatus be placed un- 
 der the receiver of an air pump, and the 
 air be exhausted, the motion will continue, 
 without visible diminution, for a very long 
 time. 
 
 In these instances, gravity, which acts 
 equally on opposite points of the wheel, 
 neither accelerates nor retards the motion ; 
 and the more care we take to remove the 
 friction, and the resistance of the air, the 
 less is the first motion diminished in a 
 given time. 
 
 From these, and similar experiments, we 
 are led to conclude, that all bodies in mo- 
 tion would uniformly persevere in that 
 motion, were they not prevented by exter- 
 nal impediments ; and that every increase 
 or diminution of velocity, every deviation 
 from the line of dirction, is to be attributed 
 to the agency of such causes. 
 
 It is in consequence of the tendency to 
 persevere in rectilineal motion that a body 
 revolving in a circle constantly endeavours 
 to recede from the centre. The effort thus 
 produced is called a centrifugal force; 
 and as it arises from absolute motion only, 
 whenever it is observed, we are convinced 
 that the motion is real. 
 
 In order to see the nature and origin of 
 this force, suppose a body to describe the 
 
 circle ABC; then, at any point A, it is 
 moving in the direction of the line A D, 
 
 and in this direction, by the first law of 
 motion, it endeavours to proceed ; also, 
 since every point D in the line is without 
 the circle, this tendency to move on in the 
 direction of the line, is a tendency to re- 
 cede from the centre of motion ; and the 
 body will actually fly off, unless it is pre- 
 vented by an adequate force. 
 
 The following experiment is given by 
 Sir I. Newton, to shew the effect of the 
 centrifugal force, and to prove that it al- 
 ways accompanies an absolute circular 
 motion. 
 
 Let a bucket, partly filled with water, 
 be suspended by a string, and turned 
 round till the string is considerably twist- 
 ed ; then let the string be suffered to un- 
 twist itself, and thus communicate a circu- 
 lar motion to the vessel. At first the water 
 remains at rest, and its surface is smooth 
 and undisturbed ; but as it gradually ac- 
 quires the motion of the bucket, the sur- 
 face grows concave towards the centre, 
 and the water ascends up the sides, thus 
 endeavouring to recede from the axis of 
 motion ; and this effect is observed gradu- 
 ally to increase with the absolute velocity 
 of the water, till at length the water and 
 the bucket are relatively at rest. When 
 this is the case, let the bucket be suddenly 
 stopped, and the absolute motion of the 
 water will be gradually diminished by the 
 friction of the vessel ; the concavity of the 
 surface is also diminished by degrees, and 
 at length* when the water is again at rest, 
 the surface becomes plane. Thus we find, 
 that the centrifugal force does not depend 
 upon the relative, but upon the absolute 
 motion, with which it always begins, in- 
 creases, decreases, and disappears. 
 
 2nd Law. The change of motion is always 
 
 proportioned to the force impressed, and 
 
 takes place in the direction in which the 
 
 force acts. 
 
 In order to understand the meaning cut 
 extent of this law of motion, it will be con- 
 venient to distinguish it into two cases, 
 
THE ARTIS AN. 
 
 and to point out such facts, under each 
 head, as tend to establish its truth. 
 
 1st. The same force, acting freely for a 
 given time, will always produce the same 
 effect, in the direction in which it acts. 
 
 Ex. 1. If a body, in one instance, fall 
 perpendicularly through 16^ f ee t in a se- 
 cond, and thus acquire a velocity which 
 would carry it, uniformly, through 32£ feet 
 in that time, it will always, under the same 
 circumstances, acquire the same velocity. 
 
 The effect is the same, whether the body 
 begins to move from rest or not. 
 
 2d. If the force impressed be increased 
 or diminished in any proportion, the mo- 
 tion comnranicated will be increased or 
 diminished in the same proportion. 
 
 Ex.’ 2. If a body descend along an inclined 
 plane, the length of which is twice as great 
 as its height, the force which accelerates 
 its motion is half as great as the force of 
 gravity; and, allowing for the effect of 
 friction, and the resistance of the air, the 
 velocity generated in any time is half as 
 great as it would have been, had the body 
 fallen, for the same time, by the whole 
 force of gravity. 
 
 In estimating the effect of any force, 
 two circumstances are to be attended to ; 
 first, we mu st consider what force is actu- 
 ally impressed ; for this alone can produce 
 a change in the state of motion or qui- 
 escence of a body. Thus, the effect of a 
 stream upon the floats of a water-wheel is 
 not produced by the whole force of the 
 stream, but by that part of it which arises 
 from the excess of the velocity of the wa- 
 ter above that of the wheel ; and it is no - 
 thing, if they move with equal velocities. 
 Secondly, we must consider in what direc- 
 tion the force acts ; and take that part of 
 it, only, which lies in the direction in 
 which we are estimating the effect. Thus, 
 the force of the wind actually impressed 
 upon the sails of a windmill, is not wholly 
 employed in producing the circular mo- 
 tion ; and therefore in calculating its effect, 
 in this respect, we must determine what 
 part of the whole force acts in the direc- 
 tion of the motion. 
 
 3d Law. The action and re-action of bo- 
 dies on one another are equal. 
 
 When motion is communicated by colli- 
 sion ’or impulse, the quantity of motion 
 gained by the one body, in any direction, is 
 just equal to that which is lost by the other 
 in the same direction. 
 
 When motion is communicated without 
 apparent contact, as i» the case of gravi- 
 tation, and what is ascribed 1o attraction 
 or repulsion, the quantity of motion gained 
 by the one body is just equal to that which 
 is gained by the other, but in the opposite 
 direction. 
 
 The first of these propositions includes 
 in it the first law of motion, and when so 
 understood, properly expresses the inertia 
 of body which has already been so fully 
 explained as to require no additional re- 
 marks in order to render it intelligible. 
 The second proposition is only known to 
 us by experience. 
 
 The first may be illustrated as follows : 
 If two bodies are equal, and have equal 
 velocities, it is evident that there must be 
 an equilibrium, when they meet, or strike 
 against each other. If the one be double 
 the other, and have half the velocity of 
 that other, an equilibrium will also take 
 place when they meet ; for the first 
 may be divided into two parts, eqch of 
 which would destroy half the velocity of 
 the other; consequently the whole mo- 
 tion of the second would thus be destroy- 
 ed. Hence it has been inferred, that bo- 
 dies that have equal quantities of motion, 
 have equal forces, or equal powers to pro- 
 duce motion. 
 
 This may be very easily and satisfacto- 
 rily proved, as follows : 
 
 Take two equal and similar cylindrical 
 pieces of wood, and from one of them let 
 a small steel point project ; suspend them 
 by equal strings, and let one of them de- 
 scend through any arc of a circle, and im- 
 pinge or strike upon the other at rest^ 
 then by means of the steel point, the two 
 bodies will move on together as one mass, 
 and with a velocity equal to half the ve- 
 locity of the body first put in motion. Thus 
 the momentum, or quantity of motion, re- 
 mains unaltered ; or, as much motion has 
 been gained by the body struck, as has 
 been lost by the body striking it. The expe- 
 riment maybe varied by loading one of the 
 bodies w ith lead, and observing the effect 
 roduced when the weight of the one bo- 
 y is any number of times that of the 
 other. * But in making experiments to es- 
 tablish this law of motion, allowance 
 must be made for the resistance of the air ; 
 and care must be taken to obtain a proper 
 measure of the velocity, both before and 
 after the bodies strike each other. 
 
 The third law of motion is not confined 
 to cases of actual impact; the effects of 
 pressure and attraction, as already stated, 
 are also equal, in opposite directions. 
 
 ti/hen two bodies sustain each other, the 
 pressures in opposite directions must be 
 equal, otherwise motion w ould ensue ; and 
 if . motion be produced by the excess of 
 pressure on one side, the case coincides 
 yvith that of impact, the effects qf w r hich 
 have just been described- 
 
 When one body attracts another, it is 
 itself also equally attracted : and the mo- 
 mentum communicated to the one, will 
 also be communicated to the other in the 
 opposite direction. A loadstone and a 
 
24 
 
 THE ARTISAN. 
 
 piece of iron, equal in weight, and floating 
 upon similar and equal pieces of cork, 
 approach each other with equal velocities, 
 and therefore with equal momenta; and 
 when they meet, or are kept asunder by 
 any obstacle, they sustain each other by 
 equal and opposite pressures. 
 
 These laws are the simplest principles 
 to which motion can be reduced, and upon 
 them the whole theory depends. They are 
 not, indeed, self-evident, nor do they ad- 
 mit of accurate proof by experiment, on 
 account of the great nicety required in ad- 
 justing the instruments, and making the 
 experiments ; and on account of the effects 
 of friction, and the air’s resistance, which 
 cannot entirely be removed. They are, 
 however, constantly and invariably sug- 
 gested to our senses, and they agree with 
 experiment as far as experiment can go ; 
 and the more accurately the experiments 
 are made, and the greater care we take to 
 remove all those impediments which tend 
 to render the conclusions erroneous, the 
 more nearly do the experiments coincide 
 with the laws. 
 
 COMPOSITION AND RESOLUTION OF FORCES. 
 
 It has already been stated at page 21, 
 that the momenta of bodies may either be 
 represented by numbers or lines ; and that 
 lines had the advantage of representing 
 the direction, as well as the forces of the 
 bodies in motion. 
 
 Two forces are said to be represented 
 by two lines, when the motions which they 
 singly produce are in the directions of 
 those lines, and proportional to them. 
 
 Let a body A be acted on by two forces 
 at the same instant, one of which acting 
 alone, would cause it to move uniformly 
 over A B in a given time ; and the other 
 acting alone, would cause it to move over 
 A C, at right angles to A B, in the same 
 time ; then the body will describe the dia- 
 gonal line A D, and at the end of the given 
 time will have arrived at the point D ; 
 
 For the motion of the body in the one of 
 these directions, will not be changed by the 
 force impelling it in the other. 
 
 If the lines which each of two forces 
 acting singly would have caused a body to 
 describe in the same time, make any angle 
 whatsoever with one another, the line 
 
 which the body will describe in that tiittey 
 when both the forces act on it at the same 
 instant, is the diagonal of the parallelogram 
 under the two first-mentioned lines * 
 
 Let A B and A C represent two forces 
 acting upon a body A , aDd let the motions 
 be communicated to the body at the same 
 instant ; and since A B and A C are the 
 spaces described by the body in the same 
 time, the line A D is equivalent to them 
 both ; and therefore the body will be found, 
 at the end of the given time, to have ar- 
 rived at the point D, as in the former case. 
 
 If two sides of a triangje, taken in order, 
 represent the spaces over which two uni- 
 form motions would separately carry a 
 body in a given time ; when these motions 
 are communicated at the same instant to 
 the body, it will describe the third side 
 uniformly in that time ; for every triangle 
 is half a parallelogram, the opposite sides 
 of which being equal to each other, the 
 diagonal must divide it into two equal 
 parts ; and it has been shown by the last 
 figure, that when two forces act upon a 
 body at the same time, with forces which 
 Would cause it singly to describe lines 
 making any angle with each other, that 
 the line the body will actually describe in 
 that time, is the diagonal of the parallelo- 
 gram under these two lines ; but the dia- 
 gonal is the third side of the triangle, 
 therefore the truth of the proposition is 
 manifest. 
 
 In the same manner, if the lines D B, 
 B C, C A, and A E, taken in order, repre- 
 sent the spaces over w hich any uniform 
 motions would, separately, carry a body 
 in any given time, 
 
 these motions, when communicated at the 
 same instant, will cause the body to de- 
 scribe the line D E, which completes the 
 figure, in that time; and motion in this 
 line will be uniform. 
 
 * A force is said to be equal or equivalent to any 
 number of forces, when it will singly produce the 
 same effect that the others produce jointly. 
 
THE ARTISAN. 
 
 HlTDllOSTATXCS. 
 
 The following table exhibits the specific 
 gravity of a great number of different sub- 
 stances, and will be found as accurate as 
 any table of the same extent which has 
 yet been presented to the public. 
 
 Distilled water, at the temperature of 
 55 degrees of Fahrenheit’s thermometer, is 
 assumed as the standard of comparison. 
 A cubical foot of water at this temperature 
 weighs nearly 62| podnds avoirdupois, 
 or 1000 avoirdupois ounces. Hence the 
 specific gravity of water being assumed at 
 1000 in the table, the specific gravities of 
 all the other bodies mentioned in the table 
 will nearly express the real weight of 
 a cubical foot of each, in avoirdupois 
 ounces. 
 
 Table of the Specific Gravities of Bodies. 
 
 SOLIDS. 
 
 Platinum 
 
 
 
 
 
 21,470 
 
 Gold 
 
 
 
 
 
 19,300 
 
 Iridium 
 
 
 
 
 
 18,060 
 
 Tungsten 
 
 
 
 
 
 17,400 
 
 Mercury 
 
 
 
 
 
 13,000 
 
 Palladium 
 
 
 
 
 
 11,800 
 
 Lead 
 
 
 
 
 
 11,350 
 
 W odanuxi 
 
 
 
 
 » 
 
 11,470 
 
 Rhodium 
 
 
 
 
 
 10,650 
 
 Silver 
 
 
 
 
 
 10,450 
 
 Bismuth 
 
 
 
 
 
 9,880 
 
 Uranium 
 
 
 
 
 
 9,000 
 
 Copper 
 
 
 
 
 
 8,900 
 
 Cabalt 
 
 
 
 
 
 8,000 
 
 Molybdenum 
 
 
 
 
 
 8,000 
 
 Nickel 
 
 
 
 
 
 8,400 
 
 Arsenic 
 
 
 
 
 
 8,350 
 
 Manganese 
 
 
 
 
 
 8,000 
 
 Iron 
 
 * 
 
 
 
 
 7,700 
 
 Tin 
 
 
 
 
 
 7,300 
 
 Zinc 
 
 
 
 -- 
 
 
 6,900 
 
 Antimony 
 
 
 
 
 
 6,700 
 
 Tellurium 
 
 
 
 
 
 6,120 
 
 Chromium 
 
 
 
 
 
 5,900 
 
 Columbium 
 
 
 
 
 
 5,600 
 
 Selenium 
 
 
 
 
 
 4,300 
 
 Ruby, oriental 
 
 
 
 
 
 4,200 
 
 Garnet, Bohemian 
 
 
 
 
 4,188 
 
 Barium 
 
 
 
 
 
 4,000 
 
 Strontia 
 
 
 * 
 
 
 
 3,800 
 
 Diamond 
 
 
 
 
 
 3,517 
 
 White lead 
 
 
 
 
 
 3,160 
 
 Island crystal 
 
 
 
 
 
 2,720 
 
 Marble 
 
 
 
 
 
 2,707 
 
 Pebble stone 
 
 
 
 
 
 2,700 
 
 Coral 
 
 
 
 
 
 2,700 
 
 Jasper 
 
 
 
 
 
 2,666 
 
 Rock crystal 
 
 
 
 
 
 2,650 
 
 Pearl 
 
 
 
 
 
 2,630 
 
 Glass 
 
 
 
 
 
 2,600 
 
 Flint 
 
 
 
 
 
 2,570 
 
 Onyx stone 
 
 
 
 
 
 2,510 
 
 Common stone 
 
 
 
 
 
 2,500 
 
 Glauber salt 
 
 
 
 
 
 2,250 
 
 Crystal 
 
 
 
 
 
 2,210 
 
 Oyster shells 
 
 
 
 
 
 2,092 
 
 Brick 
 
 
 
 
 
 2,000 
 
 Earth 
 
 
 
 
 
 1,984 
 
 Nitre 
 
 
 
 
 
 1,900 
 
 Vitriol 
 
 
 
 
 
 1,880 
 
 Alabaster 
 
 • 
 
 
 
 
 1,874 
 
 Horn. 
 
 • 
 
 
 
 
 1,840 
 
 Ivory 
 
 • 
 
 
 
 • 
 
 1,820 
 
 25 
 
 Brimstone - 
 
 
 
 
 1,800 
 
 Chalk 
 
 
 
 
 1,793 
 
 Borax 
 
 
 
 
 1,717 
 
 Allum 
 
 
 
 
 1,714 
 
 Clay 
 
 
 
 
 1,712 
 
 Dry bone 
 
 
 
 
 1,660 
 
 Human calculus - 
 
 
 
 
 1 ,542 
 
 Sand 
 
 
 
 
 1,520 
 
 Gum-arabic 
 
 
 
 
 1,400 
 
 Opium 
 
 
 
 
 1,350 
 
 Lignum-vitas 
 
 
 
 
 1,327 
 
 Coal 
 
 
 
 
 1,250 
 
 Jet - - 
 
 
 
 
 1,238 
 
 Coral 
 
 
 
 
 1,210 
 
 Ebony 
 
 
 
 
 1,177 
 
 Pilch 
 
 
 
 
 1,150 
 
 Rosin 
 
 
 
 
 1,100 
 
 Mahogany - 
 
 
 
 
 1,063 
 
 Ainber 
 
 
 
 
 1,040 
 
 Brazil wood 
 
 
 
 
 1,031 
 
 Box wood - 
 
 
 
 
 1,030 
 
 Common water 
 
 
 
 
 1,000 
 
 Bees wax 
 
 
 
 
 955 
 
 Butter 
 
 
 
 
 940 
 
 Logwood 
 
 
 
 
 913 
 
 Ice 
 
 
 
 
 908 
 
 Ash (dry) 
 
 
 
 
 838 
 
 Plumbtree (dry) 
 
 
 
 
 826 
 
 Elm (dry) 
 
 
 
 
 801 
 
 Oak (dry) 
 
 
 
 
 800 
 
 Yew 
 
 
 
 
 760 
 
 Crabtree 
 
 
 
 
 700 
 
 Beech (dry) 
 
 
 
 
 700 
 
 Walnut-tree (dry) 
 
 
 w 
 
 
 650 
 
 Cedar 
 
 
 
 
 613 
 
 Fir - - 
 
 
 
 
 580 
 
 Cork 
 
 
 
 
 238 
 
 New fallen snow 
 
 
 
 
 86 
 
 FLUIDS 
 
 
 
 
 Quicksilver 
 
 
 
 
 14,000 
 
 Oil of vitriol 
 
 
 
 
 1,700 
 
 Oil of tartar 
 
 
 
 
 1,550 
 
 Honey 
 
 
 
 
 1,450 
 
 Spirit of nitre 
 
 
 
 
 1,315 
 
 Aqua fortis 
 
 
 • 
 
 
 1,300 
 
 Treacle 
 
 
 
 
 1,290 
 
 Aqua regia 
 
 
 
 
 1,234 
 
 Spirit of urine 
 
 
 
 
 1,120 
 
 Human blood 
 
 
 
 
 1,154 
 
 Sack 
 
 
 
 
 1,033 
 
 Urine 
 
 
 
 
 1,032 
 
 Milk 
 
 
 
 
 1,031 
 
 Sea water 
 
 
 
 
 1,030 
 
 Serum of human blood 
 
 
 
 1,030 
 
 Ale - - 
 
 
 
 
 1,028 
 
 Vinegar 
 
 
 
 
 1,026 
 
 Tar 
 
 
 
 
 1,015 
 
 Water 
 
 
 • 
 
 
 1 - 
 
 Distilled waters 
 
 
 
 
 993 
 
 Red wine 
 
 
 
 
 990 
 
 Linseed oil 
 
 
 
 
 932 
 
 Brandy 
 
 
 
 
 927 
 
 Oil of olive 
 
 
 
 
 913 
 
 Spirit of turpentine 
 
 
 
 
 874 
 
 Spirit of wine 
 
 
 
 
 866 
 
 Oil of turpentine 
 
 
 
 
 810 
 
 Common air 
 
 - 
 
 
 - 
 
 0,012 
 
 The specific gravities of the bodies con- 
 tained in the foregoing table, and in all 
 tables of this kind, can only be considered 
 as the mean of a number of experiments 
 made on each, and therefore cannot be 
 considered as perfectly agreeing with the 
 result of a single experiment, made for 
 the purpose of determining the specific 
 gravity of any particular substance; be- 
 cause the purity, the temperature, and 
 several other causes, materially affect the 
 result of an experiment of this kind. 
 
THE ARTISAN. 
 
 The utility of accurate tables of this 
 kind is very great ; for, though the num- 
 bers in the table be only the relative 
 weights of the bodies opposite to them, 
 yet the real weight of a given bulk of any 
 body may easily be determined from its 
 specific gravity. An instance or two will 
 render the method of doing this perfectly 
 plain. It has been remarked above, that 
 the number opposite to any substance in 
 the table, not only expresses its specific 
 gravity , but the real weight of a cubical 
 foot of that substance in ounces avoirdu- 
 pois ; therefore to find the weight of any 
 given number of cubical feet of any sub- 
 stance, it is only necessary to multiply the 
 number of cubical feet by the number in 
 the table opposite to the substance, and 
 the product will be its weight in avoir- 
 dupois ounces. 
 
 Example : What is the weight of three 
 cubical feet of lead ? — The specific gravity 
 of lead is 11*350, which multiplied by 3 
 is 34*050 ounces, or 2128 pounds 2 ounces 
 avoirdupois. 
 
 If the given bulk be expressed in cubic 
 inches, multiply the specific gravity by the 
 number of cubic inches, and by the num- 
 ber 253*175 (which is the weight of a cubic 
 inch of water, in grains, of the above tem- 
 perature), and the product will be the 
 weight in troy grains. 
 
 Example: Required the weight of 10 
 cubic inches of iron? — The specific gravity 
 of iron is 7*700, which multiplied by 10 is 
 77*000, and this multiplied by 253*175, is 
 19*494*475 grains; which divided by 7000 
 (the number of grains in a pound avoir- 
 dupois) quotes 2 pounds 12 ounces 9 drams 
 nearly, for the weight of the 10 cubical 
 inches. 
 
 Another useful problem may be per- 
 formed by this table ; namely, to find the 
 bulk of any substance when its weight is 
 known. This is done by dividing the 
 weight in ounces ‘by the specific gravity 
 in the table, the quotient is the bulk in cu- 
 bic feet : if the quotient should not amount 
 to a cubic foot, or if the answer be wanted 
 in cubic inches, the quotient must be mul- 
 tiplied by 1728, the number of cubic inches 
 in a cubic foot. 
 
 Example : required the bulk of 4 2 ounces 
 of nickel? Here 42 divided by 8*400, the 
 specific gravity of nickel, quotes *005, or 
 the 200th part of a cubic foot, which mul- 
 tiplied by 1728, gives 8- cubic inches for 
 the bulk of 42 ounces of nickel. 
 
 By a slight attention to the foregoing 
 examples, it will be perceived, that if the 
 weight and bulk of any substance be 
 known, its specific gravity may be found, 
 for this is only to divide the weight by the 
 bulk of the body expressed in cubic feet. 
 Thus, suppose a piece of marbla to contain 
 
 4 cubic feet, and that its weight is 004 lbs, 
 or 9664 ounces ; required the specific gra 
 vity of marbles ? 
 
 The weight, 9G64 ounces, divided by 4, 
 the number of cubic feet, quotes 2,416, the 
 spacific gravity required. 
 
 SOLID BODIES FLOATING ON FLUIDS. 
 
 A solid floating on a fluid specifically 
 heavier than itself, will be in equilibrio, or 
 will rest, when it has sunk so far, that the 
 weight of the fluid displaced is equal to 
 the weight of the whole solid, and when 
 the centres of gravity of the whole solid, 
 and of the part immersed are in the same 
 vertical line. 
 
 Hence, every solid, specifically lighter 
 than a fluid which has an axis that divides 
 it into two similar and equal parts, when 
 placed in a fluid with its axis vertical, may 
 sink to a position in which it will remain 
 in equilibrio ; that is, without turning ei- 
 ther to the one side or the other.* 
 
 In such bodies there are always two op- 
 posite positions of equilibrium ; but there 
 is only one of them in which the body can 
 float permanently. 
 
 When the equilibrium of a floating body 
 is disturbed, or when the centres of gravity 
 of the whole, and the part immersed . are 
 not in the same vertical line, the body will 
 revolve on its axis, till it come into the po- 
 sition where these two points are in the 
 same vertical line. 
 
 There are some bodies that in every po- 
 sition these two points are in the same ver- 
 tical line. A homogeneous sphere, or 
 globe, is a body of this kind : and so is a 
 cylinder floating with its axis horizontal. 
 These bodies have no tendency to maintain 
 one position more than another ; and their 
 equilibrium, or floating position, is called 
 the equilibrium of indifference. 
 
 Some floating bodies, vvhen their equili- 
 brium is disturbed, return to their steady 
 position after a few oscillations back- 
 wards and forwards. Others, when ever 
 so little disturbed, do not resume their for- 
 mer position, but turn on their centres of 
 gravity, till they come into another posi- 
 tion, when they are again in equilibrio. 
 In the first case the equilibrium is said to 
 be stable, in the latter case to be unstable, 
 and then the body is said to overset. 
 
 When a floating body is made to revolve 
 from the position of equilibrium, if the line 
 of support (that is the vertical line passing 
 through the centre of gravity of the im- 
 mersed part) move so as to be on the same 
 side of the line of pressure, (or the verticle 
 passing through the centre of gravity of 
 
 * The centre of gravity of any body is that point 
 upon which the body, when acted upon only by the 
 force of gravity, will balance itself in all positions. 
 This will be more ■fully explained when treating 
 Mechanics in a future number. 
 
THE ARTISAN. 
 
 27 
 
 the whole) with the depressed part, the 
 equilibrium is stable, and the body will re- 
 sume its former position. But if the line 
 of support is on the same side of the line 
 of pressure with the elevated part, the 
 equilibrium is unstable, and the body will 
 overset.* 
 
 When a floating body revolves about a 
 given axis, the positions of equilibrium 
 through which it passes are alternately 
 those of stability ^and instability : for be- 
 tween a state in which a body has a ten- 
 dency to remain, and another in which it 
 has also a tendency to remain, as these 
 tendencies are opposite to one another, 
 there must be an intermediate position in 
 which the tendency to remain is equal to 
 nothing, or the body will revolve on its 
 axis. 
 
 If the form and size of a body, floating 
 in a fluid, be known, and its altitude above 
 the surface, and the specific gravity of the 
 fluid be also known, its 'Stability may be 
 calculated ; but as the calculation could 
 only be understood by a small portion of 
 that class of readers for whom our publi- 
 cation is chiefly designed, we have de- 
 clined to insert it here.f 
 
 JLSTROEfQirsr. 
 
 HISTORY OF ASTRONOMY. 
 
 [Continued from page 16.] 
 
 Meton and Euctemon, two Greek astro- 
 nomers, accordingly applied themselves to 
 the study of this subject with great indus- 
 try ; and by sagaciously combining all the 
 observations then known, formed a iuni- 
 solar period, Dr cycle of 19 years. This 
 eycle was adopted on the 16th July, in the 
 year 433 B. 0. and is still in use. It is 
 called the Metonic cycle, after the inventor 
 of it. In this discovery is visible very ex- 
 tensive astronomical knowledge, and every 
 appearance of great accuracy. Such was 
 its success in Greece, that the order of 
 the period was engraved in letters of gold, 
 and at this period goes by the name of the 
 Golden Number. 
 
 Among the ancients, Eudoxus is parti- 
 cularly distinguished for his knowledge, 
 and also for his attention to Astronomy. 
 He built an observatory at Cnidus, his 
 birth-place, which was shown long after 
 his death. He invented a sphere, (which 
 is called Eudoxus’ sphere,) to show the 
 
 * By the centre of gravity of the immersed part 
 a always meant its centre of gravity, supposing it 
 homogeneous. In fact, it is the centre of gravity of 
 the water displaced by the floating body. 
 
 + Those who wish to see this subject treated fully, 
 may consult Dr. Young’s Analysis of the Principles 
 of Natural Philosophy. 
 
 rising and setting of the sun and moon, &c. 
 for the climate of Greece. 
 
 He also composed two books on Astro- 
 nomy : the one was a description of the 
 constellations, the other treated on the 
 times of their rising and setting. Aratus, 
 by order of Antiochus, king of Macedon, 
 reduced all that w'as then known of Astro- 
 nomy into Greek verse, anno B. C. 276. This 
 poem is divided into two books, one of 
 which describes the sphere of Eudoxus ; 
 the other gives rules for predicting the 
 weather. Both of these have reached us 
 entire. 
 
 While Astronomy made such great pro- 
 gress in Greece, it was cultivated also by 
 some of the Western nations of Europe. 
 Pytheas, a celebrated astronomer at Mar- 
 seilles, observed in that city the meridian 
 altitude of the sun, at the time of the sum- 
 mer solstice, by a gnomon for the purpose 
 of determining the latitude of that place. 
 This man travelled to other parts of the 
 globe, for the purpose of observing the 
 phenomena of nature. He mentions having 
 visited an island, which he calls Thule, 
 where the sun rose presently after he had 
 set. As this is the case in Norway and 
 Iceland, it is inferred that he had reached 
 these countries. 
 
 The same philosopher discovered that 
 the Polar star is not precisely at the Pole 
 itself. He likewise pointed out the con- 
 nection of the tides with the motion of the 
 moon. 
 
 Alexander the Great, by his conquests, 
 rendered great service, both to Astronomy 
 and Natural Philosophy. On these sub- 
 jects, Aristotle wrote, by his order, a great 
 number of books. In one of these, en- 
 titled De Carlo, he proves the spherical 
 shape of the earth, from the circular sha- 
 dow it casts on the moon in eclipses, and 
 also from the difference of altitude observ- 
 able on any of the 'fixed stars, in travelling 
 north or south. He wrote one called De 
 Mundo, which gives an account of the 
 three quarters of the globe then known ; 
 viz. Asia, Africa, and Europe. 
 
 From this time Geography gradually 
 became (through its alliance with Astro- 
 nomy) a real science. 
 
 Horace mentions that the earth had been 
 measured before his time for he calls 
 Archytas, who had been Plato’s master, 
 the measurer of the earth. 
 
 But the first person who measured the 
 earth by a method consistent with the 
 principles of Geometry and Astronomy, 
 was Eratosthenes, librarian of the Alex- 
 andrian Museum. As this measurement 
 was performed in a somewhat curious 
 manner, it may be gratifying to the reader 
 here to mention it, as it will serve to give 
 some idea how that has lately been per- 
 formed in Europe. 
 
28 
 
 THE ARTISAN. 
 
 Eratosthenes was informed, that, on the 
 day of the summer solstice, the sun was 
 vertical at noon to the city of Syene, on 
 the borders of Ethiopia, under the tropic 
 of Cancer. A well is particularly men- 
 tioned to have been illuminated to the 
 bottom by the sun at noon on the solstitial 
 day. He knew likewise that Alexandria 
 and Syene were both under the same 
 meridian. 
 
 From these data, by means of a concave 
 hemisphere, with a stile fixed in its centre, 
 he found that theshadow of the meridian 
 sun caused by the stile at Alexandria, was 
 one-fiftieth part of the whole circumference. 
 Hence he inferred, that the arc of the 
 heavens comprised between Alexandria 
 and Syene must be the same ; and that the 
 distance between the two cities must like- 
 wise be a similar arc, or one-fiftieth part 
 of the circumference of the earth. On 
 measuring this distance, he found it to be 
 5000 stadia, which gave 250,000 stadia 
 for the circumference of the earth. As 
 there were different stadia then in use, it 
 is not well ascertained how many feet a 
 stadium contained. If it was the Egyptian 
 stadium that was used, this measurement 
 exceeds the modern measures about a 
 sixth part. 
 
 About the same time with Eratosthenes, 
 flourished Aristarchus of Samos, who has 
 given a very simple method of determining 
 the ratio of the distance of the sun and 
 moon from the earth, which, though not 
 very accurate, is yet ingenious. 
 
 Of all the ancient astronomers, no one 
 has so much enriched the science, or ac- 
 quired so great a name, as Hipparchus, a 
 native of Nice in Bithynia, 142 B. C. 
 
 One of his first cares was to rectify the 
 year, which before his time was made to 
 consist of 365 days six hours, which he 
 found to be a little too much. He also 
 found that the sun was longer in traversing 
 the six northern signs of the ecliptic than 
 the other half of it; and deduced from 
 this the eccentricity of the solar orbit. 
 
 He likewise made similar remarks and 
 calculations for the lunar orbit. 
 
 From these data, he constructed tables 
 of’the motions of the sun and moon, which 
 are the first of the kind that are mentioned. 
 
 Hipparchus made another important 
 discovery. He found that the stars always 
 preserved the same relative positions with 
 respect to each other ; but that they had 
 all a trifling motion in the order of the 
 signs of the zodiac, which was about 48'' 
 in a year. He also substituted a more 
 complete mode of measuring the ratio of 
 the distance of the sun and moon from the 
 earth, than the One given by Aristarchus. 
 He made use chiefly of parallaxes ; which 
 is the method now in use. On the dis- 
 appearance of a very large star, he set^ 
 
 about numbering the stars, and to note 
 down their configurations, respective dis- 
 tances, &c. and gave a very good catalogue 
 of them. 
 
 This immense labour laid the foundation 
 on which the whole superstructure of 
 astronomy was to be raised. He was ad- 
 mired and celebrated in all nations where 
 learning was pursued. Hipparchus was 
 the first who applied this science to fami- 
 liar purposes of the greatest utility in 
 geography, by determining the situation 
 of places by their latitudes and longitudes. 
 
 Cleomedes, who lived a little later than 
 Hipparchus, has left a work on-the sphere, 
 the periods of the planets, their distances 
 and magnitudes, with an account of an- 
 cient eclipses, which he says he derived 
 the knowledge of from Pythagoras, Era- 
 tosthenes, and Hipparchus. This work is 
 valuable, as it is the most ancient that has 
 reached us on these subjects. 
 
 The next person that claims particular 
 notice, was Julius Caesar, who rendered 
 an important service to the science • of 
 Astronomy, by new-modelling the Roman 
 calendar, B.C. 46 years. 
 
 Caesar appears to have been well versed 
 in Astronomy. He discovered that Au- 
 tumn occupied the place of the winter 
 months of the calendar, and that winter 
 occurred in the months of spring. He 
 invited the astronomer Sosigenes from 
 Athens to Rome to assist him in correcting 
 this disorder. They began by giving four- 
 teen months to the year of Rome, to re- 
 establish the order of the seasons. They 
 likewise determined that the year should 
 consist of 365 days six hours in future ; 
 but, as we shall afterwards see, this was 
 making the year too long by 11' 11"' ; ye-t 
 this was coming wonderfully near the real 
 length of the tropical year, considering 
 the state of science at that time. This is 
 still called the Julian year, out of compli- 
 ment to Julius Csesar. 
 
 Menelaus, a learned geometrician, A.D. 
 55, also distinguished himself in astro- 
 nomy, by the discovery of the principal 
 theorems of spherical trigonometry, which 
 are applicable to the purposes of Astro- 
 nomy. 
 
 i Astronomy had begun to languish in the 
 school of Alexandria, when the celebrated 
 Ptolemy made his appearance, in A.D. 140. 
 
 He was a native of Pelusium in Egypt, 
 and, when very young, came to Alexandria 
 to study in that school. His principal 
 work is entitled the Almagest , an Arabic 
 word which signifies the great collection . 
 It contains all the ancient observations and 
 theories, to which his own researches are 
 added, and is considered as the most com- 
 plete collection of ancient Astronomy that 
 ever appeared. 
 
 Ptolemy embraced the common opinion. 
 
THE ARTISAN. 
 
 20 
 
 that the sun, moon and planets moved 
 round the earth as their common centre. 
 This system continued to maintain its 
 ground till the time of Copernicus, and 
 has descended from Ptolemy to the present 
 day, under the name of the Ptolemaic 
 System. 
 
 Besides the Almagest, there exists ano- 
 ther great work of Ptolemy’s, his Geogra- 
 phy, in which he determines the situation 
 of places by their latitude and longitude, 
 according to the method of Hipparchus. 
 Ptolemy had the ambition, like Archi- 
 medes, to transmit the remembrance of his 
 labours to posterity by a public monument. 
 In the temple, of Serapis, at Canopus, 
 there is an inscription on marble, in w hich 
 are explained the hypothesis of his as- 
 tronomical system, such as the length of 
 the year, the motions of the planets, &c. 
 If there have been men of greater genius 
 than Ptolemy, there is no man that ever 
 collected a greater body of profound know- 
 ledge, or more truly conduced to the pro- 
 gress of Astronomy, considering the age 
 he lived in, and the time he wrote. 
 
 From Ptolemy to the time of the Arabs, 
 no astronomer of the first order is to be 
 found among the Greeks, except, perhaps, 
 Theon of Alexandria, who wrote a learned 
 commentary on the Almagest, about the 
 year 395. 
 
 Among the Arabs there have been many 
 excellent astronomers. As there was no 
 science to which they devoted so much at- 
 tention, there were none in which they 
 made so many discoveries. Their Caliphs 
 were particularly distinguished for their 
 knowledge and patronage of this science. 
 They soon found that Ptolemy had stated 
 the obliquity of the ecliptic a little too 
 great; and, after many observations, found 
 it to be nearly what it is at present. 
 
 The Caliph Almansor the Victorious, who 
 ascended the throne in 754, ranks among 
 the first of their astronomers. Haroun, his 
 grandson, who reigned from 786 to 809, 
 sent a present to Charlemagne of a water 
 clock, in the dial of which were twelve 
 small doors, forming the division of the 
 hours. Each of these doors opened at the 
 hour it marked, and let out little balls, 
 which, falling on 'a bell of brass, struck 
 the hours. The doors continued open till 
 12 o’clock, when 12 little knights, mounted 
 on horseback, came out together, paraded 
 round the dial, and shut all the doors. This 
 clock at that time astonished all Europe. 
 
 After Haroun, his son A1 Maimon suc- 
 ceeded to the throne. He also cultivated 
 the study of Astronomy. In his time there 
 lived several celebrated astronomers ; 
 among whom was Alfragan, who composed 
 several books on astronomy ; and from his 
 facility in calculation,, he was surnamed 
 the Calculator. 
 
 Albategni was also among the greatest 
 of the Arabian astro romers. He found 
 the year to contain only two minutes less 
 than what it was found to be by Dr. Hal- 
 ley 600 years after. 
 
 After the Arabs had conquered the 
 greater part of Spain, in the year 1020, 
 they built there many observatories to 
 conduct their observations. Alhazen, one 
 of their astronomers, has left a treatise on 
 Optics, which contains the first established 
 theory of refraction and twilight which 
 we have. 
 
 Among the Persians, also, there have 
 been many eminent astronomers. They 
 made many observations to discover the 
 real length of the solar year, which they 
 fixed at 365 days, six hours. One of their 
 chief astronomers was the famous Ulugh 
 Beg, grandson of Tamerlane ; he not only 
 encouraged the sciences as a sovereign, 
 but was himself reckoned one of the most 
 learned men of his age. To determine the 
 latitude of Samarcand, it is said he em- 
 ployed a quadrant, the radius of which 
 was 180 feet ! * He composed a catalogue 
 of the stars, and several astronomical ta- 
 bles, the most perfect then known in the 
 east. He was assassinated by his own 
 son. 
 
 From the year 800 till the beginning of 
 the fourteenth century, almost all Europe 
 was immersed in gross ignorance. The 
 only people who paid any regard to sci- 
 ence, was the Arabs that settled in Spain, 
 some of whom have been mentioned above. 
 Profiting by the books they had preserved 
 from the wreck of the Alexandrian library, 
 they cultivated and improved* all the 
 sciences, and particularly Astronomy, in 
 which they had many able professors. 
 
 From the beginning of the ninth century 
 to the year 1423, when Purbachius ap- 
 peared, there is no name that deserves to 
 be mentioned as contributing to the im- 
 provement of Astronomy. Purbachius was 
 a man of great talents ; he began an Epi- 
 tome of Ptolemy’s Almagest; but died 
 before it was completed. This was exe- 
 cuted by his friend and pupil, John Muller, 
 commonly called Regiomontanus. This 
 man made many observations, and .collect- 
 ed the writings of many of’ the ancient 
 astronomers. He published ephemerides 
 for thirty years to come, wrote a theory 
 of the planets and comets, and calculated 
 a table of sines and tangents for every de- 
 gree and minute of the quadrant. He diec 
 in the year 1476. 
 
 Nicolas Copernicus, born 1473, rose 
 next and made so great a figure in Astro- 
 nomy, that the true system, discovered, or 
 rather renewed by him, has been ever 
 
 * It is thought by many astronomers, that this 
 must have been a gnomen instead of a quadrant. 
 
30 
 
 THE ARTISAN. 
 
 since called the Copernican System. He 
 restored the old system of Astronomy 
 taught by Pythagoras, which had been set 
 aside from the time of Ptolemy. His un- 
 derstanding at once revolted against the 
 explanations which that philosopher had 
 given of the motions of our planetary sys- 
 tem ; and set about correcting his mistakes, 
 by laying the foundation of what is at this 
 day held to be the true system of the 
 world. This system he gradually im- 
 proved by a long series of observations, 
 and a close attention to the writings of 
 ancient authors. His first grand work 
 was printed in 1543, under the care of 
 Schoner and Osiander ; and he received a 
 copy of it only a few hours before his 
 death, on the 23d May 1543, at the age of 
 seventy years. 
 
 After the death of this great man, there 
 were several astronomers of considerable 
 note, that greatly improved the science ; 
 but the only one that claims particular 
 notice was Tycho Brahe, a Danish noble- 
 man, who was the inventor of a new sys- 
 tem, a kind of semi-Ptolemaic, which he 
 vainly endeavoured to establish instead of 
 the Copernican. His numerous works 
 shew that he was a man of great abilities ; 
 and it is to be regretted that he sacrificed 
 his talents, and perhaps his inward con- 
 viction, to superstitious considerations. 
 He restored the earth to its fancied immo- 
 bility, and made the sun and moon revolve 
 round it ; but the planets he made to re- 
 volve round the sun, which was a still more 
 absurd hypothesis than that of Ptolemy. 
 But we ought to forgive this error, or 
 rather weakness, in return for the many 
 observations and discoveries with which 
 he enriched Astronomy. No man ever 
 made more observations than Tycho Brahe. 
 
 Contemporary with Tycho flourished 
 several eminent astronomers, among whom 
 was the famous Kepler. To him we owe 
 the true figure of the orbits of the planets, 
 and the v proportions of the motions and 
 distances of the various bodies which com- 
 pose the solar system. The three great 
 Laws of Kepler may be said to be the 
 foundation of all Astronomy. Kepler was 
 born in 1571, and died in 1631. 
 
 Galileo was the next person who render- 
 ed any very important services to Astrono- 
 my. He was the first who applied the tele- 
 scope to astronomical observations, and with 
 it made many useful and valuable discove- 
 ries. By the observations and reasoning of 
 Galileo, the system of Copernicus acquired 
 a probability almost equivalent to demon- 
 stration. By espousing the opinions of 
 Copernicus, he drew on him the vengeance 
 of the Inquisition, who decreed that he 
 should pass his days in a dungeon ; but 
 he was liberated after the expiration of a 
 year, on condition that he should never 
 
 more teach or hold up the Copernican as 
 the true system of Astronomy. He was 
 born in the year 1564, and died in 1642. 
 
 In spite of the Inquisition, or the passages 
 in Scripture which were always brought 
 forward as objections to the motion of the 
 earth, the system of Copernicus gained 
 ground every day. 
 
 Contemporary with Galileo were a num- 
 ber of astronomers, who contributed to 
 the progress of the science. Baron Napier 
 published his tables of logarithms in 1614. 
 Bayer also, obtaining great celebrity by 
 the publication of his Uranometria , in 
 which the stars were designated by the 
 letters of the Greek alphabet, which is 
 still the case on our celestial globes and 
 planispheres. 
 
 Gassendi, a French philosopher, saw the 
 planet Mercury on the sun’s disc, which 
 was the first observation of the kind. A 
 little after this, in the year 1633, Mr Hor- 
 rox, an Englishman of very extraordinary- 
 talents, discovered that Venus would pass 
 over the disc of the sun on the 24th No- 
 vember, 1639. This event he only men- 
 tioned to one friend, a Mr. Crabtree ; and 
 these two men were the only persons in 
 the world who observed this transit, which 
 was the first transit of Venus that had 
 ever been viewed by human eyes. Mr. 
 Horrox made many useful observations 
 about this time, and had even formed a 
 new theory of the moon, so ingenious as 
 to attract the attention of Sir Isaac Newton. 
 But the hopes of astronomers, from the 
 abilities of this extraordinary young man, 
 were soon blasted, for he died in the be- 
 ginning of the year 1640, aged twenty -four 
 years. 
 
 Hevelius, burgomaster of Dantzic, also 
 rendered himself eminent by his numerous 
 and delicate observations. He founded an 
 observatory at Dantzic, and furnished it 
 with a great many excellent instruments, 
 some of which were divided into so small 
 divisions as 5". His observations on the 
 spots of the sun, and on the nature of 
 comets, were very numerous ; and his 
 catalogue of fixed stars, containing the lon- 
 gitude of above 1888, was remarkable for 
 its accuracy. It is to him also we are in- 
 debted for the first accurate description of 
 the spots on the moon. 
 
 The improvement of the telescope con- 
 tinued to lay open new sources of disco- 
 very. The celebrated Huygens construct- 
 ed two excellent telescopes, one of twelve 
 feet in length, and the other twenty-four, 
 with which he discovered the fourth satel- 
 lite of Saturn ; which he said afterwards 
 led him to discover the ring that surrounds 
 that planet. Huygens was likewise the 
 first person who applied pendulums to 
 clocks. He died in 1695, aged 66 years. 
 
 [To be continued .] 
 
THE ARTISAN. 
 
 31 
 
 ^ttferellaneous Suhjcrtss. 
 
 LIFE OF ARCHIMEDES. 
 
 Archimedes was born at Syracuse, and 
 related to Hiero, King of Sicily : he was 
 remarkable for his extraordinary applica- 
 tion to mathematical studies, but more so 
 for his skill and surprising inventions in 
 Mechanics. He excelled likewise in Hy- 
 drostatics, Astronomy, Optics, and almost 
 every other science ; he exhibited the mo- 
 tions of the heavenly bodies in a pleasing 
 and instructive manner, within a sphere of 
 glass of his own contrivance and workman- 
 ship; he likewise contrived curious and 
 powerful machines and engines for raising 
 weights, hurling stones, darts, &c. launch- 
 ing ships, and for exhausting the water out 
 of them, draining marshes, &c. When the 
 Roman Consul, Marcellus, besieged Syra- 
 cuse, the machines of Archimedes were em- 
 ployed : these showered upon the enemy a 
 cloud of destructive darts, and stones of vast 
 weight and in great quantities ; their ships 
 were lifted into the air by his cranes, levers, 
 hooks, &c. and dashed against the rocks, 
 or precipitated to the bottom of the sea ; 
 nor could they find safety in retreat ; his 
 .powerful burning glasses reflected the con- 
 densed rays of the sun upon them with 
 such effect, that many of them were 
 burned. Syracuse was however at last 
 taken by storm, and Archime.des, too deep- 
 ly engaged in some geometrical specula- 
 tions to be conscious of vdiat had hap- 
 pened, was slain by a Roman soldier. 
 Marcellus was grieved at his death, which 
 happened A. C. 210, and took care of his 
 funeral. Cicero, when he was Questor 
 of Sicily, discovered the tomb of Archi- 
 medes overgrown with bushes and weeds, 
 having the sphere and cylinder engraved 
 on it, with an inscription which time had 
 rendered illegible. 
 
 His reply to Hiero, who was one day 
 admiring and praising his machines* can 
 be regarded only as an empty boast. 
 u Give me,” said the exulting philosopher, 
 “ a place to stand on, and I will lift the 
 earth.” This however may be easily 
 proved to be impossible; for, granting him 
 a place, with the simplest machine, it 
 would require a man to move swifter than 
 a cannon shot during the space of 100 
 years, to lift the earth only one inch in all 
 that time. — Hiero ordered a golden crown 
 to be made, but suspecting that the artists 
 had purloined some of the gold and sub- 
 stituted base metal in its stead, he em* 
 ployed our philosopher to detect the cheat ; 
 Archimedes tried for some time in vain, 
 but one day as he went into the bath, he 
 observed that his body excluded just as 
 much water as was equal to its bulk ; the 
 thought immediately struck him that this 
 
 discovery had furnished ample data for 
 solving his difficulty; upon which he 
 leaped out of the bath, and ran through 
 the streets homewards, crying out, I have 
 found it! I have found it ! — The best edi- 
 tion of his works is that of Torelli, edited 
 at the Clarendon Press, Oxford, fol. 1792, 
 by Dr. Robertson, Savilian Professor of 
 Astronomy. 
 
 Longitude Scale ; or, Lunar Corrector. 
 
 By Captain Thomson. 
 
 There is, perhaps, no problem in the 
 whole circle of the physical science of 
 more practical utility, nor one which has 
 more engaged the attention of mathemati- 
 cians, than that of determining the longi- 
 tude of a ship at sea. The difficulty of 
 solving this problem, however, does not 
 consist in any deficiency in the theory, but 
 in the mechanical, or practical part of the 
 operation; for it is well known that the 
 difference of longitude between any two 
 places, is merely the difference between 
 the times at those places converted into 
 degrees, at the rate of fifteen degrees to 
 an hour. Now various plans have been 
 devised' for ascertaining this diff erence ; 
 but to put those plans in practice is found 
 to be attended with considerable trouble 
 and difficulty. The most obvious, and per- 
 haps the most easy, method of discovering 
 the difference of longitude between any 
 two places, is to have a watch, or chrono- 
 meter, well regulated according to the 
 time at one of the places, and then to 
 carry it to the other ; where, on being com- 
 pared with the time as reckoned there ‘it 
 will give the difference of longitude. This 
 is what is often done on board of .ship. 
 These chronometers are regulated to the 
 time at Greenwich previous to sailing ; 
 and were they to go regularly, and exhibit 
 the Greenwich time accurately, would af- 
 ford a simple and correct method of ascer- 
 taining the longitude of any place to which 
 they might be transferred, whenever the 
 time was determined at that place. But 
 it is well known that chronometers often 
 change their rate, at sea, from various 
 causes ; it therefore becomes' necessary not 
 only to have some means of correcting 
 them, but of ascertaining the longitude of 
 a ship independently of these instruments. 
 Now the means of accomplishing this de- 
 sirable object with great accuracy is af- 
 forded by the celestial bodies, together 
 with the Nautical Ephemeris ; for if the 
 distance between the sun and the moon, 
 or the moon arid a star, be accurately mea- 
 sured with a sextant, the longitude of the 
 place of observation can be determined 
 very correctly ; but this requires rather a 
 long and tedious calculation, even by the 
 shortest and easiest method which has yet 
 
32 
 
 THE ARTISAN. 
 
 been devised. Captain Thomson has, how- 
 ever, invented a sliding scale, which great- 
 ly shortens and simplifies the process. The 
 fact is, that by means of his scale no cal- 
 culation whatever is necessary to reduce 
 the apparent to the true distance ; and any 
 person who can take the distance between 
 the sun and the moon, will find no diffi- 
 culty in reducing it to the true distance, 
 by means of the lunar scale. This opera- 
 tion may be performed in less than two 
 minutes : and the result will generally be 
 within two or three seconds of that ob- 
 tained by the most rigid calculation. 
 
 One side of the scale is appropriated to 
 the purpose we have just stated ; and the 
 other to deducing the time from the alti- 
 tude of a celestial body: which will al- 
 ways come out exceedingly near to what 
 would be obtained by the common method 
 of calculation. 
 
 It is scarcely possible, in an article like 
 the present, either to give an adequate 
 description of the scale itself, or the man- 
 ner of using it ; but both appear to us to 
 be simple, and we are convinced that it 
 will be found exceedingly useful at sea. 
 We ought also to state, that the scale is 
 accompanied by a very neatly printed book 
 of instructions, and several tables, which 
 are indispensibly necessary to the practical 
 navigator. 
 
 We are happy to see that this excellent 
 instrument has met with the approbation 
 of some of the best judges of such instru- 
 ments that are to be found in London. 
 
 ON AQUATINTA ENGRAVING. 
 
 To the Editor of the Artisan. 
 
 Sir, — If the following short account ol 
 the method of effecting aquatinta engraving 
 is thought worthy of a place in your va- 
 luable publication, it is at your service. 
 
 After the intended figure is outlined, by 
 etching or otherwise, the plate is covered 
 all over with a ground of resin, burgundy 
 pitch, or mastic, dissolved in rectified spi 
 rits of wine ; this is done by holding the 
 plate in an inclined position, and pouring 
 the above composition over it. The spirit 
 of wine almost immediately evaporates, 
 and leaves the resinous substance in a gra- 
 nulated state, equally dissolved over every 
 part. The granulations thus produced, if 
 examined through a magnifying-glass, will 
 be found extremely regular and beautiful. 
 When the particles are extremely minute, 
 and near to each other, the impression 
 from the plate appears to the naked eye 
 exactly like a wash of Indian ink; but 
 when they are larger, the granulations ap- 
 pear more distinct. This powder, or granu- 
 lation, is called the aquatinta grain. The 
 plate is next heated to make the powder 
 
 adhere ; and in those parts where a very 
 strong shade is wanted, it is scraped away ; 
 but where strong lights are wanted, a var- 
 nish is applied. The aqua fortis, properly 
 diluted with water, is then put on with a 
 piece of wax, as in . common etching- or 
 engraving ; and by repeated applications 
 of this process, scraping where darker 
 shades are required, and covering the 
 light parts with varnish, the final effect is 
 produced. 
 
 Engraving by aquatinta was invented by 
 Le Prince, a French artist, by whom the 
 process was long kept secret. It is 
 even said, that for some time he sold his 
 prints (which are still reckoned excellent 
 specimens), for drawings. 
 
 QUESTIONS FOR SOLUTION. 
 
 To the Editor of the Artisan. 
 
 Sir, — Having carefully examined the 
 first number of your work, I am convinced 
 it must be highly useful to all those who 
 wish to become acquainted with the phy- 
 sical sciences, if continued upon the plan 
 you propose in the Introduction. As I 
 perceive by that part of your work that 
 you mean to devote a portion of each num- 
 ber to subjects of a miscellaneous nature, 
 I have taken the liberty to inclose two 
 mathematical questions, which some of 
 your ingenious readers may send you a 
 solution, if you think them deserving of a 
 place in the Artisan. — I am, Sir, &c. 
 
 Peter Plus* 
 
 1st. There is a lever, at the end of which 
 is suspended a weight of 45 pounds, and 
 at the other end a power of 2 lbs. : the 
 greater weight is one foot from the ful- 
 crum ; and each foot in length of the leaver 
 is one pound in weight : required the dis- 
 tance of the lesser weight from the ful- 
 crum, to keep the greater weight in equi- 
 librium ? 
 
 2d. If a heavy sphere, whose diameter 
 is 4 inches, be put into a conical glass, full 
 of water, whose depth is 6 inches, and 
 diameter 5 inches, how many cubical 
 inches of water will run over ? 
 
 PHILOSOPHICAL QUERY. 
 
 To the Editor of the Artisan. 
 
 Sir, — Having often heard it affirmed, 
 that a boat passes more easily over deep 
 water than shallow , and that a boatman 
 can row his boat much quicker over deep 
 than shoal water, I would be obliged to 
 you, or any of your intelligent readers, to 
 inform me if this is really the case ; and, 
 if it is so, what is the cause of so singular 
 a fact. — I am, Sir, &c. 
 
 Mercator. 
 
THE ARTISAN. 
 
 83 
 
 PNEUMATICS. 
 
 If the sole cause of the diminution of the 
 temperature of the air, in ascending from 
 the Earth’s surface, were the distance from 
 the Earth; and if it were admitted, that 
 there is no current of air perpendicularly 
 upwards, as there certainly is not, the di- 
 minution of temperature would follow the 
 inverse ratio of the distance from the cen- 
 tre of the Earth, or the greater the distance 
 from the Earth, the less would be the tem- 
 perature. 
 
 Professor Leslie, of Edinburgh, has 
 given a formula for determining the tem- 
 perature of any stratum of air, or its tem- 
 perature at any altitude, when the height 
 of the mercury in the barometer is given. 
 This formula we shall here state in words, 
 and then give an example of its application. 
 Divide the height of the column of mer- 
 cury in the barometer, at the upper station, 
 by its height at the lower station ; divide 
 also its height at the lower station by its 
 height at the upper station, and subtract 
 the former quotient from the latter, then 
 multiply the remainder by the number 25, 
 and the product is the diminution of tem- 
 perature at the upper station in degrees of 
 the centigrade thermometer, which may be 
 converted into degrees of Fahrenheit’s 
 scale, by multiplying by 9 and dividing 
 by 5. 
 
 For example Suppose the mercury in 
 the barometer- to stand at SOT inches at 
 .he bottom of a mountain, but at its top 
 the mercury stood only at 26*4 inches : re- 
 quired the diminution of temperature be- 
 tween the two stations ? Here 26*4 divided 
 by SOT, quotes *88 nearly ; and SOT di- 
 vided by 26*4, quotes 1T4, from which ’88 
 being subtracted, leaves ’26, and this mul- 
 tiplied by 25, gives 6§ nearly, for the di- 
 minution of temperature in degrees of the 
 centigrade scale, which are equal to 11 *7 
 degrees of Fahrenheit’s scale. 
 
 The fact, that the mercury in the baro- 
 meter sinks on ascending into the atmos- 
 phere, was first suggested by Pascal, and 
 ascertained by experiments made under 
 his direction. This important fact was soon 
 afterwards applied to the measurement of 
 heights, in France, by Mariotte, and in 
 England by Halley. The method of ac- 
 complishing this, however, remained very 
 imperfect, till De Luc applied the correc- 
 tions for the difference of temperature, and 
 directed simultaneous observations to be 
 made at the upper and lower station. He 
 fell into some errors, which were after- 
 wards pointed out and corrected by Trem- 
 bley, Sir George Shuckburgh, and Gene- 
 ral Roy. La Place has more recently made 
 barometrical measurement the subject of 
 his researches, but though the formula he 
 
 Vol. I. 
 
 has given is more simple than most others, 
 yet we consider it too complicated and 
 algebraical to be inserted here ; we shall 
 therefore present our readers with a rule 
 deduced by the ingenious professor Leslie, 
 for determining the height of mountains, 
 &c. which is unquestionably the simplest 
 that has yet been given, and sufficiently 
 accurate for any purpose to which that in- 
 strument may be applied. 
 
 The rule is this : — As the sum of the co- 
 lumns of mercury , in the barometer , at the 
 upper and lower stations , is to their differ- 
 ence , so is the constant number 52,000, to the 
 approximate height .* 
 
 Two corrections, depending on the vari- 
 ation of temperature, at the upper and 
 lower stations are besides required. 
 
 The first of these is for the expansion of 
 the mercury in the barometer at the upper 
 station, and is obtained thus: — Multiply 
 
 the — part of the column at the upper 
 10,000 
 
 station by twice the difference of the at- 
 tached thermometers, and add the product 
 to the upper column. This correction is, 
 however, so trifling on small heights, that 
 it may be entirely neglected. But the fol- 
 lowing correction is of much more import- 
 ance. It becomes necessary, on account 
 of the expansion of the air by heat, and is 
 
 obtained by multiplying the j—part of the 
 approximate height by twice the sum of 
 the degrees of the detached thermometers. 
 This correction being added to the ap- 
 proximate height, gives the true height.t 
 
 In order to render the method of per- 
 forming this operation as plain as possi- 
 ble, we shall here give an example of its 
 application. Suppose the barometer to stand 
 at 30’091 inches at the bottom of a moun- 
 tain which is to be measured, the attached 
 thermometer at 15°*7, and the detached at 
 15°*6, while on the top of the mountain the 
 barometer stood at 26*409 inches, the at- 
 tached thermometer at 10°, and the de- 
 tached at 8°’8. Required the height of the 
 mountain.^ 
 
 Here twice the difference of the attached 
 thermometers is 11°’4, which multiplied 
 
 into -00264, the part of 26-409 gives 
 *03 for the correction of the upper barome- 
 ter. Then the sum of 30*091 and 26-439 
 is 56-53 ; and their difference is 3*652 ; 
 therefore, 56*53 : 3*652 : : 52*000 : 3359 the 
 
 * This number is the more easily remembered, 
 from the division of the year into weeks. 
 
 + In measuring heights by the barometer, a de- 
 tached thermometer is used along with the one 
 attached to the barometer, in order to ascertain the 
 temperature of the air with exactness. The centi- 
 grade thermometer is the one supposed to be usea 
 in this rule. 
 
 J The character ( ° ) signifies degrees. 
 
 D 
 
34 
 
 THE ARTISAN. 
 
 approximate height in feet And twice the 
 sum of the degrees marked on the detach- 
 ed thermometer is 48*8, which multiplied 
 
 into 3*359, the ~^part of the approximate 
 
 height gives 164 ; this added to the ap- 
 proximate height, gives 3,533 feet for the 
 true height. 
 
 AIR AS ACCELERATING OR 
 RETARDING MOTION. 
 
 Having already stated, at page 11, that 
 if the end of a tube be immersed in water, 
 and the air extracted from the tube, the 
 water will ascend in the tube to the height 
 of 33 feet ; we have now to remark, that 
 if the tube be bent in the form of the one 
 A BC in the following figure. 
 
 
 the water will flow through the tube in 
 a continued stream, provided the height 
 from the surface of the water, to the top 
 of the bending does not exceed the height 
 stated above (33 feet). 
 
 A tube bent in this shape is called a sy- 
 phon. If the syphon, instead of having the 
 air extracted by suction, be filled with wa- 
 ter, and the ends stopped till it be invert- 
 ed, with the shorter leg immersed in wa- 
 ter, the same effect will follow. 
 
 The cause of the water descending is 
 its greater weight in the longer leg of the 
 tube, and the pressure of the air on the 
 surface of the water continues the sup- 
 ply- 
 
 The syphon may be employed to raise 
 water over a height less than 33 feet, if it 
 is to descend below the level of the foun- 
 tain on the opposite side. It could not, 
 however, be conveniently employed if the 
 height was near to 33 feet; because the ve- 
 locity with which the water in the shorter 
 
 leg is made to ascend, depending on the 
 difference between that height and 33 feet, 
 the length of the column which the air is 
 just able to sustain, might not afford a suf- 
 ficient supply for the stream descending in 
 the longer leg. 
 
 Te syphon is properly a pneumatico- 
 hydraulic machine, the action of water and 
 of air being both necessary to its effect. It 
 is, however, the simplest of all the instru- 
 ments employed for raising water. But it 
 is now more generally employed for de- 
 canting liquors, or in transferring them 
 from one vessel to another, when they are 
 to be removed to a vessel lower than the 
 one that contains them. 
 
 The Air Pump is a machine by which 
 the air is extracted from close vessels. It 
 was invented about the year 1654, by Otto 
 Guericke, a native of Magdeburgh, in 
 Germany, and marks an important era in 
 the history of the physical sciences. It 
 has, however, received great improve- 
 ments since, by several men of genius, at 
 different periods. 
 
 The air pump is in effect the same as 
 the water pump, and whoever understands 
 the one, will have little difficulty in un- 
 de* standing the other. We shall, however, 
 present our readers with the figure of one 
 of the most approved kind, and endeavour 
 to give as clear and comprehensive a de- 
 scription of its several parts as possible, 
 previous to stating some of the most im- 
 portant properties of the air which that 
 instrument has been the means of making 
 known to us. 
 
 Fig. 1st is the Air Pump complete, with 
 a glass receiver upon the pump-plate. All 
 receivers must be ground air-tight ; that is, 
 they must neither let out nor in any air at 
 its edges, when placed on the pump-plate. 
 If the receiver be not sufficiently well 
 ground for this purpose, a piece of wet 
 leather must be placed between the re- 
 ceiver aud the pump-plate. When this is 
 done the receiver may be exhausted, or the 
 air may be extracted from it by turning 
 the handle F backwards and forwards till 
 no more air can be forced out of it, which 
 may be known by observing that the mer- 
 cury ascends no higher in the tube Imn; 
 and the receiver will then be held down to 
 the plate by the pressure of the external 
 air, or atmosphere. For, as the handle (see 
 fig. 2d) is turned backwards, it raises the 
 piston d e in the barrel B K, by means of 
 the wheel F and rack D d : and, as the 
 piston is leathered so tight as to fibthe 
 barrel exactly, no air can get between the 
 piston and barrel ; and therefore, all the 
 air above d in the barrel is lifted up to- 
 wards B, and a vacuum is made in the 
 barrel from e to h; upon which, part of 
 the air in the receiver M (fig. I), by its 
 
THE ARTISAN. 
 
 U 
 
 spring, rushes through the hole r, in the 
 brass plate L L, along the pipe G C G, 
 which communicates with both barrels 
 by the hollow trunk I H K (fig. 2), and 
 pushing up the valve b, enters into the 
 
 vacant place b c of the barrel B K. For, 
 wherever the resistance or pressure is 
 taken oflT, the air will run to that place, 
 if it can find a passage. Then, as the han- 
 dle F is turned toward, the piston d e will 
 d 2 
 
36 
 
 THE ARTISAN. 
 
 be depressed in the barrel ; and, as the air 
 which had got into the barrel cannot be 
 pushed back through the valve b, it will 
 ascend through a hole in the piston, and 
 escape through the valve at d: and be 
 prevented by that valve from returning into 
 the barrel, when the piston is again raised. 
 At the next raising of the piston, a vacuum 
 is again made in the same manner as be- 
 fore, between b and e ; upon which more 
 of the air, which was left in the receiver 
 M, gets out by its spring, and runs into the 
 barrel B K, through the valve B. The 
 same thing is to be understood with regard 
 to the other barrel A I ; and as the handle 
 F is turned backwards and forwards, it 
 alternately raises and depresses the pistons 
 in their respective barrels ; always raising 
 one whilst it depresses the other. And, 
 as there is a vacuum made in each barrel 
 when its piston is raised, every particle of 
 air in the receiver M pushes out another, 
 by its spring or elasticity, through the hole 
 t, and pipe G G, into the barrels, until at 
 last the air in the receiver of the ordinary 
 air-pump comes to be so much dilated, or 
 rarefied, that it can no longer open the 
 valves ; and then no more can be taken 
 out. Hence there is no such thing as mak- 
 ing a perfect vacuum in the receiver; for 
 the quantity of the air taken out at any 
 one stroke, will always be as its density 
 in the receiver. For it has been ascertain- 
 ed, that if the number of strokes of the 
 piston increases in arithmetical progres- 
 sion, the quantity of air remaining in the 
 receiver, and also its density, will form a 
 series of terms decreasing in geometrical 
 progression. Thus, if the receiver and 
 barrels were of equal capacity, every stroke 
 of the piston will diminish the quantity 
 and density of the air one half; conse- 
 quently there will be just as much left as 
 was taken out at the last turn of the han- 
 dle. 
 
 In air-pumps of the most improved con- 
 struction, the valves are opened by a me- 
 chanical contrivance, so that the limit to 
 the perfection of the instrument, arising 
 from the spring of the air not being capa- 
 ble to open the valves, is now removed. 
 
 There is a screw k below the pump- 
 plate, which being turned, lets the air into 
 the receiver again, and then it becomes 
 loose, and may be taken off the plate. 
 
 The two barrels of the pump are fixed 
 to the frame E e e by two screw-nuts //, 
 which press down the top-piece E upon the 
 barrels : and the hollow trunk H (fig. 2) is 
 covered by a box, as G H in fig. 1. 
 
 There is a glass tube, Immn, open at 
 both ends, and about 34 inches long, at- 
 tached to some pumps; the upper end 
 communictaing with the hole in the pump- 
 plate, and the lower end immersed in 
 
 quicksilver at n in the vessel N. To this 
 tube is fitted a wooden ruler m m, called 
 the gauge, which is divided into inches and 
 parts of an inch, from the bottom at w, 
 (where it is even with the surface of the 
 quicksilver), and continued up to the- top, 
 a little below l , to 30 or 31 inches. 
 
 As the air is pumped out of the receiver 
 M, it is likewise pumped out of the glass 
 tube, Imn, because that tube opens into 
 the receiver through the pump-plate ; and 
 as the tube is gradually emptied of air, the 
 quicksilver in the vessel N is forced up 
 into the tube by the pressure of the atmos- 
 phere. And if the receiver could be per- 
 fectly exhausted of air, the quicksilver 
 would stand as high in the tube as it does 
 at that time in the barometer : for it is 
 supported by the same power or weight 
 (of the atmosphere) in both. 
 
 OPTICS. 
 
 A ray of light, CD, falling obliquely rn 
 the middle of a convex glass, as A B in the 
 annexed figure, 
 
 obliquity on a plane glass ; and will go 
 out of the glass in the same direction with 
 which it entered: for it will be equally 
 refracted at the points D and E, as if it had 
 passed through a plane surface. But the 
 rays C G and C 1 will be so refracted, as 
 
THE ARTISAN. 
 
 37 
 
 to meet again at the point F. Therefore, 
 all the rays which flow from the point C, 
 so as to go through the glass, will meet 
 again at F ; and if they go farther onward, 
 they cross at F, and go forward to the 
 opposite sides of the middle ray C D E F, 
 to what they were in approaching it in the 
 directions H F and K E. 
 
 When parallel rays, as A B C, fall di- 
 rectly upon a plano-convex glass D E, 
 
 and pass thiough it, they will be so re- 
 fracted, as to unite in a point/ behind it; 
 and this point is also called the principal 
 focus ; the distance of which, from the 
 middle of the glass, is called the focal dis- 
 tance, which is equal to twice the radius, 
 or the diameter, of the sphere of the glass’s 
 convexity. 
 
 When parallel rays, as A B C, fall di- 
 rectly upon a glass D E, 
 
 which is equally convex on both sides, and 
 pass through it; they will be so refracted, 
 as to meet in a point or principal focus /, 
 whose distance is equal to the radius or 
 semidiarneter of the sphere of the glass’s 
 convexity. But if a glass be more convex 
 on one side than on the other, the rule for 
 finding the focal distance is this : — as the 
 sum of the semidiameters of both convex- 
 ites is to the semidiameter of either, so is 
 double the semidiarneter of the other to the 
 distance of the focus; or, divide the dou- 
 ble product of the radii by their sum, and 
 the quotient will be the distance sought. 
 Thus, suppose the radius of convexity of 
 
 one side of a glass to be 6 inches, and the 
 other 3 inches ; the product of these num- 
 bers is 18, which doubled is 36, and this 
 divided by 9, the sum of the numbers, 
 quotes 4 inches for the focal distance of 
 the glass. 
 
 Since all those rays of the sun which 
 pass through a convex glass are collected 
 together in its focus , the force of all their 
 heat is also collected in that part ; and is 
 in proportion to the common heat of the 
 sun, as the area of the glass D E o the 
 area of the focus : that is, the heat in the 
 focus is as many times stronger than the 
 common heat of the sun, as the area or sur- 
 face of the glass exceeds the area or sur- 
 face of the focus. For example : if the 
 surface of a convex glass be twenty times 
 that Of its focus, the heat in the focus will 
 be twenty times that of the common heat 
 of the sun at the time. This is the reason 
 that a convex glass causes the sun’s rays 
 to burn, or set fire to substances, upon 
 which the focus is directed for some 
 time. 
 
 All the rays which pass through the 
 glass cross the middle ray in the focus /, 
 (see last fig.) and then diverge from it to 
 the contrary sides, in the same manner 
 F/G, as they converged in the space D/E 
 in coming to it. 
 
 If another glass F G, of the same con- 
 vexity as D E, be placed in the rays at the 
 same distance from the focus, it will re- 
 fract them so, as that after going out of it, 
 they will be all parallel, as a b c ; and go 
 on in the same manner as they came to the 
 first glass D E, through the space ABC; 
 but on the contrary sides of the middle 
 ray B fbt for the ray AD/ will go on 
 from / in the direction /Ga, and the ray 
 C E/in the direction /Fc; and so of the 
 others. 
 
 The rays diverge from any radiant point 
 as if they came from a principal focus : 
 therefore, if a candle be placed at/, in the 
 focus of the convex glass F G, the diverg- 
 ing rays in the space F/G will be so re- 
 fracted by the glass, as that after going 
 out of it, they will become parallel, as 
 shown in the space c b a. 
 
 If the candle be placed nearer the glass 
 than its focal distance, the rays will di- 
 verge after passing through the glass, 
 more or less, as the candle is more or less > 
 distant from the focus. 
 
 If the candle be placed farther from the 
 glass than its focal distance, the rays will 
 converge after passing through the glass, 
 and meet in a point which will be more or _ 
 less distant from the glass, as the candle 
 is nearer to, or farther from, its focus ; and 
 where the rays meet, they will form an in- 
 
THE ARTISAN. 
 
 verted image of the flame of the candle, 
 which may be seen on a paper placed 
 where the rays meet. 
 
 Hence, if any object A B C be "placed 
 beyond the focus F of the convex glass 
 def, 
 
 some of the rays which flow from every 
 point of the object, on the side next the 
 glass, will fall upon it, and after passing 
 through it, they will be converged into as 
 many points on the opposite side of the 
 glass, where the image of every point will 
 be formed ; and, consequently, the image 
 of the whole object will be formed, and 
 appear inverted. 
 
 Thus the rays Ad, Ae, A/, flowing 
 from the point A, will converge in the 
 space d af, and by meeting at a, will there 
 form the image of the point A. The rays 
 Bd, Be, B /, flowing from the point B, 
 will be united at b, by the refraction of the 
 glass, and will there form the image of the 
 point B. And the rays C d, C e, C/, flow- 
 ing from the point C, will be united at c, 
 w'here they will form the image of the 
 point C. And so of all the other interme- 
 diate points between A and C. The rays 
 which flow from every particular point of 
 the object, and are united again by the 
 glass, are called 'pencils of rays. 
 
 If the object A B C be brought nearer to 
 the glass, the picture ab c will be remov- 
 ed to a greater distance. For then, more 
 rays flowing from every single point, will 
 fall in a more diverging manner upon the 
 glass; and therefore can not be so soon 
 collected into the corresponding points be- 
 hind it. Consequently, if the distance of 
 the object ABC from the glass, be equal 
 to the focal distance of the glass, the rays 
 of each pencil will be so refracted by pass- 
 
 ing through the glass, that they will go out 
 of it parallel to each other; as represented 
 in the following figure. 
 
 Here the rays dl, eH, /h, which pro- 
 ceed from the point c, go out of the gla=s 
 parallel to each other ; the rays d G, cK, 
 /D, which proceed from B, also proceed 
 parallel to each other; and the rays d K, 
 e E, / L, which proceed from A, observe 
 the same law : this being the case, there 
 can be no picture or image formed behind 
 the glass. 
 
 If the focal distance of the glass, and the 
 distance of the object from the glass, be 
 known, the distance of the image from the 
 glass may be found as follows ; — Multiply 
 the distance of the focus by the distance of 
 the object, and divide the product hy their 
 difference, the quotient will be the distance 
 of the image from the glass. Thus : — sup- 
 pose the focal distance of the glass to be 
 6 inches, and the distance of an object 
 from it to be 8 inches, required the dis- 
 tance of the image from the glass. Here 8 
 multiplied by 6, is 48 ; which divided by 2, 
 the difference between 8 and 6, quotes 24 
 inches for the distance of the image from 
 the glass. 
 
 When any image is formed behind a 
 glass, it will be as much bigger or less 
 than the object as its distance from the 
 glass is greater or less than the distance of 
 the object. For as B e is to b e, so is A C 
 to a c.* So that, if A B C be the object, 
 c b a will be its image ; or if c b a be the 
 object, ABC will be the image. 
 
 * See the figure preceding the last. 
 
THE ARTISAN. 
 
 39 
 
 Having now given a short account of 
 the properties of convex lenses, we shall 
 proceed to state the principal properties of 
 concave ones, which will be very easily 
 understood by those who have attentively 
 read the foregoing observations upon con- 
 vex glasses or lenses. 
 
 When parallel rays, as A D, pass di- 
 rectly through a glass or lens, as B C, 
 
 H 
 
 which is equally concave on ' both sides, 
 they will diverge after passing through 
 the glass, as if they had come from a ra- 
 diant point F, in the centre of the glass’s 
 concavity ; which point is called the nega- 
 tive or virtual focus of the glass. Thus the 
 ray A, after passing through the glass B C, 
 will go on in the direction B H, as if it had 
 proceeded from the point F, and no glass 
 been in the way. The ray D, after passing 
 through the glass, will go on in the direc- 
 tion C G, and so on with the other inter- 
 mediate rays. The ray F, that falls di- 
 rectly upon the middle of the glass, suffers 
 no refraction in passing through it; but 
 goes on in the same rectilineal direction as 
 if no glass had been in its way. If the 
 glass had been concave only on one side, 
 and the other side quite plane, the rays 
 would have diverged, after passing through 
 it, as if they had come from a radiant point 
 at double the distance of F from the glass ; 
 that is, as if the radiant point had been at 
 the distance of a whole diameter of the 
 glass’s concavity. 
 
 If rays come to such a glass converging 
 more than parallel rays diverge after pass- 
 ing through it, they will continue to con- 
 verge after passing through it; but will 
 not meet so soon as if no glass had been in 
 the way; and will incline towards the 
 same side to which they would have di- 
 verged, if they had come parallel to the 
 glass. 
 
 As we have now stated the chief pro- 
 perty of lenses, we shall give a short de- 
 scription of the structure of the Eye, and 
 in doing this we shall be very brief, as we 
 ‘ntend only to give the reader some idea 
 
 how vision is performed by this most cu- 
 rious and noble organ.* 
 
 The eye is nearly globular, and consists 
 of three coats , and three humours. The 
 back part of the outer coat is called the 
 sclerotica , and the front part of it cornea. 
 The next coat within this is called the 
 choroiides, which serves, as it were, for a 
 lining to the other, and joins with the iris. 
 The iris is composed of two sets of mus- 
 cular fibres; the one of a circular form, 
 which contracts the hole in the middle, 
 called the pupil, when the light would 
 otherwise be too strong for the eye ; the 
 other consists of radial fibres, tending 
 every where from the circumference of the 
 iris towards the middle of the pupil ; these 
 fibres, by their contraction, have the effect 
 of dilating and enlarging the pupil, when 
 the light is weak, in order to let in the 
 more rays. The third coat is only a fine 
 expansion of the optic nerve, which spreads 
 like net-work all over the inside of the 
 choroides, and is therefore called the reti- 
 na ; upon which are formed the images of 
 all visible objects, by the rays of light 
 which either flow or are reflected from 
 them. 
 
 Under the cornea is a fine transparent 
 - fluid, like water, which is therefore called 
 the aqueous humour. This fluid gives a 
 protuberant figure to the cornea, and has 
 the same limpidity, specific gravity, and 
 refractive power, as water. 
 
 At the back of this lies what is called 
 the crystalline humour , which is shaped 
 like a double convex glass ; but a little 
 more convex on the back than the fore 
 part. It converges the rays which pass 
 through it from every visible object to its 
 focus, at the bottom of the eye. This hu- 
 mour is transparent like crystal, is much 
 of the consistence of hard jelly, and ex- 
 ceeds the specific gravity of water in the 
 proportion of 11 to 10. It is enclosed in a 
 fine transparent membrane, from which 
 proceed a number of radial fibres, all 
 round the edge, and join to the circumfer- 
 ence of the iris. These fibres have a power 
 of contracting and dilating occasionally, 
 by which means they alter the shape or 
 convexity of the crystalline humour, and 
 also shift it a little backward or forward 
 in the eye, so as to adopt its focal distance 
 at the bottom of the eye to the different 
 distances of objects; without this provision 
 we could only see those objects distinctly, 
 that were all at one distance from the eye. 
 At the back of the crystalline, lies the 
 vitreous humour, which is transparent like 
 glass, and is the largest of all in quantity, 
 
 * As a figure of the eye, and the necessary lines 
 for explaining how vision is performed by it, is 
 very complex, it was thought better to give only a 
 verbal dessription of that organ. 
 
40 
 
 THE ARTISAN. 
 
 filling the whole orb of the eye, and giving 
 it a globular shape. In consistence it 
 very much resembles the white of an egg ; 
 and very little exceeds the specific gravity 
 and refractive power of water. 
 
 The crystalline humour is of such a 
 convexity, that in a sound state of the eye, 
 its focus falls precisely on the retina , and 
 there paints or forms images of objects ; 
 and therefore vision is not distinct if the 
 focus should either fall short or exceed 
 the retina. If the convexity of the cornea 
 and crystalline humour should be greater 
 than the just degree for forming the 
 images of objects distinctly on the retina, 
 the focus of rays will fall short of the 
 retina, and the images of objects will be 
 formed before they fall upon the retina, 
 which is the case with near-sighted or pur- 
 blind persons. 
 
 If the convexity of those parts should 
 be less than just, the focus will fall as it 
 were beyond the retina, and the images of 
 objects will not be formed under the re- 
 tina as they should be, but above it in the 
 crystalline humour, and, therefore will ap- 
 pear indistinct or confused. 
 
 cnisMZSTXtir. 
 
 The true etymology and origin of the word 
 Chemistry is absolutely unknown. Both 
 are enveloped in mystery, and lost in the 
 darkness of ages past. Some historians of 
 this science suppose its name to be derived 
 from the word Kema, the pretended Book 
 of Secrets, entrusted to women by the De- 
 mons ; others derive it from Cham, the son 
 of Noah, from whom Egypt received the 
 name of Chemia, or Chamia ; some attri- 
 bute it to Chemnis, king of the Egyptians ; 
 and others deduce it from a Greek word, 
 which signifies juice, because they suppose 
 it to have commenced with the art of pre- 
 paring juices, or from another Greek word, 
 to melt ; because, according to them, it is 
 the daughter of the art of smelting the 
 metals. 
 
 Authors have been almost as much at 
 variance with respect to the definition as 
 to the origin and etymology of chemistry. 
 Some have confined it only to the art of 
 examining, extracting and purifying bo- 
 dies, particularly metals ; others have onjy 
 considered it as that of preparing reme- 
 dies. It is only since the middle of the 
 eighteenth century that chemistry has been 
 considered the science which ascertains 
 the principles of which bodies are compos- 
 ed, and their different properties. But 
 even this last definition is not accurate, be- 
 cause it neither comprises all the produc- 
 tions of nature, the principles of some of 
 
 which are unknown, nor all the means of 
 the science, which are not confined merely 
 to the separation of the constituent parts 
 of bodies. 
 
 The true definition which ought to be 
 given, in the present state*of the science, is 
 much more general. The following' may 
 be adopted: — Chemistry is a science by 
 which we become acquainted with the in- 
 timate and reciprocal action of all the bo- 
 dies in nature, upon each other. By the 
 words intimate and reciprocal action , the 
 science is distinguished from experimental 
 philosophy, which only considers the ex- 
 terior properties of bodies, possessing a 
 bulk or mass capable of being measured ; 
 whereas chemistry relates only to the in- 
 terior properties, and its action is confined 
 to particles whose bulk and mass cannot 
 be subjected to admeasurement or calcu- 
 lation. The action of the same cause may, 
 by a change of circumstances, pass from 
 being an object of the one of these sciences 
 to become that of the other. The action of 
 heat, when it expands or contracts the di- 
 mensions of bodies, belongs to natural phi- 
 losophy ; when the same power burns and 
 consumes bodies, its action belongs to che- 
 mistry. When it converts water into steam 
 it may belong to either science. 
 
 The object of Chemistry is to ascertain 
 the ingredients of which bodies are com- 
 posed ; to examine the. compounds formed 
 by the combination of these ingredients ; 
 and to investigate the nature of the power 
 which occasions these combinations. 
 
 The science, therefore, naturally divides 
 itself into three parts : — 1st. A descrip- 
 tion of the component parts of bodies, or 
 of simple substances , as they are called. 
 2d. A description of the compound bodies 
 formed by the union of simple substances. 
 3d. An account of the nature of the power 
 which occasions these combinations. This 
 power is now known in Chemistry by the 
 name of affinity. 
 
 All the bodies in nature, considered 
 with regard to the manner in which they 
 are affected in chemical operations, pre- 
 sent themselves to us either as simples or 
 compounds : — that is, such as have not yet 
 been decomposed, and such as have been 
 analysed, or separated into others less 
 composed, or complex. Whenever, there- 
 fore, we use the phrase simple bodies in 
 Chemistry, the term is to be understood 
 only of bodies not yet decomposed. We 
 cannot assert that those bodies are really 
 simple in themselves, or that they are not 
 formed of other elements still more simple. 
 We can only affirm, that in all the experi- 
 ments which have been made, these bodies 
 are found to act as if they were simple ; 
 that they cannot be decomposed by any 
 process yet known ; and that they can only 
 
THE ARTISAN. 
 
 41 
 
 be combined with other bodies, or made to 
 form a component part of a compound 
 body. 
 
 Natural bodies, considered under this 
 point of view, present to chemists a very 
 different aspect from what they did to 
 those who held a different doctrine. Most 
 of those bodies, which were formerly con- 
 sidered as simple and as the elements of 
 all other bodies, are found to be more or 
 less compounded; while many of those 
 that were formerly considered as com- 
 pounds are incapable of being decompos- 
 ed, and can only be ranked among simple 
 bodies. 
 
 The simple substances at present known 
 amount to about fifty. These are divided 
 by Dr. Thomson into two classes, which 
 he names confineable and unconfineable bo- 
 dies. By the first he means solids and li- 
 quids ; and by the last airs and gases, 
 heat, light, &c. The former may be exhi- 
 bited in a separate state, but the latter 
 cannot ; and their existence is inferred 
 merely from certain appearances which the 
 first class of bodies, and their compounds, 
 exhibit in particular cases, and under pe- 
 culiar circumstances. It is therefore ob- 
 vious, that an acquaintance with the pro- 
 perties of the first set of bodies, is neces- 
 sary in order to be able to investigate those 
 of the second. We shall, therefore, con- 
 sider these two classes separately. 
 
 But to form a classification of chemical 
 facts, at once adapted to lead the student 
 by easy and certain steps to a knowledge 
 of this science, and at the same time con- 
 formable to the strict rules of philosophi- 
 cal arrangement, is attended with very 
 great difficulty. For the science of Che- 
 mistry being chiefly confined to the inves- 
 tigation of the laws which bodies observe 
 in combining together, or in separating 
 from each other, it is impossible to enume- 
 rate the properties of any one substance 
 which ought to be selected as the first ob- 
 ject of investigation, without tracing the 
 effects of many other bodies upon it, which 
 must of necessity be previously known. 
 The action of certain bodies is, however, 
 much more general and extensive than 
 that of others. It therefore appears to be 
 the most natural order of considering this 
 complex and extensive science, to begin 
 by describing the properties and effects of 
 one of the most important and singular 
 substances in nature, which is oxygen. 
 
 OF OXYGEN GAS. 
 
 Oxygen gas may be obtained by the fol - 
 lowing process : — 
 
 Procure an iron bottle of the shape A, 
 B 
 
 and capable of holding rather more than 
 an English pint. To the mouth of this bot- 
 tle an iron tube bent like B is to be fitted 
 by grinding. A gun-barrel deprived of its 
 butt-end answers the purpose very well. 
 Into the bottle put any quantity of the 
 black oxide of manganese* in powder ; fix 
 the iron tube into its mouth, and the join- 
 ing must be air-tight; then put the bottle 
 into a common fire, and surround it on all 
 sides with burning coals. The extremity 
 of the tube must be plunged under the 
 surface of the water with which the vessel 
 C is filled. 
 
 This vessel may be of wood or japanned 
 tin-plate. It has a wooden shelf running 
 along two of its sides, about three inches 
 below the top, and an inch under the sur- 
 face of the water. In one part of this 
 shelf there is a slit, into which the ex- 
 tremity of the iron tube plunges. The 
 heat of the fire expels the greatest part of 
 the air contained in the bottle. It may be 
 perceived bubbling up through the water 
 of the vessel C from the extremity of the 
 iron tube. At first the air-bubbles come 
 over in torrents; but after having conti- 
 nued for some time they cease altogether. 
 
 Meanwhile the bottle is becoming gra- 
 dually hotter. When it is obscurely red 
 the air-bubbles make their appearance 
 again, and become more abundant as the 
 heat increases. This is the signal for plac- 
 ing the glass jar D, open at the lower ex- 
 tremity, previously filled with water, so as 
 to be exactly over the open end of the gun- 
 barrel. The air-bubbles ascend to the top 
 of the glass jar D, and gradually displace 
 all the water. The glass jar D then ap- 
 pears to be empty, but is in fact filled with 
 air. It may be removed in the following 
 manner: — Slide it away a little from the 
 
 * This substance shall be afterwards described. 
 It is now very well known in Britain, as it is in 
 common use with bleachers, and several other ma- 
 nufacturers, from whom it may be easily procured. 
 
42 
 
 THE ARTISAN. 
 
 gun-barrel, and then dipping any flat dish 
 into the water below it, raise it on the 
 dish, and bear it away. The dish must be 
 allowed to retain a quantity of water in it, 
 to prevent the air from escaping. Another 
 jar may then be filled with air in the same 
 manner ; and this process may be continu- 
 ed either till the manganese ceases to give 
 out air, or till as many jarfuls have been 
 obtained as are required.* This method 
 of obtaining and confining air was first in- 
 vented by Dr. Mayou, and afterwards 
 much improved by Dr. Hales. All the 
 airs obtained by this or any other process ; 
 or, to speak more properly, all the airs 
 differing in their properties from the air of 
 the atmosphere, have, in order to distin- 
 guish them from it, been called gases ; and 
 this name we shall afterwards employ, f 
 Oxygen gas may also be obtained in a 
 different manner, thus : — Let D represent 
 a Avooden trough, the inside of which is 
 lined with lead or tinned copper ; and let 
 C be a cavity in the trough, which ought to 
 be a foot deep. The trough is to be filled 
 with water at least an inch above the shelf 
 A B, which runs along the inside of it, 
 about three inches from the top. In the 
 body of the trough, which may be called 
 the cistern, the jars destined to hold gas 
 are to be filled with water, and then to be 
 lifted, and placed im erted upon the shelf 
 at B. 
 
 G F 
 
 This trough, which was invented by Dr. 
 Priestley, has been called by the French 
 chemists the pneumato-chemical, or simply 
 pneumatic apparatus, and is extremely use- 
 ful in all experiments in which gases are 
 concerned. Into the glass vessel E put a 
 
 * For a more exact description of this and simi- 
 lar apparatus, the rea ler is referred to Lavoisier’s 
 Elements of Chemistry , and Priestley on Airs ; 
 and above all to Mr. Watt’s description of a pneu- 
 matic apparatus , in Beddae’s Considerations on 
 Factitious Airs. 
 
 t The word gas was first introduced into Chemis- 
 try by Van Helmont. He seems to have intended 
 to denote by it every thing which is driven off from 
 bodies in a state of vapours by heat. 
 
 quantity of black oxide of manganese in 
 powder, and pour over it as much of that 
 liquid which in commerce is called oil of 
 vitriol , and in chemistry sulphuric acid , as 
 is sufficient to form the whole into a thin 
 paste; then insert into the mouth of the 
 vessel the glass tube F, so closely that no 
 air can escape except through the tube. 
 This may be done either by grinding, or 
 by covering the joining with a little gla- 
 zier’s putty, and then laying over it slips 
 of bladder or linen dipped in glue, or in a 
 mixture of the white of eggs and quick- 
 lime. The whole must be made fast with 
 cord.* 
 
 The end of the tube F is then to be 
 plunged into the pneumatic apparatus D, 
 and the jar G, previously filled with water, 
 to be placed over it on the shelf. The 
 whole apparatus being fixed in that situa- 
 tion, the glass vessel E is to be heated by 
 means of a lamp or candle. A quantity of 
 oxygen gas rushes along the tube F, and 
 fills the jar G. As soon as the jar is filled, 
 it may be slid to another part of the shelf, 
 and other jars substituted in its place, till 
 as much gas has been obtained as is want- 
 ed. The last of these methods of obtaining 
 oxygen gas was discovered by Scheele, the 
 first by Dr. Priestley. 
 
 The gas obtained by the above pro- 
 cesses was discovered by Dr. Priestley, 
 on the 1st of August 1774, and called by 
 him dephlogisticated air. Mr. Scheele, of 
 Sweden, discovered it before 1777, with- 
 out any previous knowledge of what Dr. 
 Priestley had done : he gave it the name 
 of empyreal air.* Condorcet gave it first 
 the name of vital air; and Mr. Lavoisier 
 afterwards called it oxygen gas ; a name 
 which is now generally received, and 
 which we shall adopt. 
 
 1. Oxygen gas is colourless, and invisi- 
 ble like common air. Like it, too, it is 
 elastic, and capable of indefinite expansion 
 and compression. 
 
 2. If a lighted taper be let down into a 
 phial filled with oxygen gas, it burns with 
 such splendour that the eye can scarcely 
 
 * This process, by which the joinings of vessels 
 are made air-tight, is called luting, and the sub- 
 stances used for that purpose are called lutes. The 
 lute most commonly used by chemists, when the 
 vessels are exposed to heat, is fat lute, made by 
 beating together, in a mortar, fine clay and boiled 
 linseed oil. Bees-wax, melted with about one-eighth 
 part of turpentine, answers very well, when the 
 vessels are not exposed to heat The accuracy of 
 chemical experiments depends almost entirely in 
 many cases upon securing the joinings properly 
 with luting. The operation is always tedious ; and 
 some practice is necessary before one can succeed 
 in luting accurately. Some very good directions 
 are given by Lavoisier. See his Elements, Part, 
 iii. chap. 7. In many cases luting may be avoided 
 altogether, by using glass vessels properly fitted to 
 each other by grinding them with emery. 
 
THE ARTISAN. 
 
 4' 
 
 bear the glare of light, and at the same 
 time produces a much greater heat than 
 when burning in common air. It is well 
 known, that a candle put into a well-closed 
 jar, filled with common air, is extinguish- 
 ed in a few seconds. This is also the case 
 with a candle in oxygen gas ; but it burns 
 much longer in an equal quantity of that 
 gas than of common air. 
 
 It has been ascertained by experiment, 
 which shall be afterwards related, that at- 
 mospherical air contains 22 parts in the 
 hundred (in bulk) of oxygen gas; and 
 that no substance will burn in common air 
 previously deprived of all the oxygen gas 
 which it contains. But combustibles burn 
 with great splendour in oxygen gas, or in 
 other gases to which oxygen gas has been 
 added. Oxygen gas, then, is absolutely 
 necessary for combustion. 
 
 It has been proved also, by many expe- 
 riments, that no breathing animal can live 
 for a moment in any air or gas. which does 
 not contain oxygen gas mixed with it. 
 Oxygen gas, then, is absolutely necessary 
 for respiration. 
 
 When substances are burnt in oxygen 
 gas, or in any other gas containing oxygen, 
 if the air be examined after the combus- 
 tion, we shall find that a great part of the 
 oxygen has disappeared. If charcoal, for 
 instance, be burnt in oxygen gas, there will 
 be found, instead of part of the oxygen, 
 another very different gas, known by the 
 name of carbonic acid gas. Exactly the 
 same thing takes place when air is respired 
 by animals ; part of the oxygen gas disap- 
 pears, and its place is occupied by sub- 
 stances possessed of very different proper- 
 ties. Oxygen gas then undergoes some 
 change during combustion, as well as the 
 bodies which have been burnt; and the 
 same observation applies also to respiration. 
 
 Oxygen gas is somewhat heavier than 
 common air. If the specific gravity of 
 common air be reckoned 1*000, that of 
 oxygen gas, as determined by Mr. Kirwan, 
 is 1*103. With this result the statement of 
 Lavoisier agrees exactly. But Mr. Davy 
 found it a little heavier; and Fourcroy, 
 Vauquelin, and Seguin, found it a little 
 lighter. Its specific gravity, according to 
 Mr. Davy’s experiments, is 1*127 :* accord- 
 ing to the French chemists, 1*087. 
 
 At the temperature of 60°, and when the 
 barometer stands at 30 inches, 100 cubic 
 inches of common air weigh very nearly 31 
 grains; and 100 cubic inches of oxygen 
 gas, at the same temperature and pressure, 
 weigh, according to Mr. Kirwan and La- 
 voisier, 34 grains; according to Sir H. 
 Davy, 34*74 grains. 
 
 * Mr. Davy’s oxygen gas was procured from ox- 
 ide of manganese. It is possible that it contained a 
 iittle carbonic acid gas. The tests used would not 
 have excluded that body. This would explain its 
 greater specific gravity. 
 
 Oxygen gas is not sensibly absorbed b; 
 water, except under great pressure ; bu 
 by forcing it into a bottle of water bj 
 strong pressure, it may be made to absorl 
 half its bulk of that gas, and to retain it it 
 solution. Water thus impregnated does 
 not sensibly differ from common water, ei- 
 ther in taste or smell. It has been found a 
 valuable remedy in several diseases. 
 
 Oxygen is capable of combining with a 
 great number of bodies, and of forming 
 compounds possessed of very different qua- 
 lities. 
 
 As the combination of substances with 
 each other is of the utmost importance in 
 chemistry, we shall here make a few ob- 
 servations on that subject before we pro- 
 ceed to the consideration of the nature and 
 properties of Hydrogen Gas. 
 
 When common salt is thrown into a ves- 
 sel of pure water, it melts, and very soon 
 spreads itself through the whole of the li- 
 quid, as any one may convince himself by 
 the taste. In this case the salt combines 
 with the water, and cannot afterwards be 
 separated by filtration, or any other me- 
 chanical means. It may, however, be 
 done by a very simple process ; for, if a 
 quantity of the spirit of wine be poured 
 into the solution, the salt will fall slowly to 
 the bottom of the vessel in the state of a 
 very fine powder. 
 
 It was long ago asked, Why does the 
 salt dissolve in water? and also, Why 
 does it fall to the bottom on pouring in spi- 
 rit of wine? These questions were first 
 answered by Sir Isaac Newton. 
 
 There is a certain attraction between the 
 particles of common salt and those of wa- 
 ter, which causes them to unite together 
 whenever they are presented to one ano- 
 ther. There is also an attraction between 
 the particles of water and spirit of wine, 
 which equally disposes them to unite, and 
 this attraction is greater than that between 
 the water and salt ; the water, therefore, 
 leaves the salt to unite with the spirit of 
 wine, and the salt being now unsupported, 
 falls down by its weight to the bottom of 
 the vessel. This power, which disposes 
 the particles of different bodies to unite, 
 was called by Newton attraction , by Berg- 
 man elective attraction, and by many of 
 the German and French Chemists affinity ; 
 and this last term is now employed in pre- 
 ference to the others, because they are ra- 
 ther general. All substances which are 
 capable of combining together, are said to 
 have an affinity for each other; on the 
 contrary, those substances which do not 
 unite, are said to have no affinity for each 
 other. Thus oil and water are said to have 
 no affinity for one another. 
 
 It appears, from the instance of the com- 
 mon salt and spirit of wine, that substances 
 differ considerably in the degree of their 
 affinity from other substances, for the spirit 
 
44 
 
 THE ARTISAN. 
 
 of wine displaced the salt, and united with 
 the water. Spirit of wine has, therefore, 
 a stronger affinity for water than common 
 salt has. 
 
 From facts of this kind tables of affinity 
 liave been formed and arranged in a very 
 peculiar manner. The substance whose 
 affinities are to be represented, is placed at 
 the top of a column ; and beneath it the 
 bodies for which it has an attraction, plac- 
 ing those nearest to it which it attracts 
 most strongly. Thus, in exhibiting the affi- 
 nities of muriatic acid, the bodies for which 
 it lias an affinity would be placed thus : 
 MUR IATIC A CID, 
 
 Barytes, 
 
 Potash, 
 
 Soda, &c. 
 
 This method is now universally adopted, 
 and has contributed very much to the ra- 
 pid progress of chemistry. 
 
 We shall treat this subject fully in a fu- 
 ture number : we introduce it here merely 
 to give the student of chemistry some idea 
 of what is meant by bodies combining to- 
 gether, as the expression will frequently 
 occur even in treating of simple bodies. 
 
 ASTS©K©MY. 
 
 HISTORY OF ASTRONOMY. 
 
 [Continued from page 30.] 
 
 About this time, the Royal Society of 
 London, and the Royal Academy of Paris, 
 were established, each of which has pro- 
 duced astronomers of the first order. The 
 first person appointed to conduct the obser- 
 vations at the royal observatory at Paris, 
 was Dominic Cassini, who soon after dis- 
 covered the first, second, third, and fifth 
 satellites of Saturn. He also discovered 
 that the planets Jupiter, Mars, and Venus 
 turned round their axes in a manner similar 
 to the earth. He died in the year 1712. 
 
 The successive propagation of light, 
 one of the most curious discoveries in 
 Astronomy, was about this time made by 
 Roemer, a Danish astronomer. This has 
 ever since been accounted a most essential 
 element in Astronomy, and must secure 
 immortality to the name of Roemer. 
 
 England, at all times, produced astro- 
 nomers of the first order ; and at this 
 period it had to boast of Hook, Flamstead, 
 and Halley. 
 
 Hook was born in 1635, and died in 1702. 
 He was not only a great observer in every 
 branch of Astronomy, but his inventive 
 powers have been exhibited in almost 
 every branch of science. He was the in- 
 ventor of the Zenith Sector, an instrument 
 which was used to determine whether or 
 not the earth’s orbit had any sensible pa- 
 rallax. He gave the first hint of making a 
 quadrant for measuring angles by reflexion ; 
 
 and he, in some measure, anticipated the 
 discoveries of Newton, by shewing that 
 the motion of the planets resulted from a 
 projectile force combined with the attractive 
 power of the sun. 
 
 Flamstead was born 1646, and died in 
 1720. After the Royal Observatory at 
 Greenwich was finished, he was appointed 
 by King Charles II. to the management of 
 it, with the title of Astronomer Royal. He 
 made a very great number of observations^ 
 which he has recorded in his Historia Ce- 
 lestis , and in the Philosophical Transac- 
 tions. But the principal service he ren- 
 dered Astronomy, was by forming a cata- 
 logue of 3000 fixed stars visible in our 
 climate. 
 
 Flamstead was succeeded, in 1719, by 
 Dr. Halley, the greatest astronomer, says 
 M. de la Lande, in England; and Dr. Long 
 adds, “ I believe he might have said the 
 whole world.” He was sent by King 
 Charles II. to St. Helena, in order to form 
 a catalogue of the stars in the southern 
 hemisphere, which was published in 1679. 
 While he was in the island of St. Helena, 
 making this catalogue, he had an oppor- 
 tunity of observing a transit of Mercuiy 
 across the sun’s disc, by which he was 
 enabled to point out the method of deter- 
 mining the parallax of the sun. 
 
 On his way between Calais and Paris y 
 he obtained a sight of the famous comet 
 that appeared in 1680, which suggested to 
 him the idea of writing a treatise on the 
 subject of comets, in which he investigates 
 the orbits of these wandering bodies, and 
 predicted the return of the one that ap- 
 peared in 1759, which is the only predic- 
 tion of the kind that ever was verified. It 
 is said that during the nine years he was 
 at Greenwich, he made 1500 observations. 
 Halley was acquainted, either personally 
 or by letter, with every astronomer of note 
 in Europe then living. He died in the 
 year 1742, aged eighty-six years ; and was 
 succeeded by Dr. Bradley, to whom we 
 are indebted for two of the most beautiful 
 discoveries of which the science can boast : 
 the aberration of light, and the nutation of 
 the earth’s axis. He also made a great 
 many observations, in order to discover if 
 the fixed stars had any sensible parallax. 
 These observations are partly published, 
 and the remainder of them are in the hands 
 of a Mr. Abraham Robertson, to whom 
 their publication was entrusted. Bradley 
 died in the year 1762. 
 
 But to no individual is the science of 
 Astronomy more indebted, than to the ce- 
 lebrated Sir Isaac Newton. This great 
 man was born on the 25th December 1642, 
 at Woolstrope in Lincolnshire. His disco- 
 veries were not confined to Astronomy 
 alone; for in Mathematics and Natural 
 Philosophy he was equally great. His 
 chief discovery in Astronomy was the law 
 
THE ARTISAN. 
 
 4a> 
 
 of gravitation, by which he was enabled 
 to account for some of the greatest pheno- 
 mena in nature. His great work, the Prin- 
 cipia, appeared in 1686. This work is one 
 of the most valuable books on Physical 
 Astronomy that ever was published. His 
 discoveries are so numerous and important 
 in this science, that the solar system, or that 
 restored by Copernicus, has received the 
 appellation of the Newtonian system. 
 
 In this country there have been several 
 distinguished astronomers since the time of 
 Newton, among whom may be mentioned 
 Dr. Long, Dr. Keil, Dr. Bliss, Mr. Fergu- 
 son, Mr. Hadley, and Dr. Herschel; the 
 latter of whom, for his many accurate ob- 
 servations, deserves to be ranked among 
 the first class of astronomers of any age or 
 nation. In the year 1781, on the 13th of 
 September, he discovered the planet Geor- 
 gium Sidus. In the year 1787, he disco- 
 vered two satellites revolving round that 
 planet; and in 1790 and 1794, he discover- 
 ed other two satellites. These discoveries 
 of Herschel form a new era in Astronomy. 
 
 Dr. Maskelyne, the late Astronomer 
 -Royal, has likewise rendered very impor- 
 tant service to the science. He was the 
 first who proposed to the Board of Longi- 
 tude the publishing of an Ephemeris or 
 Nautical Almanack, which was begun in 
 the year 1767. This almanack is still conti- 
 nued annually, and has been of the utmost 
 service to navigation. 
 
 Dr. Maskelyne died a few years ago, 
 and was succeeded by the present Astro- 
 nomer Royal, Mr. Pond, who is also a man 
 of genius, and promises to be of great ser- 
 vice to Astronomy. 
 
 On the continent also there have been 
 many astronomers of great talents since 
 the time of Newton, particularly in France. 
 Among these, La Caille deserves to be 
 mentioned with credit. He was born in 
 1713, and in the year 1751 he undertook a 
 voyage to the Cape of Good Hope, for the 
 purpose of perfecting the catalogue of the 
 stars in the southern hemisphere. After 
 incredible labour and exertion, he returned 
 to Europe with a catalogue of 9800 stars, 
 which were comprehended between the 
 south pole and the tropic of Capricorn. In 
 addition to these labours, La Caille calcu- 
 lated new tables of the Sun, made observa- 
 tions on the parallax of Mars and Venus, 
 on atmospherical refraction, on the length 
 of pendulums, and measured a degree of 
 the meridian during his stay at the Cape : 
 he died in the year 1762. Contemporary 
 with La Caille lived several very eminent 
 astronomers, of whom may be mentioned 
 Cassini, Bouguer, Condamine,Maupertuis, 
 and Clairaut, who were, all employed soon 
 after this, in measuring degrees of the me- 
 ridian in different parts of the world. Pro- 
 fessor Mayer, of Gottingen, deserves also 
 to be mentioned, as contributing greatly to 
 
 the improvement of this science, by the ex- 
 cellent set of tables which he calculated 
 for finding the place of the Moon, &c. 
 These table are now used in making the> 
 calculations of the Nautical Almanack., 
 His widow received £3,000 for them from 
 the British Government, on account of their 
 great accuracy. Mayer died in 1762, aged 
 41 years. D’Alembert also rendered great 
 service to Astronomy by his indefatigable 
 labours, particularly in resolving the prob- 
 lem of the precession of the equinoxes. 
 He died 1783. 
 
 Euler, one of the greatest geniuses and 
 calculators that any age or nation can boast 
 of, ought to be associated with the history 
 of Astronomy, as one of its most distin- 
 guished votaries and improvers. By his 
 many and accurate calculations, he has 
 rendered the most essential service, not 
 only to Astronomy, but to all the physical 
 sciences ; but his labours are too numerous 
 to be detailed here. The eighteenth cen- 
 tury was distinguished by many other 
 eminent astronomers; viz. Maclaurin, 
 Simpson, Bernoulli, Lambert, Mason, Bos- 
 covich, De Lisle, Bailly, La Lande, &c. 
 
 The celebrated La Grange, who out- 
 lived most of his contemporaries, was born 
 at Turin in 1736, and has enriched Astro- 
 nomy with some of the most splendid dis- 
 coveries of which it can boast. The sub- 
 jects of his researches in this science were, 
 the theory of Jupiter’s satellites, the mo- 
 tions of the planets, and their action on 
 each other, which he determined with 
 great accuracy. 
 
 As the labours of the most distinguished 
 astronomers that have appeared in the 
 world have now been briefly noticed, and 
 of whom their labours are the only memo- 
 rials that exist ; all that remains to com- 
 plete this short account of the improve- 
 ments that have taken place in the science, 
 down to the present day, is to mention the 
 labours of a few individuals still alive. 
 
 La Place has also distinguished himself 
 by his labours to improve Astronomy, 
 particularly in solving the problem of the 
 tides, — in adding some new corrections to 
 the lunar tables, and some discoveries re- 
 specting the precession of the equinoxes. 
 He also ascertained the mean depth of the 
 sea to be four leagues. 
 
 The name of Troughton ought also to be 
 mentioned ; for to no individual of the 
 present age is Practical Astronomy more 
 indebted than to this distinguished artist. 
 The great improvements he has made upon 
 astronomical instruments, has rendered his 
 name celebrated in every country in Eu- 
 rope. There is scarcely an observatory of 
 note to be found that does not contain 
 some of Mr. Troughton’s instruments. 
 
 The labours of Dr. Olbers, Harding, 
 and Piazzi, will be noticed in treating of 
 the new planets. 
 
46 
 
 THE ARTISAN. 
 
 THE VARIOUS SYSTEMS OF 
 ASTRONOMY. 
 
 By the word System, in Astronomy, is 
 meant a collection or assemblage of celes- 
 tial bodies, connected with each other by 
 certain or fixed laws. 
 
 The system of the world comprehends 
 the sun, the planets, and comets. 
 
 To explain the motions and appearances 
 of these bodies, various hypotheses have, 
 at different times, been formed ; some of 
 which have descended from the earliest 
 periods to the present day, bearing the 
 names of their respective inventors, and 
 carry with them marks of very great pow- 
 ers of invention. 
 
 But in the earliest ages of the world, 
 when men were ignorant of the laws of 
 motion, it is scarcely to be expected that 
 they could discover the true system of the 
 universe, or explain all the various pheno- 
 mena of the heavens. It is, however, be- 
 lieved, that the first opinions on this sub- 
 ject were much more just than those which 
 were held afterwards for many years. 
 
 Pythagoras maintained, that the Earth 
 
 was a planet, and that the sun was fixed 
 in the centre of the planetary system. 
 This is now universally believed ; but at 
 that time was only the opinion of a few in- 
 dividuals of Greece, who durst not openly 
 avow such unpopular doctrine. Hence, in 
 a very short time, the very name of the 
 Pythagorean system was almost buried in 
 oblivion. 
 
 PTOLEMAIC SYSTEM. 
 
 The first regular system of Astronomy 
 that appeared in the world was the Ptole- 
 maic, so called from Ptolemy, a native of 
 Pelusium in Egypt, as already mentioned, 
 who came to study in the school of Alex- 
 andria. 
 
 This system is represented by the fol- 
 lowing figure, where the concentric circles 
 denote the orbits of the planets, &c.*' 
 
 * The character ^ represents the Earth ; D the 
 Moon; Mercury; $ Venus; the Sun; $ 
 Mars; If, Jupiter; Tj Saturn. The circle marked 
 sjc sj 4 denotes the Firmament of Stars; I C the 
 first crystalline sphere ; II C the second crystalline 
 sphere ; and P M the Primum Mobile. 
 
 P.M 
 
THE ARTISAN. 
 
 4 ? 
 
 This system does not seem to have been 
 originally invented by him, but adopted as 
 the prevailing one of the age, which he 
 digested into a system, more regular and 
 consistent than any thing hitherto known 
 on that subject. He supposed the Earth 
 to be fixed immoveably in the centre of 
 the universe, and that the sun, moon, and 
 planets, moved round it. That above the 
 planets were placed the firmament of 
 stars, then two crystalline spheres, all of 
 which were included in the primum mo- 
 bile, which was, by some unaccountable 
 means, turned round once in twenty-four 
 hours, carrying all the rest along with it. 
 
 It is easy to see, that the confused mo- 
 tions of the planets here stated, could ne- 
 ver be accounted for on any thing like 
 rational principles. Had the planets cir- 
 culated uniformly round the Earth, their 
 apparent motions ought always to have 
 been equal and uniform, without appear- 
 ing either stationary or retrograde. 
 
 In consequence of this objection, Ptole- 
 my was obliged to invent a great many cir- 
 cles interfering with each other, which he 
 called Epicycles and Eccentrics. These 
 proved an excuse for all the defects of his 
 system ; for, when any of the planets were 
 deviating from the course they ought to 
 have kept, they were then only moving in 
 an epicycle or eccentric ! But as to the 
 natural cause which directed any of these 
 bodies to move in these epicycles, he was 
 at a loss to account, and was obliged to 
 have recource to Divine power for an ex- 
 planation ; or in other words, to own that 
 his system was unintelligible. 
 
 If this system were true, the two planets 
 nearest the sun, Mercury and Venus, could 
 never be hid behind the sun, as their orbits 
 are included in his, (according to Pto- 
 lemy's hypothesis,) and these two planets 
 would always move direct, and be as often 
 in opposition as in conjunction with him. 
 But the contrary of all this takes place ; 
 for these two planets are just as often 
 behind the sun as before him ; appear as 
 often to move backward as forward; and 
 are so far from being seen at any time in 
 the side of the heavens opposite to the 
 sun, that they were never yet seen a quar- 
 ter of a circle in the heavens distant from 
 him ; which proves that this system is con- 
 trary to what actually takes place. 
 
 Yet it continued to be in vogue till the 
 beginning of the sixteenth century, when 
 Copernicus, a native of Thorn in Prussia, 
 made his appearance. This man began, 
 in the early part of his life, to try whether 
 a more satisfactory manner of accounting 
 for the apparent motions of the heavenly 
 bodies could not be discovered, than what 
 was given by Ptolemy. From intense ap- 
 plication to the subject, and a few hints 
 obtained from the ancients, he at last de- 
 duced a most complete system, capable of 
 
 solving every phenomenon in a more satis- 
 factory manner than was ever done before. 
 This system is still called the 
 
 COPERNICAN SYSTEM. 
 
 In this system the Sun is supposed to be 
 placed in the centre ; next him revolves 
 the planet Mercury, then Venus, next the 
 Earth with the Moon ; beyond these, Mars, 
 Jupiter, and Saturn; and far beyond the or- 
 bit of Saturn is placed the fixed stars, which 
 form the boundary of the visible creation. 
 (See solar system.) 
 
 Copernicus concluded, that if the Earth 
 revolved every day round its axis from 
 west to east, all the heavenly bodies would 
 appear to revolve in a contrary direction ; 
 namely, from east to west. The diurnal re - 
 volution of the heavens, upon this hypo- 
 thesis, would be only apparent ; the firma- 
 ment, which has no other sensible motion, 
 would be perfectly at rest ; while the sun, 
 the moon, and the five planets, would have 
 no other motion beside that eastward revo- 
 lution which is peculiar to them. By sup- 
 posing the Earth to revolve with the pla- 
 nets round the sun in an orbit which in- 
 cluded the orbits of Venus and Mercury, 
 but included in those of Mars, Jupiter, 
 and Saturn — he could, without the embar- 
 rassment of epicycles, connect together the 
 apparent annual revolutions of the sun, 
 and the direct, retrograde, and stationary 
 appearances of the planets ; and by sup- 
 posing the axis of the Earth a little inclin- 
 ed to the plane of its orbit, and to remain 
 always parallel to itself, he could also ac- 
 count for the obliquity of the ecliptic, the 
 Sun's apparent progression from north to 
 south, the consequent change of seasons, 
 and the different lengths of days and 
 nights, &c. 
 
 Though this system was received by- 
 most men of science then living, yet there 
 were some who would never assent to it. 
 The motion of the Earth was so contrary to 
 what they were always accustomed to hear 
 on that subject, and, as they thought, to 
 appearances, that they could never agree 
 to support such doctrine. 
 
 Among those who opposed the system 
 of Copernicus, was the celebrated astro- 
 nomer Tycho Brahe, who has already been 
 mentioned as having greatly contributed 
 to improve the science of Astronomy, by 
 the number of observations which he 
 made, and the excellent apparatus he 
 caused to be constructed for his observa- 
 tory. As he could not entirely adopt the 
 Ptolemaic, and being a man of genius, he 
 invented anothor system, which was a 
 kind of mean between the Ptolemaic and 
 the Copernican. 
 
 TYCHONIC SYSTEM. 
 
 According to Tycho Brahe, the inventor 
 of this system, the Earth is supposed to be 
 the centre of the orbits of the sun and 
 
48 
 
 THE ARTISAN. 
 
 moon ; but the sun is supposed to be the planets then known. These orbits are re- 
 centre of the orbits of the five primary presented by the following figure. 
 
 QUESTIONS FOR SOLUTION. 
 
 To the Editor of the Artisan. 
 
 Sir, — As I find it is not inconsistent with 
 the plan of your interesting and very use- 
 ful publication, to insert Philosophical 
 Queries for solution, I have taken the li- 
 berty to enclose the following, which I 
 will thank you to insert in a future number. 
 — I am, .Sir, &c. Andrew Asker. 
 
 . Suppose a balloon, containing 10000 cu- 
 bical feet, to be filled with hydrogen gas, 13 
 times rarer than atmospheric air, under the 
 same compression; and suppose the whole 
 weight with which the balloon is loaded 
 to be 350 pounds : required to what height 
 
 it will ascend ? 
 
 To the Editor of the Artisan. 
 
 Sir, — Having noticed several Philoso- 
 phical queries in the 2d No. of the 
 “ Artisan,” of which the answers are re- 
 quired ; I would thank you to insert the 
 two following questions in one of your 
 future numbers, as I should wish to know 
 their exact answers. I have solved them 
 myself ; but not having great confidence in 
 
 my own powers of calculation, I should 
 be obliged to you, or some of your mathe- 
 matical readers, to give their answers, in 
 order that I may compare them with ray 
 own, which I shall forward to you, should 
 no one else deem them worthy of notice. 
 
 Rerum. 
 
 1. A gentleman erecting a house, whose 
 breadth was twenty-eight feet, and back 
 wall six feet nine inches higher than the 
 front, had beside him a sufficient quantity 
 of rafters for the front, each twenty-four 
 feet long ; which, to save timber, he was 
 unwilling to cut, and therefore orders his 
 builder to make the back rafters of such a 
 length as will make the declivity of them 
 and the front alike, for uniformity : re- 
 quired how he is to proceed ? 
 
 2d. The outer diameter of a ring for the 
 finger is *9 of an inch, the inner diameter 
 •7, and thickness *1 of an inch; the inside 
 half of the ring, which touches the finger, 
 is made of standard silver, and the outer- 
 half of ..standard, gold: required the value 
 of the ring, allowing five shillings for the 
 expense of making it ? 
 
THE ARTISAN. 
 
 49 
 
 GEOMETRY. 
 
 PROPOSITION VI. 
 
 Theorem. — If two angles of a triangle be 
 equal to one another , the sides which sub- 
 tend, or are opposite to, the equal angles, 
 shall also be equal to one another . 
 
 Let A B C be a triangle, having the an- 
 gle ABC equal to the angle ACB; the 
 side A B is also equal to the side A C. 
 
 For, if A B be not equal to A C, one of 
 them is greater than the other : — let A B 
 be the greater, and from it cut olf D B equal 
 to A Cj the less, and join DC; 
 
 
 therefore, because in the triangles D B C, 
 ACB, DB is equal to A C, and B C com- 
 mon to both, the two sides I) B, B C are 
 equal to the two A C, CB, each to each; 
 and the angle DBC is equal to the angle 
 ACB; therefore, by the supposition, the 
 triangle DBC is equal to the triangle 
 ACB, the less to the greater ; which is 
 absurd. Therefore D B is not equal to 
 AC, and in the same manner it may be 
 proved, that no other straight line, greater 
 or less than A B, can be equal to A C, 
 wherefore A B is equal to A C, which was 
 to be demonstrated. 
 
 Corollary . — Hence every equiangular tri- 
 angle is also equilateral. 
 
 This proposition is the converse of pro- 
 position V, and its proof is by reductio ad 
 absurdum (see page 17). 
 
 The corollary may be proved thus : — be- 
 cause the angle B is equal to the angle C, 
 the side A C is equal to the side A B ; and 
 because the angle A is equal to the angle 
 C, the side B C is equal to the side A B : 
 therefore, the three sides A B, AC, and 
 B C are equal to each other, which was to 
 be shown. 
 
 PROPOSITION VII. 
 
 Theorem. — Upon the same base, and on the 
 same side of it, there cannot be two trian- 
 gles , that have their sides which are ter- 
 minated in one extremity of the base equal 
 to one another, and likewise those which 
 are terminated in the other extremity, 
 equal to one another . 
 
 If it be possible, let there be two trian- 
 gles ACB, A D B, upon the same base 
 N° 4, Vol.I. 
 
 A B, and upon the same side of it, which 
 have their sides CA, D A, terminated in A 
 equal to one another, and likewise their 
 sides C B, D B, terminated in B, equal to 
 one another. 
 
 Join CD: then, in the case in which 
 the vertex of each of the triangles is with- 
 out the other triangle, because A C is 
 equal to A D, the angle A C D is equal to 
 the angle ADC: but the angle A C D is 
 greater than the angle BCD; therefore 
 the angle A D C is greater also than 
 BCD; much more then is the angle BDC 
 greater than the angle BCD, Again, be- 
 cause C B is equal to D B, the angle BDC 
 is equal to the angle B C D ; but it has 
 been demonstrated to be greater than it ; 
 which is impossible. 
 
 But if one of the vertices, as D, be within 
 the other triangle ACB; 
 
 produce AC, A D to E, F ; therefore, be- 
 cause A C is equal to A D in the triangle 
 A C D, the angles E C D, F D C upon the 
 other side of the base C D are equal to 
 one another, but the angle E C D is greater 
 than the angle B CD ; wherefore the angle 
 F D C is likewise greater than BCD; 
 much more then is the angle BDC greater 
 than the angle BCD. Again, because C B 
 is equal to D B, the angle B DC is equal 
 to the angle BCD; but BDC has been 
 proved to be greater than the same BCD; 
 which is impossible. The case in which 
 the vertex of one triangle is upon a side 
 of the other, needs no demonstration. 
 
 Many of the propositions in Euclid are 
 merely subsidiary; that is, they are in 
 themselves of no other use, than as neces- 
 
 E 
 
50 
 
 THE ARTISAN. 
 
 sa'ry to the proof of other propositions that 
 are useful : — of this kind are propositions 
 VII, XVI, and XVII of the first book. The 
 demonstration of this proposition is ano- 
 ther instance of reductio ad absurdum; we 
 here suppose an impossibility to be possi- 
 ble, in order to shew the absurdity of that 
 supposition : a figure is here made to re- 
 present what no figure can represent : i. e. 
 an impossibility ; — for we suppose not only 
 that the lines A C and A D are equal to 
 one another, but also thatC R and D B are 
 equal to one another, which the demon- 
 stration shews cannot be true, unless the 
 points C and D coincide, and then the two 
 triangles will altogether coincide and form 
 but one triangle. It is possible that A C 
 and A D, terminated at the extremity A, 
 may be equal ; but then C B and D B, ter- 
 minated at the extremity B, cannot be 
 equal : — in like manner, C B and D B may 
 be equal, but if they are, A C and A D can 
 not; and this is all that was required to 
 be proved 
 
 PROPOSITION VIII. 
 
 Theorem. — If two triangles have two sides 
 of the one equal to two sides of the other , 
 each to each, and have likewise their bases 
 equal ; the angle which is contained by 
 the two sides of the one shall be equal to 
 the angle contained by the two sides of the 
 other. 
 
 Let ABC, DEFbe two triangles, hav- 
 ing the two sides A B, AC, equal to the 
 two sides DE, DF, each to each; viz. 
 ABtoDE, and A C to DF ; and also the 
 base B C 
 
 equal to the base E F. The angle B A C 
 is equal to the angle E D F. 
 
 For, if the triangle A B C be applied to 
 the triangle D E F, so that the point B be 
 on E, and the straight line B C upon E F ; 
 the point C shall also coincide with the 
 point F, because B C is equal to E F ; 
 therefore B C coinciding with E F, B A 
 and A C shall coincide with E D and D F ; 
 for, if B A and C A do not coincide with 
 E I) and F D, but have a different situa- 
 tion, as E G and F G ; then, upon the same 
 base E F, and upon the same side of it, 
 there can be two triangles E D F, E G F, 
 that have their sides which are terminated 
 in one extremity of the base equal to one 
 
 another, and likewise their sides termi- 
 nated in the other extremity : — but this is 
 impossible ; therefore, if the base B C co- 
 incides with the base E F, the sides B A, 
 A C cannot but coincide with the sides ED, 
 D F ; wherefore likewise the angle B A C 
 coincides with the angle EDF, and is 
 equal to it. Therefore, if two triangles, 
 &c. Q.E.D. 
 
 This proposition is a second instance of 
 a proof, by supposing the one figure placed 
 upon the other ; and since it is shewn that 
 the triangles so applied completely coin- 
 cide, it follows from the 8th axiom, that 
 the triangles are equal ; that the sides of 
 the one are respectively equal to the sides 
 of the other; and the angles of the one 
 to the angles of the other. 
 
 Hence, if the three sides of one triangle 
 be respectively equal to the three sides of 
 another, the two triangles will be both 
 equal, and equiangular to each other : that 
 is, the angles of the one will be respec- 
 tively equal to the angles of the other.* 
 
 PROPOSITION IX. 
 
 Problem. — To bisect a given rectilineal an- 
 gle ; that is, to divide it into two equal 
 angles . 
 
 Let B A C be the given rectilineal angle, 
 it is required to bisect it. 
 
 Take any point D in A B, and from A C 
 cut off A E equal to A D ; join D E, and 
 upon it describe an equilateral triangle 
 DEF; then join AF; the straight line 
 A F bisects the angle B A C. 
 
 A 
 
 Because A D is equal to A E, and A F 
 is common to the two triangles D A F, 
 E A F ; the two sides DA, AF, are equal 
 to the two sides E A, AF, each to each; 
 but the base D F is also equal to the base 
 E F ; therefore the angle D A F is equal to 
 the angle E A F ; wherefore the given rec- 
 tilineal angle BAC is bisected by the 
 straight line A F. Which was to be done. 
 
 * The converse of this proposition, viz. that tri- 
 angles equiangular to each other, are also equilate- 
 ral to each other, is not true. (See p. 18 , and note.) 
 
THE ARTISAN. 
 
 51 
 
 From this proposition it appears, that 
 the bisection of an angle is very easily per- 
 formed; the trisection is however more 
 difficult, and cannot be performed by ele- 
 mentary Geometry. 
 
 PROPOSITION X. 
 
 Problem. — To bisect a given straight line; 
 
 that is, to divide it into two equal parts. 
 
 Let A B be the given straight line ; it is 
 required to divide it into two equal parts. 
 
 Describe upon it an equilateral triangle 
 ABC, and bisect the angle A C B by the 
 straight line CD. A B is cut into two 
 equal parts in the point D. 
 
 C 
 
 Because A C is equal to C B, and C D 
 common to the two triangles A C D, B C D : 
 the two sides A C, C D are equal to the 
 two B C, C D, eaeh to each ; but the angle 
 A C D is also equal to the angle BCD; 
 therefore the base AD is equal to the base 
 D B, and the straight line A B is divided 
 into two equal parts in the point D : which 
 was to be done. 
 
 MECHANICS* 
 
 If any lines D B, B C, C A, and A E, (see 
 the figure at page 24, col. 2d,) taken in 
 order, represent the quantities and direc- 
 tions of forces communicated at the same 
 time to a body at D, the line D E, which 
 completes the figure, will represent a force 
 equivalent to them all. For the two lines 
 D B and B C are equivalent to D C; also, 
 D C and C A, that is, D B, B C, and C A, 
 are equivalent to D A ; in the same man- 
 ner D A, and A E, are equivalent to D E. 
 Therefore, if A B and A C, in the follow- 
 ing figure, 
 
 represent the quantities and directions of 
 two forces, and if A E be drawn to bisect 
 
 B C, then will twice A E represent & force 
 equivalent to them both. For if the paral- 
 lelogram be completed, since the diagonals 
 A D and B C bisect each other, A D, which 
 represents a force equivalent to A B and 
 A C, is equal to twice A E. 
 
 If a body at rest be acted upon at the 
 same time by three forces, which are re- 
 presented in quantity and direction by the 
 three sides of a triangle, taken in order, it 
 will remain at rest. For let A B, B C, and 
 C A, represent the quantities and direc- 
 tions of three forces, acting at the same 
 time upon a body at A ; 
 
 O 
 
 then, since A B and B C are equivalent to 
 AC; A B, B C, and C A are equivalent to 
 A C and C A ; but A C and C A are equal 
 and in opposite directions, therefore, must 
 keep the body at rest, consequently the 
 three forces A B, B C, and C A will keep 
 the body at rest. 
 
 A single force may be resolved into any 
 number of forces. For since the single 
 force A D is equivalent to the two, A B and 
 B D, it may be conceived to be made up of, 
 or resolved into, the two, A B and B D. 
 
 The force A D may therefore be resolved 
 into as many pairs of forces as there can be 
 triangles described upon AD, or paral- 
 lelograms about it. In like manner A B 
 or B D may be resolved into two ; and, by 
 proceeding in the same way, the original 
 force may be resolved into any number of 
 forces. 
 
 OF FALLING BODIES. 
 
 It has already been stated, at page 8, 
 col. 1st, that when a body falls from any 
 considerable height, its motion is uniformly 
 accelerated, or its velocity increases pro- 
 portionally to the time ; this effect is pro- 
 duced by what is termed gravitation, or 
 the power of gravity, and it affects all 
 falling bodies in an equal degree ; that is, 
 e 2 
 
52 THE ARTISAN. 
 
 they all fall from equal heights in equal 
 portions of time, whatever their weights 
 may be, allowance being made for the re- 
 sistance of the air on the greater body, as 
 is proved by experiments made with the 
 air-pump. It has also been found, by ex- 
 periments made on heavy bodies, that 
 when they fall freely, in vacuo, or in a 
 vessel from which the air has been ex- 
 tracted, that they descend from rest 
 through the space of 16^ feet in the first 
 second of time. 
 
 This fact being established, every thing 
 relating to falling bodies is comprehended 
 in the few simple propositions, which fol- 
 low. 
 
 The velocity acquired by a body falling 
 from rest in any given time, is equal to 
 twice the space fallen through in one se- 
 cond of time, multiplied by the number of 
 seconds it has been in motion. 
 
 Hence, as a body falls 16^ feet in one 
 second, it acquires a velocity, at the end of 
 that time, which would carry it B2| feet in 
 the next second, although it acquired no 
 new impulse from gravity ; but as it is 
 continually accelerated, it will have ac- 
 quired a velocity, at the end of two se- 
 conds, which would carry it 04^ feet, and 
 so on, increasing proportionally to the 
 time. 
 
 The whole space fallen through in any 
 given time is equal to 16^ feet, multiplied 
 by the square of the time, reckoned in se- 
 conds: hence it is easy to ascertain the 
 space which any body has fallen through 
 when the time it has been in falling is 
 known. 
 
 The time which any body will fall 
 through any given space is obtained by di- 
 viding the space by 16^, and extracting 
 the square root of the quotient, the last 
 result is the number of seconds the body 
 has been in descending through the given 
 space. 
 
 The time that a falling body will have 
 acquired any given velocity may also be 
 determined thus : divide the velocity by 
 32£, and the quotient will be the time in 
 seconds. 
 
 These are the chief propositions relating 
 to bodies falling to the earth, which we 
 shall illustrate by one or two numerical 
 examples, in order to render them still 
 more intelligible to those who are not 
 much acquainted with calculation. 
 
 1. What is the velocity acquired by a 
 body which has fallen from a state of rest, 
 after it has been three seconds in motion ? 
 —Here 32 1, multiplied by 3, gives 96| feel, 
 the velocity required. 
 
 2. How many feet will a body, which 
 descends from rest, fall in three seconds 
 of time ?— Here 16^, multiplied by 9, the 
 square of 3, gives I44f feet, for the whole 
 space fallen through in three seconds. 
 
 3. In what time will a body descend 
 from rest through the space of 257£ feet? 
 —Here 257£, divided by 16^, quotes 16, the 
 square root of which is 4, the number of 
 seconds required. 
 
 4. In what time will a body, which has 
 fallen from rest, acquire a velocity of 128§ 
 feet? — Here 128§, divided by 321, quotes 
 4, the number of seconds in which the 
 body will acquire the given velocity. 
 
 From what has here been stated respect- 
 ing bodies falling from rest, and descend- 
 ing by the force of gravity, it appears, 
 that the spaces described by them in any 
 equal successive portions of time, reckon- 
 ing from the beginning of the motion, are 
 as the numbers 1, 3, 5, 7, &c. Thus the 
 spaces fallen through in the 1st, 2d, 3d, 
 and 4th seconds of time, are 16-^, 16^ mul- 
 tiplied by 3, 16 t i multiplied by 5, 16^ mul- 
 tiplied by 7 feet respectively. 
 
 If a body projected upwards move till 
 its whole velocity is destroyed, the spaces 
 described in equal successive port'ons of 
 time, are as the numbers 1, 3, 5, 7, &c., as 
 in falling bodies, but taken in an inverted 
 order. Thus, if the velocity be wholly de- 
 stroyed in four seconds, the spaces de- 
 scribed in the 1st, 2d, 3d, 4th seconds, are 
 16^ multiplied by 7, 16^ multiplied by 5, 
 16 t l multiplied by 3 feet respectively. 
 
 If a body be projected perpendicularly 
 upwards, the height to which it will as- 
 cend in any given time, is equal to the 
 space through which it would move with 
 the first velocity continued uniform, dimi- 
 nished by the space through which it 
 would fall by the action of gravity in that 
 time. 
 
 1. For example : To what height will a 
 body rise in three seconds, if projected 
 perpendicularly upwards, with a velocity 
 of 100 feet per second? — The space which 
 the body would describe in three seconds, 
 with the first velocity, is 300 feet ; and the 
 space through which the body would fall 
 by the force of gravity in three seconds, is 
 16^ multiplied by 9, or 144$ feet; there- 
 fore the height required is 300 diminished 
 by 144$, or 155$ feet. 
 
 2d. Again : If a body be projected per- 
 pendicularly upwards with a velocity of 
 80 feet per second, required its place at 
 the end of six seconds? — The space which 
 would be described in six seconds, with 
 the first velocity, is 480 feet, and the space 
 fallen through in the same time is 16^ 
 multiplied by 36, or 579 feet ; therefore the 
 distance of the body from the point of pro- 
 jection, at the end of six seconds, is 480 
 diminished by 579, or minus 99 feet, which 
 signifies that the body has descended 99 
 feet below the point from which it was 
 projected.* 
 
 * In all the foregoing observations on falling bo- 
 dies, the time is supposed to be reckoned in seconds. 
 
THE ARTISAN. 
 
 53 
 
 OF THE CENTRE OF GRAVITY. 
 
 The centre of gravity is that point of a 
 body in which the whole force of its gra- 
 vity or weight is united. Therefore, what- 
 ever supports that point bears the weight 
 of the whole body : and whilst it is sup- 
 ported, the body cannot fall ; because all 
 its parts are in perfect equilibrium about 
 that point. 
 
 An imaginary line drawn from the centre 
 of gravity of any body towards the centre 
 of the earth, is called the line of direction. 
 In this line all heavy bodies descend, if 
 not obstructed. 
 
 Since the whole weight of a body is 
 united in its centre of gravity, as that cen- 
 tre ascends or descends, we must look 
 upon the whole body to do so too. But as 
 it is contrary to the nature of heavy bodies 
 to ascend of their own accord, or not to 
 descend when they are permitted,’ we may 
 be sure that, unless the centre of gravity 
 be supported, the whole body will tumble 
 or fall. Hence it is, that bodies stand 
 upon their bases when the line of direction 
 falls within the base ; for in this case the 
 body cannot be made to fall without first 
 raising the centre of gravity higher than it 
 was before. Thus, the inclining body 
 A B C D, 
 
 whose centre of gravity is E, stands firmly 
 on its base C D I K, because the line of 
 direction E F falls within the base. But 
 if a weight, as A B G H, be laid upon the 
 top of the body, the centre of gravity of 
 the whole body and weight together is 
 raised up to L ; and then, as the line of 
 direction L D falls without the base at D, 
 the centre of gravity L is not supported ; 
 
 and the whole body and weight will tum- 
 ble down together. 
 
 Hence appears the absurdity of people’s 
 rising hastily in a coach Or boat when it is 
 likely to overset: for, by that means they 
 raise the centre of gravity so far as to 
 endanger throwing it quite out of the base ; 
 which, if they do, they overset the vehicle 
 effectually. Whereas, had they clapt down 
 to the bottom, they would have brought 
 the line of direction, and consequently the 
 centre of gravity, farther within the base, 
 and by that means might have saved them- 
 selves. 
 
 The broader the base is, and the nearer 
 the line of direction is to the middle or 
 centre of it, the more firmly does the body 
 stand. On the contrary, the narrower the 
 base, and the nearer the line of direction 
 is to the side of it, the more easily is the 
 body overthrown, less change of position 
 being sufficient to remove the line of direc- 
 tion out of the base in the latter case than 
 in the former. And hence it is, that a 
 sphere is so easily rolled upon a horizontal 
 plane ; and that it is so difficult, if not im- 
 possible, to make things which are sharp 
 pointed stand upright on the point. From 
 what has just been stated, it plainly ap- 
 pears that if the plane be inclined, on 
 which the heavy body is placed, the body 
 will slide down upon the plane whilst the 
 line of direction falls within the base ; but 
 it will tumble or roll down when that line 
 falls without the base. Thus, the body A 
 
 will only slide down the inclined plane 
 C D, whilst the body B rolls down upon it. 
 
 When the line of direction falls within 
 the base of our feet, we stand ; but when 
 it is without that base, we immediately 
 fall. And it is not only pleasing, but even 
 surprising, to reflect upon the various and 
 unthought-of methods and postures which 
 we use to retain this position, or to recover 
 it when it is lost. For this purpose we 
 bend our body forward when we rise from 
 
54 
 
 THE ARTISAN. 
 
 a chair, or when we go up stairs : and for 
 this purpose a man leans forward, when he 
 carries a burden on his back, and backward 
 when he carries it on his breast ; and to 
 the right or left side as he carries it on the 
 opposite side. 
 
 Every system of bodies, therefore, and 
 every individual body, (for a single body 
 may be regarded as a system of particles 
 or infinitely small bodies), has a centre of 
 gravity ; and that centre remains the same 
 while the bodies retain their position re- 
 latively to one another, however the whole 
 system may change its place relatively to 
 the horizon. 
 
 The distance of the centre of gravity of 
 any system of bodies from a given plane, 
 is equal to the sum of the products of all 
 the masses into their distances from the 
 plane, divided by the sum of the masses.* 
 
 Thus required the centre of gravity of 
 three bodies placed in the same straight 
 line, their weights being 6, 8, and 12 
 pound ; and their distances from a point 
 in the same 20, BO, and 40 inches respec- 
 tively. Here the product of each body 
 multiplied into its distance from the given 
 point, added into one sum is 840, which, 
 divided by 26, the weight of the bodies, 
 quotes 32f g inches, the distance of the cen- 
 tre of gravity from the given point. 
 
 If the bodies are on different sides of the 
 point to which their distances are referred, 
 those on one side are to be accounted 
 affirmative , and those on the other negative; 
 therefore the least of these quantities is to 
 be subtracted from the greater. 
 
 The centre of gravity of a triangular 
 “plane, all the points of which gravitate 
 equally, may be found as follows : — From 
 the two angles of the triangle, draw lines 
 bisecting the opposite sides. Their inter- 
 section is the centre of gravity. 
 
 When this is done, each of these lines 
 is divided by the point of intersection, in 
 the ratio of 2 to 1. 
 
 The centre of gravity of a given pyramid 
 may be found thus : Draw a straight line 
 from the vertex to the centre of gravity of 
 the base, and divide it in the ratio of 3 to 1, 
 the greatest segment being next the ver- 
 tex. The point thus found is the centre of 
 gravity of the pyramid. 
 
 This construction applies to a pyramid 
 of any number of sides, and consequently 
 to a cone. 
 
 The centre of gravity of any plane may 
 be found mechanically. 
 
 Suspend it by a given point in or near 
 its perimeter, and when it is at rest, draw 
 across it a vertical line passing through 
 
 * As a single body may be regarded as a system 
 of particles, this proposition applies to such bodies, 
 and is therefore universal. 
 
 that point, suspend it in like manner by 
 another point, and draw a vertical line as 
 before. The intersection of these lines is 
 the centre of gravity of the plane. 
 
 If the body be of three dimensions, that 
 
 is, solid, the same process may be follow- 
 ed ; but three suspensions will be neces- 
 sary. 
 
 In the preceding propositions, the cen- 
 tres of gravity of bodies or systems, in 
 which the parts preserved the same rela- 
 tive position, have only been considered. 
 It is evident, however, that in any system, 
 though the parts be not fixed in the same 
 relative position, the centre of gravity for 
 any given position may be found; and 
 there are some general properties of the 
 centres so found, that are very important 
 in mechanics. 
 
 If any number of bodies move uniformly 
 in straight lines, their common centre of 
 gravity will also move uniformly in a 
 straight line, or will remain at rest. 
 
 The mutual action of bodies does not 
 change the state of their centre of gravity, 
 either as remaining at rest, or as moving 
 uniformly in a straight line. 
 
 It is also known that the quantity of 
 motion in any system of bodies estimated 
 in a given direction, remains constantly 
 the same, whatever may be the mutual 
 action of these bodies on one another. 
 
 Both this and the preceding proposition 
 are consequences of the equality that takes 
 place between the action and re-action of 
 bodies. The quantity of motion in any 
 system, is the same as if all the parts of it 
 were united in the centre of gravity of the 
 whole. 
 
 ON THE MECHANICAL POWERS. 
 
 A mechanical power, is an instrument 
 by which the effect of a given force is in- 
 creased, while the force itself remains the 
 same. 
 
 The simple mechanical powers into 
 which more complex machines are re- 
 solved, are these: 1. The lever; 2. The 
 wheel and axle ; 3. The inclined plane ; 
 4. The pulley; 5. The wedge; 6. the 
 screw. 
 
 OF THE LEVER. 
 
 A lever is an inflexible rod, moveable 
 about a centre or fulcrum, and having 
 forces applied to two or more points in 
 
 it. 
 
 The simplest state of the lever is, when 
 there are only two forces; and of this 
 there are two cases ; in the first, the ful- 
 crum is between the points where the 
 forces are applied, and the forces are di- 
 rected the same way ; in the second, the 
 points to which the forces are applied, are 
 
THE ARTISAN. 
 
 55 
 
 on the same side of the fulcrum, and the 
 forces are directed opposite ways.* 
 
 In treating of the lever, it is usual to 
 distinguish the forces by the names of the 
 Power and the Weight, or the Power and 
 the Resistance, — terms that have a refer- 
 ence to the intention with which the ma- 
 chine is used, not to any real difference in 
 the action of the forces. 
 
 In treating of the lever, we shall begin 
 with abstracting entirely from its own 
 weight. 
 
 If two forces be applied to a lever hav- 
 ing equal and opposite momenta ; that is, 
 tending to produce motion in opposite 
 directions, and being inversely as the per- 
 pendiculars drawn to their direction from 
 the fulcrum, they will be in equilibrium 
 with one another. Thus, suppose the 
 length of a lever to be 8 feet long, with a 
 weight of 180 pounds at one end, 2 feet 
 from the fulcrum, or prop ; and a weight 
 of 45 pounds at the other, 6 feet from 
 the fulcrum: these weights will be in 
 equilibrium, because they are to each 
 other inversely as their perpendicular dis- 
 tances from the fulcrum upon which they 
 rest; that is, the greater weight contains 
 the lesser, as many times as the distance 
 of the lesser contains the distance of the 
 greater from the fulcrum. 
 
 When the forces or weights act parallel 
 to one another, as has been supposed in 
 the example just given, this proposition 
 coincides with the property of the centre 
 of gravity, mentioned at page 53f. When 
 they act in an oblique direction, the case 
 may be reduced to the preceding by the 
 resolution of forces. 
 
 It may be proper to remark, before pro- 
 ceeding to treat more particularly of the 
 lever, that the properties, as well as the 
 effects that may be produced by any of the 
 mechanical powers, is best explained and 
 illustrated, by showing yvhen an equili- 
 brium takes place between the power and 
 the resistance, where any of these instru- 
 ments are concerned. For when an equi- 
 librium is produced, the least addition to 
 the power must make it overcome the re- 
 sistance. 
 
 If any number of forces be applied to a 
 lever, there will be an equilibrium, if the 
 sums of the opposite momenta be equal to 
 one another, and therefore, this proposition 
 also coincides with a property of the cen- 
 tre of gravity. See page 53. 
 
 The converse of this proposition is also 
 true, and as it is common to all the mecha- 
 
 * Some writers on mechanics divide levers into 
 three kinds ; but two of these are reducible to the 
 second kind mentioned in this proposition. 
 
 t Therefore the fulcrum and centre of gravity 
 coincide; or the fulcrum supports the centre of 
 gravity of the whole. 
 
 meal powers, and in fact to all machines 
 whatever, we shall here state it in the 
 form of a distinct proposition, as' follows : 
 When there is an equilibrium in the lever 
 the sum of the momenta on one side of the’ 
 centre of motion, is equal to that on the 
 other. 
 
 This property of machines is known by 
 the name of the principle of virtual velocU 
 ties , and is of great use in mechanical in- 
 vestigations. 
 
 The different cases of the lever, whether 
 it be straight or crooked ; and the forces 
 perpendicular or oblique , are all compre- 
 hended in the preceding propositions. The 
 case of oblique forces, however, admits of 
 a very concise expression in terms of the 
 angles ; we shall therefore insert the pro- 
 position containing the principle upon 
 which this property depends, though it 
 can only be fully understood by those who 
 have a slight knowledge of trigonometry. 
 It is this,— -if two oblique forces be applied 
 to the extremities of a straight lever, there 
 will be an equilibrum between them, if 
 they be inversely as the lengths of the 
 arms by which they act, multiplied into 
 the sines of the angles, which their direc- 
 tions make with the lever. This proposi- 
 tion is general, and therefore comprehends 
 the case of perpendicular forces; it is, 
 however, unnecessary to illustrate this by 
 an example, for the reason stated above f 
 we shall, therefore, now explain the dif- 
 ferent kinds of levers, and state the par- 
 ticular properties of each variety. 
 
 A lever of the first kind is represented 
 by the bar, or rod ABC, supported by the 
 prop D : 
 
 its principal use is to loosen large stones 
 in the ground, or raise great weights to 
 small heights, in order to have ropes put 
 under them for raising them higher by 
 other machines. The parts A B and B C, 
 on different sides of the prop D, are called 
 the arms of the lever : the end A of the 
 shorter arm A B is applied to the weight 
 intended to be raised, or to the resistance 
 to be overcome ; and the power is applied 
 to the end C of the longer arm B C. 
 
 In making experiments with this instru- 
 ment, the shorter arm A B must be as 
 much thicker than the longer arm B C, as 
 will be sufficient to balance it on the prop. 
 This being supposed to be the case, let 
 P represent a power, whose weight is 
 equal to one pound, and W a body, whose 
 
THE ARTISAN,. 
 
 56 
 
 weight is equal to 12 pounds. Then, if 
 the power be twelve times as far from the 
 prop as the weight is, they will exactly 
 counterpoise ea.ch other ; and a small ad- 
 dition to the power P will cause it to de- 
 scend, and raise the weight W ; and the 
 velocity with which the power descends 
 will be to the velocity with which the 
 weight rises, as 12 to 1 : that is, directly 
 as their distances from the prop; and, 
 consequently, as the spaces through which 
 they move. Hence it is plain, that if a 
 man, by his natural strength, without the 
 help of any machine, could support an 
 hundred weight, he will, by the help of 
 this lever, be enabled to support 12 hun- 
 dred. If the weight be less, or the power 
 greater, the prop may be placed so much 
 farther from the weight; and then it can 
 be raised to a proportionably greater 
 height. For, as has already been stated, 
 if the weight, multiplied into its distance 
 from the prop, be equal to the power mul- 
 tiplied into its distance from the prop, 
 the power and weight will exactly ba- 
 lance each other ; and a little addition to 
 the power will raise the weight. 
 
 To this kind of lever may be reduced 
 several kinds of instruments, such as scis- 
 sors, pincers, snuffers, which consist of two 
 levers acting contrary to each other, their 
 prop, or centre of motion, being the pin 
 which holds them together. 
 
 In common practice the longer arm of 
 this kind of lever considerably exceeds 
 the length of the shorter arm, and, of 
 course, gives great advantage, because it 
 adds so much to the power. 
 
 A lever of the second kind has the 
 weight between the fulcrum and the pow- 
 er, as represented by A B in the following 
 figure. 
 
 F. 
 
 In this species of lever, as well as in the 
 former, the advantage gained depends 
 upon the distance of the power from the 
 fulcrum, compared with that of the resist- 
 ance, or weight from the same point ; for 
 the respective velocities of the power and 
 weight are in proportion to their distances 
 from the fulcrum, and they will be in equi- 
 librium when the weight of the power, 
 multiplied by its distance from the ful- 
 crum, is equal to the weight or resistance, 
 
 multiplied by its distance from the ful- 
 crum. 
 
 Thus, suppose the weight W equal to 36 
 pounds, and to hang one foot from the prop 
 G ; and suppose a power P, equal to six 
 pounds, to hang at B, six feet from the 
 prop, by means of the cord C D going over 
 a fixed pulley E, the power Will,* in this 
 case, just support the weight ; and a small 
 addition to the power will cause it to raise 
 the weight ; but the power will descend 
 through six times the space that the 
 weight will ascend in any given time. 
 
 A lever of this kind shows why two men 
 carrying a burden upon a stick between 
 them, bear unequal shares of the burden, if 
 it is not placed at equal distances from 
 each of them. For when a weight is placed 
 upon a lever which is supported upon two 
 props, in a horizontal position, as A and B, 
 
 — ©— 1! - 
 
 the pressure upon A is to the pressure 
 upon B, as the distance B C is to the dis- 
 tance A C. 
 
 Hence, if a weight be placed on a stick, 
 as at C, three times nearer B than A, and 
 if one man support the end A and another 
 the end B, the one at B supports three 
 times as much weight as the one at A. 
 
 This is likewise applicable to the case 
 of two horses of unequal strength, so 
 yoked, as that each horse may draw a part 
 proportionable to his strength ; which is 
 done by dividing the beam in such a man- 
 ner, as that the point of traction may be as 
 much nearer to the stronger horse as his 
 strength exceeds that of the weaker. 
 
 To this kind of lever may be reduced 
 oars, rudders of ships, doors turning upon 
 hinges, cutting-knives that are fixed at the 
 point of the blade, &c. 
 
 HYDROSTATICS. 
 
 ON THE EFFECTS OF CAPILLARY TUBES. 
 
 If a capillary tube of glass ; that is, a tube 
 of which the bore is less than one-tenth of 
 an inch, be immersed in water, the water 
 will rise within the tube to a greater height 
 than it stands at on the outside ; and this 
 height is nearly in the inverse ratio of the 
 diameter of the tube ; that is, the less the 
 diameter the higher will the water rise. 
 For a tube of which the bore is ^th of an 
 inch, the rise is 5*3 inches. So the pro- 
 duct of the diameter of the tube, into the 
 height to which the water rises, is a given 
 quantity, and nearly equal to *053, in parts 
 of a square inch. 
 
THE ARTISAN. 
 
 57 
 
 It follows also from the above, that the 
 weights of the columns of water sustained 
 in capillary tubes, are in proportion to 
 the diameters of these tubes. 
 
 Though the rise of water above its na- 
 tural level is most manifest in small 
 tubes, it appears, in a degree, in all vessels 
 whatsoever, by a ring of water formed 
 round the sides, with a concavity up- 
 wards. 
 
 Capillary suspension takes place, though 
 the tube be not immersed in water, provid- 
 ing a drop of water adhere to the lower end 
 of it. 
 
 The surface of the water in a capillary 
 tube is concave upwards ; and if by taking 
 the tube out of the water, and inclining it, 
 the fluid be made to move along it, the 
 concavity appears at both ends of the 
 column, and is the same in figure and size, 
 whether the tube be held perpendicularly, 
 horizontally, or obliquely. 
 
 When by inclining the tube, the column 
 of water is made to move, it appears to 
 suffer resistance as it approaches either 
 end, and does not completely reach the 
 end, till the tube is either altogether, or 
 very nearly inverted. 
 
 When the tube is placed in the water, 
 however far it be thrust down, the water 
 within never reaches the top, till the tube 
 is completely immersed. 
 
 If a capillary tube composed of two 
 cylinders of different bores, be immersed 
 in water, first with the widest part down- 
 wards, and afterwards with the narrowest, 
 the water will rise in both cases to the 
 same height. 
 
 If the smaller end is such as to require 
 the whole to be filled by suction, the water 
 stands at the same height as if the whole 
 tube were of the bore of the upper part. 
 This experiment, however, does not suc- 
 ceed in vacuo, and therefore the water in 
 the wide part of the tube must be con- 
 sidered as sustained by the pressure of the 
 air. 
 
 If two plates of glass be kept parallel, 
 and near to one another, and if their 
 ends be immersed in water, the water 
 will ascend between them to half the 
 height it would rise to in a tube, having 
 its diameter equal to the distance of the 
 plates. 
 
 When the plates make an angle with one 
 another, if they be immersed with the line 
 of their intersection vertical, the water 
 will ascend between them, and form a 
 hyperbola. 
 
 La Place caused experiments to be made 
 with one tube placed within another, so 
 that their axes coincided, and found that 
 the water ascended in the space between 
 them, only half as high as it would have 
 done in a single tube, in which the dia- 
 
 meter of the bore was equal to the distance 
 of the two tubes from one another. 
 
 If a glass tube of a small bore be im- 
 mersed in mercury, the mercury does not 
 rise within the tube to the height at which 
 it stands on the outside; its surface within 
 is convex, as it is also without, all round 
 the tube. 
 
 If into a conical capillary tube, held in 
 a horizontal position, a drop of water be 
 introduced, it will run toward the narrow 
 end; but if a drop of mercury be intro- 
 duced, it will run toward the wide end. 
 
 Whether a fluid rise or fall between 
 two vertical and parallel planes, immersed 
 in the fluid at their lower extremities, the 
 planes tend to approach one another. 
 
 It is from this tendency, that two small 
 vessels of glass, of a parallelepiped form, 
 floating on water or mercury, unite, 
 whenever they approach near to one ano- 
 ther. 
 
 The phenomena here enumerated, clearly 
 prove the existence of an attractive force 
 between water and glass, but require to be 
 carefully compared before we can judge 
 of the manner in which that force is ex- 
 erted. The fact that points most directly 
 to the place where the force resides, is 
 that of the concavity of the surface, as al- 
 ready mentioned. 
 
 In the case of mercury, glass either 
 repels the fluid, or attracts it less than its 
 particles attract one another. Hence, the 
 convexity of the surface that terminates 
 the column, and the depression of that 
 surface below the natural level. 
 
 FLUIDS ISSUING THROUGH APERTURES IN THE 
 BOTTOM OR SIDES OF VESSELS. 
 
 The velocity with which water spouts 
 out at a hole in the side or bottom of a 
 vessel, compared with the velocity with 
 which it spouts out at another of a different 
 depth, is as the square root* of the depths 
 or distance of the holes below the surface 
 of the water. For, in order to make dou- 
 ble the quantity of a fluid run through one 
 hole as through another of the same size, 
 it will require four times the pressure of 
 the other, and therefore must be four times 
 the depth of the other below the surface of 
 the water : and for the same reason, three 
 times the quantity running in an equal 
 time through the same form and size of 
 hole, must run with three times the velo- 
 city, which will require nine times the 
 pressure ; and consequently must be nine 
 times as deep below the surface of the 
 
 * The square root of any number is that which, 
 being multiplied by itself, produces the said num- 
 ber. Thus, 2 is the square root of 4, and 3 is the 
 square root of 9: for 2 multiplied by & produces 4, 
 and 3 multiplied by 3 produces 9, &c. 
 
58 
 
 THE ARTISAN. 
 
 fluid : and so on. To prove this by experi- sized bores, be fixed into the side of the 
 ment, let two pipes, as C and g, of equal vessel A B, as in the following figure, 
 
 the pipe g being four times as deep below 
 the surface of the water at b in the vessel, 
 as the pipe C : and whilst these pipes 
 run, let water be constantly poured into 
 the vessel, to keep the surface still at 
 the same height. Then, if a cup that holds 
 a pint be so placed as to receive the water 
 that spouts from the pipe C, and at the same 
 moment a cup that holds a quart be so 
 placed as to receive the water that spouts 
 from the pipe g, both cups will be filled at 
 the same time by their respective pipes. 
 
 The horizontal distance to which a fluid 
 will spout from a horizontal pipe, in any 
 part of the side of an upright vessel, below 
 the surface of the fluid, is equal to twice 
 the length of a perpendicular to the side of 
 the vessel, drawn from the mouth of the 
 pipe to a semicircle described upon the al- 
 titude of the fluid : and therefore, the fluid 
 will spout to the greatest distance possible 
 from a pipe whose mouth is at the centre 
 of the semicircle ; because a perpendicular 
 to its diameter (supposed parallel to the 
 side of the vessel) drawn from that point, 
 is the longest that can possibly be drawn 
 from any part of the diameter to the cir- 
 cumference of the semicircle. Thus, if 
 the vessel A B (see above figure) be full of 
 water, and the horizontal pipe D be in 
 the middle of its side, and the semicircle 
 N e d c b be described upon Das a centre, 
 with the radius or semidiameter D N, or 
 D b, the perpendicular D d to the diame- 
 ter N D b is the longest that can be drawn 
 from any part of the diameter to the cir- 
 cumference N edc b. And if the vessel be 
 
 kept full, the jet G will spout from the 
 pipe D, to the horizontal distance N M, 
 which is double the length of the perpendi- 
 cular D d. If two other pipes, as C and E, 
 be fixed into the side of the vessel at equal 
 distances above and below the pipe D, the 
 perpendiculars, C c and E e , from these 
 pipes to the semicircle, will be equal ; and 
 the jets F and H spouting from them will 
 each go to the horizontal distance N K ; 
 which is double the length of either of the 
 equal perpendiculars CcorEe. 
 
 Let a hole be made quite through the 
 bottom of the cup A, as in the following 
 figure, 
 
 and the longer leg of the bended syphon 
 D £ B 6 be cemented into the hole, so that 
 
THE ARTISAN. 
 
 59 
 
 the end D of the shorter leg D E may al- 
 most touch the bottom of the cup within. 
 Then, if water be poured into this cup, it 
 will rise in the shorter leg by its upward 
 pressure, excluding the air all the way 
 before it through the longer leg : and when 
 the cup is filled above the bend of the sy- 
 phon at F, the pressure of the water in the 
 cup will force it over the bend of the sy- 
 phon ; and it will descend in the longer 
 leg C B G, and run through the bottom, 
 until the cup be emptied. 
 
 This is generally called Tantalus’s cup , 
 and the legs of the syphon in it are almost 
 close together ; and a little hollow statue 
 or figure of a man, is sometimes put over 
 the syphon to conceal it ; the bend E being 
 within the neck of the figure as high as 
 the chin — so that poor thirsty Tantalus 
 stands up to the chin in water, imagining 
 it will rise a little higher, and he may 
 drink ; but instead of that, when the water 
 comes up to his chin, it immediately be- 
 gins to descend, and so, as he cannot stoop 
 to follow it, he is left as much pained with 
 thirst as ever. 
 
 Having now illustrated some of the facts 
 respecting the discharge of water through 
 apertures in the bottom or sides of vessels, 
 by means of the foregoing figures, we shall 
 here give some rules for calculating the 
 velocity and quantity of water discharged 
 from apertures of a given size and depth, 
 which we shall further illustrate by arith- 
 metical examples. 
 
 The velocity with which a fluid issues 
 through an orifice in the bottom or side of 
 a vessel, is equal to that which a heavy 
 body would acquire by falling from the le- 
 vel of the surface to the level of the orifice. 
 Thus : suppose the depth of an orifice in 
 the side of a vessel containing water to be 
 4 feet below the surface of the water, and 
 that the velocity acquired by a falling 
 body, in one second of time, is equal to 32 
 feet, required the velocity with which the 
 water issues from the orifice. Here, 
 32 multiplied by 4 is 128, which be- 
 ing doubled is 256, the square root of 
 which is 16 feet, the velocity that a heavy 
 body would acquire in falling 4 feet ; con- 
 sequently the water will issue with a velo- 
 city of 16 feet per second. 
 
 If the velocity with which the fluid issues 
 from the orifice were turned directly up- 
 ward, it would carry it to the level of the 
 surface of the fluid. 
 
 The quantity of water that issues in one 
 second through a given orifice, is equal to 
 a column of water having the area of the 
 orifice for its base, and the velocity with 
 which the fluid issues for its altitude. 
 
 Thus, if the area of the orifice be 2 square 
 inches, and the velocity with which it is- 
 sues be 16 feet per second, then the quan- 
 
 tity of water which issues in one second is 
 192, (the inches in 16 feet,) multiplied by 
 2, or 384 cubic inches. 
 
 It is found, however, when the experi- 
 ment is made, that the quantity is not so 
 great as this rule makes it, particularly 
 when the orifice is small, for the vein of 
 water that issues through the orifice suffers 
 a contraction, by which its section has been 
 ascertained to be diminished in the ratio 
 of 5 to T nearly. Therefore, f of the above 
 result must be taken as the true quantity 
 discharged. 
 
 We may also remark, that some writers 
 suppose that water issues only with the 
 velocity that would be acquired by a body 
 falling through half the depth of the fluid. 
 According to some very accurate experi- 
 ments of Bossut, the actual discharge 
 through a hole made in the side or bottom 
 of the vessel, is to the theoretical as 1 to *62, 
 or nearly as 8 to 5. The theoretical dis- 
 charge, when computed, must, therefore, 
 be diminished in this ratio to have the 
 true one according to this philosopher. 
 
 If the water issues, not through an aper- 
 ture in the side or bottom of the vessel, but 
 through a pipe from 1 to 2 inches in 
 length, inserted in the aperture, the con- 
 traction of the vein is prevented, and the 
 actual discharge becomes to the theoreti- 
 cal, as 8 to 10, or 4 to 5. In this way, 
 therefore, the discharge is increased nearly 
 in the ratio of 4 to 3. 
 
 Water thrown up in a perpendicular jet 
 ought to ascend to the height of the reser- 
 voir; but on account of the resistance of 
 the air, the friction of the pipe, &c. it al- 
 ways falls short of that height; and it is 
 found by experiment, that the difference 
 between the heights of the jets and of the 
 reservoirs, are as the squares of the 
 heights of the jets themselves. 
 
 The water ascends highest when the jet 
 is not quite perpendicular ; when it is per- 
 pendicular, the ascent is obstructed by the 
 water falling back on the ascending co- 
 lumn. 
 
 The height to which the water rises in 
 the jet, is called the height of the effective 
 head. 
 
 Jftiscellatteous Subjects. 
 
 BIOGRAPHICAL MEMOIR OF 
 EUCLID. 
 
 Euclid was a native of Megara, and 
 founder of the Megaric or Eristic sect, and 
 was distinguished by his subtle genius, 
 and early application to the study of phi- 
 losophy. Having acquired some know- 
 ledge of the art of disputation from the 
 writings of Parmenides, he was induced., 
 
THE ARTISAN. 
 
 by the fame of Socrates, to remove from 
 Megara to Athens, where he became the 
 auditor and disciple of this eminent philo-^ 
 sopher. Notwithstanding the terror of the 
 Decree, which enacted, u That any inha- 
 bitant of Megara, who should be seen at 
 Athens, should forfeit his life,” he fre- 
 quently came to Athens by night, from the 
 distance of about twenty miles, concealed 
 in a long female cloak and veil, to visit his 
 master. He also frequently engaged in 
 the business and disputes of the civil 
 courts, by which proceeding he offended 
 Socrates, who despised forensic contests ; 
 and this circumstance seems to have occa- 
 sioned a separation between them. After- 
 wards he put himself at the head of a 
 school in Megara, where his chief employ- 
 ment was to teach the art of disputation. 
 Although he was much addicted to vehe- 
 ment debates, he possessed so great a 
 command of temper, that in a quarrel with 
 his brother, who said to him, u Let me 
 perish if I be not revenged upon you 
 Euclid replied, “ And let me perish, if I 
 do not subdue your resentment by forbear- 
 ance, and make you love me as much as 
 ever.” 
 
 Euclid, known to every well-educated 
 youth, by his “ Elements,” was, according 
 to the testimony of Pappus and Proclus, 
 a native of Alexandria, in Egypt, where 
 he flourished and taught the mathematics 
 in the reign of Ptolemy Lagus, about 300 
 years before Christ. His was the first 
 mathematical school in that far-famed city, 
 where, till its conquest by the Saracens, 
 most of the eminent mathematicians were 
 either born or studied. To Euclid, and to 
 those immediately educated by him, the 
 world has been indebted for Eratosthenes, 
 Archimedes, Apollonius, Ptolemy, &c. 
 u The Elements,” to which we have al- 
 ready referred, are not to be wholly attri- 
 buted to Euclid ; many of the invaluable 
 truths and demonstrations contained there- 
 in were discovered and invented by Thales, 
 Pythagoras, Eudoxes, and others; but 
 Euclid was the first who reduced them to 
 regular order, and who probably interwove 
 many theorems of his own, to render the 
 whole a complete and connected system 
 of geometry. “ The Elements” consist^of 
 fifteen books, but the last two are suspect- 
 ed to have been written 200 years after 
 Euclid’s death, by Hypsicles of Alexan- 
 dria. The best edition published in this 
 country is that printed at Oxford, in folio, 
 in 1703 ; but the most common edition in 
 our schools is that by the late learned Dr. 
 Simson. Euclid is said to have been a 
 person of agreeable and pleasing manners, 
 and admitted to habits of friendship and 
 familiarity with king Ptolemy, who once 
 demanded of the mathematician if he 
 
 could not direct him to some shorter and 
 easier way of acquiring a knowledge of 
 geometrical truths than that which he had 
 exhibited in his “ Elements ;” to which 
 Euclid replied, that “ there was no royal 
 road to geometry.” 
 
 Euclid, as a writer on music, has ever 
 been held in the highest estimation by all 
 men of science who have treated of har- 
 monics, or the philosophy of sound. As 
 Pythagoras was allowed by the Greeks to 
 have been the first who found out musical 
 ratios, by the division of a monochord, or 
 single string, a discovery which tradition 
 only had preserved, Euclid was the first 
 who wrote upon the subject, and reduced 
 these divisions to mathematical demon- 
 stration. 
 
 His 4t Elements” were first published at 
 Basil in Switzerland, 1533, by Simon Gry* 
 naeus, from two MSS ; the one found at 
 Venice, and the other at Paris. His u In- 
 troduction to Harmonics,” which in some 
 MSS was attributed to Cleonidas, is in the 
 Vatican copy given to Pappus : Meibomius, 
 however, accounts for this, by supposing 
 those copies to have been only two different 
 MS editions of Euclid’s work, which had 
 been revised, corrected, and restored from 
 the corruptions incident to frequent tran- 
 scription by Cleonidas and Pappus, whose 
 names were, on that account, prefixed. It 
 first appeared in print with a Latin ver- 
 sion, in 1498, at Venice, under the title of 
 “ Cleonidse Harmonicum Introductorium,” 
 — who Cleonidas was, neither the editor, 
 George Valla, nor any one else, pretends 
 to know. It was John Pena, a mathema- 
 tician in the service of the king of France, 
 who first published this work at Paris, 
 under the name of Euclid, in 1557. After 
 this it went through second editions with 
 his other works. 
 
 His u Section of the Canon” follows his 
 u Introduction it went through the same 
 hands and the same editions, and is men- 
 tioned by Porphyry, in his Commentary on 
 Ptolemy, as the work of Euclid. This tract 
 chiefly contains short and clear definitions 
 of the several parts of Greek music, in 
 which it is easy to see, that mere melody 
 was concerned ; as he begins by telling us, 
 that the science of harmonics considers the 
 nature and use of melody, and consists of 
 seven parts: — sounds, intervals, genera, 
 systems, keys, mutations, and melopocia ; 
 all which have been severally considered 
 in the dissertation. 
 
 Of all the writings upon ancient music, 
 that are come down to us, this seems to be 
 the most correct and compressed : the rest 
 are generally loose and confused ; the au- 
 thors either twisting and distorting every 
 thing to a favourite system, or filling their 
 books with metaphysical jargon, with Py- 
 
THE ARTISAN. 
 
 thagoric dreams and Platonic fancies, 
 wholly foreign to music. Buc Euclid, in 
 this little treatise, is, like himself, close 
 and clear; yet so mathematically short 
 and dry, that he bestows not a syllable 
 more upon the subject than is absolutely 
 necessary. 
 
 His object seems to have been the com- 
 pressing into a scientific and elementary 
 abridgement, the more diffused and specu- 
 lative treatises of Aristoxenus. He was the 
 D’Alembert of that author, explaining his 
 principles, and, at the same time, seeing 
 and demonstrating his errors. The musical 
 writings of Rameau were diffused, obscure, 
 and indigested ; but M. D’Alembert, ex- 
 tracting the essence of his confused ideas, 
 methodised his system of a fundamental 
 base , and compressed, into the compass of 
 a pamphlet, the substance of many vo- 
 lumes. 
 
 According to Dr. Wallis, Euclid was the 
 first who demonstrated that an octave is 
 somewhat less than six whole tones ; and 
 this he does in the 14th theorem of his 
 u Section of the Canon.” In the 15th 
 theorem he demonstrates, that a fourth is 
 less than two tones and a half, and a fifth 
 less than three and a half; but though 
 this proves the necessity of a temperament 
 upon fixed instruments, where one sound 
 answers several purposes, yet he gives no 
 rules for one, which seems to furnish a 
 proof that such instruments were at least 
 not generally known or used by the an- 
 cients. 
 
 What Aristoxenus called a half tone, 
 Euclid demonstrated to be a smaller inter- 
 val, in the proportion of 256 to 243. This 
 he denominated a limma , or remnant ; be- 
 cause giving to the fourth , the extremes of 
 which were called soni stabiles, and were 
 regarded as fixed and unalterable, the exact 
 proportion of 4 to 3 ; and, taking from it 
 two major tones | X |> the limma was all 
 that remained to complete the diatessaron. 
 This division of the diatonic genus being 
 thus, for the first time, established upon 
 mathematical demonstration, continued in 
 favour, says Dr. Wallis, for many ages. 
 
 HEIGHTS OF THE PRINCIPAL 
 MOUNTAINS IN THE WORLD, 
 EXPRESSED IN ENGLISH 
 FEET. 
 
 Those marked with the letter B have 
 been determined by the barometer ; and 
 those marked with the letter G, by geo- 
 metrical operations 
 
 Snae Fiall Jokul, on the north-west point 
 of Iceland - - - - - 4,558 B 
 
 Hekla, volcanic mountain in Iceland - 3,950 G 
 
 Pap of Caithness - ... - 1,929 
 
 Ben Nevis, Inverness-shire - - 4*380 B 
 
 Cairngorm, Inverness-shire - - 4,080 B 
 
 Ben Lawers, Perthshire - - - 4,015 B 
 
 Ben More, Perthshire , - . 3 ,870 B 
 
 ochiliallien, Jrerthshire - • . . 3 231 q 
 
 Ben Ledi, Perthshire - - '. . 3 009 B 
 
 Ben Lomond, Stirlingshire - - - 3*240 B 
 
 Lomond Hills, east & west, Fifeshire, 1,466 & 1*721 G 
 Sodtra Hill, on the ridge of Lammermdir,l 716 G 
 Carnethy, highest point of the Pentland 
 ridge ... - 1,700 
 
 Tintoc, Lanarkshire i 720 jj 
 
 Leadhills, the house of the Director of the * 
 
 Mines - - ... 1,564 
 
 Queensbery Hill, Dunifries-shire - - 2,259 G 
 
 Dunrigs, Roxburghshire - - . 2*408 G 
 
 Elden Hills, near Melrose, Roxburghshire, 1*364 G 
 Crif Fell, near New Abbey, in thfe Stew- 
 artry of Kirkcudbright - - . 1831 G 
 
 Goat Fell, in the Isle of Arran - - 2^950 B 
 
 Paps of Jura, south arid north, in Argyll- 
 shire - - - - - 2,359 & 2,470 
 
 Snea Fell, in the Isle of Man - - 2,004 G 
 
 Macgillicuddy’s Reeks, county Kerry 3*404 
 
 Mourne Mountains, county of Down - 2,500 
 
 Helvellyn, Cumberland . - - 3*055 
 
 Skiddaw, Cumberland ... 3,022 
 
 Saddleback, Cumberland ... 2,787 
 
 Whernside, Yorkshire - - - 2,384 
 
 Ingleborough, Yorkshire - - - 2,361 
 
 Slurnnor Fell, Yorkshire - - - 2,329 
 
 Snowdown, Caernarvonshire - - 3,571 
 
 Cades Idris, Caernarvonshire - - 2,914 
 
 Beacons of Brecknock ... 2,862 
 
 Plynlimmon, Cardiganshire - - 2,463 
 
 Penmaen Mawr, Caernarvonshire - 1,540 
 
 Malvern Hills, Worcestershire - - 1,444 
 
 Cawsand Beacon, Devonshire - - 1,792 
 
 Rippon Tor, Devonshire - - - 1,549 
 
 Brocken, in the Hartz forest, Hanover 3,690 
 Schneekopf, in Silesia - 4,950 
 
 Priel, in Austria ..... 6,565 
 
 Peak of Lomnitz, in the Carpathian ridge, 8,640 
 Mont Blanc, Switzerland - - - 15,646 G 
 
 Village of Chamouni, below Mont Blanc, 3,367 G 
 Jungfrauhorn, Switzerland ... 13,730 
 
 St. Gothard, Switzerland ... 9,075 
 
 Hospice of the Great St. Barnard, on the 
 passage to Italy .... 8,040 B 
 
 Village of St. Pierre, on the road to Great 
 St. Barnard ..... 5,338 B 
 
 Passage of Mont Cenis ... 6,778 B 
 
 Ortler Spitze, in the Tyrol ... 15,430 
 
 Rigiberg, above the lake of Lucerne - 5,408 
 
 Dole,the highest point of the chain of Jura, 5,412 
 Mont Perdu, in the Pyrenees - - 11,283 
 
 Loneira, in the department of the high 
 Alps 14,451 
 
 Peak of Arbizon, in the department of the 
 high Pyrenees ..... 8,344 
 
 Puy de Dome, in Auvergne - - - 5,197 
 
 Summit of Vaucluse, near Avignon - 2,150 
 
 Soracte, near Rome .... 2,271 G 
 
 Monte Veiino, in the kingdom of Naples, 8,397 G 
 Mount Vesuvius, volcanic mountain near 
 Naplgs ...... 3,978 
 
 jEtna, volcanic mountain in Sicily - 10,963 B 
 
 St. Angelo, in the Lipari islands • 5,260 
 
 Top of the Rock of Gibraltar - - 1,439 B 
 
 Mount Athos, in Rumelia - - - 3,353 
 
 Diana's Peak, in the Island of St. Helena, 2,692 
 Peak of Teneriffe, one of the Canary Is- 
 
 lands - 12,358 B 
 
 Ruivo Peak, the highest point in the is- 
 land of Madeira .... 5,162 
 
 Table Mountain, near the Cape of Good 
 Hope ...... 3,520 
 
 Chain of Mount Ida, beyond the plain of 
 
 Troy 4,960 
 
 Chain of Mount Olympus, in Anatolia 6,500 
 
 Italitzkoi, in the Altaic chain - 10,735 
 
 Awatsha, volcanic mountain in Kamt- 
 chatka - - - - - - 9,600 
 
 Taganai, in the Uralian chain - - 4,912 
 
 The Volcano, in the Isle of Bourbon - 7,680 
 
 Ophir.in the centre of the Island of Suma- 
 tra - - ... - - 13,842 
 
 B 
 
62 
 
 THE ARTISAN. 
 
 St. Elias, on the western coast of North 
 
 America - 12,672 
 
 Chimborazo, highest summit of the Andes, 21,440 B 
 Antisana, volcanic mountain in the king- 
 dom of Quito ..... 19,150 B 
 
 Cotopaxi, volcanic mountain in the king- 
 
 dom of Quito ..... 18,890 B 
 
 Tonguragua, volcanic mountain near Rio- 
 
 bomba, in Quito .... 16,579 B 
 
 Rucu de Pichincba, in the kingdom of 
 
 Quito 15,940 B 
 
 Heights of Assuay, the ancient Peruvian 
 road - - - - - - - 15,540 B 
 
 Peak of Orizaba, volcanic mountain east 
 
 from Mexico 17,390 G 
 
 Lake of Toluca, in the kingdom of 
 
 Mexico ...... 12,195 B 
 
 City of Quito ..... 9,560 B 
 
 City of Mexico .... - 7,476 B 
 
 Silla de Caraccas, part of the chain of Ve- 
 nezuela - 8,640 B 
 
 Blue Mountains, in the Island of Jamaica, 7,431 
 Pelee, in the Island of Martinique - 5,100 
 
 Morne Garou, in the Island of St. Vin- 
 cents - 5,050 
 
 Mount Misery, in the Island of St. Chris- 
 tophers 3,711 
 
 MOUNTAINS IN THE EAST INDIES. 
 
 Himalay, or White Mountains - - 26,860 
 
 Yamunavaben, or Jamautri - - 25,500 
 
 Supposed Dhaibun .... 24,740 
 
 ON THE STUDY OF OPTICS. 
 
 To the Editor of the Artisan. 
 
 Sir. — Perceiving that part of your va- 
 luable publication is devoted to miscella- 
 neous subjects connected with the Arts 
 and Sciences, I have taken the liberty of 
 sending you a short article on the Study of 
 the pleasing and highly useful science of 
 Optics. Should you think proper to insert 
 it in any of your succeeding numbers, it 
 may, perhaps, be the means of turning the 
 attention of some of your ingenious rea- 
 ders to this interesting subject. 
 
 I have frequently felt no small surprise, 
 that a science so useful and entertaining 
 as Optics should be so much neglected as 
 it is at the present day, while many other 
 branches of practical and scientific know- 
 ledge are so eagerly cultivated, and held 
 in such high estimation. I believe there 
 has scarcely been a discovery, or even an 
 improvement, made, either in the theoreti- 
 cal or practical part of optics, since the 
 days of the celebrated Dolland, if we ex- 
 cept the camera lucida by Dr. Wolaston, 
 and the kaleidoscope by Dr. Brewster. But 
 it may, perhaps, be observed, that it does 
 not follow, because no discoveries or im- 
 provements, except those just mentioned, 
 have been made in this branch of know- 
 ledge, that the cultivation of it is neglect- 
 ed ; since it may possibly be one of those 
 sciences which has already arrived at per- 
 fection. For myself, I confess, I have yet 
 to learn what science has attained to this 
 stage. I am not aware of any ; and am of 
 
 opinion, that none offers so fair a prospect 
 for discovery, or is so susceptible of im- 
 provement, as that of optics. Although 
 we know some of the laws which light 
 obeys, in passing from one body to another, 
 and even some of its effects upon certain 
 substances, we are completely ignorant of 
 its nature. And who will say, that all its 
 effects are already known ? 
 
 The practical part of the formation and 
 combination of glasses is capable of great 
 improvement, though very few efforts have 
 of late been made to effect it. It would 
 be trifling with the time of your readers to 
 attempt any proof of so obvious a truism 
 as the former part of this assertion ; but it 
 may, perhaps, be necessary to advance 
 some arguments in support of the latter, 
 as the truth of it is more likely to be called 
 in question. Before adducing these, I beg 
 leave to observe what criteria I consider 
 necessary for deciding upon its correct- 
 ness. The popularity of any branch of 
 physical knowledge can only be judged of 
 by the following circumstances : the num- 
 ber of books published on the subject — 
 of persons employed in teaching it — of in- 
 struments manufactured for its cultivation 
 and application — and of the various disco- 
 veries made in it. And it is sufficiently 
 easy to show, that the application of any 
 of these tests will prove optics not to be at 
 present a popular branch of knowledge. 
 W e very seldom hear of a book making its 
 appearance, either on the theory or prac- 
 tice of this science : and, amid all the ad- 
 vertising of lecturers, and the puffing of 
 teachers, it is scarcely ever adverted to. 
 As to the demand for optical instruments, 
 it is only necessary to refer individuals to 
 their respective circles of acquaintance, to 
 convince them, how small is the number in 
 general use. And I have already had oc- 
 casion to remark, how very limited has 
 been the extent of discoveries in this sci- 
 ence within the last thirty years. 
 
 The utility of optics is so universally ac- 
 knowledged, that it is almost superfluous 
 to enlarge upon it. I may, however, be 
 permitted to mention one or two facts, 
 to shew the advantages which have al- 
 ready resulted to mankind from its culti- 
 vation. 
 
 The. formation and combination of 
 glasses, according to the laws of optics, 
 have been the means of exhibiting to us 
 wonders which could never have been 
 even anticipated without them. The an- 
 cients had no idea of the existence of ob- 
 jects which the invention of the micro- 
 scope and the telescope have made known 
 to us. Who would have imagined, for 
 example, that a single drop of liquid con- 
 tains more animals than there are men, 
 women, and children, on the surface of 
 
THE ARTISAN. 
 
 63 
 
 the whole earth?* Or, who could have 
 supposed, before the discovery of the tele- 
 scope, that the planet Saturn was sur- 
 rounded by a broad luminous ring ? — that 
 the face of the moon was diversified with 
 mountains and vallies, and that the milky 
 way was, to use the language of the poet, 
 u powdered with stars ?” 
 
 It is to the discoveries which have been 
 made in optics that astronomy, and conse- 
 quently geography and navigation, have 
 been indebted for the greatest part of their 
 improvements. To optics the art of draw- 
 ing and perspective likewise owe many of 
 the fundamental principles upon which 
 they depend. But had this science ren- 
 dered no other service to mankind than 
 that of supplying them with the simple 
 but highly valuable article of spectacles , it 
 would have ample claims on their grati- 
 tude and regard. This beautiful and be- 
 neficial application of glasses may indeed 
 be said to give eyes to the blind. And, 
 were we even to discard from the question 
 every consideration of utility, the intrinsic 
 pleasure and enjoyment arising from the 
 pursuit of this interesting science, should 
 recommend it to our study and attention, 
 and excite regret in the mind of every 
 scientific person, to see it falling into un- 
 deserved comparative neglect. 
 
 Oculus. 
 
 SINGULAR APPLICATION OF 
 HEAT. 
 
 Some years ago it was observed, at the 
 Conservatoire des Arts et Metiers at Paris, 
 that the two side-walls of a gallery were 
 receding from each other, being pressed 
 outwards by the weight of the roof and 
 floors. Several holes were made in each 
 of the walls, opposite to one another, and 
 at equal distances, through which strong 
 iron bars were introduced, so as to tra- 
 verse the chamber. Their ends outside of 
 the wall were furnished with thick iron 
 discs, firmly screwed on. These were suf- 
 ficient to retain the walls in their actual 
 position. But to bring them nearer toge- 
 ther would have surpassed every effort of 
 human strength. All the alternate bars of 
 the series were now heated at once by 
 lamps, in consequence of which they were 
 elongated. The exterior discs being thus 
 freed from contact of the walls, permitted 
 them to be advanced farther, on the 
 screwed ends of the bars. On removing 
 the lamps, the bars cooled, contracted, and 
 drew in the opposite walls. The other 
 bars became in consequence loose at their 
 
 * Though this is generally stated to he the case by 
 writers on the microscope, yet it would be difficult 
 to prove if in a satisfactory manner.— E d. 
 
 extremities, and permitted their end plates 
 to be further screwed on. The first series 
 of bars being again heated, the above pro- 
 cess was repeated in each of its steps. By 
 a succession of these experiments they re- 
 stored the walls to the perpendicular posi- 
 tion ; and could easily have reversed their 
 curvature inwards, if they had chosen. 
 The gallery still exists, with its bars, to 
 attest the ingenuity of its preserver, M. 
 Molard. 
 
 SOLUTION OF QUESTIONS. 
 
 To the Editor of the Artisan. 
 
 Sir. — I n the second Number of your va- 
 luable publication, I have observed a Phi- 
 losophical Query, respecting the velocity 
 with which a boat passes over water at 
 different depths. I have therefore taken 
 the liberty of sending you my opinion of 
 the cause which occasions the difference 
 of velocity which your correspondent, 
 Mercator, has stated to exist. 
 
 I apprehend, that a boat in proceeding 
 along a canal or smooth water, must, in 
 every boat’s length of her course, move out 
 of her way a body of water equal in bulk 
 to the room her bottom takes up in the 
 water ; that the water so moved, must pass 
 on each side of her, and under her bottom, 
 to get behind her ; and that, if the passage 
 under her bottom be straightened by the 
 shallows, more of that water must pass by 
 her sides, and with a swifter motion, which 
 will retard her, as moving the contrary 
 way; or that the water becoming lower 
 behind the boat than before her, she will 
 be pressed back by the weight of its differ- 
 ence in height, and her motion is retarded 
 by having that weight constantly to over- 
 come. 
 
 This, Sir, I consider to be the true cause, 
 but the quantity of difference I am unable 
 to state, having never made any experi- 
 ments to ascertain it ; but having often oc- 
 casion to be on the River Thames, I lately 
 enquired of several watermen, whether 
 they were sensible of any difference in 
 rowing over shallow or deep water, I 
 found them all agree in the fact, that there 
 was a very great difference, but they dif- 
 fered widely in expressing the quantity of 
 the difference; some supposing it was 
 equal to a mile in six, others to a mile in 
 three, &c. As I do not recollect to have 
 met with any mention of this matter in any 
 philosophical book, and conceiving, that if 
 the difference should really be great, it 
 might be an object of consideration in 
 many projects now on foot for digging new 
 navigable canals in this country. 
 
 Aouatus. 
 
64 
 
 THE ARTISAN. 
 
 To the Editor of the Artisan. 
 
 Sir. — Haying observed two Philosophi- 
 cal questions (by Peter Plus) in the second 
 number of the Artisan, of which the solu- 
 tion is required, I have amused myself by 
 undertaking this task ; and, as 1 believe I 
 have accomplished it, I here send you 
 what I conceive to be an accurate solution 
 of both questions. Moses Minus. 
 
 Example 1 : — -Let x represent A C, the 
 longer arm of the lever, A B ; 
 
 g C 
 
 EBSSSSSSSSSSBS 
 
 and let a zz B C, 
 P zz 2, then x -j- 
 length of the lever ; 
 
 
 p 6 
 
 or (1), W — 45, and 
 a — A B, the whole 
 and as it is homogene- 
 
 ous, x a , or the middle of the lever will 
 2 __ 
 be its centre of gravity, and x — will be 
 
 the distance of the centre of gravity from 
 the fulcrum , at C ; then from the property 
 x 2 — a 2 
 
 of the lever P x + — ' zz a W, or 
 
 Px-(-x 2 — a 2 ~2a W , and this quadratic 
 reduced, gives x~ s/ 2 a W + a 2 + P 2 — - P, 
 or x zz 7*7468 in this case, or the dis- 
 tance of the power from the fulcrum ; and 
 x -f- 1 — 8*7468 the whole length of the 
 lever in feet, or its weight in pounds. 
 
 Example 2 : — Let A E H represent the 
 glass, and F D G the sphere ; 
 
 the triangle A E B, and CEP are equian- 
 gular, therefore, BA : A E : : F C : C E, 
 that is, 2^ : (2| 2 + 6 2 )^ 2 : 5*2, and 
 
 BC z BE • — EC — 6 — 5*2 — *8; 
 B D — 2*8 the height of the segment im- 
 mersed, and its content is (3 X (4 — 2*8) x 2) 
 X 2*8 2 X *5236 — 26*272 cubic inches, 
 the answer. 
 
 This question was also answered, nearly 
 in the same manner, by John Boronesphi- 
 losmathematicus, Manchester; and by 
 Mr. .John Stephens, somewhat differently, 
 
 though not quite so accurately : for he 
 makes the answer 26*7036 cubic inches, 
 which is too great by *4316 of an inch. 
 
 Mr. Richard Graham, teacher of mathe- 
 matics, Ranelagh-street, Liverpool, also 
 gave a very neat solution ; but it did not 
 arrive in time for publication in the present 
 Number. 
 
 A correspondent, who signs Caldwell, 
 Warrington, also sent us a solution of this 
 question ; but it was not altogether correct. 
 
 QUESTIONS FOR SOLUTION. 
 
 To the Editor of the Artisan. 
 
 Sir. — Please to insert the following 
 question in one of your succeeding num- 
 bers, which will very much oblige your 
 obedient servant, Richard Graham. 
 Ranelagh-street , Liverpool. 
 
 My brewer requests me to inform him, 
 what thickness a solid inch of glass must 
 be blown to contain an ale gallon, or 282 
 cubic inches ? 
 
 To the Editor of the Artisan. 
 
 Sir. — I take the liberty of sending you 
 the following mathematical question, which 
 I will thank you to insert in an early num- 
 ber, which will oblige, 
 
 John Boronesphilosmathematicus. 
 
 On December 24, 1823, at night, the al- 
 titude of Pollux was observed, and that 
 of the middle star in Orion’s belt,— -their 
 difference zz 6° 35': also at the same time 
 the difference of their azimuths, from the 
 north, zz 51°. Required the latitude of 
 the place of observation ? 
 
 To the Editor of the Artisan. 
 
 Sir, — Can you, or any of your readers, 
 inform me if all dry solid bodies become 
 hot by friction, or rubbing ? I should also 
 be happy to know, if any philosophical 
 reason can be given why liquids are not 
 heated, or have their temperature raised 
 by agitation. — I am, Sir, &c. 
 
 Aquatus. 
 
 To the Editor of the Artisan. 
 
 Sir.— -Having often heard of the tempe- 
 rature of bodies being eight hundred, nine 
 hundred, and a thousand degrees of Fahren- 
 heit’s scale, I should be obliged to you, or 
 any of your philosophical correspondents, 
 to inform me, by what instrument these 
 temperatures are measured ; and what is 
 the most accurate way of measuring tem- 
 peratures between seven hundred and a 
 thousand degrees of the above scale. 
 
 A Mechanic. 
 
SIM lUlFIEI DAVY BAH? 
 
 'PRESIDENT OF TELE ROYAL SOCIETY. 
 
 Tab. I824 ,/by Hodgson & C° 10 New gate St. 
 
THE ARTISAN. 
 
 65 
 
 MEMOIR OF SIR HUMPHRY DAVY. BART. 
 
 The most gratifying theme to which the 
 pen of the biographer, or even the pencil of 
 the artist, can be devoted, is the handing 
 down to posterity correct delineations of 
 extraordinary men ; who, at different pe- 
 riods and in all ages have, like meteors, 
 burst upon the world, shedding new light 
 upon science, adding fresh beauty to lite- 
 rature, and invigorating and improving the 
 morals of mankind: — To record these, forms 
 the most delightful task of the historian. 
 
 The object of these memoirs has, per- 
 haps, done more for the chemical world 
 than any man who has preceded him ; but 
 whilst we thus pay a tribute to the man of 
 scientific research, we must not forget that 
 Sir Humphry Davy combines both the 
 scholar and the philosopher ; and although 
 apparently devoted to the mutation of forms 
 in the Laboratory, he has not been unmindful 
 even of the variation of the Muses, to which 
 the pages of the “ Annual Anthology,” now 
 discontinued, bear ample testimony, in the 
 shape of some very spirited poetical effu- 
 sions, said to have emanated from his pen 
 ere he was ten years old ; an amusement 
 he pursued to a much later period. 
 
 Descended from an ancient family in 
 Cornwall, he was born at Penzance, near 
 the Land’s End, in the year 1779, on the 
 17 th of December ; at the grammar schools 
 of which place and of Truro, he received the 
 rudiments of his education, and gave early 
 proofs of those masculine powers, which 
 have since procured him distinguished ho- 
 nours from his sovereign, and an imperish- 
 able reputation among men. 
 
 Having originally intended to pursue 
 the medical profession, he resided some 
 time at Penzance, with a friend of his ma- 
 ternal grandfather, a Mr. Tomkins, who 
 was a surgeon of considerable eminence, 
 and from whom he derived both intellec- 
 tual and professional improvement. But 
 intending to graduate at Edinburgh, he at 
 length became the pupil of Mr.Borlase, 
 who also resided at Penzance, a gentleman 
 of great intelligence, both as a surgeon and 
 a scholar; under whom, by steadily pur- 
 suing a methodical system of reading, pre- 
 viously determined upon, he became, at 
 the age of eighteen, familiar with the sci- 
 ence of Botany, Anatomy, Physiology, Ma- 
 thematics, Metaphysics, Natural Philoso- 
 phy, and Chemistry ; to the latter of which 
 his genius had decidedly devoted him. 
 
 His first discovery in the arcana of 
 science, was of great importance — no less 
 than that sea-weed rendered the air con- 
 tained in water pure, by the same agency 
 that vegetables deprive atmospheric air of 
 its noxious qualities. This at once marked 
 him as a man of unwearied research, and 
 he was looked up to as one from whose 
 perseverance much was to be expected. 
 This fact he made known to Dr. Beddoes, 
 Vol. I. — N° 5, 
 
 with whom he had beoome intimate, and 
 who was, at that time, endeavouring to 
 form an establishment, in order to ascer- 
 tain, experimentally, the power of gas as 
 applied to the cure of human diseases.— 
 Dr. Beddoes was so much pleased, that he 
 invited Davy, then under twenty, to join 
 him in his pursuit; to which the latter con- 
 sented, conditionally — that the whole of 
 the experiments should be under his im- 
 mediate control. This being conceded, he 
 relinquished his predetermination to gra- 
 duate at Edinburgh, and removed to Bris- 
 tol, where Dr. Beddoes then resided: here 
 he spent some considerable time, and con- 
 tracted an intimacy with Davies Giddy, 
 Esq. who has since taken the name of 
 Gilbert, a gentleman well known to the 
 scientific world; who being also an ad- 
 mirer of the young experimentalist, deter- 
 mined him, by his advice, to continue a ca- 
 reer, which he has since run with so much 
 honour to himself, and substantial advan- 
 tage to the world — of which the safety 
 lamp may be fairly quoted as an instance. 
 Mr. W. Clayfield frequently assisted him 
 in his labours, during his residence at Bris- 
 tol, where his indefatigable zeal, in the 
 pursuit of his favourite science, brought to 
 light the respirability of the nitrous oxide. 
 Soon after, he published his work, enti- 
 tled, “ Researches Chemical and Philoso- 
 phical,” in which he embodied the result 
 of his experiments in gaseous matter. 
 This publication procured him the Profes- 
 sor’s Chair in Chemistry, at the Royal In- 
 stitution, by introducing him to the notice 
 of Count Rumford, who deeply interested 
 himself to procure Mr. Davy’s election. 
 From this period we find him in the very 
 nucleus of scientific information, with am- 
 ple facilities to extend his inquiries into 
 the secrets of nature. Domiciliated in the 
 British metropolis, at the very head of a 
 liberal institution, he had the command of 
 a well-appointed laboratory, a complete 
 electrical apparatus, with the various sci- 
 entific instruments belonging to that estab- 
 lishment ; thus his means were more per- 
 fect than he had hitherto found them, and 
 he bent the whole force of his genius on 
 chemical science. He carefully examined, 
 but without making any new discovery, 
 the vegetable substance called Tannin. 
 
 In 1803, although he had not yet made 
 those discoveries which have since spread 
 his fame upon eagle wings, not only in the 
 estimation of his own countrymen, but in 
 that of the whole world, he was chosen a 
 member of the Royal Society ; in 1805, he 
 was made a member of the Royal Irish 
 Academy ; and, in 1806, he became the 
 Secretary to the Royal Society, and was in 
 correspondence with the most eminent che- 
 mists and literati of both hemispheres. His 
 experiments with the galvanic battery had 
 
 F 
 
THE ARTISAN. 
 
 66 
 
 now, for a considerable period, engrossed 
 his attention ; and it was at this time also, 
 he delivered his Bakerian lectures before 
 the Royal Society, the first of which made 
 known some highly important phenomena 
 of the chemical actions of electricity, espe- 
 cially relating to alkalis and acids. 
 
 In 1807, he communicated his grand 
 discoveries of the metallic bases of potash 
 and soda, which he called 'potassium and 
 sodium ; and at the same epoch, by like 
 experiments, he decomposed and ascer- 
 tained the metallic bases of other substan- 
 ces ; after which, he demonstrated, that 
 oxmuriatic acid was not, as it has been 
 supposed, a compound, but a simple sub- 
 stance, and he called it Chlorine. 
 
 At first, some of the French chemists re- 
 jected his hypothesis, that oxygen was one 
 of the alkaline principles ; nor would they 
 allow potassium and sodium to be any thing 
 but hydrates ; however they were ulti- 
 mately obliged to acknowledge its correct- 
 ness. For the honour of science it ought 
 never to be forgotten, that although Eng- 
 land and France then waged a war of un- 
 exampled inveteracy, the French Institute 
 awarded the prize to our recondite coun- 
 tryman. This was no less honourable to 
 Napoleon, who was then at the head of 
 the Institute, than that he should also send 
 him a sum of money, and further grant 
 him free passports, so that he might travel 
 wherever he listed, through the dominions 
 then under his control ; thus the rancour 
 of belligerancy bowed to the superior ge- 
 nius of Sir Humphry, then Mr. Davy. 
 
 In 1811, Mrs. Apreece, an amiable and 
 accomplished widow lady, of considerable 
 fortune, became the object of Mr. Davy’s 
 solicitude and affection ; and in the fol- 
 lowing year, (a short period previous to 
 which happy event, he had the honour of 
 knighthood conferred upon him by his 
 present Majesty, then Prince Regent,) he 
 led that lady to the hymeneal altar. 
 
 In a series of lectures began about the 
 same time, and which he continued for three 
 years before the Board of A griculture, Sir 
 Humphry particularly impressed upon 
 their minds the dependance of that branch 
 of British wealth, upon the science of che- 
 mistry. In 1814, he was chosen Vice- 
 President of the Royal Institution, and a 
 corresponding member of the French In- 
 stitute. In 1815, at the particular request 
 of a committee of gentlemen formed at 
 Sunderland, in consequence of the innu- 
 merable accidents which arose from the 
 explosion of fire damps in the coal mines, 
 and to provide, if possible, a remedy, Sir 
 Humphry examined most of the large col- 
 lieries in the north, an undertaking of equal 
 importance, both to science and humanity ; 
 and, after numerous experiments to ascer- 
 tain the qualities of the exploding gas, it 
 ended in the invention of his Safety Lamp. 
 
 This effort of his indefatigable genius was 
 considered so eminently useful, that the 
 coal owners of the Tyne and Wear pre- 
 sented him with a service of plate, estima- 
 ted at the value of 2,000Z. The originality 
 of this invention was for a time disputed : 
 but it is now generally allowed. 
 
 In 1817, Sir Humphry was created a 
 baronet, and elected an Associate of the 
 Royal Academy. During the two follow- 
 ing years, he travelled to Italy, where he 
 analyzed the colours used by the ancients 
 in their paintings ; and examined the ma- 
 nuscripts found in Herculaneum. These 
 he thought were not completely carbonized, 
 but closely adhered together by a sub- 
 stance chemically produced during the 
 long period they had remained buried, and 
 which might be dissolved : but not more than 
 one hundred out of nearly thirteen hundred 
 afforded any likelihood of their being suc- 
 cessfully unrolled. In 1820, he returned 
 to his native shores, about which period, 
 Sir Joseph Banks, the late venerable Pre- 
 sident of the Royal Society, dying, Sir 
 Humphry Davy and Dr. Wollaston were 
 looked upon as the most eligible members 
 to fill the vacancy. Dr. Wollaston, how- 
 ever, refused to stand in the way of his 
 friend ; and, notwithstanding he was op- 
 posed by Lord Colchester, who was him- 
 self proposed without his own sanction, 
 the disputed chair was given to Sir 
 Humphry Davy, by a majority of nearly 
 two hundred ; nor shall we detract from 
 the merits of the defunct President, by 
 adding, that it has never been so ably fill- 
 ed, since the days of that constellation of 
 science, Sir Isaac Newton, as it is by the 
 present noble occupant. 
 
 The last important discovery for which 
 the world is indebted to him, is the pre- 
 vention of the corrosion and decay of cop- 
 per used for lining the bottoms of ships, by 
 a very simple method, and which he com- 
 municated to the Royal Society. The 
 cause of the corrosion, he said, was a weak 
 chemical action constantly exerted between 
 the saline contents of the sea-water and 
 the copper : and he recommends the appli- 
 cation of a very small surface of tin, or 
 other oxydizable metal, which any where 
 in contact with a large surface of copper, 
 renders it so negatively electrical, that sea- 
 water has no action upon it ; and a little 
 mass of tin brought in communication by a 
 wire with a large plate of copper, entirely 
 preserves it. This discovery, by order of 
 the Lords of the Admiralty, is now coming 
 into actual practice on board ships of war. 
 The works of which Sir Humphry is the 
 author are, Chemical and Philosophical 
 Researches ; Elements of Chemical Philo- 
 sophy ; Elements of Agricultural Chemis- 
 try ; and divers pamphlets : besides a con- 
 siderable number of papers published in 
 the Philosophical Transactions, &c. 
 
THE ARTISAN. 
 
 67 
 
 PNEUMATICS. 
 
 After the full description now given of the 
 Air Pump, we shall show how a number of 
 interesting and important experiments may 
 be performed by it, which will afford the 
 most convincing and satisfactory proofs that 
 can be given of the weight, elasticity, and 
 other mechanical properties of the air. And 
 as many persons may not have it in their 
 power, either to perform, or witness the 
 .performance, of these experiments, we shall 
 endeavour to make them as interesting as 
 possible, by stating the important facts 
 which they have been the means of making 
 known to us. 
 
 EXPERIMENTS WITH THE AIR PUMP. 
 
 To show the weight or pressure of the air. 
 
 1. Procure a thin bottle or Florence flask, 
 ‘whose contents are exactly known in cubic 
 inches, then let a cap, with a valve fasten- 
 ed over it, be nicely fitted to the mouth of 
 the flak. Screw the neck of this cap into 
 the hole i of the pump-plate; then, having 
 exhausted the air out of the flask, and taken 
 it off from the pump, let it be suspended at 
 one end of a balance, and nicely counter- 
 poised by weights in the scale at the other 
 end : this done, raise up the valve with a 
 pin, and the air will rush into the flask with 
 an audible noise ; during which time the 
 flask will descend, and pull down that end 
 of the beam. When the noise is over, put 
 as many grains into the scale at the other 
 end as will restore the equilibrium ; and 
 they will shew exactly the weight of the 
 quantity of air which has got into the flask, 
 and filled it. If the flask holds an exact 
 quart, it will be found that 17 grains will 
 restore the equipoise of the balance, when 
 
 * the quicksilver stands at 29| inches in the 
 barometer : which shews, that when the 
 air is at a mean rate of density, a quart of 
 it weighs 17 grains ; it weighs more when 
 the quicksilver stands higher : and less 
 when it stands lower. 
 
 2. Place the small receiver G, which is 
 within the large one already on the pump- 
 plate of the air pump, over the hole i, in 
 the pump-plate, and upon exhausting the 
 air, the receiver will be fixed down to the 
 plate by the pressure of the air on its out- 
 side, which is left to act alone, without any 
 air in the receiver to act against it ; and 
 this pressure will be equal to as many 
 times 15 pounds as there are square inches 
 in that part of the plate which the receiver 
 covers ; which will hold down the receiver 
 so fast, that it cannot be got off, until the 
 air be let into it by turning the cock k, and 
 then it becomes loose. 
 
 3. Set the little glass AB, 
 
 (which is open at both ends) over the hole 
 i, upon the pump-plate LL, and put your 
 hand close upon the top of it at B ; then 
 upon exhausting the air out of the glass, 
 you will find your hand pressed down with 
 a great weight upon it, so that you can 
 hardly release it, until th e air be re-admit- 
 ted into the glass by turning the cock k ; 
 which air, by acting as strongly upward 
 against the hand as the external air acted 
 in pressing it downward, will release the 
 hand from its confinement. 
 
 4. Having tied a piece of wet bladder h, 
 over the open top of the glass A, 
 
 (which is also open at bottom) set it to dry, 
 and then the bladder will be tight like a 
 drum. Then place the open end A upon 
 the pump-plate, over the hole i, and begin 
 to exhaust the air out of the glass. As the 
 air is exhausting, its spring within the glass 
 will be weakened, and give way to the 
 pressure of the outward air on the bladder, 
 which, as it is pressed down, will put on a 
 spherical concave figure, which will grow 
 deeper and deeper, until the strength of the 
 bladder be ovorcome by the weight of the 
 air ; and then it will break with a report as 
 loud as that of a pistol. If a flat piece of 
 glass be laid upon the open top of this re- 
 ceiver, and joined to it by a flat ring of wet 
 leather between them, upon pumping the 
 air out of the receiver, the pressure of the 
 outward air upon the flat glass will break it 
 all to pieces. 
 
 5. Immerse the neck cd of the hollow 
 glass ball 
 phial a a; 
 
68 
 
 THE ARTISAN. 
 
 then set it upon the pump-plate, and cover 
 it and the hole i with the close receiver A : 
 and then begin to pump out the air. As 
 the air goes out of the receiver by its spring, 
 it will also by the same means go out of the 
 hollow ball eb , through the neck cd, and 
 rise up in bubbles to the surface of the wa- 
 ter in the phial; from whence it will make 
 its way with the rest of the air out of the 
 receiver. When the air has done bubbling 
 in the phial, the ball is sufficiently ex- 
 hausted ; and then, upon turning the cock 
 fc, the air will get into the receiver, and 
 press so upon the surface of the water in 
 the phial, as to force the water up into the 
 ball in a jet, through the neck c d ; and will 
 fill the ball almost full of water. The rea- 
 son why the ball is not quite filled, is, be- 
 cause all the air could not be taken out of 
 it, and the small quantity that was left, and 
 had expanded itself so as to fill the whole 
 ball, is now condensed in the same degree 
 as the outward air, and remains like a 
 small bubble at the top of the ball, which 
 keeps the water from filling that part of the 
 ball. 
 
 6. Having placed the jar A, 
 
 I 
 
 f 
 
 I - 
 
 e 
 
 with some quicksilver in it, on the pump- 
 plate, as in the last experiment, cover it 
 with the receiver B ; then push the open 
 end of the glass tube de, through the collar 
 of leathers in the brass neck C (which it fits 
 
 so as to be air tight) almost down to the 
 quicksilver in the jar. Then exhaust the 
 air out of the receiver, and it will come out 
 of the tube, because the tube is close at top. 
 When the gauge m m shews that the re- 
 ceiver is well exhausted, push down the 
 tube, so as to immerse its lower end into 
 the quicksilver in the jar. Now, although 
 the tube be exhausted of air, none of the 
 quicksilver will rise into it, because there is 
 no air left in the receiver to press upon its 
 surface in the jar. But let the air into the 
 receiver by the cock k, and the quicksilver 
 will immediately rise in the tube, and stand 
 as high in it, as it was pumped up in the 
 last experiment. 
 
 These experiments shew, that the quick- 
 silver is supported in the barometer by the 
 pressure of the air on its surface in the box, 
 in which the open end of the tube is placed. 
 And that the more dense and heavy the air 
 is, the higher does the quicksilver rise; and, 
 on the contrary, the thinner and lighter 
 the air is, the more will the quicksilver fall. 
 For if the handle F be turned ever so little, 
 it takes some air out of the receiver, by 
 raising one or other of the pistons in its bar- 
 rel ; and consequently, that which remains 
 in the receiver is so much the rarer, and has 
 so much the less spring and weight ; and 
 thereupon the quicksilver falls a little in 
 the tube; but upon turning the cock, and 
 re-admitting the air into the receiver, it be- 
 comes as weighty as before, and the quick- 
 silver rises again to the same height. Thus 
 we see the reason why the quicksilver in 
 the barometer falls before rain or snow, 
 and rises before fair weather ; for, in the 
 former case, the air is too thin and light to 
 bear up the vapours, and in the latter, too 
 dense and heavy to let them fall.* 
 
 7. Take the tube out of the receiver, and 
 put one end of a bit of dry hazel branch, 
 about an inch long, tight into the hole, and 
 the other end tight into a hole quite through 
 the bottom of a small wooden cup : then 
 pour some quicksilver into the cup, and ex- 
 haust the receiver of air, and the pressure 
 of the outward air on the surface of the 
 quicksilver, will force it through the pores 
 of the hazel, from whence it will descend 
 in a beautiful shower into a cup placed un- 
 der the receiver to catch it. 
 
 8. Put a wire through the collar of lea- 
 thers in the top of the receiver, and fix a 
 bit of dry wood on the end of the wire 
 within the receiver ; then exhaust the air, 
 and push the wire down, so as to immerse 
 
 * In all mercurial experiments with the air-pump, 
 a short pipe must be screwed into the holes, so as to 
 rise about an inch above the plate, to prevent the 
 quicksilver from getting into the air-pipe and bar- 
 rels, in case any of it should be accidentally spilt 
 over the jar : for if it once gets into the pipes or 
 barrels, it spoils them, by loosening the solder, and 
 corroding the brass. 
 
THE ARTISAN. 
 
 69 
 
 the Wood into a jar of quicksilver on the 
 pump-plate ; this done, let in the air, and 
 upon taking the wood out of the jar, and 
 splitting it, its pores will be found full of 
 quicksilver, which the force of the air, up- 
 on being let into the receiver, drove into 
 the wood. 
 
 9. Join the two brass hemispherical cups 
 A and B together, 
 
 with a wet leather between them, having a 
 hole in the middle of it ; then screw the end 
 D of the pipe C D, into the plate of the 
 pump at i, and turn the cock E, so as the 
 pipe may be open all the way into the ca- 
 vity of the hemispheres ; exhaust the air 
 out of them, and turn the cock a quarter 
 round, which will shut the pipe C D, and 
 keep out the air. This done, unscrew the 
 pipe at D from the pump, and screw the 
 piece F b upon it at D ; and let two men 
 try to puli the hemispheres asunder by the 
 rings g and h, which they will find difficult 
 to do ; for if the diameter of the hemi- 
 sphere be four inches, they will be pressed 
 together by the external air with a force 
 equal to 188 pounds. And to shew that it 
 is the pressure of the air that keeps them 
 together, hang them by either of the rings 
 upon the hook P of the wire in the receiver 
 M, (upon the air pump) and upon exhaust- 
 ing the air out of the receiver, they will fall 
 asunder of themselves. 
 
 10. Place a small receiver near the hole 
 i, on the pump-plate, as O, and cover both 
 it and the hole with the receiver M, (see 
 air pump) and turn the wire so by the top 
 P, that its hook may take hold of the little 
 receiver by a ring at its top, allowing that 
 receiver to stand with its own weight on 
 the plate. Then, upon working the pump, 
 the air will come out of both receivers ; 
 but the large one M will be forcibly held 
 down to the pump by the pressure of the 
 external air ; whilst the small one O, hav- 
 ing no air to press upon it, will continue 
 loose, and may be drawn up and let down 
 at pleasure, by the wire P P. But, upon 
 letting it quite down to the plate, and ad- 
 mitting the air into the receiver M, by the 
 
 cock k, the air will press so strongly upon 
 the small reciever O, as to fix it down to 
 the plate, and at the same time, by counter- 
 balancing the outward pressure on the large 
 receiver M, it will become loose. This 
 experiment evidently shews, that the re- 
 ceivers are held down by pressure, and not 
 by suction, for the internal receiver conti- 
 nued loose whilst the operator was pump- 
 ing, and the external one was held down ; 
 but the former became fast immediately by 
 letting in the air upon it. 
 
 11. Screw the end A, of the brass pipe 
 A B F, into the hole of the pump-plate, and 
 turn the cock e f until the pipe be open ; 
 
 then put a wet leather upon the plate c d , 
 which is fixed on the pipe, and cover it 
 with the tall receiver G H, which is close 
 at top ; then exhaust the air out of the re- 
 ceiver, and turn the cock e, to keep it out ; 
 which done, unscrew the pipe from the 
 pump, and set the end A into a bason of 
 water, and turn the cock e to open the 
 pipe; on which, as there is no air in the 
 receiver, the pressure of the atmosphere on 
 the water in the basin will drive the water 
 forcibly through the pipe, and make it play 
 up in a jet to the top of the receiver. 
 
 12. Set the square phial A 
 
70 
 
 THE ARTISAN. 
 
 upon the pump-plate, and having covered 
 it with the wire cage B, put a close recei- 
 ver over it, and exhaust the air out of the 
 receiver ; in doing of which, the air will 
 also make its way out of the phial through 
 a small hole in its neck under the valve b. 
 When the air is exhausted, turn the cock 
 below the plate, to re-admit the air into the 
 receiver : and as it cannot get into the 
 phial again, because of the valve, the phial 
 will be broken into some thousands ^of 
 pieces by the pressure of the air upon it. 
 Had the phial been of a round form, it would 
 have sustained the pressure like an arch, 
 without breaking ; but as its sides are flat, 
 it cannot. 
 
 OPTICS, 
 
 This defect of the eye (see page 40) is re- 
 medied two ways : by diminishing the dis- 
 tance between the object and the eye ; for 
 by lessening the distance of the object, the 
 distance of the focus and image will be 
 increased, till it fall on the retina , and ap- 
 pear distinct. By applying a concave glass 
 to the eye ; for such a glass makes the rays 
 diverge more as they pass to the eye, in 
 which case the distance of the focus will 
 be also enlarged, and thrown upon the 
 retina , when distinct vision will ensue. 
 
 Hence the use of concave spectacles, to 
 purblind or near-sighted persons, to whom 
 objects appear under the following pecu- 
 liarities : 
 
 1st. Objects appear nearer than they 
 really are, or do appear to a sound eye. 
 
 2d. Objects appear less bright, or more 
 obscure, than to other persons, because a 
 less quantity of the rays of light enter the 
 pupil. 
 
 The eyes of such persons grow better 
 with age ; for their defect being too great 
 a convexity of the eye, the aqueous and 
 crystalline humours waste or decrease with 
 age, and of course grow flatter, and there- 
 fore are more capable of viewing distant 
 objects distinctly. 
 
 The other defect of the eye arises from 
 a quite contrary cause ; namely, the flat- 
 ness of the cornea and crystalline humours. 
 This is generally the case with the eyes of 
 old people ; and is remedied by convex 
 glasses, such as are used in common spec- 
 tacles. For as the rays in. such eyes go 
 beyond the bottom of the eye, before they 
 come to a focus, or form dhe image, a con- 
 vex glass will make the rays converge 
 sooner, by which means the focal distance 
 will be shortened, and adjusted on the re- 
 tina, where distinct vision will be pro- 
 duced. 
 
 By convex spectacles objects appear 
 brighter, because they collect a greater 
 
 quantity of rays upon the pupil of the eye. 
 They also appear at a greater distance 
 than they are, for the nearer the rays ap- 
 proach to parallel ones, the more distant 
 will the point be to which they tend. 
 
 A reading glass only differs from one of 
 the glasses of a pair of common spectacles 
 in being larger ; the use is however some- 
 what different ; for spectacles are used to 
 render objects distinct at a given distance ; 
 but reading glasses are employed to mag- 
 nify objects, or to render the reading of 
 small print very easy, which would other- 
 wise be apt to strain the eye too much. 
 Therefore the size of glasses for spectacles 
 is not required to be larger than the eye it- 
 self ; but that of a reading glass ought to 
 be large enough to take in as much of the 
 object or print, at least, as is equal to the 
 distance between both the eyes. 
 
 If an object be placed in the focus of a 
 convex lens, or reading glass, the rays 
 which proceed from it, after they have 
 passed through the glass, will proceed pa- 
 rallel ; and therefore an eye placed any 
 where in the axis * of the glass will have 
 the most distinct view of the object pos- 
 sible ; and if it be a lens of a small focal 
 distance, the object will appear as much 
 larger than it will do to the naked eye, as 
 it is nearer the lens than to the eye. It is 
 this property which renders them of so 
 much use as single microscopes, u( which 
 we shall here give an instance. 
 
 Suppose the focal distance of a lens to 
 be of an inch, then will the length of an 
 object, viewed by it, appear 60 times longer 
 than it will do to the naked eye, at six 
 inches distance ; the breadth will also be 
 increased 60 times, consequently the area or 
 superficies will appear 3600 times greater 
 than it will appear to the naked eye, when 
 viewed at the distance of six inches. f 
 
 As we have now stated and endeavoured 
 to illustrate by figures, the chief properties 
 of convex and concave lenses, we shall give 
 a short account of the nature and theory of 
 the various kinds of Microscopes. 
 
 There are three sorts of Microscopes in 
 use; viz. the single, the double , and the 
 solar microscope. 
 
 The nature of the two first depends up- 
 on the following circumstances. 
 
 1 . That no object can be distinctly seen 
 at a less distance, with the naked eye, than 
 six inches. 
 
 2. That the nearer any object is, the 
 larger is the angle under which it is seen, 
 or the greater is the magnitude of the 
 object. 
 
 3. That parallel rays, or such as are nearly 
 
 * See page 13, coi. 2. 
 
 t This is the least distance at which an object can 
 be distinctly seen with the naked eye, in a sound 
 state. 
 
THE ARTISAN. 
 
 71 
 
 so, can only have their focus at the bot- 
 tom of the eye. 
 
 4. That the rays proceeding from an ob- 
 ject placed in the focus of a concave lens, 
 are always refracted by the lens into a di- 
 rection parallel to each other, (see 2d fig. 
 page 87.) 
 
 The Single Microscope, as has already 
 been stated, consists only of one conevx 
 lens ; and when any object is to be exa- 
 mined by it, the object is to be placed in 
 its focus, and the rays which proceed from 
 the object through the lens fall upon the 
 eye parallel to each other, and therefore 
 produce distinct vision.* 
 
 The Double or Compound Microscope 
 consists of two lens at least, but generally 
 of three, and often more. 
 
 We shall first describe the one which 
 contains two ; the lens D E, in the follow- 
 ing figure, is therefore to be overlooked in 
 comparing this description with the figure. 
 
 The first or smallest lens C is placed 
 near the small object A B, 
 
 at a little more than its focal distance from 
 it, a large image of the object is thus form- 
 ed, which will be as much larger than the 
 object, as the distance C L is greater than 
 
 * Every convex lens is therefore a single micro- 
 scope. 
 
 the distance A C ; and as this distance may 
 be made greater or less, by placing the ob- 
 ject nearer to, or farther from, the lens C, 
 the image may be increased or diminished 
 at pleasure. And as this image may be 
 distinctly viewed, and still further magni- 
 fied, by a convex lens M N, placed at its 
 focal distance from the image, it is evident 
 that small objects may be thus magnified 
 to many times their real size.* 
 
 Suppose, for example, that the distance 
 of the object CL is 12 times the distance of 
 the imaget C A, then will the length of the 
 image KL be 12 times the length of the 
 object A B, when viewed with the naked 
 eye ; but this length of the image, if view- 
 ed with an eye-glass of one inch focal dist- 
 ance, will appear six times as large as it does 
 to the naked eye, and therefore its length 
 will appear 12 times 6, or 72 times larger 
 than to the naked eye ; and, as its breadth 
 will be magnified in the same proportion, 
 its surface will be 72 times 72, or 5,184 
 times larger than that of the object when 
 viewed with the naked eye. 
 
 Though the magnifying power of this 
 microscope be very considerable, yet the 
 extent or field of view is very small and 
 confined; therefore, in order to enlarge it, 
 and to increase the quantity of light, ano- 
 ther large lens D E, is placed between the 
 two already noticed (see the figure), by 
 which means the angle DCE or A C B, 
 under which the visible part of the object 
 appears, may be considerably enlarged; 
 the image will then be formed again at 
 F G, and as the image thus formed is now 
 contained between the two extreme paral- 
 lel rays of the eye-glass M F and N G, is 
 wholly visible ; whereas before, the part 
 O Q could only be seen. But though the 
 object is not quite so much magnified on 
 the whole, in this as in the former case, yet 
 the visible surface is very much increased 
 by the addition of this third glass. 
 
 The glass R S is a plain mirror, which is 
 employed to reflect the light I, in order 
 to illuminate transparent objects, when ex- 
 amined by this instrument. 
 
 The Solar Microscope, invented by Dr. 
 Lieberkhun, is employed to represent very- 
 small objects on a very large scale, in a 
 dark room. This is accomplished in the fol- 
 lowing manner. Let A B (see next page) re- 
 present abeam of the sun’s light falllingon 
 a small mirror or looking glass D C, ad- 
 justed by two brass wheels, to such an 
 inclination as shall reflect the rays which 
 fall upon it parallel to the horizon, to a 
 large convex lens E F, which converges 
 them to a focus ; near this focus, as at 
 GH, is placed a small object, which is, by 
 this means, strongly illuminated, and the 
 
 * This lens or glass being nearest the eye, is usu- 
 ally called the eye-glass. 
 
72 
 
 THE ARTISAN. 
 
 rays which flow from it through a small 
 convex lens I, so adjusted by a slider to a 
 little more than its focal distance from the 
 object, produce a very large image K L, 
 which being received upon a white table 
 cloth, or allowed to fall on the opposite 
 wall of the darkened room, will represent 
 the object magnified in proportion to the 
 distance of the picture from the lens I.* 
 
 image K L is duly formed on a sheet or 
 table cloth, at the distance of 16 feet from 
 the small lens just mentioned : then in 16 
 feet there are 192 inches, and consequently 
 1,920 tenths of an inch ; therefore the 
 image is 1,920 times the length of the ob- 
 ject, and as many times its breadth ; the area 
 or surface of the image is therefore 1,920 
 
 * It is scarcely necessary to remark that, the 
 lenses and object to be viewed are placed in a tube, 
 which is screwed into a hole in the window shutter, 
 or a board placed in the window, which serves at 
 the same time to exclude the light. 
 
 times 1,020, or 3,086,400 times that of the 
 object. Such is the prodigious magnifying 
 power of the solar microscope. 
 
 Having now described the different kinds 
 of microscopes, and endeavoured to ex- 
 plain the principle upon which their con- 
 struction depends, we shall state the pro- 
 perties of concave and convex mirrors , 
 previous to entering upon the description 
 of reflecting and refracting telescopes. 
 
 It has already been remarked, at page 
 12, that when the rays of light fall upon 
 any surface by which they are reflected, that 
 the angle at which they are reflected is 
 equal to the angle at which they fall upon 
 that surface (see fig. 1, in page 12). From 
 this simple elementary principle may easi- 
 ly be inferred every thing relating to the 
 formation of the images of objects in a 
 concave mirror. 
 
 For let A B be such a mirror, 
 
 and O B an object placed beyond its cen- 
 tre C, then since the axis C V is perpendi- 
 cular thereto in the vertex V, the particle 
 of light coming from the point O of the ob- 
 ject in the direction of the axis, will be 
 reflected back in the same direction to its 
 focus at I, where the point at O will be re- 
 presented. Then from the other extreme 
 point B let a ray proceed to V, making the 
 angle I V M equal to B Y O, and the point 
 M will be the representation of the point 
 B. And hence all the rays proceeding 
 from every part between O and B will be 
 reflected to the line I M, and so the whole 
 line I M will be the representation or 
 image of the object O B. 
 
 Hence it appears that the position of the 
 image, with respect to that of the object, 
 must necessarily be inverted, and on the 
 contrary side of the axis. Hence also it 
 appears, since the object and the image are 
 both seen from the vertex of the mirror 
 under equal angles B V O and I V M, the 
 length of the object will be to that of the 
 
THE ARTISAN. 
 
 73 
 
 image as the distance O V, to the distance 
 of the image I V from the mirror. 
 
 Therefore, while the object is farther 
 from the glass than the centre C, the 
 image will be on the same side, but nearer 
 to it, and less than the object. If the object 
 were placed in the centre C, the image 
 would be there formed also, in an inverted 
 position, and equal to the object ; if the 
 object be placed between the centre C and 
 focus F, as at I M, then will O B be the 
 image formed beyond the centre, inverted 
 and magnified. 
 
 If the object be placed in the focus F, 
 the rays will be all reflected parallel to 
 the axis, and form the image, and at an in- 
 finite distance, and infinitely large. Lastly, 
 suppose the object placed any where be- 
 tween the focus F, and the vertex V, as at 
 K, the image will be formed behind the 
 glass^at M, in the same position^ as the ob- 
 ject, and magnified. 
 
 If the radius of the mirror’s concavity 
 and the distance of the object be known, 
 the distance of the image from the mirror 
 may be found as follows : divide the pro- 
 duct of the distance and radius by double 
 the distance diminished by the radius, and 
 the quotient is the distance required. 
 
 Thus, let the radius of the mirror’s con- 
 cavity be 8 inches, and the distance of the 
 object 5 inches, required the distance of the 
 image from the mirror ? Here the product 
 of 8 and 5 is 40, and double the distance of 
 the object from the mirror is 10, which 
 diminished by 8, the radius, leaves 2 ; and 
 40 divided by 2 quotes 20, which is the 
 number of inches that the image is distant 
 from the mirror, in this case. 
 
 If a man places himself directly before a 
 large concave mirror, but farther from it 
 than its centre of concavity, he will see an 
 inverted image of himself in the air, be- 
 tween him and the mirror, of a less size 
 than himself. And if he holds out his 
 hand towards the mirror, the hand of the 
 image will come out towards his hand, 
 and coincide with it, of an equal bulk, 
 when his hand is in the centre of the con- 
 cavity : and lie will imagine he may shake 
 hands with his image. If he reaches his 
 hand farther, the hand of the image will 
 pass by his hand, and come between his 
 hand and his body ; and if he moves his 
 hand towards either side, the hand of the 
 image will move towards the other ; so that 
 whatever way the object moves, the. image 
 will move the contrary. 
 
 All the while a by-stander wilt see no- 
 thing'of the image, because none of the 
 reflected rays that form it enter his eyes. 
 
 If a fire be made in a large room, and a 
 smooth mahogany table be placed at a good 
 distance near the wall, before a large con- 
 cave mirror, so placed, that the light of the 
 fire may be reflected from the mirror to its 
 
 focus upon the table ; if a person stand by 
 the table, he will see nothing upon it, but 
 a longish beam of light ; but if he stands 
 at a distance towards the fire, not directly 
 between the fire and the mirror, he will see 
 an image of the fire upon the table, large 
 and erect. And if another person, who 
 knows nothing of this matter before hand, 
 should chance to come into the room, and 
 should look from the fire towards the 
 table, he would be startled at the appear- 
 ance ; for the table would seem to be on 
 fire, and by being near the wainscot, to 
 endanger the whole house* In this expe- 
 riment there should be no light in the 
 room but what proceeds from the fire ; and 
 the mirror ought to be at least fifteen 
 inches in diameter. 
 
 If the fire be darkened by a screen, and 
 a large candle be placed at the back of the 
 screen, a person standing by the candle 
 will see the appearance of a fine large star, 
 or rather planet, upon the table, as bright 
 as Venus or Jupiter. And if a small wax 
 taper (with a flame much less than the 
 flame of a candle) be placed near the can- 
 dle, a satellite to the planet will appear on 
 the table ; and if the taper be moved round 
 the candle, the satellite will go round the 
 planet. 
 
 In the same manner it may be shown, 
 that the rays of light falling on a convex 
 mirror, will proceed diverging from the 
 glass in such a manner as if they came 
 from a point behind it, so that these glasses 
 have no real focus or burning point ; they 
 form the image only behind , always erect , 
 and less than the object ; so that no magni- 
 fying power belongs to these glasses, when 
 used alone. 
 
 CHEStMISTItir. 
 
 OF HYDROGEN GAS. 
 
 Another substance presents itself in the 
 same state as oxygen; for chemists have 
 never been able to procure it in a pure 
 and separate state, and they have yet no 
 proof that it exists in that state in nature. 
 In order to discover its properties, they are 
 obliged to examine the bodies which contain 
 it, and by this means they are, in some 
 measure, enabled to, discover the properties 
 it communicates to those bodies. 
 
 Though we have long possessed some 
 knowledge of the natural inflammable va- 
 pours of the mines, and coal pits, as well 
 as of those which are disengaged in many 
 operations of chemistry, such as the me- 
 tallic solutions in the acids, &c. ; it was not 
 till 1766 that M. Cavendish ascertained the 
 existence of this elastic fluid, and properly 
 distinguished it from all others, by collect- 
 
74 
 
 THE ARTISAN. 
 
 ing it separately, and distinguishing its 
 properties. 
 
 Hydrogen gas is not to be collected from 
 natural bodies. That which is abundantly 
 disengaged from fossil coal, moistened or 
 exposed to the air, of putrid vegetables at 
 the bottom of stagnant waters, of ponds, of 
 marshes, of peat soil, contains but a small 
 quantity of pure hydrogen gas. It contains 
 many different substances in solution, and 
 its properties vary singularly according to 
 the number and the proportion of these sub- 
 stances. It is the same with what exhales 
 from flaming volcanos, red lava flowing 
 into water, and from sulphureous mineral 
 waters. It will be shown hereafter, that 
 these gases are rather different species of 
 inflammable gases, of which hydrogen gas 
 indeed'constitutes the base, but in which 
 this gas is the solvent of many different 
 matters, and in various proportions. 
 
 Hydrogen gas is the lightest species of 
 ponderable matter yet known. It can be 
 procured only from water, of which it forms 
 an essential constituent. The method of 
 procuring it is as follows. Into a phial or 
 gas bottle C, 
 
 furnished with a bent tube B, which is 
 ground to fit the mouth of the phial ; 
 put some pieces of pure re-distilled zinc, or 
 harpsichord iron wire, and pour on them 
 sulphuric acid, diluted with five times its 
 bulk of water. An effervescence will en- 
 sue, occasioned by the decomposition of 
 the water, and disengagement of hydrogen, 
 which may be collected in the pneumatic 
 apparatus. For very accurate researches, 
 it must be received in jars over mercury, 
 and exposed to the joint action of dry r^u- 
 riate of lime, and a low temperature. It is 
 thus freed from hygrometric water. In 
 this state its specific gravity is 0-0694, at 
 60° F. and 30 inches of barom. pressure. 100 
 cubic inches weigh 2,118 grains. It is there- 
 fore about 14-4 times less dense than com- 
 mon air; 16 times less dense than oxygen : 
 and 14 times less dense than azote. When 
 it stands over water at 60°, its sp. gr. ac- 
 quires an increase of nearly one-seventh ; 
 and it becomes about 0-0790. From the 
 great rarity of hydrogen gas, it is employed 
 for the purpose of inflating varnished silk 
 
 bags, which are raised in the air, under the 
 name of balloons. 
 
 This gas is colourless, and posssssed of 
 all the physical properties of air. It has 
 usually a slight garlic odour, arising pro- 
 pably from arsenical particles derived from 
 the zinc. When water is transmitted over 
 pure iron in a state of ignition, it yields hy- 
 drogen gas free from smell. It is eminently 
 combustible, and, if pure, burns with a 
 yellowish- white flame ; but from accidental 
 contamination, its flame has frequently a 
 reddish tinge. If a narrow jar, filled with 
 hydrogen, be lifted perpendicularly, with 
 the bottom upwards, and a lighted taper 
 be suddenly introduced, the taper will be 
 extinguished, but the gas will burn at the 
 surface, in contactwith the air. Animal life is 
 likewise speedily extinguished by the respi- 
 ration of this gas, though Sir H.Davy has 
 shewn, that if the lungs be not previously 
 exhausted by a forced respiration, it may 
 be breathed for a fe w seconds without much 
 seeming inconvenience. 
 
 When five measures of atmospheric air 
 are mixed with two of hydrogen, and a 
 lighted taper, or an electric spark, applied 
 to the mixture, explosion takes place, three 
 measures of gas disappear, and moisture is 
 deposited on the inside of the glass. When 
 two measures of hydrogen, mixed with one 
 of oxygen, are detonated, the whole is con- 
 densed into water. Thus, therefore, we 
 see the origin of the name hydrogen, a term 
 derived from the Greek, to denote the wa- 
 ter-former. If a bottle, containing the ef- 
 fervescing mixture of iron and dilute sul- 
 phuric acid, be shut with a cork, having a 
 straight tube of narrow bore fixed upright 
 in it, then the hydrogen will issue in a jet, 
 which, being kindled, forms the philoso- 
 phical candle of Dr. Priestley. If a long 
 glass tube be held over the flame, moisture 
 will speedily bedew its sides, and harmo- 
 nic tones will then begin to be heard. Mr; 
 Faraday, in an ingenious paper inserted in 
 the 10th Number of the Journal of Science, 
 states, that carbonic oxide produces, by the 
 action of its flame, similar sounds, and that 
 therefore the effect is not due to the affec- 
 tions of aqueous vapour, as had formerly 
 been supposed. He shews, that the sound 
 is nothing more than the report of a conti- 
 nued explosion, agreeably to Sir H. Davy's 
 just theory of the constitution of flame. 
 Vapour of ether, made to burn from a small 
 aperture, produces the same sonorous effect 
 as the jet of hydrogen, of coal gas, or ole- 
 fiant gas, on glass and other tubes. Globes 
 from seven to two inches in diameter, with 
 short necks, give very low tones ; bottles, 
 Florence flasks, and phials, always suc- 
 ceeded ; air jars, from four inches diameter 
 to a very small size, may be used. Some 
 irregular tubes were constructed of long 
 narrow slips of glass and wood, placing 
 
THE ARTISAN. 
 
 75 
 
 three or four together, so as to form a tri - 
 angular or square tube, tying them round 
 with pack-thread. These held over the 
 hydrogen jet, gave distinct tones. 
 
 Hydrogen, combined with oxygen, forms 
 water — - 
 
 W ith Chlorine . muriatic acid, 
 
 Iodine _ . . hydriodic acid, 
 
 Prussine . prussic acid, 
 
 Carbon . . sub-carb. and carb. hydr. 
 Azote . . ammonia, 
 
 Phosphorus subphos, & subsul. hydr. 
 Sulphur . sulph. and subsul. hydr. 
 Arsenic . arsenuretted hydrogen, 
 Tellurium telluretted hydrogen, 
 Potassium potassuretted hydrogen. 
 
 In the Philosophical Magazine, we have 
 the following notice of the effect of hydro- 
 gen gas on the voice : “ The Journal Bri- 
 tannique, published at Geneva by Prevost, 
 contains the following article : ‘ Maunoir 
 was one day amusing himself with Paul at 
 Geneva, in breathing pure hydrogen gas. 
 He inspired it with ease, and did not per- 
 ceive that it had any sensible effect on him, 
 either in entering or passing out of his lungs. 
 But after he had taken in a very large dose, 
 he was desirous of speaking, and was 
 astonishingly surprised at the sound of his 
 voice, which was become soft, shrill, and 
 even squeaking, so as to alarm him. Paul 
 made the same experiment on himself, and 
 the same effect was produced. I do not 
 know whether any thing similar has 
 occurred in breathing any of the other 
 gases/" 
 
 OF CARBON. 
 
 The name of Carbon has been given by 
 the French chemists, to a simple or unde- 
 composed matter, abundantly contained in 
 the different known species of coal, but 
 which it 'is very essential should not be 
 confounded with what is properly called 
 charcoal. This last substance is most fre- 
 quently a black matter, which remains after 
 the partial decompositions of vegetable or 
 animal substances, effected by nature or by 
 art. Besides the carbon which it conceals 
 in its composition, it is loaded with many 
 other substances which are foreign to car- 
 bon, and cannot completely be separated 
 but by perfect combustion. 
 
 It is, therefore, necessary, in order to 
 form a proper notion of the nature of car- 
 bon, to adopt ideas similar to those which 
 were detailed in the preceding articles con- 
 cerning oxygen and hydrogen. Pure car- 
 bon does not exist in nature, nor has it yet 
 been produced by art, any more than the 
 bodies just mentioned ; or at least, if car- 
 bon exists pure, or insulated, in any part of 
 the globe, chemists have not yet discovered 
 it. But, notwithstanding this resemblance, 
 carbon differs materially from oxygen and 
 
 hydrogen ; namely, in this circumstance, 
 that it is never found united to caloric un- 
 der the gaseous form, and also that, even 
 in the state of charcoal, it may, at least, in 
 some species of the charcoals, be regarded 
 as nearer to its state of purity, and more 
 proper to exhibit the properties which cha- 
 racterise it, than these two bodies in any of 
 their combinations. 
 
 Carbon also differs essentially from oxy- 
 gen, for it is no where collected in such 
 great masses, though it is very abundant 
 among natural combinations. It is, un- 
 doubtedly one of the principles which na- 
 ture abundantly employs in the formation 
 of compounds: but it is never found com- 
 bined in a mass like oxygen gas. It ap- 
 pears, however, that though far from a state 
 of purity, if exists, at least, under the fossil 
 form in depositions, or beds, and veins, in 
 the interior of the globe. 
 
 Carbon is procured, not, however, pure 
 and separated from every other body, but 
 more or less approaching to purity, by de- 
 composing most vegetable substances, by 
 heat, especially ligneous, or woody bodies, 
 which contain a great quantity of it. From 
 these it is obtained in the state of charcoal. 
 The carbon is united with some foreign bo- 
 dies, and a little oxygen and hydrogen, the 
 volatilizing of all the evaporable substances 
 united with it in wood, constitutes the art 
 of the charcoal burner. The water, in which 
 trees are suffered to remain, produces the 
 same effect, but more slowly, upon the lig- 
 neous vegetable body. It gradually dis- 
 solves the different soluble materials of that 
 body, and leaves its charcoal free. 
 
 If a piece of wood be put into a crucible, 
 well covered with sand, and kept red hot 
 for some time, it is converted into a black 
 shining brittle substance, without either 
 taste or smell, well known under the name 
 of charcoal. Its properties are nearly the 
 same from whatever wood it has been ob- 
 tained, provided it be exposed for an hour 
 in a covered crucible to the heat of a forge. 
 
 Charcoal is insoluble in water. It is 
 not affected (provided thatallair and mois- 
 ture be excluded) by the most violent heat 
 which can be applied, excepting only that 
 it is rendered much harder and more bril- 
 liant. 
 
 It is an excellent conductor of electricity, 
 and possesses besides a number of singular 
 properties, which render it of considerable 
 importance. It is much less liable to pu- 
 trefy or rot than wood, and is not therefore 
 so apt to decay by age. This property has 
 been long known. It was customary among 
 the ancients to char the outside of those 
 stakes which were to be driven into the 
 ground or placed in water, in order to pre- 
 serve the wood from spoiling. New-made 
 charcoal, by being rolled up in cloths which 
 have contracted a disagreeable odour, el- 
 
76 
 
 THE ARTISAN. 
 
 fectually destroys it. When boiled with 
 meat beginning to putrefy, it takes away 
 the bad taint. It is perhaps the best teeth 
 powder known. Mr. Lowitz of Peters- 
 burgh has shewn, that it maybe used with 
 advantage to purify a great variety of sub- 
 stances. 
 
 New-made charcoal absorbs moisture 
 with avidity ; when heated to a certain 
 temperature, it absorbs air copiously. La 
 Metherie plunged a piece of burning char- 
 coal into mercury, in order to extinguish 
 it, and introduced it immediately after into 
 a glass vessel filled with common air. The 
 charcoal absorbed four times its bulk of 
 air. On plunging the charcoal into water, 
 one-fifth of this air was disengaged. This 
 air, on being examined, was found to con- 
 tain a much smaller quantity of oxygen 
 than atmospherical air does. He extin- 
 guished another piece of charcoal in the 
 same manner, and then introduced it into 
 a vessel filled with oxygen gas. The quan- 
 tity of oxygen gas absorbed amounted to 
 eight times the bulk of the charcoal ; a 
 fourth part of it was disengaged on plung- 
 ing the charcoal into water. 
 
 This property of absorbing air, which 
 new-made charcoal possesses, was ob- 
 served by Fontana, Priestley, Scheele, and 
 Morveau ; but Morozzo was the first phi- 
 losopher who published an accurate set of 
 experiments on the subject. 
 
 These experiments have been lately re- 
 peated upon a larger scale by Mr. Rouppe, 
 professor of chemistry at Rotterdam, and 
 Dr. Van Noorden of the same city. They 
 filled a copper box, which was made air- 
 tight, with red-hot charcoal, allowed it to 
 cool under water, and then introduced it 
 into a glass jar full of air. Seventeen cubic 
 .nches of charcoal absorbed, in five hours, 
 *48 cubic inches of air, or | nearly of its 
 bulk. This absorption, though much more 
 considerable than could have been ex- 
 pected from former experiments, has since 
 been confirmed by several chemists. 
 
 When charcoal is heated to about 802°, 
 or when it is made nearly red hot, and then 
 plunged into oxygen gas, it takes fire ; and, 
 provided it has been previously freed from 
 the earths and salts which it generally 
 contains, or if we employ lamp black, which 
 is charcoal nearly pure, it burns without 
 leaving any residuum. But the air in which 
 the combustion has been carried on has al- 
 tered its properties very considerably, for 
 it has become so noxious to animals that 
 they cannot breathe it without death If 
 small pieces of dry charcoal be placed up- 
 on a pedestal, in a glass jar tilled with 
 oxygen gas, and standing over mercury, 
 they may be kindled by means of a burn- 
 ing glass, and consumed. The bulk of the 
 gas is not sensibly altered by this combus- 
 tion, but its properties are greatly changed. 
 
 A great part of it will be found converted 
 into a new gas quite different from oxygen. 
 This new gas is easily detected by letting 
 up lime-water into the jar; the lime-water 
 becomes milky, and absorbs and condenses 
 all the new-formed gas. This new gas has 
 received the name of carbonic acid. Mr. 
 Lavoisier ascertained, by a very laborious 
 set of experiments, that it is precisely equal 
 in weight to the charcoal and oxygen 
 gas. 
 
 Carbon, when pure and free from the 
 foreign substances with which it is united 
 in charcoals, appears to exist under the 
 form of solid particles, of a black so de- 
 terminate, as would lead us to think that 
 it is essentially of that colour, and that it 
 communicates it to a number of other bo- 
 dies. It is the excess of carbon, as will be 
 noticed hereafter, which produces the 
 greater part of vegetable colours, and which 
 also renders them durable and intense. It 
 appears also that it gives the same shade 
 in some mineral compounds, of which it 
 forms an essential part. 
 
 But there are, nevertheless, reasons for 
 thinking that the black colour of charcoals 
 is not a true character of carbon , and that 
 it accompanies its union with a small por- 
 tion of oxygen and hydrogen, from which, 
 in its state of charcoal, it is never exempt. 
 
 The diamond which, under certain rela- 
 tions, nearly approaches to pure carbon, is 
 so much the more white and transparent as 
 it is less altered by foreign substances. 
 
 Carbon has neither taste nor smell, and 
 its particles never possess an adherence 
 sufficiently strong to prevent their being 
 very brittle ; this brittleness is also greater 
 in charcoals as the carbon is more conta- 
 minated with other bodies. It is probable 
 that the particles of carbon always remain 
 at a very great distance from each other. 
 They do not possess the property of dis- 
 posing themselves regularly, and never 
 permit it to assume a crystaline form in the 
 state of charcoal, although it is highly 
 probable that it is capable of this arrange- 
 ment when very pure. 
 
 ASmONOMY. 
 
 THE SOLAR SYSTEM. 
 
 The Solar, or true system of the world, as 
 already observed, was taught by Pythago- 
 ras ; but aftewards lost till the time of 
 Copernicus, who again revived it, and from 
 this circumstance it is often called the 
 Copernican System.* 
 
 In this system, the Sun is placed nearly 
 in the centre of the orbits of all the planets 
 
 * From the labours of Sir Isaac Newton to esta- 
 blish the system of Copernicus, it is sometimes 
 called the Neivtonian system. 
 
THE ARTISAN. 
 
 77 
 
 and comets ; and in these orbits they per- 
 form their revolutions round the Sun in 
 their respective periodic times. The num- 
 ber of planets at present known to belong 
 to the solar system is 29, of which 11 are 
 Primary, and 18 Secondary. 
 
 The Primary planets are those that cir- 
 culate round the Sun as their centre, viz. 
 Mercury, Venus, the Earth, Mars, Jupiter, 
 Saturn, Uranus or Georgium Sidus, Ceres, 
 Pallas, Juno, and Vesta. See the following 
 Figure.* 
 
 The first six were known to the ancients, 
 and are therefore called the old planets. 
 The five last have been discovered since the 
 year 1781, and are often called the new 
 planets. 
 
 Those planets that have their orbits in- 
 cluded within the Earth’s orbit, are called 
 Inferior , and those without the orbit of 
 the Earth, are called Superior planets. 
 
 The Moon is a secondary belonging to 
 the Earth, and circulates round it while the 
 Earth continues its annual course round 
 the Sun. Jupiter has four secondaries or 
 satellites revolving round him ; Saturn has 
 seven ; and Uranus has six. 
 
 The orbits or paths in which the Primary 
 Planets perform their revolutions round 
 the Sun, and the Secondaries round their 
 
 Primaries, are not exactly circles, but El- 
 lipses or Ovals.f 
 
 Now, though this be the form of the or- 
 bit which the planet describes, yet the place 
 
 * This figure represents the order in ■which 
 these planets move round the sun ; but the circles 
 which represent the respective orbits, do not show 
 the proportioned distance of each planet from the 
 sun. To do this accurately would require a very 
 large figure. By mistake Saturn is here represented 
 to have only six satellites instead of seven. 
 
 f If the two ends of a thread be tied together and 
 thrown loosely over two pins stuck in a table, as S 
 and F,fig. next page, and if the thread be moderately 
 stretched by the point of a pen or black lead pencil, 
 and carried round the pins by an even motion and 
 slight pressure of the hand, an ellipse or oval will 
 be described ; the points A and P , where the pins 
 were fixed, are called the foci or focuses of the el- 
 lipse. The figure described will be the more ellip- 
 tical the tighter the thread is to the pins in the foci. 
 
78 
 
 THE ARTISAN. 
 
 of the Sun is not in the centre of the orbit, 
 but in one of the Foci, as at S. 
 
 When the planet is at F, it is then nearest 
 the Sun, and is said to be in its Perihelion. 
 In moving from P, its distance from the Sun 
 gradually increases till it reaches the oppo- 
 site point A, when it is at its greatest distance 
 from the Sun, and is then said to be in its 
 Aphelion. When it arrives at the points B 
 and D, it is said to be at its Mean Distance. 
 The straight line AP, which joins the pe- 
 rihelion and aphelion, is called the line of 
 the Apsides, and sometimes the greater 
 axis or the transverse axis of the orbit. 
 The line B D, joining the points of mean 
 distance, is called the Conjugate or lesser 
 axis : SB or SD, the planet’s mean distance 
 from the Sun; SC or FC, the Eccentricity 
 of the orbit, or the distance of the Sun from 
 its centre ; S the lower Focus, or that in 
 which the Sun is placed ; F the higher Fo- 
 cus ; P the lower Apsis, and A the higher 
 Apsis. Though the Primary Planets have 
 all nearly the same common focus in which 
 the Sun is situated, yet they have not all 
 the same degree of ellipticity. Most of 
 them deviate but little from the circular 
 form, and none of them so much as the 
 last figure. The orbits of the dilferent pla- 
 nets do not all lie in the same plane, as they 
 appear to do when represented on paper. 
 
 If the Earth’s orbit be supposed to be a 
 thin solid plane, and to be extended in 
 every direction, it will mark out a line in 
 the starry heavens, which is called the 
 EclijAic, and the plane itself is called the 
 Plane of the Ecliptic. The orbits of all the 
 other planets lie in planes dilferent from 
 this plane ; but the one half of each orbit 
 rises above it, and the other falls below 
 it,* consequently the orbit of each planet 
 crosses the ecliptic in two opposite points, 
 which are called the planet’s Nodes. These 
 
 * The angle which each orbit makes with the 
 plane of the ecliptic, is called the inclination of the 
 orbit. The orbit of Mercury is inclined 7® to the 
 plane of the ecliptic; Venns 3® 23' ; Mars 1° 51"; 
 Jupiter IS 19"; Saturn 2 s * 30': Uranus 0® 46^'; 
 Ceres 10® 37' ; Pallas 34® 50' ; Juno 21® ; and Vesta 
 7® 9'. The orbits of all the old planets are included 
 in the zodiac, which is a belt or zone in the heavens, 
 extending about 8® on each side of the ediptic : but 
 the orbits of the new planets are without tike zodiac. 
 
 nodes are alhin different parts of the Eclip- 
 tic, and therefore if the planetary tracks 
 remained visible in the heavens, they would 
 in some measure resemble the differentruts 
 of waggon wheels crossing each other in 
 various parts, but never going far asunder. 
 That node or intersection where the orbit 
 ascends above the ecliptic, is called the 
 ascending node, and the other, which is 
 directly opposite to it, is called the descend- 
 ing node 
 
 While the primary planets are perform- 
 ing their revolutions round the Sun, and 
 the secondaries round their primary pla- 
 nets, they have all a motion from west to 
 east round an imaginary line passing 
 through their centres, called their axes. 
 The axis of some of the planets is much 
 more inclined to the axis of its orbit than 
 others, and on this depends the change of 
 seasons in the planet ; * for the more the 
 axis of any planet is inclined to the axis of 
 its orbit, the greater will be the variety of 
 its seasons.t The extremities of the axis 
 of any planet nre called its Poles. That 
 which points towards the northern part of 
 the heavens is called the North Pole, and 
 the other pointing towards the southern 
 part is called the South Pole. 
 
 As the Earth turns round its axis in 24 
 hours, the heavens wdll appear to make a 
 complete revolution in that time : and to a 
 spectator on any of the other planets, this 
 revolution will seem to be performed in the 
 time which this planet takes to perform a 
 revolution on its axis, which is called the 
 length of the planet’s day. 
 
 As it is necessary to have some method 
 by which the position of any celestial body 
 may be determined at any time, or its dis- 
 tance from some known point, astronomers 
 have fixed on the Ecliptic or Earth’s orbit 
 for this purpose, as well as for reckoning 
 from it the inclination of the planetary 
 orbits. The line of the Equinoxes, or tha t 
 line in which the Earth’s equator, when ex- 
 tended to the heavens, cuts the Ecliptic 
 (being always in the plane of the Ecliptic) 
 must mark out two points of that line traced 
 among the stars ; and from one of these 
 points astronomers reckon the distances 
 on the ecliptic. This point is called the 
 vernal Equinox, because the Sun appears 
 in it about the middle of Springorthe 20th 
 of March; its opposite is called the au- 
 tumnal Equinox, the Sun being in it about 
 the middle of Autumn, or the 23d of Sep- 
 tember. 
 
 The Ecliptic is supposed to be divided 
 into twelve equal parts, called signs, of 80 
 
 * The axis of the Earth is inclined 23® 2S' to the 
 axis of its orbit, which is the cause of the different 
 lengths of the days, and variety of the seasons. 
 
 t The axis of the orbit of any planet is a straight 
 line perpendicular or at right angles to the orbit. 
 
THE ARTISAN. 
 
 79 
 
 degrees each. Their names and characters 
 are the following. 
 
 Aries . . . 
 
 . nr 
 
 Libra . . . . 
 
 5 -A- 
 
 Taurus . . 
 
 • 8 
 
 Scorpio . . . 
 
 • m. 
 
 Gemini . . 
 
 . H 
 
 Saggittarius . 
 
 • t 
 
 Cancer . . . 
 
 . SB 
 
 Capricornus. 
 
 • V? 
 
 Leo .... 
 
 . a 
 
 Aquarius . . 
 
 
 Virgo . . . 
 
 . tiji 
 
 Pisces . - . . 
 
 X 
 
 The Longitude of all the heavenly bodies 
 
 is reckoned eastward on the ecliptic from 
 the vernal equinox (where the sign Aries 
 begins) quite round the heavens. 
 
 The Latitude of any celestial body is 
 reckoned from the ecliptic, north and south ; 
 but its Declination is counted from the 
 Equinoctial, in a similar manner. 
 
 The Right Ascension of any celestial bo- 
 dy is reckoned on the equinoctial from the 
 vernal equinox, or the first point of Aries, 
 eastward quite round the heavens. 
 
 Instead of the Vernal Equinox, astrono- 
 mers sometimes find it convenient to count 
 the distance of a planet from its Aphelion. 
 This distance is called the true Anomaly of 
 the planet. 
 
 OF THE SUN. 
 
 The Sun is the largest body yet known 
 in the universe. His diameter is 887,693 
 English miles ; his circumference 2,800,000, 
 and his bulk is above 1,400,000 times 
 greater than the Earth. Although the 
 Sun be the fixed centre of the universe, he 
 has been discovered to have a motion 
 round his axis in 25 days 10 hours, and 
 another round the centre of gravity of the 
 planetary motions. The motion round his 
 axis was discovered by Galileo in the year 
 1611. 
 
 When the Sun is examined with a tele- 
 scope of a tolerable magnifying power, and 
 a piece of dar] glass interposed to prevent 
 his rays from hurting the eye, a number of 
 dark Spots, of various forms and magni- 
 tudes, are frequently perceived on his disc. 
 These spots are sometimes so very large as 
 to be perceptible with the naked eye. The 
 nature and formation of the Solar Spots 
 have been the subject of much speculation 
 and conjecture. Some astronomers have 
 affirmed that the Sun is an opaque body, 
 mountainous and uneven like the Earth, 
 and covered all over with a fiery and lumi- 
 nous fluid : that this fluid ebbs and flows 
 after the manner of our tides, so as some- 
 times to leave uncovered the tops of rocks 
 or hills, which appear like black Spots, 
 and that the nebulosities about them are 
 caused by a kind of froth. Others have 
 imagined, that the fluid which sends us so 
 much light and heat contains a nucleus or 
 Solid globe, wherein are several volcanoes, 
 which, like iEtna or Vesuvius, from time 
 to time, cast up quantities of bituminous 
 matter to the surface of the Sun, and form 
 those Spots that are perceptible on his disc ; 
 
 and that this matter is gradually consumed 
 by the luminous fluid, and then the Spots 
 disappear for a time, but are seen to rise 
 again in the same places when those vol- 
 canoes cast up new matter. A third opi- 
 nion is, that the Sun consists of a fiery lu- 
 minous fluid, wherein are immersed several 
 opaque bodies of irregular shapes; and 
 that these bodies, by the rapid motion of 
 the Sun, are sometimes buoyed or raised 
 up to the surface, where they form the ap- 
 pearance of Spots, which seem to change 
 their shapes according as different sides of 
 them are exposed to our view. A fourth 
 opinion is, that the Sun consists of a fluid 
 in continual agitation ; that, by the rapid 
 motion of this fluid, some parts more gross 
 than the rest, are carried up to the surface 
 of the luminary, like the scum of melted 
 metal rising up to the top in a furnace ; 
 and that these scums, as they are differently 
 agitated by the motion of the fluid, form 
 themselves into those Spots that are visible 
 on the solar disc. 
 
 Dr. Kerschel supposes the Sun an opaque 
 body like the planets, surrounded by an at- 
 mosphere of a phosphoric nature, with a 
 number of luminous clouds floating on it; 
 and that the dark nucleus of the Spots are 
 occasioned by the opaque body of the Sun 
 appearing through openings in his Atmos- 
 phere. 
 
 The late Dr. "Wilson of Glasgow has ad- 
 vanced a new opinion respecting the solar 
 Spots. He supposes, with great appear- 
 ance of truth, that they are depressions ra- 
 ther than elevations ; and that the dark 
 nucleus of every Spot is the opaque body 
 of the Sun seen through an opening in the 
 luminous Atmosphere with which he is 
 surrounded. 
 
 Amidst all these conjectures, we are still 
 left in uncertainty: for there appears little 
 in any of them to entitle it to a superioritl 
 over the other. In one particular they aly 
 agree ; namely, that the Sun is either com - 
 posed of, or surrounded by, some very 
 powerful heating substance ; but w hat that 
 substance is, or how it is maintained, they 
 are all at a loss to determine. Many expe- 
 riments have been made, both in this coun- 
 try and on the continent, to determine the 
 Heat of the Sun, or the intensity of his rays, 
 when concentrated in the focus of a lens, 
 or by reflecting mirrors. Among these may 
 be mentioned the experiments made by 
 Dr. Harris and Dr. Desaguliers, with a 
 mirror constructed by Mr. Vilette. It was 
 3 feet 11 inches in diameter, and its focal 
 distance was 3 feet 2 inches. A fossil shell 
 was calcined by it in 7 seconds, copper ore 
 vitrified in 8 seconds ; iron ore melted in 
 24 seconds : talc began to calcine in 40 
 seconds ; a great fish’s tooth melted in 32^ 
 seconds ; a silver sixpence melted in 
 seconds ; a copper halfpenny melted in 20 
 
THE ARTISAN. 
 
 seconds ; tin melted in 8 seconds ; oast iron 
 in 16 seconds ; slate melted in 3 seconds ; 
 bone was calcined in 4 seconds. So power- 
 ful are the Sun’s rays when condensed by 
 burning glasses, that it is said Archimedes 
 set fire to the Roman fleet at the siege of 
 Syracuse by a combination of these glasses ; 
 and Buffon, in the year 1747, constructed 
 a reflecting mirrof -of 168 plane glasses, 
 moveable on hinges, with which he set 
 w ood on fire at the distance of 150 feet, and 
 melted lead at 145 feet. 
 
 To be continued. 
 
 i&tsceltoous Subjects. 
 
 SOLUTIONS OF QUESTIONS, 
 
 In No. III. 
 
 To the Editor of the Artisan. 
 
 Sir, — In the third number of your ex- 
 cellent publication, there is a question, by 
 Andrew Asker, requiring the height to 
 which a balloon, containing 10,000 cubical 
 feet, and loaded with 350 pounds, will as- 
 cend : I have solved the question, and en- 
 closed the solution, which if you think 
 proper to insert in your next number, will 
 oblige, sir, &c. &c. Lunardi. 
 
 Let y be the specific gravity of the stra- 
 tum, of air in which the balloon floats, when 
 af its greatest height ( water being unity ); 
 then, since a cubic foot of water weighs 
 62*48 lbs. avoirdupois, at the temperature 
 of 60°, the weight of the air displaced, or 
 force tending to support the balloon, is 
 62*48 X 10000 X y , or 624800 y. But the 
 whole weight of the balloon is 350 -f- 
 
 y 
 
 (62-48 x 10,000) X — , and therefore, when 
 
 the balloon is just supported, and has no 
 tendency to ascend, 624800 y — 350 + 
 
 y 
 
 (62*48 X 10,000) X — , consequently y ~ 
 
 13 
 
 455 
 
 , or *00052017, the density of the 
 
 874720 J 
 
 air at the greatest height the balloon will 
 reach. And assuming the density or elas- 
 ticity of the air at the surface of the earth 
 to be *0015224 (as it has been found to be 
 when the barometer stands at 30 inches) 
 the height is determined by the rules for 
 barometric measurement ; and in the pre- 
 sent case I shall apply the rule given at 
 page 33 of the u Artisan,” as it is less com- 
 plex than any other. 
 
 The height of the mercury in the baro- 
 meter being directly proportional to the 
 density of the air, the height of the mer- 
 cury at the balloon is determined, (sup- 
 posing it 30 inches at the surface) thus 
 105224 : 52017 : : 30 : 14 83, 
 
 Then 30 
 14.83 
 
 44*83 : 15*17 : : 52*000 : 17.596*3 feet, 
 which is only the approximate height ac- 
 cording to the rule ; but the correction to 
 be applied on account of the expansion of 
 the air is not necessary in the present ex- 
 ample, as the question states that the air 
 is to be considered “ under the same com- 
 pression.” 
 
 I have, however, computed the correc- 
 tion, by first determining the temperature 
 of the balloon, when highest, by the for- 
 mula at page 33, 1st col. of the “ Artisan,” 
 and found it to be 1801*6 feet; therefore 
 the whole height is 17596-3 -j- 1807-6 ~ 
 19397-9 feet. 
 
 TRIGONOMETRICAL SURVEY OF 
 GREAT BRITAIN. 
 
 It appears from a memoir lately read 
 before the Royal Society, that the result of 
 the Trigonometrical Survey of Altitudes in 
 Great Britain, relatively to the different 
 sections of the meridian, has not yet been 
 verified in a manner so satisfactory as 
 could be wished. 
 
 In order to rectify the anomalies which 
 some of the calculations present, and par- 
 ticularly in the one which respects Arbury 
 Hill, Northamptonshire, Sir B. Bevan(the 
 author of the memoir) has determined the 
 altitude of that station, by the process of 
 leveling with the greatest care, to theGrand 
 Junction Canal. From this he deduced the 
 altitudes of the greater part of the import- 
 ant points in the counties of Northampton, 
 Buckingham, and Bedford ; the latitude , 
 by these calculations, is found 5" less than 
 that given by the zenith sector, which renders 
 it highly probable that the difference is pro- 
 duced by the local attraction of the moun- 
 tains to the south of that station. 
 
 The altitude of the Grand Junction Ca- 
 nal near Tring, is, according to him, 402 
 feet above the level of the sea at low spring 
 tides, which gives 740| for the altitude of 
 Arbury Hill, in place of 804, as stated in 
 the Survey. Sir B. has also rectified the 
 altitudes of various other stations, which 
 he found notperfectly correct. But itought 
 to be remembered, that in operations of this 
 kind, the accuracy of the results depends 
 much upon the goodness of the instruments 
 employed in the operation. 
 
THE ARTISAN-, 
 
 81 
 
 &EOMETB>ir. 
 
 PROPOSITION XI. 
 
 Problem. — To draw a straight line at right 
 angles or 'perpendicular to a given straight 
 line, from a given point in the same. 
 
 Let A R be a given straight lino, and C 
 a point given in it : it is required to draw 
 a straight line from the point C at right 
 angles to A B. 
 
 Take any point B in A C, and make C E 
 
 
 equal to C I), and upon D E describe the 
 equilateral triangle DFE, and join F C ; 
 the straight line F C drawn from the 
 given point C, is at right angles to the 
 given straight line A B. 
 
 Because D C is equal to C E, and F C 
 common to the two triangles J) C F, E C F, 
 the two sides D C, C F, are equal to the 
 two EC, CF, each to each ; but the base DF 
 Is also equal to the base E F ; therefore 
 the angle D C F is equal to the angle ECF ; 
 hnd they are adjacent angles. But when 
 the adjacent angles which one straight line 
 makes with another straight line are equal 
 to one another, each of them is called a 
 right angle ; therefore each of the angles 
 DCF, ECF, is a right angle. Where- 
 fore, from the given point C, in the given 
 straight line A B, F C has been drawn at 
 right angles to AB. Which was to be 
 done. 
 
 PROPOSITION XII. 
 Problem. — To draw a straight line at right 
 angles ( or perpendicular J to a given 
 straight line of an unlimited length from 
 a given point without it. 
 
 Let A B be a given straight line, which 
 may be produced to any length both ways, 
 
 C 
 
 and let C be a point without it. It is 
 required to draw a straight line perpen- 
 dicular to A B from the point C. 
 
 Take any point D upon the other side of 
 A B, and from the centre C, at the distance 
 C D, describe the circle EGF meeting AB 
 in F G : and bisect F G in H, and join CF, 
 C H, C G ; the straight line C H, drawn 
 from the point C, is perpendicular to the 
 given atraight line A B. 
 
 Because F H is equal to H G, and H C 
 common to the two triangles F H C, GH C, 
 the two sides F H, H C are equal to the 
 two GH, H C, each to each ; now the base 
 C F is also equal to the base C G ; there- 
 fore the angle C H F is equal to the angle 
 C H G: and they are adjacent angles ; but 
 when a straight line standing on a straight 
 line makes the adjacent angles equal to 
 one another, each of them is a right angle, 
 and the straight line which stands upon 
 the other is called a perpendicular to it ; 
 therefore from the given point C a perpen- 
 dicular CH has been drawn to the given 
 straight line AB. Which was to be done. 
 
 PROPOSITION XIII. 
 Theorem.' — The angles ivhich one straight 
 line makes ivith another upon the one side 
 of it, are either two right angles, or are to- 
 gether equal to two right angles. 
 
 Let the straight line A B make with CD, 
 upon one side of it, the angles CBA , ABD ; 
 these are either two right angles, or are 
 together equal to two right angles. 
 
 A. 
 
 O B C 
 
 For if the angle C B A be equal to A B D, 
 each of them is a right angles but, if not, 
 
 E 
 
 G 
 
82 
 
 THE ARTISAN. 
 
 from the point B draw B E at right angles 
 to C D : therefore the angles CBE, E B D 
 are two right angles. Now, the angle 
 CBE is equal to the two angles CBA, 
 ABE together ; add the angle E B D to 
 each of these equals, and the two angles 
 CBE, E B D will be equal to the three 
 CBA, ABE, E B D. Again, the angle 
 DB A is equal to the two angles D B E, 
 E B A ; add to each of these equals the 
 angle ABC; then will the two angles 
 X> B A, A B C be equal to the three angles 
 DBE, E B A, ABC: but the angles 
 C B E, E B I) have been demonstrated to 
 be equal to the same three angles ; and 
 things that are equal to the same are equal 
 to one another : therefore the angles CBE, 
 EBB are equal to the angles DBA, ABC ; 
 but CBE, EBD are two right angles ; 
 therefore DBA, ABC are together equal 
 to two right angles. Wherefore, when a 
 straight line, &c. Q E D. 
 
 Learners are generally perplexed with 
 demonstrations of which they cannot pre- 
 viously understand something of the plan 
 and scope, and with none more frequently 
 than that of this proposition. Let such as 
 find it difficult, observe, first, that CBE, 
 EBD are, by construction , two right 
 angles ; secondly, that the three angles 
 CBA, ABE, EBD, are equal to the 
 above two, consequently to two right 
 angles ; and, thirdly, that the two given 
 angles DBA, ABC are equal to the last- 
 mentioned three, consequently to the fore- 
 mentioned two, and therefore to two right 
 angles ; which was proposed to be proved. 
 
 Corollary. — Hence, if the angles A B D, 
 A B C be unequal, the greater is obtuse, 
 and the less acute ; the former being as 
 much greater than a right angle, as the 
 latter is less, as is evident from the pro- 
 position. 
 
 PROPOSITION XIV. 
 Theorem. — If, at a point in a straight line, 
 two other straight lines, upon the opposite 
 sides of it, make the adjacent angles toge- 
 gether equal to tivo right angles, these two 
 straight lines shall be in one and the same 
 straight line. 
 
 At the point B in the straight line A B, 
 let the two straight lines B C, B D upon 
 the opposite sides of AB, make the adjacent 
 angles ABC, ABD equal together to two 
 
 A 
 
 right angles. B D is in the same straight 
 line with C B. 
 
 For if B D be not in the same straight 
 line with C B, let B E be in the same 
 straight line with it; therefore, be- 
 cause the straight line A B makes angles 
 with the straight line CBE, upon one side 
 of it, the angles ABC, ABE are together 
 equal to two right angles ; but the angles 
 A B C, A B D are likewise together equal 
 to two right angles ; therefore the angles 
 DBA, ABE are equal to the angles 
 CBA, ABD: Take away the common 
 angle ABC, and the remaining angle 
 ABE is equal to the remaining angle 
 ABD, the less to the greater, which is 
 impossible ; therefore BE is not in the same 
 staight line with B C. And in like man- 
 ner, it may be demonstrated, that no other 
 can be in the same straight line with it but 
 C D, which therefore is in the same straight 
 line with C B. Wherefore, if at a point, 
 &c. Q.E.D. 
 
 PROPOSITION XV. 
 
 Theorem. — If two straight lines cut one 
 another, the vertical,- or opposite angles 
 shall be equal. 
 
 Let the two straight lines A B, C D cut 
 one another in the point E : the angle AEC 
 shall be equal to the angle DEB and CEB 
 to A E D. 
 
 For the angles C E A, A E D, which the 
 straight line A E makes with the straight 
 line C D, are together equal to two right 
 
 angles; and the angles A ED, DEB, 
 which the straight line DE makes with 
 the straight line AB, are also together 
 equal to two right angles : therefore the 
 two angles CEA, AED are equal to the 
 two A ED, DEB. Take away the com- 
 mon angle AED, and the remaining angle 
 C E A is equal to the remaining angle 
 DEB. In the same manner it can be de- 
 monstrated that the angles CEB, AED 
 are equal. Therefore, if two straight lines, 
 &c. Q. E. D. 
 
 Corollary 1 . — From this it is manifest, that 
 if two straight lines cut one another, the 
 angles which they make at the point of their 
 intersection, are together equal to four 
 right angles. 
 
 Corollary 2.— Apd hence, all the angles 
 
THE ARTISAN. 
 
 83 
 
 made by any number of straight lines 
 meeting in one point, are together equal to 
 four right angles. 
 
 PROPOSITION XVI. 
 Theorem. — If one side of a triangle be pro- 
 duced, the exterior angle is greater than 
 either of the interior, and opposite angles. 
 Let A B C be a triangle, and let its side 
 B C be produced to D, the exterior angle 
 A C D is greater than either of the interior 
 opposite angles C B A, B A C. 
 
 A F 
 
 equal to the angle C E F, because they are 
 vertical angles ; therefore the base A B is 
 equal to the base C F, and the triangle 
 A E B to the triangle C E F, and the re- 
 maining angles to the remaining angles, 
 each to each, to which the equal sides are 
 opposite; wherefore the angle BAE is 
 equal to the angle ECF; but the angle 
 ECD is greater than the angle ECF; 
 therefore the angle ECD, that is A C D, is 
 greater than BAE: In the same manner 
 if the side B C be bisected, it may be de- 
 monstrated that the angle BCG, that is 
 the angle A C D, is greater than the angle 
 ABC. Therefore, if one side,&c. Q.E.D. 
 
 PROPOSITION XVII. 
 
 Theorem. — Any two angles of a triangle 
 are together less than two right angles. 
 Let A B C be any triangle ; any two of 
 
 A 
 
 its angles together are less than two right 
 angles. 
 
 Produce B C to D ; and because A C D 
 is the exterior angle of the triangle ABC, 
 A C D is greater than the interior and op- 
 posite angle ABC; to each of these add 
 the angles A C B ; therefore the angles 
 A C D, A C B are greater than the angles 
 ABC, ACB; but A CD, ACB are to- 
 gether equal to two right angles ; there- 
 fore the angles A B C, BC A are less than 
 two right angles. In like manner, it may 
 be demonstrated, that BAC, ACB, as 
 also C A B, A B C, are less than two right 
 angles. Therefore any two angles, &c. 
 Q. E. D. 
 
 PROPOSITION XVIII. 
 Theorem. — The greater side of every tri- 
 angle has the greater angle opposite to it. 
 Let ABC be a triangle, of which the 
 side A C is greater than the side A B ; the 
 angle A B C is also greater than the angle 
 B C A. 
 
 and because A D B is the exterior angle of 
 the triangle B D C, it is greater than the 
 interior and opposite angle D C B ; but 
 A D B is equal to A B D, because the side 
 A B is equal to the side A D : therefore 
 the angle A B D is likewise greater than 
 the angle ACB; wherefore much more is 
 the angle A B C greater than ACB. There- 
 fore the greater side, &c. Q. E. D. 
 
 PROPOSITION XIX. 
 Theorem. — The greater angle of every tri- 
 angle is subtended by the greater side, or 
 has the greater side opposite to it. 
 
 Let A B C be a triangle, of which the 
 angle ABC is greater than the angle 
 
 A 
 
 B C A ; the side A C is likewise greater 
 than the side A B. 
 
84 
 
 THE ARTISAN. 
 
 For, if it be not greater, A C must either that exerts its force to raise that weight iff 
 be equal to A B, or less than it ; it is not fixed to the bone about one-tenth part as 
 equal, because then the angle ABC would far below the elbow as the hand is. And 
 be equal to the angle A C B ; but it is not ; the elbow being the centre round which 
 therefore A C is not equal to A B ; neither the lower part of the arm turns, the muscle 
 is it less ; because then the angle ABC must therefore exert a force ten times as 
 would be less than the angle A C B : but great as the weight that is raised, 
 it is not : therefore the side A C is not less By a careful consideration of the different 
 than A B ; and it has been shewn that it is kinds of levers, it will be perceived that in 
 not equal to A B ; therefore A C is greater the first kind, the fulcrum , or prop, is 
 than A B. Wherefore the greater angle, loaded with the sum of the forces, that is 
 
 &c. Q.E.D. 
 
 MECHA^flCSs 
 
 In the third species of lever the power 
 is between the weight and the prop. There- 
 fore if the weight and the power in the se- 
 cond kind of lever, be supposed to change 
 places, it will be one of the third kind. 
 Therefore, in order that there may be an 
 equilibrium between the power and the re- 
 sistance, the intensity of the power must 
 exceed the intensity of the weight, just as 
 many times as the distance of the weight 
 from the prop exceeds the distance of the 
 power from it. Thus, let E be the prop 
 of the lever A B, 
 
 and W a weight of four pounds, placed 
 three times as far from the prop as the 
 power P acts at F, by the cord C going 
 over the fixed pully D ; in this case, the 
 power must be equal to 12 pounds, in 
 order to support the weight. 
 
 As this kind of lever is a disadvantage to 
 the movingpower,itis never used but in cases 
 of necessity ; such as that of a ladder which 
 being fixed at one end, is by the strength 
 of a man’s arms reared against a wall. And 
 in clock work, where all the wheels may 
 be reckoned levers of this kind, because 
 the power that moves every wheel, except 
 the first, acts upon it near the centre of 
 motion, by means of a small pinion, and 
 the resistance it has to overcome acts 
 against the teeth, round its circumference. 
 
 To this sort of lever are generally re- 
 ferred the bones of a man’s arm ; for when 
 we lift a weight by the hand, the muscle 
 
 with the sum of the weight to be raised, 
 and the power applied to raise it ; and in 
 the second and third kind, with the differ- 
 ence of these forces. 
 
 If we would allo w for the weight of the 
 lever itself, we must suppose its weight to 
 be united in its centre of gravity, and to 
 act there as a third force, added to the 
 power or the resistance, according to the 
 side of the fulcrum on which it is placed. 
 
 If a weight W be sustained on a hori- 
 zontal plane by three props, (not in a 
 straight line,) the pressure on each will be 
 the same as if a single weight were laid on 
 it, so that the sum of all the three weights 
 were equal to W, and their common centre 
 of gravity the same with the centre of gra- 
 vity of that body. 
 
 Thus, if the props be A, B, C, 
 
 C 
 
 and if W be placed with the centre of gra- 
 vity at D, and if the lines A D G, B D F, 
 C D E, be drawn, the pressure 
 
 . . D G _ 
 on Ais-~ x W, 
 
 „ . D F 
 
 on B is — x W, 
 t>nCis^|x W. 
 
 When the point D coincides with the 
 centre of gravity of the triangle ABC, the 
 pressure on each of the props is the same. 
 
 If W be supported by more than three 
 props, the problem appears to be inde- 
 terminate, or to admit of inn umerable so- 
 lutions. 
 
THE ARTISAN. 
 
 65 
 
 Nevertheless, if the centre of gravity of 
 the body W , (as it rests on the plane,) be 
 the same with the centre of gravity of the 
 figure made by joining the tops of the props 
 by straight lines, the pressures on the props 
 are all equal to one another. 
 
 The lever is the simplest of the mecha- 
 nical powers, and appears to be the first 
 that was attempted to be explained. Ari- 
 stotle has treated of it in his Mechanical 
 Questions, and has even endeavoured to 
 reduce some other of the mechanical powers 
 to the lever. The first accurate explana- 
 tion, however, was given by Archimedes. 
 
 The compound lever is, where one lever 
 is made to turn another, and then an equi- 
 librium takes place, when the weight is to 
 the power as the product of all the arms, 
 taken alternately beginning with that to 
 which the power is applied, to the product 
 of all the other arms. 
 
 The common apparatus for raising a 
 draw-bridge, is a combination of a lever of 
 the first kind, with a lever of the second ; 
 the two levers are parallel, and remain in 
 equilibrio in all situations. 
 
 It has already been remarked, that the 
 bones of a man’s arm form a lever of the 
 third kind : but this mechanical power is 
 much employed in the construction of the 
 animal body,: The bone is the lever, the 
 
 muscle is the power, or rather the medium 
 through which the power acts, and the 
 joint is the fulcrum. The insertion of the 
 muscle, or the point to which the power is 
 applied, is usually nearer the joint or ful- 
 crum than the weight to be raised is. A 
 different structure might have produced 
 more strength, but would have diminished 
 the activity of the animal, and the velocity 
 of its motion. 
 
 OF THE WHEEL AND AXLE.. 
 
 The wheel and axle consists of a wheel 
 having a cylindric axis passing through its 
 centre, and moveable in two grooves. The 
 power is applied to the circumference of 
 the wheel, and the weight to the circum- 
 ference of the axle. An equilibrium in this 
 instrument takes place when the radius of 
 the wheel, multiplied into the power, is 
 equal to the radius of the axle multiplied 
 into the weight ; or when the power and 
 weight are inversely as the radii of the 
 circles to which they are applied.* 
 
 Let A B be a wheel, and C D its axle ; 
 and suppose the circumference of the 
 wheel to be eight times as great as the 
 circumference of the axle ; then, a power 
 P equal to one pound, hanging by the 
 cord I, which goes round the wheel, will 
 
 * It is supposed here, that the power and the 
 weight both act at right angles to the radius. 
 
 balance a weight W, of eight pounds, 
 hanging by the rope K, which goes round J 
 the axle. And, as the friction on the 
 pivots or gudgeons of the axle, is but 
 small, as small an addition to the power 
 will cause it to descend, and raise the 
 
 weight ; but the weight will rise with only 
 an eighth part of the velocity wherewith 
 the power descends, and consequently 
 through no more than an eighth part of an 
 equal space in the same time. If the wheel 
 be pulled round by the handles S, S, the 
 power will be increased in proportion to 
 their length. And by this means, any 
 weight may be raised as high as the ope- 
 rator pleases. 
 
 From considering this mechanical power 
 with some attention, it will be discovered 
 that it is nothing else but a lever, so con- 
 trived as to have a continued motion about 
 its fulcrum. The principle of the virtual 
 velocities is here obviously applicable, (see 
 page 55, col. 2.) If the power acts not at 
 tha circumference of the wheel, but at the 
 extremity of a hand-spike inserted in the 
 wheel, the distance of that extremity from 
 the centre of the axis is to be accounted the 
 radius of the wheel. To this sort of engine 
 belong all cranes for raising great weights, 
 and in this case, the wheel may have cogs 
 alL round it instead of handles, and a small 
 lantern or trundle may be made to work in 
 the cogs, and be turned by a winch ; which 
 will make the power of the engine to ex- 
 ceed the power of the man who works it, as 
 much as the number of revolutions of the 
 winch exceed those of the axle D, when 
 multiplied by the excess of the length of 
 the winch above the length of the semi- 
 diameter of the axle, added to the semi- 
 
86 
 
 THE ARTISAN. 
 
 diameter or half thickness of the rope K, 
 by which the weight is drawn up. Thus, 
 suppose the diameter of the rope and axle 
 taken together, to be 12 inches, and con- 
 sequently, half their diameters to be six 
 inches, so that the weight W will hang at 
 six inches perpendicular distance from be- 
 low the centre of the axle. Now, let us 
 suppose the wheel A B, which is fixed on 
 the axle, to have SO cogs, and to be turned 
 by means of a winch six inches long, fixed 
 on the axis of a trundle of eight staves or 
 rounds, working in the cogs of the wheel. 
 Here it is plain that the winch and trundle 
 would make ten revolutions for one of the 
 wheel AB, and its axis D, on which the 
 rope K winds in raising the weight W ; 
 and the winch being no longer than^the 
 sum of the semidiameters of the great axle 
 and rope, the trundle could have no more 
 power on the wheel, than a man could have 
 by pulling it round by the edge ; because 
 the winch would have no greater velocity 
 than the edge of the wheel has, which we 
 here suppose to be ten times as great as 
 the velocity of the rising weight ; so that, 
 in this case, the power gained would be as 
 ten to one. But if the length of the winch 
 be twelve inches, the power gained will be 
 as twenty to one : if eighteen inches 
 (which is long enough for any man to work 
 by) the power gained would be as thirty to 
 one ; that is, a man could raise 30 times as 
 much by such an engine as he could do by 
 his natural strength without it, because the 
 velocity of the handle of the winch would 
 be 30 times as great as the velocity of the 
 rising weight; the absolute force of any 
 engine being in proportion of the velocity 
 of the power to the velocity of the weight 
 raised by it. But then, just as much 
 power or advantage as is gained by the en- 
 gine, so much time is lost in working it. In 
 machines of this sort it is requisite to have 
 a racket wheel G on one end of the axle, 
 with a catch H to fall into its teeth ; which 
 will at any time support the weight, and 
 keep it from descending, if the workman, 
 through inadvertency or carelessness, quit 
 his hold whilst the weight is raising. And 
 by this means, the danger is prevented 
 which might otherwise happen by the run- 
 ning down of the weight when left at 
 liberty. 
 
 The capstan, the windlass, and other con- 
 trivances of a similar nature, are nothing 
 else than the wheel and axle adapted to 
 particular circumstances. 
 
 The mechanical contrivance called a 
 £rank, is a species of wheel and axle. If 
 the force which acts upon a crank presses 
 it directly down and up alternately, the 
 effect, compared with what would take 
 place if the force acted at right angles to 
 the arm of the crank all round, is as twice 
 
 the diameter of a circle to its circumfer- 
 ence, or as seven to eleven nearly. 
 
 The combination of wheels, so useful in 
 mechanics, are generally reducible to the 
 wheel and axle, the wheel which turns the 
 other is not always upon the same axis 
 with it. The motion, in such cases, is 
 communicated from the one wheel'to the 
 other, either by belts and straps passing 
 over the circumference of both, or by teeth 
 cut in the circumference of each, and 
 working in one another. 
 
 When one wheel moves another in either 
 of these ways, the velocities of their cir- 
 cumferences are equal ; and therefore their 
 angular velocities, or the number of revo- 
 lutions which they make in the same time, 
 are inversely as their radii. * 
 
 In combination of wheels communicating 
 motion to one another, it is usual to call 
 the smaller wheel, acted on by a larger one, 
 a pinion; and the teeth the leaves of it. Some- 
 times the smaller wheel is a cylinder, in 
 which the top and bottom are formed by 
 circles connected by staves inserted in them 
 at equal distances along their circumfer- 
 ences ; and it is then called a lantern, the 
 staves serving for teeth. It is usual also 
 to employ the wheels and pinions, as in the 
 following figure, 
 
 where A is a large wheel, driving a pinion 
 b on the same axle with the great wheel B ; 
 B acts on the pinion c, which is on the same 
 axle with the large wheel C : and C drives 
 the pinion d, &c. 
 
 When motion is communicated through 
 a number of wheels and pinions, the angu- 
 lar velocity of the first wheel is to the an- 
 gular velocity of the last pinion, as the 
 product made by multiplying together the 
 number of the teeth in every pinion, to the 
 product made by multiplying together the 
 number of the teeth in every wheel ; and 
 that same ratio, compounded with the ratio 
 of the radius of the last pinion, to the radius 
 of the first wheel, will give the ratio of the 
 power to the resistance when an equili- 
 brium takes place. 
 
 Suppose the wheel A to contain 40, B 
 30, and C 20 teeth ; and the pinion b 10, c 8, 
 and d 5 teeth, required the number of re- 
 
 * That is, the larger the wheel, the fewer revo- 
 lutions will it make. 
 
THE ARTISAN. 
 
 87 
 
 volutions made by the last pinion d, in the 
 time of the first wheel A making one revo- 
 lution ? 
 
 TT 40 X 30 >< 20 „ il 
 
 H ere — — q =: 60, the number re- 
 
 10 X o X o 
 
 quired. Again, to illustrate the latter part 
 of the proposition ; suppose the radius of 
 this pinion (d) to be 3 inches, and that of 
 the wheel 9 inches, required the ratio of 
 
 the power to the resistance, when an equi- 
 librium takes place? The ratio of the 
 pinion’s velocity being to that of the wheel 
 as 60 to 1, and the ratio of its radius to 
 that of t he wheel is §, or 1 to 3 ; therefore 
 (60 x 1)~3— 20 ; consequently the power 
 is to the resistance as 1 to 20, or a power 
 one-twentieth part of the resistance, will 
 in this case produce an equilibrium. 
 
 hitdrauucs.* 
 
 The pressure of fluids affords the means 
 of conveying them from one place to ano- 
 ther, although considerable inequalities in 
 the surface of the ground intervene be- 
 tween the places. Water, for example, 
 may be conveyed from a reservoir across a 
 
 on one side of the valley D, and a house 
 on the other, at which the water of the 
 spring is wanted ; if the house is found to 
 be lower than the spring, the water may 
 be conveyed to it, by an iron or leaden 
 pipe, proceeding from the spring, across 
 the valley, as represented in the above 
 figure. 
 
 The depth of the valley must, however, 
 be taken into consideration, in order to 
 make the pipe of sufficient strength to re- 
 sist the pressure of the water, which de- 
 pends entirely on its depth (see page 9, 
 col. 1.) If the lowest part of the valley 
 be considerably under the spring, the pipe 
 must be made very strong at the lowest 
 part, or else it will burst. 
 
 Where an uninterrupted declivity cannot 
 be obtained, it is necessary to employ 
 
 * Hydraulics is that branch of Hydrodynamics 
 which treats of the motion of incompressible fluids, 
 and the instruments and machines connected with 
 their motion (see page 8). This division of the 
 science commenced with the account of fluids 
 issuing through apertures, at page 57, but by mistake 
 was neglected to be inserted. 
 
 valley, or to any distance, either by means 
 of open canals, aqueducts, or closed pipes, 
 provided the reservoir be situated some- 
 what higher than the level of the place at 
 which it is wanted. 
 
 Thus, suppose there is a spring at A, 
 
 pipes, which may be bent upwards or 
 downwards at pleasure, provided that no 
 part of them be more than thirty-two 
 feet above the reservoir, and when the pipe 
 is once filled, the water will continue to 
 flow from the lower orifice ; but it is best 
 in all such cases to avoid unnecessary 
 angles ; for when the pipe rises and falls 
 again, a portion of the air, which is always 
 contained in water, is frequently collected 
 in the angle, and very materially impedes 
 the progress of the water through the pipe. 
 When the bent part is wholly below the 
 orifices of the pipe, this air may be dis- 
 charged by various methods. The ancients 
 used small upright pipes, called columnaria , 
 rising from the convexity of the principal 
 pipe to the level of the reservoir, and suf- 
 fering the air to escape without wasting 
 any of the water. It may, however, fre- 
 quently be inconvenient or impossible to 
 apply a pipe of this kind ; but the same 
 purpose maybe answered, by fixing on the 
 pipe a box containing a small valve, which 
 opens downwards, and is supported by a 
 float, so as to remain shut while the box is 
 
88 
 
 THE ARTISAN. 
 
 full of water, and to fall open when any 
 air is collected in it. Thus A, in the fol- 
 lowing figure, is a box of this kind, with 
 a valve, supported by a hollow ball, for 
 letting out air from pipes, when it is below 
 the level of the reservoir. 
 
 If the pipe were formed into a syphon, 
 having its flexure above both orifices, it 
 would be necessary to bend it upwards at 
 the extremities, in order to keep it always 
 full ; but in this case the accumulation of 
 the air would be extremely inconvenient, 
 since it would collect so much the more 
 copiously, as the water in the upper part 
 of the pipe would be more free from pres-* 
 sure ; and neither of the methods which 
 
 have been mentioned would be of any use 
 in extricating it. It has been usual in 
 such cases to force a quantity of water 
 violently through the pipe, in order to carry 
 the air with it ; but it might be still simpler 
 to have a pretty large vessel of water 
 screwed on to the pipe, which would not 
 be filled with air for a considerable time, 
 and which, when full, might be taken off 
 and replenished with water. This con- 
 trivance is represented by the following 
 figure, where B is a vessel of water, 
 screwed on for receiving the air, to be 
 replenished with water as it becomes 
 empty. 
 
 When the water from a reservoir is 
 conveyed in long horizontal pipes, of the 
 same aperture, the discharges made in 
 equal times are nearly in the inverse ratio 
 of the square roots of the lengths. 
 
 Thus, if there be two pipes of the same 
 aperture, one of which is 49 , and the other 
 36 feet long, the discharge from the former 
 will be to that from the latter, as the square 
 root of 49 to the square root of 36, or as 7 
 
 to 6 ; therefore, the quantity discharged 
 from the shorter pipe will be % of that dis- 
 charged from the larger one. It is here 
 supposed that the length of the pipes to 
 which this rule is applied, are not very 
 unequal ; and even then the rule only 
 affords an approximation not deduced from 
 principle, but derived immediately from 
 experiment. Bossut has given a table of 
 the actual discharges of water pipes, as far 
 as the length of 2340 toises, or 14950 
 English feet, but it is too extensive to be 
 inserted here. 
 
 If the quantity of water discharged by a 
 pipe of a given length, be known by ex- 
 periment, we may find, by the foregoing 
 proposition, the quantity discharged by a 
 pipe of any other length. The diminution 
 of velocity being greatest when the head 
 of water is small, we may conceive the 
 head of water to be reduced to such a 
 degree, that the velocity with which the 
 water enters the pipe is not sufficiently 
 powerful to overcome the resistance arising 
 from the friction upon the pipe, and the 
 mutual cohesion of the particles of water.* 
 In order to examine this point experi- 
 mentally, M. Bossut employed a head of 
 water only 16 lines, from which the water 
 flowed into two pipes whose length were a 
 hundred and eighty feet.t In this case, the 
 water was discharged in the form of a 
 narrow fillet, and the drops succeeded each 
 other almost as if they were insulated 
 bodies. Hence it follows, that in order to 
 have a perceptible and continuous dis- 
 charge from pipes, there should be a head 
 of water of about 20 lines in 180 feet. If 
 the current of water, however, be very 
 large, such a great declivity as this will 
 not be necessary. 
 
 Pipes are usually made of wood, of lead, 
 or of cast iron; but commonly of lead: 
 and of late tinned copper has been em- 
 ployed with considerable advantage. A 
 pipe of lead will bear the pressure of a 
 column of water 100 feet high, if its thick- 
 ness be one hundredth of its diameter, or 
 even less than this ; but when any alter- 
 nation of motion is produced, a much 
 stronger pipe is required: and it is usual 
 to make leaden pipes of all kinds far 
 thicker than in the above proportion. 
 
 The form and construction of stopcocks 
 and valves arc very various, according to 
 their various situations and uses. Stopcocks 
 usually consist of a cylindrical or conical 
 part, perforated in a particular direction, 
 
 * By a head of water is meant the perpendicular 
 depth of the water in the reservoir above the axis or 
 centre of the pipe by which it is discharged. 
 
 t A Line is the one-twelfth of a Pads inch, and 
 is equaito * 08 SSof.an English inch. 
 
THE ARTISAN. 
 
 and capable of being tamed in a socket 
 formed in the pipe, so as to open or shut 
 the passage of the fluid, and sometimes to 
 form a communication with either of two 
 or more vessels at pleasure. 
 
 The following figure is a section of a 
 compound stopcock, which receives a 
 fluid from either of the pipes A, B, or C, 
 into a cavity which descends a little in the 
 direction of the axis, and communicates 
 with the pipe D by means of one of the 
 bores, represented by dotted lines, ac- 
 cording to the position into which the 
 moveable cylinder is turned. 
 
 A valve is employed where the fluid is to 
 be allowed to pass in one direction only, 
 and not to return. For water , those valves 
 are the best which interrupt the passage 
 least; and none appear to fulfil this con- 
 dition better than the common clack valve 
 of leather, which is generally either single, 
 or divided into two parts ; but it is some- 
 times composed of four parts, united so as 
 to form a pyramid, nearly resembling the 
 double and triple valves which are formed 
 by nature in the hearts of animals. A 
 board, or a round flat piece of metal, 
 divided unequally by an axis on which it 
 moves, make3 also a very good simple 
 valve. Where a valve is intended to in- 
 tercept the passage of steam , it must be of 
 metal; such a valve is generally a flat 
 plate, with its edge ground a little coni- 
 cally, and guided in its motion by a wire or 
 pin. For air, valves are commonly made 
 of oiled silk, supported by a, perforated 
 plate or grating. The following are among 
 
 the most common and approved kinds of 
 
 valves. 
 
 The figure A is the common clack valve : 
 B, a double clack valve, consisting of two 
 semicircular valves; C, a pyramidical 
 valve, consisting of four triangular pieces ; 
 
 D, a circular valve, turning on an axis ; 
 
 E, a steam valve of metal, sometimes called 
 a T valve; F, a valve of veiled silk or 
 bladder, supported by a grating for air. 
 
 Water running in open canals or in 
 rivers, is accelerated in consequence of its 
 depth, and the declivity on which it runs, 
 till the resistance, increasing with the 
 velocity, becomes equal to the acceleration, 
 and then the motion of the stream becomes 
 uniform. 
 
 It must however be evident, that the 
 amount of the resisting forces can hardly 
 be determined by principles already known, 
 and therefore it becomes necessary to as- 
 certain, by experiment, the velocity cor- 
 responding to different declivities, and 
 different depths of water, and to try, by 
 multiplying and extending these experi- 
 ments, to find out the law which is common 
 to them all. 
 
 The Chevalier Du Buat has been very 
 successful in researches of this kind, and 
 has given a formula for computing the 
 velocity of running water, whether in close 
 pipes, open canals, or rivers, which, though 
 it maybe called eynperical , is extremelyuseful 
 in practice ; but it is by far too complicated 
 to be given in a work like the present. 
 
 In a river, the greatest velocity is at the 
 surface, and in the middle of the stream, 
 
90 
 
 THE ARTISAN. 
 
 from which it diminishes towards the 
 bottom, and the sides, where it is least. It 
 has been found by experiment, that if 
 from the square root of the velocity in the 
 middle of the stream, expressed in inches 
 per second, unity be subtracted, the square 
 of the remainder is the velocity at the 
 bottom. Thus, if the velocity of the water 
 at the surface in the middie of a river, 
 be 25 inches per second, the velocity at the 
 bottom will be 16 inches ; for the square 
 root of 25 is 5, and 5 diminished by unity 
 or 1, leaves a remainder of 4, which 
 squared is 16. 
 
 The mean velocity, pr that with which, 
 were the whole stream to move, the dis- 
 charge would be the same with the real 
 discharge, is equal to half the sum of the 
 greatest and least velocities at the surface 
 and bottom, as computed by the proposition 
 just mentioned, and consequently in the 
 example now given, the mean velocity 
 would be 25 -f- 16 2, or 20§ inches per 
 second. 
 
 When the water in a river receives a 
 permanent increase, the depth and the 
 velocity are the first things that are aug- 
 mented. The increase of the velocity in- 
 creases the action on the sides and bottom, 
 in consequence of which the width is 
 augmented, and sometimes also, but more 
 rarely, the depth. The velocity is thus 
 diminished, till the tenacity of the soil, or 
 the hardness of the rock, over which it 
 passes, affords a sufficient resistance to the 
 force of the water. The bed of the river then 
 changes only by imperceptible degrees, 
 and, in the ordinary language of Hydrau- 
 lics, is said to be permanent, though in 
 strictness this epithet is not applicable to 
 the course of any river. 
 
 iHiscelkmeous Subjects. 
 
 BIOGRAPHICAL MEMOIR OF 
 THOMAS SIMPSON. 
 
 Mr.Thomas Simpson was born at Market 
 Bosworth, in the county of Leicester, Au- 
 gust the 20th, O. S. 17 10. His father was 
 
 a stuff-weaver in that town ; and, though 
 in tolerable circumstances, yet, intending 
 to bring up his son Thomas to his own bu- 
 siness, he took so little cafe of his educa- 
 tion, that he was only taught to read Eng- 
 lish. But nature had furnished him with 
 taLents, and a genius for very different 
 pursuits, which led him afterwards to the 
 highest rank in the mathematical and phi- 
 losophical sciences. 
 
 Young Simpson very soon gave indica- 
 tions of his turn for study in general, by 
 eagerly reading all books he could meet 
 with, teaching himself to write, and em- 
 
 bracing every opportunity he could find of, 
 deriving knowledge from other persons. 
 Thomas’s father observing him thus to 
 neglect his business, by spending his time 
 in reading what he thought useless books, 
 and following other such like pursuits, 
 used all his endeavours to check such pro- 
 ceeding, and to induce him to follow his 
 profession with steadiness and better effect. 
 But after many struggles for this purpose, 
 the differences thus produced between them 
 at length rose to such a height, that our 
 Author quitted his father’s house entirely. 
 
 Upon this occasion he repaired to Nun- 
 eaton, a town at a small distance from 
 Bosworth, where he went to lodge at the 
 house of a taylor’s widow, of the name of 
 Swinfield, who had been left with two 
 children, a daughter and a son, by her 
 husband, of whom the son, who was the 
 younger, being but about two years older 
 than Simpson, had become his intimate 
 friend and companion. And here he con- 
 tinued some time, working at his trade, 
 and improving his knowledge by reading 
 such books as he could procure. 
 
 Among several other circumstances, 
 which, long before this, gave occasion to 
 shew our author’s early thirst for know- 
 ledge, as well as proving a fresh incitement 
 to acquire it, was that of a large solar 
 eclipse, which took place on the 11th of 
 May 1724. This phenomenon, so awful 
 to many, who are ignorant of the cause of 
 it, struck the mind of young Simpson with 
 a strong curiosity to discover the reason of 
 it, and to be able to predict the like sur- 
 prising events. It was however five or six: 
 years before he could obtain his desire, 
 which at length was gratified by the fol- 
 lowing accident. After he had been some 
 time at Mrs. Swinfield’s, at Nuneaton, a 
 travelling pedlar came that way, and took 
 a lodging at the same house, according to 
 his usual custom. This man, to his pro- 
 fession of an itinerant merchant, had joined 
 the more profitable one of a fortune-teller, 
 which he performed by means of judicial 
 astrology. Every one knows with what 
 regard persons of such a cast are treated 
 by the inhabitants of country villages : it 
 cannot be surprising therefore that an un- 
 tutored lad of nineteen should look upon 
 this man as a prodigy ; and, regarding him 
 in this light, should endeavour to ingratiate 
 himself into his favour; in which he suc- 
 ceeded so well, that the sage was no less 
 taken with the quick natural parts and 
 genius of his new acquaintance. The 
 pedlar, intending a journey to Bristol fair, 
 left in the hands of young Simpson an old 
 edition of Cocker’s Arithmetic, to which 
 was subjoined a short Appendix on Al- 
 gebra, and a book upon Genitures, by 
 Partridge the almanac maker. These books 
 
THE ARTISAN. 
 
 91 
 
 he had perused to so good purpose, during 
 the absence of his friend, as to excite his 
 amazement upon his return. 
 
 In fact, our author profited so well by 
 the encouragement and assistance of the 
 pedlar, afforded him from time to time 
 when he occasionally came to Nuneaton, 
 that, by the advice of his friend, he at 
 length made an open profession of casting 
 nativities himself; from which, together 
 with teaching an evening school, he derived 
 a pretty pittance, so that he greatly neg- 
 lected his weaving, to which indeed he had 
 never manifested any very great attach- 
 ment, and soon became the oracle of Nun- 
 eaton, Bosworth, and the environs. 
 Scarce a courtship advanced to a match, 
 or a bargain to a sale, without previously 
 consulting the infallible Simpson about 
 the consequences. But helping folks to 
 stolen goods, he always declared above 
 his skill ; and that as to life and death, he 
 had no power : all those called lawful 
 questions , he readily resolved, provided the 
 persons were certain as to the horary data 
 of the horoscope ; and, he has often de- 
 clared, with such success, that if from very 
 cogent reasons he had not been thoroughly 
 convinced of the vain foundation and falla- 
 ciousness of his art, he never should have 
 dropt it, as he afterwards found himself in 
 conscience bound to do. 
 
 About this time he married the widow 
 Swinfield, in whose house he lodged, 
 though she was then almost old enough to 
 be his grandmother, being upwards of fifty 
 years of age, and having been looked upon 
 as an old maid before her first marriage : 
 and yet her youngest child was two years 
 older than Simpson himself. After this, 
 the family lived comfortably enough toge- 
 ther for some short time, Simpson occa- 
 sionally working at his business of a weaver 
 in the day-time, and teaching an evening 
 school or telling fortunes at night ; the 
 family being also further assisted by the 
 labours of young Swinfield, who had been 
 brought up in the professioon of his father. 
 But this tranquillity was soon interrupted, 
 and our author driven at once from his 
 home and the profession of astrology, by 
 the following accident. A young woman 
 in the neighbourhood had long wished to 
 hear or know something of her lover, who 
 had been gone to sea ; but Simpson had 
 put her off from time to time, till the girl 
 grew at last so importunate, that he could 
 deny her no longer. He asked her if she 
 would be afraid if he should raise the 
 devil, thinking to deter her ; but she de- 
 clared she feared neither ghost nor devil, 
 so he was obliged to comply. The scene 
 of action pitched upon was a barn, and 
 young Swinfield was to act the devil or 
 ghost, who, being concealed under some 
 straw in a corner of the barn, was, at a 
 
 signal given, to rise slowly out from among 
 ths straw, with his face marked so that the 
 girl might not know him. Every thing 
 being in order, the girl came at the time ap- 
 pointed ; when Simpson, after cautioning 
 her not to be afraid, began muttering some 
 mystical words, and chalking round about 
 them, till, on the signal given, up rises the 
 tailor, slow and solemn, to the great terror 
 of the poor girl, who, before she had seen 
 half his shoulders, fell into violent fits, 
 crying out it was the very image of her 
 lover; and the effect upon her was so 
 dreadful, that it was thought either death 
 or madness must be the consequence. So 
 that poor Simpson was obliged immediately 
 to abandon at once both his home and the 
 profession of a conjuror. 
 
 Upon this occasion it would seem he fled 
 to Derby, where he remained about two or 
 three years, instructing pupils in an even- 
 ing school, and working at his trade by 
 day. Here too he wrote a song on oc- 
 casion of the parliamentary election at this 
 place, in the year 1733, in favour of the 
 Cavendish family : and it is probable he 
 continued here till about the year 1735 or 
 1736. 
 
 It would seem indeed that Simpson had 
 an early turn for versifying, both from the 
 circumstance of the song abovementioned, 
 and from his first two mathematical ques- 
 tions that were published in the Ladies’ 
 Diary, which were both in a set of verses, 
 not ill written, for the occasion. These 
 were printed in the Diary for 1736, and 
 therefore must at latest have been written 
 in the year 1735. These two questions, 
 being at that time pretty difficult ones, shew 
 the great progress he had even then made 
 in the mathematics ; and from an expres- 
 sion in the first of them, viz. where he 
 mentions his residence as being in latitude 
 52°, it appears he was not then come up to 
 London, though he must have done so very 
 soon after. 
 
 Together with his astrology he had soon 
 furnished himself with enough of arith- 
 metic, algebra, and geometry to be qualfied 
 for looking into the Ladies’ Diary (of which 
 he had afterwards for several years the 
 direction), by which he came to understand 
 that there was a still higher branch of 
 mathematical knowledge than any he had 
 yet been acquainted with ; and this was 
 the method of Fluxions. But our young 
 analyst was quite at a loss to discover any 
 English author who had written on the 
 subject, except Mr. Hayes ; and his work 
 being a folio, and then pretty scarce, ex- 
 ceeded his ability of purchasing: however, 
 an acquaintance lent him Mr. Stone’s 
 Fluxions , which is a translation of the 
 Marquis de VHospitaVs Analyse des Infini- 
 ment Petits ; by this one book, and his own 
 penetrating talents, he was, as we shall 
 
THE ARTISAN. 
 
 presently see, enabled in a very few years 
 to compose a much more accurate treatise 
 on this subject than any that had before 
 appeared in our language. 
 
 After he had quitted astrology and its 
 emoluments, he was driven to hardships 
 for the subsistence of his family, while at 
 Derby, notwithstanding his other indus- 
 trious endeavours in his own trade by day, 
 and teaching pupils at evenings. This de- 
 termined him to repair to London, which 
 he did in 1735 or 1736, as before said, 
 leaving the family behind, his wife being 
 then pregnant with her first child by our 
 Author, which was contrary to the ex- 
 pectation of every one, being then about 
 fifty-five years of age, for which reason her 
 neighbours used to say, u there goes Sarah 
 the wife of Abraham. 
 
 On his first coming to London, Mr. 
 Simpson wrought for some time at his 
 business in Spitalfields, and taught ma- 
 thematics at evenings, or any spare hours. 
 His industry turned to so good account, 
 that he returned down into the country, 
 and brought up his wife and three children, 
 she having produced her first child in his ab- 
 sence. The number of his scholars in- 
 creasing, and his abilities becoming in 
 some measure known to the public, he was 
 encouraged to make proposals for pub- 
 lishing by subscription, A new Treatise of 
 Fluxions; wherein the Direct and Inverse 
 Method are demonstrated after a new , clear , 
 and concise Manner , with their Application 
 to Physics and Astronomy : also the Doctrine 
 of Infinite Series and Reverting Series uni‘ 
 versally, are amply explained , Fluxionary 
 and Exponential Equations solved; toge - 
 the.r with a variety of new and curious 
 Problems. 
 
 When Mr. Simpson first proposed his 
 intentions of publishing such a work, he 
 did not know of any English book, founded 
 on the true principles of Fluxions, that 
 contained any thing material, especially 
 the practical part : and though there had 
 been some very curious things done by 
 several learned and ingenious gentlemen, 
 the principles were nevertheless left ob- 
 scure and defective, and all that had been 
 done by any of them in infinite series, very 
 inconsiderable. 
 
 The book was published in 4to, in the 
 year 1737, although the author had been 
 frequently interrupted from furnishing the 
 press so fast as he could have wished, 
 through his unavoidable attention to his 
 pupils for his immediate support. The 
 principles of fluxions treated of in this 
 work, are demonstrated in a method accu- 
 rately true and genuine, not essentially 
 different from that of their great inventor, 
 being entirely expounded by finite quan 
 tities. In the first and second parts are 
 given a great many new, and some very 
 
 curious examples in the solutions of prob- 
 lems, rendered plain to ordinary capa- 
 cities. 
 
 The second part treats of Infinite Series . 
 And here nothing is proposed without 
 demonstration, and every thing is illus- 
 trated by easy examples. New rules are 
 also laid down for finding the forms of 
 series, without taking in any of the super- 
 fluous terms. 
 
 The third part contains a familar method 
 of finding and comparing fluents, illustrated 
 with some useful and easy applications. 
 
 In the fourth part is shewn the use of 
 fluxions in some of the most sublime 
 branches of Physics and Astronomy ; where, 
 besides several things done in a method 
 quite different from any thing to be met 
 with in other authors, there are some very 
 useful speculations relating to the doctrine 
 of Pendulums and Centripetal Forces. 
 
 To this is added a supplement ; being a 
 collection of miscellaneous problems, inde- 1 
 pendent of the foregoing four parts ; and 
 containing, among other matters, an inves- 
 tigation of the Areas of Spherical Triangles ; 
 the Curve of Pursuit : the Paths of Sha- 
 dows ; the Motion of Projectiles in a Me- 
 dium ; and the manner of finding the At- 
 tractive Force of bodies of different forms, 
 acting according to a given law. 
 
 In 1740 Mr. Simpson published a treatise 
 on the Nature and Laws of Chance, in 4to. 
 To which is annexed, Full and clear Inves- 
 tigations of two important Problems added 
 in the 2d edition of Mr. De Moivre’s book 
 on chances : as also two New Methods for 
 the Summation of Series. 
 
 Our author's next publication was a 4to 
 volume of Essays on several curious and 
 interesting Subjects in Speculative and 
 Mixed Mathematics ; printed in the same 
 year, 1740 : dedicated to Francis Blake, 
 Esq. since Fellow of the Royal Society, 
 and our author’s good friend and 
 patron. 
 
 The first of these essays shews the theory 
 of the apparent place of the stars (com- 
 monly called their A berration) arising from 
 the progressive motion of light, and of the 
 earth in its orbit; with practical rules for 
 computing the same, communicated by Dr. 
 Bevis. 
 
 The second treats of the Motion of Bodies 
 affected by projectile and centripetal forces ; 
 in which the most considerable matters in 
 the first book of Newton's Principia are 
 clearly investigated. 
 
 The 3d is a Solution of Kepler’s Problem, 
 with a concise practical rule. 
 
 The 4th treats of the Motion and Paths 
 of Projectiles in resisting mediums ; de- 
 termining the most important particulars 
 upon this head, in the 2d Book of the 
 Principia. 
 
 The oth considers the Resistances, Velo- 
 
THE ARTISAN. 
 
 cities, and Times of Vibration of Pendulous 
 Bodies in Mediums. 
 
 The 6th contains a new method of So- 
 lution of all kinds of algebraical equations 
 in numbers, more general than ever before 
 given. 
 
 The 7th is concerning the method of In- 
 crements, with examples. 
 
 The 8th is a concise Investigation of a 
 Theorem for finding the Sum of a Series of 
 Quantities, by means of their Differences. 
 
 The 9th is a general way of investigating 
 the Sum of a recurring Series. 
 
 The 10th is a new and general method 
 for finding the Sum of any Series of Powers, 
 whose roots are in arithmetical progression ; 
 being also applicable to Series of other 
 kinds. 
 
 The 11th relates to angular Sections, 
 with some remarkable properties of the 
 circle. 
 
 The 12th shews an easy and expeditious 
 method of reducing compound Fractions 
 to simple ones. 
 
 The 13th, or last, which contains a ge- 
 neral Quadrature of hyperbolical Curves, 
 is a problem that had exercised the skill of 
 several eminent mathematicians. None of 
 the solutions before published extended 
 farther than to particular cases, except 
 one, which is in the Philosophical Trans- 
 actions, without demonstration, by Mr. 
 Rlingenstierna, professor of mathematics 
 at Upsal. This is investigated by Mr. 
 Simpson in two different ways ; and the 
 general construction is rendered remark- 
 ably easy, simple, and fit for practice. 
 And, on this head, it would seem that Mr. 
 Klingenstierna was well pleased with what 
 Mr. Simpson had done ; for, being after- 
 wards appointed Secretary to the Royal 
 Academy at Stockholm, as a mark of his 
 esteem, he procured a diploma, to be 
 transmitted to him, by which he was con- 
 stituted a member of that learned body. 
 
 Our author’s next work was, The Doc- 
 trine of Annuities and Reversions, deduced 
 from general and evident Principles ; with 
 useful Tables, shewing the Values of 
 Single and Joint Lives, &c. in 8vo. 1742. 
 This was followed in 1743, by an Appendix, 
 containing some Remarks on a late Book 
 on the same Subject (by Mr. Abr. De 
 Moivre, F. R. S.) with Answers to some 
 personal and malignant representations in 
 the preface thereof. To this answer Mr. 
 De Moivre never thought fit to reply. A 
 new edition of this work has lately been 
 published, augmented with the tract upon 
 the same subject that was printed in our 
 author’s Select Exercises. 
 
 In 1743 also was published his Mathe- 
 matical Dissertations on a variety of Phy- 
 sical and Analytical Subjects, in 4to. con- 
 taining, among other particulars, 
 
 A demonstration of the true figure, which 
 
 98 
 
 the earth or any planet must acquire from 
 its rotation about an axis. A general in- 
 vestigation of the attraction at the surfaces 
 of bodies nearly spherical. A determi- 
 nation of the meridional parts, and the 
 lengths of the several degrees of the meri- 
 dian, according to the true figure of the 
 earth. An investigation of the height of 
 the tides in the ocean. A new theory of 
 astronomical refractions, with exact tables 
 deduced from the same. A new and very 
 exact method for approximating to the roots 
 of equations in numbers : which quintuples 
 the number of places at each operation. 
 Several new methods for the summation of 
 series. Some new and very useful im- 
 provements in the inverse method of 
 fluxions. The work being dedicated to 
 Martin Folkes,Esq. President of the Royal 
 Society. 
 
 His next book was a treatise of algebra, 
 wherein the fundamental Principles are 
 demonstrated, and applied to the solution 
 of a variety of Problems. To which he 
 added, the Construction of a great Number 
 of Geometrical Problems, with the Method 
 of resolving them numerically. 
 
 This work, which was designed for the 
 use of young beginners, was inscribed to 
 Wiliam Jones, Esq. F. R. S. and printed 
 in 8ivo. 1745. And a new edition appeared 
 in 1755, with additions and improvements ; 
 among which was a new and general me- 
 thod of resolving all biquadratic equations, 
 that are complete, or having all their 
 terms. This edition was dedicated to 
 James, Earl of Morton, F. R S. Mr. Jones 
 being then dead. The work has gone 
 through several other editions since that 
 time ; the 6th, or last, was in 1796. 
 
 His next work was, Elements of Geo- 
 metry, with their Application to the Men- 
 suration of Superfices and Solids, to the 
 determinasion of Maxima and Minima, and 
 to the Construction of a great Variety of 
 Geometrical Problems ; first published in 
 1747, in 8vo. And a second edition of the 
 same came out in 1760, with great altera- 
 tions and additions, being in a manner a 
 new work, designed for young beginners, 
 particularly for the gentlemen educated at 
 the Royal Military Academy at Woolwich, 
 and dedicated to Charles Frederick, Esq. 
 Surveyor General of the Ordnance. And 
 other editions have appealed since. 
 
 Mr. Simpson met with some trouble and 
 vexation in consequence of the first edition 
 of his Geometry. First, from some re- 
 flections made upon it, as to the accuracy 
 of certain parts of it, by Dr. Robert Sim- 
 son, the learned professor of mathematics 
 in the university of Glasgow, in the notes 
 subjoined to his edition of Euclid’s Ele- 
 ments. This brought an answer to those 
 remarks from Mr. Simpson, in the notes 
 added to the 2d edition as above ; to some 
 
94 
 
 THE ARTISAN. 
 
 parts of which Dr. Simson again replied, in 
 his notes on the next edition of the said 
 Elements of Euclid. 
 
 The second was by an illiberal charge of 
 having stolen his Elements from Mr. Mul- 
 ler, the professor of fortification and artil- 
 lery, at the same academy at Woolwich, 
 where our author was professor of geo- 
 metry and mathematics. This charge was 
 made at the end of the preface to Mr. Mul- 
 ler’s Elements of Mathematics, in two 
 volumes, printed in 1748. 
 
 But Mr. Simpson triumphantly refuted 
 this charge in the preface to the second 
 edition. 
 
 In 1748 came out Mr. Simpson’s Trigo- 
 nometry, Plane and Spherical, with the 
 Construction and Application of Loga- 
 rithms, 8vo. 
 
 In 1750 came out, in two volumes, 8vo. 
 The Doctrine and Application of Fluxions ; 
 containing, besides what is common on the 
 Subject, a Number of new Improvements 
 in the Theory, and the Solution of a variety 
 of new and very interesting Problems in 
 different Branches of the Mathematics. 
 
 In 1752 appeared, in 8vo. The Select 
 Exercises for young Proficients in the 
 Mathematics. 
 
 Besides the foregoing, which are the 
 whole of the regular books or treatises 
 that were published by Mr. Simpson, he 
 wrote and composed several other papers 
 and fugitive pieces. 
 
 Several papers of his were read at the 
 meetings of the Royal Society, and printed 
 in their Transactions : but as most, if not 
 all of them, were afterwards inserted, 
 with alterations, or additions, in his 
 printed volumes, it is needless to take any 
 farther notice of them here. 
 
 [To be continued.'] 
 
 NEW MACHINE FOR MAKING 
 BREAD. 
 
 A machine has just been introduced at 
 Lausanne, for making bread ; that is, for 
 promoting the fermentation of the dough, 
 which appears from its ingenuity to deserve 
 being adopted in other countries. It is 
 simply a deal box one foot high, and two 
 feet wide, which turns round on two pivots, 
 precisely in the same manner as the cylin- 
 der which is used for roasting coifee. One 
 side of the box can be opened to put in the 
 dough. The time required to produce the 
 fermentation depends on the temperature of 
 the air, the quickness of the motion, and 
 other circumstances ; but when the opera- 
 tion is completed, it can always be known 
 by the hissing of the air, which endeavours 
 to escape, and this generally takes place 
 
 in half an hour. The dough is always very 
 well raised, perhaps sometimes too much 
 so. A child can turn the machine. There 
 is no necessity for employing utensils to 
 divide the mass of dough, this operation 
 being sufliciently effected by the adhesion 
 of the dough to the sides of the box. If 
 the machine is of great length, and .divided 
 by partitions at right angles to the sides, 
 different kinds of dough can be prepared at 
 the same time. One evident advantage be- 
 longing to this invention is, that the bread 
 prepared in this manner must necessarily 
 be extremely clean. 
 
 TO PREPARE AN OIL FOR CLOCKS, 
 AND OTHER DELICATE MACHI- 
 NERY. 
 
 The oil for diminishing friction in deli- 
 cate machines, ought to be completely 
 deprived of every kind of acid and mu- 
 cilage : and to be capable of enduring a 
 very intense degree of cold without freez- 
 ing. In fact, it ought to consist entirely of 
 elaine or the oily principle of solid fat, and 
 to be perfectly free from stearine or solid 
 fat. 
 
 Now it is not a difficult matter to ex- 
 tract the ealine from all the fixed oils, and 
 even from seeds, by the process recom- 
 mended by Chevreul, which consists in 
 treating the oil in a mattras with seven or 
 eight times its weight of alchol till boiling. 
 The liquid is then to be decanted, and 
 exposed to the cold, the stearine will then 
 separate from it in the form of a crystal- 
 lized precipitate. The alcholic solution is 
 afterwards to be evaporated to a fifth part 
 of its volume, and the elaine will then be 
 obtained, which ought to be colourless, 
 insipid, without smell, and incapable of 
 altering the colour of the infusion of 
 litmus or turnsole, and having the con- 
 sistence of pure white olive oil. 
 
 CONJECTURES UPON THE UNION 
 OF THE MOON W ITH THE EARTH. 
 
 A curious pamphlet has lately been 
 published in Paris, by an officer of the 
 navy, in which he attempts to render it 
 probable that, not only the moon, or satel- 
 lite of the earth, but the satellites in gene- 
 ral, may, at some future period, unite with 
 their primaries. 
 
 To support this hypothesis, he attempts 
 to explain the cause and effects of the de- 
 luge, the varieties which formerly existed 
 among living and organic bodies, the sud- 
 den appearance or formation of other new 
 species, and even for man himself on the 
 terrestrial globe. 
 
THE ARTISAN. 
 
 95 
 
 - The author supposes that the satellites 
 were formerly small planets, which revol- 
 ved like the other primary planets, round 
 the sun; that in an infinite number of re- 
 volutions, this motion, by some unknown 
 cause, has undergone very great altera- 
 tions, which has brought them near to other 
 planets, much greater than themselves, and 
 whose attraction has become preponderant. 
 By this means these small planets have 
 been drawn from their primitive orbits to 
 circulate round greater ones. 
 
 This elfect is attributed chiefly to the 
 action of comets. 
 
 Applying this hypothesis to the moon, 
 the author thinks that these bodies have 
 produced an effect of this kind upon that 
 body, and dashed it against our globe, or 
 at least, coming suddenly near it, caused 
 such a dreadful concussion, as to throw 
 down the mountains, raise the vallies, 
 rupture the isthmuses, displace the sea, 
 &c. He even supposes that the waters of 
 the moon and its atmosphere, have been 
 carried off by the earth, or else its diver- 
 sified regions would have been suddenly 
 overflown. 
 
 We shall not follow the author in all the 
 consequences of his hypothesis. The field 
 of conjecture, as he says himself, is vast, but 
 till a supsosition has been submitted to the 
 test of experiment or calculation, it cannot 
 be regarded as an established truth. 
 
 As to the rest of the work, the lovers of 
 this kind of speculation'may read it with 
 pleasure ; and the whole is certainly 
 the work of a friend to the sciences, 
 many parts of which he appears to have 
 studied with success. 
 
 SOLUTION OF QUESTIONS. 
 
 the difference of the heights of the walls 
 zz 6f) zz a ; B A the breadth of the house 
 zz28)zz6; AD(zzDC)the length of 
 the rafters ( zz 24 feet) zz c, and' B Czi; 
 then drawing D F parallel to EB, F C will 
 b -f- x 
 
 = “ , and EC zz sja^f-x and by 
 
 the property of similar triangles, 
 
 b ~f~ x , 
 
 x(BC )V« 2 +x 2 (EC):: ~ (FC) : c 
 
 2 c x 
 
 (D C) ; therefore , - -j- x 2 zz — ", and 
 b+x 
 
 this resolved gives x (BC) zz 7-345, and 
 hence D E, the length of the back rafters 
 are found to be 14* *02288 feet nearly. 
 
 Ex. 2. — The content of the whole ring is 
 ZZ’l 2 x -785398 x *8 X 3*141592.or*0l97392; 
 and the content of the outer or golden part 
 
 iszz.l 2 X — — X* 85 X 3*141592, or 
 
 •0101864, which subtracted from *0197392, 
 the content of the whole, leaves the inner, 
 or silver part, zz 0092528 ; then as 1728 
 inches is to *0104804 of an inch, so is 
 3501 
 
 18*888 Xzztz oz. troy, to *104503188 oz. 
 
 do4U 
 
 troy gold, which at £3. 17s. 10§<Z. peroz. is 
 8s. 1 \d. — f s ; and as 1728 inches is to 
 3501 
 
 •0092528, so is*10535 X — to -05143098 
 ’ 3 8 40 
 
 of an inch silver, which at 5s. 2d. per pz, 
 s.d. 
 
 is . . o 3 — ^ value of silver, 
 and 8 If — $ do. of gold, 
 also 5 0 expense of making. 
 
 To the Editor of the Artisan. 
 
 Sir. — Being a constant reader of your 
 excellent publication, I have seen several 
 curious and useful philosophical questions 
 in the 2d and 3d Numbers, and being a 
 little acquainted with calculation, I have 
 devoted a leisure hour to the solution of the 
 two questions by your correspondent Re- 
 rum, and inserted in the 3d Number of the 
 Artisan. A Carpenter. 
 
 Example 1 : — Put B E, in the annexed 
 figure, equal to 
 
 D 
 
 13 — $ whole value.* 
 
 The last of the above questions was also 
 answered by Mr. Richard Graham, Rane- 
 lagh-street, Liverpool , but he will perceive 
 that he has mistaken the specific gravity of 
 standard gold and silver, for pure gold and 
 silver ; he will also perceive that he has 
 employed the proportion between the 
 pound l troy and avoirdupois, instead of 
 the oz. 
 
 The oz. troy contains 480 grains, and the 
 oz. avoirdupois only 437 §; and conse- 
 quently are to each other as the number 
 3840 to 3501. The troy pound contains 
 5760 grains, and the pound avoirdupois 
 7002 ; these pounds are, therefore, to each 
 other as the number 2880 to 3501 ; but the 
 oz. is in the above proportion. Edit. 
 
 3501 , 
 
 * The fraction ' denotes the proportion 
 
 * 3840 
 
 which the oz. troy bears to the oz. avoirdupois. 
 
96 
 
 THE ARTISAN. 
 
 QUESTIONS FOR SOLUTION. 
 
 To the Editor of the Artisan. 
 
 Sir. — B y inserting the following question 
 in one of the future numbers of the “ Ar- 
 tisan,” you will oblige your constant rea- 
 der, CttARON. 
 
 If the specific gravity of brandy be 886, 
 and that of sea-water 1030 ; and if a per- 
 son having a cask half full of brandy, 
 which when full would contain 10 gallons, 
 throws it overboard, for the purpose of con- 
 cealment : required what weight of lead is 
 just sufficient to keep it under water, if the 
 wood of the cask measures 216 cubic 
 inches 1 
 
 To the Editor of the Artisan. 
 
 Sir. — P lease to insert the following 
 question in your next, if convenient, which 
 will oblige your obedient servant, 
 
 Richard Graham. 
 
 Ranelagh-$treet f Liverpool. 
 
 There is a circular plot of ground to be 
 divided into four shares; the areas of 
 which are as 1, 2, 3, 4, respectively, by 
 straight lines, terminating in a pond, whose 
 outer fences are to be quadrants : required 
 the situation of the pond, that all the shares 
 may receive the benefit of the water? 
 
 To the Editor of the Artisan. 
 
 Sir, — B y inserting the following mathe- 
 matical questions in an early number of 
 the “ Artisan,” you will greatly oblige 
 your’s, &c. J. M. Edney. 
 
 3, St. John’s-streetj Clerkenwell. 
 
 1st. The diameter of a circle is 30 feet ; 
 required the side of a regular heptagan of 
 equal area? 
 
 2d. What number is that which consists 
 of two digits, to which if 64 be added, 
 there arises a number having the same 
 digits inverted ; and if from the square of 
 the second digit there be taken the square 
 of the first, the remainder will be 60 ? 
 
 We have inserted the above questions at 
 the request of our Correspondent ; but we 
 wish to confine this department of our 
 publication to questions relating to natural 
 philosophy rather than to pure mathe- 
 matics. — E dit. 
 
 To the Editor of the Artisan. 
 
 Sir.— H aving seen some of the numbers 
 of your valuable publication, which I per- 
 ceive is wholly devoted to the arts and 
 
 sciences, I have resolved; to take it in re- 
 gularly, for the use of my pupils, as I con- 
 ceive it will be the means of inducing them 
 to study the subjects which it contains with 
 more pleasure and attention than by large 
 voluminous works on the same subjects. 
 
 In the mean time I will thank you to in- 
 sert the following experiments in the mis- 
 cellaneous part of your next number, which 
 will very much oblige your obedient ser- 
 vant, Ludimagister. 
 
 Belfast , March 22, 1814. 
 
 Experiment 1 . — To exhibit the pressure 
 of the air on liquids. 
 
 Procure a tin vessel, about six inches 
 high and three inches in diameter, with a„ 
 mouth not quite a quarter of an inch wide ; 
 in the bottom make a number of small 
 holes, about the size of the point of a com- 
 mon sewing needle. Plunge the vessel in 
 water, with its mouth open, and when it is 
 full, cork it tight, and take it out of the 
 water. As long as the vessel remains 
 corked, no water will issue from the holes 
 in the bottom; but as soon as it is un- 
 corked, the water will begin to flow from 
 every one of the holes in the bottom. If 
 these holes exceed the tenth part of an inch 
 in diameter, or if they be too numerous, 
 the water will issue from them, though 
 the vessel be corked, because the pressure 
 of the air on the bottom of the vessel will 
 not be sufficient to confine the water. 
 
 Experiment 2. — To convert a drop qf 
 watei' into a microscope. 
 
 Take a long thin piece of brass, and 
 make a small hole in it, about the twenty- 
 fourth part of an inch in diameter ; then 
 holding it by one end, take up a drop of 
 water upon a pin, and lay it on the hole, the 
 water will remain on the aperture in the form 
 of a hemisphere, or plano-convex lens. Or 
 a double convex lens may be made by 
 thrusting the pin through the hole till the 
 water enters it, and then drawing the pin 
 perpendicularly through the hole. When 
 an object is to be viewed by this micro- 
 scope, take it up upon a pin, or piece of 
 glass, and holding the brass by the end, 
 move the object till it be in the focus, and 
 it will then be seen as distinctly as by a 
 single glass microscope, especially by 
 candle light. 
 
 Experiment 3.. — To produce a change of 
 colour in the sun's rays. 
 
 Hold a white card perpendicularly 
 against the solar rays collected in the focus 
 of a lens, it will exhibit on its back sur- 
 face a circle of a bright yellow colour ; 
 and if turned more and more obliquely, 
 this circle will change to an oval figure, 
 the colour will progressively deepen into 
 an orange, and at last into a dull red. 
 
THE ARTISAN. 
 
 97 
 
 MEUMATOS. 
 
 TO SHOW THE RESISTANCE OF 
 THE AIR. 
 
 13. The following figure represents a 
 small machine, consisting of two mills, a 
 and b } 
 
 which are of equal weights, and turn on 
 their axes with equal forces. Each mill 
 has four thin arms or sails fixed into the 
 axis ; those of the mill a have their planes 
 at right angles to its axis, and those of b 
 have their planes parallel to it. Therefore 
 as the mill a turns round in common air, it 
 is but little resisted thereby, because its 
 sails cut the air with their thin edges ; but 
 the mill b is considerably resisted, because 
 the broad sides of its sails move against 
 the air when it turns round. In each axle 
 is a pin near the middle of the frame, which 
 goes quite through the axle, and stands 
 out a little on each side of it : upon these 
 pins the slider d may be made to bear, and 
 so hinder the mills from going, when the 
 strong spring c is pressed against the oppo- 
 site ends of the pins. 
 
 Having set this machine upon the pump- 
 plate L L, draw up the slider d to the pins 
 on one side, and set the spring c to bend 
 upon the opposite ends of the pins ; then 
 push down the slider d, and the spring 
 acting equally strong upon each mill, will 
 set them both a-going with equal forces and 
 velocities : but the mill a will run much 
 longer than the mill b, because the air 
 makes much less resistance against the 
 edges of its sails, than against the sides, of 
 the sails of b. 
 
 Draw up the slider again, and set the 
 spring upon the pins as before, then cover 
 the machine with the receiver M, upon the 
 pump-plate (see air pump), and having ex- 
 hausted the receiver of air, push down the 
 wire P P, (through the collar of leathers in 
 the neck q) upon the slider, which will 
 disengage it from the pins, and allow the 
 
 Vol. I.— N° 7. 
 
 mills to turn round by the impulse of the 
 spring. And as there is no air in the 
 receiver to make any sensible resistance 
 against them, they will both move a con- 
 siderable time longer than they did in the 
 open air ; and the moment that one stops, the 
 other will do so too. This shows that air 
 resists bodies in motion, and that equal 
 bodies meet with different degrees of re- 
 sistance, according as they present greater 
 or less surfaces to the air, in the planes of 
 their motions. 
 
 14. Take off the receiver M, and the 
 mills employed in last experiment; and, 
 having put a guinea a, and feather b, upon 
 the brass flap e, turn up the flap, and 
 shut it into the notch d. Then, putting a 
 wet leather over the top of the tall receiver 
 A B, open at both ends, 
 
 cover it with the plate C, from which the 
 guinea and feather tongs ed, will then hang 
 within the receiver. This done, pump the 
 air out of the receiver, and then draw up 
 the wire /a little, which by a square piece 
 on its lower end will open the tongs e d ; 
 and the flap falling down as at c, the guinea 
 and feather will decend with equal velo- 
 cities in the receiver, and both will fall 
 upon the pump-plate at the same instant. 
 
 In this experiment the spectators ought 
 not to look at the top, but at the bottom of 
 the receiver, in order to see the guinea and 
 feather fall upon the plate ; for their de- 
 scent is so quick, that it is impossible for 
 the eye to observe the beginning and end of 
 their motion. 
 
 H 
 
98 
 
 THE ARTISAN. 
 
 The foregoing experiments being quite 
 sufficient to prove, that the air is a real 
 substance, possessed of weight , and ca- 
 pable of resisting bodies in motion, we 
 shall now give directions for performing a 
 £et of experiments to show the elasticity of 
 the air. 
 
 To show the Elasticity or Spring of the 
 Air. 
 
 . 15. Tie up a very small quantity of air in 
 a bladder, and put it under a receiver, 
 then exhaust the air out of the receiver, 
 and the small quantity which is confined 
 in the bladder (having nothing to act 
 against it) will expand itself so by the 
 force of its spring, as to fill the bladder as 
 full as it could be blown of common air. 
 But, upon letting the air into the receiver 
 again, it will overpower the air in the 
 bladder, and press its sides almost close 
 together. 
 
 16. If the bladder so tied up be put into 
 a wooden box, and have 20 or 30 pounds 
 weight of lead put upon it in the box, and 
 the box be covered with a close receiver, 
 upon exhausting the air out of the receiver, 
 the air which is confined in the bladder 
 will expand itself so, as to raise the lead 
 by the force of its spring or elasticity. 
 
 17. Take the glass ball mentioned in the 
 fifth experiment, which was left full of 
 water, except a small part at top, contain- 
 ing a bubble of air, and having set it with 
 its neck downward into a phial containing 
 a little water, and having covered it with 
 a close receiver, exhaust the air out of the 
 receiver, and the small bubble of air in the 
 top of the ball will expand itself, so as to 
 force all the water out of the ball into the 
 phial. 
 
 18. Screw the pipe A B into the pump- 
 plate, place the tall receiver G H upon the 
 plate c d, as in the eleventh experiment, and 
 exhaust the air out of the receiver ; then 
 turn the cock e, to keep out the air, un- 
 screw the pipe from the pump, and screw 
 it into the mouth of the copper vessel C C, 
 
 it having first been half filled with water ; 
 then open the cock e (see fig, experiment 
 
 11) and the spring of the air, which is con- 
 fined in the copper vessel, will force the 
 water up through the pipe AB in a jet into 
 the exhausted receiver, as strongly as it did 
 by its pressure on the surface of the water 
 in a basin, in the eleventh experiment. 
 
 19. If a fowl, a cat, a rat, mouse, or 
 bird, be put Vmder a receiver, and the air 
 be exhausted, the animal will be at first 
 oppressed as with a great weight, then 
 grow convulsed, and, at last, expire in all 
 the agonies of a most bitter and cruel death. 
 But as this experiment is too shocking to 
 every spectator who has the least degree 
 of humanity, a machine called the lungs 
 glass , is generally substituted instead of an 
 animal. 
 
 20. If a butterfly be suspended in a re- 
 ceiver by a fine thread, tied to one of its 
 horns, it will fly about in the receiver, as 
 long as the receiver continues full of air; 
 but if the air be exhausted, though the 
 animal will not die, and will continue to 
 flutter its wings, it cannot remove itself from 
 the place where it hangs in the middle of 
 the receiver, until the air be let in again, 
 and then the animal will fly about as 
 before. 
 
 21. Screw the end C of the pipe C D into 
 the hole of the pump-plate, 
 
 and turn all the three cocks d, G, and H, 
 so as to open the communications between 
 all the three pipes E, F, D C, and the hol- 
 low trunk A B. Then, cover the plates g 
 and h with wet leathers, which have holes 
 in their middle, where the pipes open into 
 the plates ; and place the close receiver I 
 upon the plate g. This done, shut the pipe 
 F, by turning the cock H, and exhaust the 
 air out o f the receiver I ; then turn the cock 
 d, to shut out the air, unscrew the machine 
 from the pump, and having screwed it to 
 the wooden foot L, put the receiver Kjupon 
 the plate h: this receiver will continue 
 loose on the plate as long as it keeps full 
 of air, which it will do until the cock H be 
 turned to open the communication between 
 the pipes F and E, through the trunk A B ; 
 and then the air in the receiver K, having 
 nothing to act against its spring, will run 
 
THE ARTISAN. 
 
 99 
 
 from K into I, until it be so divided be- 
 tween these receivers, as to be of equal 
 density in both; and then they will be 
 held down with equal forces to their re- 
 spective plates, by the pressure of the 
 atmosphere ; though each receiver will then 
 be kept down with only one half the for- 
 mer pressure which it had, when it was 
 exhausted of air, because it has now one 
 half of the common air in it, which filled 
 the receiver K, when it was set upon the 
 plate ; and therefore, a force equal to half 
 the force of the spring of common air, will 
 act within the receiver against the whole 
 pressure of the common air upon their out- 
 sides. This is called transferring the air 
 out of one vessel into another. 
 
 22. Put a cork into the square phial A, 
 (see experiment the twelfth) and fix it in 
 with wax or cement : put the phial upon 
 the pump-plate, with the wire cage B over 
 it, and cover the cage with a close receiver ; 
 then exhaust the air out of the receiver, 
 and the air that was corked up in the phial 
 will break the phial outwards by the force 
 of its spring, because there is no air left 
 on the outside of the phial to act against 
 the air within it. 
 
 23. Put a shrivelled apple under a close 
 receiver, and exhaust the air, then the 
 spring of the air within the apple will 
 plump it out, so as to cause all the wrinkles 
 to disappear ; but tipon letting the air into 
 the receiver again, to press upon the apple, 
 it will instantly return to its former de- 
 cayed and shrivelled state. 
 
 24. Take a fresh egg, and cut off a little 
 of the shell and film from its smallest end, 
 then put the egg under a receiver, and 
 pump out the air; upon which, all the 
 contents in the egg will be forced out into 
 the receiver, by the expansion of a small 
 bubble of air contained in the great end, 
 between the shell and film. 
 
 25. Put some warm beer in a glass, and 
 having set it on the pump, cover it with a 
 close receiver, and then exhaust the air. 
 Whilst this is doing, and thereby the pres- 
 sure more and more taken off from the beer 
 in the glass, the air therein will expand 
 itself, and rise up in innumerable bubbles 
 to the surface of the beer, and from thence 
 it will be taken away with the other air in 
 the receiver. When the receiver is nearly 
 exhausted, the air in the beer, which 
 could not disentangle itself quick enough 
 to get off with the rest, will now expand 
 itself so, as to cause the beer to be covered 
 with froth, and at last to run over the side 
 of the glass. 
 
 26. Put some warip water into a glass, 
 and a small bit of dry wainscot or other 
 wood into the water : then, cover the glass 
 with a close receiver, and exhaust the air ; 
 upon which, the air in the wood, haying 
 liberty to expand itself, will come out plen- 
 
 tifully, and make all the Water to bubble 
 about the wood, especially about the ends 
 where the pores are greatest and most nu- 
 merous. A cubic inch of dry wainscot 
 has so much air in it, that it will continue 
 bubbling for nearly half an hour. 
 
 Miscellaneous Experiments. 
 
 27. Let a large piece of cork be sus- 
 pended by a thread at one end of a balance, 
 and counterpoised by a leaden weight, 
 suspended in the same manner at the 
 other. Let this balance be hung to the 
 inside of the top of a large receiver, which, 
 being set on the pump, and the air ex- 
 hausted, the cork will preponderate, and 
 shew itself to be heavier than the lead; 
 but, upon letting in the air again, the equi- 
 librium will be restored. The reason of 
 this is, that since the air is a fluid, and all 
 bodies lose as much of their absolute 
 weight in it, as is equal to the weight of 
 their bulk of the fluid (see page 9, col. 2.) 
 the cork being the larger body, loses more 
 of its real weight than the lead does ; and 
 therefore must in fact be heavier, to balance 
 it under the disadvantage of losing some of 
 its weight ; which disadvantage being taken 
 off by removing the air, the bodies then 
 gravitate according to their real quantities 
 of matter, and the cork, which balanced 
 the lead in air, shews itself to be heavier 
 when in vacuo. 
 
 28. Set a lighted candle upon the pump, 
 and cover it with a tall receiver. If the 
 receiver holds a gallon, the candle will 
 burn a minute ; and then, after having 
 gradually decayed from the first instant, it 
 will go out ; which shows that a constant 
 supply of fresh air is necessary to feed 
 flame : and also to support animal life. For 
 a bird kept under a close receiver will 
 soon die, although no air be pumped out; 
 and it is found that, in the diving bell, a 
 gallon of air is only sufficient to support a 
 man for one minute. 
 
 29. As soon as the candle goes out, in 
 this experiment, the smoke will be seen to 
 ascend to the top of the receiver, and there 
 form a sort of cloud ; but upon exhausting 
 the air, the smoke will fall down to the 
 bottom of the receiver, and leave it as 
 clear at the top as it was before it was set 
 upon the pump. This shows, that smoke 
 does not ascend on account of its being 
 positively light, but because it is lighter 
 than air ; and its falling to the bottom of 
 the receiver when the air was taken away, 
 shows that it is not altogether destitute of 
 weight. In a similar manner, different 
 sorts of wood ascend or swim in water : 
 and yet no one doubts that every kind of 
 wood has weight. 
 
 30. Set a bell upon a cushion on the 
 pump-plate, and cover it with a receiver ; 
 then shake the pump, to make the clapper 
 
 h 2 
 
100 
 
 THE ARTISAN. 
 
 strike against the sides of the bell, and the 
 sound -will be very well heard ; but, ex- 
 haust the receiver of air, and then, if the 
 clapper be made to strike ever so hard 
 against the sides of the bell, it will pro- 
 duce no sound at all ; which shows, that 
 air is absolutely necessary for the propaga- 
 tion of sound. 
 
 The elastic air which is contained in 
 many bodies, and kept in them by the 
 weight of the atmosphere, may be got out 
 of them, either by boiling, or by the air- 
 pump, as shown in the 26th experiment : 
 but the fixed air, which is by much the 
 greater quantity, cannot be got out but by 
 distillation, fermentation, or some chemical 
 process. 
 
 If fixed air did not come out of bodies 
 with difficulty, and spend some time in ex- 
 tricating itself from them, it would tear 
 them to pieces. Trees would be rent by 
 the change of air, from a fixed to an elastic 
 state, and animals would be burst in pieces 
 by the explosion of air in their food. 
 
 Dr. Hales found, by experiment, that 
 the air in apples is so condensed, that if 
 it were let out into the common air, it would 
 fill a space 48 times as great as the bulk of 
 the apples themselves. 
 
 To the foregoing experiments of rarify- 
 ing the air, or producing a vacuum, we 
 shall add a few observations respecting the 
 condensation of air. When any vessel is 
 employed for the purpose of condensing 
 the air, it ought to be sufficiently strong to 
 bear the force, or resist the increased 
 elasticity which is thus given to it ; vessels 
 for this purpose are therefore generally 
 made of brass. If glass be used for a con- 
 denser, it will not admit of so great a de- 
 gree of condensation ; but any experiment 
 which may be performed with it will be 
 more pleasant than with abrass vessel, as the 
 experiment may be viewed in all its stages. 
 
 The following figure represents a con- 
 
 denser, with screws for confining the 
 receiver. 
 
 A is a gage for showing the degree of 
 condensation, B the piston of the syringe, 
 with a valve of the best kind, which is 
 conical, and is confined by a spiral spring. 
 But in common the valves are made of lea- 
 ther, with a plate of metal to strengthen it. 
 
 The spring or elasticity of the air will be 
 greater in proportion to its condensation, 
 and, therefore, the sound of a bell will be 
 twice as loud as in the common air, if the 
 air be made twice as dense by injection. A 
 round phial may be broken by condensed 
 air, which could not be broken by the 
 pressure of the common air; and though 
 animals soon die, by not having a requisite 
 quantity of air, yet they will not be easily 
 killed by having that quantity increased by 
 condensation. If air be condensed upon 
 water in a bottle, it will cause it to spout 
 through the tube of communication to a 
 very great height : viz. to BO feet, if only 
 one atmosphere be injected ; to 60 feet, if 
 two atmospheres be injected ; and so on. 
 
 A bladder that will sustain the spring of 
 common air, will be broken by the spring 
 of condensed air. In short, the force of 
 condensed air may be so far increased as to 
 counteract or balance the greatest power 
 which human art can apply. When air is 
 considerably condensed on the surface of 
 water, a greater quantity of caloric or heat 
 is necessary to convert the water into va- 
 pour, than when it is pressed only by air 
 of the common degree of density ; hence 
 water will boil or go into vapour at a lower 
 temperature, on the top of a high moun- 
 tain, than at the bottom of it, (see page 
 38 .) 
 
 The heat which may be communicated to 
 water by means of pressure, or inclosing 
 it in strong vessels, may be so great as to 
 melt soft solder , and even lead. 
 
 It is by this vast power of heated water 
 and steam, that Papin’s Digester effects 
 the dissolution of bones, and reduces them 
 to a jelly, so as to become wholesome and 
 savoury diet ; for which purpose they are 
 put into a metalline vessel, with a cover, 
 which is strongly screwed down, and made 
 perfectly air-tight. The Digester being 
 nearly filled with water and bones, is set 
 over a gentle fire, which by degrees con- 
 verts the water into steam, and which, 
 with the included air, in a short space of 
 time acts upon the bones with so great an 
 energy, as to effect their entire dissolution, 
 and cause them to mix and incorporate so 
 intimately with the water, or broth, as to 
 make a perfect coagulum, or jelly, when 
 all is cold, which may be then sliced out 
 with a knife. 
 
THE ARTISAN. 
 
 101 
 
 OPTICS. 
 
 The multiplying glass is made by grind- 
 ing down the round side of a convex glass 
 AB, 
 
 into several flat surfaces. An object C 
 will not appear magnified, when seen 
 through this glass by the eye at H ; but 
 it will appear multiplied into as many 
 different objects as the glass contains plane 
 surfaces. Tor, since rays will flow from 
 the object C to all parts of the glass, and 
 each plane surface will refract those rays to 
 the eye, the same object will appear to the 
 eye in the direction which the rays enter 
 it through the surface. Thus, a ray from 
 the object C, falling perpendicularly on the 
 middle surface b, will go through the glass 
 to the eye without suffering any refraction ; 
 and will therefore show the object in its 
 true place at C : whilst a ray flowing from 
 the same object, and falling obliquely on 
 the plane surface c, will be so refracted by 
 
 passing through the glas^ as to cause the 
 same object C to appear at E, in the direction 
 of the ray H E. And the ray flowing from 
 the object C, and falling obliquely on the 
 plane surface a , will be so refracted (by 
 passing through the glass) as to cause the 
 same object to appear at D, in the direction 
 HD. ' 
 
 Though a plane mirror , or common look- 
 ing glass, appears to have no other use 
 than to reflect such images as are placed 
 before it, yet we shall here introduce it for 
 the purpose of stating some of its pro- 
 perties which are not generally known. 
 
 When any object is placed before a plane 
 mirror, its image appears as large to the 
 eye as the object itself; and is erect, 
 distinct, and seemingly as far behind the 
 mirror as the object is before it ; and that 
 part of the mirror which reflects the image 
 of the object to the eye (the eye being sup- 
 posed equally distant from the glass with 
 the object) is just half as long and half as 
 broad as the object itself. 
 
 Hence it appears, that if a man sees his 
 whole image in a plane looking-glass, the 
 part of the glass that reflects his image 
 must be just half as long and half as broad 
 as himself, let him stand at any distance 
 from it whatever, and that his image must 
 appear just as far behind the glass as he is 
 before it. Thus the man A B, viewing 
 himself in the plane mirror C D, which is 
 just half as long as himself, sees his whole 
 image, as at E F, behind the glass, exactly 
 equal to his own size. 
 
 For a ray, AC, proceeding from his eye 
 at A, and falling perpendicularly upon the 
 surface of the glass at C, is reflected back 
 to his eye in the same line CA ; and the eye 
 of his image will appear at E in the same 
 line produced to E, beyond the glass. 
 
 And the ray, B D, flowing from his foot, 
 and falling obliquely on the glass at D, 
 will be reflected as. obliquely, or, in the di- 
 rection D A ; and the foot of his image 
 will appear at F, in the direction of the 
 reflected ray A D, produced to F, where it 
 
 is cut by the right line B F, drawn parallel 
 to the right line A E. 
 
 In all our preceding observations on light 
 we have considered it as a simple substance, 
 and supposed that all its parts or rays had 
 the same properties, and were equally acted 
 
102 
 
 THE ARTISAN. 
 
 upon by the bodies which refracted and 
 reflected them. This, however, though 
 believed to be the case till the time of Sir 
 Isaac Newton, has been completely dis- 
 proved by his fine experiments with the 
 prism ; we shall, therefore, now state the 
 means which were employed by that cele- 
 brated philosopher to prove that light is a 
 
 compound substance, capable of being de- 
 composed into its elements, and exhibiting 
 in its elementary state new properties of 
 the most interesting kind. That the light 
 of the sun consists of rays which differ in 
 colour and refrangibility , may be proved as 
 follows. 
 
 In a dark room make a small hole F, 
 
 in the window shutter, about one-third 
 of an inch broad ; place a glass prism ABC 
 in the beam of rays S F, in such a manner 
 that the rays may fall obliquely on one 
 side of the prism, as at A C ; the beam of 
 rays which thus fall on the prism will be 
 refracted in different degrees, and will 
 form a series of the most beautiful and 
 lively colours, P T, on the opposite wall, 
 or on a sheet of white paper, MN, held up 
 for the purpose. The image which is thus 
 formed is called the solar spectrum , and 
 when most distinctly formed is of an oblong 
 figure, exactly like the shadow of a 
 cylinder. 
 
 The colours of the spectrum are red, 
 orange , yellow , green , blue , indigo , and 
 violet , with all their intermediate shades, 
 blended in the softest and most agreeable 
 manner. 
 
 Hence the light of the sun consists of a 
 mixture of several sorts of coloured rays, 
 some of which at equal incidences are 
 more refracted than others, and therefore 
 are called more refrangible . The red atT, 
 being nearest to the place Y, where the 
 rays of the sun would go directly, if the 
 prism was taken away, is the least re- 
 fracted of all the rays ; and the orange , 
 yellow , green , blue , indigo and violet , are 
 continually more and more refracted, as 
 they are more and more diverted from the 
 course of the direct light. For, when the 
 prism is fixed in the posture above-men- 
 tioned, so that the place of the image shall 
 be the lowest possible, the figure of the 
 image ought to be round, like the spot at 
 Y, if all the rays that tended to it were 
 equally refracted. Therefore, since it is 
 
 found that this image is not round , but 
 about five times longer than it is broad, it 
 follows, that all the rays are not equally 
 refracted. 
 
 It is also found that the above colours 
 do not occupy equal spaces of the spectrum. 
 If the whole spectrum be divided into 360 
 equal parts, the red space will occupy 45 ; 
 the orange 27 ; the yellow 48 ; the green, 
 60 ; the blue , 60 ; the indigo , 40 ; and the 
 violet, 80, of these parts. 
 
 If all the above colours are blended 
 together again, they will produce a pure 
 white. This may be proved by removing 
 the paper on which the spectrum was 
 formed, and placing a large convex glass 
 in its place, the different coloured rays 
 will be so refracted in passing through it 
 as to make them unite in a point ; and if a 
 white paper be placed at this point to 
 receive them, they will excite the idea of a 
 lively white. But if the paper be placed 
 farther from the glass than this point, the 
 different colours will again appear upon it, 
 in an inverted order, on account of the rays 
 crossing each other after meeting.* 
 
 That the colours of the solar spectrum 
 produce a white, when blended together, 
 in the proportion in which they appear in 
 the spectrum, may be exhibited in a dif- 
 ferent manner, as follows : 
 
 * Light, or rays which appear red, or rather make 
 objects appear so, may, with more propriety, be 
 called red-making rays, the same may be said of 
 green, &c. For to speak properly, the rays are not 
 coloured, there is only a certain power and dispo- 
 sition in them to excite a sensation of this or that 
 colour. This subject will be treated of more fully in 
 another part of our work. t 
 
THE ARTISAN. 
 
 103 
 
 Draw two concentric circles on a smooth 
 board or card, at a little distance from 
 each other, then divide the outer circle in 
 360 equal parts, or degrees, and mark them 
 off in the proportion stated above ; then 
 draw straight lines from the centre of the 
 circles to the different divisions, and paint 
 each of the spaces included between the 
 circles of its respective colour, that is, the 
 space which contains 45 degrees is to be 
 painted red ; that which contains 27, orange: 
 and the others as stated above. When this 
 is done, paint the space within the inner 
 circle black, and put a pin through the 
 centre, then turn the card swiftly round on 
 the pin, and the space within the two circles 
 which was painted of different colours will 
 appear like a white ring, inclining to 
 grayish. 
 
 The white will be more or less brilliant 
 as the colours are skilfully or unskilfully 
 blended at the extremities of each division. 
 
 It has been lately discovered by Dr. Wol- 
 laston, that if a small aperture be viewed 
 through a prism , or if the sun’s light pass- 
 ing through a small aperture fall upon a 
 prism, the spectrum thus produced con- 
 tains only four colours ; it therefore fol- 
 lows, that the other colours in the spec- 
 trum described by Newton are compound 
 tints, and have refrangibilities, the same as 
 other rays in the Newtonian spectrum. 
 The yellow rays, for example, in the New- 
 tonian spectrum, have the same refrangi* 
 bility as some of the green , and also some 
 of the red rays in the same spectrum, and 
 their apparent existence as separate rays 
 arises entirely from the analysis not being 
 complete, in consequence of too large an 
 aperture having been used. 
 
 From these experiments Dr. Wollaston 
 and Dr. Young have concluded, that the 
 yellow rays have not a separate existence in 
 the spectrum. Dr. Young, who repeated 
 Dr. Wollaston’s experiments with perfect 
 success, remarks that there is a narrow yel- 
 lowline, generally visible at the limit of the 
 red and green , but that its breadth scarcely 
 exceeds that of the aperture by which the 
 light is admitted, and that Dr. Wollaston 
 attributes it to the mixture of the red with 
 the green light. 
 
 Dr. Brewster has, however, recently 
 shewn, that the yellow rays have a sepa- 
 rate and independent existence in the 
 spectrum, formed in the manner described 
 by Dr. Wollaston, and that they are only 
 mixed with the most refrangible red and 
 the least refrangible green, with which 
 they have the same refi angibility. By the 
 use of coloured media which absorb these 
 two kinds of rays, he has been able to 
 insulate the yellow space, so as to establish 
 its existence beyond a doubt. 
 
 W hen a pencil of white light is separated 
 into its component colours, it is said to be 
 
 dispersed by the prism ; that is, the extreme 
 red and the extreme violet rays are dis- 
 persed or separted from the middle rays 
 of the spectrum. 
 
 Light, whose rays are all alike refran- 
 gible, are called simple , homogeneous, and 
 similar ; and that whose rays are not all 
 alike refrangible, are called compound, he- 
 terogeneous and dissimilar. 
 
 The colours of homogeneous lights are 
 called primary , homogeneous and simple; 
 and those of heterogeneous lights, heter- 
 ogeneous and compound. For these are 
 always compounded of homogeneous 
 lights. 
 
 CHEMXSTRir. 
 
 Carbon is very fixed, perfectly, infusi- 
 ble, and insoluble in heat, and passes, with 
 justice, for the most refractory body in na- 
 ture. Thus it is frequently employed as a 
 crucible for containing matters difficult of 
 fusion, or, as a support, when many bodies 
 are treated by the blow-pipe. As carbon 
 is a bad conductor of heat, it is used with 
 success to line crucibles, to coat furnaces, 
 and confine the heat, the infusible pro- 
 perty of this body accompanies the pro- 
 perty of not conducting caloric. In many 
 of the arts this property becomes of the 
 greatest utility. 
 
 When the temperature of charcoal is 
 raised to ignition, and is then placed in 
 contact with oxygen gas, the carbon burns 
 with activity, sparkling, and slightly- 
 brilliant, but very sensible flame. It 
 quickly disappears, becomes fused in the 
 oxygen gas, and consequently assumes the 
 fluid elastic form. It is found, that twenty- 
 eight parts of carbon thus disappears, and 
 unites with seventy -two parts of oxygen 
 gas, and that there results from this com- 
 bustion a new gas which occupies less 
 space than the oxygen gas, but its spe- 
 cific weight is almost double. This gas 
 received the name of carbonic acid as 
 already mentioned, and will be treated of 
 under that head. 
 
 What happens when charcoal is burned 
 in a given quantity of common air, or when 
 that air is not renewed, maybe now under- 
 stood. The ignited carbon combines gra- 
 dually with the oxygen gas of the atmos- 
 phere, and becomes dissolved in such a 
 manner as to lose its visible mass, and only 
 to leave a few atoms of its ashes. 
 
 The air thus vitiated and really d estr oy ed, 
 as to its vital and respirable parts, by this 
 combustion, produces very fatal accidents. 
 It will be also seen that other circum- 
 stances, relative to charcoal, also augment 
 its danger. 
 
 Carbon unites with all the simple com- 
 
104 
 
 THE ARTISAN 
 
 bustibles, and with azote, or nitrogen; 
 with sulphur it forms a curious limpid li- 
 quid called carburet of sulphur, or sul- 
 phuret of carbon* ; with phosphorus it 
 forms a compound whose properties are 
 but imperfectly ascertained. With azote, 
 it forms cyanogen or prussic acid gas. 
 
 There exists so marked an attraction be- 
 tween carbon and hydrogen, that the com- 
 pound (which is named carbonated hy- 
 drogen, or carburetted hydrogen) is fre- 
 quently met with among vegetable com- 
 pounds, t But, besides this attraction of 
 the radicals , hydrogen gas may easily hold 
 in solution a greater or less quantity of 
 carbon, which happens whenever it is 
 disengaged from a substance which itself 
 contains carbon more or less abundant and 
 divided. This solution is obtained very 
 varied, and in a number of chemical ope- 
 rations, from the simple exposure of char- 
 coal, in a glass full of hydrogenous gas 
 to the rays of the sun. In which exposure 
 the charcoal is seen to dissipate, and the 
 hydrogenous gas to diminish in volume in 
 proportion as it is dissolved. 
 
 It is also produced by the rapid decom- 
 position of vegetables by heat, as well as 
 by the spontaneous change which vegeta- 
 ble and animal substances undergo at the 
 bottom of stagnant waters. In all these 
 circumstances, carbonated hydrogen gas 
 is obtained. Charcoal itself, when humid, 
 or when it has been for some time im- 
 mersed in hydrogen gas, begins, when 
 lighted, to exhale through the atmosphere 
 this deleterious gas, which also augments 
 the danger of its combustion in close 
 places. 
 
 Carburetted hydrogen gas, formed so 
 easily in all the conditions here explained, 
 varies according to the proportions of car- 
 bon which it contains, and assumes pro- 
 perties varied, also according to these pro- 
 portions, in such a manner, that it has 
 been regarded and described as if it formed 
 so many different inflammable gases. That 
 which is disengaged from stagnant waters 
 or bogs, from peat, privies, and sinks; 
 that which is obtained from the solution of 
 some carbonated metals during their oxy- 
 dation in the weak acids ; that which fre- 
 quently exhales from coal pits, from the 
 
 * When the simple combustibles, carbon, sul- 
 phur, or phosphorus, combines with any substance, 
 the compound is called a carburet, sulphuret, or 
 phosphuret, according as one or other of these bo- 
 dies enters into combination with the substance. If 
 any of these bodies combine with each other, the 
 compound is denoted by placing the name of that 
 substance first which predominates in the compound. 
 Thus, if phosphorus and sulphur are combined in 
 such a proportion, that the phosphorus predomi- 
 nates, it would be called phosphuret of sulphur. 
 
 + This gas is called carburetted hydrogen by some 
 chemists, and carbonated by others, we shall gene- 
 rally use the first of these terms. 
 
 mouths of volcanos ; those gases which are 
 derived from vegetable and animal matters 
 distilled at different temperatures, from al- 
 cohol, from ether, from oils, treated by 
 different re-agents, particularly by the con- 
 centrated acids ; — all these different in- 
 flammable gases, are carburetted hydrogen 
 gas, forming as many varieties as there are 
 different proportions of their principles ; 
 and sometimes also other combustible 
 matters are added to the carbon, dissolved 
 in hydrogen gas, which always forms its 
 base or radical. 
 
 However numerous the varieties of car- 
 buretted hydrogen gas may thus appear > 
 as well as the properties which it presents, 
 there may however, be discovered in the 
 whole of these varieties, a series of cha- 
 racters which connect them, and which 
 constitute them a distinct genus of com- 
 pounds. It is very evident, that we must 
 here attend only to the generic, or gene- 
 ral characters. Carburetted hydrogen gas 
 is heavier than pure hydrogen gas ; and 
 can but seldom be used for inflating aeros- 
 tatic machines ; it has a fetid odour which 
 is so much the stronger, as it holds more 
 of carbon in solution ; it extinguishes in- 
 flamed combustible bodies, and more com- 
 pletely stupifies animals than pure hydro- 
 gen gas ; it, in general, burns with less 
 rapidity than this last : its flame is often 
 blue and pale, sometimes it is red or white, 
 very brilliant, and, as it were, oily. It 
 frequently deposits carbon, distinguishable 
 by its black colour, when treated by differ- 
 ent processes ; it is, in general, more easily 
 and more abundantly condensed, or ab- 
 sorbed, by charcoal. In some circum- 
 stances, it forms oil, and it has then been 
 particularly named olefiant gas, which 
 ~ will be treated of in another part of this 
 work. 
 
 The uses of carbon are very numerous 
 in chemistry ; its strong affinity for oxygen 
 is employed with great success. After 
 hydrogen, this substance attracts it more 
 strongly than any other body ; and, at high 
 temperatures, it even attracts oxygen more 
 strongly than hydrogen itself : it is, for 
 this reason, that we have placed it im- 
 mediately after hydrogen. 
 
 It will afterwards be shown, that car- 
 bon is particularly used, to abstract oxy- 
 gen from many burned bodies, to reduce 
 them to their simple state of combustibility. 
 It is no Jonger doubtful, that carbon is a 
 principle employed by Nature, in forming 
 the greatest number of her compounds: it 
 it will be shown hereafter, that it consti- 
 tutes the base of all vegetable substances, 
 and, that it performs a very important part 
 in the great work of animal economy. 
 
 A singular and important property of 
 charcoal is that of destroying the smell, 
 colour, and taste of various substances : 
 
THE ARTISAN. 
 
 105 
 
 for the first accurate experiment on which 
 we are chiefly indebted to Mr. Lowitz, of 
 Petersburgh, though it had been long be- 
 fore recommended to correct the foetor of 
 foul ulcers, and as an antiseptic. Water, 
 that has become putrid by long keeping in 
 wooden casks, is rendered sweet by filter- 
 ing through charcoal powder, or by agita- 
 tion with it; particularly if a few drops of 
 sulphuric acid be added. Common vine- 
 gar boiled with charcoal powder becomes 
 perfectly limpid. Saline solutions, that 
 are tinged yellow or brown, are rendered 
 colourless in the same way, so as to afford 
 perfectly white crystals. Malt spirit is 
 freed from its disagreeable flavour by dis- 
 tilation with charcoal ; but if too much be 
 used, part of the spirit is decomposed. 
 Simple maceration, for eight or ten days, 
 in the proportion of about l-150th of the 
 weight of the spirit, improves the flavour 
 much. It is necessary, that the charcoal 
 be well burned, brought to a red heat be- 
 fore it is used, and used as soon as possi- 
 ble, or at least be carefully excluded from 
 the air. The proper proportion too should 
 be ascertained by experiment on a small 
 scale. The charcoal may be used repeat- 
 edly, by exposing it for some time to a red 
 heat before it is again employed. 
 
 Charcoal is used on particular occasions 
 as fuel, on account of its giving a strong 
 and steady heat without smoke. It is em- 
 ployed to convert iron into steel by cemen- 
 tation. It enters into the composition of 
 gunpowder. In its finer states, as in ivory 
 black, lampblack, &c. it forms the basis of 
 black paints, Indian ink, and printers’ ink. 
 
 It has already been remarked, that the 
 Diamond is carbon nearly pure . This was 
 verified in 1694 by the Florentine acade- 
 micians, in the presence of Cosmo III. 
 Grand Duke of Tuscany. By means of a 
 burning-glass they consumed several dia- 
 monds.* Francis I. Emperor of Germany, 
 afterwards witnessed the destruction of se- 
 veral more in the heat of a furnace. These 
 experiments were repeated by Darcet, Rou- 
 elle, Macquer, Cadet, and Lavoisier ; who 
 proved, that the diamond was not merely 
 evaporated, but actually burnt, and, that 
 if air was excluded it underwent no 
 change. 
 
 Mr. Lavoisier prosecuted these experi- 
 ments with his usual precision ; burnt dia- 
 monds in close vessels by means of pow- 
 erful burning-glasses; ascertained, that 
 dufing their combustion carbonic acid gas 
 was formed ; and, that in this respect there 
 was a striking analogy between them and 
 
 * Though the diamond, was till this period con- 
 sidered to be incombustible, yet Sir I. Newton sus- 
 pected, that it was combustible, from the great 
 power it has of refracting the rays of light. 
 
 charcoal, as well as in the affinity of both 
 when heated in close vessels. A very high 
 temperature is not necessary for the com- 
 bustion of the diamond. Sir George Mac- 
 kenzie ascertained, that they burn in a 
 mufflef when heated to the temperature of 
 14° of Wedgewood’s pyrometer; a heat 
 considerably less than is necessary to melt 
 silver. When raised to this temperature 
 they waste pretty fast, burning with a low 
 flame and increasing somewhat in bulk; 
 their surface too is often covered with a 
 crust of charcoal, especially when they are 
 consumed in close vessels by means of 
 burning glasses. 
 
 The experiments of Lavoisier have 
 often been repeated by several chemists, 
 particularly by Morveau, and Tennant ; 
 and from the result of their experiments it 
 is demonstrated, that the diamond affords 
 no other substance by its combustion than 
 pure carbonic acid gas ; and, that the pro- 
 cess is merely a solution of diamond in 
 oxygen gas, without much change in the 
 volume of the gas. 
 
 The only chemical difference perceptible 
 between diamond and the purest charcoal 
 is, that the charcoal contains a minute por- 
 tion of hydrogen ; it, therefore, becomes an 
 important question to determine if this very 
 minute portion of hydrogen can occasion 
 so great a physical difference as exists be- 
 tween these substances. This is a ques- 
 tion, however, that remains to be deter- 
 mined. 
 
 OF PHOSPHORUS. 
 
 Phosphorus, the third of the simple com- 
 bustibles, when placed in the order of its 
 affinity for oxygen, may be procured by 
 the following process : put a quantity of 
 bones into a crucible and burn or calcine 
 them, till they cease to smoke, or to give 
 out any odour, and afterwards reduce them 
 to a fine powder. Put 100 parts of this 
 powder into a basin of porcelain or stone- 
 ware, dilute it with four times its weight 
 of water, and then add gradually (stirring 
 the mixture after every addition) 40 parts 
 of sulphuric acid. The mixture will be- 
 come hot, and a vast number of air-bub- 
 bles will then be extricated. Leave the 
 mixture in this state for 24 hours ; taking 
 care to stir it well every now and then 
 with a glass or porcelain rod to enable the 
 acid to act upon the powder. 
 
 The whole is now to be poured on a filter 
 of cloth ; the liquid which runs through the 
 filter is to be received in a porcelain basin ; 
 and the white powder which remains on the 
 filter, after pure water has been poured on 
 it repeatedly, and allowed to strain into 
 the porcelain basin below, being of no use, 
 may be thrown away. 
 
 f A muffle is a kind of small earthen-ware oven, 
 open at one end, and fitted into a furnace. 
 
106 
 
 THE ARTISAN. 
 
 Into the liquid contained in the porce- 
 lain basin, which has a very acid taste, 
 pour nitrate of lead,* dissolved in water 
 very slowly ; a white powder will imme- 
 diately fall to the bottom : the nitrate of 
 lead must, however, be added as long as 
 any of this powder continues to be formed, 
 and when this ceases to be the case, throw 
 the whole upon a filter. The white pow- 
 der which remains upon the filter is then 
 to be ,well washed, allowed to dry, and 
 afterward mixed with about one-sixth of 
 its weight of charcoal powder. This mix- 
 ture is to be put into an earthen ware re- 
 tort ; and then put into a furnace, and the 
 
 beak of it plunged into a vessel of water, 
 so as to be just under the surface. Heat 
 is now to be applied gradually till the re- 
 tort be heated to whiteness. A vast num- 
 ber of air bubbles issue from the beak of the 
 retort, some of which take fire when they 
 come to the surface of the water. At last 
 there drops out a substance which has the 
 appearance of melted wax, and which con- 
 geals under the water. This substance is 
 phosphorus. 
 
 An alchemist of Hamburgh, named 
 Brandt, who, in searching for the philoso- 
 pher’s stone which he did not find, was 
 the first who, by chance, in 1677, disco- 
 vered this phosphorus for which he did 
 not seek. The singularity of this new pro- 
 duct induced Kunckel to associate with one 
 of his friends, named Kraft, to purchase 
 the secret of its preparation : but Kraft 
 having deceived his friend by procuring 
 the secret for himself, of which Kunckel 
 knew nothing more than that the phospho- 
 rus was prepared from urine, this philoso- 
 pher had the courage to undertake the 
 work of discovery. He, at last, succeeded 
 in obtaining phosphorus, which was long 
 called the phosphorus of Kunckel, on ac- 
 count of the success of his enlightened re- 
 searches. Boyle passes also for having 
 discovered phosphorus, and having de- 
 posited the process with the secretary of 
 the Royal Society of London, in 1680. In 
 1679, Kraft brought a small piece of it to 
 London to show it to the King and Queen 
 
 * This substance is procured by dissolving lead in 
 nitric acid or aquajortis ; but it, as well as the 
 other substances which may be mentioned in the 
 course of this part of our work, will be fully des- 
 cribed under their proper head, or class to which 
 they belong. 
 
 of England. Boyle gave his process to 
 Godfrey Hankwitz, a practical chemist of 
 London, who, for many years, sold the 
 product to all the philosophers of Europe, 
 This last operator, and Kunckel, were, for 
 some time, the only chemists who knew 
 how to prepare it. Boyle, however, des- 
 cribed his process in the philosophical 
 transactions for 1680 ; and Kraft inserted 
 his method in a treatise on phosphorus by 
 the Abbe de Commines published in June, 
 1683, though he had several times sold it 
 before. 
 
 That of Brandt was communicated in 
 Hooke’s Philosophical Collections, pub- 
 lished in English, in 1726, by Derham. 
 Homberg published a process, which he 
 said he had seen practised hy Kunckel, in 
 the Memoirs of the Academy of Sciences 
 for 1692. 
 
 Phosphorus was, however, made but 
 seldom, with difficulty, and in small quan- 
 tities in the laboratories, and it was a mere 
 object of curiosity, and the subject of a 
 few philosophical experiments. A small 
 stick or two of phosphorus usually com- 
 posed the whole portion in cabinets, when 
 in 1774, Gahn and Scheele in Sweden 
 made a capital discovery, which greatly 
 augmented the quantity of phosphorus pro- 
 duced in the laboratories, by showing, that 
 the acid from which it was extracted is 
 abundantly contained in the bones of ani- 
 mals ; but, notwithstanding all these re- 
 searches, it is still the scarcest, the most 
 expensive, and consequently the least em- 
 ployed of simple combustible bodies. 
 
 ASTROHOMY- 
 
 Respecting the Light of the sun, little 
 was known till the time of Sir Isaac New- 
 ton. Before his time, light had always 
 been esteemed a mere quality or modifica- 
 tion of matter; but it is now generally be- 
 lieved to be a real substance , or distinct spe- 
 cies of matter, emanating or flowing from 
 some luminous body, although in exceed- 
 ingly small particles. It is also known that 
 these particles proceed from the luminous 
 body in straight lines ; but their velocity 
 exceeds every species of motion with which 
 we are acquainted. 
 
 The velocity of light is to the velocity of 
 the earth in her oibit as 10,300 to 1, al - 
 though she moves at the rate of 68,000 
 miles per hour ; therefore light flies at the 
 rate of 187,878 miles per second, which is 
 about 1,550,000 times faster than a cannon 
 ball. This prodigious velocity of the par- 
 ticle§ of light, if they were not exceed- 
 ingly small, would prove fatal to our eye 
 sight; for they would strike with such 
 force, that our eyes could not bear the 
 shock. 
 
THE ARTISAN. 
 
 107 
 
 The time which light takes to arrive at 
 the earth from the sun is 8' 13". This was 
 discovered by Roemer, a Danish astrono- 
 mer, in the year 1644. By comparing the 
 eclipses of the first satellite of Jupiter with 
 the times of its immersions and emersions, 
 given by the tables of Cassini, he found 
 that the error of the tables depended on the 
 distance between Jupiter and the earth; 
 and hence he concluded that the motion of 
 light was not instantaneous, and that it 
 moved through the diameter of the earth’s 
 orbit in about 11 minutes. This, though a 
 sufficient discovery or proof of the pro- 
 gressive motion of light, was not accurate 
 enough to determine its true rate of velo- 
 city. However, thi3 was soon after dis- 
 covered by Dr. Bradley, to be what it is 
 stated at above. The intensity of light and 
 heat varies as the square of the distance. 
 For if an object be placed one foot distant 
 from a candle, and another two feet, the 
 one that is two feet distant will only re- 
 ceive one fourth part of the light that the 
 other does; and if it be removed to the 
 distance of three feet, it will only receive 
 one ninth part, and so on. It is the same 
 with respect to the heat imparted by any 
 body. 
 
 OF THE PLANET MERCURY. 
 
 Mercury is the nearest planet to the Sun, 
 and performs his revolution round that 
 luminary in the shortest period of all the 
 planets. The time he takes to perform 
 this revolution is 87d. 23h. 14' 32.7"*, 
 which is the length of his year. The length 
 of his day, or the time he takes to perform 
 a revolution round his axis, is not known : 
 for, by reason of his proximity to the Sun, 
 few observations can be made upon him. 
 He is so near the Sun, that he can seldom 
 be seen ; and when he does make his ap- 
 pearance, his motion is so rapid towards 
 the Sun, that he can only be discerned for 
 a very short time. When he can be seen, 
 it is a little before the Sun rises in the 
 morning, and a little after he is set in the 
 evening. His distance from the Sun is 
 36,668,373 English miles, and his diameter 
 
 is 3,241 miles, which makes him about 
 part of the size of the Earth. The rate at 
 which he moves in his orbit is not known. 
 The light and heat he receives from the 
 Sun are seven times greater than the Earth, 
 and the sun appears seven times as large to 
 him as to the Earth. 
 
 This planet appears to us with all the 
 various phases of the Moon, when viewed 
 at different times with a good telescope; 
 but he never appears quite full, because 
 his enlightened side is never turned di- 
 rectly towards the Earth, except when he 
 is so near the Sun as to be lost to our sight 
 in his beams. His enlighted side being 
 thus always turned towards the Sun, 
 proves that he shines not by any light of 
 his own ; for if he did, he would always 
 appear round and fully enlightened. It 
 is also plain he moves in an orbit within 
 that of the Earth’s, because he is never 
 seen opposite to the Sun, nor above 56 
 times the Sun’s breadth from him, his 
 greatest Elongation being about 28°; i In 
 heathen mythology, Mercury is styled the 
 Messenger of the Gods. 
 
 OF VENUS. 
 
 Venus is the next planet in order, and 
 computed to be 68,518,044 English miles 
 distant from the Sun. She moves at the 
 rate of 76,000 miles per hour ; and com- 
 pletes her revolution round the Sun in 224 
 days, 16 hours, 41 minutes, and 28 seconds. 
 
 The time she takes to revolve round her 
 axis, or the length of her day, is by some 
 astronomers stated at 23h. 21', and by 
 others at 24d. 8h. Venus is much about 
 the size of our earth, her diameter being 
 7687 English miles. When examined by 
 a good telescope, she exhibits the same 
 phases as Mercury and the Moon ; and her 
 surface is occasionally variegated by 
 darkish spots. These spots were em- 
 ployed by Cassini and Bianchini in de- 
 termining the revolution of Venus about 
 her axis. 
 
 In the following figure A represents 
 Venus, according to the late Sir William 
 Herschel, and B C according to Shroeter. 
 
 V enus is never seen opposite to the Sun, 
 nor more than 96 times the breadth of that 
 
 * The time which any planet takes to perform its 
 revolution round the sun, is called the length of its 
 year ; and the time which it takes to revolve round 
 its axis, the length of its day. 
 
 luminary from his centre, her greatest 
 elongation being about 47°, which proves 
 that her orbit includes that of Mercury. 
 When Venus is to the west of the Sun, she 
 is to be seen before the Sun rises, and is 
 then called the Morning Star ; when she is 
 
108 
 
 THE ARTISAN. 
 
 east of the Sun, she is to be seen after he 
 sets, and is then called the Evening Star. 
 Venus is in each of these situations for 
 290 days together. This may at first seem 
 surprising, that she should keep longer on 
 the east or west side of the Sun than the 
 whole time of her revolution round him. 
 But when it is recollected, that the Earth 
 is all the while going round the Sun the 
 same way, though not so quick as Venus, 
 the difficulty vanishes. For the relative mo- 
 tion of Venus to the Earth must, in every 
 period, be as much slower than her abso- 
 lute motion in her orbit, as the Earth 
 during that time advances forward in the 
 ecliptic, which is 220 degrees. To us 
 Venus appears brightest when her elon- 
 gation is about 40 degrees, both before and 
 after her inferior conjunction. 
 
 Some astronomers have imagined that 
 they perceived a satellite near Venus ; but 
 this has since been proved to have been 
 an illusion ; for, in her transit over the 
 Sun’s disc, she appeared unaccompanied 
 by any satellite.* Mr. Ferguson thinks 
 Venus may have a satellite revolving 
 round her, though it has not yet been dis~ 
 covered ; and adds, “ that this will not 
 appear very surprising, if we consider how 
 inconveniently we are placed for seeing 
 it.” 
 
 OF THE EARTH. 
 
 The Earth performs its revolution round 
 the Sun in an orbit between that of Venus 
 and Mars, at the distance of 95,173,000, in 
 365 days, 5 hours, 48 minutes, 49 seconds, 
 which is called the solar or tropical year. 
 In performing its annual circuit, the Earth 
 travels at the rate of 68,000 miles every 
 hour, which is 140 times faster than that of 
 a cannon ball. The diameter of the Earth 
 is 7,912 English miles, and its circumfer- 
 ence 24,855 ’42 miles.f That the Earth is 
 round like a globe, is evident from its sha- 
 dow in Eclipses of the Moon : for, 1st, The 
 
 * A transit of Venus happens very seldom. Only 
 two occurred in the last century ; one in 1761, and 
 the other in 1769. There will not be another till the 
 year 1874. Transists of Mercury happen much oftener. 
 There was one of this planet in 1822 ; but it was not 
 visible in Britain. 
 
 t This is what the French mathematicians have 
 lately deduced from a measurement of above 12° 
 of the meridian. 
 
 shadow is always bounded by a circular 
 line, although the Earth be constantly 
 turning its different sides to the Moon. 
 2d, By people at land only seeing the upper 
 part of the mast of a ship when she first 
 comes in sight, and as she approaches the 
 land the whole of her gradually becoming 
 visible. 2d, By its having been sailed 
 round by many navigators. 
 
 Several degrees of a meridian circle on 
 the Earth’s surface have been measured in 
 different parts, by which it has been dis- 
 covered, that a degree is longer at the poles 
 than at the equator, and therefore the true 
 figure of the Earth is that of an oblate 
 spheroid, the equatorial diameter exceed- 
 ing that of the polar by 26f miles. This 
 deviation from the real spherical shape is 
 occasioned by the diurnal rotation on its 
 axis ; for the gravity of the equatorial 
 parts is diminished by the centrifugal force 
 arising from their rapid motion, while the 
 gravity at the poles suffers no diminution. 
 
 OF MARS. 
 
 The planet Mars is 4,142 miles in dia- 
 meter, and performs his revolution round 
 the Sun in 686 days, 22 hours, 18 minutes, 
 at the distance of 144,588,575 miles. His 
 motion in his orbit is about 55,000 miles 
 per hour. The time he takes to revolve 
 round his axis is 24 h. 39' of our time. The 
 quantity of light and heat which Mars en- 
 joys is only equal to half what the Earth 
 enjoys ; and the Sun only appears to him 
 half as large as to the Earth. This planet 
 being only about a fifth part of the size of 
 the Earth, if any satellite attends him, it 
 must be very small, and has not yet been 
 discovered. To Mars the Earth and Moon 
 appear like two moons, a larger and a 
 smaller, changing places with each other, 
 and appearing sometimes horned, and 
 sometimes half or three quarters enlighten- 
 ed, but never full ; and never above a fourth 
 part of a degree distant from one another, 
 although they are 240,000 miles asunder. 
 Mars is very remarkably for the red colour 
 of his light, and for the great number and 
 variety of spots which mark his surface. 
 
 The following figure A, B, C, and D, 
 represent the different appearances of Mars 
 as seen by the late Sir W. Herschel, 
 through the astronomical telescope ; they 
 are therefore inverted. 
 
THE ARTISAN. 
 
 109 
 
 The atmosphere of this planet, which 
 astronomers have long considered as of an 
 extraordinary size and density, is the cause 
 of the singular redness of its light. 
 
 When observed by a good telescope, 
 Mars sometimes appears gibbous, or more 
 than half, but never horned ; which shows 
 that his orbit includes the Earth’s within 
 it, and also that he does not shine by any 
 light of his own. 
 
 In heathen mythology, Mars is styled the 
 God of War. 
 
 OF JUPITER. 
 
 The planet Jupiter is the largest of all 
 the planets, his diameter being 89,170 
 English miles. The time he takes to per- 
 form his revolution round the Sun is 4330 
 days, 14 hours, 39 minutes ; but his motion 
 round his axis is extremely rapid, being 
 completed in the short space of 9 hours, 
 55 minutes. His distance from the Sun is 
 stated at 492,365,207 English miles ; and 
 his hourly motion in his orbit at 25,000 
 miles. 
 
 The form of Jupiter, like that of the 
 Earth, is an oblate spheroid, the equatorial 
 diameter being to the polar at 14 to 13. 
 
 When this planet is examined through a 
 good telescope, several belts or bands are 
 perceived extending across his disc, in 
 lines parallel to his equator. 
 
 (To be continued 
 
 fBtscellaneous Subjects. 
 
 BIOGRAPHICAL MEMOIR OF 
 THOMAS SIMPSON. 
 
 ( Continued from page 94 . ) 
 
 He proposed, and resolved many ques- 
 tions in the Ladies’ Diaries, &c. sometimes 
 under his own name, as in the years 1735 
 and 1736, and Sometimes under feigned or 
 fictitious names ; such as, it is thought, 
 Hurlothrumbo, Kubernetes, Patrick O’Ca- 
 venah, Marmaduke Hodgson, Anthony 
 Shallow, Esq. and probably several others. 
 See the diaries for the years 1735 to 60. 
 Mr. Simpson was also the editor or com- 
 piler of the Diaries from the year 1754 till 
 the year 1760, both inclusive, during which 
 time he raised that work to the greatest 
 degree of respect. 
 
 It has also been commonly supposed, 
 that he was the real editor of, or had a 
 principal share in, two other periodical 
 works of a miscellaneous mathematical 
 nature ; viz. the Mathematician, and Tur- 
 ner’s Mathematical Exercises, 2 volumes 
 in 8vo. which came out in periodical num- 
 bers, in the years 1750 and 1751, &c. 
 
 In the year 1763, when the plans pro 
 posed for erecting a new bridge at Black- 
 friars were in agitation, Mr. Simpson, 
 among other gentlemen, was consulted 
 upon the best form for the arches, by the 
 New-bridge Committee. 
 
 Upon this occasion he gave a preference 
 to the semicircular form ; and besides his 
 report to the Committee, some letters also 
 appeared, by himself and others, on the 
 same subject, in the public newspapers. 
 
 From Mr. Simpson’s writings, we now 
 return to himself. Through the interest 
 and solicitations of the beforementioned 
 William Jones, Esq. he was, in 1743, ap- 
 pointed professor of mathematics, then va- 
 cant by the death of Mr. Derham, in the 
 Royal Academy at Woolwich; his w r arrant 
 bearing date August 25th. And in 1745 
 he was admitted a fellow of the Royal 
 Society, having been pyoposed as a candi- 
 date by Martin Folkes, Esq. President, 
 William Jones, Esq. /Mr. George Graham, 
 and Mr. John Machin, Secretary ; all very 
 eminent mathematicians. The president 
 and council, in consideration of his very 
 moderate circumstances, were pleased to 
 excuse his admission fees, and likewise 
 his giving bond for the settled future 
 payments. 
 
 At the academy he exerted his faculties 
 to the utmost, in instructing the pupils who 
 were the immediate objects of his duty, as 
 well as others, whom the superior officers 
 of the ordnance permitted to be boarded 
 and lodged in his house. In his man- 
 ner of teaching he had a peculiar and 
 happy address ; a certain dignity and per- 
 spicuity, tempered with such a degree of 
 mildness, as engaged both the attention, 
 esteem, and friendship of his scholars ; of 
 which the good of the service, as well as 
 of the community, was a necessary conse- 
 quence. 
 
 In the latter stage of his existence, when 
 his life was in danger, exercise and a 
 proper regimen were prescribed him, but 
 to little purpose : for he sunk gradually 
 into such a lowness of spirits, as often in 
 a manner deprived him of his mental fa- 
 culties, and at last rendered him incapable 
 of performing his duty, or even of reading 
 the letters of his friends ; and so trifling an 
 accident as the dropping of a tea-cup would 
 flurry him as much as if a house had 
 tumbled down. 
 
 The physicians advised his native air for 
 his recovery : and in February 1761, he set 
 out, with much reluctance (believing he 
 should never return) for Bosworth, along 
 with some relations. The journey fatigued 
 him to such a degree, that upon his arrival 
 he betook himself to his chamber, where 
 he grew continually worse and worse, to 
 the day of his death, which happened the 
 
110 
 
 THE ARTISAN, 
 
 14th of May, in the fifty-first year of his 
 age. 
 
 At his death, Mr. Simpson left in being, 
 besides his widow, her daughter and son 
 by her first husband, and his own daughter 
 and son, the latter of whom was born after 
 his arrival in London. The two daughters 
 had married officers of artillery, and young 
 Simpson had been presented with a com- 
 mission in the same corps, and lived to 
 have a company in the Royal Artillery ; 
 but on account of a besotted habit of 
 drunkenness, and other misconduct, he was 
 broke, and died soon after. 
 
 As to Mr. Simpson’s widow, the King, 
 at the instance of Lord Viscout Ligonier, 
 the then Master General, in consideration 
 of Mr. Simpson’s great merits, was graci- 
 ously pleased to grant her a handsome 
 pension for life, together with apartments 
 adjoining to the academy ; a favour that 
 had never been conferred on any before. 
 Here she lived, and her son Swinfield, the 
 tailor, and his wife, along with her, in the 
 same apartments, for many years. She 
 died only December the 14th, 1782, at the 
 great age of one hundred and two. Her 
 son Swinfield survived her only a few 
 years. 
 
 ON THE LINE OF PERPETUAL 
 CONGELATION. 
 
 In consequence of the diminution of tem- 
 perature which is experienced as we ascend 
 in the atmosphere, it is evident that in every 
 climate a point of elevation may be reached 
 where it will be continually freezing. The 
 altitude of the point above the surface of 
 the earth, will depend partly on the tem- 
 perature of the lower regions of the atmos- 
 phere, and partly on the decrement of heat 
 belonging to the column at the period of 
 observation. Thus, near the equator, it 
 was observed by Bouguer, that it began to 
 freeze on the sides of the lofty mountain 
 
 H 
 
 Pinchencha, at the height of 15,577 feet 
 above the level of the sea, whereas 
 congelation was found by Saussure to 
 take place on the Alps at the height of 
 13,428 feet. By tracing a line on the 
 plane of the meridian, through the points 
 at which it constantly freezes, a curve is 
 obtained, which has been denominated the 
 line of Perpetual Congelation. The height 
 at which this curve intersects a vertical line 
 in the various latitudes, has been computed 
 by Kir wan, partly from observation, and 
 partly from the mean temperature of the 
 parallel, and the decrement of heat, as we 
 ascend in the atmosphere. The following 
 table exhibits the result of his calculation \ 
 and though it is constructed on the erro- 
 neous supposion, that the mean annual 
 temperature of the pole is 31°, which ac- 
 cording to the observations of Captain 
 Scoresby and Captain Parry, must be far 
 beyond the truth, it is tolerably accurate 
 for the more accessible regions of the 
 globe. 
 
 Latitude. 
 .0 - 
 
 
 Mean Height of Lii 
 of Congelation. 
 - - 15,577 
 
 5 
 
 - 
 
 - 
 
 - - 
 
 15,457 
 
 10 
 
 - 
 
 
 - _ 
 
 15,067 
 
 15 
 
 - 
 
 
 - - 
 
 15,498 
 
 20 
 
 - 
 
 - 
 
 - - 
 
 13,719 
 
 25 
 
 - 
 
 
 - - 
 
 13,030 
 
 30 
 
 - 
 
 
 - . 
 
 11,592 
 
 35 
 
 - 
 
 
 - z 
 
 10,664 
 
 40 
 
 - 
 
 
 - - 
 
 9,016 
 
 45 
 
 - 
 
 
 - - 
 
 7,658 
 
 50 
 
 - 
 
 
 - - 
 
 6,260 
 
 55 
 
 - 
 
 
 - . 
 
 4,912 
 
 60 
 
 - 
 
 
 . •_ 
 
 3,684 
 
 65 
 
 - 
 
 
 - - 
 
 2,516 
 
 70 
 
 - 
 
 
 - -- 
 
 1,557 
 
 75 
 
 - 
 
 
 - - 
 
 748 
 
 80 
 
 - 
 
 
 - - 
 
 128 
 
 These numerical 
 
 relations will be 
 
 perceived at a glance, by means of the fol- 
 lowing diagram. 
 
THE ARTISAN, 
 
 111 
 
 , Here E P represents the rectified meri- 
 dian from the equator to the pole divided 
 nto intervals of 10° each ; and the different 
 •erpendiculars or ordinates at the point 
 , 10, 20, &c. represent the height of the 
 eezing point at the equator, and at latitude 
 0, 20, &c. to the pole P. The curve HP, 
 /hich has a contrary flexure about 60°, 
 ihibits the general form of the line of 
 ’erpetual Congelation from the equator to 
 ie pole. 
 
 NEW FRENCH WEIGHTS AND 
 MEASURES. 
 
 During the time of the French republic, 
 a new system of weights and measures was 
 introduced into France, the foundation of 
 which was the measure of a degree of the 
 meridian. 
 
 This was determined to be 57027 toises, 
 from the mean of the measurement of 12 
 degrees, about latitude 45 deg. ; hence a 
 quadrant of the meridian is 5132430 toises, 
 and from this number the weights and 
 measures now used in France are deduced. 
 
 The Metre , which is the base of the new 
 system, is the 10,000,000 part of 5132430 
 toises, or quadrant of the meridian, and is 
 equal to 39*371 English inches. The other 
 measures of length both ascend and de- 
 scend, decimally, as follows : — 
 
 10 Metres ~ 1 Decametre. 
 
 10 Decametres — 1 Hectometre. 
 
 10 Hectometres zz 1 Kilometre or mile. 
 
 10 Kilometres — 1 Myriametre or league 
 1 Metre zzlO Decimetres. 
 
 1 Decimetre zzlO Centimetres. 
 
 1 Centimetre =10 Millimetres. 
 
 The square of the Decametre constitutes 
 the Are, and that of the Hectometre, the 
 Hectare, or Acre. 
 
 The cube of a Metre forms the unit of 
 solid measure, or the Stere ; and that of a 
 Decimetre, the Litre, or Pint ; and the 
 weight of this bulk of water, at its greatest 
 contraction, makes the Kilogramme, or 
 Pound; and the weight of the cube of a 
 Centimetre of distilled water is called the 
 Gramme. 
 
 The value of these in English measure 
 are as follows : — 
 
 The Toise == 76-7344 English inches. 
 
 or 1 Toise . . . . = 1-0657 fathoms. 
 
 1 Metre . . . . = 39-371 inches.* 
 
 1 Myriametre or league= 6-213856 English miles. 
 
 1 Are = 1077-119234 square feet. 
 
 1 Hectare or Acre . = 2*47117 English acres. 
 
 1 Stere .....;= 35-3171 solid feet. 
 
 1 Litre = 61-0280 cubic inches. 
 
 1 Kilogramme or pound= 2-1133 troy ounces. 
 
 1 Gramme . . . == 15-444 troy grains. 
 
 * 1 Decimetre is— 3.93710 inches. 
 1 Centimetre = .39371 do. 
 
 1 Millimetre = .03937 do. 
 
 ANSWER TO QUERIES, 
 
 AT PAGE 64. 
 
 Not having received any answer to the 
 queries of Aquatus and of a Mechanic , we 
 shall here give our own opinion on the sub- 
 ject of these queries. And on theirs*, we 
 can only say, that, as far as our experience 
 and observations extend, we know of no 
 exception to the general law of all dry 
 solid bodies becoming hot by friction , or 
 rubbing. But we are not philosophers 
 enough to give any good reason why 
 liquids do not become hot by the same 
 means. Perhaps it may be on account of 
 the want of cohesion between their minute 
 particles, or on account of the form of their 
 particles. 
 
 On the query of a Mechanic we have to 
 remark, that we know of no instrument 
 which exhibits, by inspection , any tempe- 
 rature between seven hundred and a thou- 
 sand degrees of Fahrenheit's scale. Be- 
 tween the boiling point of mercury (about 
 660°) and the commencement of Wedg- 
 woods pyrometer (about 1077° of Fahren- 
 heit’s) there is no method of ascertaining 
 the temperature of a body but by induction, 
 or inferences drawn from a comparison of 
 the mercurial thermometer with Wedg- 
 wood’s, or other pyrometers. 
 
 Though “ V ” might have applied to 
 any other person with equal propriety as 
 to us, to solve his queries, (they having no 
 reference to the “ Artisan”) we shall, on 
 this occasion, comply with his request. 
 The 45th of Euc. b. 1, is perfectly general ; 
 and it matters not whether it be illustrated 
 by a four , or a forty-sided rectilineal 
 figure ; but in no instance could it super- 
 sede, or be superseded by, any part of the 
 32d of the 1st Book. The 32d and its 
 corollories relate entirely to angles, whereas 
 the 45 th relates to space , or area. 
 
 There is no more connection between 
 the 7th and 8th of Book 3d, than any two 
 propositions in the Elements. The fact is, 
 there is no connection at all between them ; 
 and the one is not even alluded to in the 
 proof of the other. 
 
 In the 28th of the 3d, there is no neces- 
 sity either to assert or prove that equal 
 straight lines in the same circle cut off 
 equal circumferences; because if this be 
 the case in equal circles, it is perfectly 
 evident it must do so in the same circle ; 
 and the truth is, it could not be a circle 
 unless this were the case ; ergo, “ V. is 
 wrong in every thing.” — Edit. 
 
112 
 
 THE ARTISAN. 
 
 SOLUTIONS OF QUESTIONS. 
 
 To the Editor of the Artisan. 
 
 Sir, 
 
 Please insert the following solution of 
 Mr. Graham’s question, inserted at page 
 64 of the Artisan, which will oblige, 
 your’s, &c. Vulcan. 
 
 The cubical content of the whole globe, 
 including the glass, is 282+1=283, which 
 divided by 5 ’236 (the solidity of a sphere 
 whose diameter is 1), and the cube root of 
 the quotient extracted gives 8*146 for the 
 diameter of the globe ; and 282, the cubic 
 inches of ale, divided by 5*236, and the 
 cubic root extracted, gives 8*136 for the 
 diameter of the inside of the globe ; conse- 
 , (8*146 — 8*136) *01 
 
 quently, — — — *005, or 
 
 ^ of an inch is the thickness of the 
 glass. 
 
 This question was also solved by the 
 proposer ; but he will observe by the above 
 solution, that he committed a small error, by 
 f 283 
 
 stating 1/ ~ 8*2, instead of 8*146, 
 
 which materially affects the result. — Ed. 
 
 To the Editor of the Artisan. 
 
 Sir, 
 
 Having observed in the last Number of 
 your valuable publication (page 96) two 
 questions by J. M. Edney, I have taken 
 the liberty of offering you what I conceive 
 to be a just solution, which if you think 
 proper to insert in a future Number of the 
 Artisan, will greatly oblige, your’s, &c. 
 
 Hugh Starke. 
 
 Ex. 1. The areaof the circle is 706*86, and 
 dividing this by 3*6339124, the area of the 
 heptagon whose side is l, we obtain 
 194*5176, the square of the side of the 
 heptagon ; and the square root of this is 
 13*946, which is the side of the heptagon 
 required. 
 
 Ex. 2. Let 10 x + y represent the number, 
 the digits of which are x and y. Then 
 from the first part of the question the fol- 
 lowing equation arises, 10 x + y + 54 zz 
 10 y + x ; and from the second part of 
 the question arises the second equation, 
 y 2 —x 2 ~ 60; then the value of x being 
 
 f| 7/ — — — 
 
 found in the 1st equation — — — — y—6, 
 and that of x 2 in the second ~y 2 — 60, the 
 
 first value of x squared gives x 1 ~ y 2 — 
 12y + 36IZ?/ 2 — -60, or 12yiz96, cry— 8; 
 but a* — y — 6, or 2. Hence the number 
 required is 28. 
 
 These two questions were also solved by 
 the proposer ; by Mr. A. Peacock, St. 
 George’s East ; and the last one was also 
 solved, very neatly, by Mr. J. Harding, 
 Hart-street, Grosvenor-square ; and Mr. 
 George Futooye, High-street, Marylebone. 
 
 The solution of Charon’s, and Mr. Gra- 
 ham’s question, inserted on the same page 
 of the “ Artisan” with the two foregoing, 
 will appear in our next. 
 
 The questions for solution in the present 
 sheet are numbered so as to include all 
 that have preceded them in the “ Artisan 
 and this plan will be continued, in order 
 to prevent mistakes in their solutions, and 
 to afford a ready method of referring to any 
 particular question. — Ed. 
 
 QUESTIONS FOR SOLUTION. 
 
 To the Editor of the Artisan. 
 
 Sir, 
 
 Wishing to contribute to your valuable 
 publication, as far as my humble abilities 
 will allow, I enclose you the following 
 question for insertion, if convenient, in 
 your next Number. R. Graham. 
 
 Ranelagh-st. Liverpool. 
 
 Quest. 12. — Given the versed sine 4, and 
 the length of the arc 100, to find the dia- 
 meter of the circle ? 
 
 To the Editor of the Artisan. 
 
 Sir, 
 
 Please to insert the following question in 
 one of your succeeding Numbers, which 
 will very much oblige your obedient ser- 
 vant, H. Flather. 
 
 33, Seymour -place, . Bryansto7ie-square , 
 
 April 5.th, 1824. 
 
 Quest. 13. What are the cubic contents 
 of a space 43| inches long, 13 inches wide, 
 and 7~ inches deep. This being the quan- 
 tity of water displaced by a model, on a 
 scale of 1 foot to | an inch ; it is required 
 to know how many cubic feet are con- 
 tained in the said figure according to this 
 scale ? 
 
THE ARTISAN. 
 
 113 
 
 GEOMETRY* 
 
 PROPOSITION XX. 
 
 Theorem. — Any two sides of a triangle are 
 together greater than the third side. 
 
 Let ABC 'be a triangle ; any two sides 
 of it together are greater than the third 
 side ; viz. the sides BA, A C, greater than 
 the side B Cj and A B, B C, greater than 
 A C ; and BC, C A, greater than A B. 
 
 D 
 
 Produce B A to the point D, and make 
 A X> equal to A C, and join DC. 
 
 Because D A is equal to A C, the angle 
 A D C is likewise equal to A C D ; but the 
 angle BCD is greater than the angle ACD ; 
 therefore, the angle B C D is greater than 
 the angle ADC; and because the angle 
 BCD of the triangle D C B is greater 
 than its angle B D C, and that the greater 
 side is opposite to the greater angle : there- 
 fore the side D B is greater than the side 
 B C ; but D B is equal to B A and A C to- 
 gether; therefore BA and A C together 
 are greater than B C. In the same man- 
 lier it may be demonstrated, that the sides 
 A B, B C are greater than C A, and B C, 
 CA, greater than AB. Therefore any 
 two sides, &c. Q. E. D. 
 
 Dr. Simpson remarks, (from Proclus,) 
 that u the Epicureans derided this propo- 
 sition as being manifest to asses some of 
 the moderns have done the same, but 
 equally without reason : for, according to 
 Euclid’s plan, a demonstration was neces- 
 sary. (See Prop. 3, obs.page 19.) 
 
 PROPOSITION XXI. 
 Theorem. — If from the ends of one side of a 
 triangle there be drawn two straight lines 
 to a point within the triangle , these two 
 lines shall be less than the other two sides 
 of the triangle , but shall contain a greater 
 angle. 
 
 Let the two straight lines BD, CD, be 
 drawn from B, C, the ends of the side B C 
 of the triangle A B C, to the point D within 
 it ; B D and D C are less than the other two 
 sides B A and A C of the triangle, but con- 
 tain an angle B D C greater than the angle 
 B AC. 
 
 Vol. L— N° 8. 
 
 A 
 
 Produce B D to E ; and because two 
 sides of a triangle are greater than the 
 third side, the two sides BA, AE, of the 
 triangle ABE are greater than B E. To 
 each of these add E C ; therefore the sides 
 BA, AC, are greater than BE, EC: 
 Again, because the two sides C E, ED, of 
 the triangle CED are greater than CD, 
 add D B to each of these ; therefore the 
 sides CE, E B, are greater than C D, D B ; 
 but it has been shewn that B A, A C, are 
 greater than BE, EC; much more then 
 are BA, AC, greater than B D, D C. 
 
 Again, because the exterior angle of a 
 triangle is greater than the interior and 
 opposite angle, the exterior angle BDC of 
 the triangle C D E is greater than CED; 
 for the same reason, the exterior angle 
 CEB of the triangle A B E is greater 
 than B A C : and it has been demonstrated 
 that the angle B D C is greater than the 
 angle CED; much more then is the angle 
 BDC greater than the angle BAC. 
 Therefore, if from the ends of, &c. Q.E.D. 
 
 It is essential to the truth of this pro- 
 position, that the straight lines drawn to 
 the point within the triangle, be drawn 
 from the two extremities of the base ; for 
 omitting this limitation, there are cases in 
 which the sum of the two lines drawn 
 from the base to a point within the triangle, 
 will exceed the sum of the two sides of the 
 triangle. 
 
 PROPOSITION XXII. 
 Problem. • — To construct a triangle of 
 which the sides shall be equal to three given 
 straight lines ; but any two whatever qf 
 these lines must be greater than the third. 
 
 Let A, B, C be the three given straight 
 lines, of which any two whatever are 
 greater than the third ; viz. A and B greater 
 than C ; A and C greater than B ; and B 
 and C than A. It is required to make a 
 triangle of which the sides shall be equal 
 to A, B, C, each to each. 
 
 Take a straight line D E terminated at 
 the point D, hut unlimited towards E, and 
 make D F equal to A, F G to B, and G H 
 equal to C : and from the centre F, at the 
 distance F D, describe the circle D K L ; 
 and from the centre G, at the distance GH, 
 describe another circle HLK; and join 
 i 
 
114 
 
 THE ARTISAN. 
 
 K F, KG: the triangle K F G has its sides 
 equal to the three straight lines A, B, C. 
 
 K. 
 
 B— 
 
 c — 
 
 Because the point F is the centre of the 
 circle DKL, FD is equal toFK; but 
 F D is equal to the straight line A ; there- 
 fore FK is equal to A : Again, because G 
 is the centre of the circle LKH, G H is 
 equal to G K ; but G H is equal to C ; 
 therefore also G K is equal to C; and FG 
 is equal to B ; therefore the three straight 
 lines K F, F G, G K, are equal to the three 
 A , B, C : And therefore the triangle K F G 
 has its three sides K F, F G, G K equal to 
 the three given straight lines A, B, C. 
 Which was to be done, 
 
 PROPOSITION XXIII. 
 
 Problem.— At a given point in a given 
 straight line , to make a rectilineal angle 
 equal to a given rectilineal angle . 
 
 Let A B be the given straight line, and 
 A the given point in it, and DCE the 
 given rectilineal angle ; it is required to 
 make an angle at the given point A in the 
 given straight line AB, that shall be equal 
 to the given rectilineal angle DCE. 
 
 A 
 
 Take in C D, C E any points D, E, and 
 join D E ; and make the triangle A F G, 
 the sides of which shall be equal to the 
 three straight lines C D, D E, C E, so that 
 C D be equal to A F, C E to A G, and D E 
 to F G ; and because DC, C E, are equal 
 to F A, A G, each to each, and the base 
 D E to the base EG: the angle D C E is 
 equal to the angle FAG. Therefore, at 
 the given point A in the given straight line 
 A B, the angle F A G is made equal to the 
 given rectilineal angle DCE. Which was 
 to be done. 
 
 PROPOSITION XXIV. 
 
 Theorem. — If two triangles have two sides 
 of the one equal to two sides of the other , 
 each to each , but the angle contained by 
 the two sides of the one greater than the 
 angle contained by the two sides of the 
 other ; the base of that which has the 
 greater angle shall be greater than the 
 base of the other. 
 
 Let ABC, D E F be two triangles which 
 have the two sides A B, A C, equal to the 
 two D E, D F, each to each ; viz. A B equal 
 to D E, and AC to D F ; but the angle 
 B A C greater than the angle E D F : the 
 base B C is also greater than the base EF. 
 
 Of the two sides D E, D F, let D E be 
 the side which is not greater than the 
 other, and at the point D, in the straight 
 line D E, make the angle E D G equal to 
 the angle B A C ; and make D G equal to 
 A C or D F, and join E G, G F. 
 
 Because A B is equal to D E, and A C 
 to D G, the two sides B A, A C, are equal 
 to the two E D, D G, each to each, and the 
 angle B A C is equal to the angle E D G ; 
 therefore the base B C is equal to the base 
 E G ; and because D G is equal to D F, the 
 angle D F G is equal to the angle D G F ; 
 but the angle D G F is greater than the 
 angle E G F : therefore the angle D F G is 
 greater than EGF ; and much more is the 
 angle E F G greater than the angle EGF; 
 and because the angle E F G of the triangle 
 E F G is greater than its angle EGF, and 
 that the greater side is opposite to the 
 greater angle ; the side EG is therefore 
 
THE ARTISAN. 
 
 115 
 
 greater than the side E F ; but E G is equal 
 to B C ; and therefore also B C is greater 
 than E F. Therefore, if two triangles, &c. 
 Q.ED. 
 
 PROPOSITION XXV. 
 
 Theorem. — If two triangles have two sides 
 of the one equal to two sides of the other , 
 each to each , but the base of the one greater 
 than the base of the other ; the angle con- 
 tained by the sides of that which has the 
 greater base , shall be greater than the 
 angle contained by the sides of the other. 
 Let A B C, D E F, be two triangles which 
 have the two sides A B, A C, equal to the 
 two sides DE, DF, each to each ; viz. A B 
 equal to DE, and AC to DF : but the base 
 C B is greater than the base E F ; the 
 angle B A C is likewise greater than the 
 angle EDF. 
 
 I) 
 
 For, if it be not greater, it must either be 
 equal to it, or less ; but the angle B A C is 
 not equal to the angle EDF, because then 
 the base B C would be equal to E F ; but 
 it is not ; therefore the angle B A C is not 
 equal to the angle EDF; neither is it 
 less ; because then the base B C would be 
 less than the base E F ; but it is not ; there- 
 fore the angle B A C is not less than the 
 angle EDF; and it was shewn that it is 
 not equal to it : therefore the angle BAG 
 is greater than the angle EDF. Where- 
 fore, if two triangles, &c. Q. E. D. 
 
 Th,e two last Propositions, as well as the 
 18th and 19th, are converse propositions. 
 
 MECHANICS 
 
 OF THE PULLEY. 
 
 The pulley is a wheel or cylindrical 
 piece of wood, or any other hard substance, 
 with a groove cut out of its rim, for the 
 purpose of allowing a rope to pass over it. 
 The cylinder moves round an axis, which 
 works in a frame, called the block. 
 
 A system of pulleys, or a number of 
 them combined together, is called a muffle , 
 and is either fixed or moveable, according 
 as the block which contains the pulleys is 
 fixed or moveable. When the pulley is 
 
 fixed, it gives no mechanical advantage, 
 but serves merely to change the direction 
 of the power applied to the cord which 
 passes over it. There is, therefore, an 
 equilibrium in the single fixed pulley when 
 the power and weight are equal. 
 
 Let a power and weight P, W, equal to 
 each other, act by means of a perfectly 
 flexible cord P D W, which passes over 
 the fixed pulley A D B ; 
 
 then whatever force is exerted at D, in the 
 direction DAP, by the power, an equal 
 force is exerted by the weight in the direc- 
 tion D B W ; these forces will, therefore, 
 keep each other in equilibrio. 
 
 This proposition is true in whatever 
 direction the power is applied ; the only 
 alteration made, by changing its direction, 
 is in the pressure upon the centre of 
 motion. 
 
 When the pulley is moveable, one end of 
 the cord is made fast to a fixed point ; the 
 power is applied to the other, and the 
 weight hangs by the block in which the 
 axis of the pulley is fixed. 
 
 Thus, a string fixed at E, passes under 
 the moveable pulley A, and over the fixed 
 pulley B ; 
 
 i 2 
 
116 
 
 THE ARTISAN. 
 
 the weight is fixed to tine eentre of the 
 block A, and the power is applied at P. 
 
 In a pulley of this kind, where the cords 
 are parallel, the power is to the weight as 
 1 to 2 ; that is, a body of any given weight 
 will balance another body double that 
 weight. For, since the cords EA and 
 B A are in the direction in which the 
 weight acts, they exactly sustain it ; and 
 they are equally stretched in every point ; 
 therefore, they sustain it equally between 
 them, or each sustains half the weight. 
 Therefore P is to W, as 1 to 2, as already 
 stated. 
 
 When the pulley is heavy, and acts in 
 the same direction as the resistance, the 
 weight of the pulley must be considered as 
 part of the resistance. If the direction of 
 the resistance be different from that in 
 which the block hangs, the weight which 
 it adds to the resistance, may be determined 
 by the resolution of forces : see page 24th. 
 
 In a muffle, or system, where the same 
 cord passes round any number of pulleys, 
 and the parts of it between the pulleys are 
 parallel, the power is to the resistance as 
 1 to the number of cords at the lower 
 block. 
 
 For the force being equally communi- 
 cated throughout the length of the cord, 
 each portion will co-operate equally in 
 supporting the weight, and will support 
 that portion of it which is to the whole as 
 I to the number of cords ; consequently, a 
 weight equal to that portion will retain 
 any part of the cord in equilibrium,* and 
 with it the whole cord and the whole 
 weight. And if the radii of the pulleys be 
 taken in arithmetical progression, their 
 angular velocity may be made equal *, and 
 they may be fixed in the same axis, as in 
 the annexed figure. 
 
 There is, however, various combinations 
 of pulleys, where the same cord passes 
 round all the pulleys ; but the ratio of the 
 power to the resistance is the same as that 
 just stated. 
 
 The following figure represents another 
 system of this description. 
 
 In a system where each pulley hangs by 
 a separate string, and the strings are 
 parallel, the power is to the weight as 1 to 
 
 * That is, the number of revolutions made by 
 each will be in the inverse ratio of iis radius. 
 
THE ARTISAN. 
 
 \\7 
 
 that power of 2, whose index is the number 
 of moveable pulleys.* 
 
 In the following system, a cord passes 
 over the fixed pulley A, and under the 
 moveable pulley B, and is fixed at E : 
 
 another cord is fixed at B, passes under 
 the moveable pulley C, and is fixed at F, 
 &c. in such a manner that the cords are 
 parallel. 
 
 Here the number of moveable pulleys 
 are three, and therefore the power is to 
 the weight as 1 to 2, raised to the third, 
 poiver , that is, as 1 to 8 ; consequently 
 when there are three moveable pulleys, 
 there will be an equilibrium, if the power 
 be one-eighth part of the weight. 
 
 In a system of pulleys, each hanging by 
 a separate cord, where the cords are at- 
 tached to the weighty as is represented in 
 the following figure, the power is to the 
 weight as 1 to the number 2, raised to that 
 power whose index is the number of 
 moveable pulleys, diminished by unity 
 or l.t 
 
 A cord fixed to the weight at F, passes 
 over the pulley C, and is again fixed to 
 the pulley B; another cord, fixed at E, 
 passes over the pulley B, and is fixed to 
 
 * Tf any number be multiplied into itself any 
 number of times, the products are called powers of 
 that number ; and the figure which denotes the 
 number of times it has been multiplied by itself, is 
 called the index of that pow er. 
 
 t See the preceding note. 
 
 the pulley A, &c. in such a manner that 
 the cords are parallel. 
 
 As the number of pulleys is here three, 
 2 raised to this power, and then diminished 
 by 1, is 7 ; therefore the advantage gained 
 is as 7 to 1, or there will be an equilibrium 
 between the power and the resistance, 
 when the power is one-seventh part of the 
 weight or resistance. 
 
 When the cords are not parallel, the 
 powers in each case, is to the corresponding 
 pressure upon the centre of the pulley as 
 the radius is to twice the cosine of the 
 angle made by the cord with the direction 
 in which the weight acts* Also, by the 
 resolution of forces, the power in each 
 case, or pressure upon the former pulley, 
 is to the weight it sustains, as the radius is 
 to the cosine of the angle made by the 
 cord with the direction in which the weight 
 acts. 
 
 It is obvious, that the pulley is reducible 
 to the lever of the second kind , or, still 
 more directly, to the case of a body sup- 
 ported by two props, see page 56. 
 
 From being so extremely portable, and 
 so applicable to cordage, the pulley is of 
 all the mechanical powers the most useful 
 at sea. 
 
 * To comprehend this proposition completely, it 
 is necessary to have a slight knowledge of trigono- 
 metry. (See page 21, col. 2, and note.) 
 
118 
 
 THE ARTISAN. 
 
 OF THE INCLINED PLANE. 
 
 The inclined plane is any plane surface 
 which forms an angle with the horizon, 
 and that angle is termed the inclination of 
 the plane. 
 
 When a body is placed on an inclined 
 plane, the force urging it to descend along 
 the plane, is to the whole force of gravity, 
 as the height of the plane is to its length, 
 and therefore there will be an equilibrium 
 when the power is to the resistance as the 
 height of the plane to its length. 
 
 Thus, in the following figure, the weight 
 of the body A, resting on the inclined 
 plane, whose oblique length is to its height 
 as 5 to 3, is sustained by a weight B, three 
 fifths of the weight of itself. 
 
 If bodies descend on any inclined planes 
 of equal heights, but of different inclina- 
 tions, the times of descent are as the 
 lengths of the planes, and the final velo- 
 cities are equal. Thus, a body will acquire 
 a velocity of 32 feet in a second, after 
 having descended 16 feet, either in a ver- 
 tical or oblique direction ; but the time of 
 descent will be as much greater than a 
 second, as the oblique length of the path 
 is greater than 16 feet. This may be 
 proved by experiment, allowing for the 
 retardation by friction, the times being 
 measured by a pendulum or stop watch. 
 
 There is a singular proposition, of a 
 similar nature, which is still more capable 
 of experimental confirmation ; that is, that 
 the times of falling through all chords 
 drawn to the lowest point of a circle are 
 equal. 
 
 If two or more bodies are placed at 
 different points of a circle, and allowed to 
 descend at the same instant along as many 
 planes which meet in the lowest point of 
 the circle, they will arrive there at the 
 same time. 
 
 In order that a smaller weight may 
 raise a greater to a given vertical height, 
 in the shortest time possible, by means of 
 an inclined plane, the length of the plane 
 must be to its height as twice the greater 
 weight to the smaller ; so that the acting- 
 force may be twice as great as that which 
 
 is simply required for the equilibrium. A 
 body will therefore be raised on an inclined 
 plane, in the shortest time possible, when 
 its length is twice its height. 
 
 If two weights, P and W, sustain each 
 other upon the planes A C and C B, which 
 have a common altitude C D, 
 
 c 
 
 by means of a cord P C W, which passes 
 over the pulley C, and is parallel to the 
 planes, then P is to W as A C to B C ; or 
 the weight P multiplied into the length of 
 the plane C B, is equal to the weight W 
 multiplied into the length of the plane 
 AC. 
 
 HirBB.AUl.ICS. 
 
 OF THE FORMATION OF WAVES. 
 
 When the surface of water is unequally 
 pressed on, in parts contiguous to one 
 another, the columns most pressed on are 
 shortened, and sink beneath the natural 
 level of the surface, while those that are 
 least pressed on are lengthened, and rise 
 above that level. 
 
 As soon as the former columns have sunk 
 to a certain depth, and the latter have 
 risen to a certain height, their motions are 
 reversed, and continue so till the columns 
 that were at first most depressed have be- 
 come most elevated, and those that were 
 most elevated, have become most de- 
 pressed. 
 
 The alternate elevations and depressions 
 thus produced, are called leaves. 
 
 The water in the formation of waves has 
 a vibratory or reciprocating motion, both 
 in a horizontal and a vertical direction, 
 by which it passes from the columns that 
 are shortened to those that are lengthened, 
 and returns again in the opposite direction, 
 progressive motion not being necessary to 
 undulation. 
 
 The vibrations of water in the form of 
 waves, may be compared to the recipro- 
 cations of the same fluid in a syphon or 
 bent tube ;* and it was from this that New- 
 ton deduced the velocity of waves, and the 
 time required for an undulation. 
 
 * See page 34, col . 1 . 
 
THE ARTISAN. 
 
 119 
 
 The time of an undulation, is the time 
 from the wave being highest, at any point, 
 to its being .highest at that point again. 
 The velocity of the wave is the rate at 
 which the points of greatest elevation or 
 depression seem to change their places. 
 
 If the altitude andhreadth of a wave be 
 known, the time of an undulation and the 
 space which the wave appears to pass over 
 may be determined as follows. To find 
 the time of an undulation, add half the 
 bread of the wave to its altitude, multiply 
 the sum by -3927, and the square root of the 
 product will be the time in seconds.* Thus, 
 suppose the breadth of a wave to be 14 
 feet, and its height S feet, required the 
 time of an undulation. Here the sum of 
 the height and half the breadth is 10, which 
 multiplied by *3927, becomes 3*927, the 
 square root of which is 2, nearly, the number 
 of seconds in which an undulation is per- 
 formed. 
 
 To find the space which the wave passes 
 over in one second : — divide half the 
 breadth of the wave by the square root of 
 the sum of the altitude, and half the breadth, 
 multiplied by 3*927, and the result will be 
 the space passed over by the wave in one 
 second. 
 
 Thus, suppose the breadth and height of 
 a wave to be as stated in the preceding 
 example, and it is required to find the 
 space it will pass over in a second of 
 time. Here the square root of 10 is 3*1, 
 nearly, which multiplied by *3927 is 1*22, 
 nearly ; and 7 divided by this number 
 quotes5f, nearly, which is the space passed 
 over in one second. 
 
 While the depth of the water is sufficient 
 to allow the oscillation to proceed undis- 
 turbed, the weaves have no progressive 
 motion, and are kept, each in its place, by 
 the action of the waves that surround it. 
 But if by a rock rising near the surface, or 
 by the shelving of the shore, the oscillation 
 is prevented, or much retarded, the waves 
 in the deep water are not balanced by 
 those in the shallower, and therefore ac- 
 quire a progressive motion in this last di- 
 rection, and from breakers. Hence it is, 
 that waves always break against the shore, 
 whatever be the direction of the wind. 
 
 Breakers formed over a great extent of 
 shore, are distinguished by the name of 
 surf. The surf is greatest in those parts of 
 the earth where the wind blows always 
 nearly in the same direction: but in the 
 foregoing observations, no allowance is 
 made for winds. 
 
 PERCUSSION AND RESISTANCE 
 OF FLUIDS. 
 
 When a part of the weight of any fluid 
 is expended in producing a motion in any 
 
 * This number is one-eighth of the circumference 
 of a circle whose diameter is 1. 
 
 directiori, an equal force is deducted from 
 its pressure on the vessel in that direction, 
 for the weight employed in producing mo- 
 tion cannot at the same time be c causing 
 pressure ; and when the motion produced 
 is in any other diretion than a vertical one, 
 its obliquity must be immediately derived 
 from the re-action of the vessel, or of some 
 fixed obstacle : for, it is obvious that a 
 vertical, like that of gravity, cannot of it- 
 self produce an oblique or horizontal 
 motion. 
 
 If a small stream descend from the 
 bottom of a vessel, the weight expended in 
 producing its motion is equal to that of a 
 column of the fluid standing on abase equal 
 to the contracted orifice, and of twice the 
 height of the vessel. Thus, if the vessel 
 be 16 feet high, the velocity of the stream 
 will be 32 feet in a second, and a column, 
 32 feet in length, will pass through the 
 orifice in each second, with the whole 
 velocity derive able from its weight acting 
 for the same time : so much, therefore, of 
 the pressure of the fluid in the reservoir 
 must be expended in producing this motion, 
 and must of course be deducted from the 
 whole force with which the fluid acts on 
 the bottom of the reservoir ; in the same 
 manner as when two unequal weights are 
 connected by means of a cord passing over 
 a pulley, and one of them begins to de- 
 scend, the pressure on the pulley is dimi- 
 nished, by a quantity, which is as much 
 less than the sum of the weights, as the 
 velocity of their common centre of gravity 
 is less than the velocity of a body falling 
 freely. If the stream issue from the vessel 
 in any other direction, the effect of the 
 diminution of the pressure in that direction 
 will be nearly the same as if the vessel 
 were subjected to an equal pressure of 
 any other kind in a contrary direction ; 
 and if the vessel be moveable, it will 
 receive a progressive or rotatory motion in 
 that direction. Thus, when a vessel or 
 pipe is fixed on a centre, and a stream of 
 water is discharged from it by a lateral ori- 
 fice, the vessel turns round at first with an 
 accelerated motion, but on account of the 
 force consumed in producing the rotatory 
 motion, in successive portions of the water, 
 the velocity soon becomes nearly uniform. 
 Thus, the following figure represents a 
 cylinder, moveable on an axis with two 
 curved pipes inserted in its lower part 
 seen from above. 
 
 The stream A enters at the top of the 
 cylinder, and is discharged by the orifices 
 B and C, so as to turn the vessel in the 
 direction B D, From similar reasoning it 
 appears, that the effect of a detached jeton 
 a plane surface perpendicular to it must 
 be equivalent to the weight of a portion of 
 the same stream equal in length to twice 
 the height which is capable of producing 
 
120 
 
 THE ARTISAN. 
 
 the velocity. And this result is confirmed 
 by experiments: but it is necessary that 
 the diameter of the plane be at least four 
 times as great as that of the jet, in order 
 that the full effect may be produced. When 
 also a stream acts on an obstacle in a chan- 
 nel sufficiently closed, on all sides, to pre- 
 vent the escape of any considerable portion 
 of water, its effect is nearly the same as 
 that of a jet playing on a large surface. 
 But if the plane, opposed to the jet, be 
 only equal to it in diameter, or if it be 
 placed in an unlimited stream, the whole 
 velocity of the fluid column will not be de- 
 stroyed, it will only be divided and di- 
 verted from its course, its parts continuing 
 to move on, in oblique directions, as re- 
 presented in the following figure. 
 
 In such cases, the pressure is usually 
 found to be simply equivalent to the 
 weight of a column equal in height to the 
 reservoir, the surface being subjected to a 
 pressure nearly similar to that which acts 
 on apart of the bottom of a vessel, while a 
 stream is descending through a large aper- 
 ture in another part of it. 
 
 It is obvious that in ail these cases, the 
 pressure varies as the square of the velo- 
 city, since the height required to produce 
 any velocity is proportional to its square. 
 This inference was first made in a more 
 simple manner, from comparing the im- 
 pulse of a fluid on a solid, with that of a 
 number of separate particles, striking the 
 surface of the body, each of which would 
 produce an effect proportional to its velo- 
 city, while the whole number of particles, 
 acting in a given time, would also vary in 
 the same ratio. If the plane struck by the 
 stream be itself in motion, the impulse is 
 as the square of the difference of their 
 velocities. Thus, if the velocity of a.stream 
 be 10 feet per secend, and the plane on 
 which it strikes retires from it at the rate 
 
 of 8 feet per second, the impulse will only 
 be equal to 4 feet, the square of the differ- 
 ence of the velocities. 
 
 Where the fluid is so confined that the 
 whole of the stream acts on a succession 
 of planes, each portion into which it is 
 divided may be considered as an inelastic 
 solid, striking on the surface exposed to it 
 with a certain velocity ; and in this case, 
 the force must be considered as simply 
 proportional to the relative velocity, and 
 not to its square. For want of attention to 
 this circumstance, the effects of water 
 wheels have frequently been very errone- 
 ously stated. 
 
 When a jet, or stream of water, strikes 
 a plane surface obliquely, its force, im- 
 pelling the body forward, in its own di- 
 rection, is found to be very nearly propor- 
 tional to the height to which the jetw'ould 
 rise, if it were similarly inclined to the 
 horizon. But when a plane is situated 
 thus obliquely with respect to a wide 
 stream, the force impelling it in the di- 
 rection of the stream is somewhat less 
 diminished by the obliquity, at least if we 
 make allowance for its intercepting a 
 smaller portion of the stream. Thus, if 
 the anterior part of a solid be terminated 
 by a wedge, more or less acute, the resist- 
 ance, according to the simplest theory of 
 the resolution of forces, might be found by 
 describing a circle on half the base of the 
 wed ge, as a diameter, which would cut off 
 a part from the oblique side of the wedge 
 that would be the measure of the resist- 
 ance, the whole side representing the re- 
 sistance to the same solid without the 
 wedge. But the resistance is always 
 somewhat more than this, and the portion 
 to be added may be found, very nearly, by 
 adding to the fraction, thus found, one ten 
 millionth part of the cube of the number 
 of degrees contained in the external angle 
 of the wedge. 
 
 Thus, in the following figure, where the 
 whole resistance is directly opposed to the 
 surface A B, is represented by B C, 
 
 the portion which ought to act on the wedge 
 
THE ARTISAN. 
 
 121 
 
 A B D*, is represented by B E ; and in the 
 same manner the resistance on A B F is to 
 the whole as B G to B C. 
 
 When a body moves along the surface of 
 a resisting medium at rest, or when an 
 obstacle at rest is opposed to a fluid in 
 equable motion, the pressure is increased 
 before the moving substance, and dimi- 
 nished behind it; so that the surface is 
 elevated at the one part, and depressed at 
 the other, and the more as the velocity is 
 greater. Now it is obvious that the pres- 
 sure must be greatest where the elevation 
 is gi’eatest ; and hence a perforation at the 
 centre of the surface indicates a greater 
 pressure than at the circumference. Behind 
 the body this pressure becomes negative, 
 and has sometimes been called non-pres- 
 sure; hence it happens that atube opening 
 in the centre of the posterior surface, ex- 
 hibits the fluid within it depressed below 
 the level of the general surface of the 
 water. Thus, if we suppose the velocity 
 of a body, terminated by perpendicular 
 surfaces, to be 8 feet in a second, it will 
 require the pressure of about a foot to pro- 
 duce such a velocity; and we may there- 
 fore expect an elevation of about a foot 
 before the body, and an equal pressure 
 behind it; consequently an equivalent 
 difference must be found in the pressure of 
 the water at any equal depths on the an- 
 terior and posterior surfaces of the body. 
 The water elevated before the body escapes 
 continually towards each side, and the 
 deficiency behind, is also filled up in some 
 measure by the particles rushing in and 
 following the body; but there is in both 
 cases a certain quantity of water which 
 moves forwards, and constitutes what is 
 called the dead water ; before, where it is 
 usually most observable, it forms an irre- 
 gular triangle, of which the sides are con- 
 vex inwards. If the hinder part of the 
 body be formed like a wedge, the water 
 on each side will be advancing to fill up 
 the vacuity, even while it remains in con- 
 tact with the sides, and the negative pres- 
 sure will be considerably diminished. For 
 this reason, the bottoms of ships are made 
 to terminate behind in a shape somewhat 
 resembling a wedge ; and the same economy 
 maybe observed in the forms of fishes, calcu- 
 lated by nature for following their prey 
 with the greatest possible rapidity. In 
 general, fishes, as well as ships, are of a 
 more obtuse form before than behind ;f but 
 it is not certain that there would be any 
 material difference in the resistance in a 
 contrary direction, although some experi- 
 ments seem to favour such an opinion. 
 
 * According to the principles of the resolution of 
 forces. See page 24. 
 
 + This observation does not apply to the very 
 extremities of these bodies. 
 
 Perhaps if the natural form of the dead 
 water, moving before an obtuse body, were 
 ascertained, it might serve to indicate a 
 solid calculated to move through the water 
 with the least resistance ; for the water 
 must naturally assume such a form for its 
 own motions, and the friction of fluids on 
 solids being less than that of fluids moving 
 within themselves, the resistance would be 
 diminished by substituting a solid of the 
 same form for a fluid. 
 
 Thus the form of the dead water moving 
 before an obtuse body is nearly like that 
 of A B C ; and the form adapted for moving 
 through the water with the least possible 
 resistance, like ABCD. 
 
 A 
 
 D 
 
 It is found that no calculation deduced 
 from experiments on the resistance op- 
 posed to oblique plane surfaces, will de- 
 termine with accuracy the resistance to a 
 curved surface. It appears, however, 
 from experiment, that the resistance to the 
 motion of a sphere is usually about two- 
 fifths of the resistance to a flat circular sub- 
 stance of an equal diameter. The resist- 
 ance to the motion of a concave surface is 
 greater than to a plane, and the direction 
 in which the particles of a fluid are sup- 
 posed to move when they strike against a 
 concave surface, are represented by the 
 following figure. 
 
122 
 
 THE ARTISAN. 
 
 jKflfecellancous ^utjecls. 
 
 THE LIFE OF COPERNICUS. 
 
 Nicholas Copernicus was a native of 
 Thorn, a city of note in Prussia Royal, 
 where he was born January 19th, 1473. 
 His father’s name was Nicholas, and his 
 mother was sister to Lucas Watzelrode, 
 afterwards bishop of Warmia. He learnt 
 the Latin and Greek languages, partly at 
 home, and partly at the university of Cra- 
 cow, where he studied philosophy, and 
 sometimes medicine; at length he obtained 
 the degree of Doctor. Meanwhile, as he 
 was always extremely fond of the mathe- 
 matics, he attended the lectures, private 
 and public, of Albertus Brudzevius, a pro- 
 fessor of that science in the same univer- 
 sity. Of him he learnt the use of the 
 Astrolabe, by which he got a good insight 
 into astronomy, and at length he grew so 
 emulous of the illustrious fame of Regio- 
 montanus, that he resolved to follow him 
 in all his steps. He cultivated every part 
 of the mathematics, but applied himself 
 more especially to perspective, by which 
 means he became so complete a master in 
 painting, that he drew his own picture, 
 with a surprising likeness, before a glass. 
 His view in learning to paint was, that, 
 in his travels, especially through Italy, he 
 might be enabled, not only to copy, but 
 delineate with his own pencil whatever was 
 worthy of his observation. 
 
 Being returned to Thorn, after a short 
 stay, he set out for Italy, in the 23d year 
 of his age, and proceeded to Rome, where, 
 in a short time, his fame was little inferior 
 to that of Regiomontanus. Here, in a full 
 assembly of doctors and great men, he was 
 instituted professor of the mathematics. 
 
 After some years spent at Rome, he re- 
 turned to his own country, where, on ac- 
 count of his high attainments in learning, 
 and the gentleness of his manners, he was 
 affectionately received by his uncle, Lucas 
 Watzelrode, bishop of Warmia; who, in 
 order to give him the more leisure to pur- 
 sue his mathematical studies, settled him 
 in the college of Canons at Warmia, ap- 
 pertaining to his cathedral church. How- 
 ever, he was not suffered at first to enjoy 
 his canonate in peace, as he often com- 
 plains in his letters to his uncle, who 
 remained at court, that he might be at 
 hand to defend the public cause against 
 the Cross-bearers and Teutonic knights ; 
 which so provoked them, that they libelled 
 him publicly in the Dyet of Fosnania. But 
 at length, his own merit, together with 
 that of his uncle, prevailed, and he ob- 
 tained a peaceable possession. Upon which 
 he instantly applied himself to three things 
 
 in particular. One was, diligently to 
 attend on divine offices : another, to attain 
 so much skill in medicine, as to enable 
 him to relieve the poor whenever they 
 should want his assistance: thirdly, to 
 employ the residue of his time in study. 
 For which purpose he always chose soli- 
 tude ; and, except the affairs of the See, or 
 the Chapter required it, never, but with 
 reluctance, engaged in business, which he 
 was on several occasions obliged to do. 
 
 But our principal regard will be to that 
 part of his life which he devoted to con- 
 templation and study; and as he affected 
 nothing so much as the knowledge of the 
 heavens and celestial bodies, for which 
 his name is so highly celebrated, we shall 
 relate in what order he began, and by 
 what steps he proceeded to those attain- 
 ments he acquired in this science. 
 
 In the first place, he observed, that 
 astronomers, while they would maintain 
 an equal motion in the celestial circumvo- 
 lutions, took for it, or measured from, not 
 a proper, but a wrong centre; namely, 
 that of a circle called the equant. Nor 
 could they collect the principal thing, that 
 is, the form of the word, and its fine dis- 
 position, from that heap ^of hypotheses 
 which they were forced to use. Where- 
 fore he resolved to peruse as many of the 
 books of philosophers and astronomers as 
 he could lay his hands on, examine their 
 several systems, and search out what was 
 probable in them, that, from the whole, he 
 might form a more exquisite harmony of 
 the celestial motions, and symmetry of the 
 parts of the world, than that which had 
 been universally admitted. 
 
 As he knew that the Pythogoreans had 
 removed the earth from the centre, and 
 had placed therein the sun, the most noble 
 of all bodies, he imagined he perceived 
 somewhat of a beautiful order, if he might 
 only be allowed to make a change, that is, 
 to place the sun in the centre, and make 
 the earth move round the sun. For Nicetas, 
 Echphantus, Heraclides, and others, aimed 
 well, who, though they detained the earth 
 in the centre, yet gave it a motion, by which 
 it turned on its own axis, like a sphere in a 
 wheel, and daily perfecting a circuit from 
 the west to the east, made the vicissitude 
 of day and night, and assuming the office 
 of the Primum Mobile,* discharged the 
 sphere of the fixed stars, and all the planets 
 from their rapid motion ; so that the earth 
 being turned to the east, all the stars must 
 necessarily appear turned to the west, 
 which nevertheless would appear very 
 disproportionate. Wherefore Philolaus 
 did much better, when, removing the 
 earth from the centre, he gave it not only 
 
 * See Ptolemaic System, page 47. 
 
THE ARTISAN. 
 
 123 
 
 a diurnal motion round its own axis, but 
 an annual circuit round the sun ; by which 
 means it happens, that in traversing the 
 zodiac, under whatever sign it is, the sun 
 appears in opposition ; so that the earth 
 itself, Mercury, Venus, and the rest of the 
 planets, must acknowledge the sun as 
 their centre. But it seemed absurd to 
 pluck the earth from the centre, and to 
 give it such kind of motions. Copernicus, 
 therefore, having variously canvassed the 
 matter, and ascribed a triple motion to the 
 earth, he thus writes: “ By a close and 
 long observation, I have at length found, 
 that if the motions of the rest of the planets 
 be compared with the circulation of the 
 earth, and be computed for the revolution 
 of each, not only their phenomena will 
 follow, but it will so connect the orders 
 and magnitudes of the planets, and all the 
 orbs, and even heaven itself, that nothing 
 in any part of it could he transposed* 
 without the confusion of the rest of the 
 parts, and of the whole universe.” 
 
 This was about the year 1507. But he 
 did not think it enough to establish a ge- 
 neral "ratio of hypotheses only, and accord- 
 ing to it to solve phenomena in general ; 
 but he wanted likewise to conclude upon 
 some special hypothesis, so as to define 
 the periods of all motions, that from thence 
 he might be able to erect tables for the 
 heavens, preferable to the Ptolemaic; for 
 which purpose, he judged it necessary to 
 make observations, and by comparing them 
 with those more ancient, he might attain 
 to a greater precision. To this end he 
 fabricated a quadrant, to be erected and 
 applied to the meridian line above the 
 plane of the horizon, that by the help of a 
 shadow, from a cylindrical gnomon fixed 
 at the centre, might be observed the 
 greatest and least meridian altitude of the 
 sun, in the summer and winter solstice; 
 likewise for taking the distance of the 
 tropics, and the altitude of either ; also 
 the altitude of the equator in the middle ; 
 likewise the altitude of the pole might 
 thereupon be known, by estimating the 
 altitude of the equator. He likewise con- 
 structed a parallactical instrument of fir 
 wood, whose limb was divided into 1414 
 small parts or portions, marked with ink, 
 to the end it might subtend the right angle 
 of a quadrant, whose legs were four cubits 
 long, consisting of 1000 of the same parts. 
 The use of this was for observing the 
 altitudes of any of the stars, particularly 
 of the sun, not only when he is about the 
 tropics, but also about the equinoxial ; but 
 especially in the spring, to observe his 
 entrance into Aries. Likewise of the moon, 
 but chiefly when she is in the northern 
 limit, and that limit in Cancer, to find out 
 her greatest latitude, also of Regulus, or 
 of any other remarkable fixed star, in order 
 
 to obtain the distance from the equinoxial 
 point, 
 
 Being by these instruments furnished 
 with many curious observations, he began 
 to digest them in order, and undertook a 
 work, which he finished, and divided into 
 six books, entitled, “ The Revolutions of 
 the Celestial Orbs,” which, in a geome- 
 trical point of view, included the whole 
 science of astronomy. 
 
 The first book is divided into two parts ; 
 in the latter, he handles the doctrine of 
 Sines, or chords, which he judged neces- 
 sary in solving triangles, both plane and 
 spherical: but in the former he has ex- 
 hibited a general idea, or description of 
 the world, agreeable to his own hypothe- 
 sis, in which motion is attributed to the 
 earth. In the first place, he teaches that 
 the world is of a spherical form, and as- 
 signs this reason for it ; because the sphere 
 is the most perfect of all figures, and con- 
 tains a greater quantity of space within 
 it, than any other. He observes farther 
 likewise, that fluid bodies naturally put 
 on the figure of a sphere ; that the sun, 
 the moon, the planets, and all the heaven- 
 ly bodies, are of that figure, and therefore, 
 he concludes at once, that the figure of the 
 visible world must be such likewise ; 
 though he is in all this plainly mistaken ; 
 because, properly speaking, the world has 
 no figure at all, as, it is not circumscribed, 
 or bounded by any limits ; and what we 
 call the firmament is a mere Ens Rationis, 
 or idea of the mind, and its spherical form 
 is easily accounted for on the principles 
 of optics ; as we shall hereafter see. In 
 this book, our author very much insists on 
 the spherical figure of the earth, and its 
 circular motion about the sun. He con- 
 siders theAeasons alleged by the ancients 
 for placing the earth immoveably in the 
 center of the system, and very learnedly 
 and rationally confutes them ; and having 
 settled this point, and plainly proved the 
 sun to possess the center of the system, he 
 then treats of the celestial orbits, as those 
 which the planets describe about the Sun, 
 and illustrates the same by a diagram, 
 which since this time has been usually 
 called the Copernican System of the 
 World.* He then treats of the twofold 
 motion of the earth ; viz. the diurnal mo- 
 tion about its axis, and its annual motion 
 about the sun ; and having dispatched the 
 doctrine of plane and spherical trigonome- 
 try, he proceeds to 
 
 The Second Book. In this he considers 
 the doctrine of the sphere, with a descrip- 
 tion of the various circles, great and 
 small, that compose the same, with their 
 various intersections and inclinations, one 
 with another, in regard to the different in- 
 
 * See page 77. 
 
124 
 
 THE artisan: 
 
 habitants of the globe. He considers the 
 doctrine of right and oblique ascensions, 
 the rising and setting of the sun and stars, 
 the parts of time, and particularly of days 
 and nights ; after this, he gives an account 
 of the instruments made use of for observ- 
 ing and correcting the places of the stars. 
 He then proceeds to give us a new cata- 
 logue of the stars, found in the several 
 signs and constellations, with the latitude, 
 longitude, and magnitude of each particu- 
 larly specified. 
 
 In the Third Book, he treats of the 
 Equinoxes and Solstices, and gives us a 
 history of observations, proving the in- 
 equality and precession of the same. He 
 then treats of the variation of the obliquity 
 of the Ecliptic, and shews, that it has 
 been continually changing,, and how it 
 proceeds from the libration of the earth’s 
 axis. The quantity of this motion is then 
 computed and digested, in tables. The 
 times of the Equinoxes are more particu- 
 larly enquired into, and investigated, the 
 magnitude of the solar year, and the dif- 
 ference observed in the same; and tables 
 of the equal and mean motion of the earth 
 are computed for years, days, and sexage- 
 simal parts. He then accounts for the 
 apparent inequality of the sun’s motion, 
 with all the variety observed in the same. 
 He then treats of the various Epochs, or 
 times, from whence the ancient astrono- 
 mers began to compute the mean motion of 
 the sun ; and having largely considered 
 the nature and anomaly of the sun’s mo- 
 tion, he gives us a table of the Prostha- 
 phaeresis or equation of the centre ; so 
 that, the difference between the true 
 and mean anomaly is known for every 
 part of the orbit, and, consequently, when 
 one was given, the other might be from 
 thence known. After this, he discourses 
 on the Nychthemeron, or the nature and 
 difference of the natural day of 24 hours, 
 which concludes this book. 
 
 In the Fourth Book, he treats of the 
 Lunar Motions, and considers the various 
 hypotheses of the ancients concerning 
 them : he corrects the errors of their gros- 
 ser observations, and gives us a more par- 
 ticular and correct account of those mo- 
 tions, together with new tables of the 
 same. After this, he very particularly 
 enquires into the various differences and 
 inequalities of the lunar motions. He fur- 
 ther shews how they are to be accounted 
 for, according to the hypothesis of Cycles 
 and Epicycles, which in those times they 
 were obliged to make use of, for want of 
 knowing the true theory of gravity, of 
 which the first hints, however, were found 
 in the books of this excellent writer. He 
 expounds the doctrine of the lunar Pro- 
 sthaphaeresis, and gives us tables of the 
 same ; by which the apparent motion, or 
 
 place of the moon, is found from the mean, 
 or equal motion given. He considers then 
 the motion of the moon, in latitude, of the 
 quantity of the angle wdiich the moon’s 
 orbit makes with the ecliptic. After this, 
 we have a particular account of the con- 
 struction of his Parallatic instrument, by 
 which the horizontal parallax and distance 
 of the moon from the earth, were much 
 more accurately determined, than had 
 been done before. From hence too, he 
 was able to measure the diameter of the 
 moon, and of the shadow of the earth at 
 the moon’s orb : also, he was hereby en- 
 abled to treat, in some measure, of the 
 distance of the sun, as also, of the com- 
 parative magnitude of the sun, the moon, 
 and the earth ; which, though very inac- 
 curate, were still much nearer the truth 
 than any thing that had before this time 
 been advanced upon the subject. Having 
 insisted largely on these subjects, he pro- 
 ceeds to his observations on the apparent 
 diameters of the sun and moon, with the 
 various changes they underwent at dif- 
 ferent times. After this, he considers the 
 different dimensions of the shadow of the 
 earth, according to the Apogee, or Peri- 
 gee, of the luminaries, and illustrates the 
 same by proper diagrams. Then he insists 
 largely on the doctrine of Parallaxes of 
 the sun and moon, both in latitude and 
 longitude, and gives us tables of the same. 
 He then treats of the conjunctions and 
 oppositions of the sun and moon, with 
 regard to their mean and true times and 
 places. Then the doctrine of Eclipses, 
 both of the sun and moon, is learnedly ex- 
 plained, in regard to the manner in which 
 they are produced, the times in which 
 they happen, the quantity of duration, and 
 the prognostics of the same ; which closes 
 the Fourth Book. 
 
 The Fifth Book considers the planetary 
 motions, and their various affections. He 
 gives us the number, their distances from 
 the sun, and the times of their revolution, 
 together with tables of their mean motions 
 for years, days, hours, and minutes. After 
 this, the particular theories of each planet 
 are taught and illustrated by proper figures. 
 He then gives an account of the distance 
 of those planets from the earth, the apparent 
 sides and excentricities of their orbits, the 
 mean motions and anomalies, with the 
 times or epochas from whence they have 
 been computed for each planet, with the 
 quantity of the same, in proper tables of 
 the Prosthaphaeresis, peculiar to the orbit 
 of each; and having accounted for the 
 various appearances and inequalities of 
 their motions, in regard to their direct and 
 retrograde motions and stations, he puts 
 an end to the fifth book. 
 
 The Sixth Book is wholly spent in en- 
 quiring into, and ascertaining the latitude 
 
THE ARTISAN. 
 
 4>f the planetary orbits, or the inclination 
 which they make with the ecliptic, their 
 eccentricities, the places of their nodes, 
 &c. and then the whole is concluded with 
 tables of the latitude of each planet. 
 
 His book was printed at Nurimberg, in 
 the year 1543, and till then, the world had 
 never seen any thing that looked like a 
 true system of astronomy. For what 
 Ptolemy had done in his Almagestum 
 Magnum, was entirely upon a false hy- 
 pothesis, as we have already observed 
 in treating of his system ; and what 
 had been performed by Regiomontanus 
 and Purbachius, could be deemed no other 
 than rude sketches, and outlines of the 
 science ; and though their writings were 
 in great repute, we do not find Copernicus 
 made the least use of them, since we find 
 no mention of their names, or of their 
 writings in the introduction to the present 
 work, though Copernicus wrote many 
 years after the Ephemerides of Regiomon- 
 tanus, and the theories of Purbachius were 
 published. 
 
 It appears from the writings of Gassen- 
 dus, in the life of this author, that he 
 finished this work about the year 1530 ; 
 ■what he did afterwards, was only by way 
 of correction, or Amendment of what he 
 had before written. 
 
 The system of astronomy, however, con- 
 tained in this great work, was at first 
 looked upon as a most dangerous heresy, 
 and although it had been long finished, yet 
 he could not be prevailed upon to publish 
 it, although strongly urged to it by his 
 friends. At length, yielding to their en- 
 treaties, it was printed, and he had but just 
 received a perfect copy, when he died the 
 24th of May, 1543, at TO years of age ; by 
 which it is probable he was happily re- 
 lieved from the violent fanatical persecu- 
 tions which were but too likely to follow 
 the publication of his astronomical opi- 
 nions ; and which indeed was afterwards 
 the fate of Galileo, for adopting and de- 
 fending them. 
 
 DESCRIPTION OF THE SAFETY 
 LAMP OF SIR H. DAVY. 
 
 The gas which proves so destructive to 
 miners is carburetted hydrogen, but the 
 miners themselves call it fire-damp. 
 
 To obviate the destructive effects of this 
 gas, when found in mines mixed with 
 atmospherical air, Sir H. Davy turned his 
 attention to the construction of a lamp 
 which would prevent explosion ; and upon 
 the knowledge of the fact, that flame can- 
 not pass through apertures of small diameter , 
 he constructed what is now generally 
 termed the safety-lamp, but by miners 
 the Davy. The apertures in the gauze 
 used in this lamp should not be more than 
 
 125 
 
 j^th of an inch square. As the fire-damp 
 cannot be inflamed by ignited wire, the 
 thickness of the wire is not of importance ; 
 but wire of to so an inch in diameter 
 is the most convenient. If the wire of ^ 
 be found to wear out too soon, the thick- 
 ness may be increased to any extent; but 
 the thicker the wire, the more will the 
 light be intercepted; for the size of the 
 apertures must never be more than ^ of 
 an inch square. In the model which Sir 
 II. Davy sent to the mines for use, there 
 were 74S apertures in the square inch. 
 The following is a figure of this lamp : 
 
 The foregoing figure represents the wire 
 gauze safe-lamp. A, is the cistern which 
 contains the oil ; B,the rim in which the wire- 
 gauze cover is fastened to the cistern by a 
 moveable screw ; C, an aperture for supply- 
 ing oil, fitted with a screw or a cork ; D, the 
 receptacle for the wick; E, a wire for rais- 
 ing, lowering, or trimming it, and wdiich 
 passes through a safe tube ; F, the wire- 
 gauze cylinder, which should not have less 
 than 625 apertures to a square inch ; G, 
 the second top, three quarters of an inch 
 above the first ; H, a copper-plate, which 
 may be in contact with the second top ; 
 I, I, I, I, thick wires surrounding the cage 
 
126 
 
 THE ARTISAN. 
 
 to preserve it from being bent; K, K, are 
 rings to hold or hang it by. 
 
 When the wire-gauze safe-lamp is lighted 
 and introduced into an atmosphere gradu- 
 ally mixed with fire-damp, the first effect 
 of the fire-damp is to increase the length 
 and size of the flame. When the inflam- 
 mable gas forms as much as ^5 of the 
 volume of air, the cylinder becomes filled 
 with a feeble blue flame ; but the flame of 
 the wick appears burning brightly within 
 the blue flame, and the light of the wick 
 continues, until the fire-damp increases 
 to l or I, when it is lost in the flame of the 
 fire-damp, which in this case fills the 
 cylinder with a pretty strong light. As 
 long as any explosive mixture of gas exists 
 in contact with the lamp, so long it will 
 give light, and when it is extinguished, 
 (which happens when the foul air consti- 
 tutes as much as | of the volume of the 
 atmosphere,) the air is no longer proper 
 for respiration. In cases where the fire- 
 damp is mixed only in its smallest explo- 
 sive proportion with air, the use of the 
 wire-gauze safe-lamp, which rapidly con- 
 sumes the inflammable gas, will soon 
 reduce the quantity below the explosive 
 point ; and it can scarcely ever happen, 
 that a lamp will be exposed to an explosive 
 mixture containing the largest proportion 
 of fire-damp ; but even in this case, the 
 instrument is absolutely safe ; and should 
 the wires become red hot, they have no 
 power of producing explosion. Should 
 it ever be necessary for the miner to work 
 for a great length of time, in an explosive 
 atmosphere, by the wire-gauze safe-lamp, 
 it may be proper to cool occasionally by 
 throwing water upon the top ; or a little 
 cistern for holding water may be attached 
 to the top, the evaporation of which will 
 prevent the heat from becoming excessive. 
 
 Gas in a state of combustion will not 
 pass through brass-wire-gauze with aper- 
 tures of certain dimensions, although the 
 gas itself will pass through most readily 
 when it is not in a state of combustion. 
 If a piece of wire-gauze be held horizon- 
 tally over the flame of a common gas-light, 
 the flame of the gas will burn under the 
 wire-gauze, but it will not pass through it 
 in the state of flame. If, again, whilst the 
 wire-gauze is held over the flame, a candle 
 be applied to the upper surface of the 
 gauze, the gas passing through it at the 
 time will immediately take fire. 
 
 The reason of this singular fact is this, — 
 gas must be heated to a certain degree, 
 either by the immediate contact of flame or 
 some other body, before it will either burn 
 or explode ; the gas in passing through 
 the wire-gauze, loses a considerable por- 
 tion of its heat, for the wire abstracts or 
 conducts so much of it away, as to cool it 
 below the degree at which it will bum or 
 
 explode. This is what renders the safety- 
 lamp of so much value, and in fact its 
 whole utility rests upon this very singular 
 circumstance. The wire-gauze with which 
 the lamp is completely surrounded, cools 
 the gas to a degree below the heat neces- 
 sary to produce explosion, when burning 
 in a mixture of atmospheric air and car- 
 buretted hydrogen gas. 
 
 CORRECTION OF THE BULK OF GASES FOR 
 TEMPERATURE. 
 
 Some of our elementary treatises on 
 chemistry contain an inaccurate mode of 
 estimating the change of bulk in a gas, 
 occasioned by variation of temperature. 
 They have directed the bulk of the gas to 
 be divided by 480, the quotient multiplied 
 by the number of degrees by which the 
 temperature of the gas differs from the 
 temperature to which it is to be reduced, 
 and the product added or subtracted, ac- 
 cording as the actual temperature is below 
 or above that referred to. But as the gas 
 expands only of its bulk for each de- 
 gree of Fahrenheit when its temperature 
 is 32°, but at no other temperature, the 
 rule is not correct, except when the gas is 
 actually at 32°, and to be estimated at 
 some other temperature. Mr. Briggs has 
 pointed out this error, and has given the 
 following rule, which is more correct : 
 
 Add the degrees which the gas is above 
 32° to 480, add also the degrees which the 
 required temperature is above 32° to 480, 
 then as the first number is to the second, so 
 is the volume of the gas to the volume 
 required. 
 
 Suppose, for example, that the tempe- 
 rature of 100 cubic inches of gas is 120° of 
 Fahrenheit, and that it is required to 
 find how much it would be diminished in 
 volume, if its temperature were reduced 
 to 62°. Here’ 88°, the excess of 120° above 
 32, added to 480 is 568 ; and 30°, the ex- 
 cess of 62 above 32°, added to 480 is 510 : 
 then as 568 is to 510 so is 100 cubic inches 
 of gas to 90 inches nearly. It has there- 
 fore suffered a diminution of about of 
 the whole.* 
 
 Another rule for making the correction 
 is to add the number of degrees between 
 32° and the temperature of the gas to 480, 
 divide the volume of the gas by the sum, 
 and multiply the quotient (which will be 
 the expansion for each degree), by the 
 number of degrees between the tempera- 
 ture of the gas, and the required tempera- 
 ture; if the latter be greater than the 
 former, add the product to the volume of 
 gas ; but if it be less subtract it ; and the 
 corrected volume will be obtained. As 
 
 * By the common rule the volume would have 
 been reduced to about 82 cubic inches, or nearly 
 one-tifth ot the whole. 
 
THE ARTISAN. 
 
 127 
 
 this rule gives the same result as the one 
 used in the above example, it is unneces- 
 sary to give any illustration of it. 
 
 SOLUTIONS OF QUESTIONS. 
 
 To the Editor of the Artisan. 
 
 Sir, 
 
 If you deem the following solution of 
 Boronesphilosmathematicus’ question, at 
 page 64, worthy of a place in your valu- 
 able publication, it is at your service. 
 
 Let Z in the above figure represent the 
 zenith, P the North Pole, m the star Pol- 
 lux, and n the middle star in Orion’s belt. 
 Then in the spherical triangle n P m, are 
 given ni P=61° 24', and n P=91° 23' the 
 distance of the stars from the North Pole, 
 and the included angle n P m=31° 30', 
 the difference of their right ascensions, to 
 find the side n m=42° 30'. 
 
 Then by supposing a parallel to the ho- 
 rizon to pass through n till it meets Z m 
 produced, a right angled triangle is thus 
 formed, of which the hypothenuse n m= 
 42° 30', and the difference of altitude of 
 the stars=6° 35' are given to find the 
 other side n S=42° 5 * Again, in the tri- 
 angle Z ns right angled at S, are given 
 the side n s, and the angle n Z s=51° the 
 difference of the Azimuth of the two stars, 
 to find Z n= 59° 35' from which 6° 35' be- 
 ing subtracted, leaves Z m= 53° ; then in 
 the triangle m Z P, right angled (the star 
 m being supposed on the meridian) at Z, 
 is given the side Z m= 53° and the side 
 m P=61° 24' to find the side Z P=37°18' 
 the co-latitude, — Hence the latitude of the 
 place required, is 52° 42' N. 
 
 This answer is different from that given 
 by the proposer ; but the Editor has not 
 leisure to ascertain which of these answers 
 are most correct; the proposer has how- 
 ever made an error in subtracting his co- 
 latitude (30° 10') from 90°, for he makes 
 the latitude 50° 49' instead of 59° 50'. 
 
 * There is no letter s in the figure, neither are the 
 lines n s or Z n drawn, owing to the figure being 
 cut to answer the solution sent by the proposer, 
 which we consider loo complex and Algebraical for 
 insertion in the present work. 
 
 To the Editor of the Artisan. 
 
 Sir, 
 
 Please insert the following solution of 
 Charan’s question, which appeared in page 
 96 of the Artisan, and oblige your obe- 
 dient servant. A. B. 
 
 The whole quantity of water displaced, 
 must be 231 x 10 -f- 216—2526 cubic in- 
 ches ; and 231 x 5 =1155 cubic inches, the 
 quantity of brandy in the cask, 
 in. oz. in. oz. 
 
 Now 1728 : 1000 : : 2526 : 1462 wt. of water. 
 
 And 1728 : 886 : : 1155 : 592 wt. of brandy. 
 
 1728 : 800 : : 216 : 100 wt. of wood. 
 
 Then 1462— (592+ 100)=770wt. of the wa- 
 ter above that of the brandy and cask, which 
 is the buoyant power to be counteracted by 
 the lead ; now 1 cubic inch of lead weighs 
 6* 554 ozs. and 1 cubic inch of water *596 
 oz. ; therefore 6*554 — 596=5*958, and 
 
 5*958 : 770 : : 6*554 : 847 ozs. 
 
 or 53 lb. nearly of lead, the weight ne- 
 cessary to keep the cask under water. 
 
 The following is the proposer’s (Mr. 
 Graham) solution of his question, at page 
 96, which we insert with some additions, 
 not having received any other solution.— 
 Ed. 
 
 Let A B C D represent the circular plat 
 of land, and O the situation of the pond 
 required ; inscribe the square and draw the 
 lines, A O, B O, C O, and D O. Letfall the 
 perpendiculars a O, b O c O and d O, and 
 drawl) B and let fall the perpendicular A e 
 on it. Then by rule 12th in Bonneycastle’s 
 
 Mensuration f _l£- > V=3*567=I> B (the 
 \*7854y 
 
 diameter of the circle) and in his notes un- 
 der the same rule 3*567 X *7071=2*522 — 
 A B, B C, C B, or D A. Then (2*522) -f-4 
 =1-59 the area of the triangle A e B, 
 whence the triangle AeB taken from the 
 sector e B A will leave *91 the area of the 
 respective segments separately. Again 
 
128 
 
 THE ARTISAN. 
 
 1— -91ZZ-09, 2— “ , 91~l - 09, 3— -91 -2-09 
 and 4— ’OlizS'OO the areas of the triangles 
 D O C, D O A, C O B, and B O A. Then 
 ;°9 X2 1.09x2 2,09x2 , 3.09 x2__ 
 
 2'522 ? 2-522’ 2-522’ 21-522 
 
 *0714, -8644,1-6574 and 2'45 — a Q,dO,bO 
 and c O respectively ; consequently make 
 2) d~a O, C a~b O join CD, and through 
 c draw A B parallel to C D, and join D A 
 and B C ; then draw OA,G 8,0 C, and 
 O D, and the thing is done. 
 
 To the Editor of the Artisan. 
 
 Sir, 
 
 Seeing a question in your last number, 
 page 112, by H. Flather, I beg to submit 
 the annexed solution to your notice, and 
 am, Sir, your’s, respectfully, 
 
 2_ f St John Street, J. M. Edney. 
 
 Clerkenwell. 
 
 The solid content of the space in cubical 
 half inches is =z87x26x 15—33930 : and 
 as the scale of the model is to that of the 
 figure itself as f an inch to 1 foot. The 
 solid content of the latter will be 33930 
 feet. 
 
 This question was solved exactly in the 
 same manner by Mr. Futvoye, High-street, 
 Mary-le-bone ; it was also solved by the 
 proposer, but in a very diffuse manner. 
 
 It may also be solved thus 43|xl3x7A 
 — 4241i~(t) 3 ~ 33930.— Edit. 
 
 QUESTIONS FOR SOLUTION. 
 
 To the Editor of the Artisan. 
 
 Sir, 
 
 Having myself in the early part of life 
 been an operative mechanic, and am now 
 very extensively employed as a civil en- 
 gineer, I find the great advantage of having 
 studied geometry when I was only a 
 journeyman carpenter, and 1 am even con- 
 vinced, that without a correct knowledge 
 of the principles of geometry , we never can 
 make any progress in the true principles 
 and science of mechanics , nor in fact in any 
 of the mechanical arts. 
 
 Feeling a great interest in the progress 
 and success of the Artisans’ and Mechanics’ 
 Institutions in London and elsewhere, I 
 do by all means recommend my fellow ar- 
 tisans and mechanics to begin the study of 
 geometry as soon as they become members 
 of any of these useful institutions, as it is 
 the foundation of all accurate science. 
 Without having first obtained some know- 
 ledge of geometry, the lectures on me- 
 chanics, and other subjects delivered at 
 
 those institutions, will be productive of 
 very little benefit to those who may attend 
 them. 
 
 Wishing to encourage and contribute as 
 much as possible to so useful and cheap a 
 publication as the “ Artisan,” and which is 
 so well calculated for the self-instruction of 
 mechanics in the scientific principles of 
 their respective arts; I shall be obliged to 
 you to insert the following geometrical 
 problem in one of your succeeding num- 
 bers, and I shall occasionally send you 
 such problems as I may conceive will 
 prove most useful to Artisans and Me- 
 chanics generally. 
 
 I am, Sir, your obedient Servant, 
 
 Edinburgh, An Engineer. 
 
 April 20, 1824. 
 
 Quest. 14. Given the excess of the dia- 
 gonal of a square above the side, to con- 
 struct the square geometrically. 
 
 To the Editor of the Artisan. 
 
 Sir, 
 
 Please to insert the following question, 
 if you think it worthy of a place in your 
 valuable publication, which will oblige 
 your’s, &c. 
 
 John Boronesphilosmathematicus. 
 
 Manchester, April 4, 1824. 
 
 Quest 15. Three men bought a grinding 
 stone, 36 inches in diameter ; and the 
 thickness at the centre 4 inches, and at the 
 circumference 12 inches, required how 
 much must each man grind down of the 
 stone’s semi-diameter, so that each man 
 may have an equal share thereof? 
 
 To the Editor of the Artisan. 
 
 Sir, 
 
 If you have at any time, in a future 
 number, a little corner to spare, please 
 have the goodness to pop in the following 
 simple question, as my landlord disputes 
 my abilities of solving it, and you will 
 oblige your well-wisher. 
 
 R. Graham. 
 
 Quest. 16. My landlord having a little 
 knowledge of science, and being rather 
 (what the world calls) a man of taste, 
 wishes to know how he must make an 
 equilateral grass plat at the front of his 
 house, that the area may be equal to the 
 sum of the three sides ? 
 
 Errata — The figures at page 107, in 
 some copies, were by mistake inserted, 
 instead of those at page 108, and vice 
 versa. 
 
THE ARTISAN. 
 
 129 
 
 MEMOIR OF JAMES WATT, Esq. F.R.S. 
 
 In retracing the scientific tract, which 
 has been trod by inventive , we might almost 
 add creative genius, so closely are the ad- 
 vantages derived from some connected 
 with the eventful times in which they lived, 
 that it is next to impossible to do justice 
 to the memories of the defunct, without 
 naming them in conjunction. The meri- 
 torious exertions of Watt, both in his en- 
 deavours to dispel the mists which sur- 
 rounded, and also to enlarge the hitherto 
 contracted space in which the mechanical 
 powers had moved, were productive of 
 benefits peculiarly of this class. Engaged, 
 as Great Britain then was, in a war of such 
 magnitude, that arms became the profession 
 of too large a portion of. her able-bodied 
 mechanics, some powerful substitute was 
 absolutely necessary to supply the defecit. 
 This Watt, and such as Watt, so ably con- 
 tributed, by their inventions and applica- 
 tions of machinery to almost every branch 
 of our manufactures and agriculture, 
 which otherwise must have languished for 
 want of means, that they might then justly 
 have been denominated the Atlasses of 
 British commerce. Descended from pa- 
 rents who, though not wealthy, merited 
 honourable report, Watt was born at 
 Greenock, in Scotland, A. D. 1735, where 
 he was carefully educated ; but having 
 completed hisgrammatical studies and other 
 important branches of education, he was at 
 sixteen apprenticed to learn the art of an 
 Instrument Malcer , which consisted in the 
 manufacture and repair of instruments 
 used in philosophical and mechanical ex- 
 periments, surgery, music, &c. ; an art 
 then confined to a limited sphere, and 
 little encouraged. Having completed the 
 period of his probation, he repaired to 
 London, with anticipations both of im- 
 provement and employment; but after a 
 lapse of little more than a year, he again 
 sought his native country, where, on his 
 arrival, he added measuring and surveying 
 land to his former occupations. These, 
 together, enabled him not only to live 
 respectably, but likewise to pursue a course 
 of mechanical experiments , which had pre- 
 viously been engendered in his prolific 
 mind. It was now a fortunate incident 
 gave that direction to the inventive powers 
 of Watt, in which his provident imagina- 
 tion afterwards accomplished so much, 
 and laid the foundation of his future fame. 
 The model of Newcomen’s steam engine, 
 used in his lectures by the professor of 
 natural philosophy at the University of 
 Glasgow, was sent to Watt to be repaired ; 
 penetrating instantaneously into the fu- 
 Vol. I.— No. 9. 
 
 ture, he perceived the cabability of its im- 
 provement, and the great advantages to be 
 derived from its general application to 
 machinery ; and although he continued to 
 pursue his trade, it being his only source 
 of subsistence, his genius ill brooked ;this 
 restraint, but bent its whole force on his 
 favourite subject, the improvement of the 
 steam engine. This engine had now been 
 in use more than half a century, but very 
 little had as yet been done to perfect it. 
 The first improvement which occurred to 
 Watt, was the adoption of a wooden cylin- 
 der instead of a metal one ; and to this he 
 was led by observing that th ejet of cold 
 water conveyed into the piston, in order 
 to condense the steam, cooled it to such a 
 degree, that the steam introduced for the 
 following stroke was wasted in restoring 
 the heat ; till this was remedied, it could 
 not exert its entire powers. Many physical 
 difficulties made him abandon his first idea 
 for a more fortunate one — that of passing 
 the steam into & separate condensing vessel, 
 and thereby never cooling the cylinder. 
 Necessity made him defer the application 
 of his discovery ; united at this period to 
 an amiable companion, without fortune, his 
 first concern was the means of subsistence. 
 His friends, however, appreciated his in- 
 vention, amongst whom was Dr. Roebuck, 
 a gentleman possessing an enlightened un- 
 derstanding, as well as some property. He 
 it was who associated himself with Watt, 
 at this critical moment, in order to further 
 his discovery, and to bring it to perfection. 
 But their means soon exhausted, it was 
 again on the eve of being abandoned, 
 when, in 1773, Mr. Boulton, a gentleman 
 of ample fortune, and very considerable 
 proficiency in the sciences, became ac- 
 quainted with, and saw the advantages of 
 the invention. He liberally reimbursed 
 Dr. Roebuck, and having previously erect- 
 ed a manufactory at Soho, near Birming- 
 ham, at a cost of 20,000 1. he took Mr. 
 Watt with him to reside at that place, 
 whose wife, having borne him two child- 
 ren, was then deceased. Watt was now 
 possessed of leisure and means to realize 
 any invention he might already be master 
 of, or, by the exertion of his genius, bring 
 to light. He found the advantage of 
 condensing the steam under the piston in 
 another vessel, but when the piston de- 
 scended, he imagined the cylinder to be 
 still cooled. His next important improve- 
 ment was, to shut the top of the cylinder, 
 and instead of pressing the piston down 
 by the weight of the atmosphere, he ap- 
 plied the force of steam, and restored the 
 
130 
 
 THE ARTISAN. 
 
 equilibrium , by opening a communication 
 between the upper and lower side of the 
 piston. All that was afterwards accom- 
 plished by means of the reciprocating steam 
 engine, was only to acquire perfection and 
 easy management; but there was no de- 
 parture from the first principle, nor did he 
 ever depress the piston with steam more 
 than one-tenth stronger than the atmos- 
 phere. V/hat are now termed high-pres- 
 sure engines, which have been productive 
 of so many accidents, he did not counte- 
 nance. 
 
 By this last improvement, his engineers 
 fell into an error, which retarded the pro- 
 gress of the invention for some years ; for, 
 whenever the engine did not perform well, 
 they stuffed the piston with oakum , till it 
 required nearly the whole force of the 
 steam to remove it into the cylinder. This 
 defect was remedied ; and Messrs. Boulton 
 and Watt at length offered their engine to 
 the proprietors of mines, on the most ad- 
 vantageous terms. Experiments were 
 made by men in whom all parties could 
 confide, with Newcomen’s old engine, and 
 Watt’s improved one, in order to ascertain 
 the value of the coals saved by the latter. 
 This was done by placing a counter over 
 the top of the beam or leaver, to tell the 
 number of strokes ; and then estimating 
 according to the size of the cylinder. They 
 were to receive but one-third of the coals 
 saved ; but the great obstacle to the in- 
 troduction of their engine was, the incur- 
 ring a fresh expense. This they removed 
 by taking the old in exchange, at a consi- 
 derable loss, and giving credit for the rest 
 till the advantage was felt. By the adop- 
 tion of these liberal means, they removed 
 every difficulty; but it was not till the 
 year 1778, that their engine began to be 
 duly appreciated. In 1779 Watt invented 
 a method of copying letters, which has 
 been pretty generally adopted. In 1789, 
 the Perriers, of Paris, applied to Messrs. 
 Boulton and Watt for an improved steam 
 engine, for the purpose of supplying that 
 city with water. It was made at Bir- 
 mingham, and sent to Chaillot to be put to- 
 gether, where it still remains. This circum- 
 stance the French have been at some pains 
 to conceal ; and M. Riche de Proney, an 
 eminent mathematician, and chief of the 
 school for roads and bridges in that 
 country, ingeniously contrived to 'fill the 
 pages of a quarto volume with a descrip- 
 tion of the improved steam engine, in- 
 vented by our countryman, Watt, without 
 once naming him; but the French will 
 find it difficult to get any other nation, be- 
 sides themselves, to wink at such injustice. 
 The steam engine, as invented by New- 
 comen, and improved by W att, had hitherto 
 been employed nnly as a reciprocating 
 
 power, for drawing water ; but the genius 
 of Watt did not permit him to stop there, 
 he was for converting the reciprocating 
 power into a rotative one, and thereby to 
 render it of more general utility. To this 
 end, various inventions were resorted to ; 
 but it did not occur to him, so ready is 
 genius to imagine and encounter difficulties, 
 that the simple method of a crank, as used 
 in the turning of the old spinning wheel, 
 might supply what he wanted to discover. 
 He indeed meant to employ the crank, but 
 wanted to make a further improvement by 
 introducing a second axle, with a fly- 
 wheel and heavy side, which should re- 
 volve twice during the time that the engine 
 made one stroke; intending that the heavy 
 side, when the piston was at the top, 
 should be in the act of descending ; not 
 considering, that the heavy fly was a 
 reservoir to preserve regular motion in the 
 machine. Watt, which had been his 
 usual custom from his first residence at 
 Birmingham, gave directions for a model 
 to be made according to this improvement, 
 but as he never allowed a new invention 
 to interrupt the progress of one reduced to 
 actual practice, the consequence was, that 
 which might have been brought to light in 
 one, was eight months in hand ; and, in 
 the interim, a workman employed on the 
 model communicated the invention to a 
 Mr. Rickard, who was unprincipled 
 enough to take out a patent for it ; and, 
 worked by one of Newcomen’s engines 
 but with the addition of this last discovery, 
 a corn-mill was going on within a quarter 
 of a mile of Watt, ere his model was 
 completed. The above circumstances be- 
 ing ascertained by him, though he might 
 easily have set aside the patent obtained 
 by Mr. Rickard, neither he nor his partner 
 being fond of legal remedies, he chose to 
 seek one in his own brain. The only part 
 of the last invention of any moment, and 
 for which a substitute was absolutely ne- 
 cessary, was the crank ; and here, with 
 some expense, and a little ingenuity, he 
 succeeded so well, that it . is doubtful 
 whether his substitute is not quite equal 
 to the crank. This invention of the rota- 
 tive motion by Watt, not only prevented 
 the shock at the beginning and end of every 
 stroke, by equalizing the motion, but ren- 
 dered steam the most manageable, as well 
 as the most useful of all powers, since it 
 might be supplied of any power suited to 
 the uses for which it might be required. 
 Watt’s last great improvement, which per- 
 fected his invention of the rotative motion, 
 was to give the power which communicated 
 the rotative motion, and moved in a por- 
 tion of the circumference of a circle, an accu- 
 rately perpendicular direction. This was not 
 -too great for the astonishingly pregnant 
 
THE ARTISAN. 
 
 131 
 
 imagination of Watt to accomplish ; and he 
 as said to have declared, that by what train 
 of ideas he compassed this admirable in- 
 vention, he himself was unable to commu- 
 nicate, so spontaneous were the powers of 
 his genius. With this last invention ter- 
 minated the most important of his labours. 
 Soon after he settled at Birmingham, he 
 married a second wife, a Miss McGregor, 
 of Glasgow, a lady of considerable attain- 
 ments, with whom he enjoyed a long and 
 well-spent life of conjugal happiness. She 
 bore him several children, but none of 
 them are now surviving. Having passed 
 his 70th year, about which period his 
 partner, Mr. Boulton, died, he retired into 
 private life, leaving the business to his 
 own, only surviving, and Mr. Boulton’s 
 son, by whom the steam-engine manufac- 
 tory is still conducted. Having arrived 
 at his 84th year, he sunk into the arms of 
 his Maker, (at his house at Heathfield, 
 near Birmingham, August the 25th, 1819,) 
 leaving behind him a name as imperishable 
 as the universe, and a reputation which 
 defies detraction. His genius was recog- 
 nized by the Royal Societies of London 
 and Edinburgh, of both of which he was 
 made a member; nor let it be forgotten, 
 that in 1808, when England and France 
 were waging war with uncommon invete- 
 racy, like Sir Humphrey Davy, he received 
 the same honour from the National Insti- 
 tute of France. 
 
 FlEUMATl€3a 
 
 CONDENSED AIR. 
 
 That atmospherical air may be condensed 
 into much less space, has already been 
 stated at page 100, where there is also 
 given the representation of a vessel for 
 that purpose; we shall, therefore, now 
 mention some of the effects which con- 
 densed air is capable of producing. One 
 of the most striking of these effects is ex- 
 hibited by means of an instrument called 
 the Air Gun , an instrument which would 
 actually answer the purpose of many guns, 
 were the force of condensed air equal to 
 that of gun-powder; but as it has never 
 yet been condensed to such a degree as 
 this explosive compound, the air-gun has 
 never yet been applied to any useful pur- 
 pose ; it is however necessary that we 
 should notice it in treating of condensed 
 air. 
 
 This instrument derives its power from 
 the elastic force of compressed air. As it 
 is an instrument of some antiquity, and 
 still occasionally used, we shall here give 
 a representation of it, and also a short de- 
 scription of its construction. 
 
 A ball of cast steel, a, fig. 1st, 
 
 with a conical valve that opens inward, is 
 screwed at n. upon the forcing syringe s, 
 and is kept close shut by the spiral wire 
 spring c. The syringe has a solid piston r, 
 which can be drawn below the hole z, by 
 placing the feet on the cross-bar m, and 
 pulling by the two handles y y. The air 
 will then fill the syringe through the hole 
 z. If then the piston be forced to the top 
 of the syringe, it will drive the air up 
 before it into the ball d, which the valve 
 will keep there. These strokes being re- 
 peated twenty or thirty times, will make 
 the air within the ball ten or twelve times 
 as dense as the common air, and to have 
 the force of gunpowder. The ball now 
 taken from the syringe, and screwed under 
 the gun, fig. 2, will discharge twenty balls 
 successively; for a pin, o, goes through 
 the barrel of the gun, and terminates on 
 the conical valve above mentioned ; and 
 the lock of the gun being cocked by the 
 hook s, is discharged upon the pin o, by 
 pulling at the trigger. The pin pushes 
 open the conical valve, and lets out a 
 small portion of air, but enough to force a 
 ball through an inch board at thirty yards 
 distance. This may be repeated twenty 
 times with the same charge, and almost 
 with the same force. 
 
 There is another instrument of this kind 
 still more powerful than the one just de- 
 scribed, called the Magazine Wind-gun ; 
 but it is more complex in its structure, 
 and not so often to be met with, it is therer 
 fore unnecessary to give a particular de- 
 scription of it here. 
 
 The Diving Bell is also a machine which 
 K 2 
 
132 
 
 THE ARTISAN. 
 
 has the effect of condensing the air con- 
 tained in it, when it descends into the 
 water. 
 
 As this machine is found to be of very 
 great use, in enabling engineers to perform 
 many operations under water, which could 
 not be effected by any other means, we 
 shall give a description and representation 
 of one of the most approved kind of these 
 machines. 
 
 The principle upon which the diving 
 bell becomes useful for the purpose in- 
 tended, is that of air excluding every 
 other body from the space it occupies. If 
 a bell glass, for example, be pressed per- 
 pendicularly into water, with its mouth 
 downward, the air in the glass will force 
 the water down before it, and very little 
 will enter the bell. Availing himself of 
 this principle, Dr. Halley constructed a 
 bell of copper, three feet in diameter at 
 top, five feet at bottom, and eight feet in 
 height, loaded at bottom with such a quan- 
 tity of lead as to make the whole specifi- 
 cally heavier than its bulk of water. The 
 bell was enlightened by a strong glass 
 fixed in its top, where there was also a 
 stop-cock to let out the heated air. This 
 bell was lowered from the yard-arm of a 
 ship, with two men in it, to the depth of 
 ten fathoms. In their descent they found 
 the water rise a little in the bell : the air 
 about them condensed ; which produced a 
 disagreeable pressure on every part of 
 their bodies, particularly on their ears, 
 which seemed as if quills were thrust into 
 them. They had light enough to see the 
 pebbles at bottom, but it appeared red 
 light, on every thing capable of reflecting 
 it ; the red part of light appeared to be 
 the only part capable of forcing its way 
 through the resisting or muddy medium in 
 which they were placed. The air pressing 
 through the pores of their skin, soon be- 
 came as dense within their bodies as with- 
 out, when the sense of pressure ceased, 
 and they found no difficulty in remaining 
 at the bottom several hours, where all was 
 still and tranquil, though the surface was 
 agitated with wind. Two barrels, filled 
 with air, were alternately sent down to 
 them, and the heated contaminated air 
 was let out by the stop-cock, at the top of 
 the bell. This bell, however, proved fatal 
 to two men in the bay of Dublin, by that 
 contraction which ropes suffer on being 
 wet; this caused the bell to turn round in 
 its descent, and entangle the strings by 
 which the divers meant to ring bells, and 
 indicate their wants to the people on 
 board the ship from whence they were 
 lo veered. Waiting too long for these sig- 
 nals, the bell was raised, and the divers 
 were both found dead ; but not drowned ; 
 they died, like the unhapply people in the 
 hole at Calcutta, by breathing contami- 
 nated air. 
 
 Instead of using barrels for supplying 
 the divers with air, it is now the custom 
 to force down a constant stream by means 
 of a pump , resembling a condenser in its 
 construction and operation. The heated 
 air is suffered to escape by a stop-cock at 
 the upper part of the bell. The following 
 figure represents one of the diving bells 
 now in use. 
 
 Here A is the forcing pump, B a stop- 
 cock for letting out the heated air, C a 
 strong glass for giving light, D a float for 
 the security of the diver. 
 
 When proper care is taken to lower this 
 machine gradually, the diver can support 
 the pressure of an atmosphere twice or 
 thrice the natural density. 
 
 As accidents may happen to the divers, 
 even in the best regulated machines of this 
 kind, it is highly proper that every diver 
 should be provided with a float of cork, or 
 with a hollow ball of metal, which might 
 be sufficient to raise him slowly to the 
 Surface, in case of any accident happening 
 to the bell, as several lives have been lost 
 for want of this precaution, from confusion 
 in the signals, and other causes, such as 
 the one mentioned to the two men in the 
 bay of Dublin. 
 
 Besides the form of this machine repre- 
 sented above, there are several other 
 forms, but the mode of supplying them 
 with air, and discharging the heated air, 
 is nearly the same in all. 
 
 The late Mr. Walker constructed a small 
 one of wood , for saving the wreck of the rich 
 ship Belgioso, which was of a conical form, 
 three feet diameter at bottom, two and a 
 half at top, and three feet high, which was 
 sunk by means of lead attached to its 
 bottom.* 
 
 * Mr. Walker mentions a singular circumstance 
 which happened to one of the divers, who went 
 down in this bell. As there was plenty of air to 
 spare in the bell, the diver thought that a candle 
 might be supported in it, and he could descend by 
 
THE ARTISAN. 
 
 133 
 
 Mr. Smeaton’s diving bell at Ramsgate, 
 was of cast-iron, and weighed 50 cwt. 
 which was heavy enough to sink of itself. 
 Its shape was a parallelopiped, four and 
 a half feet long, three feet wide, and four 
 and a half feet high, so that two men 
 could work under it, and could see, by 
 four strong glass lights at top. It was 
 supplied with air in a similar manner to 
 the one represented by the foregoing 
 figure. 
 
 OF PUMPS. 
 
 The common sucking pump, used for 
 raising water, may with propriety be de- 
 scribed either under the head of Pneuma- 
 tics or Hydraulics, as air and water are 
 both necessary to its action. This useful 
 
 machine consists of a tube open at both 
 ends, in which is a moveable piston, 
 bucket, or sucker, as large as the bore of 
 that part of the tube in which it works. 
 It is usually leathered round so as to fit 
 the bore exactly, and prevent the escape 
 of any air between it and the tube. 
 
 To render our explanation of the con- 
 struction of this pump as useful as possible, 
 we have represented it in the following 
 figures as made of glass ; by this means, 
 both the action of the pistons, and opera- 
 tion of the valves, may be fully under- 
 stood. 
 
 In figure 1st, a represents a ring of 
 wood or brass, 
 
 with pliable leather fastened round it, to 
 fit the cylinder A. Over the hole in this 
 ring is a trap-door, or valve of metal, co- 
 vered with leather, part of which often 
 serves as a hinge for the valve to open and 
 
 night. He made the experiment, and presently 
 found himself surrounded by fish, some very large, 
 and many such as he had never seen before ; they 
 sported about the bell, and smelt at hisZeg.?, as they 
 hung in the water; this rather alarmed him, for he 
 was not sure but some of the larger might take a 
 fancy to him, he therefore rang his bell to be taken 
 up, and the fish accompanied him, with much good 
 nature, to the surface. 
 
 shut by. The handle and rod r end in a 
 fork s, which, passing through the ring or 
 piston, is screwed fast to it on the under- 
 side. Below this, and generally over a 
 tube of a smaller bore, as z, is another 
 valve v, opening upward, which will suffer 
 water to pass up, but not down. Now, 
 when the piston a is pulled up by the 
 handle (its valve being close) the column 
 of air on its top is lifted, and a vacuum 
 underneath takes place; to supply this, , 
 the air, in the lower part of the pump/ 
 presses into the vacuum, and hence the 
 
134 
 
 THE ARTISAN. 
 
 whole column of air within the pump be- 
 comes lighter than a similar column of air 
 without the pump. By the superior pres- 
 sure on the well, the water is forced into 
 the pump, and through the valve v, which 
 shutting, prevents its return. The piston 
 being now forced down (as in the common 
 act of pumping) through the water (which 
 opens the piston valve), the next stroke 
 lifts the water to the spout of the pump, 
 and making a vacuum underneath, at the 
 same time a fresh quantity is forced 
 through the lower valve, which, if very 
 tight, will keep the water there, so that 
 the pump, remaining always full, water 
 is delivered at its spout, on the first motion 
 of the handle. As this effect is produced 
 by the pressure of the atmosphere, and as 
 it is found that a column of water, of about 
 thirty-two or thirty-three feet high, is equal 
 in weight to a column of air of the same 
 base of forty-five miles high, (or to the 
 height of the atmosphere,) therefore the 
 piston a must always work at a less dis- 
 tance than thirty-two feet from the surface 
 of the water ; but if it were never to ex- 
 ceed twenty-eight feet it would be better, 
 as the air varies considerably in its weight 
 at different times, which must materially 
 affect the rise of the water. 
 
 The force required for working a pump 
 depends upon the height to which the 
 water is to be raised, and the diameter of 
 the bore of the pump in that part where the 
 piston works. 
 
 If two pumps be of equal height, but (he 
 bore of the one double the diameter of the 
 bore of the other, the widest will raise four 
 times as much water as the other, and 
 consequently will require four times as 
 much force to work it.* 
 
 The wideness or narrowness of the 
 pump in any other part than that in which 
 the piston works, does not make the pump 
 either more or less difficult to work, ex- 
 cept what difference may arise from the 
 friction of the water on the sides of the 
 tube ; this is however always greater in a 
 narrow tube than in a wide one, on account 
 of the greater velocity of the water. 
 
 Many attempts have been made to re- 
 duce both the friction and wearing of 
 pumps ; but it is evident that it is impos- 
 sible to do away with the friction alto- 
 gether ; and that to work the pump, a force 
 must be employed capable of overcoming 
 the weight of the column of water raised 
 by the piston, and of the weight of the 
 piston itself, together with the friction of 
 the water and piston on the sides of the 
 tube. 
 
 The velocity of the stroke ought never 
 
 * This arises from the area of circles being to each 
 other as the square of their diameters : for the square 
 of 2 is 4. 
 
 to be greater than two or three feet, nor les3 
 than four inches in a second : the stroke 
 should also be as long as possible, in order 
 to avoid unnecessary loss of water during 
 the descent of the valves. The diameter of 
 the pipe through which the water rises to 
 the barrel, ought not to be less than- two 
 thirds of the diameter of the barrel or 
 pump itself. 
 
 Metallic conical valves are found to be 
 great improvements in pump work. They 
 are usually formed like the following 
 figure, which represents a section of the 
 whole piston : o, in figure 2, is the conical 
 valve, ground very even and smooth to fit 
 its cavity in the piston a a ; it is kept in 
 its cavity by the weight g, and directed 
 into it by the wire acting through w, when 
 lifted up by the water. The piston is 
 leathered as usual, and the iron crane s 
 goes through it, where it is fastened by the 
 screw nuts rr. Both the upper and lower 
 valves are made in this form : if well 
 made, they are water-tight, and never 
 wear. 
 
 The manner in which this valve is ap- 
 plied may be seen in the section of the 
 pump, figure 3. 
 
 Figure 4 represents the common piston, 
 coated with leather. 
 
 OPTICS. 
 
 OF THE RAINBOW. 
 
 The phenomena of the rainbow consists, 
 as every person knows, of two bows, or 
 arches, stretching across the sky, and 
 tinged with all the colours of the prismatic 
 spectrum. The internal or principal rain- 
 bow, which is often seen without the other, 
 has the violet rays innermost , and the red 
 rays outermost. The external, or secondary 
 rainbow, which is much fainter than the 
 other, has the violet colour outermost, and 
 the red colour inneiunost. Sometimes su- 
 pernumery bows are seen accompanying 
 the principal bows. 
 
 As the rainbow is never seen unless 
 when the sun shines, and when rain is 
 falling, it has been universally ascribed to 
 the decomposition of white light by the 
 refraction of the drops of rain, and their 
 reflection within the drops. The produc- 
 tion of rainbows by the spray of water- 
 falls, or by drops of water scattered by a 
 brush or syringe, is an experimental proof 
 of their origin. 
 
 Let an observer be placed with his back 
 to the sun, and his eye directed through a 
 shower of rain to the part of the sky oppo- 
 site to the sun. As the drops of rain are 
 spherical particles of water, they will re- 
 flect and refract the sun’s rays, according 
 
THE ARTISAN. 
 
 135 
 
 to the usual laws of refraction and reflec- 
 tion already explained in another part of 
 this work. Thus in the following figure, 
 where ssss i*epresent the sun’s rays, and 
 A the place of a spectator, in the centre of 
 
 the two bows (the planes of which are 
 supposed to be perpendicular to his view), 
 the drops a and b produce part of the 
 inner bow by two refractions and one 
 reflection ; 
 
 and the drops c and d part of the exterior 
 bow, by two refractions and one reflection. 
 
 This holds good at whatever height the 
 sun may chance to be in a shower of rain ; 
 if high, the rainbow must be low ; if the 
 sun be low, the rainbow is high : and if a 
 shower happen in a vale when a spectator 
 is on a mountain, he often sees the bow 
 completed to a circle below him. So in the 
 spray of the sea, or a cascade, a circular 
 rainbow is often seen ; and it is but the 
 interposition of the earth that prevents a cir- 
 cular spectrum from being seen at all times, 
 the eye being the vertex of a cone, whose 
 base (the bow) is in part cut off by the 
 earth. 
 
 It is only necessary, for the formation of 
 a rainbow, that the sun should shine on a 
 dense cloud, or a shower of rain, in a 
 proper situation, or even on a number of 
 minute drops of water, scattered by a 
 hrush or by a syringe, so that the light 
 may reach the eye after having undergone 
 a certain angular deviation, by means of 
 various refractions and reflections, as al- 
 ready stated. The light which is reflected 
 by the external surface of a sphere, is 
 scattered almost equally in all directions, 
 setting aside the difference arising from the 
 greater efficacy of oblique reflection : but 
 when it first enters the drop, and is there 
 reflected by its posterior surface, its devia- 
 tion never exceeds a certain angle, which 
 depends on the degree of refrangibility, 
 and is, therefore, different for light of dif- 
 erent colours : and the density of the light 
 being the greatest at the angle of greatest 
 
 deviation, the appearance of a luminous 
 arch is produced by the rays of each co- 
 lour at its appropriate distance. The rays 
 which never enter the drops produce no 
 other effect, than to cause a brightness, or 
 haziness, round the sun, where the reflec- 
 tion is the most oblique : those which are 
 once reflected within the drop, exhibit the 
 common internal or primary rainbow, at 
 the distance of about 41 degrees from the 
 point opposite to the sun : those which are 
 twice reflected, the external or secondary 
 rainbow, of 52° ; and if the effect of the 
 light, three times reflected, were sufficiently 
 powerful, it would appear at the distance 
 of about 42 degrees from the sun. The 
 colours of both rainbows encroach consi- 
 derably on each other ; for each point of 
 the sun may be considered as affording a 
 distinct arch of each colour, and the whole 
 disc, as producing an arch about half a 
 degree in breadth, for each kind of light ; 
 so that the arrangement nearly resembles 
 that of the common mixed spectrum. 
 
 A lunar rainbow is much more rarely 
 seen than a solar one ; but its colours 
 differf little, expept in intensity, from those 
 of the common rainbow. 
 
 The appearance of a rainbow may be 
 produced at any time, when the sun shines, 
 as follows; opposite to a window, into 
 which the sun shines, suspend a glass 
 globe, filled with clear water, in such a 
 manner as to be able to raise it or lower it 
 at pleasure, in order that the sun’s rays 
 may strike upon it. Raise the globe gra- 
 dually, and when it gets to the altitude of 
 
136 
 
 THE ARTISAN, 
 
 forty degrees, a person standing in a pro- 
 per situation, will perceive a purple co- 
 lour in the glass, and upon raising it higher 
 the other prismatic colours, blue, green, 
 yellow, orange, and red, will successively 
 appear. After this, the colours will dis- 
 appear, till the globe be raised to about 
 fifty degrees, when they will again be 
 seen, but in an inverted order ; the red ap- 
 pearing first, and the blue, or violet, last. 
 Upon raising the globe to about fifty-four 
 degrees, the colours will totally vanish. 
 
 In the highest northern latitudes, where 
 the air is commonly loaded with frozen 
 particles, the sun and moon usually appear 
 surrounded by halos , or coloured circles, 
 at the distances of about 22 and 46 de- 
 grees from their centres. Several new 
 forms of halos and paraselenae , or mock- 
 moons, have been described by Captain 
 Ros3 and Captain Parry. And Captain 
 Scoresby, in his account of the Arctic Re- 
 gions, has delineated an immense number 
 of particles of snow, which assume the 
 most beautiful and varied crystallizations, 
 all depending more or less on six-sided 
 combinations of minute particles of ice. 
 
 When particles of such forms are float- 
 ing or descending in the air, there can be 
 no difficulty in deriving from them those 
 various and intricate forms which are oc- 
 casionally met with among this class of 
 phenomena. 
 
 Halos are frequently observed in other 
 climates, as well as in the northern regions 
 of the globe, especially in the colder 
 months, and in the light clouds which float 
 in the highest regions of the air. The 
 halos are usually attended by a horizontal 
 white circle, with brighter spots, or par- 
 helia, near their intersections with this 
 circle, and with portions of inverted arches 
 of various curvatures ; the horizontal 
 circle has also sometimes anthelia, or 
 bright spots nearly opposite to the sun. 
 These phenomena have usually been at- 
 tributed to the effect of spherical par- 
 ticles of hail, each having a central 
 opaque portion of a certain magnitude, 
 mixed with oblong particles, of a deter- 
 minate form, and floating with a certain 
 constant obliquity to the horizon. But all 
 these arbitrary suppositions, which were 
 imagined by Huygens, are in themselves 
 extremely complicated and improbable. A 
 much simpler, and more natural, as well 
 as more accurate explanation, wffiich was 
 suggested at an earlier period by Mariotte, 
 had long been wholly forgotten, till the 
 same idea occurred to Dr. Y oung. The ex- 
 planation given by the last mentioned phi- 
 losophers is, that water has a tendency to 
 congeal or crystallize in the form of a prism, 
 and that the rays of light passing through 
 these prisms (which are disposed in various 
 positions,) by their own weight, are so 
 
 refracted as to produce the different ap- 
 pearances which halos and parhelia have 
 been observed to assume. 
 
 The colours which these phenomena 
 exhibit, are nearly the same as the rain- 
 bow; but less distinct; the red being 
 nearest to the luminary, and the whole 
 halo being very ill-defined on the exterior 
 side. Sometimes the figures of halos and 
 parhelia are so complicated, as to defy 
 all attempts to account for the formation of 
 their different parts; but if the various 
 forms and appearances which the flakes of 
 snow assume, be considered, there will be 
 no reason to think them inadequate to the 
 production of all these appearances. 
 
 OF THE COLOURS OF NATURAL BODIES. 
 
 There is no branch of optics more diffi- 
 cult, and more generally interesting, than 
 that which relates to the colours of natural 
 bodies. 
 
 The splendid tints with which nature has 
 enriched the vegetable, the mineral, and 
 the animal kingdom, have attracted the 
 admiration even of the rudest minds, and 
 have long formed a subject of perplexing 
 research to the natural philosopher. 
 
 One of the finest results of Newton’s ex- 
 periments on the colours of thin plates, 
 w as their application to the explanation of 
 the colours of natural bodies. We shall, 
 therefore, endeavour to give a general view 
 of the principles upon which that cele- 
 brated philosopher’s hypothesis rests. 
 
 His general position is, that if the sun’s 
 light consisted only of one sort of rays , 
 there would be but one colour in the whole 
 world ; and that it would be impossible to 
 produce any new colour, either by reflec- 
 tion or refraction ; consequently the variety 
 of colours, is owing to the composition of 
 light, or to light being a compound 
 body. 
 
 Homogeneous light that appears red , or 
 rather makes objects appear so, Newton 
 calls red-making rays, that which makes 
 objects yellow, green , blue, &c. he calls 
 yellow -making, green-making, blue-making, 
 &c.* The surface of transparent bodies 
 reflects the greatest quantity of light when 
 their refractive power is greatest, whether 
 the surface is in contact with air, or sepa- 
 rate two media of different refractive 
 powers. When the two media have the 
 same refractive powders, there is no reflec- 
 tion at their separating surfaces, and the 
 quantity of reflected light always increases 
 with the difference of the refractive 
 powers. 
 
 This proposition is established by nume- 
 rous experiments. Ruby -silver, red-spar , 
 diamond, and several other substances, 
 have a much higher lustre, or reflect much 
 
 * See note, page 102; and page 103, col. 2d, 
 
THE ARTISAN. 
 
 137 
 
 more light than any other substance ; and 
 ice and water reflect less light than almost 
 any other substance possessed of a refrac- 
 tive power. 
 
 If in the manufacture of glass the re- 
 fractive power be increased, by adding 
 lead, the lustre, or reflective power, will 
 be increased at the same time : and in like 
 manner, if alcohol be added to water, the 
 lustre of the compound will be increased 
 with its refractive power. 
 
 If water be poured upon a surface of 
 croicn glass , the reflective power of the 
 surface will be greatly diminished. If 
 alcohol be poured upon it, the reflective 
 power will be diminished still more. 
 
 The least or thinnest parts of almost all 
 natural bodies are in some measure trans- 
 parent, and the opacity of any body arises 
 from the reflections caused in its internal 
 parts. 
 
 The transparency of gold and silver , 
 when reduced into thin leaves, and of all 
 metalic particles, either when in a state of 
 solution, or when in the form of crystal- 
 lized salts, may be considered as a proof 
 of the proposition which has just been 
 stated. 
 
 Substances, too, that appear perfectly 
 black to the eye, become translucent,* and 
 even transparent, when reduced very thin, 
 and exposed to a strong light. 
 
 Between the parts of opaque and co- 
 loured bodies, there are many spaces, 
 either empty, or filled with media of dif- 
 ferent densities, as water, for example, as 
 well as the aqueous globules that con- 
 stitute clouds or fogs. The truth of this 
 will appear from considering what has 
 already been said on this subject ; for there 
 are numerous reflections with bodies, 
 which cannot happen unless there were 
 interstices between their particles, and of 
 at different refractive power. Besides 
 there are many opaque substances which 
 become transparent, by filling their pores 
 with any substance of nearly the same 
 density with their parts ; thus paper, vellum , 
 and various other bodies, become almost 
 transparent by absorption of oil or other 
 fluids of nearly the same refractive power. 
 On the contrary, all these bodies become 
 opaque when the water or fluid has escaped 
 from their pores. The substance Iodine, 
 which reflects light exactly like metals, is 
 perfectly opaque ; but when it is thrown 
 off into vapour by heat, it forms a purple 
 
 * A body is said to be translucent when it ad- 
 mits the light to pass through it ; and transparent 
 when objects can be seen through it. ^ r 
 
 coloured gas, which consists of the solid 
 transparent particles of iodine floating with 
 air between them. When a mixture of 
 turpentine and water, or of water and air, 
 is effected, the compounds become per- 
 fectly white and opaque, in consequence of 
 the reflection of light at the particles of 
 turpentine and water, and at the junction 
 of the bubbles of froth, with the air which 
 they enclose. 
 
 The transparent parts of bodies, ac- 
 cording to their several sizes, reflect rays 
 of one colour, and transmit those of ano- 
 ther, for the same reason that thin plates of 
 air and water reflect or transmit those 
 rays. 
 
 Sir Isaac Newton conceives, that the parts 
 of all natural bodies exhibit the same colours 
 as the bodies themseves,on the same princi- 
 ple that the parts of a film or leaf of uniform 
 thickness and colour, have the same co- 
 lour as the film, even when slit into threads, 
 or broken into fragments, that preserve 
 their thickness. The coloured plumage of 
 birds vary their tints at the same place, by 
 varying the position of the eye, in the same 
 manner as thin plates, and hence the tints 
 arise from the slenderness of the fine hairs 
 which grow out of the feathers. In like 
 manner, the colours of silks, cloths, &c. 
 when penetrated by water or oil, become 
 more faint by immersion in these liquors, 
 and again recover their original colours 
 when they are dry. Leaf-gold , some kinds 
 of painted glass, and the infusion of 
 lignum nephriticum, reflect one colour, and 
 transmit another, like thin plates, and the 
 coloured flowers of plants and vegetables 
 usually became more transparent, or in 
 some degree change their colours by being 
 bruised. The change of colours produced 
 by mixing different fluids, is ascribed by 
 Sir Isaac Newtoh to a change of bulk, and 
 of density in the saline particles of the 
 liquor, in consequence of the mutual action. 
 A coloured fluid, for example, may occur 
 transparent, if its particles are by any 
 means divided into smaller ones ; and, on 
 the contrary, two transparent fluids may 
 compose a coloured one, by the association 
 of the particles into one cluster. 
 
 The colour of a body depends on the 
 rays incident, or which fall upon it at all 
 angles, and a slight variation in the obli- 
 quity at which they fall on it, will alter 
 the reflected tint to various colours, when 
 the particles are rarer than the surround- 
 ing medium, to a much greater extent than 
 when particles are more dense than that 
 medium, and it is probable that the particles 
 are the densest 
 
135 
 
 THE ARTISAN. 
 
 CHEM1STEY. 
 
 Phosphorus, when pure, is semi-trans- 
 parent, and of a yellowish colour ; but 
 when kept some time in water, it becomes 
 externally opaque, and then has a great 
 resemblance to white wax. Its consistence 
 is nearly that of wax. It may be cut with 
 a knife, or twisted to pieces with the fin- 
 gers.* It is insoluble in water, but it melts 
 at the temperature of 100°. Its mean 
 specific gravity is 1*770. 
 
 Care must be taken to keep phosphorus 
 always under water, particularly when 
 melted; for it is so combustible, that it 
 cannot easily be melted in the open air 
 without taking fire. When phosphorus is 
 newly prepared, it is always dirty, being 
 mixed with a quantity of charcoal dust 
 and other impurities. These impurities 
 may be separated by melting it under 
 water, and then squeezing it through a 
 piece of clean shamoy leather. It may be 
 formed into sticks, by putting it into a glass 
 funnel with a long tube, stopped at the 
 bottom with a cork, and plunging the 
 whole under warm water. The phospho- 
 rus melts, and assumes the shape of the 
 tube. When cold, it may be easily pushed 
 out with a bit of wood. 
 
 If air be excluded, phosphorus evapo- 
 rates at 219°, and boils at 554°. 
 
 When phosphorus is exposed to the at- 
 mosphere, it emits a white smoke, which 
 has the smell of garlic, and is luminous in 
 the dark. This smoke is more abun- 
 dant the higher the temperature is, and 
 is occasioned by the gradual combus- 
 tion of the phosphorus, which at last dis- 
 appears altogether. 
 
 When a bit of phosphorus is put into a 
 glass jar filled with oxygen gas, part of the 
 phosphorus is dissolved by the gas at the 
 temperature of 60° ; but the phosphorus 
 does not become luminous unless its tem- 
 perature be raised to 80°. Hence we learn, 
 that phosphorus burns at a lower tempera- 
 ture in common air than in oxygen gas. 
 This slow combustion of phosphorus, at 
 the common temperature of the atmos- 
 phere, is what renders it necessary to be 
 kept in phials filled with water. The 
 water should be previously boiled to expel 
 a little air, which that liquor usually con- 
 tains. The phials should be kept in a dark 
 place ; for when phosphorus is exposed to 
 the light, it soon becomes of a white co- 
 lour, which gradually changes to a dark 
 brown. 
 
 When heated to 148°, phosphorus takes 
 fire and burns with a very bright flame, 
 and gives out a great quantity of white 
 
 * This being rather a dangerous operation, water 
 ought to be at hand to plunge it into as soon as it 
 begins to smoke. 
 
 smoke, which is highly luminous in the 
 dark. It leaves no residuum ; but the 
 white smoke, when collected, is found to 
 be an acid. Stahl considered this acid as 
 the muriatic.* According to him, phos- 
 phorus is composed of muriatic acid and 
 phlogiston,! and the combustion of it is 
 merely the separation of phlogiston. He 
 even declared, that, to make phosphorus, 
 nothing more is necessary than to combine 
 muriatic acid and phlogiston. 
 
 These assertions having gained implicit 
 credit, the composition and nature of phos- 
 phorus were considered as completely un- 
 derstood, till Margraf of Berlin published 
 his experiments in the year 1740. That 
 great man, one of those illustrious philoso- 
 phers who have contributed so much to 
 the rapid increase of the science, distin- 
 guished equally by the ingenuity of his ex- 
 periments and clearness of his reasoning, 
 attempted to produce phosphorus by com- 
 bining together phlogiston and muriatic 
 acid : but though he varied his process a 
 thousand ways, presented the acid in 
 many different states, and employed a 
 variety of substances to furnish phlogis- 
 ton, all his attempts failed, and he was 
 obliged to give up the combination as im 
 practicable. On examining the acid pro- 
 duced during the combustion of phospho- 
 rus, he found that its properties were very 
 different from those of muriatic acid. It 
 was therefore a distinct substance. The 
 name of phosphoric acid was given to it ; 
 and it was concluded that phosphorus is 
 composed of this acid united to phlogiston. 
 
 But it was observed by Margraf, that 
 phosphoric acid is heavier than the phos- 
 phorus from which it was produced ; and 
 Boyle had long before shewn, that phos- 
 phorus would not burn except when in 
 contact with air. These facts were suffi- 
 cient to prove Hie inaccuracy of the theory 
 concerning the composition of phosphorus ; 
 but they remained themselves unaccounted 
 for, till Lavoisier published those cele- 
 brated experiments which threw so much 
 light on the nature and composition of 
 acids. 
 
 He exhausted a glass globe of air by 
 means of an air-pump ; and after weighing 
 it accurately, he filled it with oxygen gas, 
 and introduced into it 100 grains of phos- 
 phorus. The globe was furnished with a 
 stop-cock, by which oxygen gas could be 
 admitted at pleasure. He set fire to the 
 phosphorus by means of a burning glass. 
 The combustion was extremely rapid, ac- 
 companied by a bright flame and much 
 heat. Large quantities of white flakes 
 
 * This acid will be afterwards described. 
 
 t The term phlogiston was applied by Stahl and 
 his followers to a substance, which, according to 
 them, exists in all combustible bodies, and separates 
 during combustion. — See page 15, col. 2. 
 
THE ARTISAN. 
 
 139 
 
 attached themselves to the inner surface of 
 the globe, and rendered it opaque; and 
 these at last became so abundant, that, 
 notwithstanding the constant supply of 
 oxygen gas, the phosphorus was extin- 
 guished. The globe, after being allowed 
 to cool, was again weighed before it was 
 opened. The quantity of oxygen employed 
 during the experiment was ascertained, 
 and the phosphorus, which still remained 
 unchanged, accurately weighed. The white 
 flakes, which were nothing else than pure 
 phosphoric acid, were found exactly equal 
 to the weights of the phosphorus and oxy- 
 gen which had disappeared during the 
 process. Phosphoric acid, therefore, must 
 have been formed by the combination of 
 these two bodies ; for the absolute weight 
 of all the substances together was the same 
 after the process as before it. It is im- 
 possible, then, for phosphorus to be com- 
 posed of phosphoric acid and phlogiston, 
 as phosphorus itself enters into the com- 
 position of that acid. 
 
 Thus the combustion of phosphorus, 
 like that of hydrogen and carbon, is nothing 
 else than its combination with oxygen : for 
 during the process no new substance ap- 
 pears, except the acid, accompanied in- 
 deed with much heat and light. 
 
 From Lavoisier’s experiment it follows, 
 that 100 parts of phosphorus during this 
 combustion, unite with 154 parts of oxygen. 
 So that a grain of phosphorus condenses 
 no less thdn 4§ cubic inches of oxygen 
 gas; and five grains are capable of de- 
 priving 102^ cubic inches of air of all its 
 oxygen gas. 
 
 Though pure phosphorus does not take 
 fire till it be heated to 148°, it is neverthe- 
 less true, that we meet with phosphorus 
 which burns at much lower temperatures. 
 The heat of the hand often makes it burn 
 vividly and it even takes fire when merely 
 exposed to the atmosphere. In all these 
 cases the phosphorus has undergone a 
 change. It is believed at present, that 
 this increase of combustibility is owing to 
 a small quantity of oxygen with which the 
 phosphorus has combined. Hence, in this 
 state, it is distinguished by the name of 
 oxide of phosphorus. When a little phos- 
 phorus is exposed in a long narrow glass 
 tube to the heat of boiling water, it con- 
 tinues moderately luminous, and gradu- 
 ally rises up in the state of a white va- 
 pour, which lines the tubes. This vapour 
 is the oxide of phosphorus. This oxide has 
 the appearance of fine white flakes, which 
 cohere together, and is more bulky than 
 the original phosphorus. When slightly 
 heated it takes fire, and burns brilliantly. 
 Exposed to the air, it attracts moisture 
 with avidity, and is converted into an acid 
 liquor. When a little phosphorus is thus 
 oxidized in a small tin box by heating it, 
 
 the oxide acquires the property of taking 
 fire when exposed to the air. In this state 
 it is often used to light candles, under the 
 name of phosphoric matches ; the phospho- 
 rus being sometimes mixed with a little 
 oil, sometimes with sulphur. But the 
 simplest mode of making matches of this 
 kind is, to put a little phosphorus, dried 
 by blotting-paper, into a small phial ; to 
 heat the phial, and when the phosphorus 
 is melted, to turn it round, so that the phos- 
 phorus may adhere to the sides. The 
 phial is then to be closely corked and pre- 
 pared for use. On putting a common sul- 
 phur-match into the bottle, and stirring it 
 about, the phosphorus will adhere to the 
 match, and will take fire when brought out 
 into the air. 
 
 When bits of phosphorus are kept for 
 some hours in hydrogen gas, part of the 
 phosphorus is dissolved. This compound 
 gas, to which Fourcroy and Vauquelin, 
 the discoverers of it, have given the name 
 of phosphorized hydrogen gas, has a slight 
 smell of garlic. When bubbles of it are 
 made to pass into oxygen gas, a very bril- 
 liant blueish flame is produced, which per- 
 vades the whole vessel of oxygen gas. It 
 is obvious that this flame is the conse- 
 quence of the combustion of the dissolved 
 phosphorus. 
 
 When phosphorus is introduced into a 
 glass jar of hydrogen gas standing over 
 mercury, and then melted by means of a 
 burning glass, the hydrogen gas dissolves 
 a much greater proportion of it. The com- 
 pound thus formed has received the name 
 of phosphuretted hydrogen gas. It was dis- 
 covered, in 1788, by Mr. Gengembre, and 
 afterwards by Mr. Kirwan, before he 
 knew of the experiments of Gengembre. 
 
 It has a very fetid odour, similar to the 
 smell of putrid fish. When it comes into 
 contact with common air, it burns with 
 great rapidity ; and if mixed with that air, 
 detonates violently. Oxygen gas pro- 
 duces a still more rapid and brilliant com- 
 bustion than common air. When bubbles 
 of it are made to pass up through water, 
 they explode in succession as they reach 
 the surface of the liquid ; a beautiful coro- 
 net of white smoke is formed, which rises 
 slowly to the ceiling. This gas is* the most 
 combustible substance known. 
 
 Pure water, when agitated in contact 
 with this gas, dissolves at the temperature 
 of between 50° and 60° about the fourth 
 part of its bulk of it, * The solution is of 
 a colour not unlike that of roll sulphur ; it 
 has a very bitter and disagreeable taste, 
 and a strong unpleasant odour. When 
 heated nearly to boiling, the whole of the 
 phosphuretted hydrogen gas is driven off 
 
 * Mr. Henry, however, found, that 100 inches of 
 water took up only 2* 14 inches of this gas at the 
 temperature of 60°. 
 
140 
 
 THE ARTISAN. 
 
 unchanged, and the water remains behind 
 in a state of parity. When exposed to the 
 air, the phosphorus is gradually deposited 
 in the state of oxide ; the hydrogen gas 
 makes its escape ; and at last nothing re- 
 mains but pure water. 
 
 When electric explosions are passed 
 through this gas, its bulk is increased pre- 
 cisely as happens to carburetted hydrogen. 
 
 The water which it contains is decom- 
 posed, phosphoric acid formed, and hydro- 
 gen gas evolved. 
 
 Phosphorus is capable of combining with 
 carbon. This compound, which has re- 
 ceived the name of phosphuret of carbon , * 
 was first examined by Mr. Proust, the 
 celebrated professor of chemistry, in Spain. 
 It is the red substance which remains 
 behind when new-made phosphorus is 
 strained through shamoy leather. In order 
 to separate from it a small quantity of 
 
 phosphorus which it contains in excess, it 
 should be put into a retort, and exposed 
 for some time to a moderate heat. What 
 remains behind in the retort is the pure 
 phosphuret of carbon. It is a light flocky 
 powder, of a lively orange-red, without 
 taste or smell. When heated in the open 
 air it burns rapidly, and a quantity of 
 charcoal remains behind. When the re- 
 tort in which it is formed is heated red hot, 
 the phosphorus comes over, and the char- 
 coal remains behind. 
 
 Such are the properties of phosphorus, and 
 the compounds which it forms with oxygen, 
 hydrogen, and carbon. Tt is capable, like- 
 wise, of combining with many other bodies : 
 the compounds produced are called phos- 
 phurets. 
 
 Phosphorus, when used internally, is 
 poisonous, even in so small a quantity as 
 one fourth of a grain. 
 
 * See note, page 104. 
 
 OSTEOTOMY. 
 
 It has already been remarked, at page 
 109, that the planet Jupiter is surrounded 
 with broad parallel belts. These belts are 
 variable, both in number and position. 
 
 Different opinions have been enter- 
 tained by astronomers respecting the cause 
 of these belts. By some they have been 
 regarded as clouds, or as openings in 
 the atmosphere of the planet ; while others 
 imagine them to be of a more permanent 
 nature, and to be marks of great physical 
 revolutions, which are perpetually chang- 
 ing the surface of the planet. 
 
 The Sun appears to Jupiter only of one 
 twenty-eighth part of the size he does to the 
 Earth : and the light and heat he derives 
 from that Luminary are in the same pro- 
 portion. But he is in some measure com- 
 pensated for this want by the quick return 
 
 The following figures, A and B, exhibit 
 the appearance of Jupiter, according to Sir 
 W. Henschel. 
 
 of the Sun, occasioned by the prodigiously 
 rapid motion round his axis ; and by four 
 satellites, which move round him, at dif- 
 ferent distances. 
 
 These four satellites were discovered by 
 Galileo, an Italian astronomer, in the year 
 1610. They may be seen by a telescope 
 which magnifies thirty times, and are found 
 to be of great use in determining the longi- 
 tude of places on the Earth, by their im- 
 mersions into his shadow, and their emer- 
 sions out of it. 
 
 These satellites are of different magni- 
 tudes ; the second being the least, the 
 third the greatest, and the fourth the second 
 
THE ARTISAN. 
 
 141 
 
 in magnitude. The time which each of 
 these satellites take to go round Jupiter 
 is as follows : The first, or nearest to him, 
 Id. 18h. 27 ' 33' : the second, 3d. 13h.l3 42" ; 
 the third, Td. 3h. 42' 33" ; and the fourth, 
 16d. 16h.32' 8". 
 
 The eclipses of these satellites, by falling 
 into the shadow of Jupiter, have not only 
 been of advantage in enabling astronomers 
 to ascertain the longitude of places* but 
 were the cause of that most curious disco- 
 very, made by Roemer, in the year 1675, of 
 the successive propagation of light. 
 
 OF SATURN. 
 
 The planet Saturn is 79,491 miles in 
 diameter, and performs his revolution round 
 the Sun in 10,746 days, 19 hours, 16 mi- 
 nutes, at the distance of 903,690,197 Eng- 
 lish miles. His motion in his orbit is said 
 to be 18,000 miles per hour ; and the time 
 he revolves on his axis lOh. 16' by some 
 astronomers, and by others only 6 hours. 
 
 Saturn is distinguished from all the 
 other planets, by a large luminous ring 
 surrounding his body, which was disco- 
 vered by the celebrated Huygens, about 
 the end of the 17th century. The same 
 astronomer also discovered the fourth sa- 
 tellite, which attends this planet, and on 
 that account is sometimes called the Huy- 
 genian satellite. The ring which surrounds 
 Saturn appears double when seen through 
 a good telescope, and is seen to cast a deep 
 shadow on the planet. Dr. Herschel is of 
 opinion that the ring has a motion round 
 its axis ; but this is doubted by Schroeter, 
 and some other astronomers. Respecting 
 the formation of this strange phenomenon, 
 astronomers have been very different in 
 their opinions : but the difficulty still re- 
 mains as formidable as ever. 
 
 The annexed figure represents this planet 
 
 as seen by Sir William Herschel, on vari- 
 ous occasions, with Ills powerful telescope. 
 
 To Saturn the Sun appears only one- 
 ninetieth part of the size it does h the 
 Earth ; and the light and heat which that 
 planet receives from the Sun are in the 
 same proportion. But to compensate for 
 the scantiness of light derived from the 
 Sun, Saturn has been observed to have no 
 fewer than seven satellites revolving round* 
 him, besides the luminous ring that sur- 
 rounds his body. The Huygenian, or 
 fourth satellite, was the first discovered; 
 the first, second, third, and fifth were some 
 years afterwards discovered by Cassini; 
 and the sixth and seventh were discovered 
 by Dr. Herschel, in the year 1789. These 
 satellites are all so small, and at such a 
 distance from the Earth, that they cannot 
 be seen, unless with very powerful tele- 
 scopes. 
 
 The orbit of the planet Saturn was long 
 considered as the boundary of the solar 
 system, except the cometary orbits, which 
 were always believed to stretch far be- 
 yond it. But by the discovery of the 
 planet Georgium Sidus, this system has 
 been extended far beyond the limits for- 
 merly assigned it. 
 
 OF GEORGIUM SIDUS, 
 
 A new planet was discovered by Dr. 
 Herschel, on the 13th of March, 1781, and 
 called by him Georgium Sidus, out of re- 
 spect to his Majesty George III., but astro- 
 nomers have given it the names of Her- 
 schel and Uranus. This planet is situated 
 far beyond the orbit of Saturn, being at the 
 immense distance of 1,822,568,000 miles 
 from the sun. The time it requires to per- 
 form its revolution round that luminary is 
 83 years, 150 days, 18 hours. Its diameter 
 is about 4§ times greater than that of the 
 
 earth, or nearly 35,000 English miles. The 
 distance of this planet from the sun being 
 about double that of Saturn, can scarcely 
 be discovered by the naked eye. How- 
 ever, when the sky is very clear, it may be 
 perceived by a good eye like a faint star of 
 the fifth magnitude ; but it cannot be readily 
 
 distinguished from a fixed star with a tele- 
 scope of a less magnifying power than 200. 
 This planet is placed at so great a distance 
 from the sun, that it can receive but a very 
 small portion of his light : however, this 
 want is in some measure supplied by six 
 satellites that revolve round it, all of which 
 
142 
 
 THE ARTISAN. 
 
 were discovered by Dr. Herschel. The 
 periodic times of these satellites are . as 
 follows: — the first, is 5d. 21h. 25'; the 
 second, 8d. 17h. 1' 19"; the third, lOd. 
 23h. 4'; the fourth, 13d. llh. 5'; the fifth, 
 38d. lh. 49'; and, the sixth, 107d. 16h. 
 40'. It is a remarkable circumstance that 
 all these satellites move round the planet 
 in a retrograde order^ and that their orbits 
 are nearly all in the same plane, almost 
 perpendicular to the ecliptic. 
 
 j^Hscellaneous Subjects. 
 
 CAPTAIN RATER’S METHOD OF 
 DETERMINING THE LENGTH OF 
 THE PENDULUM. 
 
 The celebrated Huygens, who is allowed 
 to be the original author of the Theory of 
 the Pendulum, had demonstrated, that the 
 centres of suspension and oscillation are 
 convertible with one another ; or that if in 
 any pendulum * the centre of oscillation be 
 made the centre of suspension, the time of 
 vibration will be in both cases the same. 
 
 From the consideration of this propo- 
 sition, Captain Rater discovered that its 
 converse must also be true ; namely, that if 
 the same pendulum can be made to vibrate 
 in the same time with two different points 
 of suspension, one of these points must be 
 the centre of oscillation, when the other 
 is the centre of suspension ; and thus their 
 distance, or the true length of the Pendu- 
 lum, is found.! 
 
 To reduce this principle to practice, Cap- 
 tain Rater formed a pendulum of a bar of 
 plate brass, one inch and a half wide, 
 and one-eighth of an inch thick. Through 
 this bar two triangular holes are made at 
 the distance of 89*4 inches from each other, 
 to admit the knife edges that are to 
 serve for the axes of suspension in the two 
 opposite positions of the pendulum. Four 
 strong knees of hammered brass, of the 
 same width with the bar, six inches long, 
 and three-fourths of an inch thick ? are 
 firmly screwed by pairs to each end of 
 the bar ; so that when the knife edges are 
 passed through the triangular apertures, 
 their backs may bear steadily against the 
 perfectly plane surface of the brass knees, 
 which are formed as nearly as possible 
 at right angles to the bar. The bar is cut 
 
 * This word strictly applies to a compound pen- 
 dulum, and signifies that point in it which is at such 
 a distance from the point of suspension as is equal 
 to a simple pendulum, which vibrates in the same 
 time with the compound one. 
 
 t Notwithstanding the simplicity of this well- 
 known proposition, it appears that Captain Kater, 
 was the first person who applied it to the purpose of 
 determining the length of the pendulum. 
 
 of such a length that its ends fall short of 
 the extremities of the knee-pieces about 
 two inches. 
 
 Two slips of deal, 17 inches long, are 
 inserted at either end, in the spaces thus 
 left between the knee pieces unoccupied 
 by the bar, and are firmly secured by 
 screws. These slips of deal are only half 
 the width of the bar ; they are stained 
 black, and a small whalebone point in- 
 serted at each end indicates the extent of 
 the arc of vibration. 
 
 A cylindrical weight of brass, three 
 inches and a half in diameter, and weigh- 
 ing about two pounds seven ounces, has a 
 rectangular opening in the direction of its 
 diameter, to admit the knee-pieces of one 
 end of the pendulum. This weight, being 
 passed on the pendulum, is so firmly 
 screwed in its place, as to render any 
 change impossible. It is not between the 
 knife edges, but is very near to one of 
 them. 
 
 A second weight, of about seven ounces 
 and a half, is made to slide on the bar, 
 near the knife edges, at the opposite end; 
 and it may be fixed at any point on the bar 
 by two screws with which it is furnished. 
 A third weight, or slider, of only four 
 ounces, is moveable along the bar, and is 
 capable of nice adjustment, by means of a 
 screw and a clasp. It is intended to move 
 near the centre of the bar, and has an 
 opening, through which may be seen divi- 
 sions of the twentieth of an inch engraved 
 on the bar. 
 
 It is by means of this moveable weight 
 that the direction of the vibrations in the 
 two opposite positions of the pendulum are 
 adjusted to one another, after which it is 
 secured immoveably in its place. 
 
 The knife edges, or prisms, which 
 make so important a part of this appara- 
 tus, and are to serve alternately as the 
 axes of motion, are made of the steel pre- 
 pared in India, and known by the name of 
 wootz. The two planes which form the 
 edge of each prism are inclined to one 
 another nearly at an angle of 120 degrees. 
 
 The edges are as true, or straight, as it 
 was possible to make them, and the hardest 
 temper was given to the steel ; and the 
 long series of experiments which have 
 been made with the pendulum proves that 
 they have fully answered the purpose. 
 
 As the method adopted by Captain 
 Rater, for determining the number of vi- 
 brations of his pendulum in twenty-four 
 hours, was very ingenious, we shall give 
 a short account of it previous to conclud- 
 ing our description of this interesting and 
 delicate apparatus. 
 
 It is almost needless to remark, that this 
 pendulum was not intended to be applied 
 to a clock, nor to receive its motion from 
 any thing but its own weight. 
 
THE ARTISAN. 
 
 143 
 
 After the pendulum was accurately sus- 
 pended, it was placed in front of one of 
 Mr. Arnold’s best clocks, and close to it, 
 so that it appeared to pass over the centre 
 of the dial plate, with its extremity reach- 
 ing a little below the ball of the pendulum. 
 A circular white disk was painted on a 
 piece of black paper, which was attached 
 to the ball of the pendulum clock, and was 
 of such a size, that, when all was at rest, 
 it was just hid from an observer on the 
 opposite side of the room by one of the 
 slips of deal which form the extremities of 
 the brass pendulum. On the opposite side 
 of the room was fixed a wooden stand, as 
 high as the ball of the pendulum of the 
 clock, serving to support a small telescope, 
 magnifying about four times. A dia- 
 phragm in the focus was so adjusted as 
 exactly to take in the white disk, and the 
 diameter of the slip of deal which covered 
 it. “ Supposing, now,” says the ingeni- 
 ous inventor, a both pendulums set in mo- 
 tion, the brass pendulum a little preced- 
 ing the clock, the slip of deal wall first 
 pass through the field of view at each 
 vibration, and will be followed by the 
 white disk. But the brass pendulum be- 
 ing rather the longer of the two, the pen- 
 dulum of the clock will gain upon it : the 
 white disk will gradually approach the 
 slip of deal, and, at length, at a certain 
 vibration, will be wholly concealed by it. 
 The instant of this total disappearance 
 must be noted. The pendulums will now 
 appear to separate ; and, after a certain 
 time, will again approach each other, 
 when the same phenomenon will take 
 place. The interval between the two coin- 
 cidences will give the number of vibrations 
 made by the pendulum of the clock ; the 
 number of vibrations of the brass pendulum 
 is greater by two.” 
 
 Thus was determined the number of 
 vibrations made by the brass pendulum in 
 a given interval of time ; and so, by pro- 
 portion, the number for a whole day. The 
 interval between the nearest coincidences 
 was about 132| seconds ; and four of these, 
 that is, five successive coincidences, gave 
 an interval of 530 seconds, or 8 minutes 50 
 seconds ; after which the arc described by 
 the brass pendulum became too small. The 
 pendulum was then stopped, and put in 
 motion anew as oft as it was judged pro- 
 per to repeat the observations. 
 
 Being thus enabled to determine, with 
 great accuracy, the number of vibrations 
 performed by his pendulum in a given 
 time, Captain Rater proceeded, by revers- 
 ing it, to make the vibrations equal in its 
 two oppositions. The sliding weight above 
 mentioned was used for producing this 
 equality, which, after a series of most 
 accurate and careful experiments, was 
 brought about with a degree of precision 
 that could hardly havq been anticipated. 
 
 By the means of twelve sets of experi- 
 ments, each consisting of a great number 
 of individual trials, with the same end of 
 the pendulum upwards, the number of 
 vibrations in 24 hours was 86058*71 ; and, 
 with the same end lowest, the mean of as 
 many others gave 86058*72, differing from 
 the former only by the hundredth part of a 
 vibration. The greatest difference was *43, 
 or less than a half, — a degree of exactness 
 which was never before attained. 
 
 From a mean of the twelve sets of ex- 
 periments here stated, the length of the se- 
 cond's pendulum comes out 39*13829 inches, 
 after making every allowance for tempera- 
 ture, buoyancy of the atmosphere, &c., or 
 to 39*1386, reducing it to the level of the 
 sea. 
 
 These experiments were made in the 
 house of Mr. Brown, Portland-place, the 
 latitude of which was found to be 51° 
 31' 8*4". 
 
 Thus, for the first time, after having 
 been an occasional object of research for 
 more than 160 years, has the centre of 
 oscillation of a compound pendulum been 
 found by experiment alone, according to 
 a method of universal application, and 
 admitting of mathematical precision. 
 
 ON THE CHINESE YEAR. 
 
 A paper by J. F. Davis, F. R.S. was 
 lately read before the Royal Society of 
 London, on the subject of astronomy, 
 among the Chinese, in which he attempts 
 to show the folly of attributing any thing 
 original in astronomical science to the Chi- 
 nese, who were entirely ignorant of its ob- 
 jects and principles, before its introduc- 
 tion into their empire by the Arabians, and 
 afterwards by the European missionaries. 
 On this one subject, says the author, 
 that singular nation has deviated from its 
 established prejudices and maxims, against 
 introducing what is foreign, — they have 
 even adopted the errors of the European 
 astronomy, for he discovered in a Chinese 
 book, the exact representation of the Pto- 
 lemaic system, — he adds, indeed, it is im- 
 possible not to smile at the idea of attribut- 
 ing any science to a people whose learned 
 books are filled with such trumpery as the 
 diagrams of Fo-hi, and a hundred other 
 puerilities of the same kind. Mr. Davis 
 offers several other proofs of the talent 
 which the Chinese possess of stealing the 
 discoveries of other nations and appropri- 
 ating them to themselves. 
 
 The author proceeds to show, that the 
 Chinese have no solar year, but that their 
 year is, in fact, a lunar year , consisting of 
 twelve months, of twenty-nine and thirty- 
 days alternately, with the triennial inter- 
 calation of a thirteenth month, to make 
 it correspond more nearly with the sun’s 
 course. 
 
144 
 
 THE ARTISAN 
 
 ON THE VELOCITY OF SOUND. 
 
 A paper by Dr. Gregory was lately read 
 before the Royal Society of Edinburgh, 
 containing an account of some experiments, 
 made in order to determine the velocity 
 with which sound is transmitted through 
 the atmosphere. Some of the results of 
 these experiments are the following : — 
 
 That wind greatly affects sound in point of 
 intensity , and, that it affects it also in point 
 of velocity that when the direction of 
 the wind concurs with that of the sound, 
 the sum of their separate velocities gives 
 the apparent velocity of sound ; when the 
 direction of the wind opposes that of the 
 sound, the difference of the separate velo- 
 cities must be taken ; — that in the case of 
 echoes, the velocity of the reflected sound 
 is the same as that of the direct sound, 
 that, therefore, distances may frequently 
 be measured by means of echoes ; — that 
 an augmentation of temperature occasions 
 an augmentation of the velocity of sound, 
 and vice versa. 
 
 Dr. Gregory mentions in a postscript, 
 that it appears from experiments made by 
 Mr. Goldingham, at Madras, that the velo- 
 city of sound is different in different cli- 
 mates ; and that hygrometric changes are 
 not without their influence. 
 
 SOLUTIONS OF QUESTIONS. 
 
 Quest. 12, answered by Mr. R. Graham 
 ( the proposer ). 
 
 Put x = A D, uni (DC), b — 100 
 (A C B). 
 
 a 
 
 Then by 1 and 47 Euc.^a 2 + A C and 
 
 --~ — b, (see Bonnycastle’s 
 
 Mensuration.) Then by transposing, and 
 squaring both sides, we have x 2 — 
 
 — 9 ^ 64 a an( j jjy completing the 
 
 5 ~ ' 60 
 
 square and extracting the root, we obtain 
 x~ 49-786 ~ A D : then by the property 
 
 of the circle A D 2 (49-786) — CD (4) = 
 619-661 r DE, to Avhich add C D (4) and 
 we obtain CE“ 623*661 the diameter of 
 the circle required. 
 
 Quest. 16, answered by Mr. J. M. 
 Edney. 
 
 Put am the side of the triangle; and 
 a — -4330127 the . area of an equilateral 
 triangle, whose side is unity or 1. Then 
 will x 2 am the area of the triangle : and 
 from the question arises the following 
 equation x 2 a — 3 x ; whence x is found to 
 
 1, or =6-9282 feet, yds. &c, 
 
 De — a *4330127 * ? 
 
 which must be the length of the side to 
 answer the condition of the question. And 
 (6-9282) 2 x *4330127 = 6*9282 x 3 = 
 20-7846 = the area of the triangle, and 
 also the sum of its sides. 
 
 QUESTIONS FOR SOLUTION. 
 
 To the Editor of the Artisan. 
 
 Sir, 
 
 Allow me to lay before your mathemati- 
 cal correspondents the following question 
 for solution (should it meet your appro- 
 bation), which will oblige, yours, &c. 
 
 2, Sf. John Street , J. M. Edney. 
 
 Clerkenwell. 
 
 Quest. 17. The dimensions of a block of 
 Lignum-vitce are as follows : the ends are 
 squares, each side of the greater square 
 being 1 ~ foot, and of the less § a foot ; the 
 length being 24 feet ; required its weight 
 in avoirdupoise ounces ? 
 
 To the Editor e Artisan. 
 
 Sir, 
 
 By inserting the following question in 
 one of the succeeding numbers of the 
 Artisan, you will greatly oblige your 
 very humble servant, 
 
 Holloway , Exeter. C. A. Williams. 
 
 Quest. 18. If 360 shillings be formed 
 into a circle, so that they may all touch 
 each other, and the points of contact be 
 distant § of an inch ;^what will be the area 
 of a circle passing through all the points of 
 contact ? 
 
 To the Editor of the Artisan. 
 
 Sir, 
 
 As you had the kindness to insert my 
 last geometrical question i (No. 14.), I 
 have taken the liberty of sending you 
 another, which I will thank you to insert 
 as soon as convenient , which will oblige, 
 yours, &c. 
 
 Edinburgh , An Engineer. 
 
 4£/i May, 1824. 
 
 Quest. 19. From two given points, to 
 draw straight lines, making equal angles 
 at the same point in a straight line given 
 in position. 
 
THE ARTISAN. 
 
 145 
 
 GEOMETRY. 
 
 PROPOSITION XXVI. 
 
 Theorem. — If two triangles have two angles 
 of the one equal to two angles of the other , 
 each to each; and one side equal to one 
 side , viz. either the sides adjacent to the 
 equal angles , or the sides opposite to the 
 equal angles in each ; then shall the other 
 sides be equal, each to each ; and also the 
 third angle of the one to the third angle 
 of the other. 
 
 Let A B C, D E F be two triangles which 
 have the angles A B C, B C A equal to the 
 angles DEF, EFD, viz. ABCtoDEF, 
 and B C A to E F D ; also one side equal to 
 one side ; and first let those sides be equal 
 which are adjacent to the angles that are 
 equal in the two triangles, viz. B C to EF ; 
 the other sides shall be equal, each to each, 
 viz. A B to D E, and A C to 1)F; and the 
 third angle B A C to the third angle El) F. 
 
 A S> 
 
 For, if A B be not equal to D E, one of 
 them must be the greater. Let A B be the 
 greater of the two, and make B G equal to 
 D E, and join G C ; therefore, because B G 
 is equal to D E, and BC to EF, the two 
 sides G B, B C are equal to the two D E, 
 E F, each to each ; and the angle G B C is 
 equal to the angle DEF; therefore the 
 base G C is equal to the base D F, and the 
 triangle GB C to the triangle DEF, and 
 the other angles to the other angles, each 
 to each, to which the equal sides are oppo- 
 site ; therefore the angle G C B is equal to 
 the angle D F E ; but D F E is, by the hy- 
 pothesis, equal to the angle B C A ; where- 
 fore also the angle B C G is equal to the 
 angle B C A , the less to the greater, which 
 is impossible ; therefore A B is not une- 
 qual to D E, that is, it is equal to it ; and 
 B C is equal to E F ; therefore the two A B, 
 B C are equal to the two D E, EF, each to 
 each ; and the angle A B C is equal to the 
 angle DEF; the base therefore A C is 
 equal to the base DF, and the third angle 
 B A C to the third angle E D F. 
 
 Nest, let the sides which are opposite to 
 the equal angles in each triangle be equal to 
 
 Vol. I. — No. 10. 
 
 one another, viz. A B to D E ; likewise 
 in this case, the other sides shall be equal, 
 AC to DF, and B C to E F ; and also 
 the third angle BAG to the third EDF. 
 
 A. jo 
 
 For, if B C be not equal to E F, let B C 
 be the greater of them, and make BH 
 equal to E F, and join A H ; and because 
 B H is equal to E F, and A B to D E ; 
 the two A B, B H are equal to the two 
 DE, E F, each to each ; and they con- 
 tain equal angles ; therefore the base A H 
 is equal to the base D F, and the triangle 
 A B H to the triangle D E F, and the other 
 angles are equal, each to each, to which 
 the equal sides are opposite ; therefore the 
 angle B H A is equal to the angle EFD; 
 but EFD is equal to the angle B C A ; 
 therefore also the angle B H A is equal to 
 the angle B C A, that is, the exterior 
 angle B H A of the triangle A H C is 
 equal to its interior and opposite angle 
 B C A ; which is impossible ; wherefore 
 B C is not unequal to E F, that is, it is 
 equal to it; and AB is equal to DE; 
 therefore the two A B, B C, are equal to 
 the two DE, EF, each to each; and they 
 contain equal angles ; wherefore the base 
 A C is equal to the base D F , and the 
 third angle BAG to the third angle 
 EDF. Therefore, if two triangles, &c. 
 Q.E.D. 
 
 It may be necessary to remark respecting 
 this proposition, that the two equal sides 
 (viz. one in each triangle) must be similarly 
 situated in the triangles with respect to 
 the equal angles ; that is, both must be 
 either between the given angles, or opposite 
 to equal angles, otherwise the triangles 
 will not be equal. 
 
 PROPOSITION XXVII. 
 
 Theorem. — If a straight line falling upon 
 two other straight lines makes the alter- 
 nate angles equal to one another, these 
 two straight lines are parallel. 
 
 Let the straight line E F, which falls 
 upon the two straight lines A B, CD 
 makes the alternate angles A E F, EFD 
 equal to one another ; A B is parallel to 
 CD. 
 
 L 
 
146 
 
 THE ARTISAN. 
 
 Fer, if it be not parallel, AB and CD 
 being produced shall meet either towards 
 B, D, or towards A, C; let them be pro- 
 duced and meet towards B, D in the point 
 G ; therefore G E F is a triangle, and its 
 exterior angle A E F is greater than the 
 interior and opposite angle E F G ; but it 
 is also equal to it, which is impossible • 
 therefore, AB and CD being produced 
 do not meet towards B, D. In like man- 
 ner it may be demonstrated, that they do 
 not meet towards A, C ; but those straight 
 lines which meet neither way, though pro- 
 duced ever so far, are parallel to one ano- 
 ther. AB therefore is parallel to CD. 
 Wherefore, if a straight line, &c. Q. E. D. 
 
 PROPOSITION XXVIII. 
 
 Theorem.—// a straight line falling upon 
 two other straight lines makes the exterior 
 angle equal to the interior and opposite 
 upon the same side of the line; or makes 
 the interior angles upon the same side to- 
 gether equal to two right angles; the two 
 straight lines are parallel to one another. 
 
 Let the straight line E F, which falls 
 upon the two straight lines AB, CD 
 make the exterior angle EGB equal to’ 
 the interior and opposite angle G HD upon 
 the same side; or make the interior an- 
 gles on the same side B GH, G HD toge- 
 ther equal to two right angles; A B is 
 parallel to C D. 
 
 E 
 
 equal to the angle G H D ; and they are 
 the alternate angles ; therefore A B is pa- 
 rallel to C D. Again, because the angles 
 B G H, G H D are equal to two right an- 
 gles; and, that AGH, B GH, are also 
 equal to two right angles; the angles 
 AGH, B G H are equal to the angles 
 B G H, G H D : take away the common 
 angle B G H ; therefore the remaining 
 angle AGH is equal to the remaining 
 angle G H D ; and they are alternate an- 
 gles; therefore AB is parallel to CD. 
 Wherefore, if a straight line, &c. Q. E. D. 
 
 PROPOSITION XXIX. 
 
 Theorem. — If a straight line fall upon two 
 parallel straight lines , it makes the alter- 
 nate angles equal to one another ; and the 
 exterior angle equal to the interior and 
 opposite upon the same side ; and likewise 
 the two interior angles upon the same side 
 together equal tq two right angles *. 
 
 Let the straight line EF fall upon the 
 parallel straight lines A B, C D; the alter- 
 nate angles A G H, G H D are equal to one 
 another ; and the exterior angle E G B is 
 equal to the interior and opposite, upon 
 the same side, GHD; and the two inte- 
 rior angles BGH, GHD upon the same 
 side are together, equal to two right angles. 
 
 For if A G H be not equal to G H D, one 
 of them must be greater than the other, let 
 A G H be the greater, and because it is 
 greater than the angle G H D, add B G H 
 to each of them ; therefore the angles AG H 
 and BGH are greater than the angles 
 BGH and GHD ; but the angles AGH 
 and BGH are equal to two right angles ; 
 therefore the angles BGH and GHD 
 are less than two right angles, consequently 
 if A B and C D were produced they 
 would meet, but they are parallel by the 
 hypothesis, and therefore would never 
 meet ; consequently the angle AGH is 
 not unequal to the angle GHD, that is, it 
 
 These three properties of parallel lines afford 
 the means of determining whether lines are pa- 
 rallel Or not. 
 
THE ARTISAN. 
 
 147 
 
 is equal to it. Now, the angle EGB is 
 equal to A G H ; and A G H is proved to 
 be equal to GHD; therefore E G B is 
 likewise equal to GHD; add to each of 
 these the angle B G H ; therefore the angles 
 EGB, B G H are equal to the angles 
 BGH, GHD; but EGB, BGH are 
 equal to two right angles ; therefore also 
 BGH, GHD are equal to two right 
 angles. Wherefore, if a straight line, &c. 
 Q. E. D. 
 
 This proposition is the converse of the 
 27th and 28th. It has given Geometers, 
 both ancient and modern, more trouble 
 than all the rest of Euclid’s propositions 
 put together ; in order to demonstrate it 
 the 12th axiom was assumed ; but, that 
 axiom is by no means self evident (see 
 page 17, col. 2) ; and therefore the 29th 
 proposition, which depends upon it, cannot 
 be said to be proved, unless the axiom 
 itself be previously proved, which cannot 
 easily be done, but by introducing another 
 axiom scarcely less exceptionable than 
 that which was to be demonstrated. This 
 axiom is the following. If two straight 
 lines be drawn through the same point , 
 they are not both parallel to the same 
 straight line. If this axiom be admitted, 
 the 29th proposition may be demonstrated 
 without the aid of the 12th axiom; but 
 this we shall omit here. 
 
 PROPOSITION XXX. 
 
 Theorem. — Straig ht lines which are paral- 
 lel to the same straight line , are parallel 
 
 to one another. 
 
 Let A B, C D be each of them parallel to 
 EF; A B is also parallel to C D. 
 
 Let the straight line G H K cut A B, 
 E F, C D ; and because GHR cuts the 
 parallel straight lines A B, E F, the angle 
 A G H is equal to the angle G H F. Again, 
 because the straight line GK cuts the 
 parallel straight lines E F, C D, the angle 
 G H F is equal to the angle GRD; and it 
 was shown that the angle A G K is equal 
 to the angle G H F ; therefore also A G K 
 l 2 
 
 is equal toGKD; and they are alternate 
 angles ; therefore A B is parallel to C D. 
 Wherefore straight lines, &c. Q. E. D. 
 
 PROPOSITION XXXI. 
 Problem. — To draiv a straight line through 
 a given point parallel to a given straight 
 line. 
 
 Let A be the given point, and B C the 
 given straight line ; it is required to draw 
 a straight line through the point A, paral- 
 lel to the straight line B C. 
 
 In B C take any point D, and join AD; 
 and at the point A, in the straight line A D, 
 make the angle DAE equal to the angle 
 ADC; and produce the straight line E A 
 to F. 
 
 Because the straight line AD, which 
 meets the two straight lines BC, EF, 
 makes the alternate angles E A D, ADC 
 equal to one another, EF is parallel to 
 B C. Therefore the straight line E A F is 
 drawn through the given point A parallel 
 to the given straight line B C. Which was 
 to be done. 
 
 PROPOSITION XXXII. 
 
 Theorem. — If a side of any triangle be pro- 
 duced, the exterior angle is equal to the 
 two interior and opposite angles ; and the 
 three interior angies of every triangle are 
 equal to two right angles. 
 
 Let A B C be a triangle, and let one of 
 its sides B C be produced to D ; the ex- 
 terior angle A C D is equal to the two 
 interior and opposite angles CAB, ABC; 
 and the three interior angles of the tri* 
 angle ; viz. A B C, B C A, C A B, are toge- 
 ther equal to two right angles. 
 
 Through the point C draw C E parallel 
 to the straight line A B ; and because A B 
 is parallel to C E and A C meets them, the 
 alternate angles B AC ACE are equal. 
 
148 
 
 THE ARTISAN. 
 
 Again, because A B is parallel to C E, 
 and BD falls upon them, the exterior angle 
 E C D is equal to the interior and opposite 
 angle ABC; but the angle ACE was 
 shown to be equal to the angle B A C ; 
 therefore the whole exterior angle ACD 
 is equal to the two interior and opposite 
 angles C A B, A B C ; to these angles add 
 the angle ABC, and the angles ACD, 
 A C B are equal to the three angles C B A, 
 BAC, ACB; but the angles ACD, AC B 
 are equal to two right angles; therefore 
 also the angles CBA, BAC, ACB are 
 equal to two right angles. Wherefore, if 
 a side of a triangle, &c. Q. E. D. 
 
 MECHANICS 
 
 OF THE WEDGE. 
 
 The wedge is a triangular prism, made 
 of wood or metal. It is usual to make it 
 • isosceles , that is, with its opposite sides, or 
 faces, equal. It is, however, sometimes 
 made rectangular, with one of the planes 
 or faces, containing the right angle, placed 
 horizontally. In this case the wedge co- 
 incides with the inclined plane. When it 
 , is isosceles it may be considered as two 
 equally inclined planes, D E F and CE F, 
 joined together at their bases e EF : 
 
 then, DC is the whole thickness of the 
 wedge at its back AB CD, where the 
 power is applied : E F is the depth or 
 heighth of the wedge : D F the length of 
 one of its sides, equal to C F the length of 
 the other side ; and O F is its sharp edge, 
 which is entered into the wood intended to 
 be split by the force of a hammer or mallet 
 striking perpendicularly on its back. Thus 
 A B is a wedge 
 
 driven into the cleft C DE of the wood F 
 
 When the wood does not cleave at any 
 distance before the wedge, there will be 
 an equilibrium between the power impel- 
 ling the wedge downward, and the resist- 
 ance of the wood acting against the two 
 sides of the wedge ; if the power be to the 
 resistance, as half the thickness of the 
 wedge at its back is to the length of* either 
 of its sides ; that is, as A a to A b, or B a 
 to B b. And if the power be increased, 
 so as to overcome the friction of the wedge 
 and the resistance arising from the cohe- 
 sion of the wood, the wedge will be driven 
 in, and the wood split asunder. 
 
 But, when the wood cleaves at any dis- 
 tance before the wedge (as it generally 
 does) the power impelling the wedge will 
 not be to the resistance of the wood, as half 
 the thickness of the wedge is to the length 
 of one of its sides ; but as half its thick- 
 ness is to the length of either side of the 
 cleft , estimated from the top or acting part 
 of the wedge. For, if we suppose the 
 wedge to be lengthened down from b to the 
 bottom of the cleft at E, the same propor- 
 tion will hold; namely, that the power 
 will be to the resistance, as half the thick- 
 ness of the wedge is to the length of either 
 of its sides : or, which amounts to the 
 same thing, as the whole thickness of the 
 wedge is to the length of both its sides. 
 
 If one of the resisting bodies only is 
 moveable, the power will be to the resist- 
 ance as the base of the wedge to its length. 
 
 In order to prove what is here advanced 
 concerning the wedge, let us suppose the 
 wedge to be divided lengthwise into two 
 equal parts; and then it will become two 
 equally inclined planes ; one of which, as 
 a be, 
 
 may be made use of as a half wedge for 
 separating the moulding e d from the wains- 
 cot A B. It is evident, that when this 
 half wedge has been driven its whole 
 length ac between the wainscot and mould- 
 ing, its side a c will be at e d ; and the 
 moulding will be separated to f g from the 
 wainscot. Now, from what has been 
 already proved of the inclined plane, it 
 
THE ARTISAN. 
 
 149 
 
 appears, that to have an equilibrium be- 
 tween the power impelling the half wedge, 
 and the resistance of the moulding, the 
 former must be to the latter, as a b to a c ; 
 that is, as the thickness of the back which 
 receives the stroke is to the length of the 
 side against which the moulding acts. 
 Therefore, since the power upon the half 
 wedge is to the resistance against its side, 
 as the half back a b is to the whole side 
 ac, it is plain, that the power upon the 
 Avhole wedge, must be to the resistance 
 against both its sides, as the thickness of 
 the whole back is to the length of both the 
 sides ; or as the thickness of the whole 
 back to the length of both sides of the cleft, 
 when the wood splits at any distance before 
 the wedge. For, when the wedge is driven 
 quite into the wood, and the wood splits at 
 ever so small a distance before its edge, the 
 top of the wedge then becomes the acting 
 part, because the wood does not touch it 
 any where else. And since the bottom of 
 the cleft must be considered as that part 
 where the whole cohesion or resistance is 
 accumulated, it is plain, from the nature 
 of the lever, that the farther the power 
 acts from the resistance, the greater is the 
 advantage*. 
 
 If the wedge be of a scalene form, that is, 
 all its sides unequal, and have forces 
 acting perpendicularly on its sides which 
 keep each other in equilibrio, they are pro- 
 portional to those sides. 
 
 Thus let G I, HI, and D I, the direc- 
 tion of the forces, meet in the point I ; 
 
 c 
 
 then since the forces keep each other at 
 rest they are proportional to the three sides 
 of a triangle, which are respectively per- 
 pendicular to those directions ; that is, to 
 the three sides of the wedge. 
 
 If the lines of direction, passing through 
 the points of impact, do not meet in a point, 
 the w r edge will have a rotatory motion 
 communicated to it; and this motion will 
 be round the centre of gravity of the wedge. 
 
 When the directions of the forces are not 
 perpendicular to the sides of the wedge, 
 the effective parts of the forces must be de- 
 termined by the resolution of forces, (see 
 
 * There has been a considerable difference among 
 writers on mechanics respecting the rules for deter- 
 mining the power of the wedge. But this has arisen 
 from not attending sufficiently to the direction of the 
 resistance, and to another circumstance, namely, 
 whether both the resisting bodies are moveable, or 
 one of them only moveable. 
 
 page 24,) and there will be an equilibrium 
 when those parts are to each other as the 
 sides of the wedge. 
 
 A wedge may have the form of a pyra- 
 mid , as well as of a prism ; but if the 
 wedge be of a pyramidal form, the forces 
 that act upon it must be resolved according 
 to three axes, by which three equations 
 will be obtained: it is therefore more dif- 
 ficult to determine the effect of the forces 
 on this form of .the wedge, than when it is 
 in the form of a prism. 
 
 In practice it is the custom to use very 
 small wedges at first, with small angles, 
 and when they are sunk in the body to be 
 cleft, larger wedges with larger angles are 
 successively applied till the purpose is ac- 
 complished. 
 
 Piercing instruments are all reducible to 
 wedges of this kind, nails, bayonets, stakes, 
 piles, &c. The resistance in some of these 
 increases with the surface to w hich it is 
 applied. 
 
 The common wedge is generally em- 
 ployed for cleaving, and otherwise over- 
 coming the force of cohesion in bodies: it 
 may sometimes be used with advantage for 
 raising great weights to a small height. 
 
 All cutting instruments may be referred 
 to it, knives, chissels, scissars, the teeth of 
 animals, &c. A saw is a series of wedges, 
 on which the motion impressed is oblique 
 to the resistance. A wimble is a wedge to 
 which a circular motion is given. 
 
 The power applied to the wedge, when 
 great resistance is to be overcome, is usu- 
 ally percussion; and almost the only in- 
 stance in which it is used for the purpose 
 of equilibrium, is in the construction of 
 arches, built of truncated wedges. But as 
 the consideration of this equilibrium would 
 lead to too long a digression in this place, 
 we shall consider the subject in another 
 part of this work. 
 
 OF THE SCREW. 
 
 The screw is a spiral groove or thread, 
 winding round a cylinder, so as to cut all 
 the lines drawn on its surface parallel to 
 its axis, at the same angle. If the spiral 
 is formed on the outside of the cylinder, it 
 is called the exterior or male screw ; and 
 if formed in the inside, it is called the 
 interior or female screw . 
 
 In the former the spiral is raised on the 
 surface of a cylinder; and in the latter it is 
 cut out of the inside of a hollow cylinder.* 
 In considering the screw as a mechani- 
 cal power, we must regard the male screw 
 as fixed, a^d carrying or moving a female 
 screw, which constitutes the weight or re- 
 sistance when it acts by its own gravity, or 
 carries a load. 
 
 * One turn of the spiral round the cylinder, is 
 usually called a thread of the screw. 
 
150 
 
 THE ARTISAN. 
 
 A lever is generally inserted in a hole to the end of the lever, as represented by 
 in the male screw, and the power is applied the following figure.* 
 
 The action of a screw depends on the 
 same principles as that of an inclined 
 plane ; for by rolling a thin and flexible 
 wedge, for instance, a triangular piece of 
 card round a cylinder, a screw will be 
 formed. 
 
 We may consider the force tending to 
 turn the screw round its axis, as applied 
 horizontally to the base or head of the 
 wedge. The circumference of the cylin- 
 der will represent the horizontal length 
 of the wedge, and the distance between 
 the threads will be its height,! conse- 
 quently the forces required for the equi- 
 librium, are to each other as the height of 
 one thread to the circumference of the 
 screw. But besides these forces, it is ne- 
 cessary that some obstacle be present, to 
 prevent the body on which the screw acts 
 from following it in its motion round its 
 axis, otherwise there can be no equili- 
 brium. Thus, the thin wedge A B 
 
 of which the height is one tenth of the 
 length, being rolled round the cylinder C, 
 makes the screw D, by means of which the 
 weight Eis capable of supporting a weight 
 ten times as great as F. 
 
 If the power applied to the screw, by- 
 means of a lever, be parallel to the base, 
 an equilibrium is produced, when the 
 power is to the resistance, as the distance 
 between two threads of the screw, to the 
 circumference of the circle described by 
 the point of the lever to which the power 
 is applied. 
 
 Thus, suppose the distance between the 
 threads of a screw to be half an inch, and 
 the length of the lever employed to turn it, 
 to be 24 inches ; the circumference of the 
 circle described by this lever will be 151 
 inches, or 302 half inches ; and therefore 
 a force or weight equal to 1 pound acting 
 at the end of the lever, will balance 302 
 pounds, acting against the screw. Hence 
 it appears, that the longer the lever is, 
 and the nearer the threads are to each 
 other, the greater is the power of the 
 screw. 
 
 When a convex and concave, or a male 
 and female screw are fitted to each other, 
 they are sometimes called a screw and 
 nut, as represented by the following 
 figure. 
 
 * As the cylinder is turned by a lever, the screw 
 js really a compound machine. 
 
 t The wedge here alluded to is one in the form of 
 an inclined plane. 
 
THE ARTISAN. 
 
 151 
 
 The nut acts on the screw with the same 
 mechanical power as a single point would 
 do, since it only divides the pressure 
 amongst the different parts of the spiral. 
 
 Sometimes the threads of a screw are 
 made to act on the teeth of a wheel, by 
 which means it has its energy multiplied 
 by their number. 
 
 The following is a representation of this 
 application of the screw, which is usually 
 termed the Endless screw. 
 
 Here A B is the screw which acts on 
 the teeth of the wheel C D, where a tole- 
 rably quick motion of the screw is capable 
 of producing very powerful effects. 
 
 The screw is of great use for compress- 
 ing bodies. A kind of percussion is some- 
 times added to it, as in the apparatus for 
 coining. The great attrition or friction 
 which takes place in the screw, is useful 
 by retaining it in the state to which it has 
 been once brought, and continuing the 
 effect after the power is removed. The 
 screw is also applied, with much advan- 
 tage, to raise great weights to a small 
 height, and support them in that situa- 
 tion. 
 
 The screw is also employed in the divi- 
 sion of mathematical instruments, and the 
 reading off from them. The contrivance 
 known by the name of the micrometer 
 screw, is used for measuring angles with 
 great exaptness. In Ramsden’s Dividing 
 Instrument, the screw is applied for the 
 same purpose ; but we shall treat of these 
 subjects more fully in another part of this 
 work. 
 
 HYBEMLICS. 
 
 MACHINES FOR RAISING WATER. 
 
 Having already treated of the common 
 sucking pump under the head of Pneu- 
 matics, (see page 133,) we shall here give 
 a description of several ingenious machines 
 used for raising water, which are not so 
 immediately dependent on the action of 
 the air for their successful operation. 
 
 Among these is the Screw of Archi- 
 medes, ,* This machine consists of a tube, 
 or pipe wound round a cylinder A B in a 
 spiral form, or similar to the threads of a 
 common screw. 
 
 The cylinder is inclined to the horizon 
 at an angle of about 45 degrees, and the 
 orifice of the tube B is immersed in water, 
 and w hen the screw is turned by the handle, 
 the water rises up the spiral and is dis- 
 charged at A. 
 
 This machine is capable, with very little 
 strength, of raising a considerable quantity 
 of water; it has, therefore, been found 
 very useful for raising large quantities of 
 water to small heights. 
 
 If the water is to be raised to a consi- 
 derable height, one screw will not be suffi- 
 cient ; but this may be effected by a suc- 
 cession of screws : for when the water has 
 been raised by one screw and discharged 
 into an intermediate vessel, it may again 
 be raised to a second vessel by means of 
 another screw ; and so on, till it has been 
 raised to the height required. 
 
 This instrument is sometimes made by 
 fixing a spiral partition round a cylinder, 
 and covering it with an external coating,, 
 either of wood or metal ; it should be so 
 placed with respect to the surface of the 
 water as to fill in each turn one half of a 
 convolution ; for when the orifice remains 
 always immersed, its effect is much dimi- 
 nished. 
 
 The spiral is seldom single, but usually 
 
 * In Germany this machine is called the u'ator 
 
 snail . 
 
152 
 
 TEE ARTISAN. 
 
 consists of three or four separate coils, 
 forming a screw which rises slowly round 
 the cylinder. The operation of this ma- 
 chine may be understood by ^ap^l^ a 
 cord spirally round a bottle containing a 
 little wafer, and inclining the bottle at a 
 less angle to the horizon than the incli- 
 nation of the cord to the axis.* It will 
 then be seen, that if waterfalls into the 
 lowest part of the spiral when it is at rest, 
 the motion of the bottle about its axis will 
 remove, as it were, the spiral out from 
 below the water, which must therefore 
 occupy the part of the spiral immediately 
 above it ; and so on, till the water reaches 
 the top of it. 
 
 A machine of a similar nature is called 
 by the Germans a ivater screw. It consists 
 of a cylinder w'ith its spiral projections 
 detached from the external cylinder or 
 coating, within which it revolves, as re- 
 presented by the following figure. 
 
 This machine might not improperly be 
 considered as a pump, but its operation is 
 precisely similar to that of the screw of 
 Archimides. It is evident, that some loss 
 must here be occasioned by the want of 
 perfect contact between the screw and its 
 cover; in general, at least one third of the 
 water runs back, and the machine cannot 
 be placed at a greater elevation than S0° ; 
 it is also very easily clogged by accidental 
 impurities of the water: yet it has been 
 found to raise more water than the screw 
 of Archimides, when the lower ends of 
 both are immersed to a considerable depth ; 
 so, that if the height of the surface of the 
 water to be raised were liable to any great 
 variations, the water screw might be pre- 
 ferable to the screw of Archimides. 
 
 These machines are particularly useful 
 when the water to be raised is not pure, 
 but mixed with gravel, weeds, or sand, 
 which could not be raised by ordinary 
 pumps. 
 
 The spiral pump is a very ingenious ma- 
 chine for raising water. It was invented 
 about the year 1746, by Andrew Wirtz, a 
 pewterer, at Zurich, hence it is sometimes 
 
 t The line, real or imaginury, round which any 
 body revolves, is called its axis. 
 
 called the Zurich machine. It consists Of 
 a spiral pipe, either coiled round in one 
 plane, or arranged round the circumference 
 of a cone or cylinder ; as represented in 
 the annexed figure. 
 
 One end of it is connected by a water- 
 tight joint to an ascending pipe, in which 
 the water is to be raised, and the other 
 end receives, during each revolution, 
 nearly equal quantities of air and water. 
 This end of the pipe is furnished with a 
 scoop, or spoon, containing as much water 
 as will fill half a coil, which enters the 
 pipe a little before the spoon has arrived 
 at its highest situation, the other half re- 
 maining full of air, which communicates 
 the pressure of the column of water to the 
 preceding portion; and in this manner the 
 effect of nearly all the water in the wheel 
 is united, and becomes equivalent to that 
 -of the column of water, or of water mixed 
 with air, in the ascending pipe. The air 
 nearest the joint is compressed into a space 
 much smaller than that which it occupied 
 at its entrance, so that where the height 
 is considerable, it becomes advisable to 
 admit a larger portion of air than would 
 naturally fill half the coil, and this lessens 
 the quantity of water raised, but it lessens 
 also the force required to turn the machine. 
 The joint ought to be conical, in order, 
 that it may be tightened when it becomes 
 loose, and the pressure ought to be removed 
 from it as much as possible. The loss of 
 power, supposing the machine well con- 
 structed, arises only from the friction of 
 the water on the pipe, and the friction of 
 the wheel on its axis ; and where a large 
 quantity of water is to be raised to a mo- 
 derate height, both of these resistances 
 may be rendered inconsiderable. But when 
 the height is very great, the length of the 
 spiral must be much increased, so that the 
 weight of the pipe becomes extremely cum- 
 bersome, and causes a great friction on the 
 axis, as well as a strain on the machinery : 
 thus, for a height of 40 feet, Dr. Young 
 found, that the wheel required above 100 
 feet of a pipe which was three quarters of 
 an inch in diameter ; and more than one 
 half of the pipe being always full of water, 
 it will be necessary to overcome the friction 
 
THE ARTISAN. 
 
 153 
 
 of about 80 feet of such a pipe, which raised by buckets nearly similar to those 
 will require 24 times as much excess of which are calculated for receiving it in its 
 pressure to produce a given velocity, as if descent; sometimes the buckets are hung 
 there were no friction. The centrifugal on pins, so as to remain full during the 
 force of the water in the wheel would also whole ascent ; but these wheels are liable 
 materially impede its ascent if the velocity to be frequently out of repair. We there- 
 were considerable, since it would be al- fore deem it unnecessary to give a figure 
 ways possible to turn it so rapidly as to of it. 
 
 throw the whole water back into the spoon. There is another singular machine some- 
 Sometimes a breast-wheel, which is the times used for raising water, called the 
 reverse of an undershot wheel, is employed rope pump . It consists of tw r o or three 
 as a throwing w heel, either in a vertical or hair ropes passing over a three-grooved 
 in an inclined position. The following pulley z, projecting over the well ; they 
 figure represents one of these machines. also pass under a pulley in the water, and 
 
 are kept tight by a weight e. 
 
 Wheels of this kind are frequently used 
 for draining fens, and are turned by wind- 
 mills ; the float-boards are not placed in 
 the direction which would be best for an 
 undershot wheel, but on the same prin- 
 ciple, so as to be perpendicular to the sur- 
 face when they rise out of it, in order that 
 the water may the more easily flow off 
 from them. 
 
 There is another machine for raising 
 water, which consists of a series of earthen 
 pitchers, connected by ropes, and turned 
 by trundles or pinions, over which they 
 pass, which has long been used in Spain, 
 under the name of Auoria, or Noria. In 
 this country, buckets of wood are some- 
 times employed in a similar manner, as in 
 the following figure. 
 
 A bucket wheel is the reverse of an over- 
 shot water-wheel, and the water may be 
 
 The upper pulley is put into swift motion 
 by the wheel A ; and the ascending ropes 
 draw up a certain quantity of water by 
 their friction (which is prevented from 
 being scattered by its own cohesion,) and 
 is discharged with great force into the box 
 z. The friction of the ropes is aided by 
 the pressure of the atmosphere upon the 
 water which adheres to the ropes. 
 
 By a machine of this kind a man ^an 
 raise eight or nine gallons of water per 
 minute, out of a well 100 feet deep. 
 
154 
 
 THE ARTISAN. 
 
 fBuscellattfous Subjects. 
 
 MEMOIR OF M. AGNESI. 
 
 Maria Cajetana Agnesi, an Italian lady 
 of great learning, was born at Milan, on 
 the 16th March, 1718. Her inclinations 
 from her earliest youth led her to the study 
 of science, and at an age when young per- 
 sons of her sex attend only to frivolous 
 pursuits, she had made such astonishing 
 progress in mathematics, that when in 1750 
 her father, professor in the university at 
 Bologna, was unable to continue his lec- 
 tures from infirm health, she obtained 
 permission from the pope Benedict XIV. 
 to fill his chair. Before this, at the early 
 age of nineteen, she had supported one 
 hundred and ninety-one theses, which were 
 published in 1738, under the title u Propo- 
 sitions Philosophicas.” She was also 
 mistress of Latin, Greek, Hebrew, French, 
 German, and Spanish. At length she gave 
 up her studies, and went into the monas- 
 tery of the Blue Nuns, at Milan, where 
 she died on the 9th of January, 1799. In 
 1740 she published a discourse tending to 
 prove, “ that the study of the liberal arts 
 is notincompatible with the understandings 
 of women.” This she had written when 
 scarcely nine years old. Her “ Institu- 
 zioniAnalitche,”in 1748, in 2 vols. 4to, were 
 translated in part by Antelmy, with the 
 notes of M. Bossut, under the title of 
 “ Traites Elementaires du Calcul differen- 
 tiel et du Calcul integral,” in 1775, in one 
 vol. 8vo. and into English by that eminent 
 judge of mathematical learning, the late 
 Rev. John Colson, M.A. F.R.S. and Lu- 
 casion Professor of Mathematics in the 
 university of Cambridge. This learned 
 and ingenious man, who had translated 
 Sir Isaac Newton’s Fluxions, with a com- 
 ment, in 1736, and was well acquainted 
 with what appeared on the same subject, 
 in the course of fourteen years afterward, 
 in the writings of Emerson, Maclaurin, 
 and Simpson, found, after all, the analy- 
 tical institutions of Agnesi to be so excel- 
 lent, that he learned the Italian language, 
 at an advanced age, for the sole purpose 
 of translating that work into English, and 
 at his death left the manuscript nearly 
 prepared for the press. In this state it 
 remained for some years, until the late 
 Baron Maseres, with his usual liberal and 
 active spirit, resolved to defray the whole 
 expense of printing a handsome edition, in 
 2 vols. 4to., which was published in 1801, 
 and was superintended in the press by the 
 Rev. John Hellins, B. D. F. R. S. vicar of 
 Potter’s-pury, in Northamptonshire*. Her 
 eloge was pronounced by Frisi, and trans- 
 lated into French by Boulard. 
 
 * This book is considered by some of our ablest 
 mathematicians as the best work on the application 
 of Algebra to Geometry in the English language. 
 
 ARCHITECTURE. 
 
 Without entering deeply into the subject 
 of Architecture, we propose to devote a 
 portion of our succeeding pages to the ex- 
 planation of the general and fundamental 
 principles upon which this highly interest- 
 ing and beautiful science depends. 
 
 The science of Architecture has at all 
 times, and in all civilized countries, been 
 considered not only a pleasing but a highly 
 useful branch of knowledge. 
 
 The great utility of this science, and 
 the elegant accomplishments connected 
 with its study, have almost rendered a 
 knowledge of its rules and principles ne- 
 cessary to complete a liberal education. 
 But it is not our intention to bestow enco- 
 miums on the science, nor to give any thing 
 like a detailed history of it, but to present 
 our readers with a plain and condensed 
 account of what may be termed its ele- 
 mentary principles. 
 
 Architecture is usually divided, with 
 respect to its objects, into three branches, 
 civil, military, and naval. 
 
 Civil Architecture, called also absolutely, 
 and by way of eminence, Architecture, is 
 the art of contriving and executing com- 
 modious buildings for the uses of civil life ; 
 as houses, temples, theatres, halls, bridges, 
 colleges, porticos, &c. 
 
 Architecture is scarcely inferior to any 
 of the arts in point of antiquity. — Nature 
 and necessity taught the first inhabitants of 
 the earth to build themselves huts, tents, 
 and cottages; from which, in course of 
 time, they gradually advanced to more re- 
 gular and stately habitations, with variety 
 of ornaments, proportions, &c. To what 
 a pitch of magnificence the Tyrians and 
 Egyptians carried Architecture, before it 
 came to the Greeks, may be learned from 
 Isaiah xxiii. 8. and from Vitruvius’s ac- 
 count of the Egyptian Oeci; their pyra- 
 mids, obelisks, &c. 
 
 Yet, in the common account. Architec- 
 ture should be almost wholly Grecian 
 original: three of the regular orders or 
 manners of building are denominated from 
 them; viz. Corinthian, Ionic, and Doric: 
 and there is scarcely a single member, or 
 moulding, but comes to us with a Greek 
 name. 
 
 Be this as it may, it is certain the Ro- 
 mans, from whom we derive it, borrowed 
 what they had entirely from the Greeks ; 
 nor do they seem, till then, to have had 
 any other notion of the grandeur and 
 beauty of buildings, beside what arises 
 from their magnitude, strength, &c. — Thus 
 far they were unacquainted with any other 
 beside the Tuscan. 
 
 Under Augustus, Architecture arrived at 
 its glory : Tiberius neglected it, as well as 
 
THE ARTISAN. 
 
 155 
 
 the other polite arts. Nero, amongst aheap 
 of horrible vices, still retained an uncommon 
 passion for building ; but luxury and dis- 
 soluteness had a greater share in it than 
 true magnificence. — Apollodorus excelled 
 in Architecture , under the emperor Trajan, 
 by which he merited the favour of that 
 prince ; and it was he who raised the fa- 
 mous Trajan column, subsisting to this 
 day. 
 
 After this, Architecture began to dwindle 
 again; and though the care and magni- 
 ficence of Alexander Severus supported it 
 for some time, yet it fell with the western 
 empire, and sunk into a corruption, from 
 whence it was not recovered for the space 
 of twelve centuries. 
 
 The ravages of the Visigoths, in the 
 fifth century, destroyed all the most beau- 
 tiful monuments of antiquity ; and Archi- 
 tecture thenceforward became so coarse 
 and artless, that their professed architects 
 understood nothing at all of just designing, 
 wherein its whole beauty consists: and 
 hence a new manner of building took its 
 rise, which is called the Gothic . 
 
 Charlemagne did his utmost to restore 
 Architecture; and the French applied 
 themselves to it with success, under the 
 encouragement of H. Capet: his son Ro- 
 bert succeeded him in this design ; till by 
 degrees the modern Architecture was run 
 into as great an excess of delicacy, as the 
 Gothic had before done into massiveness. 
 To these may be added, the Arabesk and 
 Morisk or Moorish Architecture , which 
 were much of a piece with the Gothic, 
 only brought ih from the south by the 
 Moors and Saracens, as the former was 
 from the north by the Goths and Vandals. 
 
 The architects of the 13th, 14th, and 
 15th century, who had some knowledge of 
 sculpture, seemed to make perfection con- 
 sist altogether in the delicacy and multi- 
 tude of ornaments, which they bestowed on 
 their buildings with a world of care and 
 solicitude, though frequently without 
 judgment or taste. 
 
 In the two last centuries, the architects 
 of Italy and France were wholly bent upon 
 retrieving the primitive simplicity and 
 beauty of ancient Architecture ; in which 
 they did not fail of success: insomuch, 
 that our churches, palaces, &c. are now 
 wholly built after the antique. Civil Ar- 
 chitecture may be distinguished, with re- 
 gard to the several periods or states of it, 
 into the antique, ancient, gothic, modern, 
 &c. Another division of civil Architecture 
 arises from the different, proportions which 
 the different kinds of buildings rendered ne- 
 cessary, that we might have some suitable 
 for every purpose, according to the bulk, 
 strength, delicacy, richness, or simplicity 
 required. 
 
 Hence arose five orders, all invented by 
 the ancients at different times, and on 
 different occasions; viz. Tuscan, Doric, 
 Ionic, Corinthian, and Composite. The 
 Gothic Architecture may also be mentioned 
 here, for it is perfectly distinct both from 
 the Grecian and Roman style, although 
 derived from the latter. 
 
 [To be continued.'] 
 
 ON THE METHOD OF DETERMIN- 
 ING THE FIGURE OF THE EARTH 
 BY THE PENDULUM. 
 
 The method of determining the figure of 
 the earth by means of the 'pendulum, de- 
 pends upon the variation of gravity at the 
 earth’s surface. 
 
 This subtile and pervading power, tends 
 to communicate to bodies exposed to its 
 influence equal velocities in equal times. 
 One of the modifications of this action is 
 the oscillation of the pendulum, which is 
 of longer or shorter duration, according to 
 the energy of the attractive force, and the 
 square root of the length of the pendulum. 
 If the earth were an exact sphere, desti- 
 tute of the motion of rotation, and possess- 
 ing the same density throughout its whole 
 mass, the force of gravity, by .which bodies 
 at its surface are drawn towards the centre, 
 would be uniform, and invariable ih every 
 latitude. But the elliptical form of the 
 earth destroys this uniformity, and causes 
 the attractive force at the poles to prepon- 
 derate over that at the equator. This in- 
 equality in the force, by which bodies at 
 the surface of the earth retain their posi- 
 tions, is augmented by the diurnal rotation,, 
 which, by its centrifugal tendency, im- 
 presses a greater disposition on bodies to 
 recede from the centre of the earth at the 
 equator than at the poles, where its effects 
 cease to be felt. By the joint operation of 
 these two causes, one of which acts with 
 a force proportional to the square of the 
 sine of the latitude, a sensible difference 
 ought to be observed in the velocity ac- 
 quired by heavy bodies, in falling through 
 the same space, as we advance from the 
 equator to the poles. An important re- 
 lation between the time of the vibration of 
 a pendulum, and that of the descent of a 
 heavy body, according to which the lengths 
 of pendulums, vibrating sychronously, are 
 directly as the force of gravity, enables us 
 to submit this conclusion to the test of expe- 
 riment. Newton long ago demonstrated, 
 that if the earth were perfectly homoge- 
 neous, the same fraction, viz. 3 ^, would 
 express both the compression of the terres- 
 trial ellipsoid, and the increase of gravity 
 from the equator to the poles. This con- 
 clusion, which was deduced from the sup- 
 
156 
 
 THE ARTIS^. 
 
 position of an uniform density, was after- 
 wards modified, with singular address, by 
 Clairaut, who showed, that the two frac- 
 tions expressing the compression, and the 
 increase of gravity, though not exactly 
 equal, must always together amount to T j} 5 . 
 Assuming the compression, therefore, to be 
 equal to the increase of gravity from 
 the equator to the poles, or the indication 
 of that increase, as given by the length of 
 the pendulum, should be ^ — 3 ^, or ^ 
 nearly. The correctness of this conclu- 
 
 sion, if not completely established, is, at 
 least, to a certain extent, confirmed, by the 
 experiments which have been made with 
 the pendulum in different latitudes. La 
 Place having selected fifteen of the best of 
 these observations, and applied to them 
 the necessary corrections, on account of 
 the resistance of the air, difference of tem- 
 perature, and elevation above the level of 
 the sea, deduced the following results, in 
 which the length of the pendulum at Paris 
 is considered to be unity. 
 
 Latitude. 
 
 Leugth of 
 the Seconds 
 Pendulum. 
 
 Names of the 
 Observers. 
 
 Places of 
 Observation. 
 
 Equator 
 
 *99669 
 
 Bouguer 
 
 Peru 
 
 9 U 
 
 32' 
 
 56' 
 
 •99689 
 
 Ditto 
 
 Portobello 
 
 II 
 
 55 
 
 30 
 
 *99710 
 
 Gentil 
 
 Pondicherry 
 
 18 
 
 0 
 
 0 
 
 •99745 
 
 Campbell 
 
 Jamaica 
 
 18 
 
 27 
 
 0 
 
 •99728 
 
 Bouguer 
 
 Petit Grave 
 
 34 
 
 7 
 
 15 
 
 •99877 
 
 LaCaille 
 
 Cape G. H. 
 
 43 
 
 35 
 
 45 
 
 •99950 
 
 Darquier 
 
 Toulouse 
 
 48 
 
 12 
 
 48 
 
 •99077 
 
 Liesganig 
 
 Vienna 
 
 48 
 
 50 
 
 0 
 
 1-00000 
 
 Bouguer 
 
 Paris 
 
 50 
 
 58 
 
 0 
 
 1 00006 
 
 Zach 
 
 Gotha 
 
 51 
 
 30 
 
 0 
 
 1*00018 
 
 
 London 
 
 58 
 
 14 
 
 53 
 
 1-00074 
 
 Mallet 
 
 Petersburgh 
 
 59 
 
 56 
 
 24 
 
 1*00101 
 
 Ditto 
 
 Ponoi 
 
 66 
 
 48 
 
 0 
 
 100137 
 
 Grischow 
 
 Arensberg 
 
 67 
 
 5 
 
 0 
 
 1-00148 
 
 Mapertius 
 
 Tornea 
 
 The above results indicate obviously an 
 increase of the force of gravity from the 
 equator towards thepoles. La Place has 
 shewn that, in whatever way they are 
 combined, it is impossible to avoid an 
 error of less than *00018, on the hypothesis 
 of the variation of gravity at the surface 
 of the earth increasing as the squares of 
 the sines of the latitude from the equator 
 to the poles. The expression for the el- 
 lipticity, which connects best the different 
 equations of condition, is a result 
 
 which accords in a very remarkable man- 
 ner with the compression deduced from 
 the measures of the French mathemati- 
 cians in France, and at the equator. 
 
 It may be inferred from these experi- 
 ments with the pendulum, that the com- 
 pression of the earth is greater than is 
 compatible with the supposition of an 
 uniform density. The same anomalies, 
 too, which are discernible in the measure- 
 ment of a degree of the meridian, and 
 which are undoubtedly owing to the dis- 
 similar structure of the globe, may be 
 traced in the results of these experiments. 
 The beautiful property of the pendulum, 
 first discovered by Huggens, that the cen- 
 tre of oscillation and the point of suspen- 
 sion, are interchangeable with each other, 
 
 and which has been so happily applied by 
 Captain Rater, to determine the length of 
 the seconds’ pendulum, (see page 142,) 
 renders this mechanical contrivance in- 
 finitely better fitted to ascertain the true 
 figure of the earth, than the complicated 
 methods which were formerly employed 
 for the same purpose. The facility with 
 which the observations may be made, and 
 the certainty of the results with which they 
 are attended, may be expected to furnish 
 much interesting information, not only with 
 respect to the general form of the globe, 
 but also with respect to its structtire and 
 composition in particular situations. , 
 
 ON ATMOSPHERICAL REFRAC- 
 TION. 
 
 A paper on astronomical refraction by Mr. 
 J. Ivory, F. R. S., was lately read before 
 the Royal Society, in which he states 
 that after a long and laborious investiga- 
 tion of this important problem, he has 
 deduced a new table, which is prefixed 
 to the paper. This table is compared with 
 other tables which have been long in use, 
 and the characters of which are well estab- 
 lished. But Mr. Ivory shows that it is 
 fruitless to expect a near agreement in 
 
THE ARTISAN. 
 
 157 
 
 every single instance, between observa- 
 tion, and any table of refractions whatever; 
 and that there is no test of their accuracy, 
 except the smallness of the mean error, in 
 a series of observations made at different 
 times. 
 
 ON THE CHANGE OF THE PLACE 
 OF THE FIXED STARS. 
 
 It appears from a paper by Mr. Pond, 
 Astronomer Royal, lately read before the 
 Royal Society, that he thinks that his 
 observations lead to the conclusion that 
 some variation, either continued or peri- 
 odical, takes place in the siderial system, 
 which producing but very small deviations 
 in a finite portion of time, has hitherto 
 escaped notice. The nature of this motion 
 appears to be such, that the stars are now 
 mostly found a considerable quantity to the 
 southward of their computed places. With 
 respect to the laws by which these motions 
 are governed, Mr. Pond admits, that his 
 observations are not sufficiently exact to 
 throw any light upon the subject. 
 
 REMARKS ON NITRIFICATION, OR 
 
 THE METHOD OF OBTAINING 
 
 SALTPETRE. 
 
 Of all the numerous arts to which che- 
 mical principles are applicable, that of the 
 saltpetre manufacturer suffers the most, 
 from blindly and absurdly following the 
 mere routine of established practice. It 
 would appear that the greater number of 
 individuals employed in it, have no dis- 
 position to be enlightened on the subject ; 
 neglecting or rejecting the information that 
 has been published by scientific persons, 
 who have turned their attention to the 
 process, they imagine themselves to possess 
 the perfection of the art, in working after 
 the method handed down to them by their 
 predecessors. When they sell their work- 
 shops, they sell their mode of practice, 
 which they dignify with the name of their 
 secret, and thus the errors which prevailed 
 in the infancy of the art are perpetuated, 
 and the consumers of the article find endless 
 faults and variations in its manufacture. 
 These considerations recently induced a 
 celebrated chemist to attempt several ex- 
 periments, with a view to its improvement, 
 both by studying the nature of the earths 
 which contain saltpetre, and that of the 
 substances which are the indispensable 
 agents of the nitrification ; and we take the 
 opportunity of laying before our readers 
 the principal results which this gentleman 
 has communicated. He affirms, 
 
 1. That air and water only co-operate 
 to produce the nitrification, and that these 
 two agents combined, could never produce 
 it without the presence of vegetable and 
 
 animal substances in a state of decompo- 
 sition, which are the fundamental base of it. 
 
 2. That calcareous sand, that is which 
 contains lime, and granite washed by 
 spring water, have sometimes presented 
 traces of it. This effect is attributable to 
 the salts which are always found in the 
 w'ater, as well as to the vegetable or ani- 
 mal substances which it always contains 
 as is shewn by the putrefaction which 
 takes place when it is kept a long time in 
 barrels. 
 
 3. That the siliceous or flinty earths are 
 improper for nitrification, and that the cal- 
 careous are preferable to the argillaceous 
 or clayey ones. 
 
 4. That vegetable and animal particles 
 are the indispensable agents of nitrification ; 
 and that the mixture of earths with vege- 
 table decompositions, is less productive 
 than with animal ones. 
 
 5. That the dung of woolly animals is 
 preferable in manufacturing saltpetre to 
 that of horses, and the latter to that of 
 cows. 
 
 6. That the best method of hastening 
 nitrification, and of obtaining the greatest 
 quantities, is to mix the pure earths with 
 decompositions, partly animal and partly 
 vegetable, in such proportions as expe- 
 rience alone can enable the operator to 
 determine. 
 
 ON A NEW PHENOMENON OF 
 ELECTRO-MAGNETISM. 
 
 BY SIR HUMPHRY DAVY, BART. PRES. R.S. 
 
 This is a contribution of a curious fact 
 to the new and interesting science of elec- 
 tro-magnetism, and it is by such contribu- 
 tions alone, that this infant science can, 
 at present, be expected to make any pro- 
 gress to maturity. Sir H. Davy found, 
 that when two wires were placed in a 
 basin of mercury, perpendicular to the 
 surface, and in the voltaic circuit of a 
 battery with large plates, and the pole of 
 a powerful magnet held either above or 
 below the wires, the mercury immediately 
 began to revolve round the wire as an axis. 
 Masses of mercury, of several inches in 
 diameter, were set in motion, and made to 
 revolve in this manner whenever the pole 
 of the magnet was held near the perpen- 
 dicular of the wire; but when the pole 
 was held above the mercury, between the 
 two wires, the circular motion ceased, and 
 currents took place in the mercury in op- 
 posite directions, one to the right and the 
 other to the left of the magnet. Other 
 circumstances led to the belief that the 
 passage of the electricity produced motions 
 independent of the action of the magnet, 
 and that the appearances were owing to a 
 composition of forces. 
 
158 
 
 THE ARTISAN. 
 
 The form of the last experiment was 
 inverted, by passing two copper wires 
 through two holes, three inches apart, in 
 the bottom of a glass basin ; the basin was 
 then filled with mercury, which stood 
 about the tenth of an inch above the wire. 
 Upon making a communication through 
 this arrangement, with a powerful vol- 
 taic circuit, the mercury was immediately 
 seen in violent agitation ; its surface be- 
 came elevated into a small cone above 
 each of the wires ; waves flowed off in all 
 directions from these cones, and the only 
 point of rest was apparently where they 
 met in the centre of the mercury, between 
 the two wires. On holding the pole of a 
 powerful magnet at a considerable dis- 
 tance above one of the oones, its apex was 
 diminished and its base extended. At a 
 smaller distance, the surface of the mer- 
 cury became plane, and rotation slowly 
 began round the wire. As the magnet ap- 
 proached, the rotation became more rapid ; 
 and when it was about half an inch above 
 the mercury, a great depression of it was 
 observed above the wire, and a vortex 
 which reached almost to the surface of 
 the wire. 
 
 The President thinks, that these phe- 
 nomena are not produced by any changes 
 of temperature, or by common electrical 
 repulsion, and concludes, that they are of 
 a novel kind. 
 
 NAUTICAL EYE-TUBE. 
 
 A trial has been made on board the Clio 
 among the Orkneys, and in the Moray 
 Frith by Mr. Adams, of the performance 
 of his eye-tube to the telescope of a sex- 
 tant for taking altitudes when the horizon 
 is invisible. In making the observations 
 the horizon was always screened from the 
 instrument, and under these circumstances 
 after rejecting a few observations the mean 
 difference of 199 altitudes of the sun, 
 moon, and stars, taken by the eye-tube, 
 from those taken at the same time in the 
 ordinary way by the officers of the Clio, 
 and corrected for dip, amounted to only 
 1' 10". The altitudes taken by tb.e eye- 
 tube are not affected by any dip or de- 
 pression of the horizon. Considerable 
 care and practice is required in the use of 
 the instrument, but that attained, the lati- 
 tude, the time at the ship, and consequently 
 the longitude may all be determined by it 
 when the horizon is invisible. By means 
 of it also either the large or the pocket 
 .sextant maybe employed on shore as a 
 substitute for the theodolite, upon making 
 the necessary allowance for the parallax 
 of the instrument in the name of the index, 
 .error, which on becoming sensible, must 
 vary inversely with the distances of the 
 reflected terrestrial objects. 
 
 ON THE TEMPERATURE AT CON* 
 
 SIDERABLE DEPTHS OF THE 
 CARIBBEAN SEA. 
 
 BY CAPTAIN EDWARI>. SABINE, F.R.S. 
 
 Captain Sabine found the temperature 
 of the water, at a depth of 6000 feet, in 
 latitude 20§ N. and long. 83§ W. near the 
 junction of the Mexican and Caribbean 
 Seas, to be 45°.5, that of the surface 
 being 83°. He infers, that one or two 
 hundred fathoms more line, would have 
 caused the thermometer to descend into 
 water at its maximum of density as de- 
 pends on heat; this inference being on 
 the presumption that the greatest density 
 of salt water occurs, as is the case in fresh 
 water, at several degrees above its freezing 
 point. 
 
 SUPPOSED EFFECT OF MAGNET- 
 ISM ON CRYSTALLIZATION. 
 
 The following is an experiment first 
 made by Professor Maschmann, of Chris- 
 tiana, and confirmed by Professor Han- 
 stein, of the same place. A glass tube is 
 to be bent into a syphon, and placed with 
 the curve downwards, and in the bend is 
 to be placed a small portion of mercury, 
 not sufficient to close the connection be- 
 tween the two legs ; a solution of nitrate 
 of silver is then to be introduced, until it 
 rises in both legs of the tube. The precipi- 
 tation of the mercury in the form of Arbor 
 Diana will then take place, slowly only 
 when the syphon is placed in a plane per- 
 pendicular to the magnetic meridian ; but 
 if it be placed in a plane coinciding with 
 the magnetic meridian, the action is rapid, 
 and the crystallization particularly beauti- 
 ful, taking place principally in that branch 
 of the syphon towards the North. If the 
 syphon be placed in a plane perpendicular 
 to the magnetic meridian, and a strong 
 magnet be brought near it, the precipita- 
 tion will commence in a short time, and be 
 most copious in that leg of the syphon 
 nearest to the south pole of the magnet. 
 
 ACTION OF SULPHUR ON IRON. 
 
 Colonel A. Evans has remarked, “ that 
 although sulphur has so strong an action 
 on heated wrought iron as immediately to 
 form holes in it, yet it does not at all affect 
 grey cast iron. A plate of wrought iron, 
 •63 of an inch in thickness, heated to 
 whiteness, and held against a roll of sul- 
 phur ^ of an inch in diameter, was in four- 
 teen seconds pierced through with a per- 
 fectly cylindrical hole. Another bar about 
 two inches in thickness, was pierced by 
 the same means in fifteen seconds. Good 
 steel was pierced even more rapidly than 
 the iron ; but a piece of grey cast iron y 
 well scaled and heated till nearly in 
 
THE ARTISAN. 
 
 159 
 
 fusion, was not at all affected by the appli- 
 cation of sulphur to its surface, not even a 
 mark being left. A crucible was made of 
 this cast iron, and some iron and sulphur 
 put into it; on applying heat the iron and 
 sulphur soon fused together, but the cast 
 iron underwent no change. 
 
 TABLE OF THE FORCE OF STEAM 
 AT DIFFERENT TEMPERATURES. 
 
 Weight in 
 Avoir, lbs. 
 000 
 •039 
 •103 
 *187 
 •285 
 •428 
 •620 
 •856 
 1-166 
 1555 
 2*047 
 2673 
 
 3- 444 
 
 4- 462 
 5*412 
 7331 
 9*201 
 
 11-662 
 14*662 
 18-006 
 21844 
 26-371 
 31-733 
 37*932 
 45113 
 53-480 
 62-975 
 73-800 
 
 The two first columns of the above table 
 were obtained from actual experiment by 
 Mr. Betancourt, and the third we have de- 
 duced from the second by calculation. It 
 may, however, be necessary to state, that 
 there are considerable differences between 
 different tables of this kind. 
 
 REMARKS ON IRON WIRE SUS- 
 PENSION BRIDGES. 
 
 The following remarks on this subject 
 are from a memoir by M. Dufour, the 
 engineer of the Geneva bridge. 
 
 Speaking of the comparative strength of 
 iron in wires and in bars, M. Dufour says, 
 “ The immense advantage of employing 
 iron in wire rather than in bars, is thus 
 rendered evident : it is more manageable, 
 its strength is double, the strength may be 
 better proportioned by putting the number 
 of wires necessary to the resistance re- 
 quired, and a certainty is obtained of the 
 state of the interior parts of the suspending 
 
 lines, which nothing can give when large 
 bars are used. 
 
 “ It appears at first that the minimum of 
 the force of the wire should be calculated 
 upon, and not the mean; but as each 
 brindle contains many wires, although 
 there may be some of a smaller strength, 
 there will be others that will surpass in 
 strength, and thus the mean should be 
 used in estimating the strength of the 
 whole, although in employing a single 
 wire the minimum only ought to be 
 taken.” 
 
 With respect to the Geneva bridge, 
 M. Dufour says, “ that after a period of 
 four months in which the bridge had been 
 in full use, it had not suffered the slightest 
 alteration in its primitive form. The path 
 has retained the degree of curvature given 
 it at first, and no sensible lengthening of the 
 wires has occurred. The bridge, however, 
 has been well tried ; curiosity has taken 
 great number of persons on it at once, and 
 all the large stones required in the latter 
 part of the work, were taken over it in 
 carriages without the slightest damage. 
 The elasticity of the bridge is also what it 
 was at first, a man walking with a mode- 
 rate step does not at all disturb the steadi- 
 ness of the path ; on walking quickly there 
 are slight vibrations produced ; but the 
 vibrations are such as never to be com- 
 municated from the one bridge to the 
 other, or in any way to affect the masonry. 
 
 The expense of the bridges was 16,350 
 francs.” 
 
 IMPROVEMENT IN LITHOGRA- 
 PHIC PRINTING. 
 
 An extract from a letter of M. Ridolfi to 
 M. Brugnatelli has just appeared in one 
 of the foreign journals, respecting some 
 improvements in lithographic printing. 
 
 It is known, that soap forms an essen- 
 tial part of the ink with which the designs- 
 are traced upon the stone. These designs 
 are at first washed with water, acidulated 
 by nitric acid, before they are put under 
 the press, which takes up the excess of 
 the alkali of the soap, and thus renders it 
 insoluble. The stone is then covered for 
 a short time with a solution of gum arabic, 
 which gives it the property of repelling 
 the printing ink more effectually, whilst 
 the roller transmits to it the traits of which 
 the designs are formed. 
 
 But the acidulated water, at present in 
 use, not only exerts an action on the soap, 
 the carbonates which constitute the litho- 
 graphic stones are attacked ; and by this 
 means it often happens, that the most de- 
 licate parts of the designs are detached 
 from the stone. This particularly happens 
 to compositions, in which there is a consi- 
 derable difference in the stronger lines, or 
 
160 
 
 THE ARTISAN. 
 
 in the intensity of the tints occasioned by 
 the different lengths of time, or the strength 
 of the acids, necessary to produce the de- 
 composition of the lithographic ink of these 
 lines or shades. 
 
 In order to obviate this inconvenience, 
 M. Ridolfi substitutes a weak solution of 
 nitrate of lime in a neutral state, for the 
 acidulated water, which has the property 
 of decomposing the soap, without exer- 
 cising any action on the stone, and there- 
 fore cannot in the smallest degree injure 
 the designs which are traced upon it. 
 
 It is however essential, that lithogra- 
 phic designers keep the stones they use 
 perfectly free from unctuous substances, 
 even from the perspiration of the hand, 
 for without this precaution, the stained 
 places give the impression of deep shades. 
 
 M. Ridolfi has followed this plan, in his 
 lithographic printing, with success, and 
 forms the nitrate which he uses, by pul- 
 verizing broken pieces of the lithographic 
 stones, and throwing them into* the aqua 
 fortis of commerce till the effervescence 
 ceases; he dilutes the liquid with rain 
 water, filters it, and then preserves it for 
 use. 
 
 SOLUTIONS OF QUESTIONS. 
 
 • Quest. 14, answered by G. G. C. 
 
 Let A E be the excess of the diagonal 
 above the side; then draw EF at right 
 angles to A E, and make it equal to A E ; 
 join AF, and produce it till FB be equal 
 to F E ; from the centre B and distance 
 B A, describe the arc A C, which will in- 
 tersect the line A E produced in C. Join 
 B C, and draw C D parallel to B A, and 
 A D parallel to B C, and A B C D will be 
 the square required. 
 
 B 
 
 Demons. Join BE, then because AEF 
 is a right angle, and A E equal to E F, the 
 angle EAF is half a right angle, Euc. 
 2 and 9 ; but A B is equal to B C, and 
 
 therefore the angle B C A is also half a 
 right angle, Euc. 1 and 5 ; hence the angle 
 A B C is a right angle, and is therefore 
 equal to the angle F E C ; from these 
 equals take away the equal angles F B E 
 and FEB, Euc. 1 and 5, and there re- 
 mains the angle E B C equal to * B E C ; 
 hence the side E C is equal to B C, the side 
 of the square ; and A C exceeds B C by 
 A E the given excess. Q, E. D. 
 
 This question was also solved very in- 
 geniously by J. B. Oldham, although 
 rather circuitously demonstrated. 
 
 0 has not understood this question. 
 
 QUESTIONS FOR SOLUTION. 
 
 Quest. 20, by Mr. H. Flather, Seymour- 
 place, Bryanstone-square. 
 
 What will a chain of standard gold 
 weigh in water when it raises the water an 
 inch, in a square vessel, whose side is 3 
 inches; and supposing the workmen to 
 have adulterated the said chain with 14§ 
 ounces of silver ; how much higher would 
 the water rise upon its immersion in the 
 vessel ? 
 
 Quest. 21, by F. Manchester. 
 
 Required the equilibrium power of an 
 overshot water wheel at its circumference 
 as arising from the weight of water only ; 
 having the following data. — Diameter of 
 the wheel 24 feet, number of buckets 60, 
 revolutions in a minute 10, feeder of water 
 for driving 1200 hogsheads per hour ; the 
 water is thrown into the third bucket from 
 the perpendicular, through and about the 
 centre, on the leading side of the wheel 
 and leaves the same 5 buckets before it 
 arrives at the said perpendicular below ; 
 the momentum of the water being allowed 
 for the friction. 
 
 Quest. 22, by A. W. a Carpenter. 
 
 To trisect a given finite straight line, 
 geometrically, and give the demonstration. 
 
 Quest. 23, by G. G. C. 
 
 Suppose a pendulum that vibrates se- 
 conds at the Pole 39*2 inches long; one on 
 the parallel of 45° to be 39*1 inches ; and 
 one at the Equator 39 inches: required 
 the force of gravity at each of these places ? 
 
 Quest. 24, by Mr. J. Tomes. 
 
 From two given points on the same side 
 of a line given in position, to draw two 
 lines which shall meet in a point in this 
 line, so that their sum shall be less than 
 the sum of any two lines drawn from the 
 same points, and terminated at any other 
 point in the same line. 
 
THE ARTISA1S# 
 
 161 
 
 PNEUMATICS. 
 
 When the height through which water 
 is to be raised, is considerable, some in- 
 convenience might arise from the length of 
 the barrel through which the piston rod of 
 a sucking pump would have to descend, 
 in order that the piston might remain 
 within the limits of atmospheric pressure. 
 
 This may, however, be avoided, by 
 placing the moveable valve below the fixed 
 valve, and introducing the piston at the 
 bottom of the barrel, as in the following 
 figure. 
 
 ' Here the piston rod A B is drawn up 
 by a frame. 
 
 Such a machine is called a lifting pump ; 
 in common with other forcing pumps, it has 
 the disadvantage of thrusting the piston 
 before the rod, and thus tending to bend 
 the rod, and produce an unequal friction 
 in the piston, while in the sucking pump, 
 the principal force always tends to 
 straighten the rod. 
 
 The rod of a sucking pump may also be 
 made to work in a collar of leather, and 
 the water may be forced through a valve 
 into an ascending pipe, as in the following 
 figure, which represents a sucking pump 
 converted into a forcing one, by the addi- 
 tion of a collar of leathers at A : 
 
 THE FORCING PUMP. 
 
 The principle of this pump may be seen 
 in the following model,. 
 
 where a represents a solid piston, some- 
 times called the plunger, which, when 
 drawn up, rarities the air below it, and, 
 of course, pressing lighter on the water 
 within the pump than the pressure is on 
 the well, that greater pressure forces up 
 the water through the valve c, which 
 (being made a little specifically heavier 
 than the water) sheets, and prevents the 
 return of the water. The piston a being 
 now pressed down, the water above c is 
 forced through the valve d, into the air- 
 vessel g. This vessel has a pipe e screwed 
 tight into its top, that reaches nearly to 
 the bottom of the air-vessel g-, and is open 
 at both ends : when the water, therefore, 
 covers the lower end of this pipe, the air 
 above it becomes a prisoner and condensed, 
 as the water is forcing in, which by its 
 reaction on the surface of the water, forces 
 that water through the pipe e with great 
 velocity, and in a continued jet. 
 
 Vol. I.— No. 11, 
 
162 
 
 THE ARTISAN. 
 
 The discharge of water either by suck- 
 ing or forcing pumps, though naturally 
 intermitting, may be rendered continual by 
 the elasticity of the air condensed in what 
 is called an air-vessel. 
 
 The following figure represents a pump 
 in which this contrivance is applied. 
 
 Here the piston is solid, and when 
 drawn up rarifies the air within the pipe 
 c, by which means the water will rise in it, 
 and ascend through the valve d : on the 
 descent of the piston, this water will be 
 forced into the air-vessel e, and a vacuum 
 will be made above the piston, which, 
 communicating with the pipe g , will rarify 
 the air so much within that pipe, that the 
 water will flow up it into the pipe c, and 
 cover the piston. This water also will be 
 forced up into the air-vessel, by the ascent, 
 or next stroke of the piston ; so that water is 
 raised both by the ascent and descent of 
 the piston. 
 
 By applying an air-vessel to the common 
 sucking pump, or to any forcing pump, its 
 motion naay be equalized, and its perform- 
 ance improved; for if the orifice of the 
 air-vessel be sufficiently large, the water 
 
 may be forced into it during the stroke of 
 the pump, with any velocity that may be 
 required, and with little resistance from 
 friction, while the loss of force, from the 
 frequent accelerations and retardations of 
 the whole body of water in a long pipe, 
 must always be considerable. 
 
 The condensed air, reacting on the water, 
 expels it more gradually, and in a con- 
 tinual stream, so that the air-vessel has 
 an effect resembling that of a fly-wheel in 
 mechanics. 
 
 For forcing pumps of all kinds, the com- 
 mon piston, with a collar of loose and elas- 
 tic leather, (see fig. 4, page 133), is pre- 
 ferable to those of a more complicated 
 structure: the pressure of the water on 
 the inside of the leather makes it suffi- 
 cienty tight, and the friction is inconsider- 
 able. 
 
 In some pumps the leather is omitted, 
 for the sake of simplicity, the loss of water 
 being compensated by the greater durabi- 
 lity of the pump ; and this loss will be the 
 smaller, in proportion as the motion of the 
 piston is more rapid. 
 
 A bag of leather has also been employed 
 for connecting the piston of a pump with 
 the barrel, and in this manner nearly 
 avoiding all friction; but it is probable, 
 that the want of durability would be a 
 great objection to a machine of this kind. 
 
 THE CENTRIFUGAL PUMP. 
 
 The centrifugal force, which is an impe- 
 diment to the operation ofWirtz’s machine, 
 mentioned at page 162, has sometimes 
 been employed, together with the pressure 
 of the atmosphere, as an immediate agent in 
 raising water, by means of the rotatory 
 pump. This machine consists of a vertical 
 pipe, caused to revolve round its axis, and 
 connected above with a horizontal pipe, 
 which is open at one or at both ends ; the 
 whole being furnished with proper valves 
 to prevent the escape of the water when 
 the machine is at rest. 
 
 As soon as the rotation becomes suffi- 
 ciently rapid, the centrifugal force of the 
 water in the horizontal pipe causes it to be 
 discharged at the end, its place being sup- 
 plied by means of the pressure of the 
 atmosphere on the reservoir below, which 
 forces the water to ascend through the 
 vertical pipe. 
 
 As this is one of the most singular me- 
 thods of raising water, and one that has 
 seldom been tried, we shall here give a 
 representation of the machine, which has 
 been employed for this purpose. 
 
THE ARTISAN. 
 
 163 
 
 A 
 
 This machine is first filled through the 
 funnel A, and when it is made to revolve 
 with considerable velocity, the water is 
 discharged into a circular trough, of which 
 a section is seen at B and C. The valve 
 at D remains shut while the pump is 
 filling. 
 
 A machine of this kind may be so 
 arranged, that, according to theory, little 
 of the force applied may be lost ; but it 
 has failed in producing a very advan- 
 tageous result in practice. 
 
 The pipes through which water is raised 
 by pumps of any kind, ought to be as 
 short and as straight as possible ; thus, if 
 we had to raise water to a height of 20 
 feet, and to carry it to a horizontal dis- 
 tance of 100 by means of a forcing pump, 
 it would be more advantageous to raise it, 
 first vertically into a cistern 20 feet above 
 the reservoir, and then let it run along 
 horizontally, or find its level in a bent 
 pipe, than to connect the pump imme- 
 diately with a single pipe carried to the 
 place of its destination. And for the same 
 reason a sucking pump should be placed 
 as nearly over the well as possible, in 
 order to avoid a loss of force in working 
 it. If very small pipes are used, they will 
 much increase the resistance, by the fric- 
 tion which they occasion. 
 
 The various methods of working these 
 pumps, or the different kinds of poiver 
 applied to raise water by them, will be 
 treated of after having described several 
 other forms of pumps, which are not so 
 immediately dependent on the pressure of 
 the atmosphere for their successful opera- 
 tion. This will be done under the head 
 of hydraulics. 
 
 OPTICS. 
 
 ON THE POLARIZATION OF 
 LIGHT. 
 
 This is a new branch of the science of 
 Optics, which sprung up about 14 years 
 ago, from the experiments and ingenuity 
 of M. Malus, Member of the Institute of 
 France; and has since been chiefly cul- 
 tivated by M. Biot, in France, and by Dr. 
 Brewster, in this country. 
 
 The term polarization is employed to 
 express a property, which may be com- 
 municated to ordinary light, by virtue of 
 which it exhibits the appearance of having 
 polarity , or poles possessing different pro- 
 perties. 
 
 If a solar ray fall on the anterior sur- 
 face of an unsil vered mirror plate, making 
 an angle with it of 35° 25', the ray will be 
 reflected in a right line, so that the angle 
 of reflection will be equal to the angle of 
 incidence. In any point of its reflected 
 path, receive it on another plane of simi- 
 lar glass, it will suffer in general a second 
 partial reflection. But this reflection will 
 vanish, or become null, if the second plate 
 of glass form an angle of 35° 25' with the 
 first reflected ray, and at the same time be 
 turned, so that the second reflection is 
 made in a plane perpendicular to that in 
 which the first reflection takes place. For 
 the sake of illustration, suppose that the 
 plane of incidence of the ray on the first 
 glass, coincides with the plane of the 
 meridian, and that the reflected ray is ver- 
 tical. Then, if we make the second in- 
 clined plate revolve, it will turn around 
 the reflected ray, forming always with it 
 the same angle; and the plane in which 
 the second reflection takes place, will 
 necessarily be directed towards the dif- 
 ferent points of the horizon, in different 
 azimuths. This being arranged, the fol- 
 lowing phenomena will be observed. 
 
 When the second plane of reflection is 
 directed in the meridian, and consequently 
 coincides with the first, the intensity of the 
 light reflected by the second glass is at its 
 maximum. 
 
 In proportion as the second plane, in its 
 revolution, deviates from its parallelism 
 with the first, the intensity of the reflected 
 light will diminish. 
 
 Finally, when the second plane of reflec- 
 tion is placed in the prime vertical, that is 
 east and west, and consequently perpen- 
 dicular to the first, the intensity of the 
 reflection of light is absolutely null on the 
 two surfaces of the second glass, and the 
 ray is entirely transmitted. 
 
 Preserving the second plate at the same 
 inclination to the horizon, if we continue to 
 make it revolve beyond the quadrant now 
 described, the phenomena will be repro* 
 M 2 
 
164 
 
 THE ARTISAN. 
 
 duced in the inverse order; that is, the 
 intensity of the light will increase, pre- 
 cisely as it diminished, and it will become 
 equal, at equal distances from the east and 
 west. Hence, when the second plane of 
 reflection returns once more to the meri- 
 dian, a second maximum of intensity equal 
 to the first recurs. 
 
 From these experiments it appears, that 
 the ray reflected by the first glass, is not 
 reflected by the second, under this inci- 
 dence, when it is presented to it by its east 
 and west sides; but that it is reflected, at 
 least in part, when it is presented to the 
 glass by any two others of its opposite 
 sides. Now if we regard the ray as an 
 infinitely rapid succession of a series of 
 luminous particles, the faces of the ray are 
 merely the successive faces of these par- 
 ticles. We must hence conclude, that 
 these particles possess faces endowed with 
 different physical properties, and that in 
 the present circumstance, the first reflection 
 has turned towards the same sides of 
 space, similar faces, or faces equally en- 
 dowed at least with the property under 
 consideration. It is this arrangement of 
 its molecules which Malus named the 
 polarization of light, assimilating the effect 
 of the first glass to that of a magnetic bar, 
 which would turn a series of magnetic 
 needles, all in the same direction. 
 
 Hitherto we have supposed that the ray, 
 whether incident or reflected, formed with 
 the two mirror plates, an angle of 35° 25' ; 
 for it is only under this angle that the phe- 
 nomenon is complete. Without changing 
 the inclination of the ray to the first plate, 
 if we vary never so little the inclination of 
 the second, the intensity of the reflected 
 light is no longer null in any azimuth, but 
 it becomes the feeblest possible in the 
 prime vertical, in which it was formerly 
 null. 
 
 Similar phenomena may be produced by 
 substituting for the mirror-glasses, polished 
 plates, formed for the greater part of trans- 
 parent bodies. The two planes of reflec- 
 tion must always remain rectangular, but 
 they must be presented to the luminous 
 ray, at different angles, according to their 
 nature. Generally, all polished surfaces 
 have the property of thus polarizing, more 
 or less completely, the light which they 
 reflect under certain incidences ; but there 
 
 is for each of them a particular incidence, 
 in which the polarization it impresses is 
 most complete, and for a great many, it 
 amounts to the whole of the reflected 
 light. 
 
 When a ray of light has received pola- 
 rization in a certain direction, by the 
 processes now described, it carries with it 
 this property into space, preserving it 
 without perceptible alteration, when we 
 make it traverse perpendicularly a con- 
 siderable mass of air, water, or any sub- 
 stance possessed of single refraction. But 
 the substances which exercise double re- 
 fraction, in general alter the polarization 
 of the ray, and apparently in a sudden 
 manner, and communicate to it a new 
 polarization of the same nature, but in 
 another direction. 
 
 ON THE REFRACTIVE POWER OF DIFFERENT 
 SUBSTANCES. 
 
 That a ray of light is refracted, in pass- 
 ing obliquely out of one medium into ano- 
 ther of a different density, has already 
 been remarked at page 12 ; but as different 
 substances possess this power in a very 
 different degree, and as the subject is not 
 only curious, but has already been the means 
 of showing much light on the chemical 
 composition of certain bodies, we shall 
 here make a few observations upon it, as 
 well as upon that of double refraction, 
 previous to leaving what may be termed 
 the theoretical part of optics. 
 
 The deviation of a ray of light from the 
 rectilineal path for any particular substance 
 depends on the obliquity of the ray to the 
 refracting surface, so that the sine of the 
 angle of refraction is to the angle of inci- 
 dence in a constant ratio. Sir I. Newton 
 found that unctuous and other inflammable 
 bodies occasioned a greater deviation in 
 the luminous rays than their attractive 
 mass or density gave reason to expect. 
 Hence he conjectured, that both diamond 
 and water contained some combustible 
 matter, which is now well known to be the 
 case : see page 105. 
 
 The ingenious Dr. Wollaston has in- 
 vented an instrument for measuring the 
 refractive density of substances. This in 
 strument consists of a rectangular prism A 
 of flint glass, under which is attached the 
 substance to be examined. 
 
THE ARTISAN* 
 
 165 
 
 B C is a rod or ruler 10 inches long, and 
 € D and DE are each 15*83 inches long. 
 When the sights at B and C are so placed, 
 that the divisions between the light and 
 dark portion of the lower surface of the 
 prism is seen through them, the rod F, 
 which carries a vernier , shows the index 
 of the refractive density, which in the si- 
 tuation represented in the above figure, is 
 1*43. 
 
 From the refractive power of bodies we 
 may, in many cases, infer their chemical 
 constitution. The purity of essential oils 
 may be pretty correctly inferred by an ex- 
 amination with Dr. Wollaston’s instrument. 
 
 In oil of cloves for instance, a very ma- 
 terial difference may often be discovered. 
 
 If this substance be genuine, its refrac- 
 tion power is as high as 1*635, but it is 
 often to be met with as low as 1*493* 
 
 Extensive tables of the refractive power 
 of substances are now inserted in some 
 modern works on optics, but our limits 
 will only permit us to insert a very small 
 table of this description. 
 
 Index of Refraction 
 
 A vacuum 
 
 1*00000 
 
 Atmospherical Air — 
 
 1*00033 
 
 Ice 
 
 1*30700 
 
 Water 
 
 1*336 
 
 Vitreous humour — 
 
 1*344 
 
 Ether 
 
 1*358 
 
 Albumen 
 
 1*360 
 
 Alcohol — — 
 
 1*370 
 
 Alum — : — 
 
 1*457 
 
 Tallow melted — — - 
 
 1*460 
 
 Borax — — 
 
 1.467 
 
 Oil of Olives 
 
 1*469 
 
 Butter cold 
 
 1*480 
 
 Linseed oil • 
 
 1*485 
 
 French plate glass — • 
 
 1*500 
 
 English ditto 
 
 1*504 
 
 Gumarabic 
 
 1*514 
 
 Crown glass, common 
 
 1*525 
 
 Phosphorus * 
 
 1*579 
 
 Flint-glass 
 
 1*586 
 
 Iceland Spar, strongest 
 
 1*657 
 
 Diamond 
 
 2*510 
 
 Chromate of lead, greatest 2*926 
 
 It may be necessary to 
 
 mention 1 
 
 that this table exhibits the refractive power 
 of different bodies, without any considera- 
 tion of their densities or specific gravities ; 
 but their absolute refractive powers may 
 be deduced from those given in the table, 
 as follows : 
 
 Square the index of the refractive power 
 of any substance, from which subtract 1, 
 then divide the remainder by the specific 
 gravity of the substance, and the quotient 
 will be the absolute refractive power of 
 that substance. This operation is so sim- 
 
 * The index of the refractive power of a vacuum 
 is considered the standard of comparison, and is 
 here supposed l'OOOOO, 
 
 pie that it is unnecessary to give an 
 example of its application. 
 
 OF DOUBLE REFRACTION. 
 
 We come now to observe, that in some 
 instances this refraction is double. 
 
 When a ray of light falls upon glass or 
 water, or even any other fluid, the image 
 formed by refraction is always single ; 
 when there is a single incident ray, there 
 is only a single refracted ray. These 
 bodies are therefore said to have single 
 refraction. There are, however, various 
 bodies, such as Iceland spar , rock crystal, 
 &c. which give two images of any object 
 seen through them, when they are bounded 
 by plane surfaces, or which give two re- 
 fracted rays when there is only one inci- 
 dent ray. 
 
 These bodies are said to have double 
 refraction , and are called doubly refracting 
 crystals. 
 
 In doubly refracting crystals, one of the 
 images or pencils is refracted according 
 to the law of the sines, mentioned at page 
 12, and is therefore called the ordmary 
 ray or image. The second pencil or image 
 is formed according to a new and entirely 
 different law, and is therefore called the 
 extraordinary ray or image. 
 
 In all doubly refracting crystals, there 
 is one or more lines along which the double 
 refraction, or the separation of the ordinary 
 and extraordinary images, is nothing, or 
 vanishes. This line is called the axis of 
 the crystal, or the axis of double refraction. 
 
 If the extraordinary ray be refracted 
 towards the axis of a crystal, that axis is 
 called a positive axis of double refraction ; 
 but if it be refracted from the axis, that 
 axis is called a negative axis of double 
 refraction. 
 
 The principle section of a crystal is any 
 plane passing through its axis of double 
 refraction. 
 
 All regular crystals which belong to the 
 rhamboidal or pyramidal systems of crys- 
 tallization, the octahedron and some others, 
 have one axis of double refraction, which 
 coincides with the common axis of their 
 crystals. 
 
 All regular crystals which belong to the 
 prismatic system, or whose primitive forms 
 are the right prism, with its base a rec- 
 tangle, a rhomb or an oblique parallelo- 
 gram, have two axis of double refraction, 
 coincident with some permanent line in 
 the primitive form of the crystal. 
 
 Rules might here be given for determin- 
 ing the law of double refraction in all 
 crystals, whether with one or two axis ; 
 but as these rules are extremely com- 
 plicated, we shall now take leave of this 
 subject without inserting them here. 
 
166 
 
 THE ARTISAN. 
 
 CHEMISTRY. 
 
 OF SULPHUR.* 
 
 Sulphur is a simple combustible body 
 like the preceding, and the fourth in the 
 order of affinity for oxygen. It is the 
 most easily procured, in a state of purity, 
 of all the simple combustibles, and often 
 found in that state in nature, particularly 
 in the neighbourhood of volcanoes. 
 
 It is also procured in large quantities 
 from the mineral substance called Pyrites , 
 by distillation. 
 
 Sulphur was the first known of all the 
 combustibles, and was long considered as 
 the general cause of combustibility. t 
 
 Though very anciently known, sulphur 
 has also been long the source of errors 
 and strange hypotheses in chemistry. It 
 was on this substance, that Stahl founded 
 his theory of phlogiston, which governed 
 the schools for more than a century. 
 
 Since the establishment of the pneu- 
 matic doctrine, the facts have been accu- 
 rately observed and much better examined, 
 and the phenomena presented by sulphur 
 have proved, that it has not been decom- 
 posed; that it only obeys the laws of 
 composition, and is acted upon in this 
 respect, like phosphorus, carbon, the 
 metals, &c. In general, sulphur has been 
 at all times one of those substances, 
 which have participated the most in the 
 different changes which the science has 
 experienced, and concerning which Phi- 
 losophers have been more particularly 
 employed. 
 
 Sulphur is consequently a body whose 
 combinations are the most numerous, and 
 at present the best understood. 
 
 1. Sulphur is a hard brittle substance, 
 commonly of a yellow colour, without any 
 smell, and of a weak though perceptible 
 taste. 
 
 It is a non-conductor of electricity, and 
 of course becomes electric by friction. Its 
 specific gravity is 1*990. 
 
 Sulphur undergoes no change by being 
 allowed to remain exposed to the open air. 
 When thrown into water, it does not melt 
 as common salt does, but falls to the 
 bottom, and remains there unchanged : it 
 is therefore insoluble in water. 
 
 2. If a considerable piece of sulphur be 
 exposed to a sudden though gentle heat, 
 by holding it in the hand, for instance, it 
 breaks to pieces with a crackling noise. 
 
 When sulphur is heated to the tem- 
 perature of about 170°, it rises up in the 
 form of a fine powder, which may be 
 
 * Sulphur is also known by the name of brim- 
 stone . 
 
 t See page 15. 
 
 easily collected in a proper vessel. This 
 powder is called flowers of sulphur .* When 
 substances fly off in this manner on the ap- 
 plication of a moderate heat, they are 
 called volatile; and the process itself, by 
 which they are raised, is called volatili- 
 zation. 
 
 When heated to the temperature of about 
 214° of Fahrenheit’s thermometer, it melts 
 and becomes as liquid as water. If this 
 experiment be made in a thin glass vessel, 
 like the following figure, the vessel may 
 
 be placed upon burning coals, without 
 much risk of breaking it. The strong- 
 heat soon causes the sulphur to boil, and 
 converts it into a brown coloured vapour, 
 which fills the vessel, and issues with con- 
 siderable force out from its mouth. 
 
 3. There are a great many bodies which, 
 after being dissolved in water or melted 
 by heat, are capable of assuming certain 
 regular figures. If a quantity of common 
 salt, for instance, be dissolved in water, 
 and that fluid, by the application of a mo- 
 derate heat, be made to fly off in the form of 
 steam; or, in other words, if the water be 
 slowly evaporated , the salt will fall to the 
 bottom of the vessel in cubes. These re- 
 gular figures are called crystals. Now 
 sulphur is capable of crystallizing. If it 
 be melted, and as soon as its surface begins 
 to congeal, the liquid sulphur beneath be 
 poured out, the internal cavity will exhibit 
 long needle-shaped crystals of an octa- 
 hedral figure. This method of crystallizing 
 sulphur was contrived by Rouelle. If the 
 experiment be made in a glass vessel, or 
 upon a flat plate of iron, the crystals will 
 be perceived beginning to shoot when the 
 temperature sinks to about 220°. 
 
 3. When sulphur is heated to the tem- 
 perature of 560° in the open air, it takes 
 fire spontaneously, and burns with a pale 
 blue flame, and at the same time emits a 
 great quantity of fumes of a very strong 
 suffocating odour. When set on fire, and 
 then plunged into a jar full of oxygen 
 gas, it burns with a bright violet coloured 
 flame, and at the same time emits a vast 
 
 * It is only ip this state that sulphur is to be found 
 in commerce tolerably pure. Roll sulphur usually 
 contains a considerable portion of foreign bodies. 
 
THE ARTISAN. 
 
 16T 
 
 quantity of fumes. If the heat be conti- 
 nued long enough, the sulphur burns all 
 away without leaving any ashes or resi- 
 duum. If the fumes be collected, they are 
 found to consist entirely of sulphuric acid. 
 By combustion, then, sulphur is converted 
 into an acid.* This fact was known se- 
 veral centuries ago; but no intelligible 
 explanation was given of it till the time 
 of Stahl, who founded the theory already 
 alluded to, upon the experiments he made 
 on this substance. 
 
 There are two facts, however, which 
 Stahl either did not know, or did not 
 sufficiently attend to, neither of which 
 was accounted for by his theory. The 
 first is, that sulphur will not burn if air be 
 completely excluded ; the second, that 
 sulphuric acid is heavier than the sulphur 
 from which it was produced. 
 
 To account for these, or facts similar to 
 these, succeeding chemists refined upon 
 the theory of Stahl, deprived his phlogiston 
 of gravity , and even assigned it a principle 
 of levity. Still, however, the necessity of 
 the contact of air remained unexplained. 
 At last Mr. Lavoisier, who had already 
 distinguished himself by the extensiveness 
 of his views, the accuracy of his experi- 
 ments, and the precision of his reasoning, 
 undertook the examination of this subject, 
 and his experiments were published in the 
 Memoirs of the Academy of Sciences for 
 1777. He put a quantity of sulphur into 
 a large vessel filled with air, which he in- 
 verted into another vessel containing mer- 
 cury, and then set fire to the sulphur by 
 means of a burning glass. It emitted a 
 blue flame, accompanied with thick va- 
 pours, but was very soon extinguished, 
 and could not be again kindled. There 
 was, however, a little sulphuric acid 
 formed, which was a good deal heavier 
 than the sulphur which had disappeared ; 
 there was also a diminution in the air of 
 the vessel proportional to this increase of 
 weight. The sulphur, therefore, during 
 its conversion into an acid, must have 
 absorbed part of the air. He then put a 
 quantity of sulphuret of iron, which con- 
 sists of sulphur and iron combined toge- 
 ther, into a glass vessel full of air, which 
 he inverted over water.t The quantity of 
 air in the vessel continued diminishing for 
 eighteen days, as was evident from the 
 ascent of the water to occupy the space 
 which it had left ; but after that period no 
 further diminution took place. On ex- 
 amining the sulphuret, it was found some- 
 what heavier than when first introduced 
 into the vessel, and the air of the vessel 
 
 * Acids are a class of compound bodies, which 
 will be afterwards described. 
 
 t This experiment was first made by Scheele, but 
 with a different vietv. 
 
 wanted precisely the same weight. Now 
 this air had lost all its oxygen ; conse- 
 quently the whole of that oxygen must 
 have entered into the sulphuret. Part of 
 the sulphur was converted into sulphuric 
 acid ; and as all the rest of the sulphuret 
 was unchanged, the whole of the increase 
 of weight must have been owing to some- 
 thing which had entered into that part of 
 the sulphur which was converted into acid . 
 This something we know was oxygen. 
 Sulphuric acid therefore must be composed 
 of sulphur and oxygen ; for as the original 
 weight of the whole contents of the vessel 
 remained exactly the same, there was not 
 the smallest reason to suppose that any 
 substance had left the sulphur. 
 
 The combustion of sulphur, then, is 
 nothing else than the act of its combination 
 with oxygen ; and for any thing which we 
 know to the contrary, it is a simple sub- 
 stance. 
 
 From the slow combustibility of sulphur, 
 and the difficulty of condensing the acid 
 fumes, it was not possible for Lavoisier to 
 ascertain with how much it unites during 
 its combustion in oxygen gas ; but it may 
 be converted into sulphuric acid by boiling 
 it in a quantity of nitric acid : * and the 
 proportion of oxygen with which it has 
 united may be deduced from the increase 
 of its weight. This experiment was first 
 tried by Berthollet, but his apparatus did 
 not enable him to attain precision. Thenard 
 and Chenevix repeated it, and with proper 
 precautions. According to the first, 100 
 parts of sulphur unite with 80 ; according 
 to the last, with 62*6 of oxygen ; the mean 
 of both gives us 71*3 of oxygen. If we 
 consider it as nearly correct, then 100 
 grains of sulphur unite, during combustion, 
 with nearly 209 cubic inches of oxygen gas ; 
 and one grain of sulphur is capable of de- 
 priving 9§ inches of common air of all its 
 oxygen. 
 
 4. But sulphur does not always unite 
 with so great a quantity of oxygen : indeed 
 it usually burns with a blue flame, and 
 emits an exceedingly offensive smell. This 
 smell is occasioned by the escape of a gas, 
 which may be confined in proper vessels : 
 it is sulphurous acid. By adding oxygen 
 to it we may convert it into sulphuric acid ; 
 a proof that it contains less oxygen than 
 that acid. 
 
 6. If sulphur be kept melted in an open 
 vessel, it becomes gradually thick and 
 viscid. When in this state, if it be poured 
 into a basin of water, it will be found to 
 be of a red colour, and as soft as wax. In 
 this state it is employed to take off im- 
 pressions from seals and medals. These 
 casts are known in this country by the 
 
 * This acid, called ia common language aqua 
 fortis, will be described hereafter. 
 
168 
 
 THE ARTISAN. 
 
 name of sulphurs. When exposed to the 
 air for a few days, the sulphur soon re- 
 covers its original brittleness, but it retains 
 its red colour. It is supposed at present, 
 that sulphur, rendered viscid and red by 
 a long fusion, has combined with a little 
 oxygen ; hence the term oxide of sulphur 
 has been applied to it. This substance, 
 when newly made, has a violet colour ; it 
 has a fibrous texture; its specific gravity 
 is 2*3 ; it is tough, and has a straw colour 
 when pounded. Dr. Thomson found that 
 100 parts of it, when converted into sul- 
 phuric acid by means of nitric acid, became 
 160 parts, and therefore had united with 
 60 parts of oxygen. 
 
 6. When sulphur is first obtained by 
 precipitation from any liquid that holds 
 it in solution, it is always of a white colour, 
 which gradually changes to greenish yel- 
 low when the sulphur is exposed to the. 
 open air. If this white powder, or lac 
 sulphuris as it is called, be exposed to a 
 low heat in a retort, it soon acquires the 
 colour of common sulphur; and, at the 
 same time, a quantity of water is deposited 
 in the beak of the retort. On the other 
 hand, when a little water is dropt into 
 melted sulphur, the portion in contact with 
 the water immediately assumes the white 
 colour of lac sulphuris. If common sul- 
 phur be sublimed into a vessel filled with 
 the vapour of water, we obtain lac sul- 
 phuris of the usual whiteness, instead of 
 the common flowers of sulphur. These 
 facts prove that lac sulphuris is a compound 
 of sulphur and water. Hence we may 
 conclude, that greenish yellow is the natu- 
 ral colour of sulphur. W hiteness indicates 
 the presence of water. 
 
 7. Sulphur unites very readily to hydro- 
 gen, and forms a compound known by the 
 name of sulphuretted hydrogen gas; but 
 this will be afterwards noticed in treating 
 of the gases. 
 
 Till lately it was supposed that sulphur 
 does not combine with carbon ; but Messrs. 
 Clement and Desormes, two French che- 
 mists, have discovered that they may be 
 made to combine; and that when this is the 
 case, the compound assumes the form of a 
 liquid, to which has been given the name 
 of carburet of sulphur. 
 
 This liquid is transparent, and colour- 
 less when pure, but very frequently it has 
 a greenish yellow tinge. Its taste is cool- 
 ing and pungent, and its odour strong and 
 peculiar. Its specific gravity is T35. It 
 does not mix with water. When put into 
 the receiver of an air pump, and the air 
 exhausted, it rises in bubbles through the 
 water, and assumes the form of a gas. The 
 same change takes place when it is intro- 
 duced to the top of a barometer tube ; but 
 it is again condensed into a liquid when 
 the tube is immersed under mercury. 
 
 This compound burns easily like spirit 
 of wine and many other liquids. During 
 the combustion it emits a sulphureous 
 odour ; sulphur is deposited, and charcoal 
 remains behind. When a little of it is put 
 into a bottle filled with oxygen gas, it 
 gradually mixes with the oxygen, and 
 assumes the gaseous form. If a burning 
 taper be applied to the mouth of the bottle, 
 the mixture burns instantaneously, and 
 with an explosion so violent as to endanger 
 the vessel. It assumes the gaseous form in 
 the same way when placed in contact with 
 air. It does not detonate when kindled, 
 but burns quietly. 
 
 This liquid dissolves phosphorus readily. 
 It also dissolves a small portion of sul- 
 phur ; but has no action whatever on char- 
 coal. 
 
 Sulphur combines with phosphorus very 
 readily. 
 
 All that is necessary to effect this is to 
 mix the two substances together, and apply 
 a degree of heat sufficient to melt them. 
 The compound has a yellowish white 
 colour, and a crystallized appearance. 
 The combination may also be obtained by 
 heating the mixture in a glass tube, having 
 its mouth properly secured from the air. 
 The sulphuret of phosphorus, thus pre- 
 pared, is more combustible than phos- 
 phorus. If it be set on fire by means of a 
 hotwire, allowed to burn for a little, and 
 then extinguished by excluding the air, 
 the phosphorus, and perhaps the sulphur, 
 is oxidized, and the mixture acquires the 
 property of taking fire spontaneously as 
 soon as it comes in contact with air. 
 
 The combination may likewise be effected 
 by putting the two bodies into a retort, or 
 flask, filled with water, and applying heat 
 cautiously and slowly. They combine 
 together gradually as soon as the phos- 
 phorus is melted. It is however necessary 
 to apply the heat cautiously, because the 
 sulphuret of phosphorus has the property 
 of decomposing water. The rate of de- 
 composition increases very rapidly with 
 the temperature, a portion of the two 
 combustibles being converted into acids by 
 uniting with the oxygen: the hydrogen at 
 the moment of its evolution unites with 
 sulphur and phosphorus, and forms sul- 
 phuretted and phosphuretted gases. This 
 evolution, at the boiling temperature, is so 
 rapid as to occasion violent explosions. 
 The circumstances attending this explosion 
 have been examined, and it has been found 
 that the gas emitted burns spontaneously, 
 and leaves phosphoric and sulphuric acids. 
 The sulphuret of phosphorus formed under 
 irater has a yellow colour. It gives to 
 the water in which it is kept an acid 
 taste, and the smell of sulphuretted hy- 
 drogen. It burns, according to Mr. Briggs, 
 at a temperature considerably lower than 
 
THE ARTISAN. 
 
 169 
 
 a similar compound made in the dry way. 
 This induces him to conclude, that during 
 the combination a little water is decom- 
 posed, and the oxygen expended in con- 
 verting the sulphur and phosphorus into 
 oxides. 
 
 This compound was particularly ex- 
 amined by Pelletier, and found to congeal 
 at different temperatures according to the 
 proportion in which the sulphur and phos- 
 phorus are combined. When the sulphur 
 predominates, the compound is called 
 phosphuret of sulphur ; and when the phos- 
 phorus predominates, it is called sulphur et 
 of phosphorus. 
 
 ASTEOIOMY* 
 
 NEW PLANETS. 
 
 OF CERES. 
 
 The planet Ceres, which is situated be- 
 tween the orbits of Mars and Jupiter, 
 was discovered at Palermo, in Sicily, on 
 the 1st of January, 1801, by M. Piazzi, an 
 ingenious astronomer, who has since dis- 
 tinguished himself by his numerous obser- 
 vations. Ceres is of a ruddy colour, but 
 not deep, and appears about the size of a 
 star of the eighth magnitude. It seems to 
 be surrounded with a large dense atmos- 
 phere, and plainly exhibits a disc when 
 examined by a telescope which magnifies 
 about 200 times. Ceres performs her revo- 
 lution round the sun in 4 years, 7 months, 
 and 10 days, and her mean distance from 
 that luminary is nearly 260,000,000 Eng- 
 lish miles. The eccentricity of her orbit 
 is a little greater than that of Mercury, 
 and its inclination to the ecliptic exceeds 
 that of all the old planets. The magnitude 
 of this planet is not yet well ascertained. 
 Dr. Herschel makes her diameter only 160 
 miles, while Schroeter makes it 1624 miles. 
 This great difference, says Schroeter, was 
 occasioned by Herschel observing with his 
 projection-micrometer at too great a dis- 
 tance from the eye, and measuring only 
 the middle clear part of the nucleus. 
 
 OF PALLAS. 
 
 The planet Pallas was discovered at 
 Bremen, in Lower Saxony, on the 28th of 
 March, 1802, by Dr. Olbers. It is situ- 
 ated between the orbits of Mars and Jupi- 
 ter, and is nearly of the same magnitude 
 with Ceres. It is of a less ruddy colour 
 than Ceres, and performs its revolution 
 round the run nearly in the same time. The 
 atmosphere of this planet, according to 
 Schroeter, is to that of Ceres in the pro- 
 portion of 2 to 3. It undergoes similar 
 changes, but the light of the planet exhi- 
 bits greater variations. 
 
 OF JUNO. 
 
 The planet Juno, situated between the 
 orbits of Mars and Jupiter, was discovered 
 by M. Harding at the Observatory of Lili- 
 enthal, near Bremen, on the evening of the 
 1st of September, 1804. While M. Hard- 
 ing was forming an atlas of all the stars 
 which were near the orbits of Ceres and 
 Pallas, he observed in the constellation 
 Pisces, a small star of the eighth magni- 
 tude, which was not mentioned by La 
 Lande in his Histoire Celeste , and being 
 ignorant of its latitude and longitude, he 
 put it down in his chart as nearly as he 
 could estimate with his eye. Two days 
 afterwards the star disappeared ; but he 
 perceived another that he had not seen be- 
 fore, resembling the first in size and colour, 
 and situated a little to the south-west of its 
 place. He observed it again on the 5th of 
 September, and finding that it had moved 
 still farther to the south-west, he concluded 
 that it was a planet. It is of a reddish 
 colour, and free from that faint whitish 
 light that surrounds Pallas. Its diameter, 
 and mean distance from the sun, are less 
 than those of Pallas or Ceres. 
 
 OF VESTA. 
 
 This planet, which appears like a star 
 of the sixth magnitude, of a dusky colour, 
 similar in appearance to Herschel, was 
 discovered on the 29th of March, 1807, by 
 Dr. Olbers, who gave it the name of Vesta. 
 In a clear evening it may be seen by the 
 naked eye. Its light is more intense, pure, 
 and white, than any of the other three new 
 planets. The time it takes to perform its 
 annual revolution is 3 years, 66 days, 4 
 hours. Its diameter is stated at 238 miles, 
 and its mean distance from the sun at 
 225,000,000 miles. 
 
 OF COMETS. 
 
 Of all celestial bodies, Comets have 
 given rise to the greatest number of specu- 
 lations. In the ages of ignorance and 
 superstition, they were believed to be the 
 harbingers of divine vengeance, and to 
 portend great political and physical con- 
 vulsions. The most ancient opinion re- 
 specting their nature was, that they w r ere 
 enormous meteors formed in the earth’s 
 atmosphere. Yet many of the ancients en- 
 tertained opinions respecting them agree- 
 ing with some parts of the modern hypo- 
 thesis respecting these bodies ; for they 
 believed that they were so far of the na- 
 ture of planets that they had their peri- 
 odical times of appearing, and that wlien 
 they were out of sight, they were carried 
 aloft to an immense distance from the 
 earth, but again became visible when they 
 descended into the lower regions of the 
 air, when they were nearer to us. Modern 
 astronomers are now generally agreed 
 
170 
 
 THE ARTISAN. 
 
 that they have no light of their own, and 
 appear luminous only by the light of the 
 sun. They have no visible disc, and shine 
 with a pale whitish light, accompanied 
 with long transparent trains or tails, pro- 
 ceeding from that side which is turned 
 away from the sun. When a comet is 
 viewed through a good telescope, it ap- 
 pears like a mass of vapours surrounding 
 a dark nucleus of different degrees of 
 opacity in different comets. As these 
 bodies approach the sun their light be- 
 comes more brilliant, and after they reach 
 their Perihelion often exceed any of the 
 planets in lustre Their tails are also ob- 
 served to increase both in length and 
 brightness as they approach the sun. The 
 opinions of astronomers respecting these 
 tails have been very different. Tycho 
 Brahe, who was the first that gave the 
 comets their true rank in the creation, 
 supposed that the tail was occasioned by 
 the rays of the sun passing through the 
 nucleus of the comet, which he believed to 
 be transparent. Kepler thought that it 
 was the atmosphere of the comet which 
 was driven behind it by the force of the 
 solar rays. Sir Isaac New ton maintained 
 that the tail was a thin vapour, ascending 
 by means of the sun’s heat, as smoke does 
 from the earth. Euler supposes that the 
 tail is produced by the impulse of the solar 
 rays driving off the atmosphere from the 
 comet. Dr. Hamilton, of Dublin, supposes 
 them to be streams of electric matter. 
 
 In any of these opinions there is little to 
 entitle it to preference above the others ; 
 and till multiplied observations shall have 
 added to the imperfect knowledge which 
 we at present possess of these bodies, it is 
 perhaps better not to give a decided pre- 
 ference to any of them. 
 
 From a number of observations made by 
 Sir Isaac Newton on the comet that ap- 
 peared in the year 1680, he was enabled 
 to discover the true motion of these bodies. 
 
 Dr. Halley, following the theory of New- 
 ton, set himself to collect all the obser- 
 vations which had been made on comets, 
 and calculated the elements of 24 of them. 
 By computations founded on these ele- 
 ments, he concluded, that the comet of 1682 
 was the same that had appeared in the 
 years 1456, 1531, and 1607 ; that it had 
 a period of 75 or 76 years; and he ven- 
 tured to predict, that it would appear 
 again about the year 1758, which it actu- 
 ally did; therefore it may be expected to 
 appear again in the year 1835. 
 
 When a comet makes its appearance, it is 
 only for a very short period, seldom ex 
 ceeding a few months, and sometimes only 
 a few weeks. Instead of moving from west 
 to east , like the planets, in orbits making 
 small angles with the ecliptic, they are 
 observed to cross it at all angles, Their pro- 
 
 gress among the fixed stars is in general 
 more rapid than that of the planets, and 
 their change of apparent magnitude is 
 much more remarkable. When a comet 
 retires from the sun, its tail decreases and 
 nearly resumes its first appearance.* Those 
 comets which never approach very near 
 the sun, have nothing but a coma or nebu- 
 losity round them during the whole time of 
 their continuance in view. 
 
 The tail of a comet is always transpa- 
 rent, for the stars are often distinctly 
 visible through it, and it has even been 
 said, that on some occasions they have 
 been seen through the nucleus or head. 
 The length and form of the tail are very 
 different. Sometimes it extends only a few 
 degrees, at others it extends more than 
 90 degrees. In the great comet that 
 appeared in the year 1680, the tail sub- 
 tended an angle of 7 0°, and the tail of the 
 one which appeared in 1618, an angle of 
 104°. The tail sometimes consists of di- 
 verging streams of light: that of the comet 
 which appeared in the year 1744, con- 
 sisted of six, all proceeding from the head, 
 and all a little bent in the same direction. 
 The tail of the beautiful comet which 
 appeared in 1811, was composed of two 
 diverging beams of faint light, slightly 
 coloured, which made an angle of 15° to 
 20°, and sometimes much more. Both of 
 them were a little bent outward ; and the 
 space between them was comparatively 
 obscure. 
 
 The apparent difference in the length 
 and lustre of the tail of comets, has given 
 rise to a popular division of these singular 
 bodies into three kinds ; viz. bearded , tailed 
 and hairy comets ; but this division rather 
 relates to the several circumstances of the 
 same comet, than to the phenomena of 
 different ones. Thus when the comet is 
 east of the sun, and moves from, him, it is 
 said to be bearded , because the light pre- 
 cedes it in the manner of a beard; when 
 the comet is west of the sun, and sets after 
 him, it is said to be tailed, because the train 
 of light follows it in the manner of a tail ; 
 and when the sun and comet are diame- 
 trically opposite, the earth being between 
 them, the train or tail is all hid behind the 
 body of the comet, except the extremities, 
 which being broader than the body of the 
 comet, appear to surround it like a border 
 of hair , and on this account it is called 
 hairy. But there have been several comets 
 observed, whose disc was as clear, round, 
 and well defined, as that of Jupiter, with- 
 out either tail, beard, or coma. 
 
 The magnitude of comets has been ob- 
 served to be very different ; many of them 
 without their coma have appeared no larger 
 than stars of the first magnitude ; but some 
 authors have given us accounts of others 
 which appeared much greater ; such was 
 
171 
 
 THE ARTISAN. 
 
 the one that appeared in the time of the 
 emperor Nero, which, as Seneca relates, 
 was not inferior, in apparent magnitude, 
 to the sun himself. The comet which 
 Hevelius observed in the year 1652, did 
 not seem to be less than the moon, though 
 it was deficient in splendour, for it had a 
 pale, dim light, and appeared with a 
 dismal aspect. Most comets have dense 
 and dark atmospheres surrounding their 
 bodies, which weaken the sun’s rays that 
 fall upon them ; but within these appears 
 the nucleus, or solid body of the comet, 
 which, when the sky is clear, will often 
 give a more splendid light. 
 
 Respecting the nature of these singular 
 and extraordinary bodies, Philosophers 
 and Astronomers in all ages and countries 
 have been very much divided in their 
 opinions. The vulgar have however in- 
 variably considered them as evil omens , and 
 forerunners of war, pestilence, famine, &c. ; 
 and to adopt the language of an old poet ; 
 
 u The blazing star was viewed — ■ 
 Threatening the world with famine, plague, 
 and war ; 
 
 To princes death ; to kingdoms many crosses 
 To all estates inevitable losses ; 
 
 To herdsmen rot; to ploughmen hapless 
 seasons ; 
 
 To sailors storms ; to cities civil treasons ;” 
 
 The Chaldeans, who were eminent for 
 their astronomical researches, were of 
 opinion, that comets were lasting bodies, 
 which had stated revolutions as well as 
 the planets, but in orbits considerably 
 more extensive, on which account they are 
 only visible while near the earth, but dis- 
 appear again when they ascend into the 
 higher regions. Pythagoras taught, that 
 comets were wandering stars, disappearing 
 in the superior parts of their orbits, and 
 becoming visible only in the lower parts 
 of them. Some of the ancient Philosophers 
 supposed, they were nothing else but a 
 reflection of the beams from the sun or 
 moon, and generated as a rainbow; others 
 supposed they arose from vapours and 
 exhalations. The illustrious Aristotle 
 was of opinion they were meteors. Modern 
 philosophers have been equally perplexed 
 as their predecessors in accounting for the 
 nature of these magnificent celestial ap- 
 pearances. The eccentric but learned 
 Paracelsus gravely affirmed, that they 
 were formed and composed by Angels and 
 Spirits to foretel some good or bad events. 
 Kepler, the celebrated Astronomer, as- 
 serted that comets were monsters, and 
 generated in the celestial spaces by an 
 animal faculty ! The sentiments of Bodin, 
 a learned French writer of the 16th cen- 
 tury, were yet more absurd ; for he main- 
 tained that comets are spirits which have 
 
 lived upon the earth innumerable ages, 
 and being at last arrived on the confines 
 of death, celebrate their last triumph, or 
 are called to the Firmament like shining 
 stars ! 
 
 James Bernoulli, acelebrated Swiss phi- 
 losopher, formed a rational conjecture rela- 
 tive to comets in viewing them as the satel- 
 lites of some very distant Planets invisible 
 on the earth on account of its distance, as 
 were also the satellites, unless when in a 
 certain part of their course. Tycho Brahe, 
 the illustrious but unfortunate Philosopher 
 of Denmark, supported a true hypothesis 
 on this subject ; he averred, that a comet 
 had no sensible diurnal parallax, and 
 therefore was not only far above the re- 
 gions of our atmosphere, but much higher 
 than the moon ; that few have come so near 
 the earth as to have any diurnal parallax, 
 yet all comets have an annual parallax, 
 the revolution of the earth in its orbit, 
 causes their apparent motion to be very 
 different from what it would be, if viewed 
 from the sun, which demonstrates, that 
 they are much nearer than the fixed stars 
 which have no such parallax. 
 
 Descartes advanced anothet opinion: 
 which is, that comets are only stars that 
 were firmly fixed like the rest, but be- 
 coming gradually covered with macula or 
 spots, and at length wholly deprived of 
 their light, cannot keep their places, but 
 are carried off by the vortices* of the cir- 
 cumjacent stars; and in proportion to the 
 magnitude and solidity moved in such a 
 manner, as to be brought nearer to the 
 orb of Saturn; and thus coming within 
 reach of the sun’s light, are rendered vi- 
 sible. 
 
 The number of comets belonging to the 
 solar system, is said not to be less than 
 450 ; but the periods of not more than 
 three of these are known. The velocity of 
 these bodies, and their distance from the 
 sun when in the remotest part of their 
 orbits, exceed all human comprehension. 
 Sir Isaac Newton calculated the velocity 
 of the comet of 1680, and found it to be 
 880,000 miles per hour, and its aphelion 
 distance not less than 11,200,000,000 miles. 
 
 Respecting the use of these bodies, many 
 conjectures have been formed. Mr. Whiston 
 
 * Descartes supposed, that every thing in the 
 Universe was formed from very minute bodies 
 called Atoms, which had been floating in open 
 space. To each atom he attributed a motion on its 
 axis ; and he also maintained, that there was a ge- 
 neral motion of the whole Universe round like a 
 vortex, or whirlpool. In the centre of this vortex 
 was the sun with all the planets circulating round 
 him, at different distances ; and that each star was 
 also the centre of a general vortex round which its 
 planets turned. Besides these general vortices, each 
 planet had a vortex of its own, by which its sa- 
 tellites (if it had any) were whirled round, and any 
 other body that came within its reach. 
 
172 
 
 THE ARTISAN. 
 
 thought it probable, that they were ap- 
 pointed by the Almighty as places of 
 punishment for sinners after death, who 
 would be alternately tormented with the 
 most insupportable heat when nearest the 
 sun ; and in the opposite point With the 
 greatest possible cold. 
 
 Sir Isaac Newton, amongst other pur- 
 poses which he thinks they may be de- 
 signed to serve, adds, u that, for the con- 
 servation of the water and moisture of the 
 planets, comets seem absolutely requisite, 
 from whose condensed vapours and exha- 
 lations, all the moisture which is spent in 
 vegetation, and turned into dry earth, &c. 
 may be supplied and recruited; for all 
 vegetables grow and increase wholly from 
 fluids ; and again, as to their greatest part, 
 by putrefaction, into earth. Hence, the 
 quantity of dry earth must continually in- 
 crease, and the moisture decrease, and be 
 quite evaporated, if it did not receive a 
 continual supply from some part or other 
 of the universe ;”■ — “ and I suspect,” adds 
 this philosopher, “ that the spirit, which 
 makes the finest, subtilest, and best part 
 of our air, and which is absolutely requi- 
 site for the life and being of all things, 
 comes from the comets.” 
 
 JBiscellaneous Subjects. 
 
 MEMOIR OF THE LIFE OF 
 GALILEO. 
 
 Galileo, the celebrated astronomer and 
 mathematician, was the son of Vincenzo 
 Galilei, a nobleman of Florence, not less 
 distinguished by his quality and fortune, 
 than conspicuous for his skill and know- 
 ledge in music; about some points in 
 which science he maintained a dispute 
 with the famous Zarlinas. His wife 
 brought this son, Feb. I9th, 1564, either at 
 Fisa, or, which is more probable, at 
 Florence. Galileo received an education 
 suitable to his birth, his taste, and his 
 abilities. He went through his studies 
 early, and his father then wished that he 
 should apply himself to medicine; but 
 having obtained at College some knowledge 
 of mathematics, his genius declared itself 
 decisively for that study. He needed no 
 directions where to begin. Euclid’s 
 Elements were well known to be the best 
 foundation in this science. He therefore 
 set out with studying that work, of which 
 he made himself master without assistance, 
 and proceeded thence to such authors as 
 were in most esteem, ancient and modern. 
 His progress in these sciences was so ex- 
 traordinary, that in 1589, he was appointed 
 Professor of Mathematics in the University 
 of Pisa, but being there continually har- 
 
 rassed by the scholastic professors, for 
 opposing some maxims of their favourite 
 Aristotle ; he quitted that place at the latter 
 end of 1592, for Padua, whither he was in- 
 vited very handsomely to accept a similar 
 professorship; soon after which; by the 
 esteem arising from his genius and eru- 
 dition, he was recommended to the friend- 
 ship of Tycho Brahe. He had already, 
 even long before 1586, written his “ Me. 
 chanics,” or a treatise of the benefits 
 derived from that science and from its 
 instruments, together with a fragment 
 concerning percussion, the first published 
 by Mercennus, at Paris, in 1634, in “ Mer- 
 senni Opera,” vol. 1. and both by Meno- 
 less, vol. 1.; as also his “ Balance,” in 
 which, after Archimedes’s problem of the 
 crown, he shewed how to find the propor- 
 tion of alloy, or mixt metals, and how r to 
 make the said instrument. These he had 
 read to his pupils soon after his arrival at 
 Padua, in 1593.* 
 
 While he was professor at Padua, in 
 1609, visiting Venice, then famous for the 
 art of making glass, he heard of the inven- 
 tion of the telescope by James Metius, in 
 Holland. This notice was sufficient for 
 Galileo ; his curiosity was raised ; and the 
 result of his inquiry was a telescope of his 
 own, produced from this hint, without 
 having seen the Dutch glass. All the dis- 
 coveries he made in astronomy were the 
 easy and natural consequences of this in- 
 vention, which opening away, till then 
 unknown, into the heavens, gave that 
 science an entirely new face. Galileo, in 
 one of his works, ridicules the unwilling- 
 ness of the Aristotelians to allow of any 
 discoveries not known to their master, by 
 introducing a speaker who attributes the 
 telescope to him, on account of what he 
 says of seeing the stars from the bottom of 
 a deep well. “ The well,” says he, M is 
 the tube of the telescope, the intervening 
 vapours answer to the glasses.” He began 
 by observing the moon, and calculating 
 the height of her mountains. He then 
 discovered four of Jupiter’s satellites, 
 which he called the Medicean stars or 
 planets, in honour of Cosmo II. grand 
 duke of Tuscany, who was of that noble 
 family. Cosmo now recalled him from 
 Padua, re-established him at Pisa, with a 
 very handsome stipend, in 1610; and the 
 same year, having lately invited him to 
 Florence, gave him the post and title of 
 his principal philosopher and mathema- 
 tician. 
 
 It was not long before Galileo disco- 
 vered the phases of Venus, and other 
 celestial phsenomena. He had been, how- 
 
 * While he was lecturer at Padua, Gustavus-Adol- 
 phus, king of Sweden, was one of his hearers. The 
 lectures then given by him still remain at Milan. 
 
THE ARTISAN. 
 
 ITS 
 
 ever, but a few years at Florence, before 
 he was convinced by sad experience, that 
 Aristotle’s doctrine, however ill-grounded, 
 was held too sacred to be called in ques- 
 tion. Having observed some Solar spots 
 in 1612, he printed that discovery the fol- 
 lowing year at Rome, in which, and in 
 some other publications, he ventured to 
 assert the truth of the Copernican system, 
 and brought several new arguments to con- 
 firm it.* This startled the jealously of the 
 Jesuits, who procured a citation for him 
 to appear before the holy office at Rome, 
 in 1615, where he was charged with he- 
 resy, for maintaining these two proposi- 
 tions ; 1st. That the sun is in the centre of 
 the world, and immoveable by a local 
 motion; and 2d, that the earth is not the 
 centre of the world, nor immoveable, but 
 actually moves by a diurnal motion. The 
 first of these positions was declared to be 
 absurd, false in philosophy, and formally 
 heretical, being contrary to the express 
 word of God ; the second was also alleged 
 to be philosophically false, and, in a theo- 
 logical view, at least erroneous in point of 
 faith. He was detained in the inquisition 
 till February, 1616, on the 25th of which 
 month sentence was passed against him ; 
 by which he was enjoined to renounce his 
 heretical opinions, and not to defend them 
 either by word or writing, nor even to in- 
 sinuate them into the mind of any person 
 whatsoever ; and he obtained his discharge 
 only by a promise to conform himself to 
 this order. It is hard to say whether his 
 sentence betrayed greater weakness of 
 understanding, or perversity of will. Gali- 
 leo clearly saw the poison of both in it; and 
 therefore following the known maxim, 
 “ that forced oaths and promises are not 
 binding to the conscience,” he went on, 
 making further new discoveries in the 
 planetary system, and occasionally pub- 
 lishing them with such inferences and 
 remarks as necessarily followed from 
 them, notwithstanding they tended plainly 
 to establish the truth of the above men- 
 tioned propositions. 
 
 He continued many years confidently in 
 this course, no juridical notice being taken 
 of it, till he had the presumption to publish 
 at Florence his “ Dialogi della due massime 
 Systeme del Mondo , Tolemaico et Coyerni- 
 cano ?’ or, Dialogues of the two greatest 
 Systems of the world, the Ptolemaic and 
 Copernican, in 1632. Here, in examining 
 the grounds upon which the two systems 
 were built, he produces the most specious 
 as well as strongest arguments for each of 
 those opinions ; and leaves, it is true, the 
 
 * He demonstrated a very sensible change in the 
 magnitude of the apparent diameters of Mars and 
 Venus; a phenomenon of great consequence to 
 prove the Copernican theory. 
 
 question undecided, as not to be demon- 
 strated either way, while many phenomena 
 remained insolvable ; but all this is done in 
 such a manner, that his inclination to the 
 Copernican system might be easily per- 
 ceived. Nor had he forborne to enliven 
 his production by several smart strokes of 
 raillery against those who adhered so 
 obstinately, and were such devotees to 
 Aristotle's opinions, as to think it a crime 
 to depart from them in the smallest de- 
 gree. This excited the indignation of his 
 former enemies, and he was again cited 
 before the inquisition at Rome ; the con- 
 gregation was convened, and, in his 
 presence, pronounced sentence against 
 him and his books. They obliged him to 
 abjure his errors in the most solemn man- 
 ner, committed him to the prison of their 
 office during pleasure, and enjoined him, 
 as a saving penance, for three years, to 
 repeat once a week the seven penitential 
 psalms; reserving, however, to them- 
 sleves, the power of moderating, changing, 
 or taking away altogether, or in part, the 
 above-mentioned punishment and penance. 
 Upon this sentence he was detained a pri- 
 soner till 1634, and his u Dalogues of the 
 System of the World,” were burnt at 
 Rome. We rarely meet with a more 
 glaring instance of blindness and bigotry 
 than this;* and it was treated with as 
 much contempt by our author as consisted 
 with his safety. 
 
 He lived ten years after it, seven of 
 which were employed in making still 
 further discoveries with his telescope; 
 but, by continual application to that instru- 
 ment, added to the damage he received in 
 his sight from the nocturnal air, his eyes 
 grew gradually weaker, till, in 1639, he 
 became totally blind. He bore this great 
 calamity with patience and resignation, 
 worthy of a philosopher. The loss neither 
 broke his spirit, nor hindered the course 
 of his studies. He supplied the defect by 
 constant meditations, by which he pre- 
 pared a large collection of materials ; and 
 began to dictate his own conceptions, 
 when, by a distemper of three months con- 
 tinuance, wasting away by degrees, he 
 expired at Arcetri, near Florence,! Jan. 
 1642, in the same year that Newton was 
 born. In stature he was small, but in 
 aspect venerable, and his constitution 
 vigorous ; in company he was affable, free, 
 and full of pleasantry. He took great 
 delight in architecture and painting, and 
 
 * It will appear more extraordinary, when it is 
 considered that the prosecution was begun and 
 carried on by the Jesuits, an order instituted to be 
 a seminary of learning, in the view of producing 
 champions of the papal chair. 
 
 f In the last eight years of his life he lived out of 
 Florence, sometimes in the neighbouring towns, and 
 sometimes at Sienna. 
 
174 
 
 THE ARTISAN. 
 
 designed extremely well. He played ex- 
 quisitely on the lute; and whenever he 
 spent any time in the country, he took 
 great pleasure in husbandry. His learn- 
 ing was very extensive, and he possessed 
 in a high degree a clearness and acuteness 
 of wit. From the time of Archimedes, 
 nothing had been done in mechanical geo- 
 metry, till Galileo, who, being possessed of 
 an excellent judgment, and great skill in 
 the most abstruse points of geometry, first 
 extended the boundaries of that science, 
 and began to reduce the resistance of solid 
 bodies to its laws. Besides applying geo- 
 metry to the doctrine of motion, by which 
 philosophy became established on a sure 
 f oundation, he made surprising discoveries 
 in the heavens by means of his telescope. 
 He made the evidence of the Copernican 
 system more sensible, when he showed 
 from the phases of Venus, like to those of 
 the moon, that Venus actually revolves 
 about the sun. He proved the rotation of 
 the sun on his axis from his spots; and 
 thence the diurnal rotation of the earth 
 became more credible. The satellites that 
 attend Jupiter in his revolution about the 
 sun, represented in Jupiter's smaller sys- 
 tem, a just image of the great solar system; 
 and rendered it more easy to conceive how 
 the moon might attend the earth, as a 
 satellite, in her annual revolution. By 
 discovering hills and cavities in the moon, 
 and spots in the sun constantly varying, be 
 showed that there was not so great a dif- 
 ference between the celestial bodies and 
 the earth, as had been vainly imagined. 
 He rendered no less service to science by 
 treating, in a clear and geometrical man- 
 ner, the doctrine of motion, which has 
 justly been called the key of nature. The 
 rational part of mechanics had been so 
 much neglected, that hardly any improve- 
 ment was made in it for almost 2000 years. 
 But Galileo has given us fully the theory 
 of equable motions, and of such as are 
 uniformly accelerated or retarded, and of 
 these two compounded together. He was 
 the first who demonstrated that the spaces 
 described by heavy bodies, from the begin- 
 ning of their descent, are as the squares of 
 the times ; and that a body, projected in 
 any dirction not perpendicular to the hori- 
 zon, describes a parabola. These were the 
 beginnings of the doctrine of the motion of 
 heavy bodies, which has been since carried 
 to so great a height by Newton. In geo- 
 metry, he invented the cycloid, though the 
 properties of it were afterwards chiefly 
 demonstrated by his pupil Torricelli. He 
 invented the simple pendulum, and made 
 use of it in his astronomical experiments : 
 he had also thoughts of applying it to 
 clocks, but did not execute that design : 
 the glory of that invention was reserved 
 for his son Vicenzio, who made the ex- 
 
 periment at Venice in 1649 ; and Huygens 
 afterwards carried this invention to perfec- 
 tion. Galileo also discovered the gravity 
 or weight of the air, and endeavoured to 
 compare it with that of water, besides 
 opening up several other enquiries in 
 natural philosophy. 
 
 Galileo wrote a number of treatises, 
 many of which were published in his life- 
 time. Most of them were also collected 
 after his death, and published by Mendessi, 
 in 2 vols. 4to. under the title of u L'Opere di 
 Galileo Galilei Lynceo ” in 1656. Some of 
 these, with others of his pieces, were trans- 
 lated into English, and published by 
 Thomas Salisbury, in his Mathematical 
 Collections, in two vols. folio. A volume 
 also of his letters to several learned men, 
 and solutions of several problems, were 
 printed at Bologna in 4to. 
 
 ARCHITECTURE. 
 
 OF THE ORDERS OF ARCHITECTURE. 
 
 The moderns have applied the term 
 order to those architectural forms, with 
 which the Greeks composed the fa 9 ades of 
 their temples. 
 
 The principle members of an order are, 
 1st, a platform; 2d, perpendicular sup- 
 ports; and 3d, a lintelling or covering 
 connecting the tops of these supports, and 
 crowning the edifice. 
 
 The proportioning of these parts to the 
 edifice and to each other, and at the same 
 time adapting characteristical decorations, 
 constitutes an order, canon or rule. 
 
 The principal member of an order is the 
 perpendicular support or column. The ac- 
 companiments being subservient to this 
 leading feature, the bottom of the column 
 is fixed either on a general artificial plat- 
 form, or each upon a particular plinth , or 
 both. The lower part of the column, 
 which rests upon the square plinth, is 
 sometimes encompassed with mouldings, 
 which in allusion to their position, are, in 
 conjunction with the plinth, called the base. 
 
 The top part of the column is also co- 
 vered with a square plinth, with its sides 
 straight or curved, and generally accom- 
 panied by circular mouldings or sculptured 
 decorations upon the top part of the co- 
 lumn, which is immediately underneath it ; 
 this, taken together, is called the capital. 
 The body of the column, which reaches 
 between the base and capital, is termed the 
 shaft: it is the frustum of a cone, with 
 sometimes a plain surface, but frequently 
 having perpendicular flutings either meet- 
 ing in an edge, or leaving a small plane 
 space between them. The lintelling or 
 covering, which lies upon and connects the 
 oolumn, is termed the Entablature, and is 
 
THE ARTISAN. 
 
 175 
 
 sub-divided into three parts, named archi- 
 trave, frieze, and cornice : the architrave 
 consists of a mere lintel laid along the tops 
 of the columns ; the frieze represents the 
 ends of the cross beams resting upon the 
 former, and having the spaces between 
 filled up, having mouldings also fixed to 
 conceal the horizontal joint, and divide it 
 from the architrave ; and the upper member 
 or cornice represents the projecting eves of 
 a Greek roof, showing the ends of the 
 rafters.* 
 
 These definitions will be easily under- 
 stood by an inspection of the following 
 figure. 
 
 * Representations of the various mouldings used 
 in architecture will be given in another part of this 
 work 
 
 SOLUTIONS OF QUESTIONS. 
 
 Quest. 15, answered by W. V. 
 
 It is evident that the grindstone in ques- 
 tion is in form a cylinder, the diameter of 
 which is 36 inches, and altitude 12 inches, 
 wanting two cones, the diameter of each of 
 which is the same as that of the cylinder, 
 viz. 36 in. and the altitude 4 in. 
 
 Put ar, 7854, then according to the rules 
 of mensuration, the solidity of the cylinder 
 will be 36 x 36 X aX 12 = 15552(a), and 
 the solidity of the two cones will be 
 36x36xax4x§ (Euclid B 12 Prop. 10) 
 “3456 (a), which taken from the solidity 
 of the cylinder will leave 12096 (a) the so- 
 lidity of the stone, consequently the solidity 
 of one third of the stone will be 4032 (a) 
 and of two thirds 8064 (a). 
 
 Let x denote the third man’s share of 
 the semidiameter, then 2 x will be the di- 
 ameter of his part of the stone, which 
 will also be a cylinder wanting two cones. 
 And these cones will evidently be similar to 
 the two beforementioned, for the solid 
 angle at each of the vertices is common to 
 the two cones on that side the stone, and 
 therefore (Euclid B 1 1 . Def. 24) as 36 the 
 the diameter of each of the larger cones is 
 to 4 the altitude, so is 2x the diameter of 
 each of the lesser cones to 3 | x or §x the 
 altitude, therefore the solidity of the two 
 lesser cones will be (Euclid B 12 Prop 10) 
 4 ax 2 x §x X § — If ax 3 . But the altitude of 
 the lesser cylinder will be the sum of the 
 altitudes of the lesser cones added to 4 
 inches, the thickness of the stone at the 
 centre (that is to §x+4), and therefore its 
 solidity will be 4 ax 2 x (fa; +4) ~ ax 3 
 
 +16 ax 2 , from which take |f ax 3 the solidity 
 of the two cones, and the remainder § faa: 3 + 
 16 ax 2 will be the solidity of the third man’s 
 share of the stone. But one third of the 
 solidity of the stone is also equal to 4032 
 (a), therefore we have the following equa- 
 tion ffaa; 3 +16eia; 2 “4032 (a) and dividing 
 it by || a we have x 3 + 2 J x 2 zz 3402, from 
 which we obtain a*:=ill*633, which will be 
 the third man’s share of the semidiameter. 
 
 Again, suppose y to be the sum of the 
 second and third men’s shares of the semi- 
 diameter, then the equation will bey 3 + | ? 
 y 2 ~ 6804 whence y" 15355, from which 
 take the third man’s share, 11*633, and the 
 remainder 3*722 will be the second man’s 
 part of the semidiameter. Again, take 
 15*355 from 18, and we have 2*645 for the 
 first man’s part of the semidiameter of the 
 stone. 
 
 This ingenious, but modest correspon- 
 dent also forwarded a very neat solution of 
 the 14th question ; but it was too late for 
 insertion ; he also sent a solution of the 
 17 th question. 
 
 The proposer of this question sent a very 
 imperfect solution. 
 
176 
 
 THE ARTISAN. 
 
 Quest. 17, answered by Mr. G. Futvoye, 
 High-street, Marylebone. 
 
 The ends of the block being squares the 
 area of the greater end is 1^ or(f) 2 ~f§; 
 
 2 
 
 and the area of the lesser end is (§)~ J or 
 t! ; also f X 1 = |, or $ Now ff + f s + 
 
 — t§ ~r- 3 — t| mean area, which multiplied 
 by 24 the length of the block, gives 19§ 
 solid feet for the content of the block ; and 
 as 1* solid feet of lignum, vitce weighs 1B27 
 ozs.*, the whole block (19f feet) must 
 weigh 25876§ ounces Avoirdupois. 
 
 This question was also answered by the 
 proposer in a somewhat different manner. 
 It was also correctly answered by H. T.; 
 W.V.; Troublesome ; and we have received 
 some solutions which are incorrect in 
 principle, and consequently, incorrect in 
 their conclusion. 
 
 Quest. 18, answered by Mr. C. A. Wil- 
 liams ( the proposer ). 
 
 It is evident that the figure formed by 
 the shillings will be a polygon of 360 
 sides, and that the angle at its centre is 1°. 
 Hence by trigonometry its sine 1° is to *75 
 in. as sine of 89° 30', to 42*973, the 
 radius of the required circle ; the diameter 
 is therefore 85*946 inches, which squared 
 and multiplied by *7854, gives 5802* square 
 inches or 40*3 square feet, nearly for the 
 area of the required circle. 
 
 The proposer will perceive that he was 
 not correct in his conclusion, from the 
 alterations we have made in his solution. 
 
 We received a solution to this question 
 from Mr. J. M. Edney, one from Mr. Geo. 
 Futvoye, and one from Mr. Hugh Starke ; 
 but each of these gentlemen supposes (in 
 this Example), that the perimeter of a 
 polygon and the circumference of a circle 
 circumscribing it, are the same. For they 
 find the circumference of the circle thus, 
 360 x f ~270. Now any person may con- 
 vince himself that this is not correct, by 
 supposing the polygon to have only 5 or 6 
 sides, instead of 360 sides. 
 
 The results obtained by the above gen- 
 tlemen, to this question are nearly correct, 
 because the perimeter of a polygon of so 
 many sides does not differ much from its 
 circumscribing circle. — Edit. 
 
 Quest. 19, answered by an Engineer, 
 ( the proposer ). 
 
 From B one of the given points let fall 
 the perpendicular B E, upon the line C D 
 given in position, and produce it till E F 
 be equal to E B, join A F meeting C B in 
 
 G; alsojoinBG; AG and BG are the 
 straight lines required. 
 
 A. 
 
 Demon. The triangles E B G and EFG 
 having the side BE equal to E F, C E 
 common, and the contained angle BEG 
 equal to F E G equal by Euc. 1 and 4, and 
 consequently the angle B G E is equal 
 F GE or A GC, which was required to be 
 done. The same construction will apply 
 when the points are on opposite sides of 
 the line. 
 
 This question was very ingeniously 
 solved by J. B. ©ldham, and likewise by 
 Mr. John Holroyd, of the same plaee. 
 
 Another gentleman in London, sent a so- 
 lution, but he will perceive from this con- 
 struction that he has mistaken the question. 
 
 QUESTIONS FOR SOLUTION. 
 
 Quest. 25, proposed by Mr. H. Flather, 
 Seymour-place. 
 
 Required the weight of one of the Port- 
 land key stones to the middle arch of West- 
 minster bridge, the diameter of the arch 
 being 76 feet, the height of the key stone 
 5 feet, the chord of its greatest breadth to 
 the front of the arch 3 ft. 4 in., and its 
 depth in the arch 4 feet? 
 
 Quest. 2 6 , proposed by Mr. J.M. Edney, 
 St. John’s-street, Clerkenwell. 
 
 Having given the diameter of a semi- 
 circle, it is required to find an algebraic 
 expression for the side of the inscribed 
 square. 
 
 Quest. 27, proposed by C. G. 
 
 Through a given point, to draw a straight 
 line such that the segments of the line in- 
 tercepted by perpendiculars let fall upon it 
 from other two given points, shall be equal. 
 
 * See the“ Artisan” page 25. 
 
THE ARTISAN- 
 
 177 
 
 GEOMETRY. 
 
 PROPOSITION XXXII.* 
 
 Corollary 1st. All the interior angles 
 of every rectilineal figure, when four right 
 angles are added to them, make twice as 
 many right angles as the figure has sides. 
 Therefore if four right angles be deducted 
 from twice as many right angles as any 
 figure has sides, it will leave the sum of 
 the interior angles of that figure. 
 
 X? 
 
 For it is evident, that any rectilineal 
 figure, as ABCDE, can be divided into as 
 many triangles as the figure has sides, by 
 drawing straight lines from a point F 
 within the figure to each of its angles. And, 
 by the preceding proposition, all the angles 
 of these triangles are equal to twice as 
 many right angles as there are triangles, 
 that is, as there are sides of the figure ; 
 and the same angles are equal to the an- 
 gles of the figure, together with the angles 
 at the point F, (which do not belong to the 
 figure), that is, together with four right 
 angles. Therefore, the angles of the figure 
 wants four right angles of being equal to 
 twice as many right angles as the figure 
 has sides. 
 
 Cor. 2. All the exterior angles of any 
 rectilineal figure formed by producing each 
 of its sides, are together equal to four right 
 angles. 
 
 Because every interior angle, as ABC, 
 with its adjacent exterior ABB, is equal to 
 two right angles ; therefore all the interior, 
 together with all the exterior angles of the 
 figure, ate equal to twice as many right 
 angles as there are sides of the figure; 
 that is, by the foregoing corollary, they 
 are equal to all the interior angles of the 
 figure, together with four right angles ; but 
 the interior angles belong to the inside, 
 and are therefore to be deducted, conse- 
 quently all the exterior angles are equal to 
 four right angles. 
 
 PROPOSITION XXXIII. 
 Theorem. — The straight lines which join 
 the extremities of two equal and parallel 
 straight lines , towards the same parts , 
 are also themselves equal and parallel. 
 
 Let AB, CD, be equal and parallel 
 straight lines, and joined towards the same 
 parts by the straight lines AC, B D ; AC, 
 B D are also equal and parallel. 
 
 Join B C ; and because A B is parallel to 
 C D, and B C meets them, the alternate 
 angles ABC, BCD are equal ; and be- 
 cause A B is equal to C D, and B C com- 
 mon to the two triangles A B C, D C B, the 
 two sides A B, B C are equal to the two 
 DC, C B ; and the angle AB C is equal to 
 the angle BCD; therefore the base A C is 
 equal to the base B D, and the triangle 
 A B C to the triangle BCD, and the other 
 angles to the other angles, each to each, to 
 which the equal sides are opposite ; there- 
 fore the angle A C B is equal to the angle 
 C B D ; and because the straight line B C 
 meets the two straight lines A C, B D, and 
 makes the alternate angles A C B, C B D 
 equal to one another, A C is parallel to 
 B D ; and it was shewn to be equal to it. 
 Therefore, straight lines, &c. Q. E. D, 
 
 PROPOSITION XXXIV. 
 
 Theorem. — The opposite sides and angles 
 of a parallelogram are equal to one ano- 
 ther, and the diameter bisects it, that is, 
 divides it into two equal parts.* 
 
 Let ACDB be a parallelogram, of 
 which BC is a diameter; the opposite 
 
 * A parallelogram is a four-sided figure, of which 
 the opposite sides are parallel ; and the diameter is 
 the straight line joining two of its opposite angles. 
 
178 
 
 THE ARTISAN. 
 
 sides and angles of the figure are equal to 
 one another ; and the diameter BC bisects it. 
 
 A... & 
 
 Because AB is parallel to CD, and 
 B C meets them, the alternate angles ABC, 
 BCD, are equal to one another ; and be- 
 cause AC is parallel to BD, and BC meets 
 them, the alternate angles A C B, C B D 
 are equal to one another ; wherefore the 
 two triangles ABC, CBD have two angles 
 ABC, B C A, in one, equal to two angles 
 BCD, CBD, in the other, each to each, 
 and one side B C common to the two tri- 
 angles, which is adjacent to their equal 
 angles; therefore their other sides are 
 equal, each to each, and the third angle 
 of the one to the third angle of the other ; 
 viz. the side A B to the side C D, and A C 
 to B D, and the angle B A C equal to the 
 angle BDC. And because the angle 
 A B C is equal to the angle BCD, and the 
 angle C B D to the an gle A C B, the whole 
 angle A B D is equal to the whole angle 
 ACD: and the angle BAC has been shown 
 to be equal to the angle BDC ; therefore the 
 opposite sides and angles of a parallelo- 
 gram are equal to one another : also, its 
 diameter bisects it ; for A B being equal 
 to C D, and B C common, the two A B, 
 B C, are equal to the two DC, C B, each 
 to each ; and the angle A B C is equal to 
 the angle BCD; therefore the triangle 
 A B C is equal to the triangle BCD, and 
 the diameter B C divides the parallelo- 
 gram A C D B into two equal parts. There- 
 fore, &c. Q. E. D. 
 
 The converse of the former part of this 
 proposition is, “ If the opposite sides of a 
 quadrilateral figure be equal, the figure is 
 a parallelogram.” 
 
 Cor. Hence if the opposite sides of a 
 quadrilateral figure be equal, its opposite 
 angles will likewise be equal ; for such a 
 figure is a parallelogram, and the opposite 
 angles are equal, by the Proposition. 
 
 PROPOSITION XXXV. 
 Theorem. — Parallelograms upon the same 
 
 base and between the same parallels , are 
 
 equal to one another. 
 
 Let the parallelograms A B C D, D BC F 
 be upon the same base B C, and between 
 the same parallels A F, BC; the paralle- 
 logram ABC1) is equal to the parallelo- 
 gram D B C F. 
 
 If the sides AD, D F of the parallelo- 
 grams A BCD, DBCF opposite to the 
 base B C be terminated in the same point 
 D ; it is plain that each of the parallelo- 
 grams is double of the triangle BDC; 
 and they are therefore equal to one ano- 
 ther. 
 
 But, if the sides AD, E F, opposite to 
 the base B C of the parallelograms ABCD, 
 EBCF, be not terminated in the same 
 point : 
 
 then, because A B C D is a parallelogram, 
 A D is equal to B C ; for the same reason 
 E F is equal to B C ; wherefore A D is 
 equal to E F ; and D E is common ; there- 
 fore the whole, or the remainder A E is 
 equal to the whole, or the remainder DF ; 
 now A B is also equal to D C ; therefore 
 the two EA, AB, are equal to the two 
 F D, D C, each to each ; but the exterior 
 angle FDC is equal to the interior E AB, 
 wherefore the base EB is equal to the 
 base F C, and the triangle E A B to the 
 triangle FDC. Take the triangle FDC 
 from the trapezium A B C F, and from the 
 same trapezium take the triangle E A B ; 
 the remainders will then be equal ; that is, 
 the parallelogram A B C D is equal to the 
 parallelogram EBCF. Therefore, paral- 
 lelograms upon the same base, &c. 
 
THE ARTISAN. 
 
 179 
 
 PROPOSITION XXXVI. 
 
 Theorem. — Parallelograms upon equal 
 bases , and between the same parallels , are 
 equal to one another. 
 
 Let ABCD, EFGHbe parallelograms 
 upon equal bases B C, F G, and between 
 the same parallels A H, B G ; the paral- 
 lelogram A B C D is equal to E F G H. 
 
 Join BE, CH; and because BC is 
 equal to F G, and F G to E H, B C is equal 
 to E H ; and they are parallels, and joined 
 towards the same parts by the straight 
 lines B E, C H : but straight lines which 
 join equal and parallel straight lines 
 towards the same parts, are themselves 
 equal and parallel ; therefore E B, C H 
 are both equal and parallel, and EBCH 
 is a parallelogram; and it is equal to 
 ABCD, because it is upon the same base 
 B C, and between the same parallels B C, 
 A H : For the like reasons, the paral- 
 lelogram EFGH is equal to the same 
 EBCH; therefore also the parallelogram 
 A B C D is equal to E F G II. Wherefore, 
 parallelograms, &c. Q. E. D. 
 
 PROPOSITION XXXVII. 
 
 Theorem. — Triangles upon the same base , 
 and between the same parallels , are 
 equal to one another. 
 
 Let the triangles ABC, D B C be upon 
 the same base B C, and between the same 
 parallels AD, B C : The triangle ABC, 
 is equal to the triangle D B C. 
 
 Produce AD both ways to the points 
 E, F, and through B draw B E parallel to 
 C A ; and through C draw C F parallel to 
 B D : therefore, each of the figures EBCA, 
 DBCF is a parallelogram ; and EBCA 
 
 is equal to D B C F, because they are upon 
 the same base B C, and between the same 
 parallels BC, E F ; and the triangle ABC 
 is the half of the parallelogram EBCA, 
 because the diameter A B bisects it ; and 
 the triangle D B C is the half of the paral- 
 lelogram DBCF, because the diameter 
 DC bisects it: but the halves of equal 
 things are equal; therefore the triangle 
 ABC is equal to the triangle D B C. 
 Wherefore triangles, &c. Q. E. D. 
 
 MECHANICS. 
 
 OF THE BALANCE. 
 
 Although the balance is not considered 
 a distinct mechanical power, being a lever 
 with equal arms, yet it is of so much use 
 in the common affairs of life, and of so great 
 utility in every nice scientific research 
 where quantity is concerned, that we shall 
 endeavour to explain the principles upon 
 which it depends. 
 
 The beam of a common balance must 
 have its arms precisely equal in length. 
 
 Its axis of motion is formed with an 
 edge like that of a knife, made of hard 
 steel, agate, or garnet; and the two dishes 
 at its extremities are hung upon edges of 
 the same kind. These edges are first 
 made sharp, and then rounded with a fine 
 bone, or a piece of buff leather. The 
 excellence of the instrument depends, in a 
 great measure, on the regular form of this 
 rounded part. When the lever, or beam, 
 is considered as a mere line, the two outer 
 edges are called points of suspension , and 
 the inner the fulcrum. 
 
 The points of suspension are supposed 
 to be at equal distances from the fulcrum, 
 and to be pressed with equal weights when 
 loaded. 
 
 The best beams are made of two hollow 
 cones of brass, united at their bases ; they 
 are lifted off their supports when the ba- 
 lance is not in use, in order to avoid acci- 
 dental injuries, the scales are also sup- 
 ported, so as not to hang from the beam, 
 until they have received their weights. 
 
 In delicate balances, a small weight is 
 sometimes inclosed within the beam, 
 which is raised or depressed at pleasure, 
 by a screw, so as to bring the centre of 
 gravity of the whole moveable apparatus 
 as near to the fulcrum as may be required, 
 in order to make the vibrations of the 
 beam slow and extensive, and to bring it 
 to the horizontal position, whether the 
 scales have weights in them or not. 
 
 The following figure represents a balance 
 made by Fidler for the Royal Institution, 
 London, and nearly resembles those made 
 by Ramsden and Troughton, which will 
 also be noticed in the course of the present 
 article. 
 
 N 2 
 
180 
 
 THE ARTISAN. 
 
 The middle column A is raised at plea- 
 sure by the cock IS, and carries the round 
 ends of the axis in the forks at its upper 
 part, in order to remove the pressure on 
 the sharp edges- of the axis within the 
 forks. 
 
 The scales are occasionally supported 
 by the pillars C and D, which are elevated 
 or depressed by turning the handle E. 
 The screw F serves for raising or lowering 
 a weight within the conical beam, by 
 means of which the place of the centre of 
 gravity is regulated. The extent of the 
 vibrations is measured on the graduated 
 arc G. This arc is useful for determining 
 the degree of inequality of the weights, by 
 enabling us to ascertain exactly the middle 
 point of the vibrations of the beam. 
 
 When a balance is well constructed, it 
 must have the following properties : 1st. 
 it should rest in a horizontal position when 
 loaded with equal weights ; 2d. it should 
 have great sensibility; that is, the addition 
 of a small weight in either scale should 
 disturb the equilibrium," and make the 
 beam incline sensibly from the horizontal 
 position ; 3d. it should have great stability ; 
 that is, when disturbed, it should quickly 
 return to a state of rest. 
 
 That the first of these requisites may be 
 obtained, the beam must have equal arms; 
 
 and the centre of suspension must be higher 
 than the centre of gravity. Were these 
 centres to coincide , the beam, when the 
 weights were equal, would rest in any 
 position, and the addition of the smallest 
 weight would overset the balance, and 
 place the beam in a vertical situation, from 
 which it would have no tendency to return. 
 The sensibility in this case would be the 
 greatest possible ; but the other two re- 
 quisites of level and stability would be 
 entirely lost. 
 
 When the centre of gravity is lower 
 than the centre of suspension, if the weights 
 be equal, the beam will be horizontal, and 
 if they be unequal, it will take an oblique 
 position, and will raise the centre of gra- 
 vity of the whole, making the momentum 
 on the side of the lighter weight, equal to 
 that on the side of the heavier, so that an 
 equilibrium will again take place. 
 
 If the centre of gra vity be higher than 
 the centre of suspension, when the beam is 
 level, it will overset by the smallest action, 
 and make a revolution of no less than a se- 
 micircle, and the motion will be the swifter 
 the higher the centre of gravity is above the 
 point of suspension, and the smaller the 
 weights with which the beam is loaded. 
 
 The second requisite, as already stated, 
 is the sensibility of the balance, or the 
 
THE ARTISAN. 
 
 181 
 
 smallness of the weight by which a given 
 angle of inclination is produced. 
 
 This depends on three circumstances; 
 namely, the length of the arm, the distance 
 between the centres of gravity and suspen- 
 sion, and the weight with which the ba- 
 lance is loaded. 
 
 For the sensibility is the greater, the 
 greater the length of the arm, the less the 
 distance between the two centres, and the 
 less the weight with which the balance is 
 loaded. 
 
 Lastly, the stability , or the force with 
 which the state of equilibrium is recovered, 
 depends chiefly on the two former circum- 
 stances ; that is, the length of the arm and 
 the distance between the centres of gravity 
 and suspension. 
 
 For the diminution of the distance be- 
 tween these centres while it increases the 
 sensibility , lessens the stability of the ba- 
 lance ; but the lengthening of the arm in- 
 creases the former of these, without di- 
 minishing the latter. 
 
 These observations, as well as the va- 
 rious kinds of equilibrium, are well illus- 
 trated by a balance of the following form. 
 
 When the scales are hung on the middle 
 pins, A and B, which are in the same ho- 
 rizontal line with the support of the beam, 
 the equilibrium is neutral, as already ob- 
 served, or the beam would rest in any po- 
 sition, because the weights would act as 
 if the centre of gravity coincided with the 
 centre of suspension. If the scales be 
 hung on the lowest pins C and B, the 
 centre of gravity will be nearly in the line 
 C D, and its path the curve E, which has 
 its concavity upward. In this case the 
 beam will be level, or the line C D will be 
 horizontal when the scales are loaded with 
 equal weights ; but if the scales are hung 
 on the points F and G, the path of the 
 centre of gravity will be convex upwards, 
 and the beam will overset. In reality, the 
 true paths of the centre would be nearly in 
 
 the curves H and I, situated between the 
 weights in the scales : but these are simi- 
 lar to the other curves. 
 
 If the equilibrium be rendered tottering 
 by the elevation of the points of suspen- 
 sion of the scales, the lower scale will not 
 rise, even if it be somewhat less loaded 
 than the upper, for in this case the lower 
 weight acts with the greatest advantage : 
 thus, the effect of the weight A is reduced 
 in the proportion of B C to D C, 
 
 by the obliquity of the arm C A, while the 
 weight E acts on the whole length of the 
 arm C F.* 
 
 The arms of a balance have sometimes 
 been made unequal for fraudulent pur- 
 poses, the weight being placed nearer to 
 the fulcrum than the substance to be 
 weighed. This fraud, however, may be 
 detected by changing the contents of one 
 scale into that of the other. 
 
 If a counterpoise to the same weight be 
 determined when put in each scale, the 
 sum of both counterpoises will be greater 
 than twice the true weight ; and the pur- 
 chaser of any commodity would be sure of 
 having even more than his due, if he could 
 prevail on the seller to weigh half in the 
 one scale and half in the other. 
 
 For example : if one arm of the beam 
 were only three fourths as long as the 
 other, the counterpoise to a weight of 
 twelve ounces, would be nine ounces in 
 one scale, and sixteen in the other, making 
 together twenty -five instead of twenty-four 
 ounces. 
 
 This fact may be illustrated by a very 
 simple figure, as follows : If A B C be a 
 
 semicircle, 
 
 * When the effective length of one or both arms 
 of the beam are capable of being varied, by changing 
 the points of suspension according to the divisions of 
 a scale, the instrument is called a steelyard. Where 
 one weight only is used, it is not necessary that the 
 two arms should exactly balance each other, for the 
 divisions may be so placed as to make the necessary 
 adjustment ; but it is sometimes convenient to have 
 two or three weights, of different magnitudes, and 
 for this purpose the instrument should be in equili- 
 brium without any weight. There are various forms 
 of the steelyard, each of which has its peculiar ad- 
 vantage. The most useful of these will be described 
 in another part of this work. 
 
182 
 
 THE ARTISAN. 
 
 and B D represent a given weight, and 
 A D its counterpoise in one of the scales of 
 an unequal balance, then D C will be its 
 counterpoise in the other scale. Now it is 
 evident that A C, or the sum of the two 
 unequal weights is more than twice B D, 
 or double the true weight. 
 
 The true weight of a substance weighed 
 in a false balance, may be easily deter- 
 mined by a little calculation, as follows : — 
 weigh the substance in each scale, then 
 multiply the two results together, and 
 extract the square root of the product, 
 which will be the true weight of the sub- 
 stance under trial. 
 
 For example — suppose a substance to 
 weigh 16 ounces in one scale, and 9 
 ounces in the other; required its true 
 weight? Here 16 multiplied by 9 is 144, 
 the square root of which is 12. The true 
 weight of the substance is therefore twelve 
 ounces. 
 
 The same thing may also be determined 
 geometrically ; thus, draw a straight line 
 A C, (see the foregoing figure), equal to 
 the sum of the two unequal weights, upon 
 which describe a semicircle, divide the 
 line into two parts A D and D C, in the 
 ratio of the weights, then at the point D 
 raise a perpendicular DB, to meet the 
 circumference of the circle, and this line 
 B D will represent the true weight.* 
 
 As very delicate balances are not only 
 useful in nice experiments, but are like- 
 wise much more expeditious than those 
 that are made for common purposes, they 
 are considered as very valuable instru- 
 ments, and consequently are not very nu- 
 merous ; we shall therefore conclude this 
 article with a short account of some of the 
 most delicate balances which have yet been 
 constructed. 
 
 In the Philosophical Transactions, vol. 
 
 * The line AC must be taken from a scale of 
 equal parts, and B D measured upon the same'scale. 
 
 That B D square is equal to the rectangle of" AD, 
 and D C, is proved in the 35th prop. 3 B. Euclid. 
 
 Ixvi. p. 509, mention is made of two accu- 
 rate balances of Mr. Bolton ; and it is said 
 that one would weigh a pound, and turn 
 with ^ of a grain. This, if the pound be 
 avoirdupoise, is 7 gkgg of the weight; and 
 shews that the balance could be well de- 
 pended on to four places of figures, and 
 probably to five. The other weighed half 
 an ounce, and turned with ^ of a grain. 
 This is of the weight. 
 
 In the same volume, p. 511, a balance of 
 Mr. Read’s is mentioned, which readily 
 turned with less than one pennyweight, 
 when loaded with fifty-five pounds, but 
 very distinctly turned with four grains, 
 when tried more patiently. This is about 
 55So3 P art l he weight; and therefore this 
 balance may be depended on to five places 
 of figures. 
 
 Also, page 576, a balance of Mr. White- 
 hurst’s weighs one pennyweight, and is 
 sensibly affected with ^g of a grain. This 
 is ?g igg part of the weight. 
 
 Dr. Ure, of Glasgow, has a pair of scales 
 of the common construction, made in Lon- 
 don. With 1200 grains in each scale, it 
 turns with ^ of a grain. This is g^oo of 
 the whole : and therefore about this weight 
 may be known to five places of figures. 
 The proportional delicacy is less in greater 
 weights. The beam will weigh nearly a 
 pound troy ; and when the scales are 
 empty, it is affected by -j^g of a grain. On 
 the whole, it may be usefully applied to 
 determine all weights between 100 grains 
 and 4000 grains to four places of figures. 
 
 A balance belonging to Mr. Alchorne, 
 of the Mint in London, is mentioned, vol. 
 Ixxvii. p. 205, of the Philosophical Trans- 
 actions. It is true to 3 grains with 15 lb. 
 an end. If these were avoirdupois pounds, 
 the weight is known to ggigg part, or to 
 four places of figures, or rarely five. 
 
 A balance, (made by Ramsden, and turn- 
 ing on points instead of edges) in the pos- 
 session of Dr. George Fordyyce, is men- 
 tioned in the seventy -fifth volume of the 
 Philosophical Transactions. With a load 
 of four or five ounces, a difference of one 
 division in the index was made by of a 
 grain. This is gg^jgg part of the weight, 
 and consequently this beam will ascertain 
 such weights to five places of figures, 
 beside an estimate figure. 
 
 The balance made by the late Mr. Rams- 
 den, for the Royal Society of London, 
 turns on steel edges, upon planes of 
 polished crystal. It is capable of weighing 
 ten pounds, and turns with the one ten 
 millionth of the weight. 
 
THE ARTISAN. 
 
 183 
 
 HYDRAULICS. 
 
 SCOOP WHEEL. 
 
 The machine called a scoop wheel is in- 
 tended to raise water to a height equal to 
 its semi-diameter. It is represented by 
 the following figure, and consists of a 
 number of semicircular partitions, as may 
 be perceived by an inspection of the fol- 
 lowing figure : 
 
 These partitions are open at both ends ; 
 that is, at the circumference, and at the 
 centre of the machine. As the wheel is 
 turned round in the direction W X W, 
 either by the hand or by any other power, 
 the scoops take up the water, which gra- 
 dually descends during the rotation of the 
 wheel, till it runs into its hollow axle, 
 which again discharges it into a spout O. 
 The scoop wheel is one of the forms in 
 which the Persian wheel is often described ; 
 but we shall here give a description of 
 that machine as it is usually constructed. 
 
 PERSIAN WHEEL. 
 
 The Persian wheel is a double water 
 wheel, with float boards on one side, and 
 a series of buckets on the other, which 
 are moveable about an axis above their 
 centre of gravity. The wheel is placed in 
 a stream, which puts it in motion by acting- 
 on its float boards. As the wheel turns 
 the moveable buckets dip in the water, and 
 ascend filled with the fluid. But when 
 they reach the highest point, their lower 
 ends strike against a fixed obstacle, so as 
 to make them empty themselves into a re- 
 servoir placed at the top of the wheel. 
 
 There is another form of the Persian 
 wheel, which is perhaps oftener employed 
 than the one just described, we shall there- 
 fore give a representation, and a short 
 description, of it. 
 
 Here W W is a common bucket wheel, 
 moving in the direction W O W. The 
 
 buckets dipping in the water MN, rise 
 filled with it, and discharge their contents 
 into the reservoir O, near the summit of 
 the wheel. A wheel of this kind has 
 lately been employed for draining the moss 
 of Blairdrummond in Scotland. It is 
 driven by floatboards fixed on its peri- 
 phery, or convex circumference, like the 
 common undershot wheel, and a current of 
 water is brought in at a side, to fill buckets 
 placed on the concave side of the rim. 
 
 CHAIN PUMP. 
 
 The chain puipp consists of an endless 
 chain W W B A, w r hich passes round the 
 wheel W W, 
 
 enters the water to be raised,’ and then 
 returns through the tube B A into the cis- 
 tern M N. This chain carries a number 
 of flat cylindrical pistons a, h , c, of nearly 
 
184 
 
 THE ARTISAN. 
 
 the same diameter as the tube A B, one 
 half of each piston being received into 
 openings in the circumference of the 
 wheel. 
 
 When the wheel is put in motion, the 
 pistons enter the barrel B A, and pushing 
 the water before them, raise it into the re- 
 servoir M N. When the wheel is turned 
 with great velocity, the barrel is generally 
 filled with water. 
 
 Pumps of this kind are frequently placed 
 in an inclined position, and they raise the 
 greatest quantity of water in this position, 
 when the distance of the flat piston is equal 
 to their breadth, and when the inclination 
 of the barrel is about 24°. The Spanish 
 Noria, described at page 153, is the same 
 as a chain pump, the earthen pitchers 
 s upplying the place of a chain. 
 
 Machines of this kind are sometimes 
 called cellular pumps , and when stuffed, 
 cushions are used in place of pistons, they 
 are called paternoster pumps. 
 
 The Chinese work their cellular pumps, 
 by walking on bars which project from the 
 axis of the wheel, or drum that drives 
 them. 
 
 Whatever objection may be made to 
 the choice of machines of this kind, the 
 Chinese mode of communicating motion to 
 them must be allowed to be advantageous. 
 
 The chain pump generally used in the 
 navy, is one with flat boards united to the 
 chain, instead of cylindrical pistons, as 
 represented in the foregoing figure. The 
 barrel is usually square, and through it 
 leathers strung on a chain, are drawn in 
 constant succession ; but these pumps are 
 only employed when a large quantity of 
 water is to be raised, and then they must 
 be worked with considerable velocity, in 
 order to produce any effect at all. 
 
 whitehorst’s engine. 
 
 Mr. Whitehurst, an ingenious watch- 
 maker of Darby, appears to have been the 
 first person who entertained the idea of 
 raising water by means of its momentum. 
 
 A machine upon this principle was erected 
 at Oulton in Cheshire, and is described in 
 the Transactions of the Royal Society of 
 London, for the year 1775 ; but as it is 
 both a simple and ingenious machine, we 
 shall here give a representation of it. 
 
 AM is the reservoir of water, whose 
 surface at M is on a level with B, the 
 bottom of the reservoir B N. The main 
 pipe A E is about 200 yards long, and If 
 inch in diameter, and the branch pipe E F 
 is of such a size, that the cock F is about 
 16 feet below the surface of the water at 
 M. A valve box with a valve a is shewn 
 at D, and C is an air vessel, into which 
 are inserted the extremities mn of the 
 main pipe, which are bent downwards for 
 the purpose of preventing the air from 
 being driven out when the water is forced 
 into it. Now, when the coek F is opened, 
 
 the water will rush out with a velocity of 
 nearly 30 feet per second. A column of 
 water, therefore, 200 yards long and If 
 inch diameter, is now put in motion, and 
 must have a considerable momentum. 
 Hence, if the cock F be suddenly shut, the 
 water will rush through the valve a into 
 the air vessel C, and condense the included 
 air. This condensation will take place 
 every time that the cock is opened, so that 
 the included air being compressed, will 
 press upon the water in the air vessel, and 
 raise it into the reservoir B N. 
 
 This machine is the same in principle as 
 
THE ARTISAN 
 
 185 
 
 the hydraulic ram, invented by Montgolfier, 
 and differs from it only in this, that a simi- 
 lar effect to opening the cock in White- 
 hurst’s machine, is produced by the motion 
 of the water in Mongolfier’s. 
 
 The hydraulic ram was constructed by 
 Montgolfier in the year 1797, and has been 
 brought to a very perfect state by a series 
 of improvements, which he has succes- 
 sively made upon it. The latest of these, 
 which has been made public, was added in 
 1816 ; but as drawings of the machine are 
 absolutely necessary, to render a descrip- 
 tion of it intelligible, we must reserve our 
 account of it for another part of this work. 
 
 fHfecellatteous Subjects. 
 
 MEMOIR OF THE LIFE OF THE 
 LATE MR. RAMSDEN. 
 
 Jesse Ramsden was born at Halifax, in 
 Yorkshire, on the 16th of October, 1730. 
 At an early period he conceived a strong 
 desire of devoting himself to literature, 
 and especially to history and antiquities : 
 the mathematics and chemistry engaged 
 his attention also in their turn ; but his 
 father was anxious that he should pursue 
 some occupation which might be useful to 
 him; and as he was a clothier, young 
 Ramsden applied to the same employment 
 till he had attained to the age of twenty- 
 one. He then went to London, to seek 
 for some occupation more suited to his 
 genius. Besides other things, he applied 
 to engraving under Burton :* and a fortu- 
 nate circumstance conducted him to that 
 object for which nature seemed to have 
 destined him, which was to be the re- 
 viver and father of the instrumental part 
 of astronomy. Mathematical instruments 
 were often brought to him to be engraven : 
 the more he examined them the more he 
 was sensible of their defects, and a secret 
 instinct made him desirous of constructing 
 better ones. He therefore resolved to 
 make an attempt in this line: he soon 
 acquired the use of the file, and made him- 
 self acquainted with the method of turning 
 
 * Mr. Burton was a thermometer and barometer 
 maker, and divider of instruments. Instruments at 
 this period were divided by means of a plate ap- 
 plied to them, and the divisions were in this man- 
 ner marked off. Mr. Burton was one of the best 
 workmen of his time, and worked for Short, Bird, 
 and other eminent artists. Mr. Ramsden bound 
 himself apprentice to Mr. Burton for four years ; 
 and after his time was expired entered into partner- 
 ship with Mr. Fairbone, who lived afterwards in 
 New-street, Shoe-lane. This partnership, however, 
 did not long continue. Mr. Ramsden opened a 
 shop on his own account in the Strand, and, having 
 married Miss Dolland, became possessed of a part 
 of Mr. Dollond’s patent for achromatic telescopes. 
 
 brass, land even of grinding glasses. In 
 the year 1763 he constructed instruments 
 for Sisson, Dolland, Nairne, Adams, and 
 other methematical instrument makers. 
 He then established a shop on his own 
 account, in the Haymarket, about the year 
 1768 ; from which he removed to Picca- 
 dilly in 1775. Having formed a design of 
 examining all the astronomical instru- 
 ments, he resolved to correct those which 
 being founded on good principles were de- 
 fective only in the construction, and to set 
 aside those which were wrong in both 
 these respects. 
 
 Hadley’s sextant, which is so much em- 
 ployed in the British navy, appeared to 
 him one of the most useful, but it was then 
 very imperfect ; the essential parts were 
 not of sufficient strength ; the centre was 
 subject to too much friction ; and the index 
 could be moved several minutes without 
 any change being produced in the position 
 of the mirror; the divisions in general 
 were very coarse : and Mr. Ramsden 
 found that the Abbfi de la!Caille was right, 
 when he estimated at five minutes the 
 error which might take place in the ob- 
 served distances of the moon and stars, 
 and which might occasion in the longitude 
 an error of fifty nautical leagues. Mr. 
 Ramsden therefore changed the construc- 
 tion in regard to the centre, and made 
 these instruments so correct as to give 
 never more than half a minute of uncer- 
 tainty. 
 
 The invention of a dividing machine 
 having now become necessary, he emo 
 ployed himself in constructing one, which 
 he did with the greatest success. The 
 dividing machines before used were far 
 from being exact. Graham and Bird em- 
 ployed beam compasses. The latter kept 
 his method a secret till it was purchased 
 from him by the Board of Longitude, in 
 order to be published. Mr. Ramsden had 
 already discovered a method of his own, 
 which in exactness surpassed that of Bird. 
 For large works he continued to use the 
 beam compasses ; but as it is necessary in 
 the greater number of common instruments 
 to save time, he employed himself for ten 
 years in improving his dividing machine, 
 and at last brought it to a state in which 
 both ease and expedition are united. With 
 this admirable machine a sextant could be 
 divided in the course of twenty minutes. 
 For the invention of this, Mr. Ramsden 
 received a premium of £600 from the 
 Board of Longitude. The Board of Lon- 
 gitude has often given greater premiums 
 for objects of less utility ; but the greatest 
 men do not always obtain the greatest re- 
 wards. Newton, indeed, got a place in the 
 mint; but he was not indebted for it to his 
 merit alone. 
 
 While Mr. Ramsden was employed oe 
 
186 
 
 THE ARTISAN. 
 
 his dividing machine, he improved at the 
 same time other instruments. The theodo- 
 lite before consisted merely of a telescope, 
 turning on a circle divided at every three 
 minutes, by means of a vernier ; but in the 
 hands of Mr. Ramsden it became a new 
 and perfect instrument, which serves for 
 measuring heights and distances as well as 
 for taking angles. He constructed the 
 great theodolite, employed by general Roy 
 for measuring the triangles which join 
 those of England and France, (and by which 
 there cannot bean error of a second, though 
 it is only eighteen inches radius. It is 
 furnished with two telescopes, each of 
 which turns on a horizontal axis, and by 
 which the angles between objects more or 
 less elevated are reduced to the horizon, 
 and measured. General Roy measured the 
 angle between the pole star and the sides 
 of his triangles, in order to have the con- 
 vergency of the meridians such as it is in 
 our oblate spheroid. These operations 
 showed, that the difference between the 
 meridians of the observatories of Paris 
 and Greenwich is 9 20 '. 
 
 The barometer employed for measuring 
 the heights of mountains has been much 
 improved by Mr. Ramsden. His method 
 of marking at the bottom the line of the 
 level, tand of looking at the top to the con- 
 tact of the index with the summit of the 
 mercury, renders it possible to distinguish 
 the hundredth part of a line, and to mea- 
 sure heights within a foot. He showed 
 M. de Luc that it is the summit of the 
 column, and not the part which touches 
 the glass, that ought to be observed ; and 
 he caused a table to be engraved, which 
 accompanies his barometers, and which, 
 without calculation, gives the heights of 
 places according to the height of the ba- 
 rometer, and even for different degrees of 
 heat. He also simplified the apparatus for 
 carrying and supporting portable baro- 
 meters. 
 
 Various other philosophical instruments 
 have been made by Mr. Ramsden, and 
 always with new improvements : such as 
 an electric machine ; a manometer for 
 measuring the density of the air ; an in- 
 strument for measuring inaccessible dis- 
 tances, and which renders it unnecessary 
 to measure a base ; assaying balances 
 which turn with a ten-thousandth part of 
 the weight. 
 
 The pyrometer, destined to measure the 
 dilatation of bodies by heat, afforded exer- 
 cise also for the talents of Mr. Ramsden ; 
 and with the happiest success, as may be 
 seen in the Philosophical Transactions for 
 1785. 
 
 Optics are also very much indebted to 
 Mr. Ramsden for its improvement. He 
 found means to correct the aberration of 
 sphericity and refrangibility in compound 
 
 eye-glasses applied to all astronomical 
 instruments, and in a new and perfect 
 manner. Opticians had imagined, that 
 this could be accomplished by making the 
 image of the object-glass fall between the 
 two eye-glasses ; which was attended with' 
 this great inconvenience, that the eye-glass 
 could not be touched without deranging 
 the line of collimation, and the value of 
 the parts of the micrometer. To remedy 
 this inconvenience Mr. Ramsden set out 
 from a very simple experiment, namely, 
 that the edges of an image observed through 
 a prism are less coloured according as the 
 image is nearer the prism ; and, in conse- 
 quence of this truth, he sought for the 
 means of placing the two eye-glasses be- 
 tween the image of the object-glass and 
 the eye, without failing to correct the two 
 aberrations, which he did ' by changing 
 the radii of the curves and placing the 
 glasses in a manner altogether different 
 from that commonly employed. 
 
 He invented also a reflecting object- 
 glass micrometer, a description of which 
 may be seen in the Transactions of the 
 Royal Society of London for 1779. In his 
 paper on this subject he points out the de- 
 fects and inconveniences of that of Bou- 
 guer, first invented in 1748, in which the 
 different positions of the eye, in regard to 
 the pencil of light, cause the two images 
 to appear sometimes to touch each other, 
 sometimes to be separated, and sometimes 
 alternately by a sort of oscillation. He 
 found also that the aberration of the rays, 
 which renders the object badly defined, 
 increased the inconvenience of that instru- 
 ment. He thought it would therefore be 
 necessary to abandon the principle of re- 
 fraction, and to substitute that of reflection. 
 This instrument, as simple as ingenious, 
 contains no more mirrors or glasses than 
 what are necessary for the telescope ; and 
 the separation of the two images depends 
 only on the inclination of the mirrors, and 
 not on the focus. 
 
 He however employed himself in im- 
 proving the refracting micrometer, and con- 
 ceived the happy idea of placing this mi- 
 crometer not towards the object-glass, 
 but exactly in the conjugate focus of the 
 first eye-glass. This micrometer is com- 
 posed of two plano-convex lenses, which 
 can be moved and form two images, as in 
 the object-glass micrometers ; but with this 
 difference, that the rays before they fall on 
 the plano-convex lenses pass through a 
 lens convex on both sides, at a certain dis- 
 tance towards the object-glass. By these 
 means the contrary refraction of the two 
 plano-convex lenses, and the convex lens, 
 corrects the error which takes place in 
 object-glass micrometers, where the image 
 depends only on the focus of the two plano- 
 convex lenses. The image being already 
 
THE ARTISAN. 
 
 187 
 
 considerably magnified before" it falls on 
 the refracting micrometer, the imperfection 
 of the glasses can occasion only an insen- 
 sible error in the measurement of angles. 
 It is true, indeed, that by this position the 
 field of the micrometer will be smaller than 
 what it would be were the micrometer 
 near the object-glass. Mr. Ramsden de- 
 vised means also for making the images to 
 be uniformly illuminated in every part of 
 the field. With this micrometer the dia- 
 meter of the planets may be measured in 
 every direction; it may be adapted to 
 achromatic telescopes of every kind; it 
 may be brought near to or removed from 
 the object-glass at pleasure, to render 
 vision distinct; and it may be taken from 
 the tube of the eye-glasses, that the teles- 
 cope may be employed without a microme- 
 ter. All these advantages have given 
 great reputation to Ramsden’s microme- 
 ters, land the astronomer who can now 
 obtain one of them may consider himself 
 fortunate. 
 
 In consequence of these and other in- 
 ventions, Mr. Ramsden was elected a fel- 
 low of the Royal Society in 1786. 
 
 The objects hitherto mentioned, how- 
 ever, are not the most important of the 
 works of Mr. Ramsden. The equatorial, 
 the transit instrument, and quadrant, re- 
 ceived in his hands new improvements. 
 The equatorial first constructed by Sisson, 
 and which was somewhat improved by 
 Short, was much further improved by 
 Ramsden; He first suppressed the end- 
 less crew, which by pressing on the centre 
 destroyed its precision. He placed the 
 centre of gravity on the centre of the base, 
 and caused all the movements to take 
 place in every direction. He pointed out 
 the means of rectifying the instrument in 
 all its parts ; and he applied to it a very 
 ingenious small machine for measuring or 
 correcting the effect of refraction. This 
 invention is much anterior to that given by 
 Mr. Dolland in the Philosophical Transac- 
 tions. Mr. Ramsden had a patent for this 
 kind of equatorial. The honourable Stew- 
 art Mackenzie, brother of the Earl of Bute, 
 the friend and patron of Mr. Ramsden, 
 wrote a description of this machine, which 
 has been printed. But Mr. Ramsden did 
 not always strictly adhere to the descrip- 
 tion; for his inventive genius rarely 
 allowed him to construct the same instru- 
 ment in the same manner. 
 
 The transit instrument is employed in 
 all the large observatories of Europe ; but 
 Mr. Ramsden has added to it several im- 
 provements. He invented a method of 
 illuminating the wires, by making the light 
 pass along the axis of the machine. The 
 reflector is placed in the inside, and ob- 
 liquely in the middle. He did not lessen 
 the aperture of the object-glass : and as the 
 
 light passes through a coloured prism, 
 which“may be moved at pleasure, the^light 
 may be increased or diminished. 
 
 Ramsden’s meridian telescopes, such as 
 those at Blenheim, at Manheim, at Dublin, 
 and such as those made for the observa- 
 tories of Paris and Gotha, are also remark- 
 able for the excellence of the object-glasses. 
 
 The mural quadrant is the most import- 
 ant of all the astronomical instruments, 
 and Mr. Ramsden has distinguished him- 
 self here also by the exactness of his divi- 
 sions : he placed the thread and plummet 
 behind the instrument, in order that it may 
 not be necessary to remove it when obser- 
 vations are made near the zenith. His 
 method of illuminating the object-glass and 
 at the same time the divisions, and of sus- 
 pending the telescope, was more perfect 
 than any previously in use. In those of 
 eight feet which he made for the observa- 
 tories of Padua and Vilna, and which Dr. 
 Maskelyne examined, the greatest error 
 does not exceed two seconds and a half. 
 
 The mural quadrant of the Duke of 
 Marlborough at Blenheim, which is six 
 feet, is one of the instruments which was 
 made by Mr. Ramsden. It is fixed to four 
 pillars which turn on two pivots, so that 
 the instrument may be placed north and 
 south in a minute. This instrument is as 
 beautiful as it is perfect. 
 
 But the quadrant was not the instru- 
 ment which Mr. Ramsden valued most. 
 It was the whole circle; and he has proved 
 that to attain to the utmost degree of pre- 
 cision of which observation is susceptible, 
 we must renounce the quadrant entirely. 
 His principal reasons are : 1st. The least 
 variation in the centre is perceived by the 
 two points diametrically opposite. 2d. 
 As the circle is turned the plane is always 
 rigorously exact ; which cannot possibly be 
 the case in the quadrant. 3d. Two mea- 
 surements can always be had of the same 
 arc; which serves for verifying the accu- 
 racy of the observation. 4th. The first 
 point of the division can be verified every 
 day with the greatest ease. 5th. The dila- 
 tation of the metal is uniform, and can 
 produce no error. 6th. This instrument is 
 a meridian telescope as well as a mural. 
 7th. It becomes a moveable azimuth circle 
 by adding a horizontal circle below the 
 axis, and then gives the refractions inde- 
 pendently of the measure of time. 
 
 Mr. Ramsden constructed a circle of 
 five feet radius for M. Piazzi, of Palermo, 
 one for the' Observatory of Paris, one for 
 Dublin, of twelve feet, besides several 
 others, and continued to exert his inge- 
 nuity in the improvement, and construc- 
 tion of philosophical instruments till within 
 a very short time of his death, which took 
 place in the year 1800. He had seven 
 children, but none of them are now alive. 
 
188 
 
 THE ARTISAN, 
 
 ARCHITECTURE. 
 
 We have already stated at page 154, 
 that the orders as now executed are five in 
 number; viz. the Tuscan, Doric, Ionic, 
 Corinthian, and Composite ; the first and 
 last of which are Roman, and the others 
 Greek. These orders are chiefly distin- 
 guished from each other by the columnwith. 
 its base and capital , and by the entablature * 
 
 TUSCAN ORDER. 
 
 The title of this order leads us to assign 
 its origin to Tuscany, in Italy ; and this 
 conjecture is strengthened by the inhabi- 
 ants of that country being admitted to be 
 the offspring of the Dorians . 
 
 The Tuscan order is characterized by 
 its plain and robust appearance, and is 
 therefore used only in works, where 
 strength and plainness are required : it has 
 been used with great effect and elegance 
 in that durable monument of ancient gran- 
 deur, Trajan’s Column, at Rome. But the 
 best modern example of this order is St. 
 Paul’s Church, Covent Garden, London. 
 
 No ancient remains of this order having 
 beem discovered with entablatures , it is only 
 
 * The Entablature is an ornament or assemblage 
 of parts, supported by a column over the capital : 
 each order of columns ‘has a peculiar entablature 
 divided into’ three principal parts, the architrave, 
 the frieze, and the cornice. See fig. page 175. ; 
 
 from the accounts given by Vitruvius, 
 that the form and ratio of its members can 
 be determined ; he allows seven diameters 
 for the height of the columns , and dimi- 
 nishes the upper part one fourth of half 
 the diameter ; the base is half a diameter 
 in height, one half of which is given to a 
 circular plinth , and the other to a torus*; 
 the capital is also half a diameter in height, 
 and one in breadth upon the abacus t ; the 
 height is divided into three parts, one of 
 which is given to the abacus , one to the 
 eschinus , and the third to the hypotrache- 
 lian and apophygis ; the architrave has two 
 faces, with an aperture between them of 
 about an inch and a half for the admission 
 of air to preserve the beams; the lower 
 face is vertical upon the edge of the top of 
 the column ; the frieze is plain and flat ; the 
 mutules, or ornamental parts of the cornice 
 project over the beams, equal to one fourth 
 of the height of the column. 
 
 DORIC ORDER. 
 
 * A torus or tore is a large semicircular moulding, 
 used in the base of a column. 
 
 + The abacus is the upper’m ember of’ a column, 
 which serves as a covering tojhe capital. 
 
THE ARTISAN. 
 
 189 
 
 This is the most ancient of the five 
 orders, and while employed by the Greeks, 
 was without a base; the surface of its 
 shaft is usually found worked into twenty 
 very flat flutes, meeting each other at an 
 edge, which is sometimes a little rounded ; 
 the upper member of the capital is a square 
 abacus or thin plinth, under which is a large 
 and elegantly formed ovolo, with a great 
 projection ; immediately under the ovolo, 
 there are three fillets or annulets, which 
 project from the continued line of the 
 under part of the ovolo, and have equally 
 recessed spaces between them; the flutings 
 of the column are terminated by the under 
 side of the last of these three fillets, and 
 either partly or entirely in a plane at right 
 angles with the axis of the column. 
 
 The architrave is composed of one verti- 
 cal face, with a band or fillet at its upper 
 edge; to the underside of this band are 
 suspended a small fillet and conical drops 
 or guttce , which, for their position, are 
 dependent upon the ordnance of the frieze. 
 
 The frieze consists of rectangular pro- 
 jections and recesses placed alternately. 
 The height of each projection or tablet is 
 rather more than its breadth. 
 
 The recesses are either perfectly or 
 nearly square. The tablets are each cut 
 vertically into two angular channels, with 
 two half ones on the extreme edges ; each 
 channel is formed by two planes meeting 
 at its bottom at a right angle, and each 
 forming an angle of 135 degrees with the 
 face of the tablet. 
 
 The upper ends of the channels are ter- 
 minated in various forms ; the tablets are, 
 from their channellings, named triglyphs; 
 in a direction immediately under each 
 triglyph, and equal to its breadth, a small 
 fillet is attached to the lower side of the 
 architrave crowning band, and from it de- 
 pend six guttae or drops, which are gene- 
 rally the frusta, or lower parts of cones 
 with their bases downwards, though they 
 are sometimes of a cylindrical shape. 
 
 The square spaces in the frieze between 
 the triglyphs, are named metopes, A and are 
 frequently decorated with sculptures. 
 
 The cornice is strongly marked by a 
 corona of great projection, forming a very 
 distinct separation between its upper and 
 lower parts ; and by having, below the 
 corona, and immediately over the tri- 
 glyphs, blocks, named mutules, which also 
 project considerably, and have the plane of 
 their soffits with an inclination from their 
 roofs towards the horizon, and these have 
 likewise guttae or drops depending from 
 their soffits. 
 
 The established proportions for the con- 
 struction of the doric order are the follow- 
 ing. Considering the diameter that of a 
 circle, at the lower end of a shaft, the 
 column is six diameters in height. The 
 
 thickness of the upper end of the shaft is 
 three-fourths of the lower, or it diminishes 
 ofie-fourth of the diameter. 
 
 The height of the Capital is half a di- 
 ameter. That of the ovolo, with the an- 
 nulets, and that of the abacus, are each 
 one-quarter of the upper diameter. The 
 annulets are one-fifth of one of the parts. 
 The horizontal dimensions of each face of 
 the abacus is six times its height. The 
 entablature is divided into four equal parts’; 
 the upper one is the height of the cornice ; 
 the remaining ones are divided equally 
 between the architrave and frieze. The 
 inner edge of the angular triglyph is placed 
 in a vertical line with the axis of the 
 column. The height of the triglyph is di- 
 vided into five equal parts; three of these 
 parts give the distance of its returning 
 face, and determine also that of the epis- 
 tyle, and consequently include the breadth 
 of the triglyph. The height of the capital 
 of the triglyph is one-seventh of its whole 
 height, and the capital of the metope one- 
 ninth. The breadth of the triglyph is di- 
 vided into nine equal parts, giving two to 
 each glyph , one to each semi-glyph, and 
 one to each of the three inter-glyphs. 
 
 The metopes are square. The height of 
 the cornice is divided into five equal parts ; 
 the lower is given to the fillet, the mutules, 
 and drops ; the next two to the corona ; 
 and the remaining two parts are subdi- 
 vided and disposed among the members. 
 
 The projection of the cornice is equal 
 to its height ; it is divided into four equal 
 parts, giving three to the projection of the 
 corona. 
 
 The number of annulets in the capital 
 vary from three to five ; and the number of 
 horizontal grooves, which separate the 
 shaft from the capital, vary from one to 
 three. 
 
 In the application of the Doric Order to 
 temples, the shafts of the columns are ge- 
 nerally placed upon three steps, which 
 are not proportioned like those inacommon 
 stair, but to the magnitude of the edifice. , 
 
 ON THE STRONGEST FORMS OF 
 COLUMNS, WALLS, &c. 
 
 The strongest form of a substance in- 
 cluded by horizontal surfaces, or cut out 
 of a horizontal plank, for supporting a 
 weight at its extremity, is that of a tri- 
 angle. The same form is also the stiffest. 
 For supporting a weight distributed uni- 
 formly throughout its length, the form 
 must be that of a parabola, with its con- 
 vexity turned inwards. 
 
 For a vertical plank, bearing a weight 
 at its extremity, the strongest and stiffest 
 form is that of a common parabola, with 
 its convexity outwards. If the weight is 
 equally divided, it must be a triangle. 
 
190 
 
 THE ARTISAN. 
 
 To support its own weight, it must have 
 for its outline a common parabola, with its 
 convexity inwards. If such a plank were 
 supported by its lateral adhesion only, its 
 outline must be a logarithmic curve, to 
 sustain its own weight. 
 
 A horizontal column turned in a lathe, 
 or having all its transverse sections simi- 
 lar, must have its outline a cubical para- 
 bola, convex outwards, in order to support 
 the greatest weight at its extremity. The 
 same form is also the stiffest. To support 
 a weight equally distributed through the 
 length, the curve must be a semicubical 
 parabola. To support its own weight, the 
 outline must be a common parabola, con- 
 vex towards the axis, having its vertex at 
 the extremity. 
 
 A triangular prism fixed at one end, 
 with its edge uppermost, is weaker than if 
 its depth were reduced to eight ninths, by 
 cutting away the edge. With a certain 
 force, such a beam would crack at its edge, 
 and not break off. 
 
 If a beam, supported at both ends, have 
 all its transverse sections similar, the two 
 portions must have their outlines cubic 
 parabolas. For a weight equally divided, 
 or applied to any point at pleasure, the 
 cube of the diameter must be as the square 
 of the segments. 
 
 A wall, turning a vertical face to the 
 wind, ought to have the other face an in- 
 dined plane, in order to resist the force of 
 the wind to the greatest advantage, if 
 made of cohesive materials ; but if loose 
 materials, it ought to be convex and para- 
 bolic behind. 
 
 A cohesive wall, supporting a bank of 
 earth or a fluid with its vertical face, 
 ought to be concave behind, in the form of 
 a semicubical parabola, with its vertex at 
 the top of the wall: but if the materials 
 are loose, the back of the wall should be 
 an inclined plane. 
 
 A pillar or column of cohesive materials, 
 formed to resist the wind, must be a cone 
 or a pyramid ; of loose materials, a para- 
 bolic conoid; to support its own weight 
 only, a pillar must have the logarithmic 
 curve for its outline. 
 
 A mortise hole should be taken out of 
 the middle of abeam, not from one side; 
 but if it is on the concave side, and is 
 filled up with hard wood, it does not 
 diminish the strength. For similar rea- 
 sons, a piece spliced on, to strengthen a 
 beam, should be on the convex side. If a 
 cylinder is to be supported at two points 
 with the least strain, the distance between 
 the points should be *5858 of the length. 
 
 If a piece be spliced on a divided beam, 
 equal in depth to half the depth of the 
 beam, the strength is greater than that of 
 the entire beam, in the ratio of 1 to 1*054, 
 very nearly. 
 
 Coulomb found the lateral cohesion of 
 brick and stone only - 4 \ more than the 
 direct cohesion, which, for stone, was 215 
 pounds for a square inch ; for good brick 
 from 280 to 300. Supposing this lateral 
 cohesion constant, a pillar will support 
 twice as much as it will suspend, and its 
 angle of rupture will be 45°. From the 
 same supposition it may be inferred, that 
 the strongest form of a body of given thick- 
 ness for supporting a weight, is that of a 
 circle, since the power of the weight in the 
 direction of every section varies as the 
 length of that section ; and the strength is 
 therefore equal throughout the substance. 
 But if the cohesion is increased, like 
 friction, by pressure, and supposing, with 
 Amantons, that this increase, for brick, is 
 three fourths of the weight, the plane of 
 rupture of a prismatic pillar will form, 
 according to Coulomb, an angle of 63° 26' 
 with the horizon, and the strength will be 
 doubled. On both suppositions the strength 
 is simply as the section. 
 
 ON THE INTENSITY OF WIND. 
 
 
 Force on a 
 
 
 Miles 
 
 square foot 
 
 
 in lh. 
 
 in pounds 
 av.jby cal- 
 
 Character. 
 
 
 culation. 
 
 
 1 
 
 0*005 
 
 Hardly perceptible. 
 
 2 
 
 0*020 
 
 Just perceptible. 
 
 3 
 
 0 049 ) 
 
 
 4 
 
 0*070 \ 
 
 Gentle winds. 
 
 5 
 
 0*123 3 
 0*130 
 
 A gentle wind. 
 
 
 0*260 
 
 Pleasant wind. 
 
 10 
 
 0*492 
 
 Pleasant brisk gale. 
 
 
 0*521 
 
 Fresh breeze. 
 
 15 
 
 1*107 
 
 Brisk gale. 
 
 20 
 
 1*968 
 
 Very brisk. 
 
 
 2*604 
 
 Brisk gale. 
 
 25 
 
 3*075 
 
 Very brisk. 
 
 30 
 
 4*429 
 
 High wind. 
 
 35 
 
 5*208 ) 
 6*027 J 
 
 High wind. 
 
 40 
 
 7*873 
 
 Very high. 
 
 45 
 
 9*963 
 
 Great storm. 
 
 
 10*416 
 
 Very high. 
 
 50 
 
 12*300 
 
 Storm, or tempest. 
 
 
 15*625 
 
 Storm. 
 
 60 
 
 17*715 
 
 Great Storm. 
 
 
 20-833 
 
 Great Storm. 
 
 66 
 
 21*435 
 
 Great Storm. 
 
 
 26*041 
 
 Very great storm. 
 
 80 
 
 31*490 
 
 Hurricane. 
 
 
 31*250 
 
 Hurricane. 
 
 
 36*548 
 
 Great hurricane. 
 
 
 41*667 
 
 Very great hurricane. 
 
 
 46*875 
 
 Most violent hurricane. 
 
 100 
 
 49*200 
 
 Hurrricane that tears up 
 
 
 52*083 
 
 trees and throws down 
 
 
 57*293 
 
 buildings. 
 
 109 
 
 58*450 
 
 Observed by Rochon. 
 
THE ARTISAN. 
 
 191 
 
 TO PREPARE STARCH FROM 
 POTATOES. 
 
 Grind a quantity of potatoes into a pulp 
 by rubbing them on a plate of tin in which 
 a number of holes have been made, then 
 put them into a hair sieve, and pour cold 
 water over them as long as a milky liquid 
 passes through. This liquid is to be re- 
 ceived into a basin, and when a whitish 
 powder has settled at the bottom, the 
 liquid is to be poured off it, and the 
 powder repeatedly washed with spring 
 water, until it become perfectly white. 
 When the last liquor has been poured off, 
 the basin is to be placed in a warm place 
 till the starch be perfectly dry. 
 
 Observation. — Twenty pounds of good 
 potatoes, treated in this way, generally 
 yields about four pounds of starch. 
 
 TO ETCH DESIGNS ON GLASS. 
 
 Cover the glass all over with a thin coat 
 of bees’ wax, and trace the design with an 
 etching needle; then spread the whole 
 over as uniformly as possible with fluor 
 spar (Derbyshire spar) to the depth of an 
 eighth of an inch, and when this is done, 
 pour sulphuric acid, diluted with three 
 times its weight of water, upon the® spar. 
 After the acid has remained upon it three 
 or four hours it is to be poured off, and 
 the glass washed with oil of turpentine ; 
 the etching will then appear, and the parts 
 that were covered with the wax will have 
 remained untouched. 
 
 Observation.-— By this means glass ves- 
 sels are graduated and ornamented very 
 easily. 
 
 SOLUTIONS OF QUESTIONS. ~ 
 
 The content of the chain is 3 x 3 — 9 
 solid inches, and the specific gravity of 
 gold is 19*300, which is also the ounces that 
 one cubic foot (1728 inches) of gold weighs* 
 Hence, 1728 : 19300 : : 9 : 100-521 oz. gold. 
 
 1728 : 1000 : : 9 : 5 21 oz. water 
 
 Weight of gold in water 95*311 
 
 And taking the specific gravity of silver at 
 
 10450, 
 
 10450 : 1728 : : 14§ : 2*4 in. nearly, which, 
 multiplied by 8*85, the difference between 
 the specific gravity of gold and silver, 
 
 * See “ Artisan,” page 25 and 26. 
 
 gives 21*24 oz. ; and this subtracted from 
 95*311 oz. (the weight, supposing the 
 whole chain gold) leaves the weight of the 
 chain 74*07 ounces. And 19300 : 1728 : : 
 74*07 : 6*632 inches pure gold, which, 
 added to 2*4 inches of silver, gives 9*032 
 cubic inches, the bulk of the chain, or the 
 number of cubic inches of water displaced ; 
 hence, 9*032 — 9 = *032, and this divided 
 by 9, the area of the bottom of the vessel 
 gives 00355 in. — the additional height to 
 which the water would rise. 
 
 In this question the words “ in water,” 
 ought to be omitted. 
 
 In the solution sent us by the proposer 
 of this question, the weight of an inch of 
 gold is taken only at 9*962 oz., and one 
 of silver at 5*556. Now the former i 3 
 11*17, &c. and the latter 6*047. This mis- 
 take has led him to a wrong conclusion 
 
 We also received a solution to this 
 question from a Correspondent, who signs 
 S., but he has not fully understood the 
 question. 
 
 Quest. 22, answered by J. Millward, 
 Hammersmith . 
 
 Let A B be the given finite straight line 
 required to be trisected; then on AB 
 
 C 
 
 describe an equilateral triangle ABC; 
 bisect the angle at B by the line B D, and 
 bisect B D in E ; from C through E draw 
 C E, and produce it till it meet A B in F • 
 take any point G in B C, and through G 
 draw G H parallel to B F, and through 
 F draw F H parallel to B G, meeting each 
 other in H ; join F G, and through H draw 
 H K parallel to G F ; and the given finite 
 straight line A B is trisected, or divided 
 into the three equal parts B F, FK, KA. 
 
192 
 
 THE ARTISAN. 
 
 * Demons. Join G K, and through H 
 draw H A parallel to G K ; then because 
 the figures H A K G, H K F G, and H F B G 
 are parallelograms, the opposite sides of 
 which are equal to one another, (Euc. 1 
 and 84,) therefore the lines B F, F K, K A 
 are respectively equal to the line G H, and 
 therefore B F, F K, K A are equal to one 
 another. Euc. Axiom 1. 
 
 This question might have been solved 
 more simply ; for by bisecting the angles 
 B A C, and ABC, and drawing H K, 
 parallel to A C, and H F parallel to B C, 
 and the thing was done, and might easily 
 be demonstrated to be so. 
 
 This question was also solved by J. B. 
 of Oldham. 
 
 5 Quest. 23, answered by G. G. C. (the 
 proposer.) 
 
 If a pendulum vibrate in a circle, and if 
 g be the velocity acquired by a body de- 
 scending freely, in one second of time, p 
 the ratio of the circumference of a circle 
 to its diameter, and l the length of the pen- 
 dulum vibrating in one second, in any 
 latitude, then it may be demonstrated that 
 g — p 2 1 Hence, in the present example,* 
 
 (3*1416) 3 X the length of the 
 
 pendulum in feet at the Pole, gives 32*24 
 feet, for the velocity acquired by a heavy 
 body falling freely in one second at the 
 Pole. 
 
 By the same theorem g, or the force of 
 gravity at latitude 45°, in the present ex- 
 ample, is 32*158 ; and at the equator 
 32*076. 
 
 Quest. 24, answered by G. G. C. 
 
 B 
 
 * The number 3*1416 is the circumference of a 
 circle, whose diameter is 1. 
 
 Let A and B be the given points, and 
 D E the line given in position ; from A and 
 B let fall the perpendiculars A D and B E, 
 and produce AD to C, making C D equal 
 to DA. Join BC cutting DEinP, and 
 also join AP* then AP and PB, shall 
 be less than any other two lines AP and 
 PB drawn from A and B to any other 
 point P in the line D E. 
 
 Demon. Because A D is equal to D C, 
 and DP common to the two triangles 
 A D P and C D P, and the angles at D 
 right angles, the sides A P and C P are 
 equal. 
 
 In the same manner it may be shown, 
 that A P and PC are equal. Hence AP 
 and B P are together equal to B C, and 
 A P and B P are equal to C P and P B. 
 Now (Eucl. 1 and 20) B C is less than 
 B P and P C, and therefore A P and P B 
 are less than AP and P B. 
 
 This question was solved nearly in the 
 same manner, by Mr. John Holroyd, 
 Teacher, Oldham . 
 
 QUESTIONS FOR SOLUTION. 
 
 Quest. 28, proposed by Alfred Equality. 
 
 In the city of Pisa in Tuscany, is a cir- 
 cular building called the Hanging-tower, 
 which is said to have been 188 feet in 
 height, its inclination from the perpen- 
 dicular is such, that the top projects 16 
 feet over the base, or horizontal plane, 6 
 feet of the tower having sunk on one side 
 below its original site. Required the dia™ 
 ameter of the tower ? 
 
 Quest. 29, proposed by Mr. G. FutVoye, 
 High-street , Mary-le-hone . 
 
 What will be the diameter of a globe, 
 when the solidity and superficial content 
 are expressed by the same number ? 
 
 Quest. 30, proposed by J. B. of Oldham. 
 
 What is the solid content of a cube, the 
 greatest line that can be drawn in it being 
 9 inches ? 
 
d© -m, 
 
 SU» BAC0ZT 
 
 
THE ARTISAN. ' 
 
 193 
 
 MEMOIR OF THE LIFE OF FRANCIS BACON, 
 
 LORD VERULAM, DISCOUNT ST. ALBAN’S. 
 
 Francis Bacon, Lord High Chancellor 
 ofJEagiand under King James I. was son 
 of Sir Nicholas Bacon, lord keeper of the 
 great seal, in the reign of Queen Elizabeth, 
 by Anne, one of the daughters of Sir 
 Anthony Cooke, and eminent for her skill 
 in the Greek, Latin, and Italian languages. 
 He was born at York House, in the Strand, 
 on the 22d January, 1560. He gave early 
 proofs of a surprising strength and preg- 
 nancy of genius, and when a mere boy, 
 was distinguished by persons of worth and 
 dignity for something far beyond his years. 
 Queen Elizabeth, a very acute discerner 
 of merit, was so charmed with the solidity 
 of his sense and the gravity of his beha- 
 viour, that she would often call him “ her 
 young Lord keeper,” an office which he 
 eventually reached, although not in her 
 reign. When qualified for academical 
 studies, he was sent to the University of 
 Cambridge, where, June 10, 1573, he was 
 entered of Trinity College, under Dr. John 
 Whitgift, afterwards Archbishop of Can- 
 terbury. Such was his progress under 
 this able tutor, and such the vigour of his 
 intellect, that before he had completed his 
 sixteenth year, he had not only run through 
 the whole circle of the liberal arts, as they 
 were then taught, but began to perceive 
 the impel fections of the reigning philoso- 
 phy, and meditated that change of system 
 which has since immortalized his name, 
 and has placed knowledge upon its most 
 firm foundation. Extraordinary as this 
 may appear, he was heard, even at that 
 early age, to object to the Aristotleian 
 system, the only one then in repute, and 
 to say, that his “ exceptions against that 
 great philosopher, were not founded upon 
 the worthlessness of the author, to whom 
 he would ever ascribe all high attributes, 
 but for the unfruitfjilness of the way : being 
 a philosophy only for disputations and con- 
 tentions, but barren in the production of 
 works for the benefit of the life of man.” 
 
 He went to France with Sir Amias Pow- 
 let, then the queen’s ambassador at Paris, 
 who intrusted him with a commission to 
 the queen, which he discharged with great 
 approbation, and returned again to France. 
 During his absence, his father died in 
 1579; upon which he returned to England, 
 and applied himself to the study of the 
 common-law, which he resolved upon as 
 his profession, though his inclinations led 
 him much more strongly to affairs of state. 
 He was appointed one of the queen’s coun. 
 Vol. I.— No. 13. 
 
 cil when he was but twenty-eight. And 
 to her he dedicated his Elements and 
 Maxims of the Common-law, in 1596, 
 though they were not printed till after his 
 death. In 1597 he published a work of 
 another kind, entitled, “ Essays, or Coun- 
 sels Civil and Moral.” This work is well 
 known, and has been often reprinted. The 
 author appears to have had a high opinion 
 of its utility ; and of the excellent morality 
 and wisdom it inculcates, there probably 
 never has been but one opinion. Some of 
 these essays had been handed about in 
 manuscript, which he assigns as a reason 
 why he collected and published them in a 
 correct form. 
 
 In the last ten years of the queen’s reign 
 he made a great figure in the House of 
 Commons, and there he applied himself 
 to politics : so much so, that the Queen 
 and Lord Treasurer Burleigh employed 
 his head and hand in matters of state. He 
 was in his younger years attached to the 
 interests of the Earl of Essex, whom he 
 endeavoured to dissuade from those rash 
 measures which proved his ruin. About 
 1605 he married Alice, daughter of Bene- 
 dict Barnham, Esq. alderman of London, a 
 lady who brought him an ample fortune, 
 but by whom he never had any children. 
 
 Upon the accession of King James he 
 was soon raised to considerable honours. 
 In the first year of his reign he was 
 knighted at W hitehall, and next year was 
 made one of the King’s counsel learned in 
 the law. He wrote in favour of the union 
 of the two kingdoms of Scotland and Eng- 
 land, which the King so passionately de- 
 sired. In 1607 he was appointed solicitor- 
 general. In 1611 he was made joint-judge 
 with Sir Thomas Vavasor, then knight- 
 marshal of the knight-marshal’s court ; and 
 in 1613 he succeeded Sir Henry Hobart as 
 Attorney-general ; in 1616 he was sworn 
 one of the Privy Council. He then applied 
 himself to reducing and recomposing the 
 Laws of England. He distinguished him- 
 self when attorney- general by his endea- 
 vours to restrain the custom of duelling 
 then very frequent. In 1617 he was ap - 
 pointed Lord-keeper of the Great Seal, 
 and in 1618 he was made Lord Chancellor 
 of England, and created Lord Verulam. 
 
 In the midst of these honours and a mul- 
 tiplicity of business, he did not forget his 
 beloved philosophy. In October, 1620, he 
 published his great work, entitled. “ No- 
 vum Organum the design of which was, 
 
 () 
 
194 
 
 THE ARTISAN. 
 
 to advance a more perfect method of using 
 tire rational faculty than men were before 
 acquainted with, in order to raise and im- 
 prove the understanding, as far as its pre- 
 sent imperfect state admits, and enable it 
 to conquer and interpret the difficulties 
 and obscurities of nature. This work his 
 majesty, (to whom he sent a copy,) re- 
 ceived as graciously as he could wish, and 
 wrote him a letter respecting it, which cer- 
 tainly does honour to both their memories. 
 He received also the compliments of many 
 learned men on the same subject, and had 
 every reason to be satisfied with the gene- 
 ral reception of a work, which cost him so 
 much time and pains. Such is said to 
 have been his anxiety for its perfection, 
 that he revised and altered twelve copies 
 before he brought it to the state in which 
 it was published. 
 
 January 27, 1621, he was advanced to 
 the dignity of Viscount St. Alban’s, and 
 appeared with the greatest splendour at 
 the opening of the session of parliament on 
 the 30th of that month. But he was soon 
 after surprised with a reverse of fortune. 
 For about the 12th of March following, a 
 committee of the House of Commons was 
 appointed to inspect the abuses of the 
 Courts of Justice. The first thing they 
 fell upon was bribery and corruption, of 
 which the Lord Chancellor was accused 
 by Aubrey and Egerton, who affirmed, 
 that they had procured money to be given 
 to him, to promote their causes depending 
 before him. On Monday, April 29, he 
 sent his confession and submission to the 
 House of Lords, in which he confessed 
 some facts, denied some, and palliated 
 others. The lords agreed to sequester the 
 seal ; and on May 3d, the Lord Chief Jus- 
 tice pronounced the following sentence: 
 “ That the Lord Chancellor should pay a 
 fine of £40,000. and be imprisoned in the 
 Tower, during the King’s pleasure ; that 
 he should be for ever incapable of any 
 office, place, or employment in the state, 
 and never to sit in Parliament, or come 
 within the verge of the Court.” There is 
 a variety of opinions concerning his guilt 
 of the points charged against him. He 
 retired after a short imprisonment, from 
 the engagement of an active life, which he 
 had been called to much against his genius, 
 to the shade of a contemplative one, w hich 
 lie had always loved. The king remitted 
 his fine, and granted it to some of his lord- 
 ship’s friends, in order to give him a little 
 respite from creditors, to whom he is said to 
 have paid £8000 after his fall. “ And the 
 poor remains (as he tells us in one of his 
 letters) which he had of his former for- 
 tunes in plate and jewels, he had paid to 
 poor men to whom he owed, scarcely leav- 
 
 ing himself a convenient subsistence.” In 
 1624, in a most pathetic letter, he implored 
 the king to grant a total remission of his 
 sentence, in order that the blot of ignominy 
 which he laboured under might be re- 
 moved. The request was granted him : 
 for we find he was summoned to Parlia- 
 ment in the first year of King Charles I. 
 It appears from the works he composed 
 during his retirement, that his thoughts 
 were still free, vigorous, and noble. In his 
 retirement he composed the greatest part 
 of his English and Latin works. He was 
 taken ill at the Earl of Arundel’s house at 
 Highgate, and there expired on the 9th of 
 April, 1626, in the 66th year of his age. 
 He was buried in St. Michael’s church, at 
 St. Alban’s, according to the direction of 
 his last will, and had a monument of white 
 marble erected to him by Sir Thomas 
 Meautys, who had formerly been his secre- 
 tary, and afterwards Clerk of the Privy 
 Council, under two kings. 
 
 If we contemplate the personal character 
 and mental powers of Lord Bacon, he will 
 appear to be one of the greatest and wisest 
 men that ever contributed to human know- 
 ledge. “ The only thing,” says Brucker, 
 “ to be regretted in the writings of Bacon 
 is, that he has increased the difficulties 
 necessarily attending his original and pro- 
 found researches, by too freely making use 
 of new terms, and by loading his arrange- 
 ment with an excessive multiplicity and 
 minuteness of divisions. But an attentive 
 and accurate reader, already not unac- 
 quainted with philosophical subjects, will 
 meet with no insuperable difficulties in 
 studying his works ; and, if he be not a 
 wonderful proficient in science, will reap 
 much benefit as well as pleasure from the 
 perusal. In fine,” adds this judicious 
 writer, “ Lord Bacon, by universal con- 
 sent of the learned world, is to be ranked 
 in the first class of modern philosophers.” 
 He unquestionably belonged to that supe- 
 rior order of men, who, by enlarging the 
 boundaries of human knowledge, have 
 been benefactors to mankind ; and he may 
 not improperly be styled, on account of the 
 new track of science which he employed, 
 the Columbus of the philosophical world. ; 
 and it may be jnstly said, that his learning 
 and knowledge was a century in advance 
 of the times in which be lived. 
 
 In his will he has this remarkable pas- 
 sage, For my name and memory I leave 
 it to men’s charitable speeches, and to 
 foreign nations, and the next ages.” 
 
 His works, collected into five vols. 4to. 
 were beautifully and accurately printed by 
 Bowyer and Strahan, in 1765, and have 
 been lately reprinted in 8vo. 
 
THE ARTISAN. 
 
 195 
 
 PNEUMATICS. 
 
 STEAM ENGINE. 
 
 The steam engine is perhaps the most 
 magnificent effort of mechanical power ; it 
 has undergone successive changes, and it 
 appears to have been brought very near to 
 perfection by the improvements of the late 
 Mr. Watt. The pressure of steam was first 
 applied by the Marquis of Worcester, and 
 afterwards by Savery, to act immediately 
 on the surface of water contained in a close 
 vessel, and this water was forced, by the 
 elasticity of the steam, to ascend through a 
 pipe, as in the following figure, which re- 
 presents the original steam engine as con- 
 structed by Mr. Savery. 
 
 The vessel A being filled with steam 
 from the boiler B, and the stopcock being 
 turned, the steam cools and is condensed, 
 and the water is foxxed into its place by 
 the pressure of the atmosphere, through 
 the valve C: the steam is then readmitted, 
 and forces the water to ascend through the 
 valve D and the pipe D E. The vessel F 
 acts alternately with A. 
 
 A great degree of heat, however, was 
 required for raising water to any consider- 
 able height by this machine : for, in order 
 that steam may be made capable of sup- 
 porting, in addition to the atmospherical 
 pressure, a column of 34 feet of water, its 
 temperature must be raised to 248° of Fah- 
 renheit, and for a column of 68 feet, to 
 271°; such a pressure, also, acting on the 
 internal surface of the vessels, made it ne- 
 cessary that they should be extremely 
 strong; and the height to which water 
 o 2 
 
 could be drawn up from below, when the 
 steam was condensed, was limited to 33 or 
 34 feet. However a still greater objec- 
 tion was, the great quantity of steam ne- 
 cessarily wasted, on account of its coming 
 into contact with the cold water and the 
 receiver, the surfaces of which required to 
 be heated to its own temperature, before 
 the water could be expelled; hence a 
 tenth or a twentieth part only of the steam 
 produced could be effective; and there 
 would probably have been a still greater 
 loss, but for the difficulty with which heat 
 is conducted downwards in fluids. These 
 inconveniences were, in a great measure, 
 avoided in Newcomen’s engine, where the 
 steam was gradually introduced into a cy- 
 linder, and suddenly condensed by a jet of 
 water, so that the piston was forced down 
 with great violence by the pressure of the 
 atmosphere, which produced the effective 
 stroke : this effect was, however, partly 
 employed in raising a counterpoise, which 
 descended upon the readmission of the 
 steam, and worked a forcing pump in its 
 return, when water was to be raised. This 
 engine is represented by the following 
 figure. 
 
 Here the steam being admitted into the 
 cylinder A below the piston, the weight B 
 is allowed to descend : a jet of water is 
 then admitted by the pipe C, which con- 
 denses the steam, and the pressure of the 
 atmosphere then depresses the piston : a 
 part of this water is admitted by the pipe 
 D into the boiler, in order to keep it suffi- 
 ciently full. 
 
 Though this manner of condensing the 
 steam was rapid, yet it was neither instan- 
 taneous nor complete, for the water injected 
 into the cylinder had its temperature con- 
 siderably raised by the heat emitted by 
 the steam during its condensation ; it could 
 only reduce the remaining steam to its own 
 temperature, and at this temperature it 
 might still retain a certain degree of elas- 
 ticity ; thus, at the temperature of 180°, 
 
196 
 
 THE ARTISAN. 
 
 steam is found to be capable of sustaining 
 about half the pressure of the atmosphere, 
 so that the depression of the piston must 
 have been considerably retarded by the re- 
 maining elasticity of the steam, when the 
 water was much heated. The water of 
 the jet was left off when the piston was 
 lowest, and was afterwards pumped up to 
 serve the boiler, as it had the advantage of 
 being already hot. In this, as well as in 
 other steam engines, the boiler is furnished 
 with a safety valve, which is raised when 
 the force of the steam becomes a little 
 greater than that of the atmospheric pres- 
 sure; and it is supplied with water by 
 means of another valve, which is opened, 
 when the surface of the water within it 
 falls too low, by the depression of a block 
 of stone, which is partly supported by the 
 water. 
 
 The alternations of heat and cold to 
 which the cylinder was exposed by the jet 
 of cold water, and by exposure to the air, 
 in the old engines, reduced their power 
 nearly to half its real value, so that the 
 moving force, instead of amounting to 14 lb. 
 on every square inch of the area of the 
 piston, was reduced to little more than 
 71b. 
 
 The late justly celebrated Mr. Watt 
 avoided this inconvenience, by performing 
 the condensation in a separate vessel, into 
 which a small jet is flowing without inter- 
 mission; and by introducing the steam 
 alternately above and below the piston, 
 the external air is wholly excluded ; the 
 piston rod working in a collar of leather, 
 so that the machine has a double action, 
 somewhat resembling that of Lahire’s 
 double pump ; and the stroke toeing equally 
 effectual in each direction, the same cylin- 
 der, by means of an increased quantity of 
 steam, performs twice as much work as in 
 the common engine. We might also em- 
 ploy, if we thought proper, a lower tem- 
 perature than that qt which water usually 
 boils, and work in this manner with a 
 smaller quantity of steam ; but there would 
 be some difficulty in completely preventing 
 the insinuation of the common air. On the 
 other hand, we may raise the fire so as to 
 furnish steam at 220° or more, and thus 
 obtain a power somewhat greater than that 
 of the atmospheric pressure; and this is 
 found to be the most advantageous mode of 
 working the engine ; but the excess of the 
 force above the atmospheric pressure, can- 
 not be greater than that which is equiva- 
 lent to the column of water descending to 
 supply the boiler, since the water could 
 not be regularly admitted, in opposition to 
 such a pressure. The steam might also be 
 allowed to expand itself within the cylin- 
 der for some time after its admission, and 
 in this manner it appears from calculation, 
 
 that much more force might be obtained 
 from it than if it were condensed in the 
 usual manner, as soon as its adnfission 
 ceases; but the force of steam thus ex- 
 panding, is much diminished by the cold, 
 which always accompanies such an ex- 
 pansion, and this method would be liable 
 to several other practical inconveniences. 
 
 The peculiarities of Mr. Watt’s construc- 
 tion require also some other additional 
 arrrangements ; thus, it is necessary to 
 have a pump, to raise not only the water 
 out of the condenser, but also the air, 
 which is always extricated from the water 
 during the process of hoiling. If the water 
 employed has been obtained from deep 
 wells or mines, it contains more air than 
 usual, and ought to be exposed for some 
 time in an open reservoir before it is used ; 
 for it appears that the quantity of air, 
 which can be contained in water, is nearly 
 in proportion to the pressure to which it is 
 subjected. The admission of the steam 
 into the cylinder is regulated by the action 
 of a double revolving pendulum. The 
 piston is preserved in a situation very 
 nearly vertical, by means of a moveable 
 parallelogram, fixed on the beam, which 
 corrects its curvilinear motion by a con- 
 trary curvature. In the old engines, a 
 chain working on an arch was sufficient, 
 because there was no thrust upwards. 
 When a rotatory motion is required, it may 
 be obtained either by means of a crank, or 
 of a sun and planet wheel, with the assis- 
 tance of a fly wheel; this machinery is 
 generally applied to the opposite end of 
 the beam ; but it is'sometimes immediately 
 connected with the piston, and the beam is 
 not employed. The cylinder is usually 
 inclosed within a case, and the interval is 
 filled with steam, which serves to confine 
 the heat very effectually. 
 
 When the water which produces the 
 condensation of the steam is to be raised 
 from a great depth, a considerable force is 
 sometimes lost in pumping it up. Hence, 
 Mr. W att proposed to employ steam at a 
 very high temperature, and to let it escape 
 when its elasticity is so reduced by expan- 
 sion, as only to equal that of the atmos- 
 phere. The air pump is also unnecessary 
 in this construction. But there must al- 
 ways be a very considerable loss of steam, 
 and though the expense of fuel may not be 
 increased quite in the same proportion as 
 the elasticity of the steam, yet the differ- 
 ence is probably inconsiderable. 
 
 But previous to considering this subject, 
 and that of the modern high pressure en- 
 gines, we shall here give a representation 
 and description of Mr. Watt’s single acting 
 engine. 
 
 The following is a representation of this 
 engine. 
 
THE ARTISAN. 
 
 MR. WATT’S STEAM ENGINE. 
 
 197 
 
 f The steam, which is below the piston, is 
 suffered to escape into the condenser A by 
 the cock B, which is opened by the rod C, 
 and at the same time, the steam is admitted 
 by the cock D into the upper part of the 
 cylinder ; when the piston has descended, 
 the cocks E and F act in a similar manner 
 in letting out the steam from above and ad- 
 mitting it below the piston. The jet is 
 supplied by the water of the cistern G, 
 which is pumped up at H from a reservoir : 
 it is drawn out, together with the air ; that 
 is, extricated from it by the fair pump I, 
 which throws it into the cistern K, from 
 whence the pump L raises it to the cistern 
 
 M ; and it enters the boiler through a valve, 
 which opens whenever the float N descends 
 below its proper place. The pipes O and 
 P serve also to ascertain the quantity of 
 water in the boiler. The piston rod is 
 confined to a motion nearly rectilinear by 
 the frame Q* ; the fly wheel R is turned by 
 the sun and planet wheel S and T ; and 
 the strap U turns the centrifugal regulator 
 W, which governs the supply of steam by 
 the valve or stopcock X. 
 
 * The nature of this motion will be fully explained, 
 in treating of the ^ different parts of the steam 
 engine. 
 
 OPTICS. 
 
 UNUSUAL REFRACTION OF THE ATMOSPHERE. 
 
 Although the phenomena of unusual re- 
 fraction have been often observed by astro- 
 nomers and navigators, yet they do not 
 seem to have attracted particular notice 
 till the year 1797. The unusual elevation 
 of coasts, mountains, and ships, have been 
 long known under the name of looming ; 
 and the same phenomena, when accom- 
 panied with inverted images, have been 
 distinguished in France by the name of 
 mirage. 
 
 Mr. Huddart seems to have been the 
 first person who described an inverted 
 image beneath the real objects ; he accounts 
 for this, and other phenomena of elevation, 
 by supposing that, in consequence of the 
 evaporation of the water, the refractive 
 
 power of the air is not greatest at the sur- 
 face of the sea, but at some distance above 
 it, increasing gradually from the surface 
 of the sea to a line, which he calls the line 
 of maximum density , and thence diminish- 
 ing gradually till it becomes insensible. 
 
 He then shows, that, in passing through 
 such a medium, the rays of light would 
 move in curve lines convex upwards, when 
 they passed above the line of maximum 
 density, and convex downwards when they 
 passed below that line. 
 
 Hence, two pencils from the object will 
 arrive at the eye, which will produce an 
 inverted image of the object. 
 
 In the year 1798, the Rev. Dr. Vince, of 
 Cambridge, made a series of interesting ob~ 
 
THE ARTISAN. 
 
 serrations at Ramsgate, on the unusual re- 
 fraction of the atmosphere. He made his 
 observations with a terrestrial telescope 
 magnifying between thirty and forty times, 
 when the height of the eye was about 25 
 feet above the surface of the sea. Some- 
 times the height of the eye was 80 feet ; 
 but this produced no variation in the phe- 
 nomena. 
 
 On the 1st of August, between four and 
 eight o’clock p.M.he saw the topmast of a 
 ship as at A, 
 
 above the horizon x y of the sea : at the 
 same time, he also discovered in the field 
 of view two complete images, B, C, of the 
 ship in the air, vertical to the ship itself, B 
 being inverted , and C erect , having their 
 hulls joined. As the ship receded from 
 the shore, less and less of it’s mast became 
 visible ; and as it descended , the images B 
 and C ascended ; but as the ship did not 
 recede below the horizon, Dr.Vince did not 
 observe at what time, and in what order, 
 the images vanished. 
 
 He then directed his telescope to another 
 
 ship A, 
 
 whose hull was just in the horizon x y, and 
 he observed a complete inverted image B, 
 the mainmast of which just touched that of 
 the ship itself. In this case there was no 
 second image as before. While the ship A 
 
 moved along, B followed its motion, with- 
 out any change of appearance. 
 
 Dr. Vince observed a number of other 
 ships, which produced variously formed 
 images ; but our limits will not permit us 
 to give a particular description of them, 
 nor of similar appearances which have 
 been observed on various occasions at 
 land.* 
 
 We shall, however, notice a few of the 
 experiments made by Dr. Wollaston, to il- 
 lustrate his theory of the cause of unusual 
 refraction. 
 
 According to this ingenious philosopher, 
 the varying density of the atmosphere is the 
 principal cause of the singular appear- 
 ances which we have just mentioned ; and 
 from a number of interesting experiments, 
 he found, that the results were perfectly 
 conformable to this hypothesis. 
 
 He took a square phial, and poured a 
 small quantity of clear syrup into it, and 
 above this an equal quantity of ivater r 
 which gradually incorporated with the 
 syrup, between the pure water and the 
 pure syrup. The word syrup written on a 
 card, and held behind the bottle, appeared 
 erect through the pure syrup ; but when 
 seen through the visible medium of the 
 syrup and water, it appeared inverted with 
 an erect image above. 
 
 Dr. W ollaston then put nearly the same 
 quantity of rectified spirit of wine above 
 the water, and he observed a similar ap- 
 pearance; only in this case, the true place 
 of the object was seen uppermost, and 
 the inverted and erect images below. 
 
 When the variations of density are great, 
 the object may be held close to the phial ; 
 but when they become more gradual, the 
 object is only elongated, and in order to be 
 seen inverted, must be held one or two 
 inches behind the phial. 
 
 By examining an oblique line seen in 
 this way, he found, that the appearances 
 continue many hours even with spirit of 
 wine; with syrup , two or three days ; with 
 sulphuric acid, four or five; and still longer 
 with a solution of gum-arabic. 
 
 Dr. Wollaston next heated a poker red 
 hot, and looked along the side of it at a 
 paper ten or twelve feet distant. A per- 
 ceptible refraction took place at a distance 
 of three-eighths of an inch from it. A 
 letter, more than three-eighths of an inch 
 distant, appeared erect as usual ; at a less 
 distance there was a faint reversed image 
 of it ; and still nearer the poker was a se- 
 cond image erect. 
 
 Although the experimental method of 
 illustrating the phenomena of unusual re- 
 fraction, as given by Dr. Wollaston, is in 
 
 * This subject has been fully treated by Dr. 
 Wollaston, in the Philosophical Transactions for 
 1310 . 
 
THE ARTISAN. 
 
 199 
 
 every respect an excellent one, yet the em- 
 ployment of different fluids does not repre- 
 sent the case which actually exists in na- 
 ture. 
 
 The method employed by Dr. Brewster 
 seems more agreeable to nature. 
 
 His method consists in holding a heated 
 iron above a mass of water, bounded by pa- 
 rallel plates of glass. 
 
 As the heat descends through the fluid, a 
 regular variation of density is produced, 
 which gradually increases from the sur- 
 face to the bottom. 
 
 If the heated iron be withdrawn, and a 
 cold body substituted in its place, or even 
 the air allowed to act alone, the superfi- 
 cial strata of water will give out their heat 
 so as to have an increase of density from 
 the surface to a certain depth below it. 
 Through the medium thus constituted, all 
 the phenomena of unusual refraction may 
 be seen in the most beautiful manner ; the 
 variation of density being produced by heat 
 alone. 
 
 ON THE COLOURS OF THE ATMOSPHERE. 
 
 If the earth’s atmosphere consisted of a 
 medium unlimited, and perfectly homoge- 
 neous, the sun and planets would shine in a 
 firmament of the most intense darkness, 
 similar to what has been observed by tra- 
 vellers on the elevated summits of the Alps 
 and the Andes. 
 
 As the atmosphere, however, is of a li- 
 mited extent, and composed of strata of va- 
 riable density, the light of the sun which 
 falls upon it is reflected in every direction, 
 and reaches the surface of the earth with 
 that chaste tinge of blue, which forms such 
 a fine relief to the yellowish light of the 
 heavenly bodies. 
 
 The blue colour of the sky was attri- 
 buted by Fromondus, Otto Guericke, Wol- 
 fius, and Muschenbroek, to a mixture of 
 light and shadow. Sir Isaac Newton and 
 Bouguer, on the contrary, were of opinion, 
 that the particles of air reflect the blue 
 rays more copiously, and transmit the red. 
 
 This explanation, which was then little 
 better than a mere conjecture, has been 
 rendered highly probable by the experi- 
 ments of Dr. Brewster on the polorisation 
 of light. 
 
 The phenomena of blue shadows, which 
 have been so often observed, arise from 
 the illumination of the shadows of bodies 
 by the blue light of the sky, the parts 
 without the shadow being illuminated by 
 some other light, such as that of the sun or 
 of a candle. These coloured shadows are 
 generally seen with most distinctness at 
 sun-rise and sun-set, when the sun’s light 
 has a yellow tinge. 
 
 The colours of shadows illuminated by 
 the shy, vary in different countries, and 
 
 with different seasons of the year, from 
 pale blue to a violet black ; and when 
 there are yellow vapours in the horizon or 
 yellow light reflected from the lower part 
 of the sky, either at sun-rise or sun-set, 
 the shadows have a strong tinge of green, 
 arising from the mixture of these accidental 
 rays with the blue tint of the shadow. 
 
 The phenomena of coloured shadows 
 are often finely seen in the interior of a 
 room. They arise from the blue light of 
 the sky, and the light reflected either from 
 the furniture, or the painted walls of the 
 room. 
 
 M. Hassenfratz has written a very ela- 
 borate memoir on the subject of coloured 
 shadows, and has deduced the following 
 conclusions from his various experiments 
 and observations. 
 
 1. That the shadows formed by the di- 
 rect light of the sun and that of the atmos- 
 phere, vary from meadow green to a violet 
 black , in a gradation through the blue , in- 
 digo. and violet; and that the variation 
 depends on the intensity of the light of the 
 sun, compared with that of the atmosphere. 
 
 2. That the shadows formed in apart- 
 ments by the light of the atmosphere and 
 reflected lights, may present all the pris- 
 matic colours, more or less changed by 
 black. 
 
 3. '-;That the shadows produced on apiece 
 of pasteboard, illuminated by artificial 
 light, are reddish and blueish, more or less 
 deep ; and, that very probably, the blueish 
 and reddish tints of the shadows, depend 
 on the proportion of hydrogen and carbon 
 in the combustible bodies. 
 
 ON CYLINDRICAL MIRRORS. 
 
 If the surface of a metalic cylinder be 
 highly polished, and the cylinder set upon 
 its base, near a picture lying horizontally, 
 the image of the picture seen by reflection 
 from the polished surface, is distorted in 
 the most irregular manner, in consequence 
 of the surface of the mirror being plane in a 
 section passing through its axis, circular in 
 a section perpendicular to this, and of a 
 different curvature in all intermediate sec- 
 tions. On the contrary, we may conceive 
 a picture distorted according to given laws, 
 which, when seen by reflection in the cy- 
 lindrical mirror, shall appear of the most 
 just and harmonious proportions. This, 
 accordingly, is the purpose for which cy- 
 lindrical mirrors are used. They are ge- 
 nerally accompanied with a set of distorted 
 figures, which have neither shape nor 
 meaning when seen by themselves; but 
 when they are placed in a particular posi- 
 tion before a cylindrical mirror, their 
 image is at once reduced into form and ex.? 
 pression. 
 
200 
 
 THE ARTISAN. 
 
 The effect of a cylindrical mirror is 
 shown by the following figure. 
 
 CBBKISTXIV. 
 
 AZOTE, OR NITROGEN.* 
 
 Azote, or nitrogen, is a simple body in 
 the same condition with respect to us as 
 oxygen, with which it has a very strong 
 tendency to combine. It cannot be pro- 
 cured perfectly pure. It is always either 
 combined with caloric in the form of a gas, 
 or exists in a liquid or solid state in cer- 
 tain natural and artificial compounds, 
 from which chemists procure it in the state 
 of gas. If it exists alone, either in the 
 sol id or liquid form, in nature, it has 
 hitherto eluded the researches of chemists. 
 
 Like oxygen, azote remained for a long 
 time unknown. It was discovered in 1772 
 by the late Dr. Rutherford, Professor of 
 Botany, in the University of Edinburgh. 
 
 It has since been procured by Scheel, 
 Berthollet, and Lavoisier, by very different 
 processes. 
 
 That by which Scheel procured it was 
 the following: He mixed about equal 
 
 weights of iron filings and sulphur into a 
 paste with water, and placed the mixture 
 in a proper vessel, over water supported 
 on a stand ; he then put an inverted glass 
 jar full of atmospherical air over it, and 
 allowed this to stand exposed to the mix- 
 ture two or three days. 
 
 He perceived by the ascent of the water, 
 that the air in the jar gradually diminished 
 in bulk, but at the end of the third day the 
 water ceased to rise in the jar: he there- 
 fore examined the air which remained in 
 the jar, and found it to be azotic gas. 
 
 Lavoisier’s method of procuring it is 
 much quicker. He decomposed atmosphe- 
 rical air by burning phosphorus in a vessel 
 containing a given quantity of it. 
 
 The readiest way of procuring it is, 
 therefore, to put a small piece of phos- 
 phorus into a tea-cup raised on a stand 
 
 * Nitrogen was the name given to this gas by the 
 French chemists, at the fr aming of the new nomen- 
 clature; but in this country it usually receives the 
 name of azote, or axbtic gas. 
 
 above the surface of the water, contained 
 in the pneumatic trough, then to set fire to 
 the phosphorus, and quickly invert a jar 
 over it filled with atmospherical air. As 
 soon as the combustion ceases, the jar will 
 appear to be about three-fourths full of air 
 of a very white colour, which, upon stand- 
 ing a short time over the water, will be- 
 come perfectly transparent. This air is 
 azotic or nitrogen gas, tolerably pure. 
 
 There are other methods of procuring 
 it, but the following process, first pointed 
 out by Berthollet, furnishes it nearly pure , 
 if the proper precautions be attended to. 
 Very much diluted nitre acid ( aqua-fortis ) 
 is poured upon a piece of muscular flesh, 
 in, a retort and a heat of about 100 degrees 
 applied to it. A considerable quantity of 
 azotic gas is then produced, which may be 
 received into proper vessels placed on the 
 shelf of the pneumatic trough. 
 
 1. The air of the atmosphere contains 
 about 0*78 parts (in bulk) of azotic gas; 
 almost all the rest of it is oxygen gas. Mr. 
 Lavoisier was the first philosopher who 
 published this analysis, and who made 
 azotic gas known as a component part of 
 air. His experiments were published in 
 1773. 
 
 2. Azotic gas is invisible and elastic 
 like common air, which it resembles in its 
 mechanical properties. It has no smell. 
 Its specific gravity, according to Kirwan, 
 is 0*985, that of air being 1*000. Lavoi- 
 sier makes it only 0*978, and with this the 
 statement of Sir H. Davy coincides exactly. 
 According to Mr. Kirwan, 100 cubic inches 
 of it, at the temperature of 60°, barometer 
 30 inches, weigh 30*535 grains; according 
 to Lavoisier and Davy, they weigh 30*338 
 grains. 
 
 3. It cannot be breathed by animals 
 without suffocation. If obliged to respire 
 it, they drop down dead almost instantly.* 
 No combustible will burn in it. Hence 
 the reason why a candle is extinguished 
 in atmospherical air as soon as the oxygen 
 near it is consumed. Mr. Goettling, in- 
 deed, published, in 1794, that phosphorus 
 shone, and was converted into phosphoric 
 acid, in pure azotic gas. Were this the 
 case, it would not be true that no combus- 
 tible will burn in this gaS ; for the conver- 
 sion of phosphorus into an acid, and even 
 its shining, is an actual though slow com- 
 bustion. Mr. Goettling’s experiments 
 were soon after repeated by Drs. Scherer 
 and Jaeger, who found, that phosphorus 
 does not shine in azotic gas when it is per- 
 fectly pure ; and that therefore the gas on 
 which Mr. Goettling’s experiments were 
 made had contained a mixture of oxygen 
 gas, owing principally to its having been 
 
 * Hence the name azote , given it by the French 
 chemists, which signifies “destructive to life." 
 
THE ARTISAN. 
 
 201 
 
 confined only by water. These results 
 were afterwards confirmed by Professor 
 Lampadius and Professor Hildebrandt. It 
 is therefore proved beyond a doubt, that 
 phosphorus does not bdrn in azotic gas ; 
 and that whenever it appears to do so, 
 there is always some oxygen gas present. 
 
 4. This gas is not sensibly absorbed by 
 water ; nor indeed are we acquainted with 
 any liquid which has the property of con- 
 densing it. Mr. Henry ascertained, that 
 when water is previously deprived of all 
 the air which it contains, 100 inches of it 
 are capable of absorbing only 1 *47 inches 
 of azotic gas at the temperature of 60°. 
 
 When electric sparks are made to pass 
 through common air confined in a small 
 glass tube, or through a mixture of oxygen 
 gas and azotic gas, the bulk of the air di- 
 minishes. This curious experiment was 
 first made by Dr. Priestley, who ascer- 
 tained at the same time, that if a little of 
 the blue infusion of litmus be let up into 
 the tube, it acquires a red colour ; hence it 
 follows that an acid is generated. Mr. Ca- 
 vendish ascertained, that the diminution 
 depends upon the proportion of oxygen 
 and azote present; that when the two 
 gases are mixed in the proper proportions, 
 they disappear altogether, being converted 
 into nitric acid. Hence he inferred that 
 nitric acid is formed by the combination of 
 these two bodies. This important disco- 
 very was communicated to the Royal So- 
 ciety on the 2d June 1785. The combina- 
 tion of the gases, and the formation of the 
 acid, was much facilitated, he found, by 
 introducing into the tube a solution of 
 potash in water. This body united with 
 the nitric acid as it was produced, and 
 formed with it the salt called nitre. In 
 Mr. Cavendish’s first experiments there 
 was some uncertainty, both in the propor- 
 tion of oxygen gas and of common air, 
 which produced the greatest diminution in 
 a given time, and in the proportion of the 
 two gases which disappeared by the action 
 of the electricity. The experiment was 
 twice repeated in the winter 1787-8 by 
 Mr. Gilpin, under the inspection of Mr. 
 Cavendish, and in the presence of several 
 members of the Royal Society. 
 
 2. Nitric acid, which will be more fully 
 described in another part of this work, is 
 a heavy liquid, usually of a yellow colour, 
 which acts with great energy upon most 
 substances, chiefly in consequence of the 
 facility with which it yields a portion of 
 its oxygen. If a little phosphorus or sul- 
 phur, for instance, be put into it, the acid 
 when a little heated gives up oxygen to 
 them, and converts them into acids pre- 
 cisely as if the two bodies were subjected 
 to combustion. In this case, the nitric 
 acid, by losing a portion of its oxygen, is 
 changed into a species of gas called nitrous 
 
 gas , which flies off and occasions the effer- 
 vescence which attends the action of nitric 
 acid on these simple combustibles. Nitrous 
 gas is procured in greater abundance, as 
 well as purity, by dissolving copper or 
 silver in nitric acid. The gas may be re- 
 ceived in a water trough in the usual way. 
 It possesses the curious property of com- 
 bining with oxygen the instant it comes in 
 contact with it, and of forming nitric acid. 
 Hence the yellow fumes which appear 
 when nitrous gas is mixed with common 
 air. This combination furnishes a suffi- 
 cient proof, that the constituents of nitrous 
 gas are azote and oxygen, and that it con- 
 tains less oxygen than nitric acid. It is 
 therefore considered as an oxide of azote. 
 
 3. When iron filings are kept for some 
 days in nitrous gas, they deprive it of a 
 portion of its oxygen, and convert it into a 
 gas which no longer becomes yellow when 
 mixed with common air, but in which 
 phosphorus burns with great splendour, 
 and is converted into phosphoric acid. 
 This combustion and acidification is a proof 
 that the new gas contains oxygen. Its 
 formation demonstrates that it contains 
 azote, and that it has less oxygen than 
 nitrous gas. It is therefore an oxide of 
 azote, as well as nitrous gas. The name 
 gaseous oxide of azote has been given to it. 
 
 Thus we find, that azote is capable of 
 uniting with three doses of oxygen, and of 
 forming two oxides and one acid. We 
 shall find afterwards that there is still 
 another acid composed of the same ingre- 
 dients. 
 
 The combinations of azote with simple 
 combustibles are scarcely so numerous; 
 but some of them are of great importance. 
 
 I. When putrid urine, wool, shavings of 
 horn, and many other animal substances, 
 are subjected to distillation, among other 
 products, there is obtained a substance 
 which has a very pungent odour, and 
 which is well known under the names of 
 hartshorn and volatile alkali .* It may be 
 procured in greatest purity from the salt 
 called sal ammoniac. Pound this salt, and 
 put it into a flask, together with thrice its 
 weight of ground quicklime, and luting on 
 a bent tube, plunge the extremity of it 
 into a mercurial trough, and apply heat to 
 the flask. A gas comes over, which is 
 hartshorn in a state of purity ; by chemists 
 it is usually called ammoniac. It is light, 
 absorbed in great abundance by water, has 
 a pungent taste, and gives a green colour 
 to vegetable blues. When electric sparks 
 are passed through this gas, its bulk is 
 doubled, and it is converted into a mix- 
 ture of hydrogen and azotic gases. This 
 
 * The term alkali is applied in chemistry to a 
 variety of substances, which have the property of 
 giving a green colour to vegetable blues. 
 
202 
 
 THE ARTISAN. 
 
 is a demonstration of its composition.* But 
 it is difficult to form ammonia by uniting 
 its two elements artficially. However, 
 Dr. Austin succeeded in combining them. 
 When both are in the gaseous state, the 
 union does not take place ; but when hy- 
 drogen, at the instant of its evolution, 
 comes in contact with azotic gas, ammonia 
 is formed. Dr. Austin filled a jar with 
 azotic gas, placed it over mercury, and let 
 up into it some moistened iron filings. 
 Now iron filings have the property of de- 
 composing water. They unite with its 
 oxygen, and allow its hydrogen to escape. 
 There was suspended in the jar a paper 
 tinged blue with radish. In a day or two 
 it became green, and thus indicated the 
 formation of ammonia; for no gas but 
 ammonia has the property of changing 
 vegetable blues to green. When nitrous 
 gas was substituted for azote, the ammonia 
 was evolved more speedily. The experi- 
 ment succeeded also with common air, but 
 more slowly. 
 
 2. No compound of azote and carbon is 
 at present known; but according to Four- 
 croy, azotic gas has the property of dis- 
 solving a little charcoal. For he says, 
 azotic gas, obtained from animal sub- 
 stances by Berthollet’s process, when con- 
 fined long in jars, deposits on the sides of 
 them a black matter, which has the pro- 
 perties of charcoal. 
 
 3. Phosphorus plunged Into azotic gas 
 is dissolved in a small proportion. Its 
 bulk is increased about^, and phosphuretted 
 azotic gas is the result, which, if mixed 
 with oxygen gas, becomes luminous, in 
 consequence of the combustion of the dis- 
 solved phosphorus. 
 
 4. Fourcroy informs us, that when sul- 
 phur is melted in azotic gas, part of it is 
 dissolved, and sulphuretted azotic gas 
 formed. 
 
 As azote has never yet been decom- 
 pounded, it must, in the present state of 
 our knowledge, be considered as a simple 
 substance. Dr. Priestly, who obtained 
 azotic gas at a very early period of his ex- 
 periments, considered it as a compound of 
 oxygen gas and phlogiston, and for that 
 reason gave it the name of phlogisticated 
 air. Stahl considered combustion as 
 merely the separation of phlogiston from 
 the burning body. But as these theories 
 are now abandoned, and as all the attempts 
 to decompose azote have hitherto failed, 
 we must of necessity consider it as a sim- 
 ple substance. It must be acknowledged, 
 however, that there are several chemical 
 phenomena altogether inexplicable at pre- 
 sent ; but which might be accounted for if 
 
 * This gas was first analysed by Sclieele, but the 
 proportions were accurately ascertained by 13er- 
 thollcl and Austin. 
 
 it were possible to prove that azote is a 
 compound, and that one of the component 
 parts of water enters into its composition. 
 One of these phenomena is the formation 
 of rain : another is, the constant disen- 
 gagement of azotic gas when ice is melted. 
 Dr. Priestly found, that when water, pre- 
 viously freed from air as completely as 
 possible, is frozen, it emits, when melted 
 again, a quantity of azotic gas. He froze 
 the same water nine times without expos- 
 ing it to the contact of air, and every time 
 obtained nearly the same proportion of 
 azotic gas. 
 
 iLSTROWOMlT. 
 
 OF THE MOON. 
 
 Next to the sun, the moon is the most 
 remarkable of all the heavenly bodies, and 
 is particularly distinguished by the peri- 
 odical changes to which figure and light 
 are subject. 
 
 The moon is not a primary planet, but 
 a secondary, or satellite , which revolves 
 round the earth, and accompanies it in its 
 annual revolution round the sun. The 
 mean time of a revolution of the moon 
 round the earth, or the time between two 
 successive conjunctions, is 29 days 12 
 hours 44 minutes ; but the time she takes 
 to perform a revolution round her orbit, is 
 only 27 days 7 hours 43 minutes. The 
 former of these periods is called the 
 synodical, and the latter the periodical re- 
 volution. The difference between these 
 periods is occasioned by the motion of the 
 earth in the ecliptic ; for while the moon 
 is going round the earth, the earth ad- 
 vances about 29° in the ecliptic, which is 
 nearly 1° per day, and, therefore, the 
 moon must advance 29° more than a com- 
 plete revolution round her orbit, before 
 she can overtake the earth, or be again in 
 conjunction with the sun, which will re- 
 quire 2d. 5 h., her daily motion being about 
 13 degrees. 
 
 Of all the celestial bodies, the moon is 
 the nearest to the earth, her mean distance 
 being only 240,000 miles, which is scarcely 
 a four-hundredth part of the sun’s distance 
 from the earth; but her apparent size is 
 nearly equal to that of the sun, she must 
 therefore be a very small body compared 
 with the sun. Her diameter is only about 
 2161 miles, and therefore the earth is 
 about 48 1 times greater ; but the density of 
 the moon is said to be to that of the earth 
 as 5 to 4 consequently the quantity of 
 matter contained in the earth, is only about 
 39 times that contained in the moon. 
 
 Although the moon moves over a very 
 
THE ARTISAN 
 
 203 
 
 considerable portion of her orbit in the 
 course of a day; yet, on account of its 
 smallness, her hourly motion is only about 
 2290 miles, which is about Jjth part of the 
 space passed over by the earth in the same 
 time. But in all her motions the moon is 
 subject to great irregularities, which arise 
 from the eccentricity of her orbit, and her 
 proximity to the earth. The eccentricity 
 of her orbit, as determined from the latest 
 and most accurate observations, is 12,960 
 miles, or nearly </ g th part of her mean dis- 
 tance, of course she is about £th part 
 nearer the earth on some occasions than at 
 others. 
 
 PHASES OF THE MOON. 
 
 By Thy command the moon as daylight fades, 
 Lights her broad circle in the deep’ning shades; 
 Array'd in glory, and enthroned in light, 
 
 She breaks the solemn terrors of the night ; 
 Sweetly inconstant in her varying flame, 
 
 She changes still, another, yet the same. 
 
 Broome. 
 
 Although the phases of the moon are 
 among the most frequently observed phe- 
 nomena of the heavens, yet they are also 
 among the most wonderful. But on ac- 
 count of the frequency and regularity of the 
 changes in the appearances and situation 
 of this beautiful object, the cause of these 
 phenomena are perhaps less thought of by 
 ordinary observers, than if they were less 
 
 frequent. The moon being an opaque sphe- 
 rical body, which appears luminous only 
 in consequence of reflecting the light of 
 the sun, can only have that side illumi- 
 nated which is at any time turned towards 
 the sun, the other side remaining in dark- 
 ness ; and as that part of her can only be 
 seen which is turned towards the earth, it 
 is evident that we must perceive different 
 portions of her illuminated, according to 
 her various positions with respect to the 
 earth and sun. 
 
 At the time of conjunction, or when the 
 moon is between the earth and sun, she is 
 then invisible on the earth, because her en- 
 lightened side is then turned towards the 
 sun, and her dark side towards the earth. 
 In a short time after the conjunction, she 
 appears like afine crescentto the eastward 
 of the sun a little after he sets. This 
 crescent begins to fill up, and the illumi- 
 nated part to increase as she advances in 
 her orbit ; and when she has performed a 
 fourth part of a revolution, she appears to 
 be half illuminated, and is then said to be 
 in her first quarter. After describing the 
 second quadrant of her orbit, she is the n 
 opposite to the sun, and shines with a 
 round illuminated disc, which is called 
 full moon. Her appearance at this time is 
 very accurately represented by the follow- 
 ing figure. 
 
204 
 
 THE ARTISAN. 
 
 After the full she begins to decrease 
 gradually as she moves through the other 
 half of her orbit; and when the eastern 
 half of her only is enlightened, she is said 
 to be in her third quarter ; thence she con- 
 tinues to decrease until she again dis- 
 appears at the conjunction, as before.* 
 These various phases plainly demonstrate 
 that the moon does not shine by any light 
 of her own ; for if she did, being globular, 
 she would always present a fully illumi- 
 nated disc like the sun. That the moon is 
 an opaque body, is not only proved from 
 her phases, but also by the occultation of 
 stars, for her body often comes between 
 the earth and a star, and while she is pass- 
 ing it, the star is hid from our view. 
 
 MOTIONS OF THE MOON. 
 
 The neighbouring moon her monthly round 
 Still ending, still renewing, through mid heaven, 
 With borrowed light her countenance triform ;t 
 Hence fills and empties to enlighten th’ earth. 
 
 And in her pale dominion checks the night. 
 
 Milton. 
 
 It has already been remarked that the 
 motions of the moon are very irregular. 
 The only equable motion she has, is her 
 revolution on her axis, which is completed 
 in the space of a month, or the time in 
 which she moves round the earth,, This 
 has been determined by the important and 
 curious circumstance, that she always pre- 
 sents the same face to the earth, at least 
 with very little variation. But as her mo- 
 tion in her orbit is alternately accellerated 
 and retarded, while that on her axis is 
 uniform, small segments on the east and 
 west sides alternately appear and dis- 
 appear. This occasions an apparent vi- 
 bration of the moon backwards and for- 
 ward, which is called her libration in 
 longitude. 
 
 A little more of her disc is also seen 
 towards one pole, and sometimes towards 
 the other, which occasions another waver- 
 ing or vacillating kind of motion, called 
 the libration in latitude. This shows that 
 the axis of the moon is not exactly, though 
 nearly, perpendicular to the plane of her 
 orbit; for if the axis of the moon were 
 exactly perpendicular to the plane of her 
 
 * These various phases may be satisfactorily and 
 pleasantly illustrated, by placing a lighted candle on 
 a table to represent the sun, a smaller at some dis- 
 tance from it to represent the earth, and then car- 
 rying a smaller white ball round it to represent the 
 moon revolving round the earth. 
 
 + Increasing with horns towards the east; de- 
 creasing with horns towards the west; and at the 
 full . 
 
 orbit, or if her equator coincided with that 
 plane, we should perceive no other libra- 
 tion than that in longitude. 
 
 When the place of the moon is observed 
 every night, it is found that the orbit in 
 which she performs her revolution round 
 the earth, is inclined to the ecliptic at an 
 angle of 5° 9' at a mean rate ; this angle is 
 not only subject to some variation, but the 
 very orbit itself is changeable, and does 
 not always preserve the same form : for 
 though it be elliptical, or nearly so, with 
 the earth in one of the foci, yet its eccen- 
 tricity is subject to some variation, being 
 greater when the line of the apsides coin- 
 cides with that of the syzygies, and least 
 when these lines are at right angles to each 
 other. But the eccentricity is always very 
 considerable, and, therefore, the motion of 
 the moon is very unequal, for like all other 
 planets, it is quickest in perigree and slow- 
 est in apogee. At a mean rate she advances, 
 in her orbit, 13° 10' per day, and comes to 
 the meridian about 48 minutes later every 
 day. As the moon’s axis is nearly perpen- 
 dicular to the plane of the ecliptic, she can 
 scarcely have any change of seasons. But 
 what is still more remarkable, one half of 
 the moon has no darkness at all, while the 
 other half has two weeks of light and 
 darkness alternately. For the earth re- 
 flects the light of the sun to the moon, in 
 the same manner as the moon does to the 
 earth; therefore, at the time of conjunction, 
 or new moon, one half of the moon will be 
 enlightened by the sun, and the other half 
 by the earth ; and at the time of opposition, 
 or full moon, one half of the moon will be 
 enlightened by the sun, but the other half 
 will be in darkness. The earth also ex- 
 hibits similar phases to the moon to what 
 she does to the earth, but in a reverse 
 order, for when the moon is full , the earth 
 is invisible to the moon ; and when the 
 moon is new, the earth will appear to be 
 full to the moon, and so on. It has been 
 already mentioned, that the moon always 
 presents the same face to the earth, from 
 hence it is inferred, that one half of the 
 moon can never see the earth at all ; whilst 
 from the middle of the other half it is 
 always seen overhead, turning round 
 almost thirty times as fast as the moon 
 does. 
 
 From the circle which limits our view of 
 the moon, only one half of the earth’s side 
 next her is seen, the other half being hid 
 below the horizon of all places on that 
 circle. 
 
 To the moon, the earth seems to be the 
 largest body in the universe, for it appears 
 about thirteen times greater than the moon 
 does to the earth. 
 
THE ARTISAN. 
 
 205 
 
 jHfaceUatteou* Subjects, 
 
 ARCHITECTURE. 
 
 IONIC ORDER. 
 
 The origin of the Ionic Order is prob- 
 lematical. Vitruvius reports it to have 
 been made in representation of the curls in 
 the head-dress of females ; but other hints 
 are quite as probable ; such as the spiral 
 shape of the horns of rams ; or that as- 
 sumed by the barks of some trees, when 
 dried in the sun ; or the beautiful spiral 
 forms of some sea shells*. 
 
 In the architrave and frieze of this order, 
 all appearances of triglyphs and guttse 
 
 * This part of the order is called the volute, and 
 forms the principal characteristic and ornament of 
 the Ionic Order. It is also used in the Composite 
 Order. 
 
 are omitted ; and in the cornice, instead of 
 the bold mutules of the Doric order, the 
 ends of smaller pieces of wood, to which 
 the covering tiles were fixed, are repre- 
 sented by what are termed dentiles or teeth. 
 This order differs also from the Doric, by 
 having a base at the lower extremity of the 
 shaft; the propriety of this might have 
 arisen from the diameter of the shaft being 
 much less than that of the Doric, in propor- 
 tion to the height of the order, or the 
 weight it had to sustain. 
 
 The rest of the Ionic order is not so pre- 
 cisely defined, nor so uniformly adhered 
 to, as similar parts of the Doric. 
 
 In all the Greek Ionics, the height of the 
 cornice, measured from the lower edge of 
 the corona upwards, appears to have a con- 
 stant ratio to the total height of the entab- 
 lature; viz. nearly as 2 to 9, which seems 
 the true one to accord with the character 
 of the order. The great recess of mould- 
 ings, under the corona, gives it a striking 
 prominence, and prevents the cornice from 
 appearing too heavy, though both the den- 
 tile band and cymatium of the frieze are 
 introduced under it. On account of the 
 frieze being wanting in most of the Asiatic 
 remains, although the architrave and cor- 
 nice have been accurately measured, the 
 height of the entablature cannot be ascer- 
 tained. The only instance in which a 
 frieze has been discovered is in the theatre 
 of Laodicea ; and there it is rather less 
 than one-fifth of the entablature. In the 
 temple of Bacchus at Zeos, and Minerva 
 Polias at Priene, the architraves are di- 
 vided into three facse below the cymatium. 
 
 Their proportions are very different 
 from those at Athens, though also elegant 
 in character and effect. 
 
 The height of the Ionic columns was ori- 
 ginally eight diameters, taken at the bot- 
 tom ; but the moderns have increased it to 
 nine. 
 
 The shaft is generally cut into 24 flutes, 
 with as many fillets. The altitude of the 
 entablature may, in general, be two diame- 
 ters ; but it may be increased, and should 
 not be less than one-fourth of the height of 
 the column in works of magnificence. 
 
 It is said, that the temple of Diana at 
 Ephesus, the most celebrated edifice of all 
 antiquity, was of this order. At present, 
 it is much used in churches, courts of jus- 
 tice, and buildings connected with the arts 
 of peace. 
 
 ON THE VERNIER SCALE. 
 
 The method of dividing, what is termed 
 a vernier scale, is founded on the differ- 
 ence of two approximating scales, one of 
 which is moveable, and the other fixed. 
 
 Thus, if a given space on the limb of an 
 instrument be divided into any number of 
 equal parts, and an equal space on an at- 
 
206 
 
 THE ARTISAN, 
 
 tached moveable scale be divided into one 
 more part, it is evident, that each of them 
 will be smaller than the former, by that 
 part of one divisioninto which this attached 
 sliding scale is divided. 
 
 Therefore, on shifting the attached 
 scale forward, the quantity of aberration, 
 or difference, will diminish at each suc- 
 cessive division, till a new coincidence 
 again takes place, and then the number of 
 divisions on the sliding scale will mark 
 the fractional value of the displacement, 
 which will be equal to one of the divisions 
 on the vernier or sliding scale. 
 
 Thus in the annexed figure, nine di- 
 
 visions of the primary, or fixed scale, oc- 
 cupy a space equal to ten on the sliding 
 scale, and the moveable zero stands be- 
 yond the thirty-eighth and thirty-ninth 
 division; therefore, to find how much 
 more than one whole division is indi- 
 cated by the vernier, it is only necessary 
 to observe, where the opposite sections or 
 lines on the scales coincide, which, in this 
 instance, is opposite to the fourth division 
 of the vernier, or sliding scale. The whole 
 quantity is therefore 38*1. 
 
 It is evident, that any fractional part of 
 a whole division on the primary or fixed 
 scale, must bear the same proportion to 
 an equal space on the vernier as a whole 
 division, or the space occupied by the 
 whole divisions of the vernier. 
 
 Hence, one division of the vernier is al- 
 ways equal in value to the quotient of the 
 smallest division on the primary scale, di- 
 vided by the number of divisions on the 
 vernier. 
 
 Thus, suppose one degree on the limb of 
 a Hadley’s quadrant to be divided into 
 three equal parts, and that the attached 
 vernier is divided into twenty equal parts : 
 then one division on the vernier indi- 
 cates one minute ; for the third part of a 
 degree is twenty minutes, which divided 
 by twenty , the number of divisions on the 
 vernier, quotes one minute. 
 
 Hence, we have the following simple 
 rule for ascertaining the value of one divi- 
 sion of any vernier, attached to a primary 
 scale. 
 
 Find the value of the smallest division 
 on the primary scale, and divide this value 
 by the number of divisions on the vernier, 
 and the quotient will be the value of one 
 division on the vernier of the same deno- 
 mination, as that to which the smallest on 
 the primary scale was reduced, previous 
 to dividing by the divisions on the vernier. 
 
 TO STAIN GLASS OF VARIOUS 
 COLOURS. 
 
 Procure a large piece of crown window- 
 glass, and place the design (which should 
 be previously drawn on paper) beneath 
 the plate of glass, then brush the upper 
 side of the glass with gum-water, and 
 when this is perfectly dry, it will form a 
 surface proper for receiving the colours 
 without danger of their spreading or run- 
 ning. The outlines of the design are then 
 to be drawn with a fine pencil, in a black 
 or blue colour, and after they are dry the 
 colours are to be laid on with larger pen- 
 cils. After the colours are all laid on, they 
 are to be again taken off those parts which 
 are intended to be very light : this may be 
 done by a goose quill, cut like a pen, 
 without a slit. The glass must now be 
 burned, in order to fix the colours, or to 
 stain the glass with the colours which 
 have been laid upon it. This operation is 
 best performed in an assayer’s furnace, the 
 fire of which must be allowed to die away 
 gradually, as soon as the colours are found 
 to be perfectly fixed, otherwise the glass 
 would become too brittle. 
 
 Observation. — The colours and effect of 
 the picture are often very different, when 
 taken out of the fire, from what they were 
 when put into it : this, however, cannot 
 be guarded against. 
 
 TO PREPARE AN AMALGAM OF 
 GOLD AND MERCURY FOR 
 WASH-GILDING. 
 
 Put a small quantity of gold, with about 
 six times its weight of mercury, into an 
 iron ladle, or crucible, which has been pre- 
 viously rubbed in the inside with whiten- 
 ing, then put it upon a charcoal fire, and 
 submit it to a gentle heat, occasionally 
 stirring the metals with an iron wire. The 
 heat should not be so strong as to evaporate 
 the mercury, at least not till the solution 
 of the gold is nearly effected ; the heat may 
 then be increased for a moment, till a va- 
 pour is Seen to rise from the crucible. 
 When the amalgam is formed, it is to be 
 thrown into water, where a small quantity 
 of mercury will be seen to separate from 
 it. To free it completely from mercury, it 
 will be necessary to twist it up in a piece 
 of fine wash leather, and to press it gently 
 betwixt the finger and thumb. The mer- 
 cury will then pass through the pores of 
 the leather, and leave the amalgam fit for 
 use, of a fine white colour. 
 
 Observation. — It is necessary that both 
 the gold and the mercury should be per- 
 fectly pure. 
 
THE ARTISAN. 
 
 207 
 
 TO GILD AN ALLOY, OR COM- 
 POUND OF BRASS AND COPPER. 
 
 Clean the surface of the article to be 
 washed or gilded, by immersing it in di- 
 luted nitric acid, and then in water, to pre- 
 vent the farther action of the acid before 
 the gilding is performed. The article is 
 then to be put into an acid called the 
 quickening , which is made by dissolving a 
 little mercury in nitric acid, so as to give 
 it a milky whiteness. The article is to be 
 dipped in this, which will give it a coat of 
 the solution in an instant. After this, the 
 amalgam prepared as directed in the last 
 article is to be applied to it with a pencil, 
 made of a piece of flattened wire fixed in 
 a handle. 
 
 This pencil is to be occasionally dipped 
 in the quickening, and the amalgam touched 
 with it ; a small quantity will thus adhere 
 to the pencil, and when rubbed upon the 
 work, will spread or flow in an instant 
 over every part which has been touched 
 with the quickening. The mercury is next 
 to be driven off, by holding the article in 
 a pair of iron pincers over a charcoal fire, 
 till it change from a white to a gold co- 
 lour; but as the mercury is apt to flow, 
 during this process, more to one part of 
 the article than another, it must be spread 
 with a brush made of soft hog’s hair. After 
 the mercury is completely driven off, the 
 article will have a dullscarfy appearance, 
 but upon being rubbed with a small brush, 
 made of fine brass wire, previously dipt in 
 small beer or ale grounds, it will assume 
 a polished surface. 
 
 Observation . — A mixture of copper and 
 brass is the metal most commonly em- 
 ployed for this kind of gilding. Silver 
 may also be gilt in the same manner ; but 
 pure copper, iron, and steel, does not take 
 the amalgam. 
 
 ON THE CAUSE OF RAIN. 
 
 Every one must have noticed an obvious 
 connexion between heat and the vapour in 
 the atmosphere. Heat promotes evapora- 
 tion, and contributes to retain the vapour 
 when in the atmosphere, and cold precipi- 
 tates or condenses the vapour. But these 
 facts do not explain the phenomenon of 
 rain, which is as frequently attended with 
 an increase as with a diminution of the 
 temperature of the atmosphere. 
 
 The late Dr. Hutton, of Edinburgh, is 
 generally allowed to be the first person 
 who published a correct notion of the 
 cause of rain. (See Edin. Trans, vol. i. 
 and ii. and Hutton’s Dissertations, &c.) 
 Without deciding whether vapour be 
 simply expanded by heat, and diffused 
 through the atmosphere, or chemically 
 
 combined with it, he maintained from the 
 phenomena that the quantity of vapour 
 capable of entering into the air increases 
 in a greater ratio than the temperature; 
 and hence he fairly infers, that whenever 
 two volumes of air of different tempera- 
 tures are mixed together, each being pre- 
 viously saturated with vapour, a precipi- 
 tation of a portion of vapour must ensue, 
 in consequence of the mean temperature 
 not being able to support the mean quan- 
 tity of vapour. 
 
 The cause of rain, therefore, is now no 
 longer an object of doubt. If two masses 
 of air of unequal temperatures, by the 
 ordinary currents of the winds, are inter- 
 mixed, when saturated with vapour, a 
 precipitation ensues. If the masses are 
 under saturation, then less precipitation 
 takes place, or none at all, according to 
 the degree. Also the warmer the air, the 
 greater is the quantity of vapour precipi- 
 tated in like circumstances. Hence the 
 reason why rains are heavier in summer 
 than winter, and in warm countries than 
 in cold. 
 
 SOLUTION OF QUESTIONS. 
 
 Quest. 21, answered by F. of Manchester , 
 ( the proposer ). 
 
 Let ABCD be the wheel whose circum- 
 ference is divided into 60 buckets, F the 
 
 B 
 
 third bucket from B, and the first that the 
 water enters from the perpendicular B E ; 
 G the fifth bucket from D, and the distance 
 at which the water leaves the wheel from 
 the perpendicular E D. 
 
 Then — g Q 1455 -=z 291060 cubic 
 
 inches of water expended every minute ; 
 
 and = 485-1 inches of water in 
 
 10x60 
 
 each bucket. Then the specific gravity of 
 an inch of w ater being -036169, we have 
 036169 X 485-1=: 17-54558 lbs. the w eight 
 of w r ater in each bucket. 
 
THE ARTISAN. 
 
 Now 360°-~60 ~6° the arc or distance 
 between the centre of each bucket on the 
 wheel ^then (per mechanics) if the natural 
 cosine of the several arcs accounted from 
 A, viz. 6°* 12°* 18°- 24°, &c. both ways to- 
 wards B and D, be multiplied severally 
 into the weight of water in each bucket, 
 the sum of fhewhole will be 311-27042 lbs. 
 the equilibrium power when applied to the 
 circumference at A, as required. 
 
 Quest. 26, answered by C. N. F. 
 Let ADBbe the semicircle, 
 
 then put a — A B, x ~ D c, consequently 
 a ;r 
 
 — C D, and «~C«; and (by Euclid 
 
 47-l)CD 2 zzDe 2 + Ce 2 , orx 2 + ^ = ~ 
 « 2 a 
 
 or, x 3 ~r-* and x zz'~7z=r the side of the 
 5 V 5 
 
 square. 
 
 This question was answered nearly in 
 the same manner, by Mr. J. Holroyd, 
 teacher at Oldham ; by a Mech an ic at Bury; 
 by Mr. John Barr, Somers Town; and by 
 the Proposer, who employed the well- 
 known property of the circle demonstrated 
 by Euclid, in his 35th prop. B 3 ; but the 
 above solution is rather shorter. 
 
 This question was also solved by Mr. 
 Richard Graham, Teacher, Liverpool; 
 and by Master James O’Reilly, Portsea. 
 
 Quest. 27, answered by a Mechanic of 
 Bury. 
 
 Let A and B 
 
 H 
 
 JD 
 
 I 
 
 E 1 F 
 
 be the points from which the perpendicu- 
 lars are to be let fall, and D the point 
 through which the straight line is to be 
 
 drawn. Join the pointsA and B, and bisect 
 the line A B in C, also join C and D, and 
 draw the indefinite lines A E and B F pa- 
 rallel to CD. From A let fall the perpen- 
 dicular A G on B F, and through D .draw 
 H I parallel to A G. And H I will be the 
 line required. 
 
 Demon. A G is perpendicular to B F, 
 but C D is parallel to B F ; therefore A K 
 is perpendicular to C K, and in the triangle 
 A G B, we have (Euclid 2-6) C A : A K :: 
 B A : A G. But B A is bisected in C, 
 therefore A G is bisected in K, and there- 
 fore AK=KG. ButAD and KI are 
 parallelograms ; hence, AKzrHD ~K G 
 — D I. Whence the two perpendiculars 
 let fall from A and B, viz. A H and B I, cut 
 off equal segments, HD and D I, from the 
 point D. Q. E.D. 
 
 This question admits of a much simpler 
 solution, and Mr. Holroyd, of Oldham , 
 employed it in the solution he sent us, but 
 we insert the above on account of its origi- 
 nality. 
 
 QUESTIONS FOR SOLUTION. 
 
 Quest. 31, proposed by a Mechanic, of 
 Bury. 
 
 Given the lines AD, DE, and A E, in 
 the following figure 
 
 B 
 
 to determine B C geometrically, —the line 
 B D being supposed equal to B E, and the 
 angle at C a right angle. 
 
 Quest. 32, proposed by Mr. S. A. Hart, 
 Student of the Royal Academy. 
 
 A painter had fixed a ladder so that the 
 upper end touched the top front of a house, 
 and the bottom of the ladder was twelve 
 feet from the street door ; and having oc- 
 casion to lower the top four feet, he found, 
 that the bottom end extended double that 
 quantity beyond the former position : re- 
 quired the height of the building and length 
 of the ladder ? 
 
 Quest. 33, proposed by An Original. 
 
 What is the area of the space inclosed 
 by four shillings placed in the form of a 
 square, each shilling being *925 of an inch 
 in diameter? 
 
THE ARTISAN. 
 
 209 
 
 &EOMETE7 « 
 
 PROPOSITION XXXVIII. 
 
 Theorem. — Triangles upon equal bases, and 
 between the same parallels , are equal to 
 one another . 
 
 Let the triangles ABC, DEF be upon 
 equal bases B C, E F, and between the 
 same parallels B F, AD: the triangle 
 A B C is equal to the triangle D E F. 
 
 Produce A D both ways to the points 
 G, H, and through B draw B G parallel 
 to C A, and through F draw F H parallel 
 to ED: then each of the figures GBCA, 
 DEFH, is a parallelogram ; and they are 
 G AD H 
 
 equal to one another, because they are 
 upon equal bases B C, E F, and between 
 the same parallels B F, G H ; and the 
 triangle A B C is the half of the parallelo- 
 gram GBCA, because the diameter A B 
 bisects it; and the triangle DEF is the 
 half of the parallelogram DEFH, because 
 the diameter D F bisects it : but the halves 
 of equal things are equal ; therefore the 
 triangle ABC is equal to the triangle DEF. 
 Wherefore triangles, &c. Q. E. D. 
 
 Cor. Hence, if the base B C be greater 
 than the base E F, the triangle ABC will 
 be greater than the triangle E D F ; and if 
 B C be less than E F, the triangle ABC 
 will be less than the triangle EDF. Also, 
 if the triangle ABC be greater than EDF, 
 then is B C greater than E F ; and if less, 
 
 PROPOSITION XXXIX. 
 
 Theorem. — Equal triangles upon the same 
 base , and upon the same side of it, are be- 
 tween the same parallels. 
 
 Let the equal triangles A B C, D B C, be 
 upon the same base B C, and upon the same 
 side of it; they are between the same pa- 
 rallels. 
 
 A D 
 
 Vol. I.. — No, 14. 
 
 Join AD; AD is parallel to BC; for, if 
 it is not, through the point A draw A E pa- 
 rallel to BC, and join EC: the triangle 
 ABC is equal to the triangle EBC, be- 
 cause it is upon the same base B C, and 
 between the same parallels B C, A E: but 
 the triangle ABC is equal to the triangle 
 B D C ; therefore also the triangle B D C 
 is equal to the triangle EBC, the greater 
 to the less, which is impossible : therefore 
 A E is not parallel to B C. In the same 
 manner, it can be demonstrated, that no 
 other line but A D is parallel to B C ; AD 
 is therefore parallel to it. Wherefore 
 equal triangles upon, &c. Q. E. D. 
 
 PROPOSITION XL. 
 
 Theorem. — Equal triangles upon equal 
 bases, in the same straight line, and to- 
 wards the same parts, are between the 
 same parallels. 
 
 Let the equal triangles A B C, DE F, be 
 upon equal bases BC, E F, in the same 
 straight line B F, and towards the same 
 parts ; they are between the same pa- 
 rallels. 
 
 A D 
 
 Join AD; A D is parallel to B C : for, 
 if it is not, through A draw A G parallel 
 to B F, and join G F. The triangle ABC 
 is equal to the triangle GEF, because they 
 are upon equal bases B C, E F, and be- 
 tween the same parallels B F, AG: but 
 the triangle ABC is equal to the triangle 
 DEF ; therefore also the triangle DEF is 
 equal to the triangle GEF, the greater to 
 the less, which is impossible : therefore 
 A G is not parallel to B F : and in the same 
 manner it can be demonstrated, that there 
 is no other parallel to it but AD; A D is 
 therefore parallel to B F. Wherefore 
 equal triangles, &c. Q. E. D. 
 
 PROPOSITION XLI. 
 
 Theorem. — If a parallelogram and a tri- 
 angle be upon the same base , and between 
 the same parallels ; the parallelogram is 
 double of the triangle. 
 
 Let the parallelogram ABCD and the 
 triangle EBC be upon the same base BC, 
 and between the same parallels BC,AE; 
 the parallelogram ABCD is double of the 
 triangle EBC. 
 
 P 
 
210 
 
 THE ARTISAN. 
 
 A D E 
 
 Join AC; then the triangle ABC is equal 
 to the triangle EBC, because they are upon 
 the same base BC, and between the same 
 parallels BC, AE. But the parallelogram 
 ABCD is double of the triangle ABC, be- 
 cause the diameter AC divides it into two 
 equal parts; wherefore ABCD is also 
 double of the triangle EBC. Therefore, 
 if a parallelogram, &c. Q. E. D. 
 
 PROPOSITION XLII. 
 
 Problem. — To describe a parallelogram 
 that shall be equal to a given triangle , and 
 have one of its angles equal to a given 
 rectilineal angle. 
 
 Let ABC be the given triangle, and D 
 the given rectilineal angle. It is required 
 to describe a parallelogram that shall be 
 equal to the given triangle ABC, and have 
 one of its angles equal to D. 
 
 Bisect BC in E, join AE, and at the 
 point E in the straight line EC make the 
 angle CEF equal to D ; and through A 
 draw AG parallel to EC, and through C 
 A F G 
 
 draw CG parallel to EF : therefore FECG 
 is a parallelogram : and because BE is 
 equal to EC, the triangle ABE is likewise 
 equal to the triangle AEC, since they are 
 upon equal bases BE, EC, and between 
 the same parallels BC, AG ; therefore the 
 triangle ABC is double of the triangle 
 AEC. And the parallelogram FECG is 
 likewise double of the triangle AEC, be- 
 cause it is upon the s^tme base, and be- 
 tween the same parallels : therefore the 
 parallelogram FECG is equal to the tri- 
 angle ABC, and it has one of its angles 
 CEF equal to the given angle D. Where- 
 fore there has been described a parallelo- 
 gram FECG equal to a given triangle ABC, 
 having one of its angles CEF equal to the 
 given angle D. Which was to be done. 
 
 PROPOSITION XLIII. 
 
 Theorem. — The complements of the paralle- 
 lograms which are about the diameter of 
 any parallelogram, are equal to one another. 
 
 Let ABCD be a parallelogram, of which 
 the diameter is AC; let EH, FG be the 
 parallelograms about AC, that is, through 
 which AC passes, and let BK, KD be the 
 other parallelograms, which make up the 
 whole figure ABCD, and are therefore 
 called the complements : the complement 
 BK is equal to the complement KD. 
 
 AH D 
 
 Because ABCD is a parallelogram, and 
 AC its diameter, the triangle ABC is equal 
 to the triangle ADC : and, because EKHA 
 is a parallelogram, and AK its diameter, 
 the triangle AEK is equal to the triangle 
 AHK : for the same reason, the triangle 
 KGC is equal to the triangle KFC. Then, 
 because the triangle AEK is equal to the 
 triangle AHK, and the triangle KGC to 
 the triangle KFC ; the triangle AEK, to- 
 gether with the triangle KGC, is equal to 
 the triangle AHK, together with the tri- 
 angle KFC: but the whole triangle ABC 
 is equal to the whole ADC ; therefore the 
 remaining complement BK is equal to the 
 remaining complement KD. Wherefore, 
 the complements, &c. Q. E. D. 
 
 PROPOSITION XLIV. 
 
 Problem. — To a given straight line to ap- 
 ply a parallelogram, which shall be equal 
 to a given triangle, and have one of its 
 angles equal to a given rectilineal angle.* 
 
 Let AB be the given straight line, and C 
 the given triangle, and D the given rectili- 
 neal angle. It is required to apply to the 
 straight line AB a parallelogram equal to 
 the triangle C, and having an angle equal 
 to D. 
 
 * To apply a parallelogram to a straight line, 
 means to form it upon that line, or to make that 
 line one of its sides. 
 
 In this proposition we are to describe a parallelo- 
 gram with the two conditions required in the 42d 
 proposition, and also one more, namely, “ to apply 
 a parallelogram to a given straight line.” 
 
THE ARTISAN. 
 
 ill 
 
 Make the parallelogram BEFG equal to 
 the triangle C, having the angle EBG 
 
 the same straight line with AB : produce 
 FG to H, and through A draw AH parallel 
 to BG or EF, and join HB. Then because 
 the straight line HF falls upon the pa- 
 rallels AH, EF, the angles AHF, HFE, 
 are together equal to two right angles; 
 wherefore the angles BHF, HFE are less 
 than two right angles : but straight lines 
 which with another straight line make the 
 interior angles, upon the same side, less 
 than two right angles, do meet if produced 
 far enough : therefore HB, FE will meet, 
 if produced ; let them meet in K, and 
 through Kdraw KL parallel to EA or FH, 
 and produce HA, GB to the points L, M : 
 then HLKF is a parallelogram, of which 
 the diameter is HR; and AG, ME are the 
 parallelograms about HR; and LB, BF 
 are the complements ; therefore L B is 
 equal to BF: but BF is equal to the tri- 
 angle C; wherefore LB is equal to the 
 triangle C ; and because the angle GBE is 
 equal to the angle ABM, and likewise to 
 the angle D ; the angle ABM is equal to 
 the angle L> : therefore the parallelogram 
 LB is applied to the straight line AB, is 
 equal to the triangle C, and has the angle 
 ABM equal to the angle D : which was to 
 be done. 
 
 Proposition xly. 
 
 Problem. — To describe a paratletogram 
 equal to a given rectilineal figure , and 
 having an angle equal to a given rectili- 
 neal angle . 
 
 Let ABCD be the given rectilineal 
 figure, and E the given rectilineal angle. 
 It is required to describe a parallelogram 
 equal to ABCD, and having an angle 
 qual to E. 
 
 K H M 
 
 Join DB,and describe the parallelograrii 
 FH equal to the triangle ADB, and having 
 the angle HKF equal to the angle E; and 
 to the straight line GH apply the parallelo- 
 gram GM equal to the triangle D B C, 
 having the angle GHM equal to the angle 
 E. And because the angle E is equal to 
 each of the angles FKH, GHM, the angle 
 FKH is equal to GHM ; add to each of 
 these the angle KHG ; therefore the angles 
 FKH, KHG are equal to the angles KHG. 
 GHM; but FKH, KHG ate equal to two 
 right angles; therefore also KHG, GHM 
 are equal to two right angles : and because 
 at the point H in the straight line GH, the 
 two straight lines KH, HM, upon the op- 
 posite sides of GH, make the adjacent 
 angles equal to two right angles, KH is in 
 the same straight line with HM. And be- 
 cause the straight line HG meets the pa- 
 rallels KM, FG, the alternate angles MHG, 
 HGF are equal ; add to each of these the 
 angle HGL; therefore the angles MHG, 
 HGL, are equal to the angles HGF, HGL : 
 but the angles MHG, HGL, are equal to 
 two right angles, wherefore also the an- 
 gles HGF, HGL are equal to two right 
 angles, and FG is therefore in the same 
 straight line with GL. And because KF 
 is parallel to HG, and HG to ML, KF is 
 parallel to ML ; but KM, FL are parallels ; 
 wherefore KFLM is a parallelogram. And 
 because the triangle ABD is equal to the 
 parallelogram HF, and the triangle DBG 
 to the parallelogram GM, the whole recti- 
 lineal figure ABCD is equal to the whole 
 parallelogram KFLM ; therefore the pa- 
 rallelogram KFLM has been described 
 equal to the given rectilineal figure ABCD, 
 having the angle FKM equal to the given 
 angle E. W hich was to be done. 
 
 Cor. From this it is manifest how to 
 apply a parallelogram to a given straight 
 line, which shall have an angle equal to 
 a given rectilineal angle, and shall be equal 
 P 2 
 
212 
 
 THE ARTISAN. 
 
 to a given rectilineal figure; viz. by apply- 
 ing to the given straight line a parallelo- 
 gram equal to the first triangle ABD, and 
 having an angle equal to the given angle. 
 
 The enunciation of this proposition is 
 general, though the truth of it is here il- 
 lustrated by employing sl four-sided figure. 
 If the given figure consist of five, six, &c. 
 sides, it will only be necessary to construct 
 a parallelogram for every triangle that the 
 figure is divided into. 
 
 HE€HM!€S. 
 
 ON FRICTION. 
 
 Having finished our description of the 
 simple mechanical powers, the nextbranch 
 of the science of mechanics, which natu- 
 rally falls to be considered, is that of fric- 
 tion. 
 
 The word friction properly signifies the 
 act of one body rubbing upon another ; but 
 in mechanics it is employed to denote the 
 degree of retardation, or of obstruction to 
 motion, which arises from one surface rub- 
 bing upon another. If we place a heavy 
 body upon a surface perfectly level, it is 
 not in a state of equilibrium between all 
 the forces which act upon it, otherwise it 
 would move by the application of the small- 
 est force, in a direction parallel to the 
 plane. Its friction upon the level surface 
 is the unbalanced force, which occasions 
 this want of perfect equilibrium : and if a 
 new force, of equal magnitude, is applied 
 so as to balance that force in any given 
 direction, the body will obey the least im- 
 pulse in that direction, and the force thus 
 employed will be an exactmeasure of the re- 
 tarding force of friction. “ Friction,” as Mr. 
 Playfair has justly remarked, “ destroys, 
 but never generates motion, and in this is 
 unlike gravity, or any of the forces hitherto 
 considered, which, if they retard motion in 
 one direction, always accelerate it in the 
 opposite. The force of friction, therefore, 
 violates the law of continuity, and cannot 
 be accurately expressed by any geometri- 
 cal line, or any algebraic formula.” Though 
 friction destroys motion, and generates 
 none ; it is of essential use in mechanics. 
 It is the cause of stability in the structure of 
 machines, and is necessary to the exertion 
 of the force of animals. A nail, or screw, 
 or a bolt, could give no firmness to the parts 
 of a machine, or of any other structure, 
 without friction. Animals could not walk, 
 or exert their force any how, without the 
 support which it affords. Nothing could 
 have any stability but in the lowest possi- 
 ble situation ; and an arch, which could 
 sustain the greatest load, when properly 
 distributed, might be thrown down by the 
 weight of a single ounce, if not placed 
 
 with mathematical exactness at the very 
 point which, it ought to occupy. 
 
 As a knowledge of the nature and ef- 
 fects of friction, and of the method of di- 
 minishing its influence in machinery, is of 
 the first importance in practical mechanics, 
 we shall offer no apology for making a few 
 observations on the subject. 
 
 The subject of friction has occupied the 
 particular attention of many distinguished 
 individuals, particularly Amontons, Bul- 
 finger, Parent, Euler, and Bossut; but 
 though their writings contain much im- 
 portant information, and many ingenious 
 views, yef it was reserved for the cele- 
 brated Coulomb, to give an accurate and 
 satisfactory investigation of this difficult 
 branch of practical mechanics. By using 
 bodies of a large size, he has corrected the 
 errors of preceding writers, and discovered 
 many new and valuable facts, which had 
 escaped the notice of his predecessors. 
 
 In treating of this important subject, we 
 shall consider it under the following heads. 
 
 The Friction of Surfaces. The Friction 
 of Axles. The Friction and Rigidity of 
 Ropes. The Friction of Pivots ; and, the 
 Means of diminishing Friction in Ma- 
 chinery. 
 
 ON THE FRICTION OF SURFACES. 
 
 There are two general modes of examin- 
 ing the nature and effects of friction. 
 
 The first, ascertains the weight required 
 to draw a body under the pressure of a 
 given load along the horizontal surface of 
 another. 
 
 The second method is still simpler, and 
 consists merely in raising the end of the 
 upper plane, till it acquires the inclination 
 at which the load it bears begins to slide. 
 The angle or inclination at which this mo- 
 tion commences, is called the angle of 
 equilibrium . 
 
 In examining the friction of surfaces, 
 M. Amontons found, that it was exactly 
 proportional to the weight of the moving 
 or rubbing body, and was in general equal 
 to one-third of the weight with which it 
 was pressed against the surface over 
 which it moved. He found also, that 
 the resistance did not increase with an 
 increase of the rubbing surfaces, nor 
 with the velocity of the body. 
 
 M. Bulfinger obtained results nearly 
 similar to those of Amontons, but he 
 made the resistance of friction equal only 
 to one-fourth of the force, with which 
 the rubbing surfaces are pressed together. 
 
 M. Parent, consideringfriction as caused 
 by small spherical eminences in one sur- 
 face, being dragged out of small spherical 
 cavities in the other, proposed to determine 
 the quantity of friction by finding the force, 
 which would move a sphere standing upon 
 three equal spheres. This force he found 
 
THE ARTISAN. 
 
 21 $ 
 
 to be to the weight of the spherb as 7 to 20, 
 or to be of the sphere’s weight. 
 
 In his experiments on friction, M. Parent 
 employed the second of the above methods; 
 that is, he placed the body upon an in<- 
 dined plane, as represented in the fol- 
 lowing figure. 
 
 Here CA represents the position of the 
 plane, at the moment the load begins to 
 slip ; and if the vertical FD represent the 
 weight, FE will express the perpendicular 
 pressure sustained by the plane, and OED 
 must denote the corresponding friction, 
 which, in this instance, is just balanced by 
 the tendency to descend. Wherefore, the 
 pressure is to the friction, as FE to ED, or 
 as AB to BC, that is, as radius to the tan - 
 gent of the angle of repose. 
 
 These two modes of experimenting, 
 however, will seldom give precisely the 
 same results. Most bodies require a 
 greater force to pull them from their con- 
 tact, than what is afterwards sufficient to 
 maintain their adhesive motion. But the 
 obliquity of the plane evidently marks 
 only the initial obstruction, and not the 
 diminished friction which afterwards 
 follows. 
 
 Thus, if the plane CA were a pine 
 board, upon which is laid a block of oak 
 with a smoothed surface, it may be ele- 
 vated to an acclivity of 30 degrees before 
 it disengages its load. But should the 
 angle of declination exceed only 10 de- 
 grees, on striking the side with a smart 
 blow, the oaken block will start from its 
 seat, and then glide downwards. While 
 the plane retains this lower position, the 
 load will not rest on being again replaced, 
 unless it be held in contact a few seconds. 
 
 The celebrated Euler considered the 
 ratio between friction and the force of 
 ; pressure , to be as 1 to 4 ; and observes, 
 that when a body is in motion, the friction 
 will be only one-half of what it is when 
 the body has begun to move, and he 
 
 shows, that if we gradually augment the 
 inclination of an inclined plane, till the 
 body which is placed upon it begins to 
 descend, the friction of the body at the 
 commencement of its motion will be to its 
 pressure against the plane, as the height of 
 the plane to its length. But when the 
 body is in motion, the friction is diminished, 
 and may be found by calculation.* 
 
 The Abbe Bossut has distinguished fric- 
 tion into two kinds ; viz. that which is ge- 
 nerated by one surface rubbing upon ano- 
 ther, and that which arises from one body 
 turning or rolling upon another. The cir- 
 cumference of a wheel rolling on the 
 ground is an example of the first of these, 
 and the friction of the axle of a wheel in 
 motion is a combination of the two kinds 
 of friction. M. Bossut agrees with Amon- 
 tons in his opinion, that an increase of sur- 
 face does not occasion an increase of fric- 
 tion. He took a rectangular parallelo- 
 piped of wood, weighing 51 lbs. and 
 having dragged it over a horizontal table, 
 and loaded it with different weights, he 
 found, that though one of its surfaces was 
 five times greater than the other, the same 
 force was capable of putting the body in 
 motion, whether it rested on the large or 
 the small base. Muschenbroek, and other 
 writers, maintained, that the friction in- 
 creased with the surface. 
 
 Bossut has remarked two very impor- 
 tant facts on the subject of friction; 
 namely, that the friction is affected by the 
 time in which the surface remains in con- 
 tact, and that it does not follow exactly the 
 ratio of the pressures. He found, that 
 when the surfaces had been for some time 
 in contact, their friction increased, either 
 in consequence of a greater number of emi- 
 nences having entered into the correspond- 
 ing cavities from a continuance of the pres- 
 sure, or from some physical cause, which 
 united the two surfaces more firmly toge- 
 ther. Bossut likewise noticed, that in large 
 masses the friction is a less part of the 
 pressure than in small masses; but he 
 does not seem to have observed, that this 
 arose from the greater velocity, which the 
 mass derived from its magnitude. “ Ship- 
 builders,” he observes, “ give only a de- 
 clivity of from 10 to 12 lines in a foot to 
 the inclined planes upon whichvessels are 
 launched. But this declivity, which is 
 sufficient for putting large masses in mo- 
 tion in spite of the resistance of friction, 
 is too small for weights of a moderate size.” 
 Bossut, however, seems to have suspected, 
 that friction might diminish as the velocity 
 increased, when he says, “ that if it hap- 
 pens on one hand, that in proportion as the 
 velocity increased, there are more points 
 
 * He has given a formula for this purpose, but we 
 consider it loo intricate to ,he inserted here; 
 
214 
 
 THE ARTISAN. 
 
 to disengage, or more springs to bend; 
 yet it may happen, on the other hand, that 
 this same velocity does not give to the 
 pressure time to permit the points to enter 
 the cavities so deeply as they would be 
 allowed to do if the velocity were less. 
 But a diminution of this depth ought to 
 produce a diminution of friction.” 
 
 Coulomb also made a number of inter- 
 esting experiments on this subject, from 
 which he has drawn the following gene- 
 ral conclusions. 
 
 1. The friction of wood upon wood, 
 when ungreased, occasions, after a suffi- 
 cient period of contact, a resistance pro- 
 portional to the pressure. This resistance 
 increases sensibly in the first instants of 
 repose, but after some minutes it generally 
 reaches its maximum. 
 
 2. When wood, ungreased, moves upon 
 wood, with any velocity whatever, the 
 friction is still proportional to the pres- 
 sure, but its intensity is much less than 
 that which is experienced in detaching the 
 surfaces after some minutes of rest. The 
 force, for example, which is necessary to 
 detach two surfaces of oak after some mi- 
 nutes of rest, is to that necessary for over- 
 coming the friction when the surfaces have 
 already any degree of velocity whatever, 
 nearly as 9*5 to 2*2. 
 
 3. The friction of metals sliding over 
 metals, ungrefised, is also proportional to 
 the pressures, but its intensity is the same, 
 whether the surfaces detached have been 
 any time at rest, or whether they have re- 
 ceived any uniform velocity whatever. 
 
 4. Heterogeneous substances, such as 
 those of woods and metals, sliding upon 
 one another without grease, give for their 
 friction very different results from the pre- 
 ceding; for the intensity of their friction 
 relative to the time in which they have con- 
 tinued in contact increases slowly, and 
 does not reach its maximum till after four 
 or five days, and sometimes more, whereas 
 in metals, it reaches its maximum in an 
 instant, and in wood, after a few minutes. 
 This increase is even so slow, that the re- 
 sistance of friction in insensible velocities 
 is nearly the same as that which takes 
 place in moving or detaching the surfaces 
 after three or four seconds of rest. In the 
 motion of wood rubbing upon wood with- 
 out grease, and in metals moving upon 
 metals, the velocity has very little influ- 
 ence upon the friction ; but, in the present 
 case, the friction increases very sensibly, 
 ?n proportion as we increase the velocities ; 
 so, that the friction increases nearly in 
 arithmetical progression, as the velocities 
 increase in geometrical progression. 
 
 When a cylinder is made to roll upon a 
 plane surface, it encounters a new sort of 
 obstruction, quite distinct in its character, 
 and generally much inferior to that of 
 
 sliding friction. These different kinds of 
 friction are strikingly contrasted, in the 
 rolling and sliding of different cylinders 
 of wood down inclined planes. These 
 cylinders will not begin to slide length- 
 wise, though disengaged by percussion, 
 unless the slope of the plane exceed 10 
 degrees ; but they will roll easily at much 
 smaller angles. 
 
 The inclination of 4 degrees will be suf- 
 ficient to enable a cylinder of elm, of one 
 inch in diameter, to roll down an oak 
 board, and an angle of 3 degrees will 
 cause a cylinder of lignum-vitae of the 
 same dimensions to roll. But a single de- 
 gree of slope will make an elm cylinder of 
 four inches diameter begin to roll, and 
 three fourths of that angle will occasion 
 the rolling of a like cylinder of lignum- 
 vitae. The loss of force in the act of roll- 
 ing is therefore inversely proportional to 
 the diameter of the cylinder. 
 
 If adhesion were confined to the mere 
 line of contact, it could have no effect 
 whatever in hindering the revolving motion 
 of a cylinder, on a horizontal plane. But 
 this power, subsisting an instant after con- 
 tact has taken place, may be conceived as 
 constantly drawing it down at a certain 
 distance behind. Thus, if A 
 
 be the contact of the cylinder, and B the 
 point where the adhesion is mainly exerted, 
 its efficacy to restrain the rolling of the 
 cylinder will evidently be as A B to A C. 
 On the supposition that A B is constant, 
 this retarding force is inversely as the 
 radius A C ; that is, the greater the dia- 
 meter of the cylinder, the less is the fric- 
 tion. In the case of elm, the distance A B 
 must be the 28th part of an inch ; but in 
 lignum-vitae it is only the 40th part. 
 
 ON THE FRICTION OF AXLES. 
 
 The principal object of Coulombe in 
 his experiments on this subject, was to 
 determine the friction of the axles of ma- 
 chines in motion. 
 
 He employed axles of iron moving in 
 boxes of brass. One of these was 19 lines 
 in diameter, and had a play of If lines in 
 
THE ARTISAN. 
 
 215 
 
 the brass box.* The pulley in which the 
 axle was fixed was 144 lines in diameter, 
 and its weight 14 pounds. The weights 
 were made to run through a space of six 
 feet, and the time employed to run through 
 the first and last three feet was separately 
 measured in half-seconds. In this way he 
 made a very great number of experiments, 
 and obtained a number of important re- 
 sults, which our limits will not permit us 
 to mention. 
 
 Coulomb likewise extended his experi- 
 ments to the friction of axles made of the 
 different kinds of wood used in rotatory 
 machines. For this purpose he used pul- 
 leys of 12 inches in diameter, with axles 
 three inches in diameter. The axles were 
 sometimes moveable and at other times 
 fixed, though in both cases the friction was 
 the same. The levelling surfaces were 
 carefully smoothed. 
 
 Names of the Wood used for the Axles. 
 
 Ratio of Friction 
 to pressure. 
 
 1. Axis of holm oak running in 
 
 a box of lignum vitae coated 
 
 with tallow .... 0,038 ^5.3 
 
 2. Do. the coating of tallow 
 
 wiped off, and the surface 
 remaining greasy . . . 0,06 
 
 3. Do. after being used several 
 
 times without renewing the 0,06 Tg . 7 
 tallow . 0,08 ^2-3 
 
 4. Do. running in a box of elm 
 
 coated with tallow . . 0,03 ^3.3 
 
 5. Do. both axis and box wiped 
 
 and the surfaces remaining 
 greasy . . . . . . . 0,05 ^ 
 
 6. Do. axis of boxwood, and box 
 
 of lignum vitae, coated with 
 tallow 0,043 ^ 
 
 7. Do. the coating wiped, and 
 
 the surfaces remaining 
 
 greasy ....... 0,07 ^.5 
 
 8. Axis of box-wood and box of 
 
 elm, coated with tallow .0,035 ^. g 
 
 9. Do. the coating wiped off, 
 
 and the surfaces remaining 
 greasy ....... 0,05 ^ 
 
 10. Axis of iron, and box of 
 lignum vitae, the coating 
 wiped off, and the pulley 
 turned for some time . . 0,05 ^ 
 
 In these experiments the velocity did 
 not appear to influence the friction unless 
 in the first instants of rest ; and in all 
 cases the friction was least when the sur- 
 faces were merely greasy, and not coated 
 with tallow. 
 
 * A line is one-twelfth of an inch. 
 
 In Wheeled Carriages , the draught is 
 facilitated by three distinct circumstances. 
 
 1. The excessive obstruction which the 
 rim of the wheel would encounter if drag- 
 ged along the road, is changed to the very 
 inferior friction of the axle against the 
 bush of the nave. 
 
 2. This reduced friction has its influence, 
 in impeding the progress of the carriage, 
 still farther diminished, in the ratio of 
 the diameter of the wheel to that of the 
 axle. 
 
 3. The dimensions of the wheel enable 
 it to surmount easily any obstacle which 
 may occur ; the effect being the same as if 
 it were drawn over an inclined plane, from 
 its point of contact to the top of the emi- 
 nence. 
 
 The friction of the rim of a locked wheel, 
 even on the smoothest road, might perhaps 
 exceed the half of the whole load; but 
 the friction of the axle in its box, which 
 is substituted for it, would amount only to 
 the eighth part, when iron is inserted in a 
 copper bush, and scarcely to the seventh 
 part when oak turns in lignum vitae, the 
 grease in both cases being worn smooth. 
 The power of this friction within the nave, 
 in retarding the motion of the carriage, 
 must be directly as the diameter of the 
 axle, and inversely as the height of the 
 wheel. A large wheel and a small axle 
 are therefore the most advantageous. For 
 this reason, an iron axle, though it has 
 twice as much friction as an oak one of 
 the same dimensions, may be preferred for 
 its smallness. In carriages rightly fitted 
 and carefully greased, the whole friction 
 seldom exceeds the thirtieth , but need not 
 amount to the sixtieth part of the load. 
 
 To assign the force expended in over- 
 coming an obstacle, let the wheel, repre- 
 sented by the following figure, touch A 
 the horizontal line of traction ; 
 
 T 
 
 if it meet a protuberance B D, it must be 
 lifted over this with the progressive mo- 
 tion A B : the draught is therefore to the 
 load, as A B to B D. Large wheels are 
 therefore best adapted, not only for di- 
 minishing the effect of friction, but for 
 surmounting the inequalities of the road. 
 
THE ARTISAN. 
 
 216 
 
 HYDRAULICS. 
 
 Montgolfier’s hydraulic ram. 
 
 This interesting machine was first con- 
 structed by Montgolfier about the year 
 1797, and has been brought to a very per- 
 
 fect state, by a series of improvements 
 which he has successively made upon it. 
 The rams represented by the following 
 figures, contain the improvements which 
 have been made so late as 1816. 
 
 The large pipe A B, called the body of 
 the ram, passes through the side of the 
 reservoir P Q, from which the fall of water 
 is obtained. It has a trumpet mouth at 
 one end A, and at the other end an opening 
 H H, which can be closed by valves C or 
 D. When these valves are open, the water 
 will issue at HH with a velocity due to 
 the height A P ; but when the internal 
 valve C is closed, as in the figure, the 
 water is prevented from issuing. When 
 the valve C opens, it descends into the 
 position shown by the dotted lines GG, 
 being guided between three or four stems 
 gg, which have hooks at the lower ends 
 for supporting the valves. In this case 
 the water has a free passage between 
 these stems, and the width of the passage 
 can be increased or diminished, by the 
 screws with which the stems are fixed. 
 The valve C is made of metal, and has a 
 hollow cup or dish of metal attached to its 
 lower surface. The seat FI H of the valve 
 is wider than the diameter of the pipe AB. 
 It consists of a short cylinder or pipe 
 screwed by its fianch h k, into the opening 
 of the upper surface of the head R of the 
 ram; and the cylinder is so formed, as to 
 have an inverted cup or annular space i i 
 round the upper part of it for containing 
 air, which cannot escape when it is com- 
 pressed by the water. A small pipe k l, 
 leading from this annular space to the 
 open air, is furnished with small valves 
 k, l , one o? which, k, opens inwards to 
 admit the air into i, i , but to prevent its 
 return ; while the other valve, l, admits a 
 certain quantity of air, and then shuts and 
 prevents any farther entrance. The valve 
 D is exactly the same as C, only it descends 
 as in the figure when it shuts, and rises 
 when it opens. 
 
 The upper part of the head of the ram at 
 E is made flat, and has several valves, 
 which allow the water to pass freely from 
 the pipe A B, but prevent its return. On 
 each side of the head of the ram, at the 
 part opposite to these valves, is a hollow 
 enlargement, shown by the dotted lines K, 
 forming a circular basin, through the cen- 
 tre of which the pipe A B R passes. This 
 part of the construction is shown more 
 distinctly in the following figure, 
 
 which is a transverse section through L E Z, 
 in a plane perpendicular to that of the paper. 
 The pipe is here made fiat instead of cir- 
 cular, for forming the seats of the valves, 
 and the basin RK is covered with an air 
 vessel F F. This air vessel communicates 
 all round the pipe B, with the basin K K, 
 and with the vertical pipe M. 
 
 The machine being thus constructed, 
 let us suppose the pipe ABR full of water, 
 and the valve C to be opened, the water 
 will lift the valve D, and escape with a 
 velocity due to the height of the reservoir. 
 In a short time, the water having acquired 
 an additional velocity, raises the valve G, 
 which shuts the passage, and prevents the 
 escape of the water. The consequence of 
 this is, that all the included water exerts 
 
THE ARTISAN. 21? 
 
 suddenly ahydrostatical pressure on every 
 part of the pipe, compressing at the same 
 time the air in the annular space i i, which, 
 by its elasticity, diminishes the violence of 
 the shock. This hydrostatical pressure 
 opens the valves at E, and a portion of the 
 water flows into the air vessel F, and con- 
 denses the air which it contains. The 
 valves at E now close, preventing the 
 return of the water into the pipe, and the 
 water recoils a little in the tube, with a 
 slight motion from B to A, in consequence 
 of the reaction or elasticity of the com- 
 pressed air in i i, and also of the metal of 
 the pipe, which must have yielded a little 
 to the force exerted upon it in every direc- 
 tion. The recoil of the water towards A 
 produces a slight aspiration within the 
 head R of the ram, which causes the valve 
 D to descend by its own weight, and pre- 
 vent the water X, which covers it, from 
 descending into the tube. The air, how- 
 ever, passes through the pipe Ik, opens 
 the valve k, and a small quantity is sucked 
 into the annular space i i ; but the quantity 
 is very small, as the valve k closes as soon 
 as the current of air becomes rapid. 
 During the recoil towards A, the valve C, 
 being unsupported, falls by its own weight ; 
 and when the force of recoil is expended, 
 by acting on the water in the reservoir 
 P Q, the water begins again to flow along 
 A B R, and the very same operation which 
 we have described is repeated without 
 end, a portion of water being driven into 
 the air vessel F, at every ascent of the 
 valve C. The air in this vessel being thus 
 highly compressed, will exert a force due 
 to its elasticity upon the surface of the 
 water in the vessel F, and will force it up 
 through the pipe M, to a height which is 
 sufficient to balance the elasticity of the 
 included air. 
 
 The small quantity of air, which is 
 drawn into the annular space ii through 
 the air tube l k at each aspiration, causes 
 an accumulation of air in the space ii; and 
 when thfe aspiration of recoil takes place, 
 a small quantity of air passes from i i, and 
 proceeds along the pipe till it arrives be- 
 neath the valve at E, and lodging in the 
 small space beneath the valves, it is forced 
 into the air vessel at the next stroke, and 
 thus affords a constant supply of air to the 
 vessel. The valves make in general from 
 50 to TO pulsations in a minute. 
 
 When the fall of water, or PQ, is five 
 feet, and the pipe AB six inches in diame- 
 ter, and 14 feet long, a machine with its 
 parts proportioned, as in the figure, will 
 raise water to the height of 100 feet. It 
 will expend about 70 cubic feet per minute 
 in working it, and will raise about 2^ cubic 
 feet per minute to the height of 100 feet. 
 Mr. Millington observes, that one of these 
 machines is said to have raised 100 hogs- 
 
 heads of water in 24 hours, to the height 
 of 134 feet, by a fall of 4£ feet. 
 
 SCHEMNITZ FOUNTAIN, OR HUNGARIAN 
 MACHINE. 
 
 A portion of air is employed for raising 
 water, not only in the spiral pump, but 
 also in the air vessels of Schemnitz. A 
 colum of water, descending through a pipe 
 into a closed reservoir, full of air, obliges 
 the air to act, by means of a pipe, leading 
 from the upper part of the reservoir or air 
 vessel, on the water in a second reservoir, 
 at any distance either below or above it, 
 and forces this water to ascend through a 
 third pipe to any height less than that of 
 the first column. The air vessel is then 
 emptied, and the second reservoir filled 
 and the whole operation is repeated. 
 
 Thus the reservoir A being filled with 
 water, and B with air, and water being 
 poured into the funnel C, the air in B acts 
 by the pipe D on the water in A, and forces 
 it up the pipe E. 
 
 The air must, however, acquire a den- 
 sity equivalent to the pressure, before it 
 can begin to act ; so that if the height of 
 the columns were 34 feet, it must be re- 
 duced to half its dimensions before any 
 water would be raised ; and thus half of 
 the force would be lost; in the same man- 
 ner, if the height were 68 feet, two thirds 
 of the force would be lost. But where the 
 height is small, the force lost in this manner 
 is not greater than that which is usually 
 spent in overcoming friction and other im- 
 perfections of the machinery employed ; 
 for the quantity of water, actually raised 
 by any machine, is not often greater than 
 half the power which is consumed. 
 
 The force of the tide, or of a river rising 
 and falling with the tide, might easily be 
 applied by a machine of this kind, to the 
 purposes of irrigation, as represented by 
 the following figure. 
 
218 
 
 THE ARTISAN. 
 
 Thus, A being the high water mark, 
 and B the low water mark, the vessels C 
 and D are filled at high water from below, 
 the air being suffered to escape by a stop- 
 cock, which is opened by the fall of the 
 ball F ; at low water, the air will enter 
 the vessel D at B ; and before the next 
 high water, the water C will be forced 
 up the pipe F. 
 
 FOUNTAIN OF HIERO. 
 
 The Fountain of Hiero precisely resem- 
 bles in its operation, the Schemnitz foun- 
 tain, which was probably suggested to its 
 inventor by that of Hiero. 
 
 The first reservoir of this fountain is 
 lower than the orifice of the jet; and a pipe 
 descends from it to the air vessel, which 
 is at some distance below, and the pressure 
 of the air is communicated by an ascend- 
 ing tube to a third cavity, containing the 
 water which supplies the jet. The follow- 
 ing figure will convey an idea of this foun- 
 tain without any particular description of 
 ^ its several parts, for it so nearly resembles 
 the Schemnitz fountain in its operation, 
 that this becomes unnecessary, except per- 
 haps to state, that the pipe D here ascends. 
 
 WATER RAISED BY THE CHANGES IN THE 
 WEIGHT OF THE AIR. 
 
 The spontaneous changes which take 
 place in the pressure of the air, occasioned 
 by the changes in the weight and tempera- 
 ture of the atmosphere, have been applied, 
 by means of a series of reservoirs, furnished 
 with proper valves, to the purpose of rais- 
 ing water by degrees to a moderate height. 
 But it very seldom happens, that such 
 changes are capable of producing an ele- 
 vation in the water of each reservoir of 
 more than a few inches, or at most a foot 
 or two in a day ; consequently, the whole 
 quantity raised in this way must be very 
 inconsiderable. 
 
 jHiscellaneous Subjects. 
 
 MEMOIR OF THE LIFE OF THE 
 LATE PROFESSOR PLAYFAIR, 
 
 OF EDINBURGH. 
 
 John Playfair, a celebrated Scotch ma- 
 thematician and natural philosopher, was 
 the eldest son of the Rev. James Playfair, 
 minister of the united parishes of Liff and 
 Benvie, in the county of Forfar. He was 
 born at Benvie, on the 10th of March, 
 1748; and after receiving a classical edu- 
 cation under the roof of his father, he 
 entered the university of St. Andrews at 
 the age of fourteen. At this ancient seat 
 of learning, Mr. Playfair soon distinguished 
 himself by the excellence of his conduct, 
 as well as the ardour of his application ; 
 and so great was his progress in natural 
 philosophy, 'that Professor Wilkie, (the 
 author of the Epigoyiad ) who taught that 
 branch of knowledge in the university, 
 selected him to teach his class during his 
 indisposition. 
 
 In the year 1760, upon the death of Mr. 
 Stewart, Professor of Mathematics in Ma- 
 rischal College, Aberdeen, seven candi- 
 dates appeared for the vacant chair. 
 Among these were the Rev. Dr, Trail, Dr. 
 Hamilton, and Mr. Playfair. The profes- 
 sorship was a private foundation, by Dr. 
 Liddel, and a clause in the deed of foun- 
 dation was considered as a direction to fill 
 up the vacancy by a disputation or com- 
 parative trial. Dr. Reid, of Glasgow, 
 Mr. Vilant, of St. Andrews, Dr. Skene, of 
 Marischal College, and Professor Gordon, 
 of King’s College, accepted the office of 
 judges on this occasion ; and after a severe 
 examination, which lasted for a fortnight, 
 Dr. Trail was appointed te the chair. 
 Mr. Playfair was excelled only by two 
 out of six candidates; viz. Dr. Trail and 
 Dr. Hamilton ; but when it is considered, 
 that Mr. Playfair was two years younger 
 
THE ARTISAN. 
 
 219 
 
 than Dr. Trail, the result of the election 
 must have been greatly affected by that 
 circumstance alone ; and ,Dr. Trail himself 
 modestly remarked, that he attributed his 
 own success to this disparity of years. 
 
 In the year 1772, when the chair of natu- 
 ral philosophy became vacant by the death 
 of Dr. Wilkie, Mr. Playfair again che- 
 rished the hopes of a permanent appoint- 
 ment; but his expectations were a second 
 time frustrated ; a disappointment which 
 was the more severe, as the death of his 
 father in the same year had devolved upon 
 him the charge of his mother and her 
 family. This circumstance appears to 
 have determined Mr. Playfair to follow the 
 profession of his father, to which he had 
 been educated, but which his ardent 
 attachment to mathematical pursuits had 
 induced him to think of abandoning. 
 Having been presented by Lord Gray to 
 his father’s living of Liff and Benvie, Mr. 
 Playfair devoted his time to the duties of 
 his sacred office, to the education of his 
 younger brothers, and to the occasional 
 prosecution of his own favourite studies. 
 In 17.74 he went to Schehallien, where 
 Dr. Maskelyne was carrying on his inter- 
 esting experiments on the attraction of 
 mountains; and while he was enjoy- 
 ing the acquaintance of that eminent astro- 
 nomer, he was little aware that he should 
 himself contribute, at some distant period, 
 to the perfection of the result which it was 
 the object of this experiment to obtain. 
 
 In the year 1777, Mr. Playfair commu« 
 nicated to the Royal Society of London, an 
 essay On the Arithmetic of Impossible 
 Quantities, which appeared in the Trans- 
 actions for that year, and which was the 
 first display of his mathematical acquire- 
 ments. In this ingenious paper, which 
 is strongly marked with the peculiar 
 talent of its author, Mr. Playfair has 
 pointed out the insufficiency of the expla- 
 nation of the doctrine of negative quanti- 
 ties given by John Bernouilli and Maclau- 
 rin ; viz. that the imaginary ' characters 
 which are involved in the expression com- 
 pensate or destroy each other ; and he has 
 endeavoured to show that the arithmetic 
 of impossible quantities is nothing more 
 than a particular method of tracing the 
 affinity of the measures of ratios and of 
 angles, and that they can never be of any 
 use as an instrument of discovery, unless 
 when the subject of investigation is a 
 property common to the measures both of 
 ratios and of angles. 
 
 In the year 1785, when Dr. Adam Fer- 
 guson exchanged the chair of Moral Phi- 
 losophy in the University of Edinburgh, 
 for that of Mathematics, which was then 
 filled by Mr. Dugald Stewart, Mr. Play- 
 fair was appointed Joint Professor of Ma- 
 thematics, a situation which had been the 
 
 highest object of his ambition, and which 
 he was in a peculiar manner qualified to 
 fill. 
 
 As Mr. Playfair was a member of the 
 Philosophical Society of Edinburgh, he 
 became one of the original fellows of the 
 Royal Society at its institution by royal 
 charter in 1783, and, by his services as an 
 office-bearer, as well as by his communi- 
 cations as a member, he contributed most 
 essentially to promote the interests, and to 
 add to the renown, of this distinguished 
 body. His memoir On the Causes ivhich 
 affect the accuracy of Barometrical Measure- 
 ments, was read on the 1st of March, 1784, 
 and on the 10th January, 1785. The men- 
 suration of heights by the barometer was 
 involved in many errors. M. De Luc had 
 applied the important correction, depend- 
 ing on the temperature of the atmospheri- 
 cal column; but when the height was 
 great, and the difference of temperature at 
 the two extremities of the column con- 
 siderable, his method of estimating the 
 temperature was liable to considerable 
 error. Mr. Playfair was therefore led to 
 give an accurate formula for this purpose, 
 and to investigate new ones, in order to 
 express those other circumstances by 
 which the density pf the atmosphere is 
 affected, 
 
 Mr. Playfair was also the author of 
 several other valuable papers, among 
 which may be mentioned the following: 
 On the Origin and Investigation of Po- 
 risms ; Remarks on the Astronomy of the 
 Brahmins ; Investigation of certain Theo- 
 rems relative to the Figure of the Earth ; 
 On Volcanoes; On the progress of Heat, 
 when communicated to Spherical Bodies ; 
 On the Solids of greatest Attraction; a 
 subject to which his attention was directed 
 during a lithological survey of the moun- 
 tain of Schehallien, which he made in con- 
 junction with Lord Webb Seymour, in 
 1807, for the purpose of obtaining an esti- 
 mate of the specific gravity of the moun- 
 tain, in order to correct the deductions of 
 Dr. Maskelyne, respecting the mean den- 
 sity of the earth. 
 
 Mr. Playfair was also the author of 
 some very able pamphlets on the memo- 
 rable Leslie controversy, which took place 
 on the appointment of Mr. Leslie to the 
 Professorship in the University of Edin- 
 burgh, in 1805. 
 
 In the year 1795, Mr. Playfair published 
 his Elements of Geometry, which consisted 
 of the first six books of Euclid, with three 
 additional ones, containing the rectification 
 and quadrature of the circle, the intersec- 
 tion of planes, and the geometry of solids, 
 with plane and spherical trigonometry, 
 and the arithmetic of sines. The notes 
 to this w'ork possess a peculiar value ; and 
 hence the work itself has been held in 
 
220 
 
 THE ARTISAN. 
 
 high estimation for the purposes of ele- 
 mentary instruction. 
 
 After five years’ labour, Mr. Playfair 
 produced, in 1802, his Illustrations of the 
 Huttonian Theory , in one volume 8vo . ; 
 and on the 10th January, 1803, he read to 
 the Royal Society of Edinburgh his Bio- 
 graphical Account of the late Dr. James 
 Hutton. These two works added greatly 
 to the fame of their author ; and whether 
 we consider them as models of composi- 
 tion or of argument, we cannot but regard 
 them as the productions by which the name 
 of Mr. Playfair must be handed down to 
 posterity. Though brought out under the 
 modest appellation of a commentary, it is 
 unquestionably entitled to be regarded as 
 an original work ; and though the theory 
 which it expounds must always retain the 
 name of the philosopher who first suggested 
 it, yet Mr. Playfair has in a great measure 
 made it his own, by the philosophical 
 generalizations which he has thrown 
 around it; by the numerous phenomena 
 which he has enabled it to embrace; by 
 the able defences with which its weakest 
 parts have been sustained ; and by the 
 relations which he has shown it to bear to 
 some of the best established doctrines, 
 both in chemistry and astronomy. 
 
 Upon the death of Dr. Robison, in 1805, 
 Mr. Playfair was elected General Secre- 
 tary to the Royal Society, and he was 
 also appointed his successor in the chair of 
 natural philosophy, — a situation which his 
 mathematical acquirements, and his powers 
 of perspicuous illustration, rendered him 
 peculiarly qualified to fill. This event, 
 however, though in every respect ad van- 
 tageous to himself, interrupted in no slight 
 degree the progress of his general studies. 
 The preparation of a course of lectures on 
 subjects which he had only indirectly pur- 
 sued, and the composition of his Outlines 
 of Natural Philosophy, which he con- 
 sidered necessary for the use of his stu- 
 dents, occupied much of that valuable 
 time on which the higher interests of sci- 
 ence possessed so many claims. 
 
 In addition to the works which bear 
 Mr. Playfair’s name, he wrote various 
 articles in the Edinburgh Review, which 
 he never hesitated to acknowledge, and 
 some of which have been reprinted among 
 his works. Of these reviews, three are 
 particularly memorable, as indicating the 
 peculiar character of Mr. Playfair’s talents, 
 as well as the great versatility of his 
 powers. His analysis of the Mecanique 
 Celeste of Laplace, while it evinces the 
 highest powers of composition, is at the 
 same time one of the choicest specimens 
 of perspicuous illustration. His review 
 of Leslie’s Geometry (the ablest, perhaps, 
 that he ever wrote) is distinguished by a 
 masterly argument in one of the most diffi- 
 
 cult topics of abstract mathematics, and 
 has been no less celebrated for the force 
 and the dignity of its satire.* The review 
 of Madame de Stael’s Corinne in the same 
 work, affords the clearest evidence that 
 its author was equally fitted to shine in 
 the field of elegant literature and in the 
 walks of abstract science. Several other 
 reviews from Mr. Playfair’s pen would 
 have been entitled to notice in a more ex- 
 tended memoir of his life, but those already 
 mentioned have been selected as particu- 
 larly characteristic of his powers as a 
 natural philosopher, a profound mathema- 
 tician, and a cultivator of the lighter 
 branches of literature. 
 
 At the restoration of peace in 1815, Mr. 
 Playfair undertook a journey to the Con- 
 tinent, for the purpose of examining the 
 stupendous phenomena presented in the 
 geology of the Alps, — of studying the 
 recent effects of volcanic eruptions in Italy, 
 and of developing those of more ancient 
 convulsions among the extinct volcanoes 
 of Auvergne. Excepting the phenomena 
 exhibited in our own island, which he had 
 personally examined, Mr. Playfair had 
 acquired his geological knowledge prin- 
 cipally from books ; and it was therefore 
 desirable, before the republication of his 
 favourite work, that his views should re- 
 ceive those modifications which the study 
 of nature in her grandest forms could not 
 fail to suggest. With this view he spent 
 about seventeen months in France, Swit- 
 zerland, and Italy, busily engaged in geo- 
 logical observations; and he returned to 
 Edinburgh in the end of 1816, eager to 
 embellish and tomplete the great fabric 
 which it had been the business of his life 
 to rear. 
 
 Unfortunately, however, for the Hutto- 
 nian School, Mr. Playfair had been urged 
 to draw up a dissertation on the progress 
 of mathematics and physics for the Supple- 
 ment to the Encyclopaedia Britannica ; and 
 the composition of this paper, interrupted 
 the execution of the second edition of his 
 Illustration. 
 
 His health, had been for some time 
 on the decline; and in the winter of 1818 
 — 1819, his labours were often inter- 
 rupted by a severe attack of a disease in 
 the bladder, which, at his advanced period 
 of life, it was not easy to subdue. An in- 
 terval of health soothed for a while the. 
 anxieties of his friends ; but it was only a 
 deceitful precursor of the fatal attack 
 which carried him off, on the 19th July, 
 1819, in the 72d year of his age. 
 
 # M. Legendre, one of the first of modern geo- 
 in eters, lias, both privately and publicly, expressed 
 Ins particular admiration of this criticism. 
 
THE ARTISAN. 
 
 221 
 
 ARCHITECTURE. 
 
 CORINTHIAN ORDER. 
 
 This order is said to have been intro- 
 duced in the fourth century before the 
 Christian asra, by Scopas,who employed it 
 in the upper range of columns in the 
 ancient temple of Minerva at Tega. Vi- 
 truvius, however, ascribes the invention of 
 the Corinthian capital to Callimachus, who 
 is said to have been an Athenian sculptor 
 contemporary with Phidias about 540 B.C. 
 
 In all the examples of Stuart’s Athens, 
 
 this order has an attic base ; the upper 
 fillet of the trochilus or scotia projects as 
 far as the upper torus. 
 
 Vitruvius observes, that the shaft has the 
 same proportions as the Ionic, except the 
 difference which arose from the greater 
 height of the capital, it being a whole 
 diameter* whereas the Ionic is only two- 
 thirds of it. But this column, including 
 the base and capital, has, by the moderns, 
 been increased to ten diameters in height. 
 If the entablature is enriched, the shaft 
 should be fluted. The number of flutes 
 ancLfillets are generally 24 ; and frequently 
 the lower one-third of the height has ca- 
 bles or reeds, husks, spirally twisted rib- 
 bands, or some sort of flowers inserted on 
 them. 
 
 The great distinguishing feature of this 
 order is its capital, which has for 2000 
 years been acknowledged the greatest or- 
 nament of this school of architecture. The 
 height is one diameter of the column, to 
 which the moderns have added one-sixth 
 more. The body, or nucleus, is in the 
 shape of a bell, basket, or vase, crowned 
 with a quadrilateral abacus, w ith concave 
 sides, each diagonal of which is equal to 
 two diameters of the column. The lower 
 part of the capital consists of two rows of 
 leaves, eight in each row ; one of the 
 upper leaves fronting each side of the 
 abacus. The height of each row is one- 
 seventh, and that of the abacus one-eighth 
 of the whole height of the capital. The 
 space which remains between the upper 
 leaves and the abacus, is occupied by little 
 stalks, or slender caulicolse, which spring 
 from between every two leaves in the upper 
 row, and proceed to the corners, and also 
 to the middle of the abacus, where they 
 are formed into delicate volutes. The 
 sides of the abacus are moulded, and the 
 curves of the sides are continued, until they 
 meet in a sharp horn or point. In the 
 attic capital, the small divisions of the 
 leaves were pointed in imitation of the 
 acanthus. In Italy they most generally 
 resembled the olive. 
 
 It may be observed generally, in the 
 Greek Corinthian, that the volutes termi- 
 nate in a point in the natural spiral, with- 
 out either coiling round a circular eye, or 
 bending backwards in a serpentine form, 
 as in most of the Roman specimens. 
 
 This order seems never to have been 
 much employed in Greece before the time 
 of the Roman conquest ; but this powerful 
 people employed it almost exclusively in 
 every part of their extensive empire ; and 
 it is accordingly in edifices constructed 
 under their influence, that the most perfect 
 specimens are found. 
 
 Of the celebrated modern architects who 
 have treated of this order, Palladio makes 
 the column diameters high, one-fifth of 
 
THE ARTISAN. 
 
 222 
 
 which he gives to the entablature, con- 
 sisting of a cornice with modillions and 
 dentils, a flat frieze, and an architrave 
 With three faciae, divided by astrigals ; the 
 base is attic. The design of Scammozzi 
 bears a general resemblance to that of 
 Palladio, but his column has ten diameters 
 in its altitude ; his entablature is one-fifth 
 of this height ; the cornice has modillions, 
 the architrave consists of three faciae, di- 
 vided by astragals, and the base is attic. 
 Serlio, following Vitruvius, has given this 
 order an Ionic entablature, with dentils, 
 and the same proportion of the capital; 
 his column is nine diameters high, and has 
 a Corinthian base. Vignola’s Corinthian 
 is a grand and beautiful composition, 
 chiefly imitative of the three columns. He 
 makes the column ten diameters and a half 
 in height; the entablature is a fourth of 
 that altitude ; the cornice has modillions 
 and dentils, the frieze is plain, the archi- 
 trave of three faciae, divided by mouldings, 
 and the base is attic. 
 
 Sir William Chambers has obsetved, 
 that “ the Corinthian order is proper for 
 all buildings where elegance, gaiety, and 
 magnificence are required. The ancients 
 employed it in temples dedicated to Venus, 
 Flora, Proserpine, and the nymphs of 
 fountains ; because the flowers, foliage, 
 and volutes, with which it is adorned, 
 Seemed well adapted to the delicacy and 
 elegance of such deities.” 
 
 ON THE IMPRACTICABILITY OF 
 PRODUCING A PERPETUAL MO- 
 TION. 
 
 Perpetual motion , is a motion which is 
 supplied and renewed from itself, without 
 the intervention of any external cause: to 
 find a perpetual motion, or to construct a 
 machine which shall have such a motion, 
 is a subject which has engaged the atten- 
 tion of mathematicians for more than two 
 thousand years; though none, perhaps, 
 have prosecuted it with so much zeal and 
 hopes of ultimate success as some of the 
 speculative philosophers of the present age. 
 
 Infinite are the schemes, designs, plans, 
 engines, wheels, &c. to which this longed- 
 for perpetual motion has given birth ; and 
 it would not only be endless but ridiculous 
 to attempt to give a detail of them all, es- 
 pecially as none of them deserve particular 
 mention, since they have all equally proved 
 abortive ; and it would rather partake of 
 the nature of an affront than a compliment, 
 to distinguish the pretenders to this dis- 
 covery ; as the very attempting of the thing 
 conveys a very unfavourable idea of the 
 mental powers of the operator. 
 
 For among all the laws of matter and 
 
 motion we know of none, which seems to 
 afford any principle or foundation for such 
 an effect. Action and reaction are allowed 
 to be ever equal ; and a body which gives 
 any quantity of motion to another, always 
 loses just so much of its own: but,- under 
 the present state of things, the resistance 
 of the air, and the friction of the parts of 
 machines, necessarily retard every motion. 
 
 To keep the motion going on, therefore, 
 there must either be a supply from some 
 foreign cause ; which, in a perpetual mo- 
 tion, is excluded : 
 
 Or, all resistance from the friction of 
 the parts of matter must be removed; 
 which necessarily implies a change in the 
 nature of things. 
 
 For, by the second law of motion, the 
 changes made in the motions of bodies are 
 always proportional to the impressed 
 moving force, and are produced in the 
 same direction with it ; no motion, then, 
 can be communicated to any engine, greater 
 than that of the first force impressed. 
 
 But, on our earth, all motion is per- 
 formed in a resisting fluid; namely, the 
 atmosphere, and must therefore, of neces- 
 sity, be retarded : consequently, a consi- 
 derable quantity of its motion will be spent 
 on the medium. Nor is there any engine 
 or machine wherein all friction can be 
 avoided; there being in nature no such 
 thing as exact smoothness, or perfect con- 
 gruity : the manner of the cohesion of the 
 parts of bodies, the small proportion which 
 the solid matter bears to the vacuities be- 
 tween them, and the nature of those con- 
 stituent particles, not admitting it. 
 
 Friction, therefore, will also in time 
 sensibly diminish the impressed or com- 
 municated force; so that a perpetual mo- 
 tion can never follow, unless the communi- 
 cated force be- so much greater than the 
 generating force, as to supply the diminu- 
 tion occasioned by all these causes : but 
 the generating force cannot communicate a 
 greater degree of motion than it had itself. 
 Therefore, the whole affair of finding a 
 perpetual motion, comes to this; viz, to 
 make a weight heavier than itself, or an 
 elastic force greater than itself: or, there 
 must be some method of gaining a force 
 equivalent to what is lost, by the artful 
 disposition and combination of the mecha- 
 nical powers : to this last point, then, all 
 endeavours are to be directed ; but how, 
 or by what means, such a force can be 
 gained, is still a mystery ! 
 
 The multiplication of powers or forces 
 avails nothing: for what is gained in 
 power, is lost in time ; so that the quan- 
 tity of motion still remains the same. 
 
 The whole science of Mechanics cannot 
 really make a little power equal or supe- 
 rior to a larger ; and wherever a less power 
 is found in equilibrio with a greater, as 
 
THE ARTISAN. 
 
 22S 
 
 for example, twenty-five pounds with a 
 hundred, it is a kind of deception of the 
 sense : for the equilibrium is not strictly 
 between one hundred pounds and twenty- 
 five pounds, but between one hundred 
 pounds, and twenty-five pounds moving, 
 (or disposed to move,) four times as fast as 
 the one hundred. 
 
 A power of ten pounds, moving with ten 
 times the velocity of one hundred pounds, 
 would have equalled the one hundred in 
 the same manner ; and the same may be 
 said of all the possible products equal to 
 one hundred : but, there must still be one 
 hundred pounds of power on each side, 
 whatever way they may be taken ; whe- 
 ther in matter, or in velocity. 
 
 This is an inviolable law of nature ; by 
 which nothing is left to art, but the choice 
 of the several combinations that may pro- 
 duce the same effects. 
 
 The only interest that we can take in the 
 projects which have been tried for procur- 
 ing a perpetual motion, must arise from the 
 opportunity that they afford of observing 
 the weakness of human reason. 
 
 For a better instance of this can scarcely 
 be supplied than to see a man spending 
 whole years in the pursuit of an object, 
 which a single week’s application to sober 
 philosophy would have convinced him was 
 unattainable. 
 
 But for the satisfaction of those who may 
 not be convinced of the impossibility of at- 
 taining this grand object, we shall add a 
 few observations on the subject of a still 
 more practical nature than the above. 
 
 The most satisfactory confutation of the 
 notion of the possibility of a perpetual mo- 
 tion, is derived from the consideration of 
 the properties of the centre of gravity ; it 
 is only necessary to examine whether it 
 will begin to descend or ascend, when the 
 machine moves, or whether it will remain 
 at rest. If it be so placed, that it must 
 either remain at rest or ascend, it is clear, 
 from the laws of equilibrium, that no mo- 
 tion derived from gravitation can take 
 place : if it may descend, it must either 
 continue to descend for ever with a finite 
 velocity, which is impossible, or it must 
 first descend and then ascend, with a vi- 
 bratory motion, and then the case will be 
 reducible to that of a pendulum, where it 
 is obvious, that no new motion is generated, 
 and that the friction and resistance of 
 the air must soon destroy the original mo- 
 tion. 
 
 One of the most common fallacies, by 
 which the superficial projectors of ma- 
 chines for obtaining a perpetual motion 
 have been deluded, has arisen from ima- 
 gining, that any number of weights as- 
 cending by a certain path, on one side of 
 the centre of motion, and descending in 
 the other, at a greater distance, must cause 
 
 a constant preponderance on the side of 
 the descent: and for this purpose weights 
 have been made to slide or roll along 
 groves or planes, which lead them to a 
 more remote part of the wheel from whence 
 they return as they ascend, as represented 
 in the following figure,* 
 
 or they have been fixed on hinges , which 
 allow them to fall over at a certain point, 
 so as to become more distant from the 
 centre ; but it will appear on the inspec- 
 tion of such a machine, that although some 
 of the weights are more distant from the 
 centre than others, yet there is always a 
 proportionally smaller number of them on 
 that side on which they have the greater 
 power; so that these circumstances pre- 
 cisely counterbalance each other. 
 
 W e have heard it proposed to attach 
 hollow arms to a wheel by joints or hinges 
 at the circumference, and to fill these arms 
 with quicksilver, or small balls, instead of 
 the plan represented by the above figure ; 
 but though we have never heard of it 
 having been tried, we are perfectly con- 
 vinced, that it would end as all other at- 
 tempts have done; that is, in a total failure* 
 
 SOLUTION OF QUESTIONS. 
 
 Quest. 25, answered by Mr. A. Peacock, 
 i St. George's East. 
 
 The figure of the stone may be reckoned 
 a prismoid, the arches being but a small 
 part of a large circle will have but a tri- 
 fling difference from the chords. 
 
 First 76 -f 5zi81 the greater diameter, 
 and 81 :3£: : 76: 3 127572 the least breadth ; 
 then 3^ X 4 zz 13§ area of the greater end ; 
 
 * In tbe model, the balls may be kept in their 
 places by a plate of glass covering the wheel. 
 
THE ARTISAN. 
 
 224 
 
 and 3-127572 X 4 “12-510288 area of the 
 lesser end ; then, 
 
 3£ -f 12-5 80288 -f-2=zl2‘921B10 mean area, 
 therefore, 3^ + 12-510288 + 12*921810 X 4 
 zz 77-53086, which multiplied by |zz 
 64-60905 solid feet the content of the stone ; 
 and as one solid foot of Portland stone 
 weighs 2570 ounces, 64*60905 X 2570“ 
 166045| ounces zz 4 tons, 12 cwt, 2 qrs. 
 17 lb, 13 oz. the weight of the stone. 
 
 This question was also answered cor- 
 rectly by Mr. H. Flatiier, the proposer ; 
 but he neglected to find the weight of the 
 stone, after determining its solid content. 
 
 Quest. 28, answered by Master James 
 O’Reilly, Portsea. 
 
 Let CBEL represent the tower : 
 
 from E (the top of it) let fall the per- 
 pendicular E D. Then by the hypothesis, 
 D O zz 16, B Ozz 6 and therefore E O “182. 
 Now, since the angles C B O, ODE are 
 right angles, and the angles at O equal, 
 the triangles CBO, ODE are equian- 
 gular ; therefore, DO:EO::BO : CO; 
 or 16 : 182 : : 6 : 68-25 = CO; 
 but ^/C O 2 — O B * = CB; therefore 
 CB=z n /(68*25) 2 — ( 6 ) 2 =67*985 the 
 diameter. 
 
 This question was also solved by the 
 proposer, and by Mr. R. Graham, Teacher , 
 Liverpool. 
 
 In the above solution the tower is sup- 
 posed to be cylindrical. 
 
 Quest. 29, answered by Mr.WHiTECOMBE, 
 Teacher of Mathematics, Cornhill. 
 
 Put azz 3*14159 m zz *5236, and let x 
 — diameter of the globe ; then pr. mensu- 
 ration ax 2 zz convex surface, and mx 3 — 
 solidity. Therefore, pr. question ax 2 ~mx 3 , 
 then -f- by x 2 we have a zz mx. Hence, 
 
 .r zz ~ zz 6 as Required. 
 
 m 
 
 This question was answered by so many 
 other Correspondents, that we cannot find 
 room to insert their names ; we may, how- 
 ever state, that the gentlemen who solved 
 the following question were among the 
 number. 
 
 Quest. 30, answered by Mr. J. Mill- 
 ward, Hammersmith. 
 
 The longest line that can be drawn in a 
 cube is the diameter of the circumscribing 
 sphere, or, the diagonal of a plane that 
 cuts the cube, by passing through the 
 diagonals of two of its opposite planes ; 
 and the square of the side or face of the 
 cube is one-third of the square of thatline. 
 
 Therefore, if the diameter of a cube be 9 
 inches, ^9 * _i_ 3 zz 5*1961524 zz the side 
 of the cube; and (5-1961524) 3 zz 
 140*296113573 zz the solidity of the cube. 
 Which was required. 
 
 This question w as also solved by the fol- 
 lowing gentlemen: Mr. J. Snart, Tooley- 
 street; Mr. R. Graham, Liverpool; Master 
 James O’Reilly, Portsea; M. J. White- 
 combe, Cornhill; Mr. A. Peacock, St. 
 George’s East; Mr. J. Stephens; Mr. 
 John Barr, Somers Town; Mr. J. Hol- 
 royd, Oldham; C. N. S.; and by the Pro- 
 poser. 
 
 QUESTIONS FOR SOLUTION. 
 
 Quest. 34, proposed by I. C. S. Church- 
 row. 
 
 Suppose the neck of the hollow glass 
 ball (see Artisan, Expt. 5, page 69) to be 
 immersed in water, and the air to be ex- 
 tracted out of it and the receiver which 
 covers it : required how much rarer was 
 the air within the receiver before admitting 
 the air from without, and how much water 
 it forced into the ball, supposing the dia- 
 meter of the water’s surface when forced 
 into the ball to be 7*2, and its height from 
 the top of the ball to be 1*8 of an inch ? 
 
 Quest. 35, proposed by Mr. R. Graham, 
 Liverpool. 
 
 There is a globe of cast-iron one foot 
 diameter, and a conical piece of dry oak six 
 feet in length on the side of the prince’s 
 dock, Liverpool ; required the diameter of 
 the cone’s base when the globe is fixed to 
 the vertex of the cone and put into the dock 
 at full tide, where it floats with its surface 
 just level with the water ? 
 
 Quest. 36, proposed by G. G. C. 
 
 Required how much higher than the cross 
 of St. Paul’s must a person be elevated, in 
 order to see the top of the Eddystone Light- 
 house ? 
 
THE ARTISAN. 
 
 225 
 
 RHEUMATICS, 
 
 STEAM ENGINE. 
 
 Having given a description and repre- 
 sentation of the steam engines of Savery 
 and Newcomen, (see page 195;} and also 
 of the double stroke engine of the late cele- 
 brated Mr. Watt, we shall now begin to 
 give a particular description of its prin* 
 cipal parts, previous to noticing some of 
 those engines for which patents have been 
 more recently obtained. But it will tend 
 very much to render a description of the 
 several parts of this master-piece of human 
 skill more easily understood, to give a 
 short account of the alterations and im- 
 provements made upon it by Mr. Watt, and 
 this we cannot do better than by quoting a 
 part of that excellent engineer’s patent. 
 
 “ My method of lessening the consump- 
 tion of steam, «and consequently fuel in fire 
 engines,” says Mr. Watt, in the specifica- 
 tions of his patent, “ consists of the follow- 
 ing principles. First, that vessel in which 
 the powers of steam are to be employed, 
 to work the engine, which is called the cy- 
 linder in common fire engines, and which 
 I call the steam vessel, must, during the 
 whole time the engine is at work, be kept 
 as hot as the steam that enters it ; first, by 
 inclosing it in a case of wood, or any other 
 materials that transmit heat slowly; se- 
 condly, by surrounding it with steam, or 
 other heated bodies ; and thirdly, by suffer- 
 ing neither water, nor any other substance 
 colder than steam, to enter or touch it 
 during that time. Secondly, in engines 
 that are to be worked wholly or partially 
 by condensation of steam, the steam is to 
 be condensed in vessels distinct from the 
 steam vessels, or cylinder, although occa- 
 sionally communicating with them ; these 
 vessels I call condensers; and, whilst the 
 engines are working, these condensers 
 ought at least to be kept as cold as the air, 
 in the neighbourhood of the engines, by 
 application of water, or other cold bodies. 
 Thirdly, whatever air or other elastic 
 vapour is not condensed by the cold of the 
 condenser, and may impede the working 
 of the engine, is to be drawn out of the 
 steam vessels, or condensers, by means of 
 pumps wrought by the engines them- 
 selves, or otherwise. Fourthly, I intend, 
 in many cases, to employ the expansive 
 force of steam to press on the pistons, or 
 whatever may be used instead of them, in 
 the same manner as the pressure of the at- 
 mosphere is now employed in common fire 
 engines : in cases where cold water cannot 
 be had in plenty, the engifies may be 
 wrought by this force of steam only, by 
 
 Vol, I.— No, 15. 
 
 discharging the steam into the open air after 
 it has done its office. Fifthly, where mo- 
 tions round an axis are required, I make 
 the steam vessels in form of hollow rings, 
 or circular channels, with proper inlets 
 and outlets for the steam, mounted on ho- 
 rizontal axles like the wheels of a water 
 mill ; within them are placed a number of 
 valves, that suffer any body to go round the 
 channel in one direction only ; in these 
 steam vessels are placed weights, so fitted 
 to them as entirely to fill up a part or por- 
 tion of their channels, yet capable of 
 moving freely in them by the means herein- 
 after mentioned or specified. When the 
 steam is admitted in these engines, be- 
 tween the weights and the valves, it acts 
 equally on both, so as to raise the weight 
 to one side of the wheel, and, by the re- 
 action of the valves, successively, to give a 
 circular motion to the wheel, the valves 
 opening in the direction in which the 
 weights are pressed, but not in the con- 
 trary ; as the steam vessel moves round, it 
 is supplied with steam from the boiler, and 
 that which has performed its office may 
 either be discharged by means of conden- 
 sers, or into the open air. Sixthly, I in- 
 tend, in some cases, to apply a degree of 
 cold, not capable of reducing the steam to 
 water, but of contracting it considerably, 
 so that the engines may be worked by the 
 alternate expansion and contraction of the 
 steam. Lastly, instead of using water to 
 render the piston or other parts of the 
 engines air and steam tight, I employ oils, 
 wax, resinous bodies, fat of animals, 'quick- 
 silver, and other metals, in their fluid 
 state.” 
 
 The term of this patent was prolonged 
 by act of parliament until the year 1799 ; 
 but although the legal privilege of the 
 original manufacturers expired, yet the 
 superiority of their workmanship still gave 
 their engines a decided preference to others. 
 It was found, that their engines saved 
 three-fourths of the fuel formerly used; 
 and that only one-fourth of the whole force 
 of the steam was wasted. One of these 
 engines, with a thirty inch cylinder, per- 
 forms the work of 120 horses, working 8 
 hours each, per day. 
 
 In order to regulate the varying quantity 
 of steam, which was produced by the dif- 
 ferent states of the fire under the boiler, 
 and admitted into the cylinder, Mr. Watt 
 thought of several methods; but the one 
 generally employed is to place a valve in 
 the pipe connecting the boiler and the cy- 
 linder, which is made to increase or dimi- 
 nish the passage for the steam. This valve 
 is called a throttle-valve, and is made to 
 act of itself, and also made to admit of 
 being so adjusted as to admit less steam 
 into the cylinder, when the piston is moving 
 
226 
 
 THE ARTISAN. 
 
 with too great velocity, and. to admit a figure, page 197), and called a lift-tenter, 
 greater quantity when it is moving too were employed by Mr. Watt to regulate the 
 slowly. opening and shutting of the throttle-valve. 
 
 The attached balls marked W, (see the Thus in the annexed figure 
 
 a , a are the two balls attached to an upright 
 spindle by a joint, and connected with the 
 throttle-valve by a series of small levers 
 resting on a pivot z. x is an endless chain 
 or cord going round a pully 0 , which is 
 fixed to the vertical stem r, and retained in 
 that position by moving in sockets at z and 
 y . a, a, are two balls fixed to levers having 
 a moveable joint at y : these levers are 
 bent after their junction, in the position 
 shown in the figure, and are connected by 
 another joint at c, c, to two short levers 
 fixed by a joint at n, n, to a broad ring or 
 strap of metal moving freely up and down 
 on the vertical spindle. On this ring or 
 strap, the ends of a lever z formed like a 
 fork, are made to fit it ; the lever is sus- 
 pended at z and has another joint at h, by 
 which it is connected with the rod S, which 
 is attached to the axis of the throttle- valve. 
 When the piston is moving with its usual 
 velocity, the balls, being connected by the 
 endless rope x, revolve and hang in the 
 situation as shewn in the figure. But 
 should the velocity of the piston be much 
 increased, its motion will be communicated 
 by the rope and pulley to the spindle r , and 
 the balls will, by their centrifugal force, 
 rise into the situation shewn by the dotted 
 lines i, i ; this will depress the ends of 
 their levers at c, c, and also the end of the 
 horizontal lever which is attached to the 
 
 moveable ring ; and the rod S, will be 
 raised, which closes in part, the steam way. 
 Should the motion of the piston be too 
 slow, instead of rising ' , the balls will fall, 
 and have quite a contrary operation on the 
 levers and throttle-valve; and diminish 
 the quantity of steam admitted into the 
 cylinder. 
 
 By these and other contrivances, having 
 made the reciprocating motion of his en- 
 gines very regular, Mr. Watt early turned 
 his attention to the important object of pro^ 
 ducing a continuous rotatory motion from a 
 reciprocating one. 
 
 “ Among the many schemes,” says 
 Mr. Watt, “ which passed through my 
 mind, none appeared so likely to answer 
 the purpose as the application of a crank 
 in the manner of a common turning lathe, 
 (an invention of great merit, of which the 
 humble inventor and even its era are un- 
 known) ; but as the rotative motion is pro- 
 duced in that machine by the impulse given 
 to the crank in the descent of the foot only, 
 and is continued in its ascent by the mo- 
 mentum of the wheel, which here acts as a 
 fly ; and being unwilling to load my engine 
 with a fly heavy enough to continue the 
 motion during the ascent of the piston (and 
 even were a counterweight employed to 
 act, during the ascent, of a fly heavy 
 enough to equalize the motion) I proposed 
 
THE ARTISAN. 
 
 227 
 
 to employ two engines, acting upon two 
 cranks, fixed on the same axis at an angle 
 of 120 degrees to one another, and a weight 
 placed on the circumference of the fly at 
 the same angle to each of the cranks, by 
 which means a motion might be rendered 
 nearly equal, and a very light fly would 
 only be requisite.” 
 
 In order to obtain a rotatory motion from 
 a rectilineal one by some other means than 
 the crank, Mr. Watt introduced what is 
 now called the Sun and Planet Wheels : 
 it is also a cardioid motion, and has several 
 
 advantages over the crank, where a more 
 rapid movement is to be given to the fly ; 
 the fly being made to revolve with double 
 the velocity as when a crank is employed. 
 It is not, however, so simple, and its con- 
 struction makes it more expensive, besides 
 it is easily put out of order, and has now 
 given place to the crank. 
 
 We shall, however, give a short descrip- 
 tion of these wheels, as they are sometimes 
 employed in other machines. In the an- 
 nexed figure 
 
 x , is an arm attached to the lever, or work- 
 ing beam ; and S, the axis which imparts 
 motion to the machinery. The wheel T, is 
 fixed to x, and the wheel S, on the axis of 
 R ; and both wheels are fixed as nearly as 
 possible in the same vertical plane. On the 
 rising and falling of the working beam, 
 the wheel T, is carried round the circum- 
 ference of the wheel S, and at the instant 
 when the motion of the lever is reversed, 
 the continuous rotatory movement is pro- 
 duced by the momentum of the fly-wheel. 
 
 In order to ascertain the elasticity or 
 
 expansive force of the steam remaining in 
 the condenser, Mr. Watt adapted a baro- 
 meter tube filled with mercury, to the con- 
 denser. The mercury in this tube is acted 
 upon nearly in the same manner, as the 
 mercury in the common barometer by the 
 atmosphere : and if a perfect vacuum were 
 produced in the condenser, the mercury in 
 the tube would stand at the same height as 
 in the common barometer ; but as a perfect 
 vacuum is never produced, the mercury in 
 the tube rises to a height corresponding to 
 the degree of elasticity possessed by the 
 Q 2 
 
228 
 
 THE ARTISAN. 
 
 steam, and shows the force with which the 
 atmospheric air presses on the mercury to 
 enter the condenser. A similar tube, 
 called the Steam-Gauge, was fixed on the 
 boiler which indicated, by the ascent and 
 descent of the mercury, the elasticity of 
 the steam, and consequently shows the 
 
 force with which the steam presses upon 
 the boiler, in order to make its escape, 
 when its temperature exceeds 212 degrees. 
 At a less temperature than this, it will 
 stand at the same degree as the condenser 
 gauge. 
 
 OPTICS. 
 
 CAMERA OBSCTJRA. 
 
 The camera obscura, or the dark chamber, 
 is a name given to a very amusing optical 
 instrument invented by Baptista Porta. 
 
 If a room be made entirely dark, and a 
 convex lens of one or more feet focal length 
 be placed in a small hole in the window 
 shutter, it will form behind it, on a sheet of 
 white paper, a beautiful picture of all the 
 objects before it, in which will be seen all 
 
 those movements and changes of colour 
 and of position, which characterize the 
 living picture without. 
 
 In order, however, to have this picture 
 formed upon a horizontal surface for the 
 purpose of copying it, the rays proceeding 
 from it must be received upon a plane mir- 
 ror, inclined to the horizon at an angle of 
 45°, as shown in the following figure : 
 
 where A B is the object without the win- 
 dow, CD the lens, G’H the image that 
 would be formed upon a vertical sheet of 
 paper if the plane mirror EF were not in- 
 terposed, and I K the image formed upon a 
 plate of ground glass whose rough surface 
 is placed uppermost. 
 
 The picture may then be traced with 
 great accuracy on the surface of the ground 
 glass. But if it be required to throw the 
 image upon a sheet of white paper, we 
 have only to conceive the whole inverted, 
 and E F placed a little nearer to C D, ip 
 order to throw I K to a greater distance, 
 and leave room for the introduction of the 
 hand of the artist between E and K. 
 
 The foregoing figure represents the con- 
 struction of the portable camera obscura, 
 the outside of which is exhibited by the 
 following figure : 
 
 It consists of two square drawers, D and 
 E F, the drawer D containing the lens at 
 C D, and capable of being moved out or in 
 within the tube E for the purpose of ad- 
 justing the focus of the lens to the distance 
 of the object. The other drawer E con- 
 tains the inclined mirror E F, which re- 
 flects the rays upon the ground glass G, 
 and has a lid which turns up in order to 
 keep off the light from the picture on the 
 ground glass. 
 
 When it is required to draw upon the 
 surface of paper, the camera obscura must 
 have the form represented by the following 
 figure, 
 
 f 
 
THE ARTISAN.- 
 
 229 
 
 where A B is the lens, and CD a mirror 
 on the outside of it, which is placed in 
 such a manner as to reflect the landscape 
 downwards, on the ground E F. The ob- 
 server places his head through an opening 
 on one side, and introduces his hand with 
 the pencil through another opening, so 
 that no light whatever may be admitted at 
 these apertures to efface the distinctness of 
 the picture. 
 
 A camera obscura for public exhibition 
 requires to be on a large scale ; so that 
 several persons may see it distinctly at the 
 same time. Instruments of this kind are 
 generally erected in public Observatories, 
 such as that of Greenwich, Edinburgh, and 
 Glasgow, where three very fine camera ob- 
 scuras have been fitted up ; but our limits 
 will not permit us to give a description of 
 them. 
 
 In the construction of the camera ob- 
 scura, the splendour of the picture depends 
 on various circumstances which have not 
 hitherto been sufficiently attended to. It 
 has been found from experience, that a 
 common lens, is preferable to the best 
 achromatic object glass; and Dr. Wollaston 
 has suggested the application of the peris- 
 copic principle to the lens of the camera. 
 M. Cauchoix has found, that the most ad- 
 vantageous ratio of the radii of curvature 
 is that of 5 to 8, the shortest of the two 
 being that which is turned towards the 
 image. 
 
 Next to the optical perfection of the 
 image is the nature of the surface upon 
 which it is received. When paper is em- 
 ployed, it should be made as smooth as 
 possible by burnishing the surface; and 
 when a stucco surface is used, the greatest 
 care must be taken to remove all asperities, 
 and make it perfectly uniform. With the 
 view of obviating the imperfection of the 
 ordinary opaque grounds, Dr. Brewster 
 made a great variety of experiments. 
 Though he did not find any white surfaces 
 superior to those in common use, he was 
 surprised to observe the brilliancy and 
 distinctness with which the pictures were 
 represented when received upon the sil- 
 vered back of a looking-glass ; and he gave 
 additional perfection to the images, by 
 removing the protuberances and roughness 
 of the tinfoil, by carefully grinding the 
 surface with a soft kind of bone. Not- 
 withstanding the bluish colour of the me- 
 tallic ground, while objects are represented 
 in their true tints, and so brilliant is the 
 colouring, and so rich the verdure of the 
 foliage, that the image seems to surpass in 
 beauty even the object itself. Various ex- 
 periments have also been made by the same 
 author, to discover a good transparent sur- 
 face as a substitute for ground glass, which 
 
 would permit the application of an eye- 
 glass. The loss of light, when the image 
 is received on ground glass is enormous. 
 In order to prevent this, and give brilliancy 
 to the colouring, Dr. Brewster places ano- 
 ther plate of glass above the ground one, 
 and introduces between them water, or any 
 other fluid of a different refractive power 
 from the ground glass; the dispersion of 
 the light at the separating surface of the 
 ground glass and the fluid being sufficient 
 to detain the convergent pencils without 
 greatly weakening their intensity. As 
 such a ground, however, cannot be used for 
 copying, he put a slightly opaque varnish 
 upon the surface of a glass plate, and also 
 upon thin squares of mica, and he found, 
 that these varnishes might be marked with 
 the finest lines of a pencil, and that an 
 impression of the sketch might be conveyed 
 by the slightest pressure of the hand on a 
 piece of paper. One of the simplest and 
 best of all the varnishes which he used 
 was that of milk dried upon the glass, after 
 it had been freed entirely from its buty- 
 raceous particles. The beauty and dis- 
 tinctness is such, that it will even admit the 
 application of a lens to magnify the image, 
 and when properly made, will receive the 
 mark of a black lead pencil. 
 
 ON THE MEGASCOPE. 
 
 The name of megascope has been given 
 to the camera obscura, when employed to 
 represent, or to take copies of objects 
 placed in front of the window, or of the lens 
 in the portable camera obscura, and placed 
 at a short distance from it. In this case, the 
 image is generally received at a distance 
 from the lens greater than that of the ob- 
 ject ; and is consequently very much mag- 
 nified. By altering the distance of the 
 object, the size of the image may be in- 
 creased or diminished at pleasure; and 
 when the object does not reflect much 
 light, we have it in our power to illuminate 
 it artificially. The megascope may be made 
 to magnify as much as fifteen times with 
 great advantage, and is an instrument of 
 very great use in taking correct outlines or 
 representations of natural objects, which, 
 from their smallness or other causes, are 
 not susceptible of being submitted to exact 
 mensuration. The megascope may even 
 be employed for copying plans or drawings 
 on an enlarged or a reduced scale. 
 
 ON THE MAGIC LANTERN. 
 
 The magic lantern, an optical instru- 
 ment invented by Athanasius Kircher, 
 differs from the megascope only ip the way 
 in which it is fitted up, and in the purposes 
 to which it is applied. It consists of a lens 
 AB, 
 
230 
 
 THE ARTISAN. 
 
 which forms on the wall 'an enlarged 
 image of any object placed before it, and 
 at a greater distance than its anterior prin- 
 cipal focus. The objects used in the magic 
 lantern, are pictures painted with transpa- 
 rent varnishes in the form of sliders, which 
 move through a groove in front of the lens 
 AB. These paintings are strongly illumi- 
 nated with a lamp inclosed in a lantern, 
 which admits no light whatever into the 
 room excepting what passes through the 
 lens A B. The light of the lamp is 
 thrown in a condensed state upon the pic- 
 tures by means of an illuminating lens, 
 which is sometimes nearly hemispherical, 
 and the illumination is still farther in- 
 creased by a concave mirror, which 
 throws back the light of the lamp, that 
 radiates in the direction of the object. 
 The painting on the sliders being thus 
 strongly illuminated, a very distinct and 
 enlarged image of it is represented on the 
 wall according to principles already 
 described ; and the magnitude of the 
 image will be to the magnitude of the ob- 
 ject as their respective distances from the 
 lens A B. Hence, the magnifying power 
 
 may be diminished or increased, by bring- 
 ing the white screen that receives the 
 image either nearer to the lantern, or re- 
 moving it to a greater distance. The images 
 in the magic lantern are much improved by 
 substituting two lenses in place of A B, 
 having greater focal lengths than the single 
 lens. 
 
 The magic lantern, which for a long time 
 was used only as an instrument for amus- 
 ing children and astonishing the ignorant, 
 has recently been fitted up for the purpose 
 of conveying scientific instruction ; and is 
 now universally used by popular lecturers 
 on astronomy for representing the phases 
 and the motions of the heavenly bodies, 
 all of which are minutely painted on the 
 sliders. 
 
 The magic lantern may be employed in 
 almost every branch of scientific instruc- 
 tion' where it is desirable to give a distinct 
 and enlarged representation of pheno- 
 mena to a public class. The lecturer is 
 thus saved the trouble of carrying about 
 with him unwieldy diagrams, ^ which are 
 soon destroyed by use, and rendered unfit 
 for their intended purpose. 
 
 CHEZ^XSTI&'Sr. 
 
 MURIATIC ACID. 
 
 According to Dr. Thomson there are 
 only two simple incombustible substances 
 which unite to oxygen ; viz. Azote and 
 Muriatic Acid; the former of these has 
 already been treated of, and the second we 
 shall make the subject of the present article. 
 
 The name muriatic acid is taken from the 
 substance which most plentifully aEffords it, 
 namely, sea or marine salt, the muria of 
 the Latins. This name is given to it, 
 because its radical, or base, has not yet 
 been discovered in nature. Before the 
 framing of the methodical nomenclature, it 
 was called spirit of salt, marine acid, and 
 sometimes acid of salt. 
 
 The muriatic acid exists abundantly in 
 nature in combination with common salt and 
 the waters of the ocean. And though we 
 are almost witnesses of this formation, we 
 are yet unacquainted with the principles 
 employed by nature, the proportion in 
 which she combines them, and the mode 
 in which the combination is effected. 
 
 Muriatic acid may be procured by the 
 following processes: 
 
 Let a small pneumatic trough be pro- 
 cured, hollowed out of a single block of 
 wood; about 15 inches long, 7 broad, and 
 6 deep. After it has been hollowed out 
 to the depth of an inch, leave three inches 
 
THE ARTISAN. 
 
 231 
 
 by way of a shelf on one side, and cut out 
 the rest to the proper depth, giving the in- 
 side of the bottom a circular form, as re- 
 presented by the annexed figure*. 
 
 This trough is to be filled with mercury 
 to the height of a quarter of an inch above 
 the surface of the shelf. A small glass 
 jar is then to be filled with the mercury, 
 and placed on the shelf of the trough over 
 one of the slits made on purpose. 
 
 The apparatus being thus disposed, two 
 or three ounces of common salt are to be 
 put into a small retort, and an equal quan- 
 tity of sulphuric acid added ; the beak of 
 the retort plunged below the surface of the 
 mercury in the trough, and the heat of a 
 lamp applied to the bottom of the retort. 
 A violent effervescence will then take 
 place ; and air bubbles will rush in great 
 numbers from its beak, and rise to the sur- 
 face of the mercury in a visible white 
 smoke, which has a very peculiar odour. 
 After allowing a number of them to escape, 
 till it is supposed that the common air 
 which previously existed in the retort has 
 been displaced, plunge its beak into the 
 slit in the shelf over which the glass jar 
 has been placed. The air bubbles will 
 soon displace the mercury and fill the jar. 
 The gas thus obtained is called muriatic 
 acid gas. 
 
 This substance in a state of solution in 
 water was known even to the alchymists ; 
 but in a gaseous state it was first examined 
 by Dr. Priestley, in an early part of that 
 illustrious career in which he added so 
 much to our knowledge of gaseous bodies. 
 
 1 . Muriatic acid gas is an invisible elas- 
 tic fluid, resembling common air in its me- 
 chanical properties. Its specific gravity, 
 according to the experiments of Mr. Kirwan 
 is 1*929, that of air being 1*000, at the tem- 
 perature of 60°, barometer 30 inches ; 100 
 cubic inches of it weigh 59*8 grains. Its 
 smell is pungent and peculiar ; and when- 
 ever it comes in contact with common air, 
 it forms with it a visible white smoke. If 
 
 * Troughs of this kind are to be got ready made 
 at all the shops where chemical apparatus are 
 sold. 
 
 a little of it be drawn into the mouth, it i 3 
 found to taste excessively acid ; much more 
 so than vinegar. 
 
 2. Animals are incapable of breathing 
 it; and when plunged into jars filled with 
 it, they die instantaneously in convulsions. 
 Neither will any combustible burn in it. 
 It is remarkable, however, that it has a 
 considerable effect upon the flame of com- 
 bustible bodies ; for if a burning taper be 
 plunged into it, the flame, just before it 
 goes out, may be observed to assume a 
 green colour, and the same tinge appears 
 next time the taper is lighted. 
 
 3. If a little of the blue coloured liquid, 
 which is obtained by boiling red cabbage 
 leaves and water in a tin vessel, be let up 
 into a jar filled with muriatic acid gas, it 
 assumes a fine red colour. This change is 
 considered by chemists as a characteristic 
 property of acids ; but this will be fully 
 treated of afterwards. 
 
 4. If a little water be let up into a jar 
 filled with this gas, the whole gas diap- 
 pears in an instant, the mercury ascends, 
 fills the jar, and forces the water to the 
 very top. The reason of this is, that there 
 exists a strong affinity between muriatic 
 acid gas and water ; and whenever they 
 come in contact, they combine and form a 
 liquid ; or, which is the same thing, the 
 water absorbs the gas. Hence arises the 
 necessity of making experiments with this 
 gas over mercury. In the water cistern 
 not a particle of gas would be procured. 
 The water of the trough would even rush 
 into the retort and fill it completely. It is 
 this affinity between muriatic acid gas and 
 water, which occasions the white smoke 
 that appears when the gas is mixed with 
 common air. It absorbs the vapour of 
 water which always exists in common air. 
 The solution of muriatic acid gas in water 
 is usually denominated simply muriatic 
 acid by chemists. 
 
 In this state it appears to have been 
 known to the alchymists ; but Glauber was 
 the first who extracted it from common salt 
 by means of sulphuric acid. It is prepared 
 for commercial purposes, by mixing toge- 
 ther one part of common salt and seven or 
 eight parts of clay, and distilling the mix- 
 ture ; or by distilling the usual proportion 
 of common salt and sulphuric acid, and 
 receiving the product in a receiver con- 
 taining water. For chemical purposes it 
 may be procured pure in the following 
 manner : 
 
 A hundred parts of dry common salt are 
 put into a glass matrass, to which there is 
 adapted a bent glass tube that passes into 
 a small Wolf’s apparatus, which is repre- 
 sented by the following figure. 
 
232 
 
 THE ARTISAN. 
 
 The first jar which is immediately con- tained was 1*203. If we suppose that the 
 nected with the receiver is employed for water in this experiment absorbed as much 
 condensing the vapour that issues from the gas as in the last, it will follow from it, that 
 retort, and the first bottle contains a quan- six parts of water, by being saturated with 
 tity of water equal in weight to the com- this gas, expanded so as to occupy very 
 mon salt employed, but part of the water nearly the bulk of 11 parts ; but in all the 
 may be put into the second bottle. When trials which were made upon it, the expan- 
 the apparatus is properly secured by luting, sion was only nine parts. This would indi- 
 pour gradually through the bent tube 75 cate a specific gravity of 1*477 ; yet upon 
 parts of sulphuric acid, or three-fourths actually trying water thus saturated, its 
 the weight of the salt, making the addi- specific gravity was only 1*203. Can this 
 tions at considerable intervals. On each difference be owing to the gas that escapes 
 effusion of the acid a large quantity of mu- during the acquisition of the specific gra- 
 riatic gas will pass along the bent tube, vity? 
 
 and will be absorbed by the water in the During the absorption of the gas, the 
 first bottle till this has become saturated; water becomes hot. Ice also absorbs this 
 it will then pass on to the second bottle, gas, and is at the same time liquified. The 
 and so on to more if they are deemed ne- quantity of this gas absorbed by water 
 cessary. diminishes as the heat of the water in- 
 
 The gas that is not absorbed by the creases, and at a boiling heat water will 
 water at its exit from the last bottle is con- not absorb any of it. When water impreg- 
 veyed, by means of the recurved tube, into nated with it is heated, the gas is again ex- 
 a jar standing in a mercurial trough, as pelled unaltered. Hence muriatic acid gas 
 represented in the foregoing figure. may be procured by heating the common 
 
 When the whole of the sulphuric acid muriatic acid of commerce. It was by this 
 has been added and the gas no longer process, that Dr. Priestley first obtained it. 
 issues, heat is then to be applied which The acid thus obtained is colourless : it 
 will renew the production of the gas. At has a strong pungent smell similar to the 
 this period it will be necessary to keep the gas, and when exposed to the air is con- 
 luting which connects the retort and re- stantly emitting visible white fumes. The 
 ceiver perfectly cool, otherwise it will be muriatic acid of commerce is always of a 
 apt to melt. pale yellow colour, owing to a small quan- 
 
 When no more gas is produced, the tity of iron which it holds in solution, 
 operation maybe suspended, and the liquid As muriatic acid can only be used con- 
 in the two bottles, which is muriatic acid, veniently when dissolved in water, it is of 
 put into others with ground stoppers and much consequence to know how much 
 preserved for use. pure acid is contained in a given quantity 
 
 A cnbic inch of water at the temperature of liquid muriatic acid of any particular 
 of 60°, barometer 29*4°, absorbs 515 inches density. Now the specific gravity of the 
 of muriatic acid gas, which is equivalent to strongest muriatic acid that can easily be 
 308 grains nearly. Hence water thus im- procured and preserved is 1*196 : it would 
 pregnated contains 0*548, or more than half be needless, therefore, to examine the 
 its weight of muriatic acid, in the same purity of any muriatic acid of superior 
 state of purity as when gaseous. Dr. Thom- density. Mr. Kirwan calculated that mu- 
 son caused a current of gas to pass through riatic acid, of the density of 1*196, con- 
 water till it refused to absorb any more, tains 0*2528 of pure acid. 
 
 The specific gravity of the acid thus ob- Muriatic acid was long considered as 
 
THE ARTISAN. 
 
 233 
 
 being capable of combining with oxygen, 
 and forming with it compounds possessed 
 of very different properties from the acid 
 itself. But this theory has lately been 
 abandoned by most of the leading chemists 
 of the day, in consequence of the results of 
 a number of experiments made upon this 
 substance by Sir H. Davy, and subsequently 
 by several other distinguished chemists 
 both in this country and on the continent. 
 
 The result of these experiments, and the 
 consequent change which they have pro- 
 duced on the whole science of chemistry, 
 will be particularly noticed in treating of 
 Chlorine.* 
 
 Jt may, however be necessary to state 
 here, that muriatic acid is now generally 
 believed to be a compound of this substance 
 and hydrogen. 
 
 ASTRONOMY. 
 
 OF THE HARVEST MOON. 
 
 It has long been known that the moon 
 when full, about the time of harvest, rises 
 for several nights nearly at the time of sun 
 setting ; but the cause of this remarkable 
 phenomenon has not been so long known. 
 This appearance was observed by the hus- 
 bandman long before it was noticed by the 
 Astronomer : and on account of its benefi- 
 cial effects in affording a supply of light 
 immediately after sun-set, at this impor- 
 tant season of the year, it is called the 
 harvest moon. 
 
 In order to conceive the reason of this 
 phenomenon it must be recollected, that 
 the moon is always opposite the sun when 
 she is full, and of course in the opposite 
 sign and degree of the zodiac. Now the 
 sun is in the signs Virgo and Libra in Au- 
 gust and September, or the time of har- 
 vest ; and therefore the moon when full, in 
 these months, is in the signs Pisces and 
 Aries. But that part of the ecliptic in 
 which Pisces and Aries is situated makes 
 a much less angle with the horizon of 
 places that have considerable northern la- 
 titude, than any other part of the ecliptic, 
 and therefore a greater portion of it rises 
 in any given time than an equal portion at 
 any other part of it. Or, which is the same 
 thing, any given portion of the ecliptic 
 about Pisces and Aries rises in less space 
 of time than an equal portion of it does at 
 any other part. And as the moon’s daily 
 motion in her orbit is about 13°, this portion 
 of it will require less time to rise about 
 those signs, than an equal portion at any 
 
 * This substance was formerly called oxymuriatic 
 acid ; but Sir H. Davy gave it this name in conse- 
 quence of its green colour. 
 
 other part of the ecliptic ; consequently, 
 there will be less difference between the 
 times of the moon’s rising when in this 
 part of her orbit than in any other.* 
 
 At a mean rate the moon rises 50 minutes 
 later on any evening than she did the pre- 
 ceding evening ; but when she is full about, 
 the beginning of September, or when she 
 is in that part of her orbit which rises 
 with the signs Pisces and Aries, she rises 
 only about 16 or 17 minutes later than on 
 the preceding evening ; consequently, she 
 will seem to rise for a few evenings at the 
 same hour. 
 
 Although this is the case every time that 
 the moon is in this part of her orbit ; yet it 
 is little attended to, except when she hap- 
 pens to be fidl at the time, which can only 
 be in August or September. 
 
 In some years this phenomenon is much 
 more perceptible than in others, even al- 
 though the moon should be full on the same 
 day, or in the same point of her orbit. 
 This is owing to a variation in the angle 
 which the moon’s orbit makes with the 
 horizon of the place where the phenomenon 
 is observed. If the moon moved exactly 
 in the ecliptic, this angle would always be 
 the same at the same time of the year. But 
 as the moon’s orbit crosses the ecliptic and 
 makes an angle with it of 5°* 9', the angle 
 formed by the moon’s orbit and the horizon 
 of any place is not exactly the same as 
 that made by the ecliptic and the horizon. 
 Some years it is greater and others less, 
 even at the same time of the year, for it is 
 subject to considerable variations, owing to 
 the retrograde motion of the moon’s 
 nodes.f 
 
 If the ascending node should happen to 
 be in the first degree of Aries, it is evident, 
 that this part of the moon’s orbit will rise 
 with the least possible angle, and of course 
 any given portion of it will require less 
 time to rise than an equal portion in any 
 other part of the orbit. The most favour- 
 able position of the nodes for producing 
 the most beneficial harvest moons, is there- 
 fore, when the ascending node is in the 
 first of Aries , and of course the descending 
 in the first of Libra. W hen the nodes are 
 in these points 13° of the moon’s orbit, 
 about the first of Aries, rises in the space 
 of 16 minutes, in the latitude of London, 
 and consequently, when the moon is in this 
 part of her orbit, the time of her rising 
 will differ only 16 minutes from the time 
 
 * It would tend very much to make this pheno- 
 menon understood if a terreetrial globe were athand 
 and rectified for the latitude of London, when read- 
 ing this description. 
 
 t The nodes, or points where the moon’s orbit 
 crosses the ecliptic, move backward about 19 ° in a 
 year, by which means they move round tbe ecliptic 
 in 18 years 226 days. 
 
234 
 
 THE ARTISAN. 
 
 she rose on the preceding evening. When 
 the moon is in the opposite part of her 
 orbit, or about the signs Virgo and Libra, 
 which make the greatest angle with the. 
 horizon at rising, 13° of her orbit will re- 
 quire 1 h. 15' to rise, although it were co- 
 incident with the ecliptic ; and if the nodes 
 be in the points just mentioned, the same 
 portion of the orbit Will require 1 h, 20' to 
 ascend above the horizon of the same 
 place ; and so much later will the moon 
 rise every night for several nights when in 
 this part of her orbit. As the moon is full 
 in these signs in the months of March and 
 April they may be called vernal full 
 moons. 
 
 Those signs of the ecliptic which rise 
 with the greatest angle set with the least ; 
 and those that rise with the least set with 
 the greatest. Therefore, the vernal full 
 moons differ as much in their times of 
 rising , every night, as the autumnal, or 
 harvest moons differ in the times of their 
 setting ; and they set with as little differ- 
 ence of time as the autumnal ones rise, 
 supposing the full moons to happen in op- 
 posite points of the moon’s orbit, and the 
 nodes to remain in the same points of the 
 ecliptic. 
 
 In southern latitudes, the harvest moons 
 are just as regular as in the northern, be- 
 cause the seasons are contrary ; and those 
 parts of the moon’s orbit about Virgo and 
 Libra, where the vernal full moons happen 
 in northern latitudes, (and the harvest ones 
 in southern latitudes) rise at as small ah 
 angle at the same degree of south latitude, 
 as those about Pisces and Aries in north 
 latitude, where the autumnal full moons 
 take place. 
 
 At places near the Equator, this pheno- 
 menon does not happen ; for every point of 
 the ecliptic, and nearly every point of the 
 moon’s orbit, makes the same angle with 
 the horizon, both at rising and setting, and 
 therefore equal portions of it will rise and 
 set in equal times. 
 
 As the moon’s nodes make a complete 
 circuit of the ecliptic in 18 years 225 days, 
 it is evident, that when the ascending node 
 is in the first of Aries at any given time, 
 the descending one must be in the same 
 point about 9 years 112 days afterwards; 
 consequently, there will be a regular in- 
 terval of about 9 1 years between the most 
 beneficial and least beneficial harvest 
 moons. 
 
 APPARENT SIZE OF THE MOON. 
 
 It has been already remarked at page 
 202, that the apparent size of the moon is 
 nearly equal to that of the sun ; but the 
 apparent size of the moon is not always 
 
 the same, for she is often much nearer the 
 earth at one time than another : hence, it is 
 evident, her apparent magnitude must vary, 
 and that it will be greatest when she is 
 nearest the earth. (See page 203.) 
 
 But she appears larger when in the ho- 
 rizon than in the zenith even on the same 
 evening; and yet it may easily be proved, 
 that she is a semi-diameter of the earth, or 
 about 4000 miles farther from the spectator 
 when she is in the horizon than when she 
 is in the zenith, and consequently ought to 
 appear smaller, which will be found to be 
 really the case if accurately measured. 
 
 This apparent increase of magnitude in 
 the horizontal moon, must therefore be con- 
 sidered as an optical illusion ; and may be 
 explained upon the well known principle, 
 that the eye in judging of distant objects is 
 guided entirely by the previous knowledge 
 which the mind has acquired of the inter- 
 vening objects. Hence arise the erroneous 
 estimates we make of the size of distant 
 objects at sea, of objects below us when 
 viewed from great heights, and of objects 
 highly elevated when viewed from below. 
 Now when the moon is near the zenith, she 
 is seen precisely in this last situation, of 
 course there is nothing near her, or that can 
 be seen at the same time with which her 
 size can be compared ; but the horizontal 
 moon may be compared with a number of 
 objects whose magnitude is previously 
 known. 
 
 That the moon appears under no greater 
 an angle (or is not larger) in the horizon, 
 than when she is on the meridian, may be 
 proved by the following simple experi- 
 ment. 
 
 Take a large sheet of paper and roll it 
 up in the form of a tube of such width as 
 just to include the whole of the moon when 
 she rises : then tie a thread round it to 
 keep it exactly of the same size, and when 
 the moon comes to the meridian, where she 
 will appear to the naked eye to be much 
 less, look at her again through the same 
 tube and she will fill it as completely as 
 she did before. 
 
 When the moon is full and in the hori- 
 zon, she appears of an oval form, with her 
 longest diameter parallel to the horizon. 
 This appearance is occasioned by the re- 
 fraction of the atmosphere, which is always 
 greatest at the horizon, consequently the 
 lower limb or edge must be more refracted 
 than the upper edge, and therefore these 
 two edges will appear to be brought nearer 
 each other, or the vertical diameter will 
 appear to be shortened ; and as the hori- 
 zontal diameter is very little affected by 
 the refraction, she must appear to have 
 somewhat of an oval shape. The sun is 
 affected in the same manner when in the 
 horizon. 
 
THE ARTISAN. 
 
 235 
 
 JMisceltemeous J&hjects. 
 
 MEMOIR OF THE LIFE OF JAMES 
 FERGUSON. 
 
 James Ferguson, an eminent Experimen- 
 tal Philosopher, Mechanist, and Astrono- 
 mer, was born in Banffshire, in Scotland, 
 1710, of very poor parents. At the very 
 earliest age his extraordinary genius began 
 to unfold itself. He first learned to read, 
 by overhearing his father teach his elder 
 brother : and he had made this acquisition 
 before any one suspected it. He soon dis- 
 covered a peculiar taste for Mechanics, 
 which first arose on seeing his father use a 
 long pole as a lever, to raising the roof of 
 his cottage, which had sunk below the 
 walls. He pursued this study a consider- 
 able length, while he was yet very young ; 
 and made a watch in wood work, from 
 only once having seen one. As he had at 
 first no instructor, nor any help from 
 books, every thing he learned had all the 
 merit of an original discovery; and such, 
 with inexpressible joy, he believed it to be. 
 
 As soon as his age would permit, he 
 went to service, in which he met with 
 hardships, that rendered his constitution 
 feeble through life. While he was servant 
 to a farmer (whose goodness he acknow- 
 ledges in the modest and humble account 
 of himself, which he prefixed to his “ Me- 
 chanical Exercises/’) he contemplated and 
 learned to know the stars, while he tended 
 the sheep ; and began the study of Astro- 
 nomy, by laying down, from his own obser- 
 vations only, a celestial globe. His kind 
 master, observing these marks of his in- 
 genuity, procured him the countenance 
 and assistance of some neighbouring gen- 
 tlemen. By their help and instructions he 
 went on gaining farther knowledge, having 
 by their means been taught Arithmetic, 
 with some Algebra and Practical Geome- 
 ry. He had also got some notion of draw- 
 ing, and being sent to Edinburgh, he there 
 began to take portraits in miniature, at a 
 small price, an employment by which he 
 supported himself and family for several 
 years, both in Scotland and England, 
 while he was pursuing more serious 
 studies. In London he first published 
 some curious astronomical tables and cal- 
 culations ; and afterwards gave public 
 Lectures in Experimental Philosophy, both 
 in London and most of the country towns 
 in England, with the highest marks of 
 general approbation. He was elected a 
 fellow of the Royal Society, and was ex- 
 cused the payment of the admission fee, 
 and the usual annual contributions. He 
 enjoyed from the king a pension of fifty 
 
 pounds a year, besides other occasional 
 presents, which he privately accepted and 
 received from different quarters, till the 
 time of his death ; by which, and the fruits 
 of his own labours, he left behind him a 
 sum to the amount of about six thousand 
 pounds, although all his friends had always 
 entertained an idea of his great poverty. 
 He died in 1776, at sixty-six years of age, 
 though he had the appearance of many 
 more years. 
 
 Mr. Ferguson must be allowed to have 
 been a very uncommon genius, especially 
 in mechanical contrivances and executions, 
 for he executed many machines himself in 
 a very neat manner. He had also a good 
 taste in Astronomy, as well as in Natural 
 and Experimental Philosophy, and was 
 possessed of a happy manner of explaining 
 himself in an easy, clear, and familiar way. 
 His general mathematical knowledge, how- 
 ever, was very limited. Of algebra he 
 understood but little more than the nota- 
 tion ; and he has often told the late Dr. 
 Hutton, that he could never demonstrate 
 one proposition in Euclid’s Elements; his 
 constant method being to satisfy himself as 
 to the truth of any problem, with a mea- 
 surement by scale and compasses. He 
 was a man of a very clear judgment in any 
 thing that he professed, and of unwearied 
 application to study; benevolent, meek, 
 and innbcent in his manners as a child: 
 humble, courteous, and communicative : 
 instead of pedantry, philosophy seemed to 
 produce in him only diffidence and urba- 
 nity. 
 
 The following is a list of Mr. Ferguson’s 
 works : — 
 
 1. “ Astronomical Tables and Precepts, 
 for calculating the true Times of New and 
 Full Moons, &c.” 1763; 2. “Tables and 
 Tracts, relative to several Arts and Scien- 
 ces;” 3. “An easy Introduction to Astro- 
 nomy, for young Gentlemen and Ladies ;” 
 4. “ Astronomy explained upon Sir Isaac 
 Newton’s Principles;” 5. “ Lectures on 
 select Subjects in Mechanics, Hydrostatics, 
 Pneumatics, and Optics;” 6. “ Select 
 Mechanical Exercises, with a short Account 
 of the Life of the Author by himself,” a 
 narrative highly interesting and amusing : 
 7. The Art of Drawing in Perspective made 
 Easy;” 8. u An Introduction to Electricity,” 
 1775 ; “ Three Letters to the Rev. Mr. John 
 Kennedy.” He communicated also several 
 papers to the Royal Society, which were 
 printed in their Transactions. In 1805 a 
 very valuable edition of his Lectures was 
 published in Edinburgh by Dr. Brewster, 
 in 2 vols. 8vo. with notes and an appen- 
 dix. 
 
236 
 
 THE ARTISAN. 
 
 ARCHITECTURE. 
 
 COMPOSITE ORDER. 
 
 The Composite Order, is the last of the 
 five orders of columns ; so called, because 
 its capital is composed out of those of the 
 other orders. 
 
 It borrows a quarter-round from the 
 Tuscan and Doric; a double row of leaves, 
 from the Corinthian; and Volutes from the 
 Ionic : its cornice has simple modillions, or 
 dentils. 
 
 The composite is also called the Roman 
 
 and Italian order ; as having been invented 
 by the Romans ; conformably to the rest, 
 which are denominated from the people 
 among whom they had their rise. 
 
 Most authors rank this after the Corin- 
 thian ; either as being the richest, o'r as 
 the last that was invented : Scamozzi alone 
 places it between the Ionic and Corinthian ; 
 out of a view to its delicacy and richness, 
 which he esteems inferior to that of the 
 Corinthian ; and therefore makes no scru- 
 ple to use it under the Corinthian : wherein 
 he is followed by M. le Clerc. The pro- 
 portions of this order are not fixed by Vi- 
 truvius; he only marks its general charac- 
 ter, by observing, that its capital is com- 
 posed of several parts taken from the Doric, 
 Ionic, and Corinthian: he does not seem 
 to regard it as a particular order ; nor does 
 he vary it at all from the Corinthian, ex- 
 cept in its capital. In effect, it was Serlio 
 who first added the composite order to the 
 four of Vitruvius, forming it from the re- 
 mains of the temple of Bacchus, the arches 
 of Titus, Septimus, and the Goldsmiths at 
 Rome : till then, this order was esteemed 
 a species of the Corinthian, only differing 
 in its capital. 
 
 The order being thus left undetermined 
 by the ancients, the moderns have a kind 
 of right to differ about its proportions, &c. 
 Scamozzi, and after him M. le Clerc, make 
 its column 19 modules and a half ; which is 
 less by half a module than the Corinthian. 
 Vignola makes it 20 ; which is the same 
 with that of his Corinthian: but Serlio, 
 who first formed it into an order, by giving 
 it a proper entablature and base, and after 
 him M. Perrault, raise it still higher than 
 the Corinthian. 
 
 This last does not think different orna- 
 ments and characters sufficient to constitute 
 a different order, unless it have a different 
 height too: agreeably, therefore, to his 
 rule of augmenting the heights of the se- 
 veral columns by a series of two modules in 
 each ; he makes the composite 20 modules, 
 and the Corinthian 18 ; which, it seems is 
 a medium between the porch of Titus and 
 the temple of Bacchus. 
 
 M. Perrault, in his Vitruvius, distin- 
 guishes between composite and composed 
 order. The latter, he says, denotes any 
 composition whose parts and ornaments 
 are extraordinary, and unusual ; but have, 
 withal, somewhat of beauty ; both on ac- 
 count of their novelty, and in respect of the 
 manner, or genius of the architect: so 
 that a composed order is an arbitrary, hu- 
 morous composition, whether regular or 
 irregular. 
 
 The same author adds, that the Corin- 
 thian order is the first composite order, as 
 being composed of the Doric and Ionic ; 
 which is the observation of Vitruvius him* 
 self. 
 
THE ARTISAN. 
 
 237 
 
 CELESTIAL ATLAS BY ALEX- 
 ANDER JAMEISON, A. M. ^ 
 
 It is a species of anomaly in the litera- 
 ture of this country to see a work make its 
 appearance on certain sciences, which are 
 not only useful in themselves, but are the 
 foundation of almost all accurate science. 
 Among these it is only necessary to mention 
 Mathematics and Astronomy. For though 
 we have Systems, Courses, Preceptors and 
 Catechisms in abundance, on those sciences 
 as well as on music, dancing and boxing, 
 yet they contain nothing that has not been 
 before the public a thousand times in as 
 many different shapes. Every teacher of 
 a petty boarding school has either got his 
 system of Arithmetic, Mathematics, or As- 
 tronomy, although he can neither demon- 
 strate a proposition in Euclid, nor tell the 
 time of new moon without his Moor’s Alma- 
 nack. 
 
 But with all these works on the sciences 
 just mentioned, we have nothing original, 
 nothing that is even new in appearance to 
 those who have made a little progress in 
 the sciences of mathematics or astronomy. 
 
 We may venture to assert, that there has 
 scarcely been a single work published in 
 this country within the last forty years, 
 which lias added any thing to our stock of 
 mathematical or astronomical knowledge. 
 Discoveries and improvements have been 
 made in those sciences within this period, 
 and we are now in possession of some of 
 them; but this is by means of translations 
 from works which have first appeared in 
 other countries, and not by having been 
 originally published here. The fact is, 
 that instead of mathematical and astrono- 
 mical knowledge having increased in this 
 country, during the above period it has 
 diminished. And instead of the high rank 
 which we once held in this respect among 
 our neighbours, we are now unquestion- 
 ably inferior to them. What has caused 
 this change we shall not at present enquire 
 into; but the effect of it has been such as 
 to go far in not only preventing original 
 publications from making their appearance 
 among us on these sciences, but even of 
 translations. For where is the individual 
 who will venture to publish a work, how- 
 ever valuable that work may be to the pub- 
 lic, when he is almost certain that he 
 must lose by its publication. 
 
 There are certainly exceptions to this, 
 for some persons are to be found who pub- 
 lish valuable works, when there is scarcely 
 a possibility of their sale defraying the ne- 
 cessary expenses attendant upon bringing 
 them before the public. 
 
 An instance of this we believe we have be- 
 fore us in the case of the “ Celestial Atlas,” 
 lately published by Mr. Jamieson. This is 
 a work completely new in its kind, at least 
 
 we have no work of the kind in this coun- 
 try, to which the public have access. 
 
 It consists of thirty beautifully engraved 
 maps of the heavens, on which are deli- 
 neated the figures of the most conspicuous 
 constellations in the Zodiac, and the North- 
 ern and Southern hemispheres, with the 
 greater number of the stars that are visible 
 in each. The stars appear to be very ac- 
 curately laid down, and consequently must 
 render the maps very useful to those who 
 wish to become acquainted with the rela- 
 tive situations of the stars in the heavens. 
 
 Mr. Jamieson has also explained the 
 manner of using these maps, and subjoined 
 a number of problems with appropriate 
 exercises to each map, by which means his 
 atlas may supply the place of a Celestial 
 Globe. But what is perhaps of more impor- 
 tance to the scientific astronomer, is the ex- 
 tensive and accurate Catalogues of the Stars 
 in each constellation, with their Right As- 
 cension and Declaration for the beginning 
 of the year 1820. 
 
 To render this work still more valuable, 
 Mr. J. had added a number of astronomical 
 Tables, and given very clear definitions of 
 the principal circles of the Sphere. On 
 the whole we consider this Atlas as a very 
 great addition to the works we already 
 possess on the sublime and almost neg- 
 lected science of astronomy; and we are 
 convinced, that not only the student, but 
 the proficients in this branch of physical 
 knowledge will derive advantage from the 
 perusal of the Celestial Atlas. 
 
 We are happy to see that a work which 
 has cost so much expense and research, 
 has met with the patronage of his present 
 Majesty, to whom it is dedicated by per- 
 mission. 
 
 ANALOGY BETWEEN THE PHENO- 
 MENA OF GALVANISM AND THAT 
 
 OF FERMENTATION. 
 
 M. Schweigger, a German chemist, has 
 remarked that there is a very great analogy 
 between the phenomena produced by the 
 galvanic pile, and those which accompany 
 fermentation. 
 
 1. Piles, as well as all fermentable mix- 
 tures, only exhibit their effects by the reci- 
 procal action of three different bodies. 
 
 2. The products of galvanic action are 
 two in number ; namely, oxygen and hy- 
 drogen. The same number are produced 
 by fermentation ; viz. alcohol and carbonic 
 acid. 
 
 3. What is little known, and what M. 
 Schweigger believes, he can establish by 
 experiment is, that the presence of bodies 
 negatively electrified, favour the de- 
 composition of water, whilst, from the 
 nice experiments of M. Dobereiner, bodies 
 positively electrified aid its formation ; and 
 
238 
 
 THE ARTISAN. 
 
 the same bodies negatively electrified, 
 augment the effects of fermentation. 
 
 Mr. Schweigger thinks that the same 
 results may yet be obtained with ferment- 
 able mixtures as with electric batteries. 
 
 To these considerations he adds some 
 simple experiments made upon the produc- 
 tion of light by crystallization, and advises 
 philosophers not to neglect the study of 
 these phenomena. 
 
 TO IMITATE LEAF-GILDING ON 
 LEATHER. 
 
 Take some calf-skins which have been 
 softened in water, and beat on a stone to 
 their greatest extent whilst wet ; rub the 
 grain side of the leather with a piece of 
 size, whilst in a state of jelly ; and before 
 this size dries, lay on a number of silver 
 leaves. When covered with the silver 
 leaf, the skins are to be dried till they are 
 in a proper state for burnishing, which is 
 performed by a piece of large flint fixed in 
 a wooden handle ; the appearance of gold 
 is then given to the silvered surface by 
 covering it with a yellow varnish, or 
 lacker, which is composed of four parts of 
 white resin, the same quantity of common 
 resin, two parts of gum sandarac, and two 
 parts of aloes. These ingredients are to be 
 melted together in an earthen vessel, and 
 after being well mixed by stirring, twenty 
 parts of linseed oil is to be poured in, and 
 when the composition is sufficiently boiled 
 to make a perfect union, and to have the 
 consistence of a syrup, half an ounce of 
 red-lead is to be added, and the liquid 
 passed through a flannel bag. To apply 
 this varnish, the skins must be spread out 
 upon a board, fastened down by nails, and 
 exposed to the rays of the sun, and when 
 thus warmed, the white of an egg is to be 
 spread over the silver. After it is dry the 
 varnish is laid on, which will dry in a few 
 hours, and is very durable. 
 
 TO ASCERTAIN THE QUANTITY 
 OF ALCOHOL CONTAINED IN 
 ALE OR PORTER. 
 
 Take any measured quantity of ale, 
 or porter, and put it into a glass retort, 
 connected with a close receiver; distil 
 with a gentle heat as long as any spirit 
 passes over into the receiver, which may be 
 known by heating a small quantity of the 
 fluid in a tea-spoon over a candle, from 
 time to time. If the vapour catches fire, 
 the distillation must be continued till the 
 vapour ceases to burn when brought in 
 contact w r ith flame. The distilled liquid is 
 the spirit of the beer combined with water ; 
 put this spirit into a tube divided into one 
 hundred equal parts, and add pure dry 
 
 subcarbonate of potash till it fail undis- 
 solved to the bottom of the tube ; the spirit 
 will thus be separated from the water, and 
 float on the top ; hence the quantity of real 
 spirit, or alcohol, per cent, may be easily 
 determined. 
 
 CONSTRUCTION OF BALLOONS. 
 
 The shape of the balloon is one of the 
 first objects of consideration. As a sphere 
 admits the greatest capacity under the 
 least surface, the spherical figure, or that 
 which approaches nearest to it, has been 
 generally preferred. However, since bodies 
 of this form oppose a great surface to the 
 air, and, consequently, a greater obstruc- 
 tion to the action of the oar or wings, than 
 those of some other form, it has been pro- 
 posed to construct balloons of a conical or 
 oblong figure, and to make them proceed, 
 with their narrow end forward. Some 
 have suggested the shape of a fish ; others, 
 that of a bird ; but either the globular, or the 
 egg-like shape, is, all things considered, 
 certainly the best which can be adopted. 
 
 The bag or cover, of an inflammable -air 
 balloon, is best made of the silk stuff called 
 lustring, varnished over. But for a Mont- 
 golfier, or heated-air balloon, on account of 
 its great size, linen cloth has been used, 
 lined within or without with paper, and 
 varnished. Small balloons are made either 
 of varnished paper, or simply of paper un- 
 varnished, or of gold-beaters’ skin, and 
 such like light substances. The best way 
 to make up the whole coating of the bal- 
 loon, is by different pieces, or slips, joined 
 lengthways from end to end, like the pieces 
 composing the surface of a geographical 
 globe, and contained between one meridian 
 and another; or like the slices into which 
 a melon is usually cut, and supposed to be 
 spread out flat. 
 
 After providing the necessary quantity 
 of the stuff, and each piece having been 
 properly prepared with drying oil, let the 
 corresponding edges be sewed together in 
 such a manner as to leave about half, or 
 three quarters, of an inch of one piece, be- 
 yond the edge of the other ; in order that 
 this may, in a subsequent row of stitches, 
 be turned over the latter, and both again 
 sewed down together ; by so doing, a con- 
 siderable degree of strength is given to the 
 whole bag at the seams, and the hazard of 
 the gas escaping, is doubly prevented. 
 Having gone in this manner through all 
 the seams, the following method of M. 
 Blanchard is admirably calculated to ren- 
 der them yet more perfectly air tight. The 
 seam being doubly stitched, as above, lay 
 beneath it a piece of brown paper, and also 
 another piece over it on the outside ; upon 
 this latter, pass several times a common 
 fire-iron, heated just sufficiently to softern 
 
THE ARTISAN. 
 
 239 
 
 the drying oil in the seam ; this done, every 
 interstice will be now closed, and the 
 seams rendered completely air tight. The 
 neck of the balloon being left a foot in dia- 
 meter, and three in length, and all the 
 seams finished, the bag will be ready to 
 receive the varnish, a single coating of 
 which on the outside is found preferable to 
 the former method of giving an internal as 
 well as an external coat. 
 
 The car, or boat, is best made of wicker- 
 work, covered with leather, and painted; 
 and the proper method of suspending it, is 
 by ropes proceeding from the net which 
 goes over the balloon. The net should be 
 formed to the shape of the balloon, and 
 fall down to the middle of it, with various 
 cords proceeding from it to the circumfer- 
 ence of a circle about two feet below the 
 balloon ; and from that circle other ropes 
 should go to the edge of the boat. This 
 circle may be made of wood, or of several 
 pieces of slender cane bound together. The 
 meshes of the net may be small at top, 
 against which part of the balloon, the in- 
 flammable air exerts the greatest force ; and 
 increase in size as they recede from the top. 
 
 If a parachute is required, it should be 
 constructed so, as, when distended, to 
 form but a small segment of a sphere, and 
 not a complete hemisphere ; as the weight 
 of this machine is otherwise considerably 
 increased, without gaining much in the 
 opposing surface. The parachute of M. 
 Garnerin is perticularly defective in the 
 too great extension of its diameter ; viz. by 
 an unnecessary addition to its weight of 
 a lining of paper, both withinside, *and 
 without; and in the too near approxima- 
 tion of the basket to the body of the para- 
 chute; but especially, in the want of a 
 perpendicular cord passing from the car to 
 the centre of the concave of the umbrella ; 
 by the absence of which, the velocity of the 
 descent is certain to be very rapid before 
 the machine becomes at all distended. 
 Whereas, if a cord were thus disposed, the 
 centre of the parachute would be the por- 
 tion first drawn downwards by the ap- 
 pended weight, and the machine would be 
 almost immediately at its full extension. 
 Having found, by experiment, the diame- 
 ter, required for insuring safety, the further 
 the basket, or car, is from the umbrella, 
 the less fear shall we have of an inversion 
 of the whole from violent oscillations ; yet, 
 the longer the space between the car and 
 the head of the machine, the longer will be 
 the space run through, in each vibration, 
 when once begun ; still, by so much the 
 more, will they be steadier. This ought to 
 be attended to, as, when by the violence of 
 the oscillations, the car became (in Garne- 
 ring experiment) on a line with the hori- 
 zontal axis of the machine ; the gravitating 
 power of the weight in the car, on the um- 
 
 brella, being at that crisis reduced to 
 nothing, the slightest cause might have 
 carried the body of the machine in a lateral 
 direction, reversing the concavity of the 
 umbrella; and M. Garnerin, might, per- 
 haps, have fallen upon the (now) convex, 
 yet internal portion of the bag: conse- 
 quently the whole would have descended 
 confusedly together. 
 
 MANUFACTURE OF MOSAIC AT 
 ROME. 
 
 It is well known that Mosaic-work con- 
 sists of variously shaped pieces of coloured 
 glass enamel ; and that when these pieces 
 are cemented together, they form those re- 
 gular and other beautiful figures which 
 constitute tessellated pavements. These 
 pavements, the work of the ancient Ro- 
 mans, have frequently been dug up in 
 England and other countries. The princi- 
 pal manufactory of Mosaic pictures in the 
 present day, is at Rome, and belongs to his 
 Holiness the Pope. 
 
 The enamel, consisting of glass mixed 
 with metallic colouring matter, is heated 
 for eight days in a glass-house, each colour 
 in a separate pot. The melted enamel is 
 taken out with an iron spoon, and poured 
 on polished marble placed horizontally ; 
 and another flat marble slab is laid upon 
 the surface, so that the enamel cools into 
 the form of a round cake, of the thickness 
 of of an inch. 
 
 In order to divide the cake into smaller 
 pieces, it is placed on a sharp steel anvil, 
 called Tagliulo, which has the edge upper- 
 most ; and a stroke of an edged hammer is 
 given on the upper surface of the cake, 
 which is thus divided into long parallelo- 
 pipeds, or prisms, whose bases are ^ of an 
 inch square. These parallelopipeds are 
 again divided across their length by the tag- 
 liulo and hammer into pieces of the length 
 of T | of an inch, to be used in the Mosaic 
 pictures. Sometimes the cakes are made 
 thicker, and the pieces larger. 
 
 For smaller pictures, the enamel, whilst 
 fused, is drawn into long parallelopipeds, 
 or quadrangular sticks; and these are 
 divided across by the tagliulo and hammer, 
 or by a file ; sometimes, also, these pieces 
 are divided by a saw without teeth, con- 
 sisting of a copper blade and emery ; and 
 the pieces are sometimes polished on a hori- 
 zontal wheel of lead with emery. 
 
 Gilded Mosaic is formed by applying the 
 gold-leaf on the hot surface of a brown 
 enamel, immediately after the enamel is 
 taken from the furnace ; the whole is put 
 into the furnace again for a short time, and 
 when it is taken out the gold is firmly fixed 
 on the surface. In the gilded enamel, used, 
 in Mosaic, at Rome, there is a thin coat of 
 transparent glass over the gold. 
 
240 
 
 THE ARTISAN. 
 
 SOLUTIONS OF QUESTIONS. 
 
 Quest. 31, answered by a Mechanic, qf 
 Bury ( the proposer ). 
 
 Demons. Produce BE to F, 
 
 B. 
 
 making F B — B A. Draw A F, which 
 will evidently be parallel to D E. Let 
 fall the perpendicular B M, which will 
 bisect A F. Draw E G parallel to A D. 
 Let fall the perpendiculars E H and 
 E L, and draw the Diameter D G. Now 
 D G is a parallelogram and its opposite 
 sides and angles are equal (Euc. 34-1) ; 
 hence A G and G E are known because 
 D E and A D are given, and by subtraction 
 we have EF zz A DzzE G.\ E F is known. 
 But A E is given, now A E 2 — E G 2 -j- A G 2 
 -f 2 A G X G H (Euc. 12-2). Now AE 2 , 
 E G 9 , and A G 2 are known ; therefore 2 
 ( A G X G H) and consequently A G X G H 
 are known ; and since A G is known G H 
 is so likewise. But GHzrHF: there- 
 fore H F is known also, whence by addi- 
 tion A F becomes known, and AMzMF 
 is known by division. Then by similar 
 triangles HF: FE: : M F : F B zz A B 
 which is therefore known. Now, by Bon- 
 nycastle’s Geometry, Book 2. Prop. 21. 
 A E and D G bisect each other in K and 
 A E 9 -j-D G 2 zzAD 2 -f D E 2 + E G 2 -j-GA 2 , 
 but the four last, and also the first, viz. A E 2 
 are known ; therefore D G 9 is known by 
 subtraction and by extracting root D G is 
 G D 
 
 known. But DKz-^ - , hence D K is 
 
 known : and as we found G H so we find 
 KL: therefore by (Euc. 47-l)D Lis known, 
 then by similar triangles A D : D L : : A B : 
 BC. Q. E. D. 
 
 Quest. 32, answered by Mr. J. Holroyd, 
 Of Oldham. 
 
 Let x represent the h eight of the house, 
 then by Euc. 1 and 47>/x 9 -j- (12) 2 — the 
 le ngth of the ladd er in the 1st position ; and 
 
 (a; — 4)2-f-(20) 2 ,the same in the2d position ; 
 therefore 9 + (12)* =\/(a*— 4) 2 -f(20) 9 , 
 or x 9 -j- 144 z: x 2 — 8 x -f- 416, conse- 
 
 quently x zz 34 feet, the height of the 
 house required; and the length of the 
 ladder is therefore 36*055 feet. 
 
 This question was also correctly solved 
 by the following Correspondents : Messrs. 
 A. Peacock, St. Georges , East; -John 
 Barr, Somer’s Town; Georgr Futvoye, 
 High-street , Mary -la-bonne ; and J. White- 
 combe, Cornhill. 
 
 Quest. 33, answered by Mr. John Barr, 
 Somer's Town. 
 
 The nature of the question is to deter- 
 mine the difference between the area of the 
 circumscribing square and the inscribed 
 circle, therefore put x for the difference. 
 a zz *925 the diameter of the circle ; 
 then a 2 zzthe area of the square; 
 and let r and s represent the numbers 113 
 and 355 respectively. 
 
 When r : s : : a : S — the circumference of 
 r 
 
 the circle ; 
 
 and « X ~ zz “ the area of the circle : 
 4 r 4r * 
 
 S(] fi 
 
 whence x zz a 2 — — zz *1837 parts of an 
 4r 
 
 inch, the area of the space required. 
 
 This question was also answered by all 
 the gentlemen who solved the 32d ques- 
 tion, and by S. A. Hart, Student, Royal 
 Academy ; Subpreceptor ; and the Pro- 
 poser. 
 
 QUESTIONS FOR SOLUTION. 
 
 Quest. 37, proposed by Fr — d-}-F — lk 
 — wo— th. 
 
 Required a theorem for finding the area 
 of a circle, having only the cord of half 
 the arch, and the versed sine of it given ? 
 
 Quest. 38, proposed by Mr. R. Graham, 
 Liverpool. 
 
 There is a regular tetrahedron of pebble 
 on the side of the Queen’s Dock, Liver- 
 pool, whose whole surface in feet is equal 
 to the sum of its linear edges; it is required 
 to determine the least quantity, and the 
 value of standard gold added to the sur- 
 faces that will make it a globe, and also 
 the diameter of a globe of cork, which, 
 when fixed to the foresaid globe, and put 
 into the Dock at full tide, the cork globe 
 may be just covered with water? 
 
 Quest. 39, proposed by G. G. C. 
 
 Suppose a pillar 150 feet high, on which 
 is placed a statue 10 feet high ; required a 
 point on a level with the base of the pillar, 
 such that the angle subtended by the sta- 
 tue may be the greatest possible, and also 
 to determine what that angle is ? 
 
THE ARTISAN. 
 
 241 
 
 GEOMETEY. 
 
 PROPOSITION XLVI. 
 
 Problem. — -To describe a square upon a 
 given straight line. 
 
 Let A B be the given straight line ; it is 
 required to describe a square upon A B. 
 
 From the point A draw A C at right 
 angles to A B ; and make A D equal to 
 A B, and through the point D draw D E 
 parallel to A B, and through B draw B E 
 parallel to AD; therefore ADEB is a 
 parallelogram : 
 
 Whence A B is equal to I) E, and A D to 
 B E : but B A is equal to A D ; therefore 
 the four straight lines BA, AD, DE, EB, 
 are equal to one another, and the parallels 
 ogram ADEB is equilateral : it is like- 
 wise rectangular; for the straight line 
 A D meeting the parallels A B, D E, makes 
 the angles BAD, A D E equal to two right 
 angles ; but B A D is a right angle ; there- 
 fore also A D E is a right angle ; now the 
 opposite angles of parallelograms are 
 equal ; therefore each of the opposite angles 
 A B E, B E D is a right angle ; wherefore 
 the figure ADEB is rectangular, and it 
 has been demonstrated that it is equilate- 
 ral ; it is therefore a square, and it is desr 
 cribed upon the given straiget ling A B. 
 Which was to be done. 
 
 Cor. Hence every parallelogram that 
 has one right angle has all its angles right 
 angles. 
 
 PROPOSITION XLYII, 
 Theorem. — In any right angled triangle , 
 the square which is described upon the 
 side subtending the right angle , is equal 
 to the squares described upon the sides 
 which conta in the right angle .* 
 
 * This proposition is often called the Pythagorean 
 Theorem, from Pythagoras, who is said to have 
 been the discoverer of the remarkable property here 
 proved by it; and it ig also said, that he considered 
 it of so great importance, that he sacrificed a heca- 
 tomb or 100 oxen, on making the discovery of its 
 ^ruth. 
 
 Vol. I.— No. 16 . 
 
 Let ABC be a right angled triangle, 
 having the right angle B AC; the square 
 described upon the side B C is equal to the 
 squares described upon BA, AC. 
 
 On BC describe the square BDEC, 
 and on BA, AC the squares GB, HC; 
 and through A draw A L parallel to B D 
 or C E, and join A D, F C ; then, because 
 each of the angles BAC, BAG is a right 
 
 angle, the two straight lines AC, AG 
 upon the opposite sides of A B, make with 
 it at the point A the adjacent angles equal 
 to two right angles ; therefore C A is in 
 the same straight line with AG; for the 
 same reason, A B and A H are in the same 
 straight line. Now because the angle 
 D B C is equal to the angle F B A, each of 
 them being a right angle, adding to each 
 the angle ABC, the whole angle DBA 
 will be equal to the whole F B C ; and be- 
 cause the two sides A B, B D, are equal to 
 the two F B, B C, each to each, and the 
 angle DBA equal to the angle F B C, 
 therefore the base A D is equal to the base 
 F C, and the triangle A B D to the triangle 
 F B C : but the parallelogram B L is double 
 of the triangle ABD, because they are 
 upon the same base B D, and between the 
 same parallels, B D, A L; and the square 
 G B is double of the triangle B F C, be- 
 cause these also are upon the same base 
 F B, and between the same parallels F B, 
 GC. Now the doubles of equals are 
 equal to one another ; therefore the paral- 
 lelogram B L is equal to the square G B : 
 And, in the same manner, by joining A E, 
 B K, it is demonstrated that the parallelo- 
 gram CL is equal to the square H C. 
 Therefore, the whole square B D E'C is 
 equal to the two squares GB, HC ; and 
 the square B D E C is described upon the 
 straight line B C, and the squares GB, 
 HC upon B A, A C ; wherefore the square 
 upon the side B C is equal to the square 
 
242 
 
 THE ARTISAN. 
 
 upon the sides BA, AC. Therefore, in 
 any right angled triangle, &c. Q. E. D. 
 
 Observation. — This famous proposition 
 has been proved in a variety of ways by 
 several celebrated mathematicians. The 
 following, however, appears to be one of 
 the most simple : 
 
 Let the triangle A B C be right-angled 
 at B. 
 
 Upon A C describe the square AGED, 
 and upon A B and BC describe the 
 squares A B G F, and B C I H, and pro- 
 duce DA to R and E C to H ; produce 
 I H and F G till they meet in L, and 
 through B draw LB M parallel to D A or 
 EC. 
 
 L 
 
 Because the angle C A K, adjacent to 
 C A D, is a right angle, it is equal to BAF ; 
 from each of these take away the angle 
 BAR, and there remains the angle B A C 
 equal to FAR. But the angle A B C is 
 equal to A F R, both being right angles. 
 Wherefore the triangles ABC and A F R, 
 having thus two angles in the one respec- 
 tively equal to those of the other, and the 
 interjacent side AF equal to AB, are 
 equal (I. 26), and consequently the side 
 A R is equal to A C. Hence the parallelo- 
 gram AM is equal to the parallelogram 
 or rhomboid A B L R, since they stand 
 upon equal bases A D and A R, and be- 
 tween the same parallels D R and M L. 
 But A B L R is equal to the square B F, 
 for it stands on the same base A B, and 
 between the same parallels F L and A H. 
 Wherefore the parallelogram A M is equal 
 to the square on A B. And in the same 
 manner it may be proved, that the paral- 
 lelogram C M is equal to the square des- 
 cribed on B C. Consequently the whole 
 square A D EC, on the side A C, contains 
 
 the same space as both the squares des- 
 cribed on the two sides A B, and B C.* 
 
 As it may gratify the young student in 
 Geometry, to be able to prove this propo- 
 sition experimentally, we shall show that 
 the two squares on the sides containing 
 the right angle may be cut, so that the 
 parts will just make up the square on the 
 hypothenuse. 
 
 Let ABC be a right angled triangle 
 right angled at B. Upon A C describe the 
 square AEDC; from the points DE, 
 draw D F, and E G, perpendicular to B A 
 produced ; and through E and C draw EH, 
 and C I, parallel to A B. 
 
 iy 
 
 Now, in the triangles A B C, D I C, the 
 angles B and I, being right angles, are 
 equal; and because each of the angles 
 B C I, AC D, is a right angle, take away 
 the angle A C I, which is common to both, 
 and the remaining angles ACB, I CD, 
 will be equal ; hence the triangles are 
 equiangular ; and since the sides A C, C D, 
 opposite the right angles, are equal, the 
 triangles are, therefore, equal, and the re- 
 maining sides of the one, equal to those of 
 the other, each to each, to which the equal 
 angles are opposite ; that is, D I is equal 
 to A B, and C I to B C. Now, since the 
 figure B C I F has all its sides equal, and 
 all its angles right angles, it is, therefore, 
 a square ; and it is the square of B C. In 
 like manner it may be shewn, that the 
 triangles E HD, EGA, are each similar 
 and equal to ABC; and hence also, the 
 figure E G F H, is the square of A B. Now, 
 the portions of the two squares, contained 
 within the square A C D E, together with 
 the triangles EHD, DIC, make up the 
 whole of that square. But the triangles 
 
 * The side opposite to the right angle, is called 
 the Hypothenuse. 
 
THE ARTISAN. 
 
 24 3 
 
 EHD, DIC, are equal to the triangles 
 EGA, ABC: hence the square of A C is 
 equal to the sura of the squares A B and 
 
 BC.* 
 
 PROPOSITION XLVIII. 
 
 Theorem. — If the square described upon one 
 of the sides of a triangle, be equal to the 
 squares described upon the other two sides 
 of it; the angle contained by these two 
 sides is a right angle. 
 
 If the square described upon B C, one of 
 the sides of the triangle A B C, be equal to 
 the squares upon the other sides BA, AC, 
 the angle B AC is a right angle. ’ 
 
 From the point A draw AD at right 
 angles to AC, and make A D equal to BA, 
 and join B C. Then, because D A is equal 
 
 D 
 
 put the parts together, so as to form the large square 
 out of the parts into which the two small ones are 
 here divided, by the lines drawn in the figure. 
 
 to AB, the square of DA is equal to the 
 square of A B : To each of these add the 
 square of AC; therefore the squares of 
 DA, AC, are equal to the squares of B A, 
 A C. But the square of D C is equal to 
 the squares of DA, A C, because D A C is 
 a right angle ; and the square of B C, by 
 hypothesis, is equal to the squares of B A, 
 A C ; therefore, the square of D C is equal 
 to the square of B C : and therefore also 
 the side D C is equal to the side B C. 
 And because the side D A is equal to A B, 
 and AC common to the two triangles 
 D AC and BAC, and the base DC being 
 likewise equal to the base B C, the angle 
 BAC is equal to the angle BAC: but 
 DAG is a right angle; therefore also 
 B A C is a. right angle. Q. E. D. 
 
 Having now arrived at the conclusion of 
 the first book of the Elements, we may 
 remark that many of these proposition are 
 only useful in proving others. 
 
 The 16th proposition, for example, is 
 evidently implied in the 32d., and is there- 
 fore useless after the 32d is demonstrated. 
 But the propositions are all arranged in 
 the order in which they are wanted for the 
 demonstration of those that follow, without 
 any regard to their subjects. By this 
 means nothing is ever assumed in any pro- 
 position that has not been previously 
 proved in some preceding proposition. 
 Hence arises the advantage of following 
 the arrangement which Euclid has adopted, 
 rather than making partial selections of 
 particular propositions. 
 
 MEC^HAIICS. 
 
 ON THE FRICTION AND RIGIDITY OF ROPES. 
 
 The first experiments that appear to 
 have been made on the rigidity of ropes, 
 i were those of Amontons, who contrived an 
 j ingenious appartus for this purpose. He 
 has published, in the Memoirs of the Aca- 
 demy of Sciences for 1699, a table of the 
 forces required to bend ropes, founded on 
 J the supposition that the difficulty of bend- 
 ing a rope of the same thickness, and 
 l loaded with the same weight, u decreases 
 i when the diameter of the roller or pulley 
 increases, but not so much as that diame' 
 
 I ter increases. 
 
 Another series of experiments was after- 
 wards made by Desaguliers, who pub- 
 
 lished a table, u shewing what forces 
 were required to bend ropes of different 
 diameters, stretched by different weights 
 round rollers of different sizes.” The 
 general result of these experiments was, 
 that the difficulty of bending a rope round a 
 roller, is, cwteris paribus , inversely as the 
 diameter of the roller. 
 
 The experiments on the rigidity and 
 friction of ropes made by Coulomb, were 
 performed, both with the apparatus used 
 by Amontons, and another of his own, 
 which is represented by the following 
 figure : 
 
 R 2 
 
244 
 
 THE ARTISAN. 
 
 It consists of two tressels 0 feet high, on 8. The rigidity of ropes is increased,* 
 which are laid two pieces of square wood, and their .strength diminished, when they 
 a b, c d. On these two pieces are fixed are covered with pitch ; but when ropes of 
 two rulers of oak, DD C C, well planed this kind are alternately immersed in the 
 and polished with fish-skins. With two sea and exposed to the air, they last longer 
 cylinders of lignum, vita, one 6 inches in than when they are not pitched. This 
 diameter, and the other 2 iuches ; and with increase of rigidity, however, is not so 
 several cylinders of elm, from 2 to 12 perceptible in small ropes as in those 
 inches in diameter, the apparatus was ready which are pretty thick, 
 for the experiments being made. 9. The rigidity of ropes covered with 
 
 In order to ascertain the friction of the pitch is a sixth part greater during frost 
 rollers, they were laid on planks, as shown than in the middle of summer ; but this in- 
 in the above figure. crease of rigidity does not follow the ratio 
 
 A weight of 50 lbs. was suspended on each of their tensions, 
 side of the roller, with very fine and flex- 
 ible pack-thread ; and the weights could 0 n the friction and form of pivots. 
 be increased in any degree, by laying 
 
 additional weights of 50 lbs. by different The needles of compasses are generally 
 threads, so as to give any required pressure suspended upon a pivot, by means of caps 
 to the rollers. By adding a counterweight of agate, or other hard substances. The 
 on each side of the roller alternately, till cap has a conical form, terminated above 
 they received a motion barely sensible, with a small concave summit, whose radius 
 Coulomb ascertained the friction of the of curvature is very small. The pivots 
 rollers. themselves are generally of tempered steel, 
 
 The following are the general results of but frequently reduced to the state of a 
 Coulomb’s experiments : spring. The point of the pivot which 
 
 1. The rigidity of ropes increases the supports the cap is a small curve surface, 
 
 more that the fibres of which they are com- whose radius of curvature is smaller than 
 posed are twisted. that of the summit of the cap. Coulomb 
 
 2. The rigidity of ropes increases in the generally found, that even when every 
 
 duplicate ratio (or as the squares) of their care was taken by the artist, the curvature 
 diameters. According to Amontons and of the summit of the cap was very irregu- 
 Desaguliers, the rigidity increases in the lar, and that the friction of an agate cap, 
 simple ratio of the diameters of the ropes ; turning upon the point of a pivot, was often 
 but this probably arose from the flexibility five or six times greater than the momen- 
 of the ropes which they employed. turn of friction of a highly polished agate 
 
 3. The rigidity of the ropes is in the plane'turning on the same pivot. 
 
 simple and direct ratio of their tension. Coulomb, in his experiments on pivots, 
 
 4. The rigidity of the ropes is in the in- supported the body by a highly polished 
 
 verse ratio of the diameters of the cylinders plane in place of a cap, and having given 
 round which they are coiled. This result it a rotatory motion, he noted, by means of 
 was obtained also by Desaguliers. a seconds w atch, the time employed in 
 
 5. In general, the rigidity of the ropes making the four ox five first turns, from a 
 
 is directly as their tensions and the squares mean of which he obtained the primitive 
 of their diameters, and inversely as the velocity ; and he next counted the number 
 diameters of the cylinders round which of turns which it made before it stopped, 
 they are coiled. The revolving body is obviously brought 
 
 6. The rigidity of ropes increases so to rest by the friction of the point of the 
 
 little with the velocity of the machine, that pivot, and also by the resistance of the air ; 
 it need not be taken into the account when but in order to get rid of this last resist- 
 computing the effects of machines. ance, Coulomb gave tire body the form of a 
 
 7. The rigidity of small ropes is dimi- glass receiver, and found, that when the 
 
 pished when penetrated with moisture ; velocity was not great, and when the re- 
 but when the ropes are thick, their rigi- ceiver weighed 5 or 6 gros (a gros is the 
 4j£y is increased . ght h of an ounce), the resistance of the 
 
THE ARTISAN. 
 
 245 
 
 air bore nb sensible ratio to that of the 
 friction. In order to render the results 
 more certain, he made several of the ex- 
 periments in vacuo. 
 
 The following are some of the results 
 which Coulomb obtained : 
 
 1. The friction of pivots is independent 
 of the velocities, and bears some proportion 
 to the pressure. 
 
 2. The friction of garnet is less than 
 that of agate, and that of agate less than 
 that of glass ; but the friction of different 
 parts of a plane of polished glass is less 
 irregular. 
 
 3. The angles of the points of pivots has 
 an influence on the friction. When the 
 body weighs five or six gros, the best 
 angle is from 30 to 45 degrees. When th® 
 body weighs less, the angle of the pivot 
 may be progressively diminished without 
 the friction experiencing any sensible in- 
 crease. We may even without much in- 
 convenience, and when the steel is good, 
 reduce it to 10 and 12 degrees, provided 
 the weight of the body does not exceed a 
 hundred grains. 
 
 4. With a pivot of the best steel, well 
 tempered, and brought to the first degree 
 of steel temper, and having an angle of 
 45 degrees, the momentum of friction varies 
 as the |d power of the pressure.* When 
 the pressure was very considerable, and 
 the pivot shaped to any angle, the friction 
 varied nearly as the pressure. 
 
 5. All the caps which Coulomb procured 
 from the best workmen, appeared to be 
 very irregular in their concavity. The 
 momentum of their friction, under pres- 
 sures of even more than five or six grains, 
 is always quadruple of that of a well- 
 polished plane of the same substance ; and 
 in order to support these caps, it is neces- 
 sary that the points of the pivots be shaped 
 to an angle less than that which is neces- 
 sary to support planes. 
 
 METHODS OF DIMINISHING FRICTION IN 
 MACHINERY. 
 
 The experiments which have been de- 
 tailed above, will furnish the practical me- 
 
 Fig. 1. 
 
 chanic with various rules respecting the 
 nature and form of the materials which 
 should form the supports and communicate 
 ing parts of machines, respecting the 
 nature of the unguents which should be 
 applied to them, and the mode of their 
 application. 
 
 The most efficacious contrivances for di- 
 minishing friction, are friction wheels ,t by 
 means of which, that species of friction 
 which arises from one body being dragged 
 over another, is changed into that which 
 arises from one body rolling upon another* 
 The application of friction-wheels is shown 
 in the following- figures: 
 
 Fig. 1st represents 01. Gottlieb’s anti- 
 attrition axle-tree, and which consists of a 
 steel roller R, about five inches long, turn- 
 ing in a groove cut in the lower part of 
 the axle-tree C, which works on the nave 
 AB. 
 
 Fig. 2d, shows the method of applying 
 friction- rollers used by Mr. Garnett. A 
 space between the axle E, and the nave of 
 the wheel A B D C, is filled with friction- 
 rollers, R, R, R, &c. whose axes are in- 
 serted in circles of brass, which are rivet- 
 ted together by means of bolts which pass 
 between the rollers, in order to keep them 
 separate and parallel. When the moving 
 force is not exerted in a perpendicular 
 direction, but obliquely, as in undershot- 
 wheels, the gudgeon will press with 
 greater force on one part of the socket 
 than on any other part. This point will 
 evidently be on the side of the bush oppo- 
 site to that where the power is applied ; 
 and its distance from the lowest point of 
 the socket, which is supposed circular and 
 
 Fig. 2. 
 
246 
 
 THE ARTISAN, 
 
 Concentric with the gudgeon, and may be 
 determined by calculation. 
 
 Friction-wheels seem to have been first 
 recommended by Casatus. They were 
 afterwards mentioned by Sturmius and 
 Wolfius, but were not in actual use till 
 Sully applied them to clocks in 1716, and 
 Mondran to cranes in 1725. They re- 
 mained, however, almost unnoticed till the 
 celebrated Euler explained their nature 
 and advantages in his memoirs on Friction. 
 Another method of diminishing friction, is 
 to apply the impelling power (when it can 
 be done) in such a way, as to act either in 
 opposition or obliquely, to the force of 
 gravity. 
 
 If we suppose, for example, that the 
 weight of a wheel, whose iron gudgeons 
 move in bushes of brass, is 100 pounds, 
 then the friction arising from both its gud- 
 geons will be equivalent to 25 pounds : 
 If we suppose also that a force equal to 
 40 pounds is employed to impel the wheel, 
 and acts in the direction of gravity, as in 
 the cases of overshot-wheels, the pressure 
 of the gudgeons upon their supports will 
 then be 140 pounds, and the friction 35 
 pounds. But if the force of 40 pounds 
 could be applied in such a manner, as to 
 act in direct opposition to the wheel’s 
 weight, the pressure of the gudgeons upon 
 their supports would be 100, minus 40, or 
 60 pounds, and the friction only 15 pounds. 
 It is impossible, indeed, to make the moving 
 force act in direct opposition to the gravity 
 of the wheel, in the case of water-mills; 
 and it is often impracticable for the en- 
 gineer to apply the impelling power but in 
 a given way : but there are many cases in 
 which the moving force may be exerted, so 
 as not to increase the friction, which arises 
 from the weight of the wheel. 
 
 A contrivance for diminishing friction 
 by rendering an axis of rotation unneces- 
 sary, is shown in the following figure. 
 
 Where A is a cylindrical wheel, without 
 an axis of rotation, but turned by the rope 
 r r, passing round a groove in its circum- 
 ference. The wheel A is supported by the 
 three wheels, or rollers w, iv, w, which 
 have a groove hollowed cut upon their 
 circumference. 
 
 Another method of diminishing friction, 
 proposed by M. Gaston de Thiville, is 
 shown in the following figure. 
 
 The wheel R has two hollow cylinders, 
 m,n, fixed to its axle A B. These cylin- 
 ders are made to float in boxes filled with 
 water in such a manner, that the gudgeons 
 pass through the boxes of water, so as to 
 be water tight without preventing their 
 rotation. The weight of the wheel is thus 
 supported upon the floating cylinders, and 
 it is kept in its place by the gudgeons x, y. 
 
 As it appears from the experiments of 
 Coulomb, that the least friction is gene- 
 rated when polished iron moves upon 
 brass, the gudgeons and pivots of wheels, 
 and the axles of friction rollers, should all 
 be made of polished iron ; and the bushes 
 in which these gudgeons move, and the 
 friction wheels, should be formed of po- 
 lished brass. In small and delicate ma- 
 chinery, the cups or planes which support 
 pivots, or upon which knife-edges rest, as 
 in balances and pendulums, should be 
 made of garnet in preference to any other 
 substance. 
 
 When every mechanical contrivance has 
 been adopted for diminishing the obstruc- 
 tion which arises from the attrition of the 
 communicating parts, it may be still farther 
 removed by the judicious application of 
 unguents. The most proper for this pur- 
 pose are swine’s grease and tallow, when 
 the surfaces are made qf wood ; and oil 
 when they are made of metal. When the 
 force with which the surfaces are pressed 
 together is very great, tallow will diminish 
 the friction more than swine’s grease. 
 When the wooden surfaces are very small, 
 unguents will lessen their friction a little, 
 but will be greatly diminished if wood 
 moves upon metal greased with tallow. 
 If the velocities, however, are increased, 
 or the unguent not often enough renewed, 
 in both these cases, but particularly in the 
 last, the unguent will be more injurious 
 than useful. The best mode of applying 
 
THE ARTISAN. 
 
 247 
 
 it, is to cover the rubbing surfaces with as 
 thin a stratum as possible, for the friction 
 will then be a constant quantity, and will 
 not be increased by an augmentation of 
 velocity. 
 
 In small works of wood, the interposition 
 of the powder of black lead has been found 
 very useful in relieving the motion. The 
 ropes of pulleys should be rubbed with 
 tallow, and whenever the screw is used, 
 the square threads should be preferred. 
 
 In order to apply unguents to the com- 
 municating parts of machines, various con- 
 trivances have been adopted. The spindles 
 of trundles have been made hollow, to con- 
 tain oil, so that when they had a horizontal 
 position, they allowed it to drop from small 
 apertures upon the wheel below, by which 
 they were driven. 
 
 As we have now considered the subject 
 of friction under each of the heads men- 
 tioned at page 212, we shall conclude this 
 article by stating a few of the effects of this 
 force which have not yet been noticed. 
 
 The distance to which a given body will 
 be moved by percussion, in opposition to 
 friction, is as the square of the velocity 
 communicated to it, or the distance will be 
 proportional to the square of the velocity. 
 On this principle, some paradoxical ap- 
 pearances may be explained, which are 
 not so easily accounted for on any other. 
 When a carpenter, for example, would 
 drive the handle of an axe into the head, 
 he strikes against the handle after it is 
 slightly inserted into the head, holding it 
 loosely in his hand, without any firm sup- 
 port, and even the head downward ; at each 
 blow the handle is driven farther than if 
 the blow had been given to the head itself. 
 The reason is, that the handle is the lighter 
 body, and, therefore, the velocity which a 
 blow communicates to it, is greater than 
 that which the same blow would communi- 
 cate to the head. The friction is of course 
 more effectually overcome. 
 
 A nail, too, is driven by a blow of no 
 great force, into a piece of wood where 
 the mere friction is sufficient to retain it 
 against a great force applied to draw it 
 out. 
 
 The same thing is exemplified in the 
 method now practised, of raising a stone 
 by an iron plug, driven into a circular hole 
 cut in the stone. A few blows of a small 
 hammer are sufficient to fix the plug, so 
 that it will serve not only to suspend the 
 stone, though of several hundred pounds 
 weight, but even to draw it out of the 
 earth, in which it is perhaps sunk to a con- 
 siderable depth. Such is the effect of per- 
 cussion, that a few blows of a hammer, 
 given obliquely to the plug, are sufficient 
 to disengage it from the stone. The stones 
 on which this experiment has been made, 
 
 have always possessed great hardness and 
 cohesion. 
 
 Though friction destroys motion and ge- 
 nerates none, it is of essential use in Me- 
 chanics. It is not only the cause of sta- 
 bility in the structure of machines; but it 
 is necessary to the exertion of the force of 
 animals. 
 
 A nail, a screw, or a bolt, could give no 
 firmness to the parts of a machine, or of 
 any other structure without friction. Ani- 
 mals could not walk, or exert their force 
 in any way without the support which it 
 affords. Nothing would have any stability 
 but in the lowest situation possible, and an 
 arch that could sustain the greatest load 
 when properly distributed, might be thrown 
 down by the weight of a single ounce, if 
 not placed with mathematical exactness at 
 the very point it ought to occupy. 
 
 HYBEATO1CS. 
 
 Having now given a very full account of 
 the various instruments and machines em- 
 ployed for raising water from a lower to a 
 higher situation, we shall here enter upon 
 the important subject of water wheels. Of 
 these there are various kinds ; but they 
 are usually classed under the folio wing- 
 heads ; viz. those that are moved by the 
 weight of water, those that are moved by 
 the impulse of water, and those that are 
 moved by the re-action of water. 
 
 When a wheel receives the water into 
 buckets, at or near its highest point, it is 
 put in motion by the weight of the water 
 with which it is loaded on one side, and it 
 is then called an Overshot-wheel. 
 
 CONSTRUCTION OF OVERSHOT-WHEELS. 
 
 An overshot-wheel of the common kind, 
 is represented as in the following figure. 
 
 JE 
 
THE ARTISAN. 
 
 248 
 
 Where A B C D is the rim of the wheel, 
 having a number of backets a, b, c, d, ar- 
 ranged round its circumference. When 
 the wheel is in a state of rest upon its axis 
 O, and water is introduced into the bucket 
 c from the horizontal mill course or canal 
 E F, the weight of the water in the bucket, 
 acting at the end of a lever equal to m O, 
 puts the wheel in motion in the direction 
 c d. When the subsequent bucket b comfes 
 into the position c, it is also filled with 
 water, and so on with all the rest. When 
 the bucket c reaches the situation of d, its 
 mechanical effect to turn the wheel is in- 
 creased, being now equal to the weight of 
 water acting at the end of a lever n O, 
 equal to the distance of its centre of gravity 
 d, from a vertical line passing through the 
 axis O, so that the mechanical effect of the 
 water in the bucket increases all the way 
 to B, and of course diminishes while the 
 buckets are moving from B to C. 
 
 The buckets, however, between B and C, 
 have not the same power upon the wheel 
 as those between A and B ; for the water 
 begins to fall out of the buckets before 
 they approach to B, and are almost com- 
 pletely empty when they reach the point 
 H. The construction of the buckets, 
 therefore, as shewn in the figure, is very 
 improper, as it not only allows the water 
 to escape before it has reached the point B, 
 where its mechanical effect is a maximum ; 
 but also to escape completely, long before 
 they have reached the lowest point C of the 
 wheel, "the power, therefore, of an over- 
 shot-wheel must depend principally upon 
 the form which is given to the buckets, 
 which should always be fullest when they 
 are at the point B, and should retain the 
 water as long as possible. If the buckets 
 were to consist of a single partition in the 
 direction of the radii of the wheel, all the 
 water would escape from the buckets be- 
 fore they passed the point B on a level with 
 the axis O. 
 
 It has in general been assumed by writers 
 on waterwheels, that the diameter of over- 
 shot-wheels should always be less than the 
 height of the fall of water by which it is to be 
 put in motiofi, and various ratios have been 
 assigned between the height of the fall and 
 the diameter of the wheel. The Chevalier 
 de Borda has shewn, that overshot-wheels 
 Will produce a maximum effect when their 
 diameter is equal to the greatest height of 
 the fall, but that a slight diminution of the 
 wheel’s diameter produces only a very 
 small diminution of the maximum effect. 
 If the height of the fall, for example, is 12 
 feet, and if the diameter of the wheel is 
 made only 11 feet, the effect is diminished 
 only -jL . This theoretical result has been 
 confirmed by the admirable experiments of 
 Mr. Smeaton, who found, “ that the higher 
 $ke wheel is in proportion to the whole des- 
 
 cent, the greater will be the effect be- 
 cause, as he remarks, u it depends legs 
 upon the impulse of the head, and more 
 upon the gravity of the water in the buck- 
 ets ; and if we consider how obliquely the 
 water issuing from the head must strike 
 the buckets, we shall not be at a loss to 
 account for the little advantage that arises 
 from the impulse thereof, and shall imme- 
 diately see of how little consequence this 
 impulse is to the effect of an overshot- 
 wheel.” 
 
 If the diameter of the wheel were equal 
 to the whole height of the fall, the water 
 would be laid in the buckets without 
 having acquired any velocity; so that a 
 portion of the power of the wheel would 
 be spent in dragging this inert mass into 
 motion, and also by the impulse of the 
 buckets against the water, which will dash 
 a part of it over the wheel. Hence, it is 
 necessary, that the difference between the 
 head of water and the diameter of the 
 wheel should be such, that the water may 
 acquire in its descent through that space a 
 velocity a little greater than that of the cir- 
 cumference of the wheel. In this view of 
 the subject, the water should fall through 
 a height of 2\ or S inches per second, in 
 order to acquire the velocity of the wheel ; 
 and therefore the diameter of the wheel 
 should be only 3 inches less than the height 
 of the fall. 
 
 The determination of the diameter of an 
 overshot-wheel, as given by Borda, Smea- 
 ton, Robinson, and other Authors, is 
 founded upon the assumption, that it never 
 should exceed the height of the fall. Let 
 us suppose that we have a fall of 12 feet, 
 and that the wheel should have a diameter 
 of 11 feet according to Borda, then it ap- 
 pears to us, that a great advantage will be 
 derived from making the wheel 15 feet. 
 Now it is obvious, that the advantage of 
 using the 15 feet wheel is, that we apply 
 the water where it will act most perpendi- 
 cularly to the line O D, in the foregoing 
 figure, or the radius of the wheel; whereas 
 the disadvantage of such a wheel is, that 
 it begins to lose its water much sooner 
 than the small one. We differ in opinion 
 from Robinson when he says, that the loss 
 of power in the latter case exceeds what is 
 gained in the former case ; but we shall 
 admit that it is so, and still maintain the 
 superiority of the 15 feet wheel. When 
 the wheel has a diameter less than the 
 height of the fall, any augmentation of the 
 quantity of water discharged by the mill 
 course is of no use in increasing the effect 
 of the wheel. The issuing water indeed 
 acquires a velocity greater than it usually 
 has, but this additional velocity is injurious 
 to the motion of the wheel instead of being 
 of any advantage. In the case of a 15 feet 
 Tall, however, when the water rises 1 or 2 
 
the Artisan. 
 
 2 40 
 
 feci above its usual level, we have it in 
 our power, by a particular form of the de- 
 livering sluice, to introduce this water 
 upon the wheel 1 or 2 feet higher up the 
 wheel, so that we are actually enabled to 
 increase the height of the fall by this quan- 
 tity. 
 
 From a series of experiments on over- 
 shot-wheels, by M. Deparcieu, and pub- 
 lished in 1754 j he has concluded, that 
 most work is performed by an overshot- 
 wheel when it moves slowly, and that the 
 more we retard its motion by increasing 
 the work to be performed, the greater will 
 be the performance of the wheel. These 
 experiments were made with a wheel 20 
 inches in diameter, and having 48 buckets. 
 Cylinders of different diameters were 
 placed upon the axle, and the effect of the 
 wheel under different velocities was mea- 
 sured by the height to which it raised a 
 weight suspended to a rope, which was 
 wound round the different cylinders ; and 
 the general result was, that the slower the 
 wheel turns, the greater is the effect, or 
 the height to which the weight is raised. 
 
 In opposition to these results, the Cheva- 
 lier D’Arcy maintained, that there is a 
 certain velocity when the effect is a maxi- 
 mum ; and he has shewn, from a compa- 
 rison of Deparcieu’s experiments with his 
 own formulae, that the wheel never moved 
 with such a small velocity fas would have 
 given the maximum effect, and that if he 
 had increased the diameter of his cylin- 
 ders, he w ould have found that there was 
 a velocity when the maximum effect began 
 to diminish. 
 
 The experiments of Smeaton afford an 
 excellent confirmation of the preceding 
 reasoning. The wheel which he used was 
 25 inches in diameter. The depth of the 
 buckets or of the shrouding was 2 inches, 
 and the number of buckets 36. When it 
 made about 20 turns in a minute, the effect 
 was nearly the greatest. When the number 
 of turns was 30, the effect was diminished 
 ^th part. When the number was 40, the 
 diminution was ^th; when the number 
 was less than 18^ its motion was irregular; 
 and when it was loaded so as not to be 
 able to make 18 turns, the wheel was over- 
 powered by its load. 
 
 “ It is an advantage in practice,” says 
 Mr. Smeaton, u that the velocity of the 
 ■wheel should not be diminished farther 
 than what will procure some solid advan- 
 tage in point of power ; because, cceteris 
 aribus, as the motion is slower the 
 uckets must be made larger; and the 
 wheel being more loaded witn water, the 
 stress upon every part of the work will be 
 increased in proportion. The bestvelocity 
 for practice, therefore, will be such as when 
 the wheel here used made about 30 turns 
 4n a minute ; that is, when the velocity of 
 
 the circumference is a little more than 
 three feet in a second. 
 
 Experience confirms, that this velocity 
 of three feet in a second is applicable to 
 the highest overshot-wheels as well as the 
 lowest ; and all other parts of the work 
 being properly adapted thereto, will pro- 
 duce very nearly the greatest effect possi- 
 ble; however, this also is certain from 
 experience, that high wheels may deviate 
 farther from this rule before they will lose 
 their power by a given aliquot part of the 
 whole, than low ones Can be admitted to 
 do; for a wheel of 24 feet high may move 
 at the rate of six feet per second without 
 losing any considerable part of its power ; 
 and, on the other hand, I have seen a 
 wheel of 33 feet high, that has moved 
 very steadily and well with a velocity but 
 little exceeding two feet.” 
 
 The experiments of the Abbe Bossui 
 afford the same results. He used a wheel 
 three feet in diameter. The height of the 
 buckets was three inches, their width five 
 inches, and their number 48; and the 
 canal which conveyed the water furnished 
 uniformly 1194 cubic inches in a minute. 
 When the wheel was unloaded, it made 
 40^ turns in a minute. 
 
 In comparing the relative effects of water 
 wheels, the Chevalier de Borda maintains, 
 that an overshot-wheel will raise through 
 the height of the fall a quantity of water 
 equal to that by which it is driven ; while 
 Albert Euler affirms, that the effect is 
 greatly inferior to this. The experiments 
 of Mr. Smeaton shew, that when the heads 
 and quantities of water are least, the ratio 
 between the power and the effect at the 
 maximum is nearly as 4 : 3 ; but when the 
 heads and quantities of water were greater, 
 it is as 4:2; and by a medium of the 
 whole, it is as 3 : 2. When the powers of 
 the water, computed for the height of the 
 wheel only, are compared with the effects, 
 they observe a more constant ratio, the va- 
 riation being only between the ratio of 
 10:8*1 and 10 : 8*5. Hence the ratio of 
 the power, computed upon the height of 
 the wheel only, is to the effect, at a maxi- 
 mum, as 10 : 8, or as 5 : 4 nearly, and the 
 effects, as well as the powers, are as the 
 quantities of water and perpendicular 
 heights multiplied together respectively. 
 
 The form of the delivering sluice, and 
 the method of introducing the water into 
 the buckets, will be best explained in the 
 description of different overshot-wheels. 
 
 smeaton’s improved overshot-wheel. 
 
 Mr. Smeaton constructed a wheel which 
 he considered as of an improved form. 
 
 In the following figure A B represents 
 this wheel, and M N the extremity of the 
 mill course, where the water is delivered 
 into the buckets. - 
 
250 
 
 THE ARTISAN. 
 
 The vertical lever a b c turning round b 
 as a centre, gives motion to the horizontal 
 arm c d , and causes one of the shuttles ef 
 to advance or recede ; in consequence of 
 which, the aperture on the right hand of/ 
 maybe either increased or diminished, for 
 the purpose of regulating the supply of 
 water which the wheel may require. An 
 iron bolt goes through the bottom of the 
 trough between the two shuttles, and is in- 
 tended to prevent the bottom from sinking 
 by the weight of the water. From the 
 form of the aperture at /, it will be seen 
 that the water will glide easily into the 
 buckets without any waste. In both these 
 machines, the water is turned back on the 
 near half of the wheel ; the consequence 
 of which is, that the resistance of the lower 
 water is removed, as it runs off in the same 
 direction with the motion of the wheel. 
 
 DOUBLE OVERSHOT-WHEEL WITH A CHAIN 
 OF BUCKETS. 
 
 When there is a very small supply of 
 water falling from a very great head, the 
 overshot-wheel, which it is necessary to 
 employ is so large and expensive, and so 
 apt to be injured from its unwieldy size, 
 that few persons would be disposed “to 
 erect one. In circumstances like this, 
 the double overshot-wheel, with a chain of 
 buckets, is a most invaluable machine, not 
 merely from the small price at which it can 
 be erected, but from the great power which 
 it possesses. A machine of this kind 
 seems to have been first erected byM. 
 Francini in 1668, in the garden of the king 
 of France’s old library. This machine of 
 Francini was driven by waste of water, 
 and raised water from a natural spring, by 
 means of another chain of buckets fixed 
 upon the same wheel. 
 
 M. Costar substituted a similar machine 
 in place of the overshot- wheel j and more 
 recently Mr. Gladstone’s, an ingenious 
 millwright at Castle Douglas, in Scotland, 
 erected several in Galloway for the pur- 
 pose of giving motion to threshing mills. 
 
 The double overshot-wheel is repre- 
 sented in the/ollowing figure, 
 
 where A and B are two rag wheels, as they 
 are called, andCDEF a series of buckets 
 fixed to an endless chain, whose links fall 
 into notches in the circumference of the rag 
 
THE ARTISAN. 
 
 251 
 
 wheels. The water issuing from the mill 
 course at M N, is introduced into the buck- 
 ets on the side C. The descent of the 
 loaded buckets on the side C puts the 
 wheels A and B in motion, and the power 
 is conveyed from the shaft of the wheel A 
 to turn any kind of machinery. When the 
 buckets reach F, they allow the water to 
 escape, and ascending empty on the side 
 E, they again return to the spout M N, to 
 be filled as before. In this machine, the 
 buckets have in every part of their path 
 the same mechanical effect to turn the 
 wheels, and they will not allow the water 
 to escape till they have reached almost the 
 lowest part of the fall. 
 
 This species of wheel possesses another 
 advantage, which can be obtained from no 
 other; namely, that by raising the wheel 
 B, and taking out two or three of the buck- 
 ets, it may be made to work when there is 
 such a quantity of back-water as would 
 otherwise prevent it from moving. 
 
 Dr. Robison, in his Dissertation onW ater 
 Works, published in the second volume of 
 his System of Mechanical Philosophy, has 
 described a machine of this kind, in which 
 plugs, or horizontal float boards, are fixed 
 to a chain. On the side C these plugs pass 
 through a tube, a little greater in diameter 
 than that of the floats, as it does in the 
 case of a breast wheel, giving motion to 
 the wheels A and B. 
 
 The double overshot-wheel is the best 
 and the most economical which can be 
 adopted for a small supply of water falling 
 from a great height; but it is liable to get 
 out of order, unless the chain which car- 
 ries the buckets is made with great care 
 and nicety. 
 
 fHtscellaneous duijecte. 
 
 MEMOIR OF THE LIFE OF WIL- 
 LIAM EMERSON. 
 
 William Emerson, a very eminent ma- 
 thematician, was born May 14, 1701, at 
 Hurworth, a village about three miles 
 south of Darlington, on the borders of the 
 county of Durham, at least it is certain he 
 resided here from his childhood. His fa- 
 ther, Dudly Emerson, taught a school, and 
 was a tolerable proficient in mathematics ; 
 and without the benefit of his books and 
 instructions, perhaps his son’s genius 
 might never have been unfolded. Besides 
 his father’s instructions, our author was 
 assisted in the learned languages by a 
 young clergyman, then curate of Hurworth, 
 who was boarded at his fathers house- In 
 the early part of his life, he attempted to 
 teach a few scholars ; but whether from 
 his concise method (for he was not happy 
 in expressing his ideas), or the warmth of 
 
 his natural temper, he made no progress 
 in this profession ; he therefore soon left 
 it off, and satisfied with a small paternal 
 estate of about 60 or 70 pounds a year, 
 devoted himself to study, which he closely 
 pursued in his native place through the 
 course of a long life, being mostly very 
 healthy, till towards the latter part of it, 
 when he was much afflicted with the 
 stone : towards the close of the year 1781, 
 being sensible of his approaching dissolu- 
 tion, he disposed of the whole of his ma- 
 thematical library to a bookseller at York; 
 and on May the 26th, 1782, his lingering 
 and painful disorder put an end to his life 
 at his native village, in the eighty-first 
 year of his age. In his person he was 
 rather short, but strong and well-made, 
 with an open countenance and ruddy com- 
 plexion. He was never known to ask a 
 favour, or to seek the acquaintance of a 
 rich man, unless he possessed some emi- 
 nent qualities of the mind. He was a 
 very good classical scholar, and a tolerable 
 physician, so far as it could be combined 
 with mathematical principles, according 
 to the plan of Keil and Morton. The latter 
 gentleman he esteemed above all others, as 
 a physician — and the former as the best 
 anatomist. He was very singular in his 
 behaviour, dress, and conversation. His 
 manners and appearance were that of a 
 rude and rather boorish countryman ; he 
 was of very plain conversation, and indeed 
 seemingly rude, commonly mixing oaths in 
 his sentences. He had strong natural 
 parts, and could discourse sensibly on any 
 subject; but was always positive and im- 
 patient of any contradiction. He spent 
 his whole life in close study and writing- 
 books; with the profits of which he re- 
 deemed his little patrimony from some 
 original incumbrances. He had but one 
 coat, which he always wore open before, 
 except the lower button; no waistcoat; 
 his shirt quite the reverse of one in com- 
 mon use, no opening before, but buttoned 
 close at the collar behind; a kind of flaxen 
 wig, which had not a crooked hair in it ; 
 and probably had never beentortured with 
 a comb from the time of its being made. 
 This was his dress when he went into com 
 pany. One hat he made to last him the 
 best part of his lifetime, gradually lessen- 
 ing the flaps, bit by bit, as it lost its elasti- 
 city and hung down, till little or nothing 
 but the crown remained. | He never rode , 
 although he kept a horse, but was fre- 
 quently seen to lead the horse, with a kind 
 of wallet stuffed with the provisions he 
 had bought at the market. He always 
 walked up to London when he had any 
 thing to publish, revising sheet by sheet 
 himself; trusting no eyes but his own, 
 which was always a favorite maxim with 
 him. He never advanced any mathemati- 
 cal proposition thathe had not first tried in 
 practice, constantly making all the differ- 
 
252 
 
 THE ARTISAN. 
 
 ent parts himself on a small scale, so that 
 his house was filled with all kinds of me- 
 chanical instruments together or disjointed. 
 He would frequently stafid up to his mid- 
 dle in water while fishing, a diversion he 
 was remarkably fond ofi He Used to 
 study incessantly for some time, and then 
 for relaxation take a ramble to any pot ale 
 house where he could get any body to 
 drink with and talk to. The Duke of 
 Manchester was highly pleased with his 
 company, and used often to come to him 
 in the fields and accompany him home, but 
 could never persuade him to get into a car- 
 riage. When he wrote his small treatise 
 on navigation, he and some of his scholars 
 took a small vessel from Hurworth, and 
 the whole crew soon got swampt ; when 
 Emerson, smiling and alluding to his trea- 
 tise, said “ They must not do as I do, but 
 as I say.” He was a married man ; and 
 his wife used to spin on an old-fashioned 
 Wheel, of which a very accurate drawing is 
 given in his mechanics. He was deeply 
 skilled in the science of music, the theory 
 of sounds, and the various scales both an- 
 cient and modern, but was a very poor per- 
 former. He carried that singularity which 
 marked all his actions even into this sci- 
 ence. He had, if we may be allowed the 
 expression, two first strings to his violin, 
 which, he said, made the E more melodi- 
 ous when they were drawn up to a perfect 
 unison. His virginal , which is a species of 
 instrument like the modern spinnet, he had 
 cut and twisted into various shapes in the 
 keys, by adding some occasional half-tones 
 in order to regulate the present scale, and 
 to rectify some fraction of discord that will 
 always remain in the tuning. He never 
 could get this regulated to his fancy, and 
 generally concluded by saying, “ It was a 
 bad instrument, and a foolish thing to be 
 vexed with.” 
 
 Mr. Emerson’s Works are too numerous 
 to be inserted here. 
 
 SYMPATHETIC INKS. 
 Sympathetic ink is a substance with 
 which writings may be formed, which are 
 invisible till they are subjected to some 
 process, which immediately renders the 
 whole distinct. This purpose was fulfilled 
 among the ancients by means of milk, or 
 some other viscous substance, which was 
 rendered legible by means of soot thrown 
 over the writing; part of it adhering 
 wherever the lines were drawn, while 
 from every other part it was blown en- 
 tirely off. 
 
 There are some articles employed for 
 this purpose, which are rendered visible by 
 the addition of a substance which acts che- 
 mically. The materials of writing ink 
 may, for example, be employed in a sepa- 
 rate state. Invisible words may be first 
 written with a solution of the sulphate of 
 iron. If a rag, dipped in a decoction of 
 
 galls, be drawn over them, they become 
 immediately legible. If this be afterwards 
 rubbed over with sulphuric acidj it is 
 effaced. But the application of a saturated 
 solution of potassa, will make it re-appear 
 like yellow writing. 
 
 The golden sympathetic ink consists of a 
 solution of gold in nitro -muriatic acid, 
 diluted with six times its quantity of water. 
 Letters traced with this are invisible ; but 
 when a similar solution of tin is applied to 
 them, the writing appears in the form of 
 beautiful purple letters, 
 f Nitromuriatic acid is now capable of 
 effacing them, and the re-application of 
 the muriate of tin will restore them. Let- 
 ters made with the muriate of gold, indeed, 
 become spontaneously visible when ex- 
 posed to the air. This, however, requires 
 several days, and, if kept closely shut up> 
 they remain invisible for two or three 
 months. The acid evaporates, and leaves 
 a violet oxide or submuriate. Nitrate of 
 silver affords invisible letters, which be- 
 come black by long exposure. 
 
 There are many sympathetic inks which 
 are rendered visible by exposure to a fire. 
 Solutions of muriate of ammonia, and 
 various other neutral salts, act on paper 
 by means of heat, in such a way as adapts 
 them to this use ; but the letters become, in 
 process of time, confused and illegible. 
 
 The best sympathetic inks are those 
 made from ores of arsenic, bismuth, or 
 cobalt. Diluted nitric acid is poured on 
 arsenic ore, and afterwards carefully de- 
 canted, treated with nearly half the quan- 
 tity of dried muriate of soda, and evapo- 
 rated. Letters or figures formed with this 
 are invisible till held near the fire, which 
 renders them visible, and of a beautiful 
 blueish green colour. This disappears 
 again when it is removed from the fire. 
 Allum, with the sulphate of soda, used in- 
 stead of muriate of soda, renders the sub- 
 stance red. Borate of soda, or nitrate of 
 potassa, also makes the letters appear 
 red. 
 
 The nitro -muriate of cobalt forms a simi- 
 lar ink, which appears on exposure to 
 heat, and disappears in the cold. The 
 heat applied to it, however, must not ex- 
 ceed a certain strength, otherwise the 
 letters become permanently visible both in 
 heat and cold. These inks are employed for 
 making amusing landscapes, in which the 
 trees acquire a summer foliage as often as 
 they are brought near a fire. 
 
 A sympathetic ink may be obtained from 
 fresh urine, evaporated, then dissolved in 
 nitric acid, and saturated with ammonia 
 or its carbonate. Lines drawn with this 
 become visible, of a fine red, on exposure 
 to a gentle heat. Sulphate of zinc applied 
 to them gives them a rich yellow. This 
 ink must be applied, however, immediately 
 after it is formed. It becomes deteriorated 
 in so short a time as twenty minutes. 
 
THE ARTISAN. 
 
 253 
 
 ARCHITECTURE. 
 
 GOTHIC ARCHITECTURE, 
 
 After having described the five Orders, 
 It will naturally be expected that we should 
 say something of the Gothic style; we 
 shall therefore give a general view of the 
 distinguishing features of this species of 
 Architecture. 
 
 The attention to Gothic architecture 
 having only been lately revived, the prac- 
 tice has not hitherto been digested into so 
 systematic order as the Greek or Roman ; 
 and it is not a little extraordinary, consider- 
 ing that during the ages in which it w r as ex- 
 tensively practised, its operations were di- 
 rected by men of science and literary habits, 
 that no written rules have been discovered 
 in the religious houses, which were then the 
 only depositories of knowledge. This has 
 led Mr. Knight, and other men of observa- 
 tion, to assert, that each architect proceeded 
 independently of rules, and worked in the 
 manner, which to him appeared best calcu- 
 lated to produce a striking effect, and that 
 it was in consequence of the absence of 
 determined rules, that this school rose to 
 the degree of sublimity it attained. This 
 is denied by other able and enlightened 
 men, who have paid much attention to the 
 subject, especially Dallaway, Milner, and 
 Hawkins, who maintain, that although 
 few arranged rules and proportions have 
 been published in books, yet architects 
 and workmen were constantly guided by 
 known rules agreeable to the prevailing 
 mode. It is evident, although not so 
 rigidly confined as the Egyptian, that the 
 Gothic architects were fully as much 
 limited as the Roman; for the contrast 
 between the massy plain Norman style, 
 and the latter or florid Gothic, is not greater 
 than what was produced by varying from 
 the plainness, simplicity, and oblong forms 
 of the ancient Greek temples, to the circu- 
 lar, delicate, and highly ornamented edi- 
 fices of the latter Roman. 
 
 The Gothic style having been employed 
 almost exclusively in edifices appropriated 
 to the purposes of the Christian religion, 
 the outlines of the ground plan have almost 
 uniformly been a cross. In the Greek and 
 Roman oblong temples, the ratio of the 
 length and breadth was determined by the 
 number of columns placed at nearly equal 
 distances along the ends and sides, while 
 that of the height was regulated by the 
 diameter of the column ; but in the Gothic, 
 where seldom any columns have been 
 placed on the outside of the edifice, and 
 the use of arches proving a relief from 
 constraint within it, it is alleged, that the 
 proportion of the length to the breadth has 
 been determined by triangles and squares. 
 
 Of this, Mr. Hawkins, in his History of 
 the Origin and Establishment of Gothic 
 Architecture, (chap. 10), has produced an 
 early instance from Caesar Caesarianus, a 
 celebrated architect of Milan, who, in an 
 elaborate commentary annexed to his 
 translation of Vitruvius, has explained the 
 principles of Gothic architecture. 
 
 With regard to the form of the essential 
 parts , they are mostly defined in the fol- 
 lowing description of the three orders of 
 Architecture, as given by Dr. Milner. 
 
 The first order is characterised during its 
 formation ; that is to say, till near the latter 
 end of the 12th century, chiefly by its acute 
 arch (its pillars and other members being 
 frequently Saxon), but after its formation, 
 not only by the narrowness and acuteness 
 of its arch, but also by its detached slender 
 shafts, its groining of simple intersecting 
 ribs, its plain pediments without crockets 
 or side pinnacles, and its windows, which 
 were either destitute of mullions, or have 
 only a simple bisecting mullion, with a 
 single or triple trefoil, quatrefoil, or other 
 flower, in the head of them. Of this order 
 are the east end of Canterbury, the west 
 end of Lincoln, and the whole of Salisbury 
 Cathedrals, besides the transepts of York 
 Minster and Westminster Abbey. 
 
 The second order is marked, not only by 
 the fine turn of its perfect equilateral arch, 
 but also by the cluster columns, being, for 
 the most part, formed each course out of 
 the same stone; by the elegant, but not 
 over crowded tracery of its windows and 
 groining; by its crocketted pinnacles, 
 tabernacles, and pediments, the latter of 
 which, towards the conclusion of the four- 
 teenth century, were made with an ogee 
 sweep towards the arch they covered. To 
 this order belong the nave of Westminster 
 Abbey, the nave and choir of York Minster, 
 the naves of Winchester, Exeter, and Can- 
 terbury Cathedrals, Wykeham’s two Col- 
 leges, St. Stephen’s Chapel, &c. 
 
 The third order is known, not only by the 
 flatness of the point of the arch, but also by 
 its numerous, large, and low descending 
 windows, together with the multiplicity and 
 intricacy of its tracery; by its pendents 
 from the roof ; by the minuteness and pro- 
 fusion of its ornaments, both exteriorly and 
 interiorly; by its fan-work and numerous 
 shields and devices on the ceiling. To this 
 order belong St. George’s Chapel, Windsor, 
 King Henry the Seventh’s Chapel, West- 
 minster, and King’s College Chapel, Cam- 
 bridge, of which the following is an eleva- 
 tion, showing on one side the buttresses, 
 the tower being supposed to be removed, 
 and on the other the tower ; which not 
 only supplies the place of a buttress at the 
 end, but assists also in supporting a con- 
 siderable portion of the thrust in the direc- 
 tion of the length of the Chapel. 
 
254 
 
 THE ARTISAN. 
 
 One of tlie finest features of Gothic 
 architecture, and which, in many instances, 
 still forms the most striking ornaments of 
 our cities, is the tall tapering spire, which 
 was first built of wood by the Normans, 
 and afterwards in stone early in the 13th 
 century. In the course of the 14th and 
 15 centuries, they were greatly increased 
 in number. 
 
 MEDICAL PUMP. 
 
 Having received a drawing and descrip- 
 tion of an instrument called the Medical 
 Pump, we have embraced the first oppor- 
 tunity of laying them before our readers. 
 
 “ The instrument/’ says the Inventor, 
 “ is here represented as performing some 
 of the operations in which it is used. 
 The cylinder of the pump or syringe 
 (made in brass and in silver) is about 
 seven inches in length, and one inch in 
 diameter, contracted at its apex into a small 
 opening for receiving the extremity of an 
 elastic tube, which is passed into the sto- 
 mach. Within this opening is a chamber 
 containing a spherical valve, which, by 
 rising into the upper part of the chamber 
 where a vacuum is formed by elevating the 
 piston, admits the atmosphere (or whatever 
 it may be desirable to operate upon) to 
 pass freely into the syringe, but as soon as 
 the piston is depressed, the contents of the 
 syringe presses the valve close upon the 
 aperture, and prevents its escape through 
 the opening by which it was received. 
 
 To give exit to the contents of the sy- 
 ringe, a side branch is constructed, fur- 
 nished with a valved chamber similar to 
 
 the one above described ; but so placed as 
 to act in direct opposition to it, so that 
 when the syringe has been filled from the 
 extremity, and pressure is made by de- 
 pressing the piston, the fluid closes the 
 lower valve and opens the lateral one, 
 and consequently escapes through the 
 latter aperture. To facilitate the operation 
 of the instrument, a small pipe communi- 
 cates with the upper extremity of the sy- 
 ringe, which gives free ingress and egress 
 to the atmosphere during the action of the 
 piston, a circumstance essentially neces- 
 sary in causing the instrument to work 
 easily and perfectly. Thus it is seen, that 
 the syringe is furnished with two valvular 
 apertures, through one of which the fluid 
 to be injected is pumped from the vessel 
 that contains it, and then immediately 
 forced through the other into the part des- 
 tined to receive it : this double operation is 
 effected by repeated strokes of the piston, 
 which slides so easily that an. infant may 
 use it, and any quantity of fluid may be 
 thus made to pass through the syringe. 
 
 In cases of obstruction and constipation 
 of the bowels, the injection of fluids is of 
 the utmost importance ; and as this instru- 
 ment gives to the surgeon the means of 
 throwing into the intestinal tube any quan- 
 tity he may think proper with a distending 
 power, sufficient even to overcome the tone 
 of the fibrous texture of the bowels them- 
 selves, it has been found by many experi- 
 enced practitioners eminently successful 
 in cases of this description. As a glyster 
 apparatus in simple cases, and for do- 
 mestic purposes, it possesses advantages 
 over every other instrument hitherto in- 
 vented, for it may be used by the patient 
 himself with the greatest ease, safety, and 
 convenience. 
 
 The patent syringe has been proved by 
 the experiments of Mr. Scott and Mr. 
 Jukes to be the most effective apparatus 
 for removing poisons from the stomach 
 that can be employed ; and this opinion is 
 corroborated by the testimony of Sir Astley 
 Cooper, (see Lancet, No. 8, Vol. 1.) and 
 the most eminent physicians and surgeons 
 of Paris, before whom these gentlemen 
 have lately performed the operation. 
 
 In cases of retention of urine, it fre- 
 quently happens that in consequence of hae- 
 morrhage and other causes the catheter 
 becomes so obstructed that the bladder 
 cannot be emptied : it was suggested by 
 Dr. Cloquet, a celebrated surgeon of Paris, 
 to effect this purpose by fixing a pump to 
 the catheter. The patent syringe performs 
 this operation with extreme facility, and 
 has been honoured with the entire appro- 
 bation of Dr. Cloquet. For injecting tlie 
 bladder, which is an operation every day 
 becoming mofe frequent, it is of course 
 equally eligible. 
 
THE ARTISAN. 
 
 255 
 
 As an apparatus for conveying nourishment into the stomach of persons afflicted with 
 stricture of the oesophagus, the patent syringe is found to possess obvious advantages. 
 
 This pump is also capable of being adjusted to cupping glasses, by which any 
 degree of exhaustion can be made that the operator desires ; and in the same manner 
 it may be rendered a very effectual instrument for drawing the breasts of puerperal 
 females. A small metallic canister has also been added for burning tobacco, as the 
 syringe is found to be an effectual instrument for injecting tobacco fumes in cases of 
 cholic, introsusception, hernia, &c. 
 
 The plate represents the instrument in the performance of 
 three offices : 1st, that of injecting fluid into the stomach : 
 
 2dly, of withdrawing the contents of the stomach; and 3dly, 
 of introducing tobacco fumes into the bowels. The inventor 
 and patentee of this useful instrument is a Mr. Read, No. 30, 
 
 Bridge-house Place, Newington 
 Causeway, who has the satisfac- 
 tion of knowing, that his labours 
 have been crowned with success in 
 numerous cases of diseases, which 
 had resisted all other means, and 
 of finding that many valuable lives 
 have been saved from the des- 
 tructive effects of poisons, by the 
 timely application of this product 
 of his industry and ingenuity.” 
 
228 
 
 THE ARTISAN. 
 
 SOLUTIONS OF QUESTIONS. 
 
 Quest. 34, answered by J. C. S. (the 
 proposer ). 
 
 Put A zl-8 the height of the segment, 
 F ~ the content of ditto, B ~ the height of 
 the frustrum, Cm 7*2 the base or diame- 
 ter of the water’s surface, D — diameter of 
 the ball G~ content of ditto, and Em 
 523598. 
 
 , C 3*6 2 + A 2 16-2 
 
 Here - = 3-6 and j = pg- 
 
 m 9 m D ; and D a x E m 729 x E m 
 C 2 
 
 381*7029m G ; and - m 3 6 2 x 3 =38*88 
 2 
 
 -}-(3*G) 2 m 90*72 which multiplied by 7*2 m 
 653 184, and this multiplied by *5236, 
 gives 342*0058 inches, the quantity of water 
 forced into the ball, which, subtracted 
 from G or 381*7029 —39*6971 m 39*6971 — 
 F m the air left in the ball — and G-j-Fm 
 rarer the air was, within the receiver, 
 than it is without. (See the fig. page 67.) 
 
 Mr. J. Barr also states the quantity of 
 water, forced into the ball, at 342*066 
 inches, but does not show how he found it 
 to be so ; he has also omitted to state the 
 rarity of the air in the ball. 
 
 Quest. 35, answered by Mr. J. Snart, 
 Tooley -street. 
 
 Taking the specific gravity of cast iron 
 at 7*207, sea water at 1*025, distilled 
 water at 1*000, and dry oak at -920, (that 
 being the mean of *915 and 9*25.) Then, 
 as a cubic foot of distilled water m 62*5 lbs. 
 ~ 1000 ozs. avoirdupoise, this last weight 
 X *5236 m 32*725 lbs. m the weight of a 
 solid sphere of distilled water 12 inches 
 diameter, which x 7*207= 235*849075 lbs m 
 a sphere of cast iron (if solid) of same di- 
 mensions, and a similar sphere of sea water 
 “33*543125 lbs. Consequently 235*849075 
 minus 33*543125 (quantity of water dis- 
 placed) m 202*30595 lbs. tendency to sink 
 the cone’s base in sea water. 
 
 Again, the difference between the specie 
 fic gravities of sea water (1*025) and dry 
 oak (*920) m *105 m 6*5625 m 6 lbs, 9 ozs. 
 per cubic foot. Therefore 202*30595 
 (weight of the ball) — 6*5625 m 30*8276m 
 the cubic feet of a cone of dry oak, com- 
 petent to counteract the tendency of des- 
 cent induced by the cast iron sphere. 
 
 Then as the solid content of a cone is m 
 i that of a cylinder of the same base and 
 altitude ; 30*8276 X 3 m 92*4828 m the 
 solidity of the cylinder. And 92 4828 -f- 
 *7854 m 117*7525 m the quadrangular 
 prism, which -j- 6 (the stipulated heigh t)m 
 19*625416* the square root of which is = 
 4*43 feet = 4 feet 5| inches, being the 
 diameter of the base of a solid cone of dry 
 oak 6 feet high, competent to sustain a 
 
 cast iron ball 12 inches diameter of 202 lbs. 
 5 ozs. in equilibrio with sea water. 
 
 N.B. As specific gravities are liable to 
 varieties, so shades of difference sometimes 
 may exist in solutions of this kind of prob- 
 lems without error. The iron ball, as well 
 as the cone, is here supposed to be solid , 
 and without hoops, &c. : therefore Mr. G. 
 from his local knowledge, will be able to 
 appreciate the performance. 
 
 The observation contained in the above 
 note of our intelligent correspondent, res^ 
 pecting specific gravities, is perfectly just ; 
 for we have received two other solutions 
 to the above question, and in each, the spe- 
 cific gravity of dry oak is taken at 800, 
 which we believe is nearer the truth than 
 920, at which it is taken in the above 
 solution. 
 
 This difference has occasioned a material 
 difference between the above answer and 
 those sent us by the other two gentlemen 
 who solved the question. The proposer 
 (Mr. Graham), makes it 3*044 inches ; and 
 Mr. John Barr makes it 3*334 inches. 
 
 We have to remark respecting Mr. Barr’s 
 solution, that it is too algebraic. In ques- 
 tions where there are so many known 
 quantities, and so few unknown ones, there 
 can be no use for treating them in the form 
 of equations. 
 
 We have also to remark that we wish 
 Correspondents who have occasion to quote 
 numbers, contained in tables, to refer to, 
 the “ Artisan,” when the tables are to be 
 found in that work. 
 
 There is a very accurate table of specific 
 gravities inserted at page 25. Edit. 
 
 QUESTIONS FOR SOLUTION. 
 
 Quest. 40, proposed by G. G. C, 
 
 If a particle of a fluid, at any depth, 
 press with a force equal to that which it 
 would acquire in falling down a perpendi- 
 cular space, equal to its depth below the 
 surface ; and if a ship has been bored by 
 a 32 pounder, 8 feet below the surface of 
 the water, what weight of water will rush 
 in to the vessel, at the bore, in 10 minutes. 
 
 Quest. 41? proposed by Mr. Whitcombe, 
 Cornhill. 
 
 Mr. Graham, in his late ascent with his 
 balloon, says, “ he was elevated 2f miles 
 above the earth quaere the quantity of 
 square miles of the earth’s surface he 
 could have seen with an excellent telescope 
 at that elevation, admitting the air favor- 
 able for such observation ? 
 
 In page 237— ^ne 23— col. 2, for Declaration read 
 Declination. 
 
— -1824 
 
THE ARTISAN. 
 
 257 
 
 MEMOIR OF THE LIFE OF THE LATE DR. HUTTON. 
 
 Charles Hutton, LL.D and F.R.S. 
 of London and Edinburgh, also an hono- 
 rary member of several other learned 
 societies, both in Europe and America, 
 was born at Newcastle-upon-Tyne, on the 
 14th of August, 1737. He was descended 
 from a family in Westmoreland, who had 
 the honour of becoming connected, by mar- 
 riage, with that of Sir Isaac Newton. His 
 father, who was a viewer or superin- 
 tendant of mines, gave his children such 
 education as his circumstances would per- 
 mit, which was confined to the ordinary 
 branches ; but Charles, the youngest of 
 his sons, (the subject of this memoir) 
 early manifested an extraordinary predi- 
 lection for mathematical studies, in which 
 he made considerable progress, while yet 
 at school, with very little aid from his mas- 
 ter; for, like most other eminent mathema- 
 ticians, he was in a great measure self- 
 taught. After the death of his parents, 
 which took place at an early period of his 
 he determined on undertaking the pro- 
 fession of a teacher, and commenced his la- 
 bours at u e neighbouring village of Jes - 
 mond, before he was twenty years of age; 
 his master, who was a clergyman, having, 
 upon being presented to a living, resigned 
 the school in his favour. 
 
 In the year 1760, Dr. Hutton removed 
 to Newcastle, where he soon experienced 
 great encouragement; and, among his 
 earliest pupils, was the present Lord 
 Chancellor. We here call him Doctor 
 prematurely, he not having received the 
 diploma of LL.D. until the year 1779, 
 when that honour was conferred upon him 
 by the University of Edinburgh; but, as it 
 is the title by which he is best known in 
 the scientific world, we thus early adopt it. 
 
 It appears, that neither the duties of his 
 profession, nor the cares of an increasing 
 family, interrupted his favourite studies, 
 as he devoted all his leisure hours to ma- 
 thematical pursuits. In 1764 he published 
 u A Treatise on Arithmetic and Book-keep- 
 ing, ” which soon passed through numerous 
 editions, and is still held in high estima- 
 tion. His next publication was “ A Trea- 
 tise on Mensuration, both in theory and 
 practice,” and is considered the most com- 
 plete work on the subject ever published. 
 It established his reputation as a mathe- 
 matician, although numerous proofs of his 
 superior talents and acquirements had 
 been already manifested, by his able solu- 
 tions of mathematical questions in various 
 scientific journals. Among these reposi- 
 tories, the celebrated Almanac, under the 
 title of the Ladies’ Diary, particularly 
 
 Vol. [. — No. 17. 
 
 attracted his attention. This work had 
 been conducted with great ability, from 
 its commencement in 1704 ; numerous 
 learned correspondents contributing, an- 
 nually, curious mathematical questions, 
 and answers, with enigmas, &c. Dr. Hut- 
 ton collected the Diaries of fifty years, and 
 republished their Questions and Solutions, 
 in five volumes, with notes and illustra- 
 tions, which form a very useful and in- 
 teresting miscellany. He some time after- 
 wards became the editor of the Diary, and 
 conducted it for nearly half a century, 
 with such ability and judgment, as greatly 
 to increase the number of eminent mathe- 
 maticians, and to enlarge the boundaries 
 of useful science. Dr. Hutton’s office of 
 editor of this work, also afforded him an 
 opportunity of procuring biographical 
 notices of the most eminent of his corres- 
 pondents : with which he afterwards en- 
 riched his Mathematical Dictionary, and 
 his Abridgement of the Philosophical 
 Transactions. 
 
 We should not neglect to notice here, 
 that Dr. Hutton, about the year 1770, was 
 employed by the magistrates of Newcastle, 
 to make a survey of the town and the 
 adjoining country, in order that a correct 
 plan of it might be engraved and published. 
 In this laborious undertaking, the Doctor 
 gave great satisfaction, the plan having 
 been executed with much beauty and ac- 
 curacy. 
 
 On the 17th of November, 1771, the 
 bridge of Newcastle was almost entirely 
 destroyed, by a very great flood, which 
 swelled the waters in the river about nine 
 feet higher than the usual spring-tides. 
 This event was the means of considerably 
 increasing Dr. Hutton’s mathematical re- 
 putation. Previous to commencing the 
 repairs of the extensive damage which the 
 bridge had sustained, it was desirable to 
 endeavour to prevent, as far as possible, 
 the recurrence of similar accidents; and 
 the principal architects and civil engineers 
 of the country were invited to furnish 
 plans for the purpose. Dr. Hutton now, 
 for the first time, directed his attention to 
 the subject; and his suggestions were 
 adopted, in preference to numerous others, 
 which had been presented from various 
 quarters. On the spur of the occasion, 
 the Doctor drew up a Treatise on the 
 Principles of Bridges, demonstrating the 
 best mathematical curves for the arches, 
 with the due proportion of the piers, 
 &c. 
 
 It may here be remarked, that Dr. Hut- 
 ton’s early publications, particularly his 
 S 
 
25 B 
 
 THE ARTISAN. 
 
 Mensuration, the Diarian Miscellany, and 
 his Work on Bridges, were the means of 
 rearing and bringing into notice the inge- 
 nious Mr. Bewicke of Newcastle, the 
 most celebrated wood-engraver that the 
 world has, perhaps, ever produced. Nor 
 should it be forgotten, that, by Dr. Hut- 
 ton’s suggestions and observations, the 
 art of printing has been very considerably 
 improved. 
 
 In 1773, the situation of Mathematical 
 Professor to the Royal Military Academy 
 at Woolwich having become vacant, nu- 
 merous gentlemen of the first eminence in 
 science applied for the appointment ; and, 
 among the number, Dr. Hutton presented 
 himself as a candidate. The office was in 
 the gift of the Master- General of the Ord- 
 nance, and the strongest interest was made 
 by various noblemen and gentlemen for 
 their respective friends ; but, to the honour 
 of the then Master-General, Lord Viscount 
 Townshend, nothing but superior qualifica- 
 tions were allowed to avail. His Lordship 
 gave public notice, that merit alone should 
 decide the preference, which must be de- 
 termined by a strict and impartial exami- 
 nation. With this view, four eminent 
 mathematicians were selected as examiners 
 on the occasion; viz. Dr. Horsley, after- 
 wards Bishop of Rochester, Dr. Maske- 
 lyne, the Astronomer Royal, Colonel 
 Watson, the Chief Engineer to the East 
 India Company, and the celebrated Mr. 
 Landen. 
 
 Nothing could be more strictly impartial 
 than the examination. The candidates 
 were eight in number, and each was sepa- 
 rately examined, not only in the principles, 
 but in the history of mathematics. Several 
 abstruse problems were afterwards given 
 for solution ; and, when the answers were 
 received, the report of the examiners ex- 
 pressed high approbation of all the can- 
 didates, but gave a decided preference in 
 favour of Dr. Hutton. This was, indeed, 
 an unequivocal test of superior merit. 
 The judicious determination of the Master- 
 General, by conferring the appointment on 
 Dr. H. was in a short time found to be 
 most advantageous to the Institution. It 
 is, indeed, well known, that Dr. Hutton 
 raised the Royal Military Academy, from 
 a state of comparative inferiority, to the 
 highest degree of celebrity and national 
 importance. To his steady and persever- 
 ing conduct for thirty -five years, and his 
 improvements in military science, his 
 country is essentially indebted for the 
 success of the British artillery and engi- 
 neers in all parts of the world, during the 
 last half century. 
 
 His removal from Newcastle to so dis- 
 tinguished a situation near the metropolis, 
 and his election, soon after, as a fellow of 
 the Royal Society, gave him new opportu- 
 
 nities for the advancement and diffusion of 
 the most useful knowledge-; for, it should 
 be observed, that, at all times, his atten- 
 tion was particularly directed to those 
 branches of the mathematics which are 
 most conducive to the practical purposes 
 of life. In a short time, he became an 'im- 
 portant contributor to the Philosophical 
 Transactions, which, from the specimens 
 he gave, it is probable he would have en- 
 riched more than any other member either 
 ancient or modern, had not a stop been 
 put to his valuable labours by unfortunate 
 dissentions in the Royal Society, which 
 nearly gave a death-blow to that excellent 
 institution. 
 
 It were tedious here to detail the sub- 
 jects of the several papers which Dr. Hut- 
 ton, in a few years, submitted to the Royal 
 Society, especially as they may be seen in 
 the Philosophical Transactions of that 
 period : but two papers deserve particular 
 notice, as the most useful and important 
 that, perhaps had been communicated 
 since the chair of that learned institution 
 was filled by Sir Isaac Newton. 
 
 The first of these communications was 
 on the u Force of fired, Gunpowder , and 
 the initialVelocities of Cannon-balls ” Th^ ^ 
 results had been determined by a cries of 
 experiments, made with a new .nstrument 
 of the Doctor’s own invention , and, so sen- 
 sible was the Royal Society of the value 
 of the communication, that the annual gold 
 prize-medal was immediately voted as due 
 to Dr. H. and it was accordingly presented 
 to him by the President, Sir John Pringle, 
 with an address expressed in the most flat- 
 tering terms. 
 
 The other paper just alluded to, among 
 Dr. Hutton’s communications, was on the 
 subiect of the u Mean Density of the 
 Earth ,” a laborious work, deduced from 
 experiments and surveys of the mountain 
 of Schehallien, in Perthshire. This opera- 
 tion, which had always been considered a 
 desideratum, in the scientific world, was 
 commenced in 1775, by order of the Royal 
 Society, and chiefly under the direction of 
 Dr. Maskelyne, the Astronomer Royal. 
 After the dimensions of the mountain had 
 been taken, and the deflections of the 
 plumb-line ascertained with great accu- 
 racy, and verified by repeated experiments, 
 the most difficult and important part of the 
 undertaking yet remained to be executed]; 
 namely, the calculations and the deductions, 
 which required profound science, as well 
 as immense labour. The attention of the 
 Royal Society was at once directed to Dr. 
 H. as the person "most competent to this 
 arduous undertaking. He undertook the 
 task ; and, in the course of a year, presented 
 his report, which will be found in the 
 “ Phil Trans.” of 1778, and 1821. 
 
 [To be continued.'] 
 
THE ARTISAN. 
 
 259 
 
 PNEUMATICS. 
 
 STEAM ENGINE. 
 
 As we have given a drawing and des- 
 cription of Mr. Watt’s most improved 
 Engine in a working state, and, likewise 
 of some of its principal parts when sepa- 
 rated from the others, we shall here resume 
 this part of the subject by describing the 
 contrivance which Mr. Watt fell upon for 
 keeping the piston rods in a perpendicular 
 or vertical position, both when ascending 
 and descending. 
 
 This contrivance depends upon a geome- 
 trical theorem, and Mr. Watt’s successful 
 application of it to the practical purpose to 
 which he has applied it, proves that he 
 was not only a practical mechanic, but a 
 theoretical mathematician. 
 
 The manner of producing the 'parallel 
 motion, as this contrivance is termed, is by 
 means of the frame Q : see fig. page 197, 
 which is constructed thus. 
 
 Let C in the following figure represent 
 the centre of the working beam, 
 
 A 
 
 n . a 
 
 and let an arm B E turn about the firm 
 joint B and guide the end E of the frame or 
 parallelogram ADEF, then if CD be 
 taken a mean proportional to A D and B E, 
 the other end F, carrying the rod of a 
 piston, will ‘describe a vertical and rectili- 
 neal line, as represented by the dotted line 
 A. 
 
 This beautiful contrivance was first em- 
 ployed in the engines erected at the Albion 
 Mills, London. 
 
 We have now described the principal or 
 most important parts of Mr. Watt’s engine, 
 represented at page 167, and though there 
 are several other parts of that machine 
 which we intend to notice, yet we must 
 defer this till we enter upon the description 
 of one of the high pressure engines, which 
 have been erected still more recently ; this, 
 we shall do in another part of our work, 
 and at present introduce to the notice of 
 our readers an invention, which has just 
 been completed by an ingenious engineer 
 in London, which has every probability 
 in its favour of effecting a complete revo- 
 lution in the application of elastic fluids to 
 the motion <ff machinery. 
 
 NEW GAS VACUUM ENGINE. 
 
 This is an engine similar in its effects 
 to the steam engine ; but differing from 
 it so far as not to require the aid of 
 steam at all. The immediate nause of 
 motion in this engipe is Hydrogen gas; 
 which, as the Inventor and Patentee Mr. 
 Brown says, in his description of it, “is in- 
 troduced along a pipe into an open cylinder 
 or vessel, whilst a flame, placed on the 
 outside of and near a cylinder, is con- 
 stantly kept burning, and at proper times 
 comes in contact with, and ignites the gas 
 therein; the cylinder is then closed air- 
 tight, and the flame prevented from enter- 
 ing it. The gas continues to flow into the 
 cylinder for a short period of time, 
 and then is stopped off ; during that time 
 it acts, by its combustion, upon the air 
 within the cylinder, and at the same time a 
 part of the rarefied air escapes through one 
 or more valves, and thus a vacuum is ef- 
 fected; the vessel or cylinder being kept 
 cool by water. On the same principle, the 
 vacuum may be effected in one, two, or 
 more cylinders or vessels.” 
 
 A vacuum having been thus produced, 
 the motion of any form of machinery fol- 
 lows as a matter of course, and need 
 scarcely be described ; but we may be al- 
 lowed to point out an instance or two in 
 which it appears, that the pneumatic will 
 be far more advantageous than the steam 
 engine; while, with respect to power, 
 the only assignable difference between 
 them, will arise from the saving^of friction 
 in this, because the power of each is de • 
 rived from the production of a vacuum 
 — in one by means of the condensation 
 of steam, in the other by means of the 
 combustion of gas. The respective powers 
 being thus easily compared, it only remains 
 to calculate the advantages of the new en- 
 gine, leaving our readers to decide between 
 the two. The pneumatic engine is light and 
 portable; averaging less than one-fifth the 
 weight of a steam engine of the same power. 
 Hence it is peculiarly advantageous for 
 ships, as it saves tonnage both in its own 
 weight and in the reduced quantity of fuel. 
 The danger arising from the possibility of 
 bursting a boiler in the steam engine (too 
 many unfortunate instances of which are on 
 record) is entirely obviated in the pneumatic 
 engine ; and the very small quantity of gas 
 requisite shews, that no fears are to be en- 
 tertained from any irregular ignition. The 
 necessary fuel being reduced to a very 
 small quantity, owing to there not being 
 any boilers , the expense of working one of 
 these engines (exclusive of the abatement 
 of tonnage) will be very considerably less 
 than that requisite for a steam engine, even 
 of much less power. 
 
 S2 ' 
 
260 
 
 THE ARTISAN. 
 
 The atmospheric pressure may be in- square inch, after deducting friction, is the 
 creased with perfect safety, by the extended limit of available power ; in the pneumatic 
 dimensions of the cylinder. In the steam engines, we may estimate it at from 9 to 12. 
 engines, from seven to eight pounds on the The mechanical means by which this inven- 
 
THE ARTISAN. 
 
 261 
 
 tion can be applied to produce motion, may 
 be very much varied;' and any rapidity of 
 motion that may be required, may be 
 obtained. The combustion of gas is a more 
 speedy operation than the condensation 
 of vapour; and this fact alone would 
 be sufficient to demonstrate the possibility 
 of obtaining a more rapid motion than 
 steam can afford. In the progress of 
 chemical discovery, if (as is not at all 
 improbable) a cheap mode of extracting 
 hydrogen gas from water should be dis- 
 covered, the pneumatic engines on board a 
 ship or other vessel, would be every where 
 supplied without the loss of an ounce of 
 tonnage, at it is at present, they may ex- 
 tract the gas from oil, tar, &c. mater ials 
 which occupy a very small space in pro- 
 portion to the quantity of gas which they 
 evolve. 
 
 But in order to give as accurate an idea 
 as possible of this beautiful and truly 
 original engine, we here present a very 
 correct representation of it, which, along 
 with the subjoined description of its seve- 
 ral parts, will, we trust, render its con- 
 struction and operation tolerably well un- 
 derstood, by all who take any interest in 
 the improvement of the mechanical arts. * 
 
 The figure represents a front view of the 
 engine as used for raising water and turn- 
 ing an overshot-wheel — the front part of 
 the frame work being removed to give a 
 clearer view of it. 
 
 A and B are the two cylinders in which 
 the vacuum is affected alternately. A is 
 represented shut and B open, the latter in 
 section. These vessels are placed within 
 two other cylinders, leaving a free passage 
 between the inner and the outer cylinders, 
 along which, when the vacuum is effected, 
 the water rises, keeping both cool, and 
 flows into the inner cylinder. 
 
 C and C are the entrances from the 
 inner cylinders leading to the discharging 
 valves, which are opened by the force of 
 the water when it leaves the vessel, but 
 which, being behind, are not shown in the 
 drawing. 
 
 c and d are two caps or covers forming 
 valves, and fitting close to the outer 
 cylinders when shut, but leaving a pas- 
 sage under them for the water to flow 
 through into A and B. In these caps are 
 small valves, through which a part of the 
 rarefied air escapes. 
 
 a & is the jbeam to which the covers are 
 suspended by chains and rods. 
 
 I) and E are two cylindrical water ves- 
 sels open at their tops. 
 
 K and L are two cylindrical boxes or 
 
 * This drawing, as well as the description, has 
 been seen and minutely examined by the Patentee. 
 
 floats, air-tight, suspended in the last men- 
 tioned vessels, and are raised or depressed 
 as the water in the vessels ascends or re- 
 cedes. 
 
 F * F is a pipe leading from the cylinder 
 A to the vessel E, and G j G is another 
 pipe leading from the cylinder B to the 
 vessel D. Through these two pipes the 
 water is raised, and in them are clacks at 
 i and j, to prevent the return of the water 
 when the air is admitted into the cy- 
 linder. 
 
 / is a reservoir into which the water is 
 received from the wheel along a case or 
 trough e e , which surrounds the lower part 
 of the wheel. From this reservoir the 
 water flows alternately into the vessels D 
 and E along the pipes gg , which are 
 opened and closed by the movement of a 
 slide y attached to two cranks. 
 
 k k k is the gas pipe leading from the 
 gasometer, and terminating in gas burners 
 in the inside of the cylinders. In this pipe 
 are cocks to regulate the supply of 
 gas. 
 
 ttt is a smaller gas pipe (leading alsu 
 from the gasometer), and terminating at 
 each end near to orifices in the cylinders. 
 The gas being lighted at both ends of this 
 pipe, will burn while the engine works. 
 
 u and u, are pipes along which the air 
 is admitted into the cylinders alternately, 
 by the movement of a slide-valve o over 
 the entrances to the pipes. 
 
 m m and n n are rods attached to the 
 beam, and leading into the vessels D and 
 E. These rods are pushed up by the floats 
 K and L as they rise, and thus the ends a 
 and b of the beam are alternately raised. 
 
 v and v are arms (projecting from the 
 rods m and n) to which are attached small 
 rods, which move up and down two slide 
 valves s and s. These slide valves close 
 and open the orifices in the cylinders, to- 
 wards which jets proceed from the gas 
 burners. 
 
 h is an iron or glass tube half filled with 
 mercury, fixed on a metal plate, from the 
 ends of which proceed chains with weights 
 at their ends, to open and shut the gas cocks 
 alternately. The metal plate is raised and 
 depressed by the projecting arms r, and to 
 h are attached two long rods, which, 
 when drawn up, operate on the cranks in 
 the reservoir/, and move the slide y back- 
 wards and forwards. 
 
 X 24, is the mercurial gauge for ascer- 
 taining the power of the engine. 
 
 I and l are two chains attached to the 
 floats K and L, and to the cranks connected 
 with the slide o, which is therefore moved 
 right and left by the alternate fall of the 
 floats. 
 
 H is the trough or reservoir, into which 
 the water flows from the discharging valves. 
 
262 
 
 THE ARTISAN. 
 
 and from whence it passes on the overshot 
 wheel. 
 
 To effect the vacuum, the requisite quan- 
 tity of gas is admitted along the pipe kk into 
 the burners, and also along the pipe £, at 
 the ends of which it must be lighted. Then 
 draw down the end a of the beam, when 
 the cover c'will fall and close the top of the 
 cylinder A ; the fall also of the rod m and 
 the arm v will likewise push down the slide 
 valve s, and close the orifice, making the 
 cylinder air-tight. The flame from the 
 pipe t, having issued through the orifice 
 while open and ignited, the gas issuing 
 from the burner and jet, a vacuum will be 
 instantaneously effected by the combustion 
 of the gas, and the water as rapidly raised 
 from the vessel E by the pressure of the 
 atmosphere on its surface, lifting the clack 
 i by its force upwards, and rushing along 
 the pipe F, and the passage way into the 
 inner cylinder over its top. The fall of the 
 float L, will now by the chain l , pull the 
 crank and draw along the slide o, and thus 
 admit the air into the cylinder. The water 
 (closing by its gravity the clack at i) will 
 then be discharged through the pipe C and 
 its valve into the trough H, from whence it 
 flows on the overshot wheel, and from 
 thence along the case e into the receiver /. 
 The cylinder D being full of water, the 
 float K pushing up the rod m, now lifts the 
 end a of the beam— the end b and the cover 
 d consequently fall — the gas has been ad- 
 mitted into the cylinder B and ignited — 
 the orifice is closed, and a vacuum is ef- 
 fected in that cylinder in the same manner 
 as it was in the other. The water will now 
 be discharged as before, and the rotatory 
 motion of the water-wheel be continued. 
 The rise and fall of the rod n carrying up 
 and down the arms r, which strike against 
 a pin in the tube, raise and lower that end 
 of the tube h, and allow the mercury to run 
 alternately from one end to the other, by 
 the action of which the gas cocks are 
 opened and shut, and the slide y moved 
 backwards and forwards over the en- 
 trances to the pipes g and g*, to allow the 
 water to flow alternately into the vessels 
 D and E, and thus the engine continues to 
 work — the action being on both sides ex- 
 actly the same. 
 
 When water is intended to be raised 
 from any place and discharged, the wheel 
 is taken away, and a pipe or passage way 
 is brought into communication between the 
 place and the reservoir /, which is placed 
 just above the level of the water to be 
 raised. 
 
 When pistons are worked, the vacuum is 
 produced in the same manner, under the 
 piston which is forced down by the pres- 
 sure of the atmosphere, when the operation 
 is repeated in another cylinder, so that 
 
 one or other of the pistons is constantly in 
 motion, and the fly-wheel thereby impelled. 
 In this case the air is admitted through 
 large valves placed in the pistons— or the 
 vacuum may be effected in two cylinders, 
 as it is done in the engine above described, 
 and the piston worked in a separate cylin- 
 der, the air being admitted alternately un- 
 der and over the piston, while the vacuum, 
 being extended by means of a pipe from 
 the other cylinders, acts during the same 
 periods on the opposite side of the piston, 
 by which contrivance any number of strokes 
 per minute may be given as required. 
 
 A spectator who views this interesting 
 piece of mechanism is surprised to see its 
 effects, as they are produced without the 
 least noise and in the smoothest manner 
 possible. And it is only by inspecting the 
 mercurial gauge attached to the engine, 
 that one can discover that a vacuum is 
 actually produced. But upon carefully 
 observing the mercury it will be perceived, 
 that it rises to 24 inches, which is equal to 
 a pressure of about 13 lbs. upon every 
 square inch, even in the working model 
 which we have just described, the writer 
 of the present article having seen it rise to 
 this height. 
 
 If this is the ease at present in the first 
 engine of the kind which has ever been 
 constructed, it is only reasonable to expect 
 that, by experience in their effects and 
 construction, which time and observation 
 can only supply, that the power of the 
 engine may be increased even beyond this 
 extent, which already so far exceeds that 
 of the best condensing steam engines of the 
 present day. 
 
 The present model is estimated by the 
 inventor as equal to about a one and a half 
 horse power steam engine. The working- 
 cylinders are about eight inches diameter, 
 and the length of the beam about four feet. 
 The whole engine not occupying an area 
 of more than about four feet six inches by 
 two feet. But the frame-work of this 
 engine would be sufficiently strong for an 
 engine of ten times the power; there being 
 neither any lateral pressure, nor strain on 
 the materials ; nor vibratory motion from 
 the working of the engine. 
 
 To those who consider the wonderful ef- 
 fects of the steam engine, and the revolu- 
 tion it has effected in all the great opera- 
 tions where force i 3 required, the Pneu- 
 matic Engine must prove a most interesting 
 object; and should the principle upon 
 which it acts be found to be free from all 
 physical objection, when the engines are 
 constructed upon a larger scale and ap- 
 plied to the purposes to which the steam 
 engine is at present, it is highly probable 
 that gas engines will, in many cases, be 
 preferred to steam engines. 
 
THE ARTISAN. 
 
 26S 
 
 As hydrogen gas forms a constituent 
 part of water, from which it may be ob- 
 tained very easily, the means of pro- 
 ducing power, in machines upon this 
 principle, can never be wanting if a 
 cheap and convenient apparatus can be 
 obtained for decomposing water, which 
 we doubt not w ill soon be supplied, as we 
 consider no great effort of genius necessary 
 for effecting this. 
 
 The power of the pneumatic engine, as 
 we have already remarked, may be in- 
 creased to any extent by enlarging the di- 
 mensions of the cylinder ; and may always 
 be ascertained by the mercurial gage at- 
 
 tached to the engine, as already noticed. 
 — The mechanical parts of such engines 
 will doubtless be continually varied, and 
 this is amply provided for in the specifica- 
 tion, but the combination by which the va- 
 cuum is effected and for which the patent 
 is obtained, must always form the moving 
 poiver, and can only be varied in the form 
 of its construction or arrangement. 
 
 After the description which we have 
 here given of this singular engine, we shall 
 only add, that we are glad to find that the 
 Patentee has secured a patent both in 
 America and in France, as well as in this 
 country. 
 
 OPTICS. 
 
 ON THE PHANTASMAGORIA* 
 
 The term phantasmagoria, signifies the 
 raising of spectres, and has been given to 
 an optical apparatus similar to the magic 
 lantern. 
 
 The following figure represents an ar- 
 rangement, which has been proposed by 
 Dr. Young for exhibiting objects according 
 to the plan of phantasmagoria. 
 
 The light of the lamp A is thrown by 
 the mirror B, and the lenses C and D, on 
 the painted slider at E, and the magnifier 
 F forms the image on the screen at G. This 
 lens is fixed to a slider, which may be 
 drawn out of the general support or box H, 
 and when the box is drawn back on its 
 wheels, the rod I K lowers the point K, 
 and by means of the rod K L adjusts the 
 slider in such a manner, that the image is 
 always distinctly painted on the screen G. 
 When the box advances towards the screen, 
 in order that the images may be diminished 
 and appear to vanish, the support of the 
 lens F suffers the screen M to fall, and in- 
 tercept a part of the light. The rod K N 
 
 must be equal to I K, and the point I must 
 be twice the focal length of the lens F 
 before the object, L being immediately 
 under the focus of the lens : the screen M 
 may have a triangular opening, so as to 
 uncover the middle of the lens only, or the 
 light may be intercepted in any other 
 manner. 
 
 In order to favour the deception, the 
 sliders are made perfectly opaque, except 
 where the figures are introduced, the glass 
 being covered in the light parts with a 
 more or less transparent tint, according to 
 the effect required. Several pieces of 
 glass may also be occasionally placed be- 
 hind each other, and may be made capable 
 
264 
 
 THE ARTISAN. 
 
 of such motions as will nearly imitate the 
 natural motions of the objects which they 
 represent. 
 
 The figures may also be drawn with 
 water colours on thin paper, and after- 
 wards varnished. By removing the lan- 
 tern to different distances, and altering at 
 the same time, more or less, the position of 
 the lens, the image may be made to in- 
 crease or diminish, and to become more or 
 less distinct at pleasure, so that, to a 
 person unaccustomed to the effects of 
 optical instruments, the figures will ap- 
 pear actually to advance and retire. In 
 reality, however, these figures become 
 much brighter as they are rendered smaller, 
 while in nature the imperfect transpa- 
 rency of the air causes them to appear 
 fainter when they are remote than when 
 they are near. This imperfection might be 
 easily remedied by the interposition of 
 some semi-opaque substance, which might 
 gradually be caused to admit more light, 
 as the figure became larger, or by uncover- 
 ing a larger or a smaller portion of the 
 lamp or of its lens. Sometimes, by throw- 
 ing a strong light upon an actual opaque 
 object, or on a living person, its image is 
 formed on the curtain, retaining its natural 
 motions ; but in this case the object must 
 be considerably distant, otherwise the ima- 
 ges of its nearer and remoter parts will 
 never be sufficiently distinct at once, the 
 refraction being either too great for the re- 
 moter, or too small for the nearer parts ; 
 
 and there must also be a second lens 
 placed at a sufficient distance from the 
 first, to allow an inverted image to be 
 formed between them, and to throw a se- 
 cond picture of this image on the screen 
 in its natural erect position, unless 'the 
 object be of such a nature, that it can be 
 inverted without inconvenience. This 
 effect was very well exhibited at Paris, by 
 Robertson; he also combined with his 
 pictures the shadows of living objects, 
 which imitate tolerably well the appear- 
 ance of such objects in a dark night, or by 
 moon-shine; and while the room was in 
 complete darkness, concealed screens were 
 probably let down in various parts of it, on 
 which some of the images were projected ; 
 for they were sometimes actually situated 
 over the heads of the audience. 
 
 CAMERA LUCIDA. 
 
 The Camera Lucida is an ingenious and 
 simple instrument lately invented by Dr. 
 Wollaston for drawing objects in perspec- 
 tive ; and for copying, reducing, or en- 
 larging other drawings. 
 
 It consists of a small prism, supported 
 on a stem, or rod of brass, which turns 
 upon a pin, and may be placed in any po- 
 sition required. The eye is then to be di- 
 rected through a hole, to the prism ; any 
 object may then be delineated which is 
 placed before it for that purpose. 
 
 This instrument is represented by the 
 following figures. 
 
THE ARTISAN. 
 
 265 
 
 The instrument being fixed by the screw 
 and clamp to the table and paper on which 
 the drawing is to be made, its stem should 
 be inclined so as to bring the prism nearly 
 over the centre of the paper, and the pin, 
 on which the prism turns, placed truly ho- 
 rizontal. 
 
 The instrument, as represented in the 
 figures, may be used either with the small 
 round glass turned up in front, figure 1, or 
 with the larger glass turned up level un- 
 derneath the instrument, figure 2. (Seen 
 from above.) But those who are short- 
 sighted can only use the former, and 
 persons that are long-sighted must use 
 the latter. 
 
 The prism is next to be turned upon its 
 pin, till the transparent rectangular face 
 be placed opposite to the objects to be de- 
 lineated, when the upper black surface of 
 the eye-piece (E, figure 2) will be on the 
 top of the instrument; and through the 
 aperture in this, the artist is to look per- 
 pendicularly downwards at his paper. 
 
 The black eye-piece E, is moveable, and 
 in ordinary circumstances is to be in such 
 a position, that the edge of the small 
 transparent part at the back of the prism 
 shall intercept about half the eye-hole. 
 The artist then, looking through the eye- 
 hole directly downwards at his paper, 
 should see the objects he wishes to draw, 
 apparently distributed over the paper. For, 
 since his eye is larger than the eye-hole, 
 he sees through both halves of the hole at 
 the same time, without moving his head. 
 He sees the paper through the nearer half, 
 and sees the objects at the same time 
 through the farther half, apparently in the 
 same direction, by means of reflection, 
 through the prism. 
 
 The position of the eye-hole, is the cir- 
 cumstance, above all others, necessary to 
 be attended to in adjusting the Camera 
 Lucida for use ; for on the due position of 
 this hole depends the possibility of seeing 
 both the pencil and the objects distinctly at 
 the same time. 
 
 If the eye-hole be moved, so that nearly 
 the whole of its aperture be over the 
 paper, and a very small portion over the 
 prism, then the pencil and paper will be 
 very distinctly seen ; but the objects to be 
 delineated, very dimly. If, on the other 
 hand, the aperture be mostly over the 
 prism, and but a small portion over the 
 paper, then the objects will be seen dis- 
 tinctly, but the pencil and paper will be 
 very faint. But there will always be an 
 intermediate position (varying according as 
 the objects or the paper happen to be most 
 illuminated) in which both will be suffici- 
 ently visible for the purpose of delineation, 
 though not quite so clear as to the naked 
 eye. This intermediate position is easily 
 found, with a little practice. 
 
 If objects can be seen distinctly on the 
 upper part of the paper, but not upon the 
 lower, the instrument requires to be turned 
 upon its pin, so that the transparent face 
 may be inclined rather downwards, and 
 the contrary for seeing the upper part of 
 the view. 
 
 Many persons, upon first attempting to 
 use this instrument, occasionally Jose sight 
 of their object or their pencil, merely by 
 means of a little motion of their head, 
 backwards and forwards, of which they are 
 not aware, in breathing ; but a very little 
 practice soon obviates this difficulty. 
 
 Those who cannot sketch comfortably, 
 without perfect distinctness of both the 
 pencil and object, must draw out the stem 
 to the mark D, for all distant objects, and 
 to the numbers 2, 3, 4, 5, &c. for objects 
 that are at the distances of only 2, 3, 4, or 
 5 feet respectively, the stem being duly in- 
 clined according to a mark placed at the 
 bottom; but after a very little practice, 
 such exactness is wholly unnecessary. 
 
 The farther the prism is removed from 
 the paper, that is, the longer the stem is 
 drawn out, the larger the objects will be 
 represented in the drawing, and, accord- 
 ingly, the less extensive the view. 
 
 In copying drawings, the copy will be 
 larger or smaller than the original, accord- 
 ing as the prism is more or less distant 
 from the paper than it is from the drawing 
 to be copied. Thus, if the drawing be two 
 feet from the prism, and the paper only 
 one foot, the copy will be half the size of 
 the original. If the drawing be at one 
 foot, and the paper three feet distant, the 
 copy will be three times as large as the 
 original ; and so for all other distances. 
 
 Some caution is requisite in placing the 
 instrument directly before the drawing to 
 be copied, otherwise it will become dis- 
 torted by a new perspective. 
 
 In copying a landscape, the eye-hole 
 should be drawn so far off the prism as to 
 leave the reflected images barely distinct, 
 for the more complete command of the 
 pencil, which is intended to be brought 
 into coincidence with the images, and to be 
 employed in rendering their outlines per- 
 manent. 
 
 OF THE TELESCOPE. 
 
 The Telescope is an instrument em- 
 ployed for viewing distant objects, and is, 
 perhaps, one of the most valuable and re- 
 markable instruments that has ever been 
 constructed for gratifying our curiosity 
 and extending our knowledge. 
 
 Telescopes may be divided into two 
 kinds, Refracting and Reflecting ; these we 
 shall describe in their order. 
 
 Refracting telescopes are of two kinds, 
 Astronomical and Terrestrial. 
 
26G 
 
 THE ARTISAN. 
 
 astronomical telescope. invented by Kepler is represented by the 
 
 The Astronomical Telescope which was following figure. 
 
 It consists of two convex glasses placed 
 in a tube ; the one next the object is called 
 the object-glass, and the one next the eye, 
 as B E, the eye-glass, which is always of a 
 much less focal length than the object-glass. 
 The focal length of the object-glass is a 
 little greater than the tube into which it 
 is screwed, and the eye-glass is fixed into 
 a small tube, which can be moved out and 
 in at tire other extremity of the longer tube. 
 When such an instrument is directed to a 
 distant object, and distinct vision obtained 
 by adjusting the tube containing the eye- 
 glass, the magnified object is formed by 
 the rays A B C and DEC, which come 
 from the extremities of the visible field 
 through the middle of the object-glass, and 
 produce an inverted image nearly in the 
 principal focus of the eye-glass, through 
 which this image is viewed as by a simple 
 microscope, and therefore still remains 
 apparently inverted. This, however, is 
 not considered a disadvantage by astrono- 
 mers, and therefore it has received the 
 name of the astronomical telescope. 
 
 In order to find the magnifying power, 
 we must divide the focal length of the 
 objeet-glass by that of the eye-glass : this 
 quotient is consequently the greater as the 
 focal length of the object-glass is greater, 
 and as that of the eye-glass is smaller; 
 but the power of the instrument cannot be 
 increased at pleasure by lessening the focal 
 length of the eye-glass, because the object- 
 glass would not furnish light enough to 
 render the view distinct, if the magnifying 
 power were too great. 
 
 GALILEAN TELESCOPE. 
 
 The Galilean Telescope received its 
 name from its having been first used by 
 Galileo, and differs in no respect from the 
 astronomical telescope, excepting in the 
 substitution of a concave eye-glass in place 
 of a convex eye-glass. This eye-glass is 
 placed between the object-glass and its 
 principal focus, and receives the converg- 
 ing rays before they form the image. 
 
 The magnifying power of this telescope 
 will be equal to the focal length of the 
 object-glass divided by that of the eye- 
 glass ; for the extreme pencils which were 
 formerly made to converge, are now made 
 to diverge. 
 
 This telescope possesses some advan- 
 tages over the astronomical telescope. 1st. 
 It has the same magnifying power under a 
 shorter length, the length of the telescope 
 being equal to the difference of the focal 
 lengths of the object-glass and the eye- 
 glass, whereas in the astronomical teles- 
 cope it is equal to their sum. 2d. It gives 
 us an erect view of the object without using 
 three eye-glasses, which must occasion a 
 great loss of light, even if the lenses are 
 ground to a perfect figure. Bd. There is 
 less absorption of light, in consequence of 
 the rays passing through a less thickness 
 of eye-glass ; and 4th. the vision is much 
 more perfect; a circumstance which no 
 doubt arises from the rays never coming 
 to a positive focus, and never crossing one 
 another in a condensed state during the 
 whole of their progress through the in- 
 strument. For it cannot be doubted that 
 the rays of light, notwithstanding their 
 extreme tenuity, interfere with one ano- 
 ther, and produce an indistinctness of 
 vision. 
 
 The disadvantages of the Galilean te- 
 lescope arise solely from its limited field 
 of view. Since the lateral pencils now 
 diverge from the axis of the lenses, the 
 field of view depends solely on the dia- 
 meter of the pupil of the eye, and as this 
 cannot be increased at pleasure, there are 
 no means of remedying this evil in the Ga- 
 lilean telescope. 
 
 The imperfections of the common refract- 
 ing telescope with a single object-glass, are 
 so great, that in order to obtain a high 
 magnifying power, it is necessary to use 
 object-glasses of a great focal length, such 
 as those of Huygens, some of which were 
 not less than 24 feet in length*. 
 
 It follows from the theory of aberration, 
 arising from the spherical figure of the 
 surface, that the apparent indistinctness 
 of a given object seen through a refract- 
 ing telescope, is directly as the area of 
 the object-glass, and inversely as the 
 square of the focal distance of the eye- 
 
 * This excellent astronomer while in England 
 presented the Roy al Society with two object-glasses, 
 one of which had a focal length of 120, and the 
 other of 123 feet. 
 
THE ARTISAN. 
 
 267 
 
 glass. In like manner, it may be shown, 
 that the apparent brightness of a given 
 object is directly as the square of the lineal 
 aperture of the object glass, and inversely 
 as the square of its magnifying power. 
 Hence, it follows, that in refracting teles- 
 copes of different lengths, a given object 
 will appear equally bright, and equally 
 distinct, when their linear apertures, and 
 the focal distances of the eye-glasses, are 
 as the square roots of the focal distances 
 of their object-glasses, and consequently 
 their magnifying powers will be as the 
 square roots of the focal distances of the 
 object-glasses. 
 
 Upon these principles, we may compute 
 the focal distance of the eye-glasses suited 
 to object-glasses of different focal lengths, 
 provided we have once ascertained by ex- 
 periment the highest magnifying power 
 that an object-glass of a given focal length 
 will bear with perfect distinctness. One 
 of Huy gen’s best telescopes, 30 feet long, 
 had an aperture of three inches, with an 
 eye-glass three inches and in focal 
 length, and from this telescope, as a stand- 
 ard, the editors of his Dioptrics computed 
 the table given in p. 21 1 of that work, and 
 reprinted by Dr. Smith in the 148th page 
 of the first volume of his Optics. It ap- 
 pears, however, from Astroscopia Compen- 
 diaria of Huygens, that he possessed a 
 telescope superior even to this, whose 
 object-glass was 34 feet in focal length, 
 and which had a magnifying power of 168 
 times, with an eye-glass of 2 ~ inches focal 
 length. 
 
 In order to render the common refracting 
 telescope as perfect as possible, without 
 making it achromatic, the spherical aber- 
 ration should be reduced by grinding the 
 exterior surface of the object-glass to a 
 radius equal to five-ninths of its focal 
 length, and the interior surface to a radius 
 equal to five times its focal length. In the 
 eye-glasses, the radius of the surface next 
 the object should be nine times its focal 
 length, and that of the surface next the 
 eye, three-fifths of the same distance. 
 
 When the object to which the telescope 
 is directed is luminous, such as the Sun, 
 and Jupiter, and Venus, when they are 
 near the earth, considerable advantage 
 may be derived from the use of red or 
 green eye-glasses, or, if the telescope is 
 large, from the interposition of plane pieces 
 of green and red glass.* 
 
 * Pieces of plane glass, when smoked in the 
 flame of a lamp, serve the same purpose. 
 
 CHEMISTRIT. 
 
 CHLORINE. 
 
 The introduction of the term Chlorine 
 marks an important era in the science of 
 chemistry. It originated with Sir H. 
 Davy, about the year 1811. At that time 
 he was engaged in making some experi- 
 ments on oxy muriatic acid gas*, which 
 after resisting the most powerful means of 
 decomposition which he could employ, he 
 declared to be an elementary body, or 
 simple substance ; and not a compound of 
 muriatic acid and oxygen as was previ- 
 ously imagined, and as its name indicated. 
 He accordingly gave it the name of Chlo- 
 rine, a term merely descriptive of its co- 
 lour, which is that of a greenish -yellow. 
 
 Without venturing to give any opinion 
 respecting the propriety of this name, or 
 the composition of the body, we may re- 
 mark, that it cannot be in conformity with 
 the rules of a strict and accurate nomen- 
 clature to call a body by a name, which 
 indicates properties it does not possess. 
 
 Chlorine, or chloric gas, may be obtained 
 as follows : 
 
 Mix three parts of common salt with one 
 of black oxide of manganise. Introduce 
 this mixture into a glass retort, and add 
 two parts of sulphuric acid. Gas will then 
 issue from the retort in considerable quan- 
 tity, which may be collected in jars over 
 water in the usual way. The production 
 of the gas will be favoured by the appli- 
 cation of a gentle heat. As part of the con- 
 sistance formed by the ingredients used in 
 this process is apt to boil over into the 
 neck of the retort, a mixture of liquid 
 muriatic acid and manganise is more con- 
 venient for producing chlorine. When 
 this process is employed, a very slight de- 
 gree of heat is sufficient to extricate the 
 gas. The red oxide of lead, or mercury, 
 may be employed instead of manganise. 
 
 This gas, as already remarked, is of a 
 greenish-yellow colour, which is quite* 
 perceptible by day-light ; but scarcely dis- 
 cernible by candle-light. 
 
 Its odour and taste are disagreeable, 
 strong, and so characteristic, that it is im- 
 possible to mistake it for any other gas. 
 
 When it is breathed, even much diluted 
 with atmospherical air, it occasions a sense 
 of strangulation, constriction of the thorax , 
 and a copious discharge from the nostrils. 
 If respired in larger quantity, it excites 
 violent coughing, with spitting of blood, 
 and would speedily occasion the death of 
 the individual in great distress. 
 
 * This gas was discovered by Schdfcle, and called 
 by him dephlogisticated muriatic acid ; but was 
 afterwards called oxymurhnic acid, by the French 
 chemists. 
 
25S 
 
 THE ARTISAN. 
 
 Its specific gravity is 2*473. This is 
 better inferred from the specific gravities 
 of hydrogen and muriatic acid gas, than 
 from its direct weight, on account of the 
 impossibility of confining it over mercury. 
 
 One volume, or measure of hydrogen, 
 added to one of chlorine, form two of the 
 acid gas. Hence, if from twice the spe- 
 cific gravity of muriatic gas,which is 2*543, 
 we subtract that of hydrogen, which is 
 0*069, the difference, or 2*474, is the spe- 
 cific gravity of chlorine. At a mean tem- 
 perature and pressure, 100 cubic inches 
 weigh 75 1 grains. 
 
 In its perfectly dry state it has no effect 
 on dry vegetable colours ; but with the aid 
 of a little moisture it bleaches or turns 
 them of a yellowish-white colour. 
 
 Scheele who discovered this gas, was also 
 the first who discovered its bleaching pro- 
 perty. Berthollet applied it to the art of 
 bleaching in France, from whom the late 
 Mr. Watt learned the process, while in 
 Paris, and introduced it into this country, 
 where it is now employed to a very great 
 extent in bleaching both linen and cotton. 
 
 If a lighted taper be immersed rapidly 
 into this gas, it consumes very fast, burn- 
 ing with a dull reddish flame, and giving 
 out much smoke. The taper will not burn 
 at the surface of the gas. Hence if it be 
 slowly introduced, it is apt to be extin- 
 guished. 
 
 Potassium, sodium, copper, tin, arsenic, 
 zinc, antimony, and several other metals, 
 take fire and burn spontaneously in this gas 
 if introduced in fine laminse, or filings. 
 
 Phosphorus also takes fire at ordinary 
 temperatures. 
 
 The result of the combustion of any sub- 
 stances in chlorine is termed a chloride, 
 as chloride of zinc, chloride of phospho- 
 rus, &c. Sulphur may be melted in chlo- 
 rine without taking fire, and in this state 
 it forms a liquid chloride, of a reddish 
 colour. When dry, it is not altered by any 
 change of temperature ; but when enclosed 
 in a phial with a little moisture, it concretes 
 into crystalline needles, at 40° of Fahren- 
 heit’s scale. 
 
 According to M. Thenard water con- 
 denses If times its bulk of chlorine, at the 
 temperature of 68° F. and 29*92 Barom., 
 and forms aqueous chlorine, or what was 
 formerly called liquid oxymuriatic acid. 
 This combination is best effected in the 
 second bottle of a Woolfe’s apparatus: see 
 the figure in page 232, the first bottle being 
 charged with a little water to intercept 
 the muriatic acid gas, while the third 
 bottle may contain a solution of potash in 
 water or milk of lime, to condense the su- 
 perfluous gas. M. Thenard says, that a 
 kilogramme, or about 2^ pounds avoirdu- 
 poise of salt, is sufficient to saturate 10 
 litres, or about 21 English pints of water. 
 
 Mr. Tennent, of Glasgow has superseded 
 the necessity of saturating water with this 
 gas for the purpose of bleaching, by sub- 
 stituting slaked lime for water. 
 
 This liquid chloride of lime congeals at 
 a temperature of 40° of Fahrenheit, and 
 affords crystallized plates of a deep yellow 
 colour, containing a less portion of water 
 than the liquid combination. Hence, when 
 chlorine is passed into water at a tempera- 
 ture under 40° the liquid finally becomes a 
 concrete mass, which a gentle heat liquifies 
 with effervescence from the escape of the 
 excess of chlorine. 
 
 It is in the liquid state that it is employed 
 in bleaching, and when used in this way it 
 is always decomposed : for the liquor after 
 it has been employed in bleaching will be 
 found to have lost its smell ; and to preci- 
 pitate nitrate of mercury, which it will not 
 do before, if it be pure. In fact, this is 
 the best test for determining whether it be 
 pure or not. It often contains a portion of 
 muriatic acid, and when this is the case, it 
 has the effect of precipitating mercury from 
 its solution in nitric acid, which it does not 
 do when perfectly free from muriatic acid. 
 
 The watery solution is also decomposed 
 when exposed to the direct rays of the sun ; 
 therefore when it is intended for bleaching, 
 it ought to be kept from the direct rays of 
 the sun. 
 
 It has already been remarked, that slaked 
 lime saturated with chlorine has been em- 
 ployed in bleaching as well as the watery 
 solution of it ; but we ought to add, that it 
 is found to answer much better for this 
 purpose than the watery solution, and is 
 less dangerous both to the goods and the 
 constitutions of those who are employed in 
 using it for this purpose. 
 
 When the gas is passed into a trough 
 containing slacked calcined lime in the 
 state of a paste, it combines with the lime 
 and converts it into a dry powder ; which 
 when mixed with water has also the power 
 of discharging colour, and is therefore now 
 much employed in the bleaching of goods. 
 Magnesia is also employed in the same 
 way in bleaching the finer kinds of muslin. 
 
 When steam and chlorine are passed to- 
 gether through a red-hot porcelain tube, 
 they are converted into muriatic acid and 
 oxygen. Aqueous chlorine attacks almost 
 all the metals at an ordinary temperature, 
 forming muriates or chlorides, and heat is 
 evolved* It has the smell, taste, and co- 
 lour of chlorine; its taste is somewhat as- 
 tringent, but not in the least degree aci- 
 dulous. 
 
 When we put in a perfectly dark place, 
 at the ordinary temperature, a mixture of 
 chlorine and hydrogen, it experiences no 
 kind of alteration, even in the space of a 
 great many days. But, if at the same low 
 temperature, we expose the mixture to the 
 
THE ARTISAN. 
 
 diffuse light of day, by degrees the two 
 gases enter into chemical combination, and 
 form muriatic acid gas. There is no change 
 in the volume of the mixture, but the change 
 of its nature may be proved, by its rapid 
 absorption by water, its not exploding 
 | by the lighted taper, and the disappearance 
 i of the chlorine hue. To produce the com- 
 plete discoloration, we must expose the 
 mixture finally for a few minutes to the 
 | sun-beam. If exposed at first to this in- 
 tensity of light, it explodes with great 
 violence, and instautly forms muriatic acid 
 gas. The same explosive combination is 
 produced by the electric spark and the 
 lighted taper. M. Thenard says, a heat of 
 892° is sufficient to cause the explosion. 
 The proper proportion is an equal volume 
 of each gas. Chlorine and nitrogen com- 
 bine into a remarkable detonating com- 
 pound, by exposing the former gas to a 
 solution of an ammoniacal salt. (See Ni- 
 j trogen.) 
 
 Chlorine is now much employed in puri- 
 ! fying places of noxious vapours, as it soon 
 neutralizes every species of noxious ef- 
 fluvia. It is also said to have the effect 
 i of recovering putrid animal matter. 
 
 If diluted muriatic acid be added to 
 ' chlorate of potash, (potash combined with 
 chlorine) another gas will be produced. 
 
 It is of a deeper yellow colour than 
 chlorine, and has also the effect of dis- 
 charging vegetable colours; but it first 
 i gives blue colours a tint of red. When a 
 vessel of this gas is exposed to a moderate 
 heat, it explodes and is decomposed into a 
 mixture of chlorine and oxygen gas. 
 
 Thus gas was discovered by Sir H. Davy 
 in 1811, and called by him Euchlorine. 
 
 It has the effect of inflaming sulphuric 
 j ether, alcohol, and oil of turpentine when 
 I poured into it. 
 
 As we have now described the chief pro- 
 perties of chlorine, and mentioned some of 
 ! the uses to which it is now successively 
 applied in the arts ; it may not be impro- 
 per to add a short account of the experi- 
 ments made upon it by Sir H. Davy ; and 
 ! the Reasoning he has employed to prove 
 i that it is a simple or elementary body. 
 
 He subjected oxymuriatic gas to the ac- 
 tion of many simple combustibles, as well 
 
 I as metals, and from the compounds formed, 
 j| endeavoured to eliminate oxygen, by the 
 most enegetic powers of affinity and voltaic 
 
 ! electricity, but without success, as the fol- 
 lowing abstract will shew : 
 
 He admitted the ammoniacal gas over 
 Mercury to a small quantity of the liquor 
 of Libavius ; it was absorbed with great 
 heat, and no gas was generated ; a solid 
 result was obtained, which was of a dull 
 white colour : some of it was heated, to 
 ascertain if it contained oxide of tin; but 
 I the whole volatilized, producing dense 
 | pungent fumes. 
 
 Another experiment of the same 
 ma.de with great care, and in whichL 
 ammonia was used in great excess, proved 
 that the liquor of Libav ius ^cannot be de- 
 compounded by ammonia; but that it forms 
 a new combination with this substance. 
 
 He made a considerable quantity of the 
 solid compound of oxymuriatic acid and 
 phosphorus by combustion, and saturated 
 it with ammonia, by heating it in a proper 
 receiver fitted with ammoniacal gas, on 
 which it acted with great energy, produc- 
 ing much heat : and they formed a white 
 opaque powder. Supposing that this sub- 
 stance was composed of the dry muriates 
 and phosphates of ammonia; as muriate 
 of ammonia is very volatile, and as ammo- 
 nia is driven off from phosphoric acid, by 
 a heat below redness, he conceived that, 
 by igniting the product obtained, he should 
 procure phosphoric acid ; he therefore in- 
 troduced some of the powder into a tube of 
 green glass, and heated it to redness, out 
 of the contact of air, by a spirit lamp ; but 
 found, *to his great surprise, that it was not 
 at all volatile nor decomposable at this 
 degree of heat, and that it gave off no gas- 
 eous matter. 
 
 The circumstance, that a substance com- 
 posed principally of oxymuriatic acid and 
 ammonia, should resist decomposition or 
 change at so high a temperature, induced 
 him to pay particular attention to the pro- 
 perties of this new body. 
 
 He mixed together sulphuretted hydro- 
 gen in a high degree of purity, and oxymu- 
 riatic acid gas, both dried in equal volumes. 
 In this instance the condensation was not ^ ; 
 sulphur, which seemed to contain a little 
 oxymuriatic acid, was formed on the sides 
 of the vessel ; no vapour was deposited ; 
 and the residual gas contained about of 
 muriatic acid gas, and the remainder was 
 inflammable. 
 
 He caused strong explosions from an 
 electrical jar to pass through oxymuriatic 
 gas, by means of points of platina, for 
 several hours in succession ; but it seemed 
 not to undergo the slightest change. 
 
 He electrized the oxymuriates of phos- 
 phorus and sulphur for some hours, by the 
 power of the voltaic apparatus of 1000 
 double plates. No gas separated, but a 
 minute quantity of hydrogen, which he 
 was inclined to attribute to the presence of 
 moisture in the apparatus employed ; for 
 he once obtained hydrogen from Libavius's 
 liquor by a similar operation. But he as- 
 certained that this was owing to the decom- 
 position of water adhering to the mercury ; 
 and in some late experiments made with 
 2000 double plates, in which the discharge 
 was from platina wires, and in which the 
 mercury used for confining the liquor was 
 carefully boiled, there was no production 
 of any permanent elastic matter. 
 
270 
 
 THE ARTISAN. 
 
 AsraoioMY 
 
 SPOTS, MOUNTAINS, &C. IN THE MOON. 
 
 Turn’d to the sun direct, her spotted disk 
 Shows mountains rise, umbrasjeous dales descend. 
 And caverns deep, as optic tube descries. 
 
 Thomson. 
 
 When the moon is viewed through a 
 good Telescope, her surface appears to be 
 diversified with hills and valleys; but this 
 is most discernable when she is observed a 
 few nights after the Change or Opposition, 
 for when she is either horned or gibbous , 
 the edge about the confines of the illumi- 
 nated part is jagged and uneven. 
 
 Many celebrated Astronomers have de- 
 lineated maps of the face of the moon ; but 
 the most celebrated are those of Hevelius, 
 Grimaldi, Riccioli, and Cassini ; in which 
 the appearance of the moon is represented 
 in its different states, from new to full, and 
 from full to new . 
 
 The plate which we have given at page 
 203, represents the face of the moon as 
 viewed by the most powerful telescopes, 
 the light or illuminated parts being ele- 
 vated tracts, some of which rise into very 
 high mountains, while the dark parts ap- 
 pear to be perfectly smooth and level. 
 This apparent smoothness in the faint 
 parts, naturally led Astronomers to con- 
 clude that they were immense collections 
 of water; and the names given to them, 
 by some celebrated Astronomers, are 
 founded on this supposition. For Hevelius 
 distinguished them by giving them the 
 names of the seas on the earth; while he 
 distinguished the bright parts by the 
 names of the countries and islands on the 
 earth. But Riccioli and Langreni dis- 
 tinguished both the dark and light spots, 
 by giving them the names of celebrated 
 Astronomers and Mathematicians, which is 
 now the general manner of distinguishing 
 them. 
 
 That the spots which are taken for 
 mountains and valleys are really such, is 
 evident from their shadows. For in all 
 situations in which the moon is seen from 
 the earth, the elevated parts are constantly 
 found to cast a triangular shadow in a 
 direction from the sun ; and on the con- 
 trary, the cavities are always dark on the 
 side next the sun, and illuminated on the 
 opposite side, which is quite conformable 
 to what we observe of hills and valleys on 
 the earth. And as the tops of these moun- 
 tains are considerably elevated, above the 
 other parts of the surface, they are often 
 illuminated when they are at a consider- 
 able distance from the line which separates 
 the enlightened from the unenlightened 
 part of the disc, and by this means afford 
 us a method of even determining their 
 height. 
 
 Previous to the time of Dr. Herchel, 
 some of the lunar mountains were con- 
 sidered to be double the height of any on 
 the earth ; but by the observations of that 
 celebrated Astronomer, their height is con- 
 siderably reduced. 
 
 For after measuring many of the most 
 conspicuous prominences, he says, “ From 
 these observations I believe it is evident, 
 that the height of the lunar mountains is, 
 in general, overrated ; and that when we 
 have excepted a few, the generality do not 
 exceed half a mile in their perpendicular 
 elevation.” 
 
 As the moon’s surface is diversified by 
 mountains and valleys as well as the 
 earth, some modern Astronomers say they 
 have discovered a still greater similarity ; 
 namely, that some of these are really vol- 
 canoes, emitting fire, as those on the earth 
 do. An appearance of this kind was dis- 
 covered by Don Ulloa in an eclipse of the 
 sun, which happened on the 24th June, 
 1778. It was a small bright spot like a 
 star near the margin of the moon, which 
 he supposed at the time to be a hole or 
 valley, which permitted the sun’s light to 
 shine through it. Succeeding observations 
 have, however, led Astronomers to believe, 
 that appearances of this kind are occa- 
 sioned by the eruption of volcanic fire. 
 Dr. Herschel, in particular, has observed 
 several eruptions of this kind, the last of 
 which he has described in the Philosophi- 
 cal Transactions for 1787, as follows: 
 “ On April the 19th, at lOh. C m. I per- 
 ceived three volcanoes in different places 
 of the dark part of the new moon. Two of 
 them are either already nearly extinct, or 
 otherwise in a state of going to break out, 
 which perhaps may be decided next luna- 
 tion. The third shows an actual eruption 
 of fire or luminous matter: its light is 
 much brighter than the nucleus of the 
 comet which M. Mechaiu discovered at 
 Paris on the 10th of this month.” The 
 following night the Doctor found it burned 
 with greater violence; and by measure- 
 ment he found that the shining or burning 
 matter must be more than three miles in 
 diameter, of an irregular round figure, and 
 very sharply defined about the edges. The 
 other two volcanoes resembled large faint 
 nebulae, which appeared to be gradually 
 brighter towards the middle, but no well 
 defined luminous spot could be discovered 
 in them. Dr. Herschel adds, “ the ap- 
 pearance of what I have called the actual 
 fire, or eruption of a volcano, exactly re- 
 sembled a small piece of burning charcoal, 
 when it is covered by a very thin coat of 
 white ashes, which frequently adhere to it 
 when it has been some time ignited ; and it 
 had a degree of brightness about as strong 
 as that with which a coal would be seen to 
 glow in fair day light.” 
 
THE ARTISAN. 
 
 271 
 
 The appearance which Dr. Herschel 
 here describes so minutely, was also 
 observed at the Royal Observatory of 
 Paris, about six days before, by Dominic 
 Nonet, like a star of the sixth magnitude, 
 the brightness of which occasionally in- 
 creased by flashes. Other Astronomers 
 also saw the same thing, for M. de Ville- 
 neuve observed it on the 22d of May, 
 1787. This volcano is situated in the 
 north-east part of the moon, about 3' from 
 her edge, towards the spot called Helicon. 
 After considering all the circumstances 
 respecting these appearances which have 
 just been mentioned, we must subscribe to 
 Dr. Herschel’s opinion, that volcanoes 
 exist in the moon as well as the earth. 
 
 It has long been a disputed point among 
 Astronomers, whether or not the moon is 
 surrounded by an atmosphere. Those who 
 deny that she is, say that the moon always 
 appears with the same brightness when our 
 atmosphere is clear ; which could not be 
 the case if she were surrounded by an 
 atmosphere like ours, so variable in den- 
 sity, and so often obscured by clouds and 
 vapours. 
 
 A second argument is, that when the 
 moon approaches a star, before she passes 
 between it and the earth, the star neither 
 alters its colour nor its situation, which 
 would be the case if the moon had an at- 
 mosphere, on account of the refraction 
 which would both alter the colour of the 
 star, and also make it appear to change 
 its place. 
 
 A third argument is, that as there are no 
 seas or lakes in the moon, there is, there- 
 fore, no atmosphere, as there is no water 
 to be raised up into vapour. But those 
 who contend that the moon is surrounded 
 by an atmosphere, deny that she always 
 appears of the same brightness, even when 
 our atmosphere appears equally clear. 
 Instances of the contrary are mentioned by 
 Hevelius and some other Astronomers, but 
 it is unnecessary to take any farther notice 
 of them here. In the case of total eclipses 
 of the moon, it is well known that she ex- 
 hibits very different appearances, which it 
 is supposed are owing to changes in the 
 state of her atmosphere. It is remarked by 
 Dr. Long, that Newton has shown that the 
 weight of any body on the moon, is but a 
 third part of the weight of what the same 
 body would be on the earth, from which 
 he concludes that the atmosphere of the 
 moon is only one third part as dense as 
 that of the earth, and therefore it is impos- 
 sible to produce any sensible refraction on 
 the light of a fixed star which may pass 
 through it. Other Astronomers assert 
 that they have observed such a refraction ; 
 and that Jupiter, Saturn, and the fixed 
 stars had their circular figures changed 
 into an elliptical one, on these occasions. 
 
 But although the moon be surrounded by 
 an atmosphere of the same nature as that 
 which surrounds the earth, and to extend 
 as far from her surface ; yet no such effect 
 as a gradual diminution of the light of a 
 fixed star could be occasioned by it, at 
 least none, that could be observed by a 
 spectator on the earth. For at the height 
 of 44 miles our atmosphere is so rare, that 
 it is incapable of refracting the rays of 
 light, now this height is only the 180th 
 part of the earth’s diameter ; but as clouds 
 are never observed higher than 4 miles, it 
 therefore follows that the obscure part of 
 our atmosphere is about the 2000th part of 
 the earth’s diameter, and if the moon’s 
 apparent diameter be divided by this num- 
 ber, it will give the angle under which 
 the obscure part of her atmosphere will be 
 seen from the earth, which is not quite 
 one second, a space passed over by the 
 moon in less than two seconds of time. 
 It can, therefore, scarcely be expected that 
 any obscuration of a star could be observed 
 in so short a time, although it do take 
 place. 
 
 As to the argument against a lunar at- 
 mosphere drawn from the conclusion, that 
 there are no seas or lakes in the moon, it 
 proves nothing, because it is not positively 
 known whether there is any water in the 
 moon or not. 
 
 The question of a lunar atmosphere 
 seems to be at last settled by the numerous 
 and accurate observations of the celebrated 
 Astronomers Shroeter and Piazzi, who 
 have proved as convincingly as the nature 
 of the subject seems to allow, that the 
 moon has really an atmosphere, though 
 much less dense than ours, and scarcely 
 exceeding in height some of the lunar 
 mountains. 
 
 It is remarked by Dr. Brewster, u The 
 mountain scenery of the moon bears a 
 stronger resemblance to the lowering sub- 
 limity and terrific ruggedness of the Alpin 
 regions, than to the tamer inequalities of 
 less elevated countries. Huge masses of 
 rock rise at once from the plains, and 
 raise their peaked summits to an immense 
 height in the air, while projecting craggs 
 spring from their rugged flanks, and 
 threatening the valleys below seem to bid 
 defiance to the laws of gravitation. Around 
 the base of these frightful eminences, are 
 strewed numerous loose and unconnected 
 fragments, which time seems to have de- 
 tached from their parent mass, and when 
 we examine the rents and ravines which 
 accompany the overhanging cliffs, we ex- 
 pect every moment that they are to be torn 
 from their base, and that the process of 
 destructive separation which we had only 
 contemplated in its effects, is about to be 
 exhibited before us in tremendous reality. 
 The mountains called the Appennines, 
 
272 
 
 THE ARTISAN. 
 
 which traverse a portion of the moon’s 
 disc from north-east to south-west, rise 
 with a precipitous and craggy front from 
 the level of the Mare Imbrum. In some 
 places their perpendicular elevation is 
 above four miles ; and though they often 
 descend to a much lower level, they pre- 
 sent an inaccessible barrier to the north- 
 east, while on the south-west they sink in 
 gentle declivity to the plains.” 
 
 The caverns which are observed on the 
 moon’s surface, are no less remarkable 
 than the rocks and mountains, some of 
 them being three or four miles deep, and 
 forty in diameter. A high angular ridge 
 of rocks marked with lofty peaks and 
 little cavities, generally encircles them, an 
 insulated mountain frequently rises in 
 their centre, and sometimes they contain 
 smaller cavities of the same nature with 
 themselves. These hollows are most nu- 
 merous in the south-west part of the moon, 
 and it is from this cause that this part of 
 the moon is more brilliant than any other 
 part of her disc. The mountainous ridges 
 which encircle the cavities, reflect the 
 greatest quantity of light; and from their 
 lying in every possible direction, they 
 appear, near the time of full moon, like a 
 number of brilliant radiations issuing from 
 the small spot called Tycho. 
 
 It is difficult to explain, with any degree 
 of probability, the formation of these im- 
 mense cavities ; it is highly probable that 
 the earth would assume the same figure, if 
 all the seas and lakes were removed ; and 
 that the lunar cavities are either intended 
 for the reception of water, or that they are 
 the beds of lakes and seas which have 
 formerly existed in the moon. 
 
 The circumstance of there being no water 
 in the moon, affords a strong proof of the 
 truth of this theory.” 
 
 SOLUTIONS OF QUESTIONS. 
 
 Quest. 36, answered by Mr. S, A. Hart, 
 Artist. 
 
 The distance between St. Paul’s and the 
 Eddy stone Light-house, on the arc of a 
 great circle, is 2° 54'. 
 
 H 
 
 Then let P denote the base of St. Paul’s 
 Pa: the height of the cross 344 feet, C de- 
 note the centre of the earth, E the Eddy- 
 stone, ETthe height, of the Eddystone 100 
 feet, PE = 2° 54, and x H the height 
 above the cross, which the observer must 
 be elevated, and let CE + ET = CT = 
 3978 miles. 
 
 Then by Trigonometry. As Cosine L C 
 = cos. 2° 54' : CT=3978 :: rad. 90°: Cl 
 = 3983'. Then Cl minus CP = PH = 
 3983 miles— 3978,875 = 4-125 miles = 4 
 miles 660 feet. Lastly, P H minus P x = 
 x I zz 4 miles 660 feet minus 344 feetzz 4 
 miles 316 feet above the cross, the ob- 
 server must be elevated to see the top of 
 the Eddystone required. 
 
 This question was also answered by 
 Mr. J. Whitcomb exactly in the same 
 manner. 
 
 The answer would have been closer 
 had CT been reduced to feet, and the 
 difference between English and Geo- 
 graphical miles attended to. — E d. 
 
 Quest. 37, answered by Mr. J. Taylor, 
 Clement’ s-lane, Lombard-street. 
 
 Add the square of half the chord of the 
 arc, to the square of the versed sine, and 
 divide the sum by the versed sine, which 
 will quote the diameter of the circle, the 
 square of which, multiplied by *7854, will 
 be the area of the circle. 
 
 This question was also correctly answered 
 by Messrs. Hugh Starke; J. Holroyd, 
 Oldham ; John Barr; and the Proposer; 
 but we prefer the above, because no 
 figure is wanted. — E d. 
 
 QUESTIONS FOR SOLUTION. 
 
 Quest. 41, proposed by J. Taylor. 
 
 I have an old clock, whose pendulum 
 vibrates as many times in a minute as it is 
 inches in length ; I demand the length of 
 the pendulum and number of vibrations in 
 an hour ? 
 
 Quest. 42, proposed by A. B. Walworth. 
 
 Suppose a tube 30 inches long, filled 
 with mercury, except 8 inches, to be in- 
 verted in a basin of mercury, at what 
 height will the mercury stand in this tube, 
 when the common barometer is at 28 
 inches ? 
 
 ERRATA. 
 
 Inpage 228— line 13— col. 1,/or 3*2 read 
 7*2. 
 
 17 dele -f- 39-6971. 
 
 24 and 25 — col. 2, for 
 
 inches read feet. 
 
THE ARTISAN. 
 
 278 
 
 MOMETEY, 
 
 BOOK II. 
 
 DEFINITIONS. 
 
 The second Book of Euclid treats wholly 
 of rectangles and squares, shewing that 
 the squares or rectangles of the parts of a 
 line, divided in a specified manner, are 
 equal to other squares or rectangles of the 
 parts of the same line, divided differently ; 
 and also that the square of any side of a 
 triangle exceeds or falls short of the sum 
 of the squares of the other two sides by a 
 constant and known rectangle, or square. 
 
 As Rectangles and Squares may be re- 
 presented by letters or numbers, as well as 
 by geometrical diagrams, some editors of 
 the Elements prefer the Algebraic mode 
 of demonstrating the propositions in the 
 second book to the Geometrical method. 
 
 This we cannot give our sanction to, 
 because it is not only deviating from the 
 mode by which the other books are de- 
 monstrated, but it possesses no advantages 
 over that method. 
 
 \V e shall, therefore, continue to employ 
 the geometrical mode of demonstrating this 
 book as well as the former ; but in order 
 to render the propositions as intelligible 
 and easily understood as possible, we shall 
 illustrate most of them by numbers.* 
 
 Every right angled parallelogram is said 
 to be contained by any two of the straight 
 lines which contain one of the right 
 angles. 
 
 In every parallelogram, any of the pa- 
 rallelograms about a diameter, together 
 with the two complements, is called a 
 Gnomon. “ Thus the parallelogram H G, 
 together with the complements A F, F C, is 
 the gnomon, which is more briefly ex- 
 pressed by the letters A G K, or E H C, 
 which are at the opposite angles of the pa- 
 rallelograms which make the gnomon.” 
 
 E 
 
 G 
 
 * This is what any person may do who can multi- 
 ply, divide and extract the square root of numbers; 
 for if the word number be inserted instead of line, 
 in the enunciation of any theorem where rectangles 
 only are concerned, the truth of the proposition 
 may be established numerically, as well as geome- 
 trically. 
 
 Vol. I.— No, 18. 
 
 Every right angled parallelogram is 
 called a rectangle .* 
 
 PROPOSITION I. 
 
 Theorem.-—//’ there be two straight lines, 
 one of which is divided into any number of 
 parts; the rectangle contained by the two 
 straight lines is equal to the rectangles 
 contained by the undivided line, and the 
 several parts of the divided line . 
 
 Let A and B C be two straight lines ; and 
 let B C be divided into any parts in the 
 points D,E; the rectangle contained by 
 the straight lines A, BC is equal to the 
 rectangle contained by A, BD, together 
 with that contained by A, D E, and that 
 contained by A, E C. 
 
 B DEC 
 
 From the point B draw B F at right an- 
 gles to BC, and make B G equal to A ; 
 and through G draw G H parallel to B C ; 
 and through D, E, C, draw D K, EL, C H, 
 parallel to B G ; then the rectangle BH is 
 equal to the rectangles B K, D L, EH; 
 and B H is contained by A, B C, for it is 
 contained by G B, B C, and G B is equal 
 to A ; and B K is contained by A, B D, for 
 it is contained by G B, B D, of which G B 
 is equal to A ; and D L is contained by A, 
 D E, because D K, that is B G, is equal to 
 A ; and in like manner the rectangle E H 
 is contained by A, E C : therefore the rec- 
 tangle contained by A, B C, is equal to the 
 several rectangles contained by A, B D, 
 and by A, DE; and also by A, EC. 
 Wherefore, if there be two straight lines, 
 &c. Q. E. D. 
 
 This proposition simply amounts to this : 
 any number, or any space included by lines, 
 is equal to the sum of all its parts, there- 
 fore it requires no illustration. 
 
 PROPOSITION II. 
 
 Theorem. — Jf a straight line be divided 
 into any two parts, the rectangles con- 
 tained by the whole and each of the parts , 
 are together equal to the square of the 
 whole line. 
 
 Let the straight line AB be divided into 
 
 * The word rectangle in Geometry, corresponds 
 to that of product in Arithmetic. 
 
 T 
 
274 
 
 THE ARTISAN. 
 
 any two parts in the point C; the rectangle 
 contained by A B, B C, together with the 
 rectangle AB, AC, shall be equal to the 
 square of A B. 
 
 A C B 
 
 D F E 
 
 Upon A B describe the square ADEB, 
 and through C draw C F, parallel to A D 
 or B E ; then A E is equal to the rectan- 
 gles A F, C E ; and A E is the square of 
 A B ; and A F is the rectangle contained 
 by AB, A C ; for it is contained by D A, 
 A C, of which A D is equal to A B ; and 
 C E is contained by A B, B C, for B E is 
 equal to A B ; therefore the rectangle con- 
 tained by A B, AC together with the rec- 
 tangle A B, B C, is equal to the square of 
 A B. If therefore a straight line, &c. 
 Q. E. D. 
 
 Let the line be represented by the num- 
 ber 8, and let it be divided into the two 
 parts 5 and 3 ; then the rectangles con- 
 tained by the whole and each of the parts 
 are, 8 multiplied by 5, or 40; and 8 mul- 
 tiplied by 3 or 24 : these together make 64, 
 which is just equal to 8 squared, or multi- 
 plied by itself. Hence, the truth of the 
 proposition is established numerically as 
 well as geometrically. 
 
 PROPOSITION III. 
 
 Theorem. — If a straight line be divided 
 into any two parts , the rectangle contained 
 by the whole and one of the parts, is equal 
 to the rectangle contained by the two 
 I parts, together with the square of the fore- 
 said parts. 
 
 Let the straight line A Bbe divided into 
 any two parts in the point C; the rectangle 
 A B, B C is equal to the rectangle A C, 
 CB, together with the square of B C. 
 
 A C B 
 
 E 
 
 Upon BC describe the square CDEB, 
 and produce E D to F, and through A 
 draw A F parallel to C D or B E ; then the 
 rectangle A E is equal to the rectangles 
 AD, CE; and AE is the rectangle con- 
 tained by A B, B C, for it is contained by 
 A B, BE, of which B E is equal to B C ; 
 and A D is contained by A C, C B, for CD 
 is equal to C B ; and D B is the square of 
 B C ; therefore the rectangle A B, B C is 
 equal to the rectangle A C, C B, together 
 with the square of B C. If therefore a 
 straight line, &c. Q. E. D. 
 
 Let the line be represented by 8, and its 
 parts by 5 and 3, as in last prop, then the 
 rectangle contained by the whole (8) and 
 one of the parts, namely 5, is 40 ; which is 
 equal to 5 multiplied by 3 or 15, added to 
 the square of 5 or 25. 
 
 What is meant here by the foresaid part 
 is, that part which is employed with the 
 whole to form the rectangle. 
 
 PROPOSITION IV. 
 
 Theorem. — If a straight line be divided 
 into any two parts, the square of the 
 ivhole line is equal to the squares of the 
 two parts, together with twice the rectan- 
 gle contained by the parts. 
 
 Let the straight line A B be divided into 
 any two parts in C ; the square of A B is 
 equal to the squares of A C, C B, and to 
 twice the rectangle contained by AC, CB. 
 
 Upon A B describe the square ADEB, 
 and join B D, and through C draw C G F 
 parallel to AD or BE, and through G 
 draw H K parallel to AB or D E : And 
 because C F is parallel to A D, and B D 
 falls upon them, the exterior angle BGC 
 is equal to the interior and opposite angle 
 A D B ; but A D B is equal to the angle 
 A B D, because B A is equal to A D, being 
 sides of a square; wherefore the angle 
 A C B 
 
 G 
 
 
 /' 
 
 
 D F E 
 
 C G B is equal to the angle G B C ; and 
 therefore the side B C is equal to the side 
 CG: ButCB is equal also to G K, and 
 C G to B K ; wherefore the figure CGRB 
 is equilateral : It is likewise rectangular ; 
 for C G is parallel to B K, and C B meets 
 them ; the angles K B C, G C B are there- 
 fore equal to two right angles ; and K B C 
 is a right angle ; wherefore GCB is a 
 right angle ; and therefore also the angles 
 
 F 
 
 D 
 
THE ARTISAN. 
 
 275 
 
 C G K, G K B opposite to these, are right 
 angles, and C G K B is rectangular : But it 
 is also equilateral, as was demonstrated ; 
 wherefore it is a square, and it is upon the 
 side C B : For the same reason H F also is 
 a square, and it is upon the side H G, 
 which is equal to A C : Therefore H F, 
 C K are the squares of A C, C B ; and be- 
 cause the complement A G is equal to the 
 complement G E, and that A G is the rect- 
 angle contained by AC, CB, for C G is 
 equal to C B ; therefore G E is also equal 
 to the rectangle AC, CB; wherefore AG, 
 GE are equal to twice the rectangle AC, 
 CB: And HF, CK are the squares of 
 AC, C B ; wherefore the four figures H F, 
 CK, A G, GE are equal to the squares of 
 AC, C B, and to twice the rectangle A C, 
 CB: But H F, C K, AG, GE make up 
 the whole figure A DEB, which is the 
 square of A B : Therefore the square of 
 A B is equal to the squares of A C, C B, 
 and twice the rectangle AC, C B. Where* 
 if a straight line, &c. Q. E. D. 
 
 Cor. From the demonstration, it is ma- 
 nifest, that the parallelograms about the 
 diameter of a square, are likewise squares. 
 
 Let the line be 8, and the two parts 5 
 and 3 as before ; then the square of (8) the 
 whole is 64; and the sum of the squares 
 of the parts (5 and 3) is 34 ; and twice 
 the product or rectangle of the parts is 
 30 ; therefore the square of these parts, or 
 34 added to twice their rectangle, or 30, 
 make 64, which Is the same as the square 
 of the whole, which was to be shown. 
 
 PROPOSITION V. 
 
 Theorem. — If a straig ht line be divided into 
 two equal parts , and also into two unequal 
 parts ; the rectangle contained by the un- 
 equal parts, together with the square of 
 the line between the points of section , are 
 equal to the square of half the line. 
 
 Let the straight line A B be divided into 
 two equal parts in the point C, and into 
 two unequal parts at the point D ; the rect- 
 angle A D, D B, together with the square 
 of CD, is equal to the square of C B. 
 
 Upon CB describe the square CEFB, 
 join B E, and through D draw D H G pa- 
 rallel to C E or B F ; and through H draw 
 KLM parallel to CBorEF; and also 
 through A draw A K parallel to CL or 
 B M : And because the complement C H is 
 equal to the complement H F, to each of 
 these add D M ; therefore the whole C M 
 A C D B 
 
 
 
 7 
 
 Oj 
 
 / 
 
 K 
 
 E G F 
 
 is equal to the whole DF; but CM is 
 
 equal to A L, because A C is equal to C B ; 
 therefore also AL is equal to DF. To 
 each of these add C H, and the whole 
 A H is equal to D F and C H : but A H is 
 the rectangle contained by A L>, D B, for 
 D H is equal to D B ; and D F together 
 with CH is the gnomon CM G; therefore 
 the gnomon CMGis equal to the rectangle 
 AD, DB: To each of these add LG, 
 which is equal to the square of CD; 
 therefore the gnomon C M G, together 
 with L G, is equal to the rectangle A D, 
 D B, together with the square of C D ; but 
 the gnomon C M G and L G make up the 
 whole figure CEFB, which is the square 
 of CB : Therefore the rectangle A D, D B, 
 together with the square of C D, is equal 
 to the square of C B. Wherefore if a 
 straight line, &c. Q. E. D. 
 
 Cor. From this proposition it is mani- 
 fest, that the difference of the squares of 
 two unequal lines AC, C D, is equal to the 
 rectangle contained by their sum and dif- 
 ference. 
 
 Let the whole line be 12, then each of 
 the two equal parts will be 6. Again, 
 let the unequal parts be 8 and 4, con- 
 sequently the line between the points of 
 section will be 2 ; then the rectangle of the 
 unequal parts, namely, 8 and 4, is 32, and 
 the square of 2, the line between the 
 points of section, is 4 ; and this added to 
 32, makes 36, which is just equal to the 
 square of 6, or half the line. 
 
 PROPOSITION VI. 
 
 Theorem. — If a straight line be bisected, 
 and produced to any point ; the rectangle 
 contained by the whole line thus pro- 
 duced, and the part of it produced , to- 
 gether with the square of half the line 
 bisected, is equal to the square of the 
 straight line, which is made of the half 
 and the part produced. 
 
 Let the straight line AB be bisected in 
 C, and produced to the point D ; the rect- 
 angle A D, D B, together with the square 
 of C B, is equal to the square of C D. 
 
 Upon C D describe the square C E F D, 
 join DE, and through B draw BHG 
 parallel to CEorDF, and through H 
 draw KLM parallel to AD or EF, and 
 also through A draw A K parallel to C L 
 
 or D M : and because AC is equal to C B, 
 the rectangle A L, is equal to C H ; but 
 T 2 
 
276 
 
 THE ARTISAN. 
 
 C H is equal to H F ; therefore also AL is 
 equal to H F : To each of these add C M ; 
 therefore the whole A M is equal to the 
 gnomon CMG: And AM is the rectangle 
 contained by AD, DB, for DM is equal 
 to DB : therefore the gnomon C M G is 
 equal to the rectangle AD, DB: Add to 
 each of these L G, which is equal to the 
 square of C B, therefore the rectangle AD, 
 DB, together with the square of CB, is 
 equal to the gnomon CMG and the figure 
 L G : But the gnomon CMG and LG make 
 up the whole figure C E F D, which is the 
 square of C D ; therefore the rectangle 
 A D, D B, together with the square of C B, 
 is equal to the square of C D. Wherefore, 
 if a straight line, &c. 
 
 Let the line be 12, when it is bisected, 
 each part will be 6; let it also be pro- 
 duced or increased to 16, then the rect- 
 angle contained by the whole or 16, and 4 
 the part produced, is 64 : to which the 
 square of 6 being added, makes 100; but 
 this is just the square of 10, or the line 
 made up of the half line and produced 
 part, which was to be shown. 
 
 MECHANICS. 
 
 ON MECHANICAL AGENTS. 
 
 The powers which are usually employed 
 on a great scale as the first movers of ma- 
 chinery, are, 1. The strength of men and 
 animals ; 2. The elastic force of steam 
 and heated air ; 3. The force of water ; and 
 4. The force of wind. 
 
 As the three last of these agents are 
 either already, or will be, treated of under 
 the heads of Pneumatics, Hydraulics, and 
 Chemistry, we shall only notice the first of 
 them in this place. 
 
 ON THE STRENGTH OF ANIMALS. 
 
 The form and construction of the human 
 body renders it peculiarly applicable as 
 the first mover of machinery, and what it 
 wants in strength is compensated in a 
 great degree, by the skill and judgment 
 with which it can be applied. When we 
 consider the great number of cases in 
 which it is preferable to employ the action 
 of men rather than that of inanimate agents, 
 and the still greater number in which it is 
 out of our power to employ any other, it 
 becomes a matter of the highest impor- 
 tance, both to workmen and to those who 
 employ them, to ascertain the way in which 
 the greatest quantity of work can be ob- 
 tained from their exertions, with the 
 least quantity of bodily fatigue, or with 
 such a quantity of fatigue as they can 
 easily bear from day to day, without in- 
 juring their corporeal functions. 
 
 Daniel Bernoulli indeed maintained, 
 that the degree of fatigue is always pro- 
 portional to the quantity of action by 
 
 which it is produced; that whether he 
 walks or carries a load, or draws, or 
 pushes, or works at a winch, or raises a 
 weight, he will always produce with the 
 same degree of fatigue the same quantity 
 of action, and therefore the same effect; and 
 that the daily labour of a man, whatever 
 be the work to which he is set, may be rec- 
 koned at 1,728,000 pounds raised through 
 the height of one foot, or 60 pounds 
 raised through the height of one foot in a 
 second, when his day’s labour amounts to 
 eight hours. These opinions were adopted 
 by almost all subsequent authors, on the 
 authority of vague and inconclusive ex- 
 periments, till the subject received a full 
 investigation from the celebrated Coulomb, 
 Amontons, and others. 
 
 According to M. Amontons, a man 
 weighing 133 French pounds, ascended 
 62 French feet by steps in a minute, but 
 was completely exhausted. 
 
 A sawyer, according to the same author, 
 made 200 strokes of 18 French inches 
 each, with a force of 25 pounds, in 145 
 seconds. 
 
 An ordinary man, according to Desagu- 
 lier§, can turn a winch with the force of 
 30 pounds for 10 hours, with a velocity of 
 2f feet per second. 
 
 Two men, according to Desaguliers, 
 working at a windlass with handles at 
 right angles to each other, can raise 70 
 pounds more easily than one man can 
 raise 30, an additional effect of five pounds 
 being produced on the work of each man, 
 in consequence of the uniform action 
 arising from the handles being at right 
 angles to each other. 
 
 A man may, according to the same 
 author, exert a force of 80 lbs. with a fly, 
 when the motion is pretty quick.. 
 
 V A man may also, with a good pump, 
 raise a hogshead of water 10 feet high in a 
 minute, and continue the work for a whole 
 day. 
 
 According to Dr. Robinson, a feeble old 
 man raised 7 cubic feet of water, “ 437f 
 lbs. avoirdupoise, Ilf feet high in a mi- 
 nute, for 8 or 10 hours a day, by walking 
 backwards and forwards on a lever. 
 
 ’ A young man, weighing 135 pounds, 
 and carrying 30 pounds, raised 9f cubic 
 feet of water, zr 578-^ avoirdupoise, Ilf 
 feet high for 10 hours a-day without being 
 fatigued. 
 
 The strength of men, and of all animals, 
 is most powerful when directed against a 
 resistance that is at rest: when the re- 
 sistance is overcome, and when the animal 
 is in motion, its force is diminished ; lastly, 
 with a certain velocity, the animal can do 
 no work, and can only keep up the motion 
 of its own body. 
 
 The effect of animal force, or the quan- 
 tity of work done in a given time by any 
 working animal, is greatest when the 
 
THE ARTISAN. 
 
 27? 
 
 ©ftiiMl moves with one-third of the speed 
 with which it is able only to move itself, 
 and is loaded with four-ninths of the 
 greatest load it is able to put in motion. 
 
 According to this estimate, a man who 
 can move 120 lbs. and walk at the rate of 
 4 miles an hour, when working to the 
 greatest advantage, should carry a load of 
 54 pounds, and walk at the rate of two 
 feet in a second, or a mile and one third 
 in an hour. 
 
 In raising a weight, a man will produce 
 the greatest effect, when his weight is to 
 that of his load as 4 to 3 nearly. 
 
 When a horse’s work is estimated by 
 the load he draws in a cart or waggon, a 
 great reduction must be made, in order to 
 compare the force he exerts with that 
 which is necessary for raising a weight, 
 by drawing it over a pulley. Though ac- 
 curate experiments on the friction of 
 wheel carriages are wanting, we proba- 
 bly shall not err much in supposing the 
 friction, on a road, and with a carriage of 
 the ordinary construction, to amount to a 
 twelfth part of the load. If then, a horse 
 draws a ton in a cart, which a strong 
 horse will continue to do for several hours 
 together, we must suppose his action the 
 same as if he raised up the twelfth part of 
 a ton (2240 lb.) or 186 lb. perpendicularly 
 against the force of gravity. To raise a 
 weight of 186 lb. therefore, at the rate of 
 two miles, or two miles and a half an hour; 
 (that is, 2*9, or 3*6 feet per second), may 
 be taken as the average work of a strong 
 draught horse in good condition. 
 
 On this subject, however, many more 
 experiments are wanting; to determine, 
 for instance, the friction of wheel car- 
 riages ; the difference of the exertion re- 
 quired to walk on a horizontal plane, and 
 on one of a given declivity ; the quantity 
 of work done in a given time by the same 
 animal, carrying different loads. The dif- 
 ference between the effective exertion of a 
 man’s strength when he moves along with 
 his load, and when he stands, as in turn- 
 ing a wheel; or sits, as in rowing a boat, &c. 
 
 MECHANICAL CONTRIVANCES USED IN THE 
 CONSTRUCTION OF MACHINES. 
 
 In all machines beyond the limits of the 
 simple mechanical powers, the power of 
 the first mover must be conveyed to the 
 place where the work is to be performed, 
 by means of mechanical contrivances, 
 which vary according to the hature of the 
 impelling power and the work to be 
 performed, the respective localities of 
 the first mover, and the working part of 
 the machine. The skill of the engineer is 
 is no way more conspicuous than in the 
 intermediate machinery by which he trans- 
 mits and modifies the action of the prime 
 mover ; and the general machine must de- 
 rive its character of utility and durability 
 from the simplicity of the intermediate 
 
 machinery, and the judgment with which 
 the individual contrivances are selected. 
 
 In order to convey some general idea of 
 the composition of machines, we shall lay 
 before our readers a description of some of 
 the leading mechanical contrivances w hich 
 are in constant use in machinery, and ex- 
 plain the methods by which the direction 
 of motion may be any way changed, and by 
 which one kind Of motion may be con- 
 verted into another. 
 
 Belts , Bands , and Ropes . — When it is 
 required to convey the force of one wheel 
 to another, the simplest of all methods is 
 to connect them by means of leather belts 
 passing over the circumference of each. 
 The great advantage of belts is, that by 
 means of them we may convey the motion 
 of one w heel to another at a very great 
 distance, which could not be done without 
 a considerable expense by wheels and 
 pinions ; but they have the disadvantage 
 of stretching so as to become loose, and 
 thus lose their pow er of turning the wheel. 
 This evil, however, may be instantly re- 
 medied by shortening them, or by increas- 
 ing the friction by means of chalk. Some- 
 times this evil is remedied by having 
 grooves of different diameters in one or 
 both of the wheels; and when the belt or 
 rope becomes slack, it is shifted to the fol- 
 lowing groove ; but this can be permitted 
 only in machines, such as turning lathes, 
 where a change of velocity is of no impor- 
 tance. When ropes are used, they always 
 move in grooves cut in the circumference 
 of the sheaves or wooden wheels round 
 which they pass. 
 
 When there is a great strain upon the 
 machinery, and when its motions are 
 required to be regular,’ belts and ropes 
 cannot safely be employed. Chains are 
 therefore substituted in their place with 
 peculiar advantage. 
 
 The Lever of Lagaroust. — This con- 
 trivance, w hich has the property of pro- 
 ducing a continued rectilineal motion 
 from an alternating circular motion, is 
 shown in the following figure. 
 
278 
 
 THE ARTISAN. 
 
 The lever A B moves round an axis C 
 attached to a fixed beam M N. A toothed 
 rack or beam F G, is capable of descend- 
 ing and ascending freely by the action of 
 the hooks or teeth at the end of the two 
 secondary levers D E, D' ¥J fixed at the 
 points D, D' of the great lever A B, When 
 the end A descends, the hook IT falls 
 down upon the teeth below it, while the 
 simultaneous ascent of the end B C causes 
 the hook E to draw upwards the beam 
 F G. By now depressing B C, the hook 
 E falls down upon the teeth below it, 
 while the ascent of A C causes the hook 
 E' to draw upwards the beam F G. The 
 very same contrivance may be employed 
 to give a circular motion to a wheel, having 
 its circumference furnished with teeth 
 like those upon F G. 
 
 Crank. — When the communicating parts 
 have a permanent connection, it is necessary 
 to employ other contrivances, besides the 
 foregoing, among which are the Crank, 
 which is one of the simplest and most dur- 
 able of any for conveying motion. It is 
 in principle the same as a wheel with the 
 power applied at or near its circumference. 
 A double crank is shown in the following 
 figure. 
 
 6 
 
 Where mw is the revolving axis, which 
 by means of the double crank, communi- 
 cates a reciprocating motion to the two 
 beams ab, c d, the one ascending when the 
 other is descending. 
 
 A triple crank is shown in the following 
 figure, 
 
 where three beams are made to ascend 
 and descend ; but the planes passing 
 through each of the three cranks, must be 
 inclined 120° to one another. A change- 
 able crank, in which the radius is variable, 
 is shown in the following figure : 
 
 where m n is the axis, and a b the beam, 
 which can be set to different distances 
 from m n, by drawing up the four parallel 
 bars, c, d, e,f, and fixing them in any posi- 
 tion by pins passing through the small 
 holes. 
 
 Hooke's universal joint. — This ingenious 
 contrivance, which is shown in the follow- 
 ing figure, 
 
 consists of two shafts, or axis, A, B, ter- 
 minating in a semicircle, and connected by 
 means of a cross CD, E F. As the 
 branches CD, E F, have a motion round 
 their pivots at C D, E, and F, it is obvious 
 that when the shaft A. is turned round, a 
 similar motion will also be communicated 
 to the shaft B. This joint may be used 
 when the inclination of the shaft does not 
 exceed 40°, or rather 140°, its sup- 
 plement. When the inclination of the 
 shafts is between 50° and 90°, a double uni- 
 versal joint is employed. In this case 
 there are two crosses, the extremities of 
 which move on their pivots in the semicir- 
 cles at the ends of the shafts. These joints 
 may also be constructed with four pins, 
 fastened at right angles upon the circum- 
 ference of a hoop, or solid ball. 
 
 The sun and planet wheel is also ''em- 
 ployed for communicating motion to ma- 
 chines ; but as we have fully explained 
 this contrivance at page 227, it is unneces- 
 sary to describe it here. 
 
 Ball and Socket. — Although the ball 
 and socket is not used in general ma- 
 
THE ARTISAN. 
 
 279 
 
 chinery, yet we may regard it as a mecha- 
 nical contrivance, by which two parts of a 
 machine are permanently connected. The 
 object of it is to give a motion in various 
 directions to one axis, while the other re- 
 mains fixed. This is generally done in 
 telescopes, by the joint effect of a horizon- 
 tal and a vertical movement; but when the 
 telescope is not heavy, a ball and socket is 
 the simplest and most commodious con- 
 trivance. It is represented in the follow- 
 ing figure, 
 
 A 
 
 where B is a ball of brass, fixed at 
 
 lower extremity of the axis A B, on which 
 a telescope or any other body is supported. 
 This ball is of the same diameter as the 
 interior diameter of the socket or cap 
 CSD, with which the lower axis S T is 
 terminated. This socket consists of two 
 parts, C E F D, E F $, the former of which 
 can be removed, slackened, or tight- 
 ened, by turning the milled circumference 
 E F. On the bottom of the socket is 
 placed a piece of cork, against which the 
 lower part of the ball E presses, so that 
 whenever the ball moves too loosely in the 
 socket, it may be pressed against the 
 elastic cork, by turning E F, which draws 
 the ball downwards, by which means its 
 motion is rendered as stiff as we choose. 
 In the upper edge of the moveable part 
 CD, a groove n is cut, to allow the axis 
 A B to come into a position at right angles 
 to ST. 
 
 A MACHINE IN WHICH ALL THE MECHANI- 
 CAL POWERS ARE UNITED. 
 
 The following figure represents a ma- 
 chine, in which all the simple mechanical 
 powers are combined. 
 
280 
 
 THE ARTISAN. 
 
 fit consists of a frame A B C D fastened 
 upon the stand O o by the nut o, and kept 
 together by the pillars V W and B q. The 
 piece E F is first fitted to the frame, having 
 vanes E F, which may be either moved by 
 the wind, or by a cord fastened at F. This 
 part represents the lever, whose fulcrum is 
 
 G. A perpendicular axis G A is joined to 
 this lever, and carries the endless screw 
 
 H, which may be considered as a wedge. 
 This endless screw works in the teeth of 
 the wheel K, which is the wheel and 
 axle ; and when K is turned round, it 
 winds upon the axle IL the cord LM, 
 
 which passing round the tackle of pulleys 
 M N, raises the weight P. In order ’to 
 include the inclined plane in this combina- 
 tion, we must add the plane R Q r q, and 
 make it rest on the ground at QR, and on 
 the pillar Bq at q r. When the weight P 
 is placed on this plane, the power will be 
 farther increased in the ratio of Q T to TS. 
 The power gained by this combination will 
 be found, by comparing the space described 
 by the point F, with the height through 
 which the weight rises in any determinate 
 number of revolutions of F. 
 
 HYDRAULICS. 
 
 ON UNDERSHOT 
 An undershot water-wheel is a wheel 
 with a number of floatboards, or plane sur- 
 faces arranged round its circumference, 
 for the purpose of receiving the impulse of 
 the water, which is conveyed to the under 
 part of the wheel from an inclined canal. 
 A wheel of this kind of the ordinary con- 
 struction, is shewn in the following figure, 
 
 WATER WHEELS. 
 
 boards, erf, a floatboard receiving the im- 
 pulse of the water, which moves with 
 great velocity in consequence of having 
 fallen from a considerable height down the 
 inclined mill-course M N. The principal 
 points to be attended to in the construction 
 of undershot wheels, are the construction 
 of the mill course, the number, form, and 
 position of the floatboards, and the velocity 
 of the wheel in relation to that of the wa- 
 ter when the effect is a maximum . The 
 following rules for the construction of mill 
 courses are given in the Appendix to Fer- 
 guson’s Lectures, vol. ii. 
 
 i( As it is of the highest importance to 
 have the height of the fall as great as 
 possible, the bottom of the canal, or dam, 
 which conducts the water from the river, 
 should have a very small declivity ; for the 
 height of the water-fall will diminish in 
 proportion as the declivity of the canal is 
 increased. On this account, it will be suf- 
 ficient to make A B slope about one inch in 
 20h yards, as in the following figure, 
 
 taking care to make the declivity about 
 half an inch for the first 48 yards, in order 
 that the water may have a velocity suf- 
 ficient to pre vent it from flowing back into 
 the river. The inclination of the fall, re- 
 presented by the angle G C R, should be 
 25 ° 50' ; or CR, the radius, should be to 
 
 G R, the tangent of this angle, as 100 to 
 48, or as 25 to 12 ;* and since the surface 
 
 * A tangent is a line touching a circle, ©r any 
 other curve; and the tangent of an angle is the side 
 of a triangle, which is perpendicular to the side of 
 it that is made radius. 
 
THE ARTISAN. 
 
 281 
 
 of the water $ b is bent from a b into a c, 
 before it is precipitated down the fall, it 
 will be necessary to incurvate the upper 
 part B C D of the course into B D, that the 
 water at the bottom may move parallel to 
 the water at the top of the stream. For 
 this purpose, take the points B, D, about 
 12 inches distant from C, and raise the 
 perpendiculars BE, D E : the point of in- 
 tersection E will be the centre, from which 
 the arch B D is to be described ; the ra- 
 dius being about 10^ inches. Now, in 
 order that the water may act more advan- 
 tageously upon the floatboards of the 
 wheel W W, it must assume a horizontal 
 direction ;H K, with the same velocity 
 which it would have acquired when it 
 came to the point G : But in falling from 
 C to G, the water will dash upon the ho- 
 rizontal part H G, and thus lose a great 
 part of its velocity; it will be proper, 
 therefore, to make it move along FH an 
 arch of a circle, to which D F and K H 
 are tangents in the points F and H. For 
 this purpose make G F and G H each 
 equal to three feet, and raise the perpendi- 
 culars H I, F I, which will intersect one 
 another in the point I, distant about 4 feet 
 9 inches and ^ths from the points F, and 
 H, and the centre of the arch F H will be 
 determined. The distance H K, through 
 which the water runs before it acts upon 
 the wheel, should not be less than two or 
 three feet, in order that the different por- 
 tions of the fluid may have obtained a ho- 
 rizontal direction ; and if H K be much 
 larger, the velocity of the stream would be 
 diminished by its friction on the bottom of 
 the course. That no water may escape 
 between the bottom of the course K H and 
 the extremities of the floatboards, K L 
 should be about three inches, and the ex- 
 tremity o of the floatboard n o should be 
 beneath the line H K X, sufficient room 
 being left between o and M for the play 
 of the wheel, or K L M may be formed into 
 the arch of a circle K M concentric with 
 the wheel. The line L M V, called by M. 
 Fabre, the course of impulsion, should be 
 prolonged, so as to support the water as 
 long as it can act Jupon the floatboards, 
 and should be about 9 inches distant from 
 O P, a horizontal line passing through O, 
 the lowest point of the fall ; for if O L 
 were much less than 9 inches, the water 
 having spent the greater part of its force 
 in impelling the floatboards, would accu- 
 mulate below the wheel and retard its mo- 
 tion. For the same reason, another course, 
 which is called by M. Fabre, the course of 
 discharge should be connected with LMV 
 by the curve V N, to preserve the remain- 
 ing velocity of the water, which would 
 otherwise be destroyed by falling perpen- 
 dicularly from V to N. The course of 
 discharge is represented by V Z, sloping 
 
 from the point O. It should he about 16 
 yards long, having an inch of declivity in 
 every two yards. The canal which recon- 
 ducts the water from the course of dis- 
 charge to the river, should slope about 4 
 inches in the first 200 yards, 3 inches in 
 the second 200 yards, decreasing gradu- 
 ally till it terminates in the river. But if 
 the river to which the water is conveyed, 
 should, when swollen by the rains, force 
 the water back upon the wheel, the canal 
 must have a greater declivity, in order to 
 prevent this from taking place. Hence it 
 will be evident, that very accurate level- 
 ling is necessary for the proper formation 
 of the mill course.” 
 
 The general ideas contained in the pre- 
 ceding constructions appear to have been 
 first suggested by Du Buat, and afterwards 
 fully explained by M. Fabre, in his Traite 
 sur les Machines Hydrauliques. 
 
 The diameters of undershot wheels must 
 in general be accommodated to the nature 
 of the machinery which they are to 
 put in motion. If a great velocity is ne- 
 cessary, the wheel should for this purpose 
 be made of a less diameter than would 
 otherwise be adviseable ; but if a great 
 velocity is not required, the diameter of the 
 wheel ought to be considerable. 
 
 M. Pitot, one of the earliest writers who 
 attended to this subject, recommended that 
 the number of floatboards should be equal 
 to 360° divided by the arch of the circle 
 plunged in the canal, and that their depth 
 should be equal to the versed sine of that 
 arch * The slightest consideration, how- 
 ever, is sufficient to convince us that the 
 number of floatboards obtained by this rule 
 is greatly too small. M. Du Petit, Van- 
 din, and afterwards M. Fabre, have, on 
 the other hand, maintained, that the 
 greatest possible number of floatboards 
 should be used, provided the wheel is not 
 too much loaded by them. 
 
 In Mr. Smeaton’s model, by which his 
 experiments were performed, the diameter 
 of the wheel was 24 inches, and the num- 
 ber of floatboards 24. When the number 
 was reduced to 12, a diminution in the ef- 
 fect was produced on account of a greater 
 quantity of water escaping between the 
 floats and the floor ; but a circular sweep 
 being adapted thereto of such a length, 
 that one float entered the curve before the 
 preceding one quitted it, the effect came 
 so near to the former, as not to give hopes 
 of advancing it, by increasing- the number 
 of floats beyond 24 in this particular 
 wheel. 
 
 The experiments of Bossut were made 
 with a wheel, whose exterior diameter was 
 
 * The versed sine of an arch is that part of the 
 diameter which is intercepted between the circle 
 and the chord, or stiaighi line, which will cut oS 
 t be arch from the rest of the circle. 
 
282 
 
 THE ARTISAN. 
 
 3 feet 1 inch and 10 lines. It was used 
 successively with 48, 24, and 12 float- 
 boards directed to the centre. They M ere 
 exactly 5 inches wide, and from 4 to 5 
 inches high. The edges and the extremi- 
 ties of the floatboards were distant about 
 half aline from the bottom and sides of the 
 inclined canal in which the wheel was 
 placed, and the arch plunged in the water 
 was 24° 54'. When this wheel was tried, 
 it made 33§ turns in a minute, when it had 
 48 floatboards, and when the weight raised 
 was 12 pounds. When 24 floatboards 
 were put on, it made only 29 turns in a mi- 
 nute, the weight raised being the same ; 
 and when 12 floatboards were used, it 
 made no more than 25§ turns in a minute. 
 The velocity of the water in the canal 
 which had a declivity of lOf feet in .50, 
 was 300 feet in 33 seconds. Hence Bossut 
 concludes, that the wheel ought to have at 
 least 48 floatboards, whereas wheels 20 
 feet in diameter, and with only 25° or 30° 
 of the circumference immersed, have ge- 
 nerally only 40 floatboards. 
 
 When wheels are moved by a river, they 
 ought to have a different number of float- 
 boards. In order to find the number, 
 M. Bossut used a different wffieel, 
 in which the floatboards were so placed 
 that he could set them at any inclina- 
 tion to the radius, and employ any num- 
 ber of them at pleasure. The exterior 
 diameter was 3 feet, the width of the float- 
 boards 5 inches, and their height 6 inches. 
 This wheel was made to move in a cur- 
 rent from 12 to 13 feet wide, and in a 
 depth of water of from 7 to 8 inches. The 
 floatboards were plunged four inches in 
 the water, so that the circumstances were 
 the same as in an open river. When 24 
 floatboards w r ere used, a load of 40 pounds 
 was raised with a velocity of 15$ turns in 
 40 seconds ; whereas when 12 floatboards 
 were used, the velocity with which the 
 same load was raised was only 13$ turns 
 in the same side. Whei/ 48 floatboards 
 were put on, 24 pounds were raised, with 
 a velocity of 27$ turns in a minute ; and 
 24 floatboards raised the weight with a 
 velocity of 27| g , the difference being per- 
 fectly trifling. Hence 24 floatboards at 
 least should be used in cases of this kind. 
 A smaller number would be sufficient, if a 
 greater arch of the wheel were plunged in 
 the stream. In practice, it was the general 
 custom to use only 8 or 10 floatboards, and 
 sometimes fewer, on wheels placed in ri- 
 vers ; but the number ought to have been 
 from 12 to 18. 
 
 From theoretical considerations, M. Pi- 
 lot has shewn, that floatboards should al- 
 ways be a continuation of the radius ; but 
 this rule is found to be quite incorrect in 
 practice. The advantages arising from in- 
 clining the floatboards, were first pointed 
 
 out, in” 1753, by Deparcieux, who shews, 
 that the water will thus heap up upon 
 them, and acts by its weight as well as by 
 its impulse. This opinion has been amply 
 confirmed by the experiments of Bossut 
 with the wheel already mentioned, moving 
 in a canal where the velocity of the water 
 was 300 feet in 27 seconds. When the 
 floatboards were a continuation of the ra- 
 dius, a weight of 34 pounds was raised 
 with a velocity of 20$ turns in 40 seconds. 
 When their inclination was 8°, the same 
 load was raised with a velocity of 19$ in 
 40 seconds. When the inclination was 12°, 
 the velocity was 19$ in 40 seconds ; and 
 when the inclination was 16°, the velocity 
 was 20$ turns in 40 seconds, nearly the 
 same ; but still a little less than when the 
 floatboards were a continuation of the ra- 
 dius. Hence it follows, that a wheel 
 placed upon canals which have little de- 
 clivity, and in which the water is at liberty 
 to escape easily after the impulse, the 
 floatboards ought to be a continuation of 
 the radius. 
 
 The same wheel being placed in the cur- 
 rent already mentioned, viz. from 12 to 13 
 feet wide, and from 7 to 8 inches deep, 
 floatboards w hich w ere a continuation of 
 the radius, raised 40 pounds with a velo- 
 city of 13$ turns in 40 seconds. With 
 those inclined 15°, the number of turns in 
 the same time was 14$ ; with those in- 
 clined 30°, the number was 14$ ; and with 
 those inclined 37°, the number was 14$. 
 Hence it follows, thgt the most advantage- 
 ous obliquity is, in this case, about 15 or 
 30 degrees. The difference of effect, how- 
 ever, appears to be very trifling, particu- 
 larly beyond 15°. M. Fabre is of opinion, 
 that when the velocity of the stream is 11 
 feet per second or greater, the inclination 
 should never be less than 30° ; that, as the 
 velocity diminishes, the number of float- 
 boards should diminish in proportion ; and 
 that when the velocity is 4 feet or under, 
 the floatboards should be a continuation of 
 the radius. The experiment of inclining 
 the floatboards a little in the opposite di- 
 rection, has not been tried by any of the 
 authors whom we have quoted, but we 
 think it worth trying, as it might increase 
 the effect, by allowing the water to escape 
 more readily from below the floatboards. 
 
 In order to determine the ratio between 
 the velocity of the wheel and that of the 
 water which drives it, Parent and Pitot 
 considered only the action of the fluid 
 upon one floatboard, and consequently they 
 made the force of impulsion proportional 
 to the square of the relative velocity, or to 
 the square of the difference between the 
 velocity of the stream and that of the float- 
 board. Desaguliers, Maclaurin, Lambert, 
 Atwood, Du Buat, and Dr. Robinson, have 
 gone upon the same principle, and have 
 
THE ARTISAN. 
 
 283 
 
 therefore fallen into the same error, of 
 making the velocity of the wheel § of the 
 velocity of the current, when the effect is 
 a maximum The Chevalier de Borda, 
 whose valuable Memoirs have been too 
 much overlooked by later writers, has, 
 however, corrected this error. ‘He has 
 shewn, that the supposition is perfectly 
 correct when the water impels a single 
 floatboard ; for as the number of particles 
 which strike the floatboard in a given 
 time, and also the momentum of these, are 
 each as the relative velocity of the float- 
 boards, the momentum must be as the 
 square of the relative velocity ; that is, the 
 momentum varies as the square of the re- 
 lative velocity. But as the water acts on 
 more than one floatboard at once, the num- 
 ber acted upon in a given time will be as 
 the velocity of the wheel, or inversely as 
 the relative velocity ; for if we increase the 
 relative velocity, the velocity of the water 
 remaining the same, we must diminish the 
 velocity of the wheel; consequently, the 
 momentum will vary as the relative ve- 
 locity. 
 
 u The velocity of the stream,” says Mr. 
 Smeaton, “ varies at the greatest between 
 one-third and one-half that of the water ; 
 but in all the cases in which most work is 
 performed in proportion to the water ex- 
 pended, and which approach the nearest 
 to the circumstances of great works, when 
 properly executed, the maximum lies 
 much nearer to one-half than one-third ; 
 one half seeming to be the true maximum, 
 if nothing were lost by the resistance of 
 the air, the scattering of the water carried 
 up by the wheel, &c. all which tend to di- 
 minish the effect, consequently the maxi- 
 mum would be greater if these did not 
 take place.” Smeaton considers 5 to 2 as 
 the best general proportion. 
 
 A result, nearly similar to this, was de- 
 duced from the experiments of Bossut. 
 He employed a wheel whose diameter was 
 three feet. The number of floatboards was 
 at one time 48, and at another 24, their 
 width being five inches, and their depth 
 six. The experiments with the wheel, 
 when it had 48 floatboards, were made in 
 the inclined canal, in which the velocity 
 was 300 feet in 27 seconds. The experi- 
 ments with the wheel, when it had 24 
 floatboards, were made in a canal con- 
 tained between two vertical walls, 12 or 
 13 feet distant. The depth of the water 
 was about 7 or 8 inches, and its mean ve- 
 locity about 2740 inches in 40 seconds. 
 The floatboards of the wheel were im- 
 mersed about four inches in the stream. 
 
 The following are the other results which 
 Mr. Smeaton deduced from his experi- 
 ments. He found, that in undershot 
 wheels, the power employed to turn the 
 wheel is to the effect produced as 3 to 1 ; 
 and that the load which the wheel will 
 
 carry at its maximum, is to the load which 
 will totally stop it, as 3 to 4. The srfme 
 experiments show, that the impulse of the 
 water on the wheel, in the case of a maxi- 
 mum, is more than double of what is as- 
 signed by theory ; that is, instead of four- 
 sevenths of the column, it is nearly equal 
 to the whole column. In order to account 
 for this, Mr. Smeaton observes, that the 
 wheel was not, in'this case, placed in an open 
 river, where the natural current, after it 
 had communicated its impulse to the float, 
 has room on all sides to escape, as the 
 theory supposes ; but in a conduit or race,, 
 to which the float being adapted, the wa- 
 ter could not otherwise escape than by 
 moving along with the wheel. He like- 
 wise remarks, that when a wheel works in 
 this manner, the water, as soon as it meets 
 the float, receives a sudden check, and 
 risjes up against it like a wave against a 
 fixed object; insomuch, that when the sheet 
 of water is not a quarter of an inch thick 
 before it meets the float, it will not act 
 upon the whole surface of a float, whose 
 height is three inches. Were the float, 
 therefore, no higher than the thickness of 
 the sheet of water, as the theory supposes, 
 a great part of the force would be lost by 
 the water dashing over it. Mr. Smeaton 
 likewise deduced, from his experiments, 
 the following maxims. 
 
 1 . That the virtual or effective head be- 
 ing the same, the effect will be nearly as 
 the quantity of water expended. 
 
 2. That the expense of water being the 
 same, the effect will be nearly as the 
 height of the virtual or effective head. 
 
 3. That the quantity of water expended 
 being the same, the effect is nearly as the 
 square of the velocity. 
 
 4. That the aperture being the same, the 
 effect will be nearly as the cube of the ve- 
 locity of the water. 
 
 UNDERSHOT WHEELS MOVING AT RIGHT 
 ANGLES TO THE STREAM. 
 
 Undershot wheels have sometimes been 
 constructed like windmills, having large 
 inclined floatboards, and being driven in a 
 plane perpendicular to the direction of the 
 current. Albert Euler, who has examined 
 theoretically this species of water wheel, 
 concludes that the effect will be twice as 
 great as in the common undershot wheels, 
 and that in order to produce the effect, the 
 velocity of the wheel, computed from the 
 centre of the impression, should be to the 
 velocity of the water as radius is to thrice 
 the sine of the inclination of the floatboards 
 to the plane of the wheel. When the in- 
 clination is 60°, the ratio will be at 5 to 
 13 nearly, and when it is 30°, it will be 
 nearly as 2 to 3. In this kind of wheel, a 
 considerable advantage may also be gained 
 by inclining the floatboards to the radius. 
 In this case, the area of the floatboards 
 
*284 
 
 THE ARTISAN. 
 
 ought to be much greater than the section 
 of Ihe current, and before one fioatboard 
 leaves the current, the other ought to have 
 fairly entered it. This construction may 
 be employed with advantage in deep ri- 
 vers that have but a small velocity. 
 besant’s undershot wheel. 
 
 This wheel, invented by Mr. Besant, of 
 Brompton, is constructed in the form of a 
 hollow drum, to resist the admission of 
 water; but its principal peculiarity con- 
 sists in the arrangement of floatboards in 
 pairs on the periphery of the wheel. Each 
 fioatboard is set obliquely to the plane of 
 the wheel’s motion, and the corresponding 
 fioatboard is inclined at the same angle, 
 but in an opposite direction, the plane of 
 the wheel bisecting the angle formed by 
 the two floatboards. The acute angle 
 which the one fioatboard forms with its 
 corresponding one is open at the vertex ; 
 but one of the floatboards extends beyond 
 the other. By this construction, the re- 
 sistance from the tail watei i i diminished ; 
 but so far as we know, the machine has 
 never come into use. 
 
 HORIZONTAL WATER WHEELS. ’ 
 
 Horizontal water wheels differ in no 
 respect from common undershot wheels, 
 except in the circumstance of their extre- 
 mities being placed vertically. The mill- 
 course is constructed nearly in the same 
 manner for both. The principal object of 
 this form of the water wheel is to save ma- 
 chinery by placing the mill-stone directly 
 on the vertical shaft of the wheel. The 
 water must therefore move with a very 
 great velocity, so as to enable the mill- 
 stones to perform their work. The water 
 is turned into a* horizontal direction before 
 it strikes the floatboards, which may be ei- 
 ther vertical or inclined to the radius, as in 
 undershot wheels. 
 
 Horizontal wheels are often constructed 
 so that the floatboards have a very great 
 inclination to the radius. In this case, the 
 water is not turned into a horizontal di- 
 rection, but is made to strike the float- 
 boards perpendicularly, as represented in 
 the following figure, 
 
 where A Bis the wheel, MN the mill- 
 course discharging its contents perpendi- 
 cularly upon the fioatboard C, which 
 ought to have a surface more than twice 
 the area of the section of the stream. 
 
 In the southern departments of France, 
 the floafboards are made of a curvilineal 
 form, so as to present a concave surface to 
 the stream. 
 
 The Chevalier Borda remarks, that in 
 theory a double effect is produced when 
 the floatboards have this form; but that 
 the advantage is not so great in practice, 
 from the difficulty of making the fluid enter 
 and leave the course in a proper manner. 
 They appear, however, to be decidedly su- 
 perior to those in which the floatboards are 
 plane, as the water acts by its weight as 
 well as by its impulsive force. The ratio 
 of the effects in the two cases, with five or 
 six feet of fall, is nearly as 3 to 2. An ad- 
 vantage may be gained by dividing the cur- 
 rent, and throwing it in separate portions 
 upon different floatboards. 
 
 WHEELS WITH SPIRAL FLOATBOARDS. 
 
 In some of the southern provinces of 
 
 France, a conical horizontal wheel with 
 spiral floatboards is frequently used. It 
 has the form of an inverted cone, with a 
 number of spiral floatboards winding round 
 its surface, so as to be nearer one another 
 at the smaller or lower end of the cone, 
 than at the larger or upper end. When the 
 water has acted upon these floatboards by 
 its impulse, it descends along the spirals, 
 and continues to drive the machine by its 
 weight. 
 
 Dr. Robinson describes another wheel 
 with spiral floatboards, which was moved 
 by a screw. “ It was,” he says, “ along 
 cylindrical frame, having a plate standing 
 out from it about a foot broad, and sur- 
 rounding it with a very oblique spiral like 
 a cork screw. This was plunged about $th 
 of its diameter (which was about 12 feet), 
 having its axis in the direction of the stream. 
 By the work which it was performing, it 
 seemed more powerful than a common 
 wheel, which occupied the same breadth 
 of the river.” 
 
THE ARTISAN. 
 
 285 
 
 ' jHitfcettaueous ^uhiects. 
 
 MEMOIR OF THE LIFE OF THE 
 LATE DR. HUTTON. 
 
 ( Continued from page 258 .) 
 
 Such were among the invaluable but 
 short-lived labours of Dr. H. in the Royal 
 Society : and here it may be proper to 
 state the circumstances by? which they 
 were unfortunately terminated. 
 
 When Dr. Hutton first entered the So- 
 ciety, Sir John Pringle was the President. 
 He was a person of great acquirements, 
 and eminently well qualified to fill the 
 chair of Newton. He always manifested a 
 particular»regard for the Doctor, which 
 probably excited the jealousy of many per- 
 sons, who were not attached to mathemati- 
 cal investigations : among the members of 
 this description, was Mr. (afterwards Sir 
 Joseph) Banks, a gentleman too well 
 known to render it necessary to add any 
 thing further here concerning him, except 
 that he had acquired sufficient influence 
 over the majority of the members of the 
 Society to obtain his election as President, 
 upon the resignation of Sir John Pringle. 
 Dr. H. had for some time held the office 
 of Foreign Secretary with the greatest 
 credit ; but the new President, who wished 
 the situation to be filled by a friend of his 
 own, procured a vote to be passed by the 
 Society, that it was requisite this secretary 
 should reside constantly in London; a 
 condition with which the Doctor could not 
 possibly comply; and he therefore re- 
 signed the situation. Many of the most 
 valuable members of the Society, however, 
 warmly espoused Dr. H.’s cause, and dis- 
 continued their accustomed attendance at 
 the usual periodical meetings: among the 
 number may be mentioned Dr. Horsley, 
 Dr. Maskelyne, Baron Maseres, and many 
 other distinguished characters ; who, find- 
 ing that the disciples of Newton were 
 always outvoted by those of Linnaeus, re- 
 tired, with Dr. Hutton, from the Society. 
 When the mathematicians were preparing 
 to secede, Dr. Horsley expressed himself 
 in the following energetic words: — “ Sir, 
 (addressing himself to the President,) 
 when the hour of secession comes, the 
 President will be left with his train of 
 feeble amateurs and that toy — (pointing to 
 the mace on the table,) the ghost of the 
 Society where philosophy once reigned, 
 and Newton was her minister.” 
 
 This secession took place in 1784, since 
 which period very few papers on ma- 
 thematical subjects have appeared in 
 the “ Philosophical Transactions and 
 it is even said, that the late President uni- 
 formly opposed the admission of mathema- 
 ticians into the Royal Society, unless they 
 were persons of rank. 
 
 Although Dr. Hutton’s retirement f de- 
 prived him of the great stimulous to exer- 
 tion which such a Society must have 
 afforded, he still continued to give to the 
 world, from time to time, various valuable 
 works. In 1785 he published his u Mathe- 
 matical Tables” and in 1786 appeared his 
 u Tracts on Mathematical and Philosophical 
 Subjects ” in three volumes, which contain 
 much new and valuable matter. In the 
 following year, he published his “ Ele- 
 ments of Conic Sections ,” with select exer- 
 cises in various branches of mathematics 
 and philosophy, for the use of the Royal 
 Military Academy at Woolwich. This 
 work was warmly patronized by the Duke 
 of Richmond, then Master-general of the 
 Ordnance, who, on that occasion, presented 
 Dr. Hutton at court to his Majesty. 
 
 In 1795 appeared his “ Mathematical 
 and Philosophical Dictionary ” in two large 
 volumes, quarto, which was the result of 
 many years’ preparation, and has since 
 advanced to a second edition. It has sup- 
 plied all subsequent works of the kind, 
 and even the most voluminous Cyclo- 
 paedias, with valuable materials, both in 
 the sciences, and in scientific biography. 
 
 His next publication was “ A Course of 
 Mathematics in two volumes, octavo, com- 
 posed for the use of the students of the 
 Royal Military Academy ; which has since 
 become a standard work in many eminent 
 schools, both in Great Britain and America. 
 
 In the year 1803, he undertook the 
 arduous task of abridging the “ Philoso- 
 phical Transactions ” in conjunction with 
 Dr. Pearson and Dr. Shaw. Dr. Hutton 
 is said to have executed the chief part of 
 the work, and to have received for his 
 labour no less a sum than six thousand 
 pounds. It was completed in 1809, and 
 the whole comprised in eighteen quarto 
 volumes. About the same period was pub- 
 lished his translation of “ Montucla’s Re- 
 creations in Mathematics and Natural Phi- 
 losophy ” and an improved edition of the 
 same work appeared in 1814. 
 
 In 1806 the Doctor became afflicted with 
 a pulmonary complaint, which confined 
 him for several weeks ; but in the follow- 
 ing year he resumed his professional 
 duties. His medical friends, however, 
 advised him to retire from the labours of 
 the Academy, as soon as it might be 
 deemed convenient; and, in consequence 
 of an application to this effect, the Master- 
 general and Board of Ordnance acceded 
 to his wishes, and manifested their appro- 
 bation of his long and meritorious services, 
 by granting him a pension for life, of £500 
 per annum. This annuity, together with a 
 large property which he had realised, 
 chiefly by his publications, enabled him to 
 retire in affluent circumstances. But in his 
 retirement, his constant amusement con- 
 
286 
 
 THE ARTISAN. 
 
 tinued to be, the cultivation and diffusion Dr. Hutton bequeathed his marble bust 
 of useful science. He officiated for some to the Philosophical Society of Newcastle. 
 
 time, every half-year, as the principal 
 examiner to the Royal Military Academy, 
 and also to the East India College, at 
 Addiscombe. 
 
 During this period, as well as pre- 
 viously, he was indefatigable in kind 
 offices, especially in promoting the interest 
 of scientific men, and recommending them to 
 situations, where their talents might prove 
 
 It is to be placed in their new and splendid 
 Institution, where it will be long regarded 
 with pride and veneration. He always 
 manifested a laudable affection for* his 
 native place, of which he gave a proof 
 soon after his retirement from Woolwich, 
 by investing sums of money for the per- 
 petual support of education, &c. at New- 
 castle. His benevolence was extensive. 
 
 most useful both to themselves and to To merit in distress, and more especially 
 
 to the votaries of science, he was always a 
 kind friend and benefactor. 
 
 Dr. Hutton was twice married : his sur- 
 viving family consist of a son and two 
 daughters. The former was educated at 
 
 their country. To his recommendations, 
 as well as to his instructions, our most 
 eminent scientific institutions have been 
 chiefly indebted for their Professors of 
 Mathematics during the last thirty years. 
 
 Lieut.-General in the army. General 
 Hutton is ‘also a member of several learned 
 societies, and has been honoured with the 
 degree of D.C.L. 
 
 ARCHITECTURE. 
 
 MOULDINGS. 
 
 Mouldings are those parts which pro- 
 ject beyond the face of a wall, a column, 
 &c. and are employed as ornaments in 
 most Architectural operations. 
 
 The regular mouldings are eight in num- 
 ber, and are represented by the following 
 figures. 
 
 Annuler List, or Square. 
 
 His death was caused by a cold, which the Royal Military Academy, and at an 
 brought on a return of his pulmonary com- early age he obtained a commission in the 
 plaint. His illness was neither tedious Royal Regiment of Artillery, and is^ now a 
 nor painful ; and his valuable life termi- 
 nated on the 27th of January, 1823, in the 
 eighty-sixth year of his age. His remains 
 were interred in the family vault at Charl- 
 ton, in Kent. 
 
 It is worthy of remark, that only three 
 days previous to his death, he received 
 certain scientific questions from the corpo- 
 ration of London, which he answered im- 
 mediately in the most masterly manner. 
 
 These questions related to the intended 
 arches of the new London bridge ; and his 
 paper on the subject is considered not 
 only as a valuable document, but also 
 highly interesting, as being the last pro- 
 duction of this great man, and at such a 
 period of his advanced age and illness. 
 
 During the last year of Dr. Hutton’s 
 life, many of his scientific friends, wishing 
 to possess as correct and lasting a resem- 
 blance of his person as his valuable works 
 exhibit of his mind, entered into a sub- 
 scription for a marble bust, from which 
 casts might be taken in any number that 
 might be required. This bust has been 
 admirably executed by Mr. Sebastian 
 Gahagan. The subscription was sup- 
 ported by many of the Doctor’s early 
 pupils, and other eminent men, who seemed 
 emulous in manifesting their gratitude and 
 esteem. The sums subscribed having been 
 found greatly to exceed the disbursements, 
 the committee resolved to employ the sur- 
 plus in executing a medal; to contain, on 
 one side, the head of Dr. Hutton, and, on 
 the father, emblems of his discoveries on 
 the force of gunpowder, and the density of 
 the earth. These medals have been finely 
 executed by Mr. Wyon, and one has been 
 given to each subscriber to the bust. 
 
 About three months before his death, 
 the bust was presented to the Doctor ; but 
 the medals were finished only in time to 
 be presented to his friends who attended 
 his funeral. 
 
 Astragal, or Bead. 
 
THE ARTISAN. 
 
 28T 
 
 Ovolo, or Quarter round. 
 
 The forms of all mouldings are referred 
 to a section at right angles to their longitu- 
 dinal direction, when prismatic, or passing 
 through the axis, if annular ; and this ig 
 simply denominated the section, on account 
 of its frequent use, as oblique sections 
 only occur in mitres. The names of mould- 
 ings depend upon their form and situation. 
 
 If the section is a semicircle which pro- 
 jects from a vertical diameter, the moulding 
 is called an Astragal, Bead, or Torus : if a 
 torus and bead be both employed in the 
 same order of architecture, they are only- 
 distinguished by the bead being the small- 
 est. The tori are generally employed in 
 bases and capitals. 
 
 If the moulding be convex, and its sec- 
 tion be the quarter of a circle or less, and 
 if the one extremity project beyond the 
 other equal to its height, and the projecting 
 side be more remote from the eye than the 
 other, it is termed a Quarter-Round; this 
 in Roman architecture, is always employed 
 above the level of the eye. 
 
 If the section of a moulding be concave, 
 but in all other respects the same as the 
 last, it is denominated a Cavetto. They 
 are never employed in bases or capitals, 
 but frequently in entablatures. 
 
 If the section of a moulding is partly 
 concave and partly straight, and if the 
 straight part be vertical and a tangent to 
 the concave part, and if the concavity be 
 equal or less than the quadrant of a circle, 
 the moulding is denominated an Apophyge, 
 Scape, Spring, or Conge: it is used in the 
 Ionic and Corinthian orders for joining the 
 bottom of the shaft to the base, as well as 
 to connect the top of the fillet with the shaft 
 under the astragal. 
 
 If the section be one part concave and 
 the other convex, and so joined that they 
 may have the same tangent, the moulding 
 is named a Cymatium ; but Vitruvius calls 
 
 all crowning or upper members cymatiums, 
 whether they resemble the one now de» 
 scribed or not. 
 
 Tf the upper projecting part of the cyma- 
 tium be a concave, it is called a Cima- 
 recta, they are generally the crowning 
 members of cornices, but are seldom found 
 in other situations. 
 
 If the upper projecting part of the cyma- 
 tium be convex, it is called acima-reversa, 
 and is the smallest in any composition of 
 mouldings, its office being to separate the 
 larger members : it is seldom used as a 
 crowning member of cornices, but is fre- 
 quently employed with a small fillet over 
 it, as the upper member of architraves, 
 capitals, and imposts. 
 
 If the section of the moulding be the 
 two sides of right angles, the one vertical, 
 and the other of course horizontal, it is 
 termed a fillet, hand, or corona A fillet is 
 the smallest rectangular member in any 
 composition of mouldings. Its altitude is 
 generally equal to its projection; its pur- 
 pose is to separate two principal members, 
 and it is used in all situations under such 
 circumstances. The corona is the principal 
 member of a cornice. The beam ; or facia 
 is a principal member in an architrave as 
 to height, but its projection is not more 
 than that of a fillet. 
 
 METHOD OF REPRESENTING 
 TREES UPON POTTERY. 
 
 When the pottery has received from the 
 workman its form, and after it has ac- 
 quired some degree of consistence, the sur- 
 face, on which the representation of trees is 
 desired, must be steeped in a vessel, con- 
 taining a solution of argile (clay) very 
 much diluted, either coloured or not as 
 may be required, until it is perfectly moist. 
 This process will give to the pot, the same 
 colour, as the clay, in which it has been 
 steeped. 
 
 When this process is finished, in order 
 that trees may be produced, it is sufficient, 
 whilst the solution of clay is yet moist, and 
 even at the moment when taken from the 
 steeping vessel, to place lightly with a 
 brush in different parts of the surface spots 
 of whatever colour the trees may be re- 
 quired ; each spot producing a tree of a 
 large or small size according to the quan- 
 tity of colour used upon each, and also to 
 the manner in which the workman acts 
 with the hand in which the pot is held. 
 
 The trees may be of any colour what- 
 ever, but the most agreeable colour is 
 bistre, which is thus composed : take one 
 pound of manganese calcined ; 6 ounces 
 of iron rust, or 1 lb of iron ore ; and three 
 ounces of ground flint. The manganese 
 and the iron rust, or iron ore, must be 
 bruised separately in a mortar, after which 
 they must be put together into a crucible 
 
288 
 
 THE ARTISAN. 
 
 and calcined. The mixture thus prepared 
 may again be bruised, and afterwards put 
 into a small tub of water, in order to 
 render it moist. 
 
 For blue, green, or other colours, the 
 materials which are generally used for 
 producing them may be prepared in the 
 same manner as above. But to apply these 
 different colours to the articles, it is neces- 
 sary, as in ordinary painting, to use a mor- 
 dant instead of moistening with water. 
 
 The best mordant that can be employed 
 is urine, and the essence, or juice of tobacco. 
 
 In order to obtain tobacco water for this 
 purpose, it is sufficient to steep two ounces 
 of good leaf tobacco in a bottle of cold 
 water for 10 or 12 hours, or simply to infuse 
 two ounces of tobacco in a bottle of hot 
 water. 
 
 SOLUTIONS OF QUESTIONS. 
 
 Quest. 38, answered by Mr. Graham, 
 Teacher, Liverpool, ( the proposer ). 
 
 Put x equal one of the lenear edges of 
 the regular tetraedron, then arises the fol- 
 lowing equation 2 x 6x, reduced, 
 
 4 
 
 gives x equal 2^/3 the lenear edge of the 
 tetraedron. Thus, at page 185, Dr. Hut- 
 ton’s large mensuration, the content of the 
 tetraedron is 2^6, and the diameter of the 
 circumscribed sphere is 3^/2. Then 3^/2 
 cubed and multiplied into *5236 (the soli- 
 dity of a sphere whose diameter is 1), gives 
 39*9868 solid feet, which is evidently the 
 least circumscribed sphere : also the solid 
 content of the tetraedron taken from the 
 content of the circumscribed sphere is 
 
 feet 
 
 35.0878 solid feet of gold. Then, 1 : 
 
 oz. av. feet oz. 
 
 18888 x it : : 35 0878 : 6042311583 Troy, 
 at 3 1. 17 s. 10 §d. per oz. comes to2413148Z. 
 3s. 9 d. Again, the content of the pebble 
 tetraedron is 2^/6 feet, multiplied into 
 2700 oz. av. (the weight of a solid foot of 
 pebble) is 13227*2446 oz. av. which, added 
 to the weight of the gold in avoidupoise 
 ounces (662738-5169), gives 675965 7615 oz 
 av. the weight of the whole globe ; also the 
 weight of the globe’s bulk of sea- water is 
 39.9867 multiplied into 1030 oz. (the 
 weight of a solid foot of sea water) or 
 41186.39 oz. av., which, taken from the 
 weight of the whole globe, is 634779*37 
 oz. av. which is the weight that will just 
 sink the required cork globe below the 
 surface of the water. Then it is plain that 
 every solid foot of cork will take 1030—288. 
 
 oz. av. ft. 
 
 or 792 oz. to sink it. Hence, 792 : 1 : : 
 
 oz, av, 
 
 634779 37 : 801.489 solid feet of cork. 
 Lastly, 801*489 solid feet divided by *5236 
 (the solidity of a sphere whose diameter 
 
 is 3) and the cube root extracted, gives 
 11-523 feet, the diameter of the cork globe 
 required. 
 
 This question was also answered by 
 Mr. J. Barr, but by taking the price of 
 standard gold too high, and the specific 
 gravity of sea- water too low, with some 
 other slight mistakes, he makes the value 
 of the gold by far too great, and the dia- 
 meter of the cork globe considerably too 
 little. 
 
 Quest. 39, answered by Mr. Whitcombe, 
 Mathematician, Cornhill. 
 
 Let A C denote the pillarzzlSO feet B C 
 — the height of the statue = 10 feet, and 
 D the required point, then per a fluxionary 
 process (rather too long for the limits of the 
 Artizan) A D is found to be a mean pro- 
 portional between the distance A B and 
 AC, consequently AD“ 154*91, and the 
 ADBz 45° 55' 65", also A DCzz44° 
 4' 24", : A D B — A D C~ BD C “ 1 Q 
 51' 31" as required. 
 
 This question was also answered cor- 
 rectly by Mr. J. Taylor, Clement's -lane, 
 and by a correspondent in Bristol, who 
 
 signs T. D y ; but there must be some 
 
 mistake injhis solution, for he only makes 
 the required angle 52' 62", and we know it 
 is 1° 51' at least. 
 
 As this question may be solved geome- 
 trically, we will thank some of our mathe- 
 matical correspondents to send us the con- 
 is struction and demonstration. Ed. 
 
 QUESTIONS FOR SOLUTION. 
 
 Quest. 43, proposed by Mr. J. Whit- 
 combe. 
 
 In a given segment of an Elipsis, it is re- 
 quired to inscribe (geometrically) a rect- 
 angle, whose length shall be to its breadth 
 as a to c ? 
 
 Quest. 44, proposed by C. G. 
 
 Required to divide £20 between A and 
 B, so that the cube of B’s share may be 
 £602 less than the cube of A.’s 1 
 
THE ARTISAN. 
 
 289 
 
 PNEUMATICS. 
 
 STEAM ENGINE. 
 
 In our last article on Pneumatics, we 
 gave a description and drawing of a newly- 
 invented Gas Engine, which is intended, 
 and will, in all probability, be applied, to 
 perform the same operations as the high 
 pressure steam engines are at present. 
 
 Leaving time and experience to decide 
 whether this can be accomplished or not, 
 we shall again resume the subject of the 
 steam engine ; and in doing this we shall 
 select Mr. Maud slay’s Portable Engine for 
 
 the object of our present remarks, beeause 
 it differs materially, not only from Mr. 
 Watt’s, but from all those for which 
 patents have been more recently obtained. 
 maudslay’s steam engine. 
 
 This engine differs from all others, in 
 not having the beam usually employed for 
 connecting the fly-wheel crank with the 
 piston rod, in the working of the valves, 
 and in several other respects; but in order 
 to render the construction and operation of 
 this engine more easily understood, we 
 shall give an exact representation of the 
 front elevation, as well as two sections of 
 a ten-horse power engine. 
 
 FRONT ELEVATION. 
 
290 
 
 THE ARTISAN. 
 
 END VIEW.* 
 
 A. Is the cast iron frame of the engine. 
 
 B. The cylinder. 
 
 C. The piston, furnished with the rod 
 B, and a. cross head and socket E. 
 
 F. Guide wheels, which keep the piston 
 and rod in a vertical position. 
 
 G. Frame for ditto, in which the wheels 
 F F are made to work. 
 
 H. Side rods, which serve to connect 
 the cross head with the double crank 1 1. 
 
 1 1. Two cranks, made to turn in the 
 pluminer-blodr, or bearing J J at each 
 
 * The Longitudinal Section will be given in our 
 
 nr-*'.. 
 
 side of the frame, and to which the fly- 
 wheel shaft K is connected by a coupling- 
 box or clutch, at the end next the engine. 
 
 K. Fly- wheel shaft, working in a plum- 
 mer-block on the wall. 
 
 L. Coupling-box, connecting the engine 
 with the fly-wheel shaft. 
 
 M. The fly-wheel. 
 
 N N. Two eccentric wheels, supported 
 by the crank-shaft K, the action of which 
 give motion to the two beams O and T, by 
 means of the connecting rods P P. 
 
 O. The beam which works the cold 
 water pump S. 
 
 PP. Two connecting rods. 
 
THte artisaM. 
 
 291 
 
 Q. Yhe double bearing, on which the 
 Cold water pump-beam works. 
 
 R. A rod which serves to connect the 
 backet of the cold water pump with the 
 beam O. 
 
 S. The barrel of the cold water pump. 
 
 T. Beam which works the air and hot 
 water pumps, and to which motion is com- 
 municated by the connecting rods P, as 
 before described. 
 
 U. The slings which connect the air- 
 pump rod with the end of the beam T. 
 
 V. The double bearing or centre, on 
 which the air-pump beam T works. 
 
 W. The air-pump bucket. 
 
 X. Air-pump cylinder. 
 
 Y. Hot water pump, worked by a small 
 rod, attached to the air-pump beam. 
 
 Z. Feed-pipe, to supply the boiler with 
 hot water. 
 
 a. Cross rail, on which a guide is fixed 
 to confine the air-pump rod in a vertical 
 position. 
 
 b. The condenser. 
 
 c. The cold water cisterns, connected by 
 a pipe (L 
 
 e. Eduction pipe, or passage for the 
 steam from the cylinder to the condenser. 
 
 /. Injection cock, to admit the cold 
 water into the condenser. 
 
 g. Foot valve at the bottom of the air- 
 pump, and communicating from thence to 
 the condenser. 
 
 h. Hand gear, for stopping or starting 
 the engine. 
 
 i . A rod, connecting the hand gear with 
 an eccentric 7c, fixed on the crank shaft; 
 the action of which communicates a vibra- 
 tory motion to the rod i. 
 
 1. Connecting rod, and double ended 
 lever m, fixed at the extreme end of a 
 spindle, while a beveled wheel is attached 
 to the other ; the latter of which works the 
 spindle of the steam-cone n. 
 
 o. The steam-cone or cock, for admitting 
 the steam from the boiler to the cylinder ; 
 beyond which is a contrivance for shutting 
 otf the steam, at the half or any other pat 
 of the stroke, by which a very considerable 
 saving in the steam, and consequently ip 
 the fuel, is effected. 
 
 ©TT1CS. 
 
 OF THE REFLECTING TELESCOPE. 
 
 The great difficulty of managing refract- 
 ing telescopes when of great length, and 
 the impossibility of obtaining a higher mag- 
 nifying power than 500 times, even by 
 making them 600 feet long, stimulated 
 philosophers to attempt a different mode of 
 constructing telescopes, which they have 
 effected by applying the principle of re- 
 flection, instead of that of direct vision. 
 By this means instruments of a much 
 shorter length answer the purpose much 
 
 better; for a reflecting telescope 6 feetlong, 
 will magnify as much as a refracting one 
 100 feet long. 
 
 GREGORIAN TELESCOPE. 
 
 The first telescope of the reflecting kind, 
 which was found to answer the purpose, 
 was invented by Dr. James Gregory, a 
 Scotsman, about the year 1661. 
 
 The instrument which he invented, is 
 represented by the following figure. 
 
 At the bottom of the great tube TTTT 
 is placed the large concave mirror DUVF, 
 whose principal focus is atm; and in its 
 middle is a round hole P, opposite to 
 which is placed the small mirror L, con- 
 cave toward the great one ; and so fixed to 
 a strong wire M, that it may be moved 
 farther from the great mirror, or nearer to 
 it, by means of a long screw on the outside 
 of the tube, keeping its axis still in the 
 same line P m n with that of the great 
 one. Now, since in viewing a very remote 
 
 object, we can scarcely see a point of it but 
 what is at least as broad as the great mir- 
 ror, we may consider the rays of each pen- 
 cil, which flow from every point of the 
 object, to be parallel to each other, and to 
 cover the whole reflecting surface D UV F. 
 But to avoid confusion in the figure, we 
 shall only draw two rays of a pencil flow- 
 ing from each extremity of the object into 
 the great tube, and trace their progress, 
 through all their reflections and refrac- 
 tions, to the eye/, at the end of the small 
 
292 
 
 THE ARTISAN. 
 
 tube tt , which is joined to the great 
 one. 
 
 Let us then suppose the object A R to be 
 at such a distance, that the rays C may 
 flow from its^ lower extremity B, and the 
 rays E from its upper extremity A. Then 
 the rays C falling parallel upon the great 
 mirror at D, will be thence reflected con- 
 verging, in the direction D G ; and by cross- 
 ing at I in the principal focus of the mir- 
 ror, they will form the upper extremity I 
 of the inverted image I K, similar to the 
 lower extremity B of the object A B : and 
 passing on to the concave mirror L (whose 
 focus is at n) they will fall upon it at g, 
 and be thence reflected converging, in the 
 direction g N, because g m is longer than 
 g n ; and passing through the hole P in the 
 large mirror, they would meet somewhere 
 about r, and form the lower extremity d of 
 the erect image a d, similar to the lower 
 extremity B of the object A B. But by 
 passing through the plano-convex glass R 
 in their way, they form that extremity of 
 the image at b. In like manner, the rays 
 E, which come from the top of the object 
 AB, and fall parallel upon the great mir- 
 ror at F, are thence reflected converging 
 to its focus, where they form the lower ex- 
 tremity K of the inverted image I K, simi- 
 lar to the upper extremity A of the object 
 A B ; and thence passing on to the small 
 mirror L, and falling upon it at h, they are 
 thence reflected in the converging state h O ; 
 and going on through the hole P of the 
 great mirror, they will meet somewhere 
 about q, and form there the upper ex- 
 tremity a of the erect image a d, similar to 
 the upper extremity A of the object A B : 
 but by passing through the convex glass 
 R in their way, they meet and cross sooner, 
 as at a, where that point of the erect 
 image is formed. The like being under- 
 stood of all those rays which flow from the 
 intermediate points of the object, between 
 A and B, and enter the tube T T ; all the 
 intermediate points of the image between 
 a and b will be formed : and the rays pass- 
 ing on from the image through the eye- 
 glass S, and through a small hole e in the 
 end of the lesser tube t t, they enter the 
 eye/, which sees the image a d (by means 
 of the eye-glass) under the large angle 
 c e d, and magnified in length, under that 
 angle from c to d. 
 
 In the best reflecting telescopes, the 
 focus of the small mirror is never coin- 
 cident with the focus m of the great one, 
 where the first image I K is formed, but a 
 little beyond it (with respect to the eye) as 
 at n : the consequence of which is, that the 
 rays of the pencils will not be parallel 
 after reflection from the small mirror, but 
 converge so as to meet in points about 
 q , e, r ; where they will form a larger 
 upright image than a d, if the glass R was 
 
 not in their way : and this image might be 
 viewed by means of a single eye-glass 
 properly placed between the image and the 
 eye : but then the field of view would be 
 less, and consequently not so pleasant, 
 for which reason, the glass R is still re- 
 tained, to enlarge the scope or area of the 
 field. 
 
 To find the magnifying power of this te- 
 lescope, multiply the focal distance of the 
 great mirror by the distance of the small 
 mirror from the image next the eye, and 
 multiply the focal distance of the small 
 mirror by the focal distance of the eye- 
 glass: then, divide the product of the 
 former multiplication by the product of the 
 latter, and the quotient will express the 
 magnifying power. 
 
 One great advantage of the reflecting 
 telescope is, that it will admit of an eye- 
 glass of a much shorter focal distance than 
 a refracting telescope will; and, con- 
 sequently, it will fhagnify so much the 
 more : for the rays are not coloured by re- 
 flection from a concave mirror, if it be 
 ground to a true figure, as they are by 
 passing through a convex-glass, let it be 
 ground ever so true. 
 
 The adjusting screw on the outside of 
 the great tube fits this telescope to all sorts 
 of eyes, by bringing the small mirror either 
 nearer to the eye, or removing it farther 
 from it: by which means, the rays are 
 made to diverge a little for short-sighted 
 eyes, or to converge for those of a long 
 sight. 
 
 The nearer an object is to the telescope, 
 the more its pencils of rays will diverge 
 before they fall upon the -great mirror, 
 and therefore they will be the longer of 
 meeting in points after reflection ; so that 
 the first image I K will be formed at a 
 greater distance from the large mirror, 
 when the object is near the telescope, than 
 when it is very remote. But as this image 
 must be formed farther from the small 
 mirror than its principal focus n, this mir- 
 ror must be always set at a greater dis- 
 tance from the large one, in viewing near 
 objects, than in viewing remote ones. And 
 this is done by turning the screw on the 
 outside of the tube, until the small mir- 
 ror be so adjusted, that the object (or 
 rather its image) appear perfect. 
 
 CASSEGRAINIAN TELESCOPE. 
 
 Soon after the discovery of the Grego- 
 rian telescope, Mr. Cassegrain, a native of 
 France, produced a reflecting telescope, 
 which he pretended was an original inven- 
 tion ; but it differs in no respect from the 
 Gregorian, except in having a convex in- 
 stead of a concave mirror. This form of 
 the small mirror has the effect of shorten- 
 ing the telescope twice the focal length of 
 the small speculum. But notwithstanding 
 
THE ARTISAN, 
 
 293 
 
 this and some other advantages, which it 
 has in theory over the Gregorian teles- 
 cope, it is but little used. Captain Kater 
 has, however, made several astronomical 
 observations with it, and found it much 
 superior to a Gregorian one of the same 
 magnifying power. This led him to under- 
 take a comparison of the two instruments, 
 for which purpose he caused one of each 
 to be made, having the specula of the same 
 metal, and of the same pattern ; their mag- 
 nifying powers were also nearly the same. 
 He varied the aperture of the Cassegrai- 
 nian telescope, till he found that both in- 
 struments exhibited the letters of a printed 
 card, with equal clearness and distinct- 
 ness; and after deducting from the ex- 
 posed area of each, the area of the small 
 speculum and its arm, he found that the 
 reflecting surface of the Cassegrainian was 
 4*63, while that of the Gregorian was 
 10*87, making the light of the former, 
 (from equal surfaces) to that of the latter, 
 nearly as seven to three. 
 
 NEWTONIAN TELESCOPE. 
 
 The Newtonian telescope, which de- 
 rives its name from its illustrious inventor, 
 Sir I. Newton, can only be considered as 
 an improvement, or rather a variety of the 
 Gregorian telescope, which was described 
 
 in 1663, in a work called the Optica Pro- 
 mota. But though Newton says he was 
 acquainted with this work, before he in- 
 vented his reflecting telescope, which was 
 not till after 1664 ; yet he did not mention 
 the telescope of Gregory, till he was called 
 upon to make some remarks upon that of 
 Cassegrain, who brought it forward as a 
 new discovery, and disputed the invention 
 with him. 
 
 In a letter to a friend, dated February 
 23, 1669, Sir Isaac gives an account of “ a 
 small prospective, ” made to try the truth 
 of his conjecture respecting reflecting 
 telescopes. It was 6£ inches long, had an 
 aperture about an inch and a third, a 
 plano-convex eye-glass |4h or |th of an 
 inch deep, and magnified about 35 times, 
 which he considered as more than could 
 be done by a six feet refracting telescope. 
 With this instrument he saw the horns of 
 Venus and the satellites of Jupiter ; but 
 not content with such an experiment, he 
 completed another speculum 2| inches 
 broad, and satisfied himself completely of 
 the superiority of these instruments, which 
 were afterwards brought to such perfection 
 by the labours of Mr. Hadley and the late 
 Sir W. Herschel. 
 
 The Newtonian Telescope is represented 
 by the following figure. 
 
 A B CD is a tube or case; EF a large 
 polished speculum, whose focus is at 0 ; 
 GH a plane speculum truly concentred, 
 and fixed at half a right angle with the 
 axis of the large one. Then parallel rays, 
 as a E, h F, falling on the large speculum 
 E F, instead of being reflected to the focus 
 o, are intercepted by the small plain specu- 
 lum G H, and by it reflected towards a 
 hole c d in the side of the tube, crossing 
 each other in the point O, which now be- 
 comes the true focal point; and from 
 thence they proceed to an eye-glass ef 
 placed in that hole, whose focal distance 
 is very small, and therefore the power of 
 magnifying may be very great in this form 
 of the telescope ; because the image I M is 
 made by one reflection (for that of the 
 plane speculum only alters the course of 
 rays, and adds nothing to the confusion of 
 the image ), and will, for that reason, bear 
 
 being viewed by a glass of a very deep 
 charge , in comparison with an image formed 
 by differently refrangible rays. 
 
 In order to obtain a reflection with less 
 loss of light, Sir Isaac Newton proposed to 
 substitute a rectangular prism in place of 
 the small mirror, having its sides perpen- 
 dicular to the incident and the emerging 
 rays, so that the light might suffer total re- 
 flection from its posterior surface. By 
 making these two faces of the prism con- 
 vex, the object will be seen erect instead 
 of inverted. 
 
 As it is more difficult to find any of the 
 celestial bodies with a Newtonian than 
 with a Gregorian telescope, it has been 
 customary to fix a small astronomical 
 telescope on the tube of the former, so 
 that the axis of the two instruments may be 
 parallel. 
 
 The aperture of the object-glass is large, 
 
294 
 
 THE ARTISAN. 
 
 and cross hairs are fixed in the focus of the 
 eye-glass. The object is then found by 
 this small telescope, which is called the 
 finder ; and if the axis of the instruments 
 are rightly adjusted, it will be seen also in 
 the field of the large telescope. 
 
 But notwithstanding this contrivance, 
 the Newtonian telescope is not so com- 
 modious for common use as the Gregorian, 
 it is therefore very seldom employed either 
 for astronomical or terrestrial observations. 
 
 Should any of our readers wish to see a 
 fuller account of this telescope, they may 
 consult Sir I. Newton’s Optics, and seve- 
 ral papers in the Transactions of the Royal 
 Society, written about the time of its con- 
 struction. 
 
 CHBMIgTEtlT. 
 
 IODINE. 
 
 Iodine was accidentally discovered in 
 1812, by Mi de Courtois, a manufacturer 
 of saltpetre at Paris. In his processes for 
 procuring soda from the ashes of seaweeds, 
 he found the metallic vessels much cor- 
 roded ; and in searching for the cause of 
 the corrosion, he made this important dis- 
 covery. But for this circumstance, merely 
 accidental, one of the most curious of sub- 
 stances might have remained for ages 
 unknown, since Nature has not distributed 
 it, in either a simple or compound state, 
 through her different kingdoms, but has 
 confined it, to what the Roman satirist con- 
 siders as the most worthless of things, the 
 vile sea weed. 
 
 Iodine derived its first illustration from 
 M. M. Clement and Desormes. In their 
 memoir, read at a meeting of the Institute 
 of France, these able chemists described 
 its principal properties. They stated its 
 specific gravity to be about 4 ; that it be- 
 comes a violet coloured gas at a tempera- 
 ture below that of boiling water, whence it 
 received the name of Iodine , which is a 
 word derived from the Greek, signifying, 
 like a violet; that it combines with the 
 metals, and with phosphorus, and sulphur, 
 and likewise with thb alkalis and metallic 
 oxides; that it forms a detonating com- 
 pound with ammonia ; that it is soluble in 
 alcohol, and still more soluble in ether ; 
 and that by its action upon phosphorus 
 and upon hydrogen, a substance is formed, 
 having the characters of muriatic acid. In 
 this communication they offered no de- 
 cided opinion respecting its nature. 
 
 In 1813 Sir H. Davy happened to be on a 
 visit to Paris, and when M. Clement 
 shewed him Iodine, he said that he be- 
 lieved it w as a substance analogus in its 
 Chemical relations to chlorine. 
 
 Iodine has been found in various kinds 
 
 of sea weed. But it is from the incinerated 
 sea weed or kelp, that Iodine is to be ob- 
 tained in quantities. Dr. Wollaston first 
 communicated a precise formula for ex- 
 tracting it, which is as follows: Dissolve 
 the soluble part of kelp in water ; concen- 
 trate the liquid by evaporation, and sepa- 
 rate all the crystals that can be obtained. 
 Pour the remaining liquid into a clean 
 vessel, and mix with it an excess of sul- 
 phuric acid. Boil this liquid for some 
 time. Sulphur is precipitated, and mu- 
 riatic acid driven off. Decant off the clear 
 liquid, and strain it through wool. Put it 
 into a small flask, and mix it with as much 
 black oxide of manganese, as was used be- 
 fore of sulphuric acid. Apply to the top 
 of the flask a glass tube, shut at one end. 
 Then heat the mixture in the flask. The 
 Iodine sublimes into the glass tube. 
 
 None can be obtained from sea water. 
 
 In repeating this process, Dr. U*e, of 
 Glasgow, obtained from similar quantities 
 of kelp such variable products of Iodine, 
 that he was induced to institute a series of 
 experiments for discovering the causes of 
 these anomalies, and for procuring Iodine 
 at an easier rate. In this he appears to 
 have been successful, for instead of pro- 
 curing this singular element in such small 
 quantity as a few grains, he has obtained 
 ounces at a time, and at a moderate ex- 
 pense. But our limits wall not permit us 
 to give a detail of the process he pur- 
 sued.*' 
 
 The substance he obtained it from was 
 the residuum of soap leys, the alkaline 
 matter of which consisted solely of kelp. 
 From this residuum he first obtained a 
 brown oily liquid, and from 'this liquid he 
 procured Iodine in considerable quantity. 
 
 Iodine is a solid, of a greyish-black 
 colour and metallic lustre. It is often in 
 scales similar to those of micaceous iron 
 ore, semetiines in rhomboidal plates, very 
 large and very brilliant. It has been 
 obtained in elongated octahedrons, nearly 
 half an inch in length ; the axis of which 
 were shown by Dr. Wollaston to be to each 
 other, as the numbers 2, 3, and 4, at least 
 so nearly, that in a body so volatile, it is 
 scarcely possible to detail an error in this 
 estimate, by the reflective goniometer. 
 Its fracture is lamellated, and it is soft 
 and friable to the touch. Its taste is very 
 acrid, though it is very sparingly soluble 
 in water. It is a deadly poison. It gives 
 a deep brown stain to the skin, which soon 
 vanishes by evaporation. In odour, and 
 power of destroying vegetable colours, it 
 resembles very dilute aqueous chlorine. 
 The specific gravity of Iodine at 62|° is 
 4*948. It dissolves in 7000 parts of water. 
 
 * This will be found in the 50th voi. of the PhU 
 losophical Magazine. 
 
THE ARTISAN. 
 
 295 
 
 The solution is of an orange yellow colour, 
 and in small quantity tinges raw starch of 
 a purple hue, which vanishes on heating it. 
 It melts, according to M. Gay Lussac, at 
 227° F., and is volatilized under the com- 
 mon pressure of the atmosphere, at the 
 temperature of 350°. According to Ure,it 
 evaporates pretty quickly at ordinary tem- 
 peratures. Boiling water aids its subli- 
 mation, as is shown in the above process 
 of extraction. The specific gravity of its 
 violet vapour is *8678. It is a non-con- 
 ductor of electricity. When the voltaic 
 chain is interrupted by a small fragment of 
 it, the decomposition of water instantly 
 ceases. 
 
 Iodine is incombustible, but with azote 
 it forms a curious detonating compound ; 
 and in combining with several bodies, the 
 intensity of their mutual action is such, as 
 to produce the phenomena of combustion. 
 
 Iodine combines with oxygen and with 
 chlorine; but these combinations will be 
 described when treating of iodic acid. 
 
 With a view of determining whether it 
 was a simple or compound form of matter, 
 Sir FI. Davy exposed it to the action of 
 the highly inflammable metals. When its 
 vapour is passed over potassium heated in 
 a glass tube, inflammation takes place, and 
 the potassium burns slowly with a pale 
 blue light. There was no gas disengaged 
 when the experiment was repeated in a 
 mercurial apparatus. The iodide of potas- 
 sium is white, fusible at a red-heat, and 
 soluble in water. It has a peculiar acrid 
 taste.* When acted on by sulphuric acid, 
 it effervesces, and iodine appears. It is 
 evident, that in this experiment there had 
 been no decomposition ; the result depend- 
 ing merely on the combination of iodine 
 with potassium. By passing the vapour 
 of iodine over dry red hot potash, formed 
 from potassium, oxygen is expelled, and 
 the above iodide results. Hence we see, 
 that at the temperature of ignition, the 
 affinity between iodine and potassium, is 
 superior to that of the latter for oxygen. 
 But iodine in its turn is displaced by 
 chlorine, at a moderate heat; and if the 
 latter be in excess, chloriodic acid is 
 formed. M. Gay Lussac passed vapour of 
 iodine in a red heat over melted sub-car- 
 bonate of potash ; and he obtained carbo- 
 nic acid and oxygeu gases, in the propor- 
 tions of two in volume of the first, and one 
 of the second, precisely those which exist 
 in the salt 
 
 The oxide of sodium, and the sub-car- 
 bonate of soda, are completely decom- 
 posed by iodine. From these experiments 
 it would seem, that this substance ought to 
 
 * When iodine is combined with any other sub- 
 stance, the compound is called an iodide- of that 
 Substance. 
 
 disengage oxygen, from most of the oxides ; 
 but this happens only in a small number of 
 cases. The protoxides of lead and bis- 
 muth are the only oxides not reducible by 
 mere heat, with which it exhibited that 
 power.* Barytes, strontian, and lime, 
 combine with iodine, without giving out 
 oxygen gas, and the oxides of zinc and 
 iron undergo no alteration in this respect. 
 From these facts we must conclude, that 
 the decomposition of the oxides by iodine 
 depends less on the condensed state of the 
 oxygen, than upon the affinity of the metal 
 f »r iodine. Except barytes, strontian, and 
 lime, no oxide can remain in combination 
 with iodine at a red heat. 
 
 M. Gay Lussac says, “ Sulphate of pot- 
 ash was not altered by iodine; but what 
 may appear astonishing, I obtained oxy- 
 gen with the fluate of potash, and the 
 glass tube in which the operation was 
 conducted was corroded. On examining 
 the circumstances of the experiment, I 
 ascertained that the fluate became alka- 
 line when melted in a platinum crucible: 
 This happened to the fluate over which 
 I passed iodine. It appears then that the 
 iodine acts upon the excess of alkali, and 
 decomposes it. The heat produced dis- 
 engages a new portion of fluoric acid or 
 its radical, which corrodes the glass ; and 
 thus by degrees the fluate is entirely de- 
 composed.” These facts seem to give 
 countenance to the opinion, that the fluoric 
 is an oxygenized acid ; and that the salt 
 called fluate of potash is not a fluoride of 
 potassium. 
 
 Iodine forms with sulphur a feeble com- 
 pound of a greyish-black colour, radiated 
 like sulphuret of antimony. When it is 
 distilled with water iodine separates. 
 
 Iodine and phosphorus combine with 
 great rapidity at common temperatures, 
 producing heat without light. From the 
 presence of a little moisture, small quan- 
 tities of hydriodic acid gas are exhaled. 
 
 Oxygen expels iodine from both sulphur 
 and phosphorus. “ Hydrogen,” says Gay 
 Lussac, “ whether dry or moist, did not 
 seem to have any action on iodine at the 
 ordinary temperature of the atmosphere ; 
 but if, as was done by Clement, in an ex- 
 periment in which I was present, we 
 expose a mixture of hydrogen and iodine 
 to a red heat in a tube, they unite together, 
 and hydriodic acid is produced, which 
 gives a reddish-brown colour to water.” 
 Sir H. Davy, with his characteristic inge- 
 nuity, threw the violet coloured gas upon 
 the flame of hydrogen, when it seemed to 
 support its combustion. He also formed a 
 compound of iodine with hydrogen, by 
 
 t A protoxide signifies a substance combined with 
 one, or the first, dose of oxygen. 
 
296 
 
 THE ARTISAN. 
 
 heating to redness the two bodies in a 
 glass tube. 
 
 Charcoal has no action upon iodine, 
 either at a high or low temperature. 
 Several of the common metals, on the con- 
 trary, as zinc, iron, tin, mercury, attack it 
 readily, even at a low temperature, pro- 
 vided they be in a divided state. Though 
 these combinations take place rapidly, 
 they produce but little heat, and but 
 rarely any light. 
 
 When iodine and oxides act upon each 
 other in contact with water, the water is 
 decomposed; its hydrogen unites with 
 iodine, to form hydriodic acid ; ( while its 
 oxygen, on the other hand, produces with 
 iodine, iodic acid. All the oxides, how- 
 ever, do not give the same results. We 
 obtain them only with potash, soda, bary- 
 tes, strontian, lime, and magnesia. 
 
 From all the above recited facts, we are 
 warranted in concluding iodine to be an 
 undecompounded body. In its specific gra- 
 vity, lustre, and magnitude, it resembles 
 the metals ; but in all its chemical agen- 
 cies, it is analogous to oxygen and chlorine. 
 It is a non-conductor of electricity, and 
 possesses, like these two bodies, the ne- 
 gative electrical energy with regard to 
 metals, inflammable, and alkaline sub- 
 stances ; and hence, when combined with 
 these substances in aqueous solution, and 
 electrized in the voltaic circuit, it separates 
 at the positive surface. But it has a posi- 
 tive energy with respect to chlorine; for 
 when united to chlorine, in the chloriodie 
 acid, it separates at the negative surface. 
 This likewise corresponds with their 
 relative attractive energy, since chlorine 
 expels iodine from all its combinations. 
 Iodine dissolves in carburet of sulphur, 
 giving, in very minute quantities, a fine 
 amethystine tint to the liquid. 
 
 Iodide of mercury has been proposed 
 for a pigment ;* in other respects, iodine 
 has not been applied to any purpose of 
 common life. M. Orfila swallowed 6 
 grains of iodine; and was immediately 
 affected with heat, constriction of the 
 throat, nausea, eructation, salivation, and 
 cardialgia. In ten minutes he had copious 
 bilious vomitings, and slight colic pains. 
 His pulse rose from 70 to about 90 beats 
 in the minute. By swallowing large 
 quantities of mucilage, and emollient clys- 
 ters, he recovered, and felt nothing next 
 day but slight fatigue. About 70 or 80 
 grains proved a fatal dose to dogs. They 
 usually died on the fourth or fifth day. 
 
 * There are two iodides of mercury, the one yel- 
 low and the other red ; both are fusible and vola- 
 tile. 
 
 ABTEONOMY a 
 
 OF THE FIXED STARS. 
 
 The fixed stars are considered by Astro- 
 nomers as forming no part of the solar 
 system ; but as placed far beyond the ut- 
 most limits of it. They have supposed, 
 that each star is a sun, having a number 
 of planets and comets circulating round it ; 
 and that each of the planets, thus circulat- 
 ing round these luminaries, may be a 
 habitable world like our own. 
 
 The strongest argument for this hypo- 
 thesis is, that fixed stars cannot be mag- 
 nified by the most powerful telescopes, on 
 account of their extreme distance. Hence 
 it is concluded, that they shine by their % 
 own light ; and that each of them is a sun 
 equal, if not superior, in lustre and mag- 
 nitude to our own. 
 
 When the stars are examined through a 
 telescope, they rather seem diminished 
 than increased in size. This circumstance 
 alone would have been a striking proof of 
 the immeasurable distance of these bodies, 
 had we not been in possession of still mora 
 convincing evidence. In every attempt 
 which Astronomers have made with the 
 best of instruments, to discover the parallax 
 of the stars, they never found it to amount 
 to one second, even when the earth was in 
 opposite points of her orbit ; and there- 
 fore they have determined that the nearest 
 of these luminaries cannot be less than 
 206,265 times the radius of the earth’s 
 orbit. As light traverses the latter in 
 8,' IS'', it will require 8 years and 79 days 
 to come from a fixed star to the earth. 
 And it is believed some of them may be so 
 remote, that their light has not yet reached 
 the earth since they were created ; — while 
 others, which have disappeared, or have 
 been destroyed many ages ago, may con- 
 tinue to shine in the heavens, till the last 
 ray, which they emitted, has reached our 
 globe. 
 
 The number of stars discoverable at any 
 time in the heavens, by the naked eye, is 
 not above a thousand. This may at first 
 appear incredible to some, because they 
 seem to be innumerable ; but the decep- 
 tion arises from looking upon them hastily, 
 without reducing them into any kind of 
 order. For let any person look steadily a 
 little time upon a large portion of the 
 heavens, and count the number of the stars 
 in it, and he will be surprised to find the 
 number so small. And if the moon be 
 observed for a short space of time, she will 
 be found to meet with very few in her 
 way, although there are as many about her 
 path as in any other part of the heavens. 
 
 Flamstead’s catalogue of the stars in 
 both hemispheres, contains only 3000 ; 
 and a great number of these cannot be 
 
THE ARTISAN. 
 
 297 
 
 seen without the assistance of a. telescope. 
 When the heavens are examined with a 
 good telescope, the stars are not found to 
 be uniformly scattered over the firmament. 
 In some places they are crowded together ; 
 and, in other parts, there are large spaces 
 where no stars can be seen. Besides 
 these starry groups, where the individual 
 stars are distinctly visible, there are num- 
 bers of smalt luminous spots, of a cloudy 
 appearance, called Nebulae. The largest 
 of these nebulae is the galaxy or milky 
 way, a white luminous zone, which nearly 
 encircles the heavens ; and which appears 
 to be the nearest of all the nebulae. 
 
 While the heavens exhibit these appear- 
 ances, which may be termed constant , they 
 occasionally exhibit others of a different 
 kind, which seem to arise from some great 
 physical changes that are going on in the 
 universe. Several new stars have ap- 
 peared for a time, and then vanished; 
 some that are inserted in the ancient 
 catalogues can no longer be found, while 
 others are constantly and distinctly visible, 
 which have not been described by any of 
 the ancients. Some have gradually in- 
 creased in lustre ; others have been gra- 
 dually diminishing, and a great /lumber 
 sustain a periodical variation in their bril- 
 liancy. 
 
 In order to explain these singular 
 changes, Astronomers have supposed that 
 the stars are suns, having part of their 
 surface occupied by large black" spots, 
 which, in the course of their rotation about 
 an axis, present themselves to us, and thus 
 diminish the brilliancy of the star. Some 
 Astronomers suppose the black spots to be 
 permament ; but others are of opinion that 
 the luminious surface of these bodies is 
 subject to perpetual change, which some- 
 times increase ‘their light, and at others 
 extinguish it. 
 
 The stars are divided into orders or 
 classes, according to their apparent mag- 
 nitudes. Those that appear largest to the 
 naked eye have been called stars of the 
 first magnitude ; those that appear next 
 largest the second magnitude, and so on, 
 to the sixth, which comprehends the small- 
 est stars that are visible to the naked eye. 
 All those that can only be perceived by 
 the help of a telescope, are called teles- 
 copic stars. 
 
 The stars of each class are not all of the 
 same apparent magnitude. In the first 
 class, or those of the first magnitude, there 
 are scarcely two that appear of the same 
 size. 
 
 There are also other stars, of interme- 
 diate magnitudes, which astronomers can- 
 not refer to any particular class, and there- 
 fore they place them between two ; but on 
 this subject Astronomers differ considera- 
 bly ; some of them classing a star among 
 
 those of the first magnitude, while others 
 class it among those of the second, and 
 so on with others. 
 
 r In fact it may be said, that there are 
 almost as many orders of stars as there 
 are stars, on account of the great varia- 
 tions observable in their magnitude, colour, 
 brightness, &c. Whether these varieties 
 of appearance are owing to a diversity in 
 their real magnitudes, or from their dif- 
 ferent distances, it is impossible to deter- 
 mine ; but it is highly probable that both 
 of these causes contribute to produce these 
 effects. 
 
 To the naked eye the stars appear of a 
 sensible magnitude, owing to the glare of 
 light arising from the numberless reflec- 
 tions from the serial particles, &c. about 
 the eye ; this makes us imagine the stars 
 to be much larger than they would appear, 
 if we saw them only by the few rays 
 which come directly from them, so as to 
 enter our eyes without being intermixed 
 with others. Any person may be sensible 
 of this, by looking at a star of the first 
 magnitude through a long narrow tube, 
 which, though it takes in as much of the 
 heavens as would hold a thousand such 
 stars, it scarcely renders that one visible. 
 The stars being so immensely distant from 
 the earth, there seems to be but little pro* 
 bability of ascertaining with certainty, the 
 real magnitude of any of them. 
 
 And as the late Sir W. Herschel has 
 very justly remarked, “that in the classifi- 
 cation of stars into magnitudes, there is 
 either no natural standard, or at least 
 none that can be satisfactory; and that 
 the Astronomers who have thus classed 
 them, have referred their size or lustre to 
 some imaginary standard.” 
 
 The same illustrious Astronomer ob- 
 serves, u That the inconvenience arising 
 from this unknown, or at least ill-ascer- 
 tained standard, to which we are to refer 
 is such, that all our most careful observa- 
 tions labour under the greatest disad- 
 vantage. If any dependance could be 
 placed on the method of magnitudes, it 
 would follow that many of the stars had 
 undergone a change in their lustre, or 
 apparent magnitude even since the time of 
 Dr. Flamstead. Not less than eleven 
 stars in the constellation Leo have under- 
 gone a change of lustre since his time.” 
 This change Sir W. Hershel believes has 
 arisen from the uncertainty of the standard 
 of magnitudes, and not from any real 
 change in the lustre of stars : and in order 
 to prevent mistakes of this nature to future 
 observers, Sir William proposes to com- 
 pare the lustre of any particular star with 
 one that is greater, and also with one that 
 is less, both of which are to be as near the 
 proposed star as possible. This he thinks 
 would answer much better for detecting 
 
The artisan. 
 
 -2 §3 
 
 a change in the lustre of any suspected 
 star, than the vague method of magnitudes, 
 which has been hitherto in use among 
 Astronomers. 
 
 As a full display ofSirW/s method would 
 occupy more space than can be allotted to 
 it in this work, those who wish to have 
 more information on the subject, may con- 
 sult the Philosophical Transactions, vol. 
 86, — or a popular work on Astronomy, 
 now publishing by the publishers of this 
 work. 
 
 The variation in the light of the stars 
 has been ascribed to the interposition of 
 the planets that revolve round them ; but it 
 is not probable that the planets are sullici- 
 ciently large, to produce any sensible effect 
 of this kind, at least. 
 
 fHtscellaneous Subjects. 
 
 MEMOIR OF THE LIFE OF NICO- 
 LAS SAUNDERSO'N, L.L.D. 
 
 Nicolas Saunderson, an illustrious Pro- 
 fessor of the Mathematics in the University 
 of Cambridge, and Fellow of the Royal 
 Society, was born in 1682, at Thurlston in 
 Yorkshire; where his father, besides a 
 small estate, enjoyed a place in the excise. 
 When he was a year old, he was deprived 
 by the small-pox, not only of his sight, but 
 of his eye-halls, which were dissolved by 
 abscesses, so that he retained no more idea 
 of light and colours, than if he had been 
 horn blind. He was sent early to a free- 
 school at Penniston, and there laid the 
 foundation of that knowledge of the Greek 
 and Roman languages, which he after- 
 wards improved so far, by his own appli- 
 cation to the classic authors, as to hear the 
 works of Euclid, Archimedes, and Dio- 
 phantus, read in their original Greek. 
 When he had passed some time at this 
 school, his father, whose occupation led 
 him to be conversant in numbers, began to 
 instruct him in the common rules of arith- 
 metic. Here it was that his genius first 
 appeared ; for he very soon became able to 
 work the common questions, to make long 
 calculations by the strength of his memory, 
 and to form new rules to himself for the 
 more ready solving of such problems as are 
 often proposed to learners as trials of skill. 
 At eighteen, he was introduced to the ac- 
 quaintance of Richard West, of Pnder- 
 bank, Esq. a gentleman of fortune, and a 
 lover of the mathematics, who, observing 
 his uncommon capacity, took the pains to 
 instruct him in the principles of Algebra 
 and Geometry, and gave him every encou- 
 ragement in the prosecution of those studies. 
 Soon after, he became acquainted with Dr. 
 Nettleton, who took the same pains with 
 
 him ; and it was to these gentlemen that he 
 owed his elementary knowledge of the ma- 
 thematical sciences. They furnished hint 
 with books, and often read and expounded 
 them to him ; but he soon surpassed his 
 masters, and became fitter to teach them 
 than to learn any thing from them. His 
 passion for learning growing up with him, 
 his father sent him to a private academy at 
 Atlercliff, near Sheffield. But Logic and 
 Metaphysics being the principal learning 
 of this school, were neither of them agree- 
 able to the genius of our author; and there- 
 fore he made but a short stay. He re- 
 mained some time after in the country, 
 prosecuting his studies in his own way, 
 without any other assistant than a good au- 
 thor, and some person that could read it to 
 him : being able, by the strength of his 
 own abilities, to surmount all difficulties 
 that might occur. His education had hi- 
 therto been at the expense of his father, 
 who, having a numerous family, found it 
 difficult to continue it ; and his friends 
 therefore began to think of fixing him in 
 some Avay of business, by which he might 
 support himself. His own inclination led 
 him strongly to Cambridge; and after 
 much consideration, it was resolved he 
 should make his appearance there in a 
 way very uncommon ; not as a scholar, but 
 a master ; for his friends, observing in him 
 a peculiar felicity in conveying his ideas to 
 others, hoped that he might teach the Ma- 
 thematics with credit and advantage, even 
 in the University ; or, if this design should 
 miscarry, they promised themselves success 
 in opening a school for him in London. 
 
 Accordingly, in 1707, being now twenty- 
 five, he was brought to Cambridge by Mr. 
 Joshua Dunn, then a fellow-commoner of 
 Christ’s College; where he resided with 
 that friend, but was not admitted a mem- 
 ber of the college. The society, however, 
 much pleased with so extraordinary a 
 guest, allotted him a chamber, the use of 
 their library, and indulged him in every 
 privilege that could be of advantage to 
 him. But still many difficulties obstructed 
 his design : he was placed here without 
 friends, without fortune, a young man, un- 
 taught himself, to be a teacher of philoso- 
 phy in a university, where it then flourished 
 in the greatest perfection. Whiston was at 
 this time Mathematical Professor, and read 
 lectures in the manner proposed by Saun- 
 derson, so that an attempt of the same 
 kind by the latter, looked like an encroach- 
 ment on the privileges of his office ; but, 
 as a good-natured man, and an encourager 
 of learning, Whiston readily consented to 
 the application of friends, made in behalf 
 of so uncommon a person. Mr. Dunn had 
 been very assidious in making known his 
 character; his fame in a short time had 
 filled the university ; men of learning and 
 
THE ARTISAN. 
 
 
 curiosity grew ambitious and fond of his 
 acquaintance, so that his lecture, as soon 
 as opened, was frequented by many, and in 
 a short time very much crowded. “ The 
 Principia Mathematical Optics , and Arith- 
 metica Universalis , of Sir Isaac Newton,” 
 were the foundation of his lecture ; and 
 they afforded a noble field for displaying 
 his genius. It, was indeed an object of the 
 greatest curiosity to hear a blind youth 
 read lectures in optics, discourse on the 
 nature of light and colours, explain the 
 theory of vision, the effect of glasses, the 
 phenomena of the rainbow, and other ob- 
 jects of sight; nor was the surprise iff his 
 auditors much lessened by reflecting, that 
 as this science is altogether to be explained 
 by lines, and is subject to the rules of 
 geometry, he should be master of these 
 subjects, even under the loss of sight. 
 
 As he was instructing the academical 
 youth in the principles of the Newtonian 
 philosophy, it was not long before he be- 
 came acquainted with the incomparable 
 author, although he had left the university 
 several years ; and enjoyed his frequent 
 conversation concerning the more difficult 
 parts of his works. He lived in friendship 
 also with the most eminent mathematicians 
 of the age; with Halley, Cotes, De Moivre. 
 Upon the removal of Whiston from his 
 professorship, Saunderson’s mathematical 
 merit was universally allowed to be so 
 much superior to that of any other com- 
 petitor, that an extraordinary step was 
 taken in his favour, to qualify him with a 
 degree, which the statutes require. Upon 
 application made by the heads of colleges 
 to the Duke of Somerset, their chancellor, 
 a mandate was readily granted by the 
 queen for conferring on him the degree of 
 Master of Arts : upon which he was chosen 
 Lucasian Professor of the Mathematics, 
 Nov. 1711, Sir Isaac Newton all the while 
 interesting himself very much in the affair. 
 His first performance after he was seated 
 in the chair, was an inaugural speech made 
 in very elegant Latin, and a style truly 
 Ciceronian ; for he was well versed in the 
 writings of Tully, who was his favourite in 
 prose, as Virgil and Horace were in verse. 
 From this time he applied himself closely 
 to the reading of lectures, and gave up his 
 whole time to his pupils. He continued 
 among the gentlemen of Christ’s College 
 till 1723 ; when he took a house in Cam- 
 bridge, and soon after married a daughter 
 of the Rev. Mr. Dickens, Rector of Box- 
 worth, in Cambridgeshire, by whom he had 
 a son and a daughter. In 1728, when 
 George II. visited the university, he was 
 pleased to signify his desire of seeing so 
 remarkable a person ; and accordingly the 
 professor waited upon his majesty in the 
 Henate-house, and was there created Doc- 
 tor of Laws by royal favour. 
 
 Saunderson was naturally of a strong 
 healthy constitution, but being too seden- 
 tary, and constantly confining himself to 
 the house, he became at length a valetudL 
 narian. For some years he frequently com- 
 plained of a numbness in his limbs, which 
 in the spring of 1739, ended in an incurable 
 mortification of his foot. He died April 
 19, aged fifty-seven, and was buried accord- 
 ing to his request, in the chancel at Box- 
 worth. He had. much wit and vivacity in 
 conversation, and many reckoned him a 
 good companion. He had also a great re- 
 gard to truth, but was one of those who 
 think it their duty to express their senti- 
 ments on men and opinions, without re- 
 serve or restraint, or any of the courtesies 
 of conversation, which created him many 
 enemies, and by the obtrusion of infidel 
 opinions, which last he held throughout 
 his extraordinary life.* He is said, how- 
 ever, to have received the notice of his ap- 
 proaching death with great calmness and 
 serenity ; and after a short silence, re- 
 suming life and spirit, talked with as much 
 composure as he usually did when in per- 
 fect health. 
 
 A blind man moving in the sphere of a 
 mathematician, seems a phenomenon dif- 
 ficult to be accounted for, and has excited 
 the admiration of every age in which it has 
 appeared. Tully mentions it as a thing 
 scarcely credible in his own master in phi- 
 losophy, Diodotus, that “ he exercised 
 himself in that science with more assiduity 
 after he became blind, and, what he thought 
 almost impossible to be done without sight, 
 that he described his geometrical diagrams 
 so accurately to his scholars, that they 
 could draw every line in its proper direc- 
 tion.” Jerome relates a more remarkable 
 instance in Didymus of Alexandria, who, 
 “ though blind from his infancy, and there- 
 fore ignorant of the very letters, appeared' 
 so great a miracle to the world, as not only 
 to learn logic, but geometry also, to perfec- 
 tion, which seems the most of any thing to 
 require the help of sight.” But, if we consi- 
 der that the ideas of extended quantity, 
 which are tire chief objects of mathematics, 
 may as well be acquired from the sense 
 of feeling, as that of sight; that a fixed 
 and steady attention is the principal quali- 
 fication for this study, and that the blind 
 are by necessity more abstracted than 
 others, for which reason Democritus^ is 
 . said to have put out his eyes, that he 
 might think more intensely. 
 
 * “ With respect to the infidel part of Saunder- 
 son’s character,” says the Monthly Reviewer, “ we 
 are here naturally reminded of the joke that was- 
 passed on the learned university, on his being 
 elected to fill the Lucasian chair — they have turned 
 out Whiston for believing in but one God , and 
 they have put in Saunderson, who believes iu sm. 
 God at all.” — Monthly Review, v,ol. 3G« 
 
300 
 
 THE ARTISAN. 
 
 An exact and refined ear is what such 
 are commonly blessed with who are de- 
 prived of their eyes ; and Saunderson was 
 perhaps inferior to none in the excellence 
 of his. He could readily distinguish to 
 the fifth part of a note ; and, by his per- 
 formance on the flute, which he had learned 
 as an amusement in his younger years, dis- 
 covered such a genius for music, as, if he 
 had cultivated the art, would have proba- 
 bly appeared as wonderful as his skill in 
 the mathematics. By his quickness in the 
 sense of hearing, he distinguished persons 
 with whom he had only once conversed. 
 He could judge of the size of a room, into 
 which he was introduced, of the distance 
 he was from the wall ; and if ever he had 
 walked over a pavement in courts, piazzas, 
 &c. which reflected a sound, and was after- 
 wards conducted thither again, he could 
 exactly tell whereabouts in the walk he 
 was placed, merely by the note it sounded. 
 
 There was scarcely any part of the ma- 
 thematics on which he had not written 
 something for the use of his pupils : but he 
 discovered no intention of publishing any 
 of his works till 1733. Then his Mends, 
 alarmed by a violent fever that had threat- 
 ened his life, and unwilling that his la- 
 bours should be lost to the world, impor- 
 tuned him to spare some time from his lec- 
 tures, and to employ it in finishing some of 
 his works ; which he might leave behind 
 him, as a valuable legacy both to his fa- 
 mily and the public. He yielded so far to 
 these entreaties, as to compose jn a short 
 time his “ Elements of Algebra which 
 he left perfect, and transcribed fair for the 
 press. It was published by subscription at 
 Cambridge, 1740, in 2 vols. 4to. with a good 
 mezzotinto print of the author, and an ac- 
 count of his life and character prefixed. 
 
 The mode by which Saunderson per- 
 formed his calculations, was by a species 
 of palpable arithmetic; that is, a method 
 of performing operations in arithmetic, 
 solely by the sense of touch. The appara- 
 tus he employed, consisted of a table raised 
 upon a small frame, so that he could apply 
 his hands with equal ease both above and 
 below it. On this table were drawn a 
 great number of parallel lines which were 
 crossed by others at right angles ; the 
 edges of the table were divided by notches 
 half an inch distant from one another, and 
 between each notch there were five pa- 
 rallels ; so that every square inch was 
 divided into a hundred little squares. At 
 each angle of the squares where the pa- 
 rallels intersected one another, a hole was 
 made quite through the table. In each 
 hole he placed two pins, a large and a small 
 one. It was by the various arrangements 
 of the pins, that Saunderson performed all 
 his operations. 
 
 ARCHITECTURE. 
 
 ON THE CONSTRUCTION OF ARCHES. 
 
 As we have now given a short account 
 of the five Orders, and also pointed out 
 the peculiarities of Gothic Architecture, 
 we shall here endeavour to explain the 
 particular parts and properties of arches 
 and bridges. 
 
 A series of truncated wedges resting on 
 two immoveable supports, and having the 
 planes of the faces that press against each 
 other, perpendicular to a vertical plane 
 (represented by the plane of the paper), 
 as in the following figure, form what are 
 called arches in Architecture. 
 
 0 ME 
 
 The most advantageous construction of 
 arches, requires that the parts should be 
 so adjusted as to be in equilibrio, or to 
 balance one another by their weight only ; 
 when this is the case, the arch is called an 
 arch of equilibration. 
 
 Some other definitions are necessary for 
 understanding the construction of these 
 arches. The truncated wedges of which 
 the arch is composed, and which are 
 usually of stone, are called the voussoirs ; 
 each course of these wedges forming one 
 voussoir. The central voussoir is called 
 the key-stone. The surfaces which sepe- 
 rate the voussoirs from one another, are 
 called the joints. The interior curve of 
 the arch is called the intrados ; the exte- 
 rior, or that which limits all the voussoirs, 
 when they are in equilibrium, is called the 
 extrados. The abutments are masses of 
 masonry, at each end, that support the 
 arch. The beginning of the arch is called 
 the spring of the arch ; the middle, the 
 crown ; the parts between the spring and 
 the crown, the haunches. The part of the 
 abutment from which the arch springs, is 
 termed the impost. 
 
 If the weights of the voussoirs be to each 
 other, as the difference of the tangents 
 which A B, D C, E F, &c. make with the 
 verticle MN (see the foregoing figure), 
 the whole will be in equilibrio. This fol- 
 lows from the properties of the wedge. 
 See page 148. 
 
 This theorem is sufficient for the con- 
 struction of arches of any form, because 
 when the curve of the intrados is given, it 
 
THE ARTISAN. 
 
 301 
 
 determines the weight of every individual 
 voussoir. The application of it in par- 
 ticular cases, admits, however, of being 
 greatly simplified. 
 
 A remarkable instance of this happens 
 when the arch is a circle, and when the 
 joints, (which are usually made perpen- 
 dicular to the curve of the intrados) inter- 
 sect in the same point. 
 
 In a circular arch , the weights of the 
 voussoirs should be as the differences of 
 the tangents of the arches, reckoned from 
 the crown. 
 
 This is nothing more than the above 
 proposition, applied to a particular case. 
 Thus in the following figure : 
 
 If B be the crown of a circular arch, the 
 weight of the voussoir LKNM should be 
 to that of the voussoir M N P O, as the 
 tangent of B N, minus the tangent of B K, 
 to the tangent of B P, minus the tangent of 
 B N ; or if, from a given point D, DH be 
 drawn perpendicular to AC; and if the 
 joints KL, &c. be produced, to cut in 
 E, F, and G, the weights of the voussoirs 
 must be as the segments D E, E F, F G, in 
 order to produce an equilibrium. 
 
 As the stones themselves cannot always 
 be made in the proportion thus required, 
 the wedges, of which they make parts, are 
 supposed to be extended upward by 
 courses of masonry. The whole mass in- 
 cluded between the plane of the joints 
 
 produced, as far as that masonry extends, 
 is understood to make up the, weight of 
 the voussoir. It is the business of the 
 theory to calculate this weight; and con- 
 struct the curve which bounds the vous- 
 soirs, when so produced. 
 
 To the Editor of the Artisan. 
 
 Sir, 
 
 Impelled by the dictates of humanity, 
 and perceiving that a miscellaneous part 
 always forms a portion of each number of 
 your valuable scientific work, I am induced 
 to request a place in it on a subject of par- 
 ticular interest to those who are obliged to 
 navigate the seas in the coasting trade 
 during the stormy months of Winter, and 
 also to many humane individuals residing 
 on the coast, who at that boisterous season 
 have been so often called upon to witness 
 the dreadful effects of a “ Winter’s Gale,” 
 when 
 
 “ Again the dismal prospect opens round. 
 
 The wreck, the shore, the dying, and the drown’d. ’ 
 
 It is not my intention to attempt a des- 
 cription of what must be the feelings of 
 those, who are in many cases obliged to be 
 helpless spectators of such distressing 
 scenes ; but by pointing out the means of 
 assistance, which, though long since par- 
 tially known, has been too much generally 
 neglected, I hope to enable them to ex- 
 change their hitherto melancholy feelings 
 on such occasions, for those of joy as in- 
 describable, when they shall have rescued 
 their fellow-creatures from a watery grave, 
 instead of being constrained to witness 
 their premature destruction. 
 
 In the year 1791, Mr. John Bell, a Ser- 
 jeant of Artillery, made several experi- 
 ments before a committee of the Society of 
 Arts, at Woolwich, wherein he plainly 
 proved the practicability of throwing a 
 rope from a mortar over a stranded vessel ; 
 by which means such a communication 
 might be established between the people 
 on shore, and the wreck, as would enable 
 the former to save the lives of the crew. 
 
 The following is a figure and brief de- 
 scription of Mr. Bell’s apparatus. 
 
3 02 
 
 THE ARTISAN. 
 
 Fig. 1, represents an 8-inch mortar on 
 its carriage, the chamber of which being 
 constructed to contain only one pound of 
 powder, effectually secures it from burst- 
 ing — -2. A cast-iron shell filled with lead, 
 which weighed 75 lbs — 3. The grommet, 
 or double rope, which was white three- 
 inch; this connected the shell and line — 
 4. The line wound round poles or hand- 
 spikes, which were withdrawn when the 
 mortar was fired.— -A reel has lately been 
 invented as a substitute for the handspikes : 
 but if the line is coiled in a ziz-zag direc- 
 tion before, and on one side of the mortar, 
 it will be found to go out more freely than 
 in any other way. The rope first tried by 
 Mr. Bell, was a deep-sea line, of which 
 ICO yards weighed 18 lbs: this line with 
 the shell was thrown 400 yards from the 
 mortar, at the elevation of 45°, with a 
 charge of only 15 oz. of powder. 
 
 Fig. 2 is a seperate view of the shell, 
 with the grommet and end of the line 
 attached thereto, explained by the same 
 figures. 
 
 This excellent invention, which, as Mr. 
 Bell observes, is so exceedingly simple, 
 that any person once seeing it done, would 
 want no farther instructions, I trust, 
 through the medium of your widely cir- 
 culating work, will become more generally 
 known and practised upon the coast ; for 
 as it is the exclusive attribute of the Al- 
 mighty to give life, the most exalted act of 
 man must be to save the life of his fellow 
 man. 
 
 Should a farther description be required, 
 I beg leave to refer you and your numerous 
 readers to the 10 vol. of the Trans. Soc. 
 Arts, and 20th vol. of Nicholson’s Phil. 
 Journal, from which 1 have made this 
 abridgment, for the benefit of those who 
 may not be able to consult these expensive 
 works. I am, Sir, 
 
 Your obedient humble servant, 
 
 Navarchus. 
 
 ON THE METHOD OF WARMING 
 APARTMENTS BY HEATED AIR. 
 
 Sn place of an expensive apparatus, 
 which is attainable by the rich alone, M. 
 Meissner has given us a method, which is 
 equally adapted to the use of a palace or 
 a cottage; costing little, and piesenting 
 every advantage possessed by the most ex- 
 pensive, at the same time that its use is 
 unattended by their inconveniences ; con- 
 tributing very much towards the salubrity 
 of the air in houses, and is at the same 
 time proof against fire. 
 
 In a small room called the stove-room, 
 and where lie places a stove (either ot iron 
 or earthenware) Mr. Meissner conducts, by 
 means of sheet iron pipes, a current of 
 
 heated air, into those apartments which he 
 would warm ; at the same time that a cur- 
 rent of cold air is forced back into the 
 chamber of heat, from the room where the 
 heated air has found admission, thus es- 
 tablishing a circulation which includes the 
 whole mass of air in the room, the tempe- 
 rature of which is desired to be encreased ; 
 and which does not cease until there no 
 longer exists any difference in the tempe- 
 rature of the different strata of air, which 
 are in communication with the stove appa- 
 ratus. To produce this effect, the current 
 of heated air be : ng specifically the lightest, 
 must necessarily pass through pipes which 
 are placed high in the walls of the stove- 
 room, near the ceiling, and flows at different 
 heights into the room to be heated ; on 
 the other hand the cold air being specifi- 
 cally the densest, will flow through corres- 
 ponding pipes fixed low down in the wall 
 of the rooms to be heated from other pipes, 
 placed at the same part in the walls of the 
 stove-room. 
 
 The apparatus may be constructed either 
 on the ground floor or in the cellar ; it may 
 also be placed in a corner of a kitchen or 
 in a chimney, which has a general commu- 
 nication with the chimneys of the house ; 
 in this case, the communication between 
 the rooms and the apparatus maybe formed 
 by simply making holes in the chimney- 
 walls of each room; in the former by 
 means of the pipes. These holes and the 
 pipes likewise, must each be furnished 
 with dampers with which to increase, di- 
 minish, or exclude altogether the currents 
 of air to or from the stove-room at the will 
 of its occupants. 
 
 But, that each room must necessarily be 
 furnished with a double communication 
 with the stove-room will be sufficiently un- 
 derstood, when the above description is 
 carefully perused. 
 
 When a change of air is requisite, there 
 is a communication between the outward 
 air and each room, and also one between 
 the outward ajr and the stove-room, fur- 
 nished likewise with the same means of 
 diminishing or excluding its admission ; 
 thus enabling the rooms to be thoroughly 
 aired without opening the doors or win- 
 dows. 
 
 It is to Mr. Meissner, also, that w r e owe 
 an apparatus which he designates a man- 
 tle ; to be used in case only one apartment 
 is required to be heated. The stove is en- 
 closed in a sort of envelope (formed of 
 potters’ earth) and of its exact form. The 
 intermediate space between this covering 
 and the stove is necessarily filled with air, 
 and in this way the whole may be carried 
 into the room where the heat is required. 
 The upper orifices of the envelope repre- 
 sent the highest pipes of the stove-room; 
 and the lower ones, the lower pipes. Tho 
 
THE ARTISAN. 
 
 303 
 
 instant the temperature of the air in the in- 
 termediate space is heightened, it flows 
 through the upper orifices and is immedi- 
 ately succeeded by the cold air flowing 
 through the lower orifices, thus exhibiting 
 in miniature the action of the stove-room. 
 
 Of the advantages to be derived from 
 the use of this apparatus it is almost un- 
 necessary to speak. Economy in fuel, pre- 
 vention of any accidents by fire : should it 
 be constructed in the kitchen, a great 
 baving in coals will take place ; and it will 
 be much easier to take care of one Are than 
 of several. 
 
 METHOD OF POUNCING UPON 
 
 CLOTH," THE DESIGNS WITH 
 WHICH THEY ARE TO BE EM- 
 BROIDERED. 
 
 The ordinary means employed in this 
 art, are as follows. Having pricked any de- 
 sign upon paper with a needle, it is dusted 
 over with a piece of muslin containing 
 charcoal very finely pounded and sifted, 
 the dust gets through the holes pricked on 
 the design, and settles on the cloth which 
 is to be embroidered ; then with a black 
 or white pencil, according to the colour of 
 the cloth, the marks left by the charcoal- 
 dust are exactly to be followed. 
 
 The person who does this ought either 
 to possess a knowledge of drawing, or else 
 to have much adroitness, in order that the 
 form of the design may be exactly pre- 
 served ; but often before the pattern can 
 be finished the dust flies off, and thus occa- 
 sions much embarrassment to the workers. 
 Messrs. Revol and Rigoudet perceiving all 
 the difficulties which attend this method 
 of proceeding, have sought for, and at 
 length ingeniously contrived a remedy ; 
 and the patent which they obtained for 
 their invention having expired, we shall 
 proceed to describe the means they em- 
 ploy. 
 
 Previously to this process no means of 
 fixing the dust upon the cloth had ever 
 been ascertained, and every person who 
 was employed in this work was obliged to 
 trace with a pen or pencil the design form- 
 ed by the dust, which not only occupied a 
 great part of their time, but often occa- 
 sioned mistakes in the figure to be em- 
 broidered. The new method possesses the 
 advantages of being able to convey to the 
 cloth the exact figure of the design, and 
 facilitates the progress of the embroiderers, 
 allowing them to attain the greatest exac- 
 titude in their work, and sparing them the 
 trouble and time they had employed in re- 
 tracing the design. 
 
 The method of preparing the composition 
 of the powder for pouncing in black, is as 
 follows : 
 
 Place an earthen pot over the fire, and 
 put into it a given quantity of gum mastic, 
 adding thereto one-thirtieth part of wax, 
 oil, tar, or pitch ; when this is melted, 
 throw into the pot as much lampblack as 
 may be deemed necessary for the colour of 
 the pounce, stirring the mixture all the 
 time with an iron spoon. W hen all is well 
 mixed, take it from the fire and pour it into 
 sheets of paper, with the corners turned 
 up to prevent its running over, and, when 
 well cooled, pound and sift it, and enclose 
 it in a piece of muslin. Pounce with this 
 whatever design it is intended to form upon 
 any kind of cloth, and then it is instantly 
 to be fixed on the cloth, by passing it over 
 a pan of coals of a gentle heat, or by going 
 over it with a hot iron. In this latter case 
 it is necessary to put a sheet of paper be- 
 tween the design and the iron. Then the 
 design will remain on the cloth neatly and 
 correctly. 
 
 To make a white powder, — Take a 
 known quantity of gum mastic, and melt 
 it. in a glazed earthen pot over a slow 
 fire ; add to this ^th part of virgin wax, 
 and when the whole is melted, add as 
 much fine white silver as the gum and wax 
 will imbibe, taking great care all the while 
 to stir it in proportion as the white is 
 added. The whole, when well mixed, 
 must undergo the same preparation as the 
 black powder. 
 
 DIRECTIONS FOR ACQUIRING A 
 KNOWLEDGE OF THE FIXED 
 STARS. 
 
 BY DAVID THOMSON. 
 
 In a recent number of this work we gave 
 a short account of an extensive and neatly 
 executed Celestial Atlas. Since the pub- 
 lication of that number we have seen a 
 small work, containing directions for ac- 
 quiring a knowledge of the principal fixed 
 stars, without maps or diagrams. The 
 method of accomplishing this is by imagi- 
 nary lines, which are supposed to be drawn 
 from some conspicuous star, or cluster of 
 stars, previously known, through others 
 that are also known, in order to point out 
 some star which is unknown ; "and after- 
 wards to serve as an index to it, when it is 
 required to be distinguished from others. 
 
 This plan is not neiv, but it is here 
 adopted more extensively than in any other 
 work we have met with ; and we are con- 
 vinced, that if the imaginary lines and 
 figures to which the stars are referred in 
 this little work, be traced by the eye of a 
 discerning spectator, they will point out, 
 and also serve to fix on the mind the rela- 
 tive places of the principal fixed stars. 
 This to some may appear a matter of little 
 
304 
 
 THE ARTISAN. 
 
 moment; but to the mariner who traverses 
 the pathless ocean, and has not only the 
 'property, but the lives of lus fellow-crea- 
 tures under his care, it is of the very utmost 
 importance. And, as the intelligent author 
 of this little work very justly observes, 
 “ It is much to be lamented that many who 
 have the charge of vessels at sea, should 
 have so little knowledge of the stars, 
 which often afford opportunities of ascer- 
 taining the situation of a ship during the 
 night, when observations of the sun cannot 
 be obtained perhaps for several days toge- 
 ther. The navigator, therefore, who is 
 accustomed to determine the place of his 
 ship by means of the stars, has a very 
 great advantage, both as regards safety 
 and dispatch, over the one who trusts en- 
 tirely to observations of the sun” 
 
 The justness of these observations cannot 
 be denied ; and yet, strange to say, a very 
 great proportion of mates and captains of 
 merchant vessels are so little acquainted 
 with the stars, as to be incapable of dis- 
 tinguishing one from another, at least for 
 any useful purpose. But the intelligent 
 seaman knows that the true situation of 
 any place upon the earth can only be de- 
 termined by means of a body in the hea- 
 vens, and that every star he can see has its 
 latitude, longitude, &c. better settled than 
 any spot upon the earth ; and consequently 
 may be employed for this latter purpose, 
 even in the midst of the trackless ocean, 
 when the sun and moon are not to be seen. 
 
 The little work before us cannot fail to 
 be useful to those who go to sea, as it con- 
 tains a number of examples of finding the 
 latitude, &c. both by the Sun and Stars ; 
 and likewise several valuable tables, one 
 of which appears to us to be new, and must 
 be useful both at sea and land, to all those 
 who are accustomed to make observations 
 on the stars. 
 
 This is a table containing the time to be 
 added to the right ascension of a star, to 
 find the time of its passing the meridian on 
 any day of the year. This table we may, 
 perhaps, take the liberty of inserting in 
 another part of this work. 
 
 We perceive that the small work which 
 we have here thought proper to notice, is 
 to form an appendix or supplement to a 
 larger work, containing a set of Lunar and 
 Horary Tables, intended for finding the 
 Longitude at Sea by means of Lunar Obser- 
 vations and Chronometers. This work we 
 may also be induced to notice when it 
 makes its appearance, as we conceive that 
 whatever tends to improve the art of navi- 
 gation, must also improve the trade and 
 resources of this commercial country. 
 
 SOLUTIONS OF QUESTIONS. 
 
 Quest. 40, answered by G. G. C. ( the 
 proposer.) 
 
 As the weights of balls are as the cubes 
 of their diameters ; and as an iron ball 4 
 inches diameter, weighs 9 lbs ; the diame- 
 ter of the ball or orifice in question, will 
 
 be (32x7^) ^ zz 6*105142 inches, and its 
 area (6T05142) 3 x *7854-r-144, or *2032914 
 sq. foot. Now the velocity with which the 
 water is z: 2 (16^ X 8) f ~ 22*686266 
 feet per second, and the quantity of water 
 that enters in 1 second, is 22*68626 X 
 *2032914, or 4*611922 cubic feet ; conse- 
 quently, in 10 minutes there will enter 
 4*611922 X 600 =z 2767*1532 cubic feet of 
 sea water, which at 1030 oz. per cubic 
 foot, weighs, 79 tons 10 cwt 1 qr. 27 lb 7oz. 
 
 As the actual discharge rs to the theore- 
 tical discharge as 62 to 1 (see. Artisan, 
 page 59), the above quantity diminished in 
 this ratio, is 49 tons, 6 cwt. 12 lb. 
 
 Another gentleman sent us a solution of 
 this question ; but he will perceive, by 
 the above, that the latter part of his solu- 
 tion is erroneous. Ed. 
 
 Quest. 41, (page 272) answered by J. 
 Johnston, Elm-street , Gray’s-inn-lane. 
 
 Multiply the number of beats in a mi- 
 nute by itself, and divide the number 
 141120* by the product, which will give 
 the length in inches. 
 
 To apply this in the present question, let 
 equal the number of beats, and it must 
 also equal the number of inches. Then, 
 141120 
 
 — — 2 — — a, or L41120 “a 3 , the cube of 
 
 a 7 7 
 
 the unknown number : the cube root of 
 which is 52*7, the number of inches in 
 length, and beats in a minute, or 3124 in 
 an hour. 
 
 This question was also correctly solved 
 by Mr. J. Whitcombe, Cornhill, and by 
 the Proposer. 
 
 By mistake there is a question at page 
 228, which is also numbered 41 ; but though 
 we have received four different solutions 
 to it, we cannot insert any of them, till we 
 have leisure to examine them, for no two 
 of them nearly agree. Ed. 
 
 QUESTIONS FOR SOLUTION. 
 
 Quest. 45, proposed by Mr. J. Taylor. 
 
 Observing 2 men forcing round a screw, 
 whose threads were one inch asunder; 
 and the lever applied to the head of the 
 screw, was 10 feet long : from this data I 
 demand the pressure of the screw, the 
 workmen urging the fever with a force 
 equal to 200 pounds ? 
 
 * This number is found by squaring 60, the beats 
 in a minute, and multiplying the product by 39*2 
 inches, the length of a pendulum that vibrates 
 seconds. 
 
THE ARTISAN. 
 
 305 
 
 GEOMETEY. 
 
 PROPOSITION VII. 
 Theorem, — If a straight line he divided 
 into any two parts, the squares of the whole 
 line, and of one of the parts, are equal to 
 twice the rectangle contained by the whole 
 and that part, together ivith the square of 
 the other part. 
 
 Let the straight line A B be divided into 
 any two parts in the point C ; the squares 
 of A B, B C, are equal to twice the rect- 
 angle AB, BC, together with the square 
 of A C. 
 
 Upon AB describe the square of ADEB, 
 and construct the figure as in the preced- 
 ing propositions ; and because A G is equal 
 to GE, add to each of them CK; the 
 whole A K is therefore equal to the whole 
 A C B 
 
 CE; therefore A K, CE, are double of 
 A K : But A K, C E, are the gnomon AKF, 
 together with the square CK; therefore 
 the gnomon AKF, together with the 
 square CK, is double of AK: But twice 
 the rectangle A B, B C, is double of A K, 
 for B K is equal to B C : Therefore the 
 gnomon A K F, together with the square 
 C K, is equal to twice the rectangle A B, 
 BC: To each of these equals add HF, 
 which is equal to the square of A C ; there- 
 fore the gnomon AKF, together with the 
 squares C K, H F, is equal to twice the 
 rectangle A B, B C, and the square of AC : 
 But the gnomon AKF, together with the 
 squares CK, HF, make up the whole 
 figure ADEB and CK, which are the 
 squares of AB and BC: therefore the 
 squares of A B and B C are equal to twice 
 the rectangle AB, BC, together with the 
 square of A C. Wherefore, if a straight 
 line, &c. Q. E. D. 
 
 Cor. The square on the difference of two 
 lines, is equal to the square of those lines 
 diminished by twice their rectangle. 
 
 Let the whole line be 12, and let it be 
 divided into the two parts 8 and 4 : Then 
 the square of (12) the whole line is 144, 
 and the square of (4) one of the parts, is 
 16; the sum of these is 160. Now the 
 
 Vol. I.— No. 20, 
 
 rectangle of 12 and 4 is 48, and twice their 
 rectangles is 96, to which add the square 
 of the other part (8), or 64, and the sum 
 will also be 160. Hence the truth of the 
 proposition is established. 
 
 PROPOSITION VIII. 
 
 Theorem. — If a straight line be divided 
 into any two parts, four times the rect- 
 angle contained by the whole line, and 
 one of the parts, together with the square 
 of the other part, is equal to the square of 
 the straight Vine, which is made up of the 
 whole and that part. 
 
 Let the straight line AB be divided into 
 any two parts in the point C ; four times 
 the rectangle AB, BC, together with the 
 square of A C, is equal to the square of the 
 straight line made up of A B and B C 
 together. 
 
 Produce A B to D, so that B D be equal 
 to C B, and upon A D describe the square 
 AEFD; and construct two figures such 
 as in the preceding. Because C B is equal 
 to B D, and that C B is equal to G K, and 
 B D to K N ; therefore G K is equal to 
 K N : For the same reason, P R is equal to 
 RO; and because CB is equal to BD, 
 and G K to K N, the rectangle C K is 
 equal to B N, and G R to R N ; but C K is 
 equal to RN, because they are the com- 
 plements of the parallelogram C O ; there- 
 fore also B N is equal to GR ; and the four 
 rectangles BN, CK,GR, RN are there- 
 fore equal to one another, and so are quad- 
 ruple of one of them C K : Again, because 
 A C B D 
 
 C* 
 
 K 
 
 
 P 
 
 
 R 
 
 
 
 
 E H L F 
 
 C B is equal to BD, and that B D is equal 
 to B K, that is, to C G ; and C B equal to 
 GK, that is, to GP; therefore CG is 
 equal to GP : and because CG is equal to 
 GP, and P R to R O, the rectangle A G is 
 equal to M P, and P L to RF : But M P is 
 equal to P L, because they are the comple- 
 ments of the parallelogram M L ; where- 
 fore A G is equal also to R F : Therefore 
 the four rectangles AG, M P, PL, R F, 
 are equal to one another, and so are quad- 
 ruple of one of them A G. And it was de- 
 monstrated, that the four CK, B/N, GR, 
 and RN are quadruple of CK. There- 
 X 
 
306 
 
 THE ARTISAN. 
 
 fore the eight rectangles which contain the 
 gnomon A OH, are quadruple of AK: 
 and because A K is the rectangle con- 
 tained by A B, B C, for B K is equal to 
 B C, four times the rectangle A B, B C is 
 quadruple of A K : But the gnomon AOH 
 was demonstrated to be quadruple of A K ; 
 therefore four times the rectangle AB, B C, 
 •is equal to the gnomon A O H. To each 
 of these add X H, which is equal to the 
 square of A C : Therefore four times the 
 rectangle A B, B C together with the 
 square of AC, is equal to the gnomon 
 AOH and the square X H : But the 
 gnomon AOH and X H make up the 
 figure AEFD, which is the square of 
 A D : Therefore four times the rectangle 
 A B, B C, together with the square of A C, 
 is equal to the square of A D ; that is, of 
 A B and B C added together in one straight 
 line. Wherefore, if a straight line, &c. 
 Q. E. D. 
 
 Let the whole line be 12, and the parts 
 8 and 4, as in the last proposition. Four 
 times the rectangle of 12 and 4 is 192 ; to 
 which add the square of (8) the other 
 part, and the sum will be 256. Now the 
 line made up of the whole (12) and the 
 part (4) employed to form the rectangle, is 
 16, the square of which is 256, the same as 
 the sum of the rectangles and square, 
 which was to be shown. 
 
 PROPOSITION IX. 
 
 Theorem. — If a straight line be divided 
 into two equal , and also into two unequal 
 parts; the squares of the two unequal 
 parts are together double of the square of 
 half the line , and of the square of the line 
 between the points of section . 
 
 Let the straight line A B be divided at 
 the point C into two equal, and at D into 
 two unequal parts : The squares of A D, 
 D B are together double of the squares of 
 AC, CD. 
 
 From the point C draw CE at right 
 angles to A B, and make it equal to A C 
 or C B, and join E A, E B ; through D 
 draw D F parallel to C E, and through F 
 draw FG parallel to AB ; and join AF : 
 Then, because A C is equal to C E, tho 
 angle EAC is equal to the angle AEC ; 
 and because the angle ACE is a right 
 angle , the two others AEC, EAC to- 
 gether make one right angle ; and they 
 are equal to one another; each of them, 
 
 therefore, is half of a right angle. For the 
 same reason each of the angles CEB, 
 EB C is half a right angle ; and therefore 
 the whole A E B is a right angle : And be- 
 cause the angle GEF is half a right 
 angle, and EGF a right angle, for it is 
 equal to the interior and opposite angle 
 E C B, the remaining angle E F G is half a 
 right angle; therefore the angle GEF is 
 equal to the angle E FG, and the side EG 
 equal to the side G F : Again, because the 
 angle at B is half a right angle, and FDB 
 a right angle, for it is equal to the interior 
 and opposite angle ECB, the remaining 
 angle B F D is half a right angle ; therefore 
 the angle at B is equal to the angle B F D, 
 and the side D F to the side D B : And be- 
 cause A C is equal to C E, the square of 
 AC is equal to the square of CE ; there- 
 fore the squares of A C, C E, are double 
 of the square of A C : But the square of 
 E A is equal to the squares of AC, C E, 
 because A C E is a right angle ; therefore 
 the square of E A is double of the square 
 of A C : Again, because E G is equal to 
 G F, the square of E G is equal to the 
 square of GF; therefore the squares 
 of E G, G F are double of the square of 
 G F ; but the square of E F is equal to the 
 squares of E G, G F ; therefore the square 
 of E F is double of the square G F ; and 
 G F is equal to C D ; therefore the square 
 of E F is double of the square of C D : 
 But the square of A E is likewise double 
 of the square of A C ; therefore the squares 
 of A E, E F are double of the squares of 
 A C, CD : And the square of A F is equal 
 to the squares of A E, E F, because A E F 
 is a right angle ; therefore the square of 
 A F is double of the squares of A C, C D : 
 But the squares of A D, D F are equal to 
 the square of A F, because the angle AD F 
 is a right angle ; therefore the squares of 
 A D, D F are double of the squares of AC, 
 C D : And D F is equal to D B ; therefore 
 the squares of A D, D B are double of the 
 squares of A C, C D. If therefore a 
 straight line, &c. Q. E. D. 
 
 Let the whole line be 12, then each of 
 the equal parts will be 6 ; and let the un- 
 equal parts be 8 and 4, consequently the 
 part between the points of section, will be 
 2. Now the sum of the squares of the un- 
 equal parts is 80; and double^the square of 
 (6) half the line, is 72, [to which add 
 double the square of (2) the part between 
 the points of section, and the sum will also 
 be 80. Hence the truth of the proposition 
 is established. 
 
 PROPOSITION X. 
 
 Theorem. — If a straight line be bisected , 
 and produced to any point , the square of 
 the whole line thus produced , and the 
 square of the part of it produced, are to- 
 gether double of the square of half the line 
 bisected , and of the square of the line 
 B made up of the half and the part produced. 
 
THE ARTISAN 
 
 807 
 
 Let the straight line AB be bisected in 
 C, and produced to the point D ; the 
 squares of AD, D B are double of the 
 Squares of AC, C B. 
 
 From the point C draw C E at right 
 angles to A B : And make it equal to A C 
 or CB, and join AE, EB; through E 
 draw E F parallel to A B, and through D 
 draw D F parallel to CE: And because 
 the straight line EF meets the parallels 
 EC, FD, the angles C E F, EFD are 
 equal to two right angles ; and therefore 
 the angles BE F, EFD are less than two 
 right angles ; but straight lines which with 
 another straight line make the interior 
 angles upon the same side less than two 
 right angles, do meet if produced far 
 enough : Therefore E B, F D shall meet, if 
 produced towards B D : Let them meet in 
 G, and join A G : Then, because A C is 
 equal to C E, the angle C E A is equal to 
 the angle EAC; and the angle A C E is a 
 fight angle ; therefore each of the angles 
 CEA, EAC is half a right angle: For 
 the same reason each of the angles CEB, 
 E B C is half a right angle ; therefore 
 A E B is a right angle ; And because EB C 
 is half a right angle, DBG is also half a 
 right angle, for they are vertically opposite ; 
 but B D G is a right angle, because it is 
 equal to the alternate angle D C E ; there- 
 fore the remaining angle DGB is half a 
 right angle, and is therefore equal to the 
 angle DBG; wherefore also the side B D 
 is equal to the side D G : Again, because 
 E F 
 
 E GF is half a right angle, and that the 
 angle at F is a right angle, because it is 
 equal to the opposite angle E C D, the re- 
 ihaining angle F E G is half a right angle, 
 and equal to the angle EGF; wherefore 
 also the side G F is equal to the side F E. 
 And because EC is equal to C A, the 
 square of E C is equal to the square of C A ; 
 therefore the squares of E C, C A are 
 double of the square of CA: But the 
 square of E A is equal to the squares of 
 EC, CA; therefore the square of EA is 
 double of the square of AC: Again, be- 
 cause G F is equal to FE, the square of 
 GF is equal to the square of FE; and 
 therefore the squares of G F, F E are dou- 
 ble of the square of E F : But the square 
 of E G is equal to the squares of G F, F E; 
 
 therefore the square of E G is double of 
 the square of E F : And E F is equal to 
 C D ; wherefore the square of E G is dou- 
 ble of the square of CD: But it was de- 
 monstrated, that the square of E A is dou- 
 ble of the square of AC; therefore the 
 squares of A E, E G are double of the 
 squares of AC, CD: And the square of 
 A G is equal to the squares of AE , E G ; 
 therefore the square of A G is double of 
 the squares of A C, CD: But the squares 
 of A D, G D are equal to the square of A G ; 
 therefore the squares of A D, D G are dou- 
 ble of the squares of A C, C D : But D G is 
 equal to DB; therefore the squares of 
 A D, D B are double of the squares of 
 AC, CD. Wherefore, if a straight line, 
 &c. Q. E. D. 
 
 This proposition is exactly like the pre- 
 ceding, if the sum of the half line and pro- 
 duced part be considered the part between 
 the points of section. 
 
 Thus let the line be 12 as before, and 
 the part produced, or added 2; then the 
 whole linedhus produced or s formed, will be 
 14, and the half line and produced part will 
 be 8. Now the square of the whole line 
 (14) is 196, and the square of (2) the part 
 produced, or added is 4, therefore their 
 sum is 200 ; but double the square of half 
 the line (6) is 72, and double the square of 
 the half line and produced part (8) is 
 128, the sum of which is 200, therefore the 
 truth of the proposition is established. 
 
 MBCHAH1CS. 
 
 ON THE REGULATION OF MACHINERY. 
 
 Amid the great variety of machines 
 which have been applied to the practical 
 purposes of life, there is scarcely one in 
 which there is not a deviation from a uni- 
 formity of action, arising either from the 
 nature of the impelling power, from the 
 nature of the machinery to which it is 
 applied, or from the nature of the work to 
 be performed. 
 
 1. When horses or men are the first 
 movers of machinery, the mechanical 
 force which they exert is liable to great 
 variation. When fresh and vigorous, they 
 act with considerable force and steadiness ; 
 but after pulling for some time, the com- 
 mencement of fatigue impairs their activity; 
 and when they have to strive against a 
 great resistance, they indulge in frequent 
 and short relaxations, and then recom- 
 mence their labour with renewed vigour. 
 A constant variation in the velocity of the 
 machine, is the necessary consequence of 
 this unequal action, and by this means the 
 communicating parts of the machinery are 
 not only injured, but the work itself is 
 often ill performed, and the animal is sub- 
 ject to additional fatigue, in dragging the 
 whole machinery from a state of resfc» 
 
SOS 
 
 THE ARTISAN. 
 
 When the first mover is inanimate, 
 an inequality of force evidently arises 
 from a variation in the velocity of the 
 wind, from an increase or diminution of 
 water, arising from sudden rains and great 
 droughts ; or from an increase or decrease 
 of steam in the boiler, arising from a varia- 
 tion in the heat of the furnace. In the 
 spiral spring, too, its force is a maximum 
 when it begins to uncoil itself, and it gra- 
 dually diminishes till its force is entirely 
 exhausted. 
 
 A desultory motion in machines 
 arises also from the nature of the machi- 
 nery by which the power is applied. In 
 the single-stroke steam engine, the impel- 
 ling power is so unequal, that for two or 
 three seconds it does not act at all ; and 
 even in the double-stroke steam engine, 
 the beam and all its appendages are 
 brought completely to rest, and must be 
 again dragged into motion at the returning 
 stroke. In applying his power by means 
 of a crank, a man exerts the greatest force 
 when he pulls the handle upwards from 
 the height of his knee ; and his force is a 
 minimum, when the handle being in a ver- 
 tical position, is thrust from him in a hori- 
 zontal direction. Hence Desaguliers 
 found, that when this irregularity was cor- 
 rected by placing two handles at right 
 angles to one another, and making two 
 men drive them, their individual action 
 was 35, whereas with one handle it was 
 only 30. 
 
 A variation of velocity may frequently 
 arise from the nature of the work to be 
 performed. In thrashing-mills on a small 
 scale, when too much of the corn is taken 
 in by the fluted rollers, the increase of re- 
 sistance immediately retards the machi- 
 nery, and^communicates a desultory motion 
 even to the water-wheel itself. In the 
 pile engine invented byM. Vauloue, a si- 
 milar variation arises from the nature of 
 the work, which is to raise a great weight 
 in order to drive piles. The machine is 
 drawn by horses, and as soon as the ram 
 or weight is elevated and discharged, the 
 resistance against which the horses have 
 been struggling is suddenly removed, and 
 they would instantly fall to the ground, 
 were not this sudden diminution in the re- 
 sistance counteracted by a mechanical con- 
 trivance. 
 
 The simplest of all contrivances for re- 
 gulating machinery, are fly-wheels, which 
 are nothing more than large heavy wheels 
 driven with great velocity, by the ma- 
 chinery to which they are attached. 
 
 The use of the fly-wheel is to facilitate 
 the motion of engines, by accumulating and 
 retaining the power communicated to it 
 gradually and equally in each revolution 
 of the machine ; whence it comes to pass 
 that the motion of the machine is rendered 
 very nearly uniform and equal in all parts 
 
 of the revolution, and therefore more easy, 
 pleasant, and convenient.* 
 
 The best form for a fly is that of a heavy 
 wheel or circle, of a fit size ; for this will 
 meet with less resistance from the air ; 
 and being continuous, and the weight 
 every where equally distributed through 
 the perimeter of the wheel, the motion will 
 be more easy, equable, and regular. In 
 this form the fly is most aptly applied to 
 the perpendicular drill, where it not only 
 gives weight and regularity of motion, but 
 contributes to keep the drill upright by its 
 centrifugal power. 
 
 In this form it is also best applied to a 
 windlass or common winch, where the mo- 
 tion is pretty quick ; for when a man turns 
 the bended handle of the winch, his 
 strength is not, nor can be equally exerted 
 in every part of the revolution; for in 
 pulling upwards from the lower quarter, 
 he can exercise more power than in thrust- 
 ing forward in the upper quarter, where, 
 of course, part of his former force would 
 be lost, were it not accumulated and con- 
 served in the equable motion of the fly. 
 By this means a man may work all day in 
 drawing up a weight of 401b.; whereas 
 30 lb. would create him more labour in a 
 day without the fly. 
 
 When a fly-wheel is put in motion, it 
 derives a very high momentum from its 
 great weight and velocity, and may there- 
 fore be regarded as a sort of reservoir of 
 power, by which the machine is supplied 
 with velocity whenever there is any defal- 
 cation in the moving power, any intervals 
 of rest arising from the nature of the ma- 
 chinery, or any inequality of resistance 
 arising from the nature of the work to be 
 performed. In the single steam-engine, for 
 example, while the piston is descending, 
 and when no impelling power is exerted, 
 the momentum of the fly keeps up the ro- 
 tatory motion of the machinery, till the 
 impelling force is again exerted during the 
 ascent of the piston. In Vauloue’s pile 
 engine, when the resistance is suddenly 
 removed, the horses are prevented from 
 falling solely by the momentum of a heavy 
 fly-wheel, against which their force is ex- 
 erted, till the ram or weight is again raised. 
 Fly-wheels are sometimes made with vanes, 
 which regulate the descent of a weight by 
 the increased resistance of the air ; but 
 they are not much used in machinery. 
 
 * The fly does not give any new power to an en- 
 gine as some have imagined : as is evident for the 
 following reasons : — 1. The fly has no motion hut 
 what it receives at first from the machine. 2. A de- 
 gree of force is always necessary to maintain the 
 motion of the fly, which must be supplied from the 
 machine. 3. The friction of the pivot, screw, &c. of 
 the fly, is a resistance to the impressed force, and 
 must abate it. 4. The air likewise makes resistance 
 to the weights at the end of the fly. Upon all which 
 accounts it is easy to understand, that the fly, instead 
 of adding, does very much decrease or lessen the 
 power impressed on the machine. 
 
THE ARTISAN. 
 
 309 
 
 - OF ATWOOD’S MACHINE. 
 
 This ingeuious machine, which is re- 
 presented by the following figure, 
 
 was invented by Mr. Atwood, for the pur- 
 pose of illustrating the doctrines of acce- 
 lerated and retarded motion ; and by means 
 of it we are enabled to ascertain experi- 
 mentally, l.The quantity of matter moved; 
 2. The moving force; 3. The space des- 
 cribed ; 4. The time in which the space is 
 described ; and 5. The velocity acquired 
 at the end of that time. 
 
 This machine consists of a fixed brass 
 pulley or wheel abed , moving upon a 
 horizontal axis of steel. Each extremity 
 of this axis rests upon two friction wheels, 
 whose axis are horizontal, and the whole 
 is placed upon a platform C D, placed at 
 the top of a vertical pillar C Q, whose 
 base can be put into a true horizontal 
 position by the screws s, s, s. The height 
 of the machine is about eight feet, the 
 greatest diameter of the wheel abed, 
 is about seven inches and five-tenths, the 
 depth of the groove upon its circumfer- 
 ence about one-fourth of an inch, and the 
 diameter of the friction rollers about five 
 inches. 
 
 A pendulum P W is carried by the shelf 
 R S T, as in the following figure. 
 
 The plane of the dial plate is parallel to 
 that of the wheel abed. Between the 
 platform C D, and the base ss of the pillar 
 C Q, there rises an upright E F, whose 
 section is a rectangular parallelogram, the jj 
 length of the sides being about one inch 
 and six-tenths, and two inches and one- 
 tenth. The narrowest face is parallel to 
 that of the wheel abed, and carries 
 a divided scale about 64 inches long, and 
 subdivided into inches and tenths. 
 
 In the following account of the method 
 of using this machine, w r e have implicitly 
 followed the description given by Mr. 
 Atwood himself. 
 
 Of the quantity of matter moved . — In 
 order to observe the effects of the moving 
 force, which is the object of any experi- 
 ment, the interference of all other forces 
 should be prevented ; the quantity of mat- 
 ter moved, therefore, considering it before ! f 
 any impelling force has been applied, 
 should be without weight ; for though it 
 be impossible to abstract weight from any 
 substance whatever, yet it may be so coun- 
 teracted as to produce no sensible effect 
 Thus in the machine, Fig. 1. A and B re- 
 
THE ARTIS A N» 
 
 1 m 
 
 j| I present two equal weights affixed to the ex- 
 tremities of a very fine silk thread, stretched 
 I over a wheel or fixed pulley abed , 
 
 1 moveable round a horizontal axis: the 
 two weights A, B, being equal, and acting 
 ^ against each other, remain in equilibrio ; 
 and when the least weight is superadded 
 to either (setting aside the effects of fric- 
 tion), it will preponderate. When A, B 
 j are set in motion by the action of any 
 weight m, the sum A+ B -f m, would con- 
 I stitute the whole mass moved, but for the 
 || inertia of the materials which must neces- 
 !, sarily be used in the communication of 
 motion. These materials consist of, 1. The 
 wheel abed, over which the thread sus- 
 taining A and B passes. 2. The four fric- 
 tion wheels on which the axle of the wheel 
 abed rests. 3. The thread by which the 
 bodies A and B are connected, so as when 
 set in motion to move with equal veloci- 
 ties. The weight and inertia of the thread 
 are too small to have any sensible effect on 
 the experiments ; but the inertia of the 
 other materials constitute a considerable 
 proportion of the mass moved, and must 
 therefore be taken into account. Since 
 when A and B are put in motion, they 
 must move with a velocity equal to that of 
 i the circumference of the wheel abed, to 
 which the thread is applied ; it follows, 
 that if the whole mass of the wheels were 
 accumulated in this circumference, its 
 inertia would be truly estimated by the 
 quantity of matter moved ; but since the 
 parts of the wheels move with different 
 velocities, their effects in resisting the com- 
 munication of motion to A and B by their 
 
 I inertia, will be different ; those parts which 
 are furthest from the axis, resisting more 
 than those which revolve nearer in a du- 
 ll plicate proportion of those distances. If 
 1 the figures of the wheels were regular, the 
 distances of their centres of gyration from 
 their axis of motion would be given, and 
 consequently an equivalent weight, which 
 | being accumulated uniformly in the cir- 
 cumference abed, would exert an inertia 
 equal to that of the wheels in their con- 
 j structed form, would also be given. But 
 | as the figures are irregular, recourse must 
 S be had to experiment, to assign that quan- 
 1 tity of matter, which being accumulated 
 uniformly in the circumference of the wheel 
 abed , would resist the communication of 
 motion to A in the same manner as the 
 wheels. 
 
 In order to ascertain the inertia of the 
 wheel abed with that of the friction 
 wheels, the weights A, B being removed, 
 the following experiment was made : 
 
 A weight of 30 grains was affixed to a 
 silk thread of inconsiderable weight ; this 
 thread being wound round the wheel abed, 
 the weight 30 grains by descending from 
 j rest communicated motion to the wheel, 
 i j and by many trials was observed to des- 
 
 cribe a space of about 38§ inches in 3 se- 
 conds. From these data the equivalent 
 mass or inertia of the wheels will be known 
 from this rule. 
 
 Let a weight P, suppose 30 grains, fig. 
 2, be applied to communicate motion to a 
 system of bodies, by means of a very slen- 
 der and flexible thread going round the 
 wheel SLDIM, through the centre of 
 which the axis passes, (G being the com- 
 mon centre of gravity, R the centre of gra- 
 vity of the matter contained in this line, 
 and O the centre of oscillation). Let this 
 weight descend from rest through any 
 convenient space, suppose 38f inches, and 
 suppose that the observed time of its des- 
 cent is 3 seconds; then, as the space 
 through which bodies descend by the force 
 of gravity, in one second of time, is 16^ 
 feet, or 193 inches; the equivalent weight 
 
 sought will be — - — - — —30 
 
 oo’5 
 
 zz 1323 grains, or 2 and | ounces. 
 
 This is the inertia or resistance equivalent 
 to that of the wheel abed, and the friction 
 wheels together; for the rule extends to 
 the estimation of the intertia of the mass 
 contained in all the wheels. 
 
 The resistance to motion, therefore, 
 arising to Jthe wheels’ inertia, will be the 
 same as if they were absolutely removed, 
 and a mass of ounces uniformly accu- 
 mulated in the circumference of the wheel 
 abed. This being premised, let the boxes 
 A and B be re-placed, and suspended by 
 the silk thread over the wheel or pulley 
 abed,, and exactly balancing each other : 
 then let any weight (m), suppose 4 ounces, 
 be added to A, so that it shall descend, 
 the exact quantity of matter moved during 
 the descent of the weight A, will be as- 
 certained ; for the whole will be A -f- B -f- 
 4 -J-2f ounces. 
 
 In order to avoid troublesome computa- 
 tions, in adjusting the quantities of matter 
 moved and the moving forces, some deter- 
 minate weight of convenient magnitude 
 may be assumed as a standard, to which 
 all the others are referred. This standard 
 weight in the subsequent experiments is f 
 of an ounce, and is represented by the let- 
 ter m. The inertia of the wheels being 
 therefore zz 2f or ^ ounces, will be de- 
 noted by 11 m. A and B are two boxes, 
 constructed so as to contain different quan- 
 tities of matter, according as the experi- 
 ment may require them to be varied ; the 
 weight of each box, including the hook to 
 which it is supended zz If oz. or accord- 
 ing to the preceding estimation, the weight 
 of each box will be denoted by 6 m ; these 
 boxes contain weights, each of which 
 weights is an ounce, equivalent to 4m; 
 other weights of f os. zz 2 m, \~m, and 
 aliquot parts of m, such as"f m, f m, may be 
 also included in the boxes. 
 
THE ARTISAN. 
 
 311 
 
 HYDRAULICS. 
 
 ON BREAST WHEELS. 
 
 A breast water wheel is a wheel in 
 which the water is delivered at a point in- 
 termediate between the upper and under 
 point of a wheel with float-boards. It is 
 generally delivered at a point below the 
 level of the axis, but sometimes at a point 
 
 a little higher than the level of the axis. 
 On breast wheels buckets are never em- 
 ployed, but the float boards are fitted accu- 
 rately, with afe little play as possible, to 
 the mill course, so that the water, after 
 acting upon the float-boards by its impulse, 
 is retained between the float-boards and 
 the mill course, and acts'by its weight till 
 it reaches the lowest part of the wheel. 
 
 A breast wheel, as constructed by Mr. 
 Smeaton, is represented by the following 
 figure, 
 
 where A B is a portion of the wheel, M N 
 the canal which conveys the water to the 
 wheel, MOP the curvilineal mill course 
 accurately fitted to the extremities of the 
 float-boards, and c d the shuttle moved by 
 a pinion a, for the purpose of regulating 
 the admission of water upon the wheel. 
 
 M. Lambert observes, that when the 
 fall of water is between 4 and 10 feet, a 
 breast water wheel should be erected, 
 provided there is enough of water ; that 
 an undershot wheel should be used when 
 the fall is below 4 feet, and an overshot 
 wheel when the fall exceeds 10 feet. He 
 recommends also that when the fall exceeds 
 10 feet, it should be divided into two, and 
 two breast wheels erected upon it. These 
 rules are, however, not of great value. 
 
 COMPARATIVE EFFECTS OF WATER WHEELS. 
 
 M. Belidor very strangely maintained, 
 that overshot wheels were inferior to un- 
 dershot ones. It appears, however, from 
 Smeaton’s experiments, that in overshot 
 
 wheels the ratio of the power to the effect 
 is nearly as 3 to 2, or as 5 to 4, whereas, 
 in undershot wheels the ratio is only as 3 
 to 1 ; from which it follows, that the effect 
 of overshot wheels is nearly double of the 
 effect of undershot wheels. The Che- 
 valier de Borda has concluded, that over- 
 shot wheels will raise through the height 
 of the fall, a quantity of water equal to 
 that by which they are driven ; that under- 
 shot wheels moving vertically, will pro- 
 duce fths of this effect; that horizontal 
 wheels will produce a little less than £ of it 
 when the float-boards are plain, and a lit- 
 tle more than \ when they are curvilineal. 
 
 MACHINES MOVED BY THE RE-ACTION OF 
 WATER. 
 
 Some machines are moved, not directly 
 by the impulse of a stream of water, but 
 indirectly by the relief from pressure 
 which the motion of the stream occasions. 
 
 The machine known by the name of 
 Barker’s mill, is of this kind. 
 
312 
 
 THE ARTISAN. 
 
 re-action of water were called Barker's 
 barker’s mill. mill, and sometimes Parent's mill. 
 
 This machine is represented by the fol- 
 < The first mills which were driven by the lowing figure, 
 
 in which, A is a pipe or channel that 
 b »ings water to the upright tube B. The 
 water runs down the tube, and thence 
 into the horizontal trunk C, and runs out 
 through holes at d and e , near the ends of 
 the trunk on the contrary sides thereof. 
 
 The upright spindle D is fixed in the 
 bottom of the trunk, and screwed to it 
 below by the nut g ; and is fixed into the 
 trunk by two cross bars at/; so that, if 
 the tube B and trunk C be turned round, 
 the spindle D will be turned also. 
 
 The top of the spindle goes square into 
 the rynd of the upper mill-stone H, as in 
 common mills; and, as the trunk, tube, 
 and spindle turn round, the mill-stone is 
 turned round thereby. The lower, or 
 quiescent mill- stone is represented by I ; 
 and K is the floor on which it rests, and 
 wherein is the hole L for letting the meal 
 mn through, and fall down into a trough 
 
 which may be about M. The hoop or 
 case that goes round the mill-stone rests 
 on the floor K, and supports the hopper, 
 in the common w'ay. The lower end of 
 the spindle turns in a hole in the bridge- 
 tree GF, which supports the mill-stone, 
 tube, spindle, and trunk. This tree is 
 moveable on a pin at h, and its other end 
 is supported by an iron rod N fixed into it, 
 the top of the rod going through the fixed 
 bracket O, and having a screw-nut o upon 
 it, above the bracket. By turning this nut 
 forward or backward, the mill-stone is 
 raised or lowered at pleasure. 
 
 ^Whilst the tube B is kept full of water 
 from the pipe A, and the water continues 
 to run out from the ends of the trunk ; the 
 upper mill-stone H, together with the 
 trunk, tube, and spindle, turns round. But, 
 if the holes in the trunk were stopt, no 
 motion would ensue ; even though the tube 
 
THE ARTISAN. 
 
 313 
 
 and trunk were full of water. >For, if 
 there were no hole in the trunk, the pres- 
 sure of the water would be equal against 
 all parts of its sides within. But, when 
 the water has free egress through the holes, 
 its pressure there is entirely removed: 
 and the pressure against the parts of the 
 sides which are opposite to the holes, turns 
 the machine. 
 
 In the preceding form of Barker’s mill, 
 the length of the axis must always exceed 
 the height of the fall, and therefore when 
 the fall is very high, the difficulty of erect- 
 ing such a machine would be great. In 
 order to remove this difficulty, M. Mathon 
 de la Cour proposes to introduce the water 
 from the mill course into the horizontal 
 arms, which are fixed to the upright spin- 
 dle, but without any tube. The water 
 will obviously issue from the apertures, in 
 the same manner as if it had been intro- 
 duced at the top as high as the fall. Hence 
 the spindle D may be made as short as we 
 please. The practical difficulty which 
 attends this form of a machine, is to give 
 the arms a motion round the mouth of the 
 feeding pipe, which enters the arm without 
 any great friction, or any considerable loss 
 of water. 
 
 In the year 1747, Professor Segner, of 
 Gottingen, published, in his Exercitationes 
 Hydraulics, an account of a machine which 
 differs only in form from Dr. Barker’s mill. 
 It consisted of a number of tubes arranged 
 as it were in the circumference of a trun- 
 cated cone ; the water was introduced into 
 the upper ends of these tubes, and flowing 
 out at the lower ends, produced, by virtue 
 of its re-action, a motion round the axis of 
 the cone. 
 
 Another form of this machine has been 
 suggested 'by Albert Euler. He proposes 
 to introduce the water from the mill course 
 into an annular cavity in a fixed vessel, of 
 the shape nearly of a cylinder. The bot- 
 tom of^ this vessel has several inclined 
 apertures, for the purpose of making the 
 water flow out with a proper obliquity into 
 the inferior and moveable vessel. This in- 
 ferior vessel, which has the form of an in- 
 verted frustum of a cone, moves about an 
 axis passing up through the centre of the 
 fixed vessel, and has a variety of tubes 
 arranged round its circumference. These 
 tubes do not reach to the very top of the 
 vessel, and are bent into right angles at 
 their lower ends. The water from the 
 upper and fixed vessel being delivered into 
 the tubes of the lower vessel, descends in 
 the tubes, and issuing from their horizontal 
 extremities, gives motion to the conical 
 drum by its re-action. 
 
 The excellence of this method of employ- 
 ing the re-action of water, was first slightly 
 pointed out by Dr. Desaguliers, and no 
 further notice seems to have been taken of 
 
 the invention, till the appearance of Seg=* 
 ner’s machine in 1747. The attention of 
 Leonhard Euler, John Bernoulli, and 
 Albert Euler, was then directed to the 
 subject, and it would appear, from the re- 
 sults of their investigations, that this is 
 the most powerful of all hydraulic ma- 
 chines, and is therefore the best mode of 
 employing water as a moving power. 
 Leonhard Euler published his theory of 
 this machine in the Memoirs of the Berlin 
 Academy, and the application of the ma- 
 chine to all kinds of work, was explained 
 in a subsequent paper in the same work, 
 for 1752, p. 271. John Bernoulli’s inves- 
 tigations will be found at the end of his 
 Hydraulics. 
 
 Albert Euler concluded, that when the 
 machine had the form given to it by Seg- 
 ner, the effect was equal to the power, and 
 that the effect is a maximum when the 
 velocity is infinite. Mr. Waring makes 
 the effect of the machine equal only to that 
 of a good undershot wheel, driven with 
 the same quantity of water falling through 
 the same height. The Abbb Bossut has 
 likewise investigated the theory of this ma- 
 chine, and has found that an overshot 
 wheel, and a wheel of the form given 
 to it by Albert Euler, will produce equal 
 effects with the same quantity of water, if 
 the depth of the orifice below the mill- 
 course in the latter machine, be equal to 
 the vertical height of the loaded arch in 
 the overshot wheel; and he, upon the 
 whole, recommends the overshot wheel as 
 preferable in practice. The preceding re- 
 sult, however, proves the inferiority of the 
 overshot wheel, as the height of the loaded 
 arch must be always much less than that 
 of the fall. A new and ingenious theory 
 of this machine has lately been given by 
 Mr. Ewart in the Manchester Memoirs. 
 
 pitot’s bent tube for measuring the. 
 
 VELOCITY OF WATER. 
 
 One of the most ingenious instruments 
 for measuring the velocity of water, is the 
 tube recourbt , or bent tube invented by M. 
 Pitot. It is represented by the following 
 figure, 
 
m 
 
 THE ARTISAN. 
 
 and consists of a prism of wood ABCDEF, 
 one of the angles of which is presented to 
 the current. On the hinder face B C F E are 
 fixed two tubes of glass parallel to each 
 other, and having a graduated scale be- 
 tween them: one of them; viz. M NO, 
 being bent into a right angle at O, so that 
 the part M N may pass through the prism 
 horizontally. When this instrument is 
 plunged into a running stream, the general 
 level of the current is shown by the rise of 
 the water in the straight tube P Q, while 
 the height of the water in the bent tube 
 M N O, becomes the measure of the force 
 of the stream. The difference between 
 these heights will therefore be the height 
 due to the velocity. In the practical use of 
 this instrument, it is, however, difficult to 
 fix it sufficiently steady to prevent the 
 water from oscillating in the tubes. 
 
 M . Du Buat having examined the instru- 
 ment experimentally, found that it could 
 be trusted no further, than to give the ratio 
 of different velocities. He therefore sup- 
 pressed the tube P Q altogether, and sub- 
 stituted in place of the bent tube of glass 
 M N O, a simple tube of white iron, suffi- 
 ciently large to admit a float for pointing 
 out the height of the water in the tube. 
 The lower end of this tube is bent back as 
 at M N, and is terminated by a plane sur- 
 face perforated at its centre with a small 
 orifice, which will greatly diminish the os- 
 cillations of the elevated column. 
 
 If we then take two-thirds of the height 
 of the water in the tube above the level of 
 the stream, we shall have, very exactly, 
 the height due to the velocity of the cur- 
 rent, for the depth to which the orifice is 
 immersed. 
 
 HYDRAULIC QUADRANT FOR MEASURING 
 THE VELOCITY OF WATER. 
 
 The hydraulic qiiadrant which has been 
 recommended by several authors for mea- 
 suring the velocity of water, is represented 
 by the following figure. 
 
 It consists of a quadrant ABC, with a 
 divided arch A B, and having two threads 
 
 moving round its centre. One of these; C P 
 is short, and carries a weight P, which 
 always hangs in the air, while the other 
 CH or CM is longer, and caries a weight, 
 whose specific gravity is greater than that 
 of water, and which plunges more or less 
 deep in the current as the thread is length- 
 ened. The instrument is then held as in 
 the figure, so that the plummet C P passes 
 through O; and the angle A CD, or the 
 angular distance of the other thread from a 
 vertical line, will be a measure of the 
 force, and consequently of the velocity of 
 the current. 
 
 fHiscellaneous Subjects. 
 
 MEMOIR OF THE LIFE OF ROGER 
 BACON, COMMONLY CALLED 
 FRIAR BACON. 
 
 Roger Bacon, a learned English monk 
 of the Franciscan order, who flourished in 
 the thirteenth century, was born near 
 Ilchester, in Somersetshire, in 1214, and 
 was descended of a very ancient and 
 honourable family. He received the first 
 tincture of letters at Oxford, where having 
 gone through Grammar and Logic, the 
 dawnings of his genius gained him the 
 favour and patronage of the greatest lovers 
 of learning, and such as were equally dis- 
 tinguished by their high rank, and the ex- 
 cellence of their knowledge. “ It is not 
 very clear,” says the Biographia Britan- 
 nica, “ whether he was of Merton College, 
 or of Brazen-nose Hall, and perhaps he 
 studied at neither, but spent his time at 
 the public schools.” It appears, however, 
 that he went early over to Paris, where he 
 made still greater progress in all parts 
 of learning, and was looked upon as the 
 glory of that University, and an honour 
 to his country. In those days, persons who 
 wished to distinguish themselves by an early 
 and effectual application to tfieir studies, 
 resorted to Paris, where not only many of 
 the greatest men in Europe resided and 
 taught, but many of the English nation, by 
 whom Bacon was encouraged and caressed. 
 At Paris he did not confine his studies to 
 any particular branch of literature, but 
 endeavoured to comprehend the sciences in 
 general, fully and perfectly, by a right 
 method and constant application. When 
 he had attained the degree of Doctor, 
 he returned again to his own country, 
 and, as some say, took the habit of the 
 Franciscan order, in 1240, when he was 
 about twenty-six years of age. After 
 his return to Oxford, he was considered, 
 by the greatest men of that University, 
 as one of the ablest and most indefatiga- 
 ble enquirers after knowledge that the 
 world had ever produced ; and therefore 
 
THE ARTISAN, 
 
 315 
 
 they not only showed him all due respect, 
 but likewise conceiving the greatest 
 hopes from his improvements in the me- 
 thod of study, they generously contri- 
 buted to his expenses, so that he was 
 enabled to lay out, within the compass of 
 twenty years, no less than two thousand 
 pounds in collecting curious Authors, 
 making experiments of various kinds, and 
 in the construction of different instruments, 
 for the improvement of useful knowledge. 
 But if this assiduous application to his 
 studies, and the stupendous progress he 
 made in them, raised his credit with the 
 better part of mankind, it excited the envy 
 of some, and afforded plausible pretences 
 for the malicious designs of others. It is 
 very easy to conceive, that the experiments 
 he made in all parts of Natural Philoso- 
 phy and the Mathematics, must have made 
 great noise in an ignorant age, when 
 scarcely two or three men in a whole 
 nation were tolerably acquainted with 
 those studies, and when all the pretenders 
 to knowledge affected to cover their own 
 ignorance, by throwing the most scan- 
 dalous aspersions on those branches of 
 science, which they either wanted genius 
 to understand, or which demanded greater 
 application to acquire, than they were 
 willing to bestow. They gave out, therefore, 
 that Mathematical studies were in some 
 measure allied to those magical arts which 
 the church had condemned, and thereby 
 brought suspicions upon men of superior 
 learning. It was owing to this suspicion, 
 that Bacon was restrained from reading 
 lectures to the young students in the Uni- 
 versity, and at length closely confined and 
 almost starved, the Monks being afraid, 
 lest his writings should extend beyond the 
 limits of his convent, and be seen by any 
 besides themselves and the Pope. But 
 there is great reason to believe, that 
 though his application to the occult scien- 
 ces was their pretence, the true cause of 
 his ill-usage w as, the freedom with which 
 he had treated the clergy in his writings, 
 in which he spared neither their ignorance 
 nor their want of morals. But notwith- 
 standing this harsh feature in the character 
 of the times, his reputation continued to 
 spread over the whole Christian world, 
 and even Pope Clement IV. wrote him a 
 letter, desiring that he would send him all 
 his works. This was in 1266, when our 
 author was in the flower of his age, and to 
 gratify his Holiness, collected together, 
 greatly enlarged and ranged in some order, 
 the several pieces he had written before 
 that time, and sent them the next year by 
 his favourite disciple, John of London, or 
 rather of Paris, to the Pope. This collec- 
 tion, which is the same that he entitled 
 Opus Majus, or his great work, is yet ex- 
 tant, and was published by Dr. Jebb, in 
 
 1773. Dr. Jebb had proposed to have 
 published all his works about three years 
 before his edition of the Opus Majus, but 
 while he was engaged in that design, he 
 was informed by letters from his brother 
 in Dublin, that there was a manuscript in 
 the College library there, which contained 
 a great many treatises generally ascribed 
 to Bacon, and disposed in such order, that 
 they seemed to form one complete work, 
 but the title was wanting, which had been 
 carelessly torn off from the rest of the 
 manuscript. The Doctor soon found that 
 it was a collection of those tracts which 
 Bacon had written for the use of Pope 
 Clement IV. and to which he had given 
 the title of Opus Majus, since it appeared, 
 that what he said of that work in his Opus 
 Tertium, addressed to the same Pope, ex- 
 actly suited with this ; which contained an 
 account of almost all the new discoveries 
 and improvements that he had made in the 
 sciences. Upon this account Dr. Jebb laid 
 aside his former design, and resolved to 
 publish only an edition of his Opus Majus. 
 The manuscripts which he made use of to 
 complete this edition, are, 1. MS. in the 
 Cotton library, inscribed “ Jul. D. V.” 
 which contains the first part of the Opus 
 Majus, under the title of a treatise, “ De 
 utilitate Scientiarum.” 2. Another MS. 
 in the same library, marked “ Tib. C. V.” 
 containing the fourth part of the Opus 
 Majus, in which is shown the use of the 
 mathematics in the sciences and affairs of 
 the world; in the MS. it is erroneously 
 called the fifth part. 3. A MS. in the 
 library belonging to Corpus Christi, in 
 Cambridge, containing that portion of the 
 fourth part which treats of Geography. 
 4. A MS. of the fifth part, containing a 
 treatise upon perspective, in the earl of 
 Oxford’s library. 5. A MS. in the library 
 of Magdalen College, Cambridge, compre- 
 hending the same treatise of perspective. 
 6. Two MSS. in the king’s library, com- 
 municated to the editor by Dr. Richard 
 Bentley, one of which contains the fourth 
 part - of Opus Majus, and the other the 
 fifth part. It is said that this learned 
 book of his procured him the favour of 
 Clement IY. and also some encouragement 
 in the prosecution of his studies ; but this 
 could not have lasted long, as that Pope 
 died soon after, and then we find our 
 author under fresh embarrassments from 
 the same causes as before ; but he became 
 in more danger, as the general of his order, 
 Jerom de Ascoli, having heard his cause, 
 ordered him to be imprisoned. This is 
 said to have happened in 1278, and to pre- 
 vent his appealing to Pope Nicholas III. 
 the general procured a confirmation of his 
 sentence from Rome immediately, but it is 
 not very easy to say upon what pretences. 
 Yet we are told by others, that he was im* 
 
316 
 
 THE ARTISAN. 
 
 prisoned by Reymundus Galfredus, who 
 was general of his order, on account of 
 some alchemical treatise which he had 
 written, and that Galfredus afterwards set 
 him at liberty, and became his scholar. 
 However obscure these circumstances may 
 be, it is certain that his sufferings for many 
 years must have brought him low, since he 
 was sixty-four years of age w hen he was 
 first put in prison, and deprived of the 
 opportunity of prosecuting his studies, at 
 least in the way of experiment. That he 
 was still indulged in the use of his books, 
 appears very clearly, from the great use he 
 made of them in the learned works he com- 
 posed. 
 
 After he had been ten years in pri- 
 son, Jerom de Ascoli, who had con- 
 demned his doctrine, was chosen Pope, 
 and assumed the name of Nicholas IV. 
 As he vras the first of the Franciscan order 
 that had ever arrived at this dignity, he was 
 reputed a person of great probity and much 
 learning, our author, notwithstanding what 
 had before happened, resolved to apply to 
 him for his discharge ; and in order to pa- 
 cify his resentment, and at the same time 
 to show both the innocence and the useful- 
 ness of his studies, he addressed to him a 
 very learned and curious treatise/ 4 On the 
 means of avoiding the infirmities of old Age,” 
 printed first at Oxford, 1590, and translated 
 and published by Dr. Richard Browne, 
 under the title of 44 The cure of old Age 
 and preservation of Youth/’ London, 1683, 
 8vo. It does not appear, however, that his 
 application had any effect; on the contrary, 
 some writers say that he caused him to be 
 more "Jclosely confined. But towards the 
 latter end of his reign, Bacon, by the inter- 
 position of some| nobleman, obtained his 
 release, and returned to Oxford, where he 
 spent the remainder of his days in peace, 
 and dying in the college of his order, on 
 the 11th of June, 1292, was interred in the 
 church of the Franciscans. The monks 
 gave him the title of 44 Doctor Mirabilis,” 
 or the Wonderful Doctor, which he de- 
 served, in whatever sense the phrase is 
 taken. 
 
 He was certainly the most extraordinary 
 man of his time. He was a perfect master 
 of the Latin, Greek, and Hebrew, and has 
 left posterity such indubitable marks of 
 his critical skill in them, as might have 
 secured him a very high character, if he 
 had never distinguished himself in any 
 other branch of literature. In all the 
 branches of the mathematics he was well 
 versed, and there is scarcely any part of 
 them, on which he has not written with a 
 solidity and clearness,” which have been 
 deservedly admired by the greatest masters 
 in that science. In Mechanics particularly, 
 the learned Dr. Freind says, that a 
 greater genius had not arisen since the 
 
 days of Archimedes. He understood, 
 likewise, the whole science of Optics, with 
 accuracy; and is very justly allowed to 
 have understood both the theory and prac- 
 tice of those discoveries, which have be- 
 stowed such high reputation on those of 
 our own and of other nations, who have 
 brought them into common use. In Geo- 
 graphy also he was admirably well skilled, 
 as appears from a variety of passages in 
 his works, which was the reason that in- 
 duced the judicious Hackluyt to transcribe 
 a long discourse out of his writings, into 
 his Collection of Voyages and Travels. 
 But his skill in Astronomy was still more 
 remarkable, since it appears, that he not 
 only pointed out that error which occa- 
 sioned the reformation in the Calendar, 
 and the distinction between the old stile 
 and the new, but also offered a much 
 more effectual and perfect reformation, 
 than that which was made in the time of 
 Pope Gregory XIII. There are also re- 
 maining some w r orks of his relating to 
 Chronology, which would have been 
 thought worthy of very particular notice, 
 if his skill in other sciences had not made 
 his proficiency in this branch of know- 
 ledge the less remarkable. The history of 
 the four great empires of the world, he 
 has treated very accurately and succinctly, 
 in his great work addressed to Pope Cle- 
 ment IV. He was so thoroughly acquainted 
 with Chemistry, at a time that it was 
 scarcely known in Europe, and principally 
 cultivated among the Arabians, that Dr. 
 Freind ascribes the honour of [introducing 
 it to him, who speaks in some part or 
 other of his works, of almost every opera- 
 tion now used in Chemistry. Three 
 capital discoveries made by him deserve ta 
 be particularly considered. The first is, 
 the invention of gun-powder, which how- 
 ever, confidently ascribed to others, was 
 most unquestionably known to him, both 
 as to its ingredients and effects. The 
 second is that which commonly goes under 
 the name of Alchemy, or the art of trans- 
 muting metals, of which he has left many 
 treatises, some published, and some still 
 remaining in MS., which, whatever they 
 may be thought of now, contain a mul- 
 titude of curious and useful passages, in- 
 dependently of their principal subject. 
 The third discovery in Chemistry, not so 
 deserving of the reader’s attention, was the 
 tincture of gold for the prolongation of 
 life, of which Dr. Freind says, 44 he has 
 given hints in his writings, and has said 
 enough to show that he was no pretender 
 to this art, but understood as much of it as 
 any of his successors. That he was far 
 from being unskilled in the art of Physic, 
 we might rationally conclude, from his 
 extensive knowledge in those sciences, 
 which are connected with it : but we have 
 
THE ARTISAN. 
 
 317 
 
 a manifest proof of his perfect acquain- 
 tance with the most material and useful 
 branches of physic, in his Treatise of Old 
 Age, which, as Dr. Freind, whose autho- 
 rity on that subject cannot well be dis- 
 puted, observes, is very far from being ill- 
 written; and Dr. Brown, who published 
 it in English, esteemed it one of the best 
 performances that ever was written. In 
 this work he has collected whatever he 
 had met with upon the subject, either in 
 Greek or Arabian writers, and has added 
 a great many remarks of his own. In 
 logic and metaphysics he was excellently 
 well versed, as appears by those parts of 
 his works, in which he has treated of 
 these subjects : neither was he unskilled 
 in Philology and the politer parts of 
 learning. In Ethics, or Moral Philosophy, 
 he has laid down some excellent principles 
 for the conduct of human life. 
 
 As to the vulgar imputation on his cha- 
 racter, of his leaning in magic, it was 
 utterly unfounded; and the ridiculous 
 story of his making a brazen head, which 
 spoke and answered questions, is a ca- 
 lumny indirectly fathered upon him, having 
 been originally imputed to Robert Grosse- 
 tete, Bishop of Lincoln. That he had too 
 high an opinion of judicial astrology, and 
 some other arts of that nature, was not so 
 properly an error of his as of the age in 
 which he lived : and considering how few 
 errors, among the many which infected 
 that age, appear in his writings, it may be 
 easily forgiven. As his whole life jwas 
 spent in labour and study, and he was 
 continually employed, either in writing for 
 the information of the world, or in reading 
 and making experiments, that might enable 
 him to write with greater accuracy ; so we 
 need not wonder his works were extremely 
 numerous, especially when it is considered, 
 that on the one hand his studies took in 
 the whole circle of the sciences, and that 
 on the other, the numerous treatises as- 
 cribed to him, are often in fact, but so 
 many chapters, sections, or divisions ; and 
 sometimes we have the same pieces under 
 two or three different names : so that it is 
 not at all strange before these points were 
 well examined, that the accounts we have 
 of his writings, appeared very perplexed 
 and confused. 
 
 ARCHITECTURE. 
 
 CONSTRUCTION OF ARCHES. 
 
 If the weights of the voussoirs in an 
 arch are all equal, the arch of equilibra- 
 tion is what is termed a Catenarian curve, 
 the same that a chain or cord of uniform 
 thickness would assume if hanging freely, 
 the horizontal distance of the points of sus- 
 
 pension, being equal to the span of the 
 arch, and the depth of the lowest point of 
 the chain being equal to the greatest height 
 of the arch. 
 
 If the figure of the chain were reversed, 
 the joints being such, that the force which 
 was a pull in the first situation, becomes a 
 thrust in the second, the chain would sup- 
 port itself, and remain in equilibria. 
 
 The catenaria is remarkable for this me- 
 chanical property. That a chain hanging 
 in that curve, has its centre of gravity 
 lower than if it were disposed in any other 
 line, its length continuing the same, and 
 also the points from which it is suspended. 
 Therefore an arch constructed in this form, 
 has its centre of gravity the highest pos- 
 sible. 
 
 But the supposition of an arch resisting 
 a weight, which acts only in a vertical 
 direction, is by no means perfectly ap- 
 plicable to cases which generally occur in 
 practice. The pressure of loose stones and 
 earth, moistened as they frequently are by 
 rain, is exerted very nearly in the same 
 manner as the pressure of fluids, which 
 act equally in all directions : and even if 
 they were united into a mass, they would 
 constitute a kind of wedge, and would 
 thus produce a pressure of a similar na- 
 ture, notwithstanding the precaution re- 
 commended by some authors, of making 
 the surfaces of the arch-stones vertical and 
 horizontal only. This precaution is, how- 
 ever, in all respects unnecessary, be- 
 cause the effect which it is intended to ob- 
 viate, is productive of no inconvenionce, 
 except that of exercising the skill of the 
 architect. The effect of such a pressure 
 only requires a greater curvature near the 
 abutments, reducing the form nearly to 
 that of an ellipsis, and allowing the arch 
 to rise at first in a vertical direction. 
 
 A bridge must also be so calculated, as 
 to support itself without being in danger of 
 falling by the defect of the lateral adhe- 
 sion of its parts, and in order that it may 
 in this respect be of equal strength through- 
 out its depth at each point, must be pro- 
 portional to the weight of the parts beyond 
 it. This property particularly belongs fto 
 the curve denominated logarithmic , 'the 
 length corresponding to the logarithm of 
 the depth. If the strength were afforded 
 by the arch stones only, this condition 
 might be fulfilled by giving them tie re- 
 quisite thickness, independently o' the 
 general form of the arch : but the wlole of 
 the materials employed in the constriction 
 of the bridge, must be considered as adding 
 to the strength, and the magnitude of the 
 adhesion, as depending in a great rmasure 
 on the general outline. 
 
 We must examine in the next place what 
 is the most advantageous form for support- 
 ing any weight which may occasionally be 
 
318 
 
 THE ARTISAN. 
 
 placed on the bridge, particularly at its 
 weakest part, which is usually the middle. 
 (Supposing the depth at the summit of the 
 arch at the abutments to be given, it may 
 be reduced considerably, in the interme- 
 diate parts, without impairing the strength, 
 and the outline may be composed of para- 
 bolic arcs , having their convexity turned 
 towards each other. This remark also 
 would be only applicable to the arch 
 stones, if they afforded the whole strength 
 of the bridge, but it must be extended in 
 some measure to the whole of the materials 
 forming it. 
 
 If, therefore, we combine together the 
 
 curve best calculated for resisting the pres- 
 sure of a fluid, which is nearly elliptical, 
 the logarithmic, and the parabolic curv es, 
 allowing to each its due proportion of in- 
 fluence, we may estimate, from the com- 
 parison, which, is the fittest form for an 
 arch intended to support a road. And in 
 general, whether the road be horizontal, 
 or a little inclined, we may infer that an 
 ellipsis, not differing much from a circle, is 
 the best calculated to comply as much as 
 possible with all the conditions, as repre- 
 sented by the following figure, which ex- 
 hibits a view of the middle arch of 
 
 BLACKFRIAR’S BRIDGE. 
 
 A complete System of Theoretical and Prac- 
 tical Arithmetic. By Geo. G. Carey, 
 
 1 rol. 8vo. pp. 5T4. Hodgson and Co. 
 
 London, 1824. 
 
 The science of arithmetic being the foun- 
 dation of all accurate science, it is not sur- 
 prising that so many works should have 
 lately appeared upon that subject. The 
 science of numbers has, at all times, not 
 only been considered an amusing, but a 
 very useful branch of study; it has there- 
 fore engaged the attention of the inquisi- 
 tive part of mankind in all ages of the 
 worlil. ^ Hence this species of know- 
 ledge advanced with more rapid strides 
 to tie perfection at which we now 
 find i^ than any other, which it is possible 
 to naiiie. For, notwithstanding the number 
 of bovjks which have been published with- 
 in thejlast thirty years upon this interest- 
 ing sibject, scarcely a single discovery 
 has btlen made in the theory of numbers or 
 even ah improvement in their practical ap- 
 plication to the purposes of the abstract, or 
 mixed Mathematical sciences. 
 s In commercial or mercantile affairs it is 
 
 somewhat different. Improvements in the 
 modes of calculation have certainly been 
 made within the period we have men- 
 tioned ; but these, we are persuaded, are 
 much better known to the practical ac- 
 countant, than to those who not only 
 pretend to teach the whole science of 
 Arithmetic, but publish works upon that 
 subject, professing to be superior to all 
 others, and to contain methods of compu- 
 tation hitherto unknown. 
 
 The taste which now prevails among all 
 classes of society for accurate scientific 
 knowledge, and the value of Arithmetic to 
 those who are engaged in scientific as well 
 as commercial pursuits, have led us to 
 examine the present volume with some 
 degree of care, in order to ascertain if it 
 possesses any superiority over those which 
 are already before the public. 
 
 The result of our examination is highly 
 favourable both to the talents and industry 
 of the author, who appears to us to be 
 completely master of the subjects which he 
 has introduced into the present volume ; 
 and to have treated them not only more 
 
THE ARTISAN. 
 
 319 
 
 fully than we have ever seen in works of 
 this kind ; but to have explained and il- 
 lustrated his rules with greater care and 
 clearness than any author we have perused 
 on the science of Arithmetic. 
 
 The first part of Mr. Carey’s work is de- 
 voted to the abstract part of arithmetic, 
 and may be termed the theoretical part of 
 the work. 
 
 This is followed by a number of very ex- 
 tensive and useful tables, relating to 
 weights and measures. The fundamental 
 rules are then applied to commercial and 
 other computations, which are followed by 
 the rules of Practice, Interest, Partner- 
 ship, &c. Rut what appears to us to be 
 not only the most original subjects in this 
 volume, but the most valuable, (to those 
 who already know the elements of arith- 
 metic,) is the articles upon the Stocks, 
 Public Funds, or Marine Insurance, Ex- 
 change, Compound Interest, and Annuities 
 on Lives, with the tables on this last sub- 
 ject. 
 
 The subject of Marine Insurance is 
 one which has not hitherto found its way 
 into works on Arithmetic, at least dn the 
 regular and distinct manner it is treated of 
 in the volume before us. W e might say the 
 same thing of the Stocks, and Annuities 
 on Lives. These and Foreign Exchanges, 
 are, however, very fully treated of by Mr. 
 Carey, who appears to be well acquainted 
 with all of them. 
 
 The work also contains a very neat and 
 extensive table of the Logarithms of num- 
 bers, and an interesting and scientific arti- 
 cle on Arithmetical Scales, in which the 
 advantages and disadvantages of the Bi- 
 nary, Ternary, Quaternary, and other 
 Scales, are very cleaily and accurately 
 pointed out. 
 
 On the whole, we have no hesitation in 
 saying that this is the most extensive and 
 comprehensive System of Arithmetic which 
 has made its appearance for many years ; 
 and we have not the smallest doubt, but it 
 will be found to be one of the most useful 
 on that subject to those who may wish to 
 make themselves master of Arithmetic. 
 
 ELECTRIC EFFECTS OF WATER 
 AND OTHER LIQUIDS ON THE 
 METALS, BY M. BECQUEREL. 
 
 A memoir on the electrical or galvanic 
 effect of water and other liquids on the 
 metals, was lately read before the Aca- 
 demy of Sciences at Paris, from which we 
 make the following extract : 
 
 The author begins with showing the 
 causes which have hitherto prevented him 
 from observing some very feeble electrical 
 effects, especially those that take place in 
 the contact of water and metals. In his 
 memoir he mentions the following appear- 
 ances ; when a capsule of wood or china 
 
 is placed upon the upper plate of a very 
 sensible condenser, and any liquid poured 
 into it, the capsule immediately acquires'a 
 very perceptible conducting quality, suffi- 
 ciently powerful to transmit the electricity 
 which it receives to the plate upon which 
 it rests ; but as it sometimes happens, that 
 this same capsule exercises a very weak 
 electric action upon the metal, it may be 
 destroyed by touching the lower plate with 
 another capsule of the same nature. The 
 apparatus being thus arranged, and' after 
 taking all the care necessary in such expe- 
 riments, different metals are plunged into 
 the water contained by the capsule ; it is 
 then seen that iron, zinc, lead, &c. becomes 
 negatively electrified, whilst platina, gold, 
 silver, &c. become positively electrified. 
 Thus water,' in its contact with the non- 
 oxidizable metals, acts in the same manner 
 as acids do in their contact with alkalies, 
 when there is no chemical action. 
 
 M. Becquerel afterwards shows, that 
 platina and gold, previously plunged into 
 nitric acid, and afterwards washed, ac- 
 quires more marked electrical effects in 
 their contact with water. He also notices 
 the remarks of Messrs Dulong and The- 
 nard, upon the [means of giving to fine 
 platina wire the property of instantaneously 
 communicating inflammability to detonating 
 mixtures, which they did not before possess ; 
 the result of the comparison of these differ- 
 ent effects is, that the modification or the 
 arrangement which the particles acquire, 
 by the immersion of platina wires in nitric 
 acid, seems to be the cause which more 
 promptly determines the combination of 
 two gasses, and heighten the electrical 
 properties of the metaj. 
 
 M. Becquerel repeated his experiments 
 on the electric effects resulting from the 
 contact of two metals with the same liquid j 
 and found the effects to be perfectly similar. 
 He therefore deduces a process from these 
 experiments, for ascertaining which of any 
 two metals exercises the strongest electric 
 action upon a liquid. 
 
 He afterwards tried the electrical effects 
 produced by the contact of certain flames 
 and metals ; the flames he submitted to 
 trial, are those that arise from the burning 
 of alcohol, from hydrogen gas, or from a 
 sheet of paper. He placed upon the 
 wooden capsule, which was set over the 
 upper plate of the condenser, a wire or thin 
 plate of platina, one of the extremities of 
 which passed through the flame of one of 
 the substances just mentioned!; and if the 
 metal attained a red heat, he found that it 
 became negatively electrified, but if it did 
 not, it became positively electrified. In 
 both of these cases the flame has always 
 a contrary electrical effect. When it is in- 
 tended to collect the electricity acquired by 
 the flame, a piece of damp wood is to be 
 
THE ARTISAN. 
 
 32© 
 
 placed upon the capsule, which not taking 
 fire serves as a conductor. Every other 
 metal presents analogous effects ; we may 
 therefore conclude from these experiments, 
 that when a piece of metal is placed in a 
 flame supported by a current of hydrogen 
 gas, it becomes either negatively or posi- 
 tively electrified, according as the tempe- 
 rature is more or less elevated. The author 
 of this memoir fully discusses these pheno- 
 mena, and finishes by stating the result of 
 some experiments upon the electric effects 
 that accompany combustion. He placed 
 upon the capsule of wood already noticed, 
 a sheet of paper rolled up : and as soon as 
 set on fire, and the flame has communicated 
 to the common reservoir, it is known, by 
 means of the condenser, that the paper be- 
 comes positively electrified. In operating 
 in the contrary manner, that is, by holding 
 the paper in the hand, and making the 
 flame touch a bit of damp wood placed 
 upon the capsule, the flame become nega- 
 tively electrified. We may therefore con- 
 clude from these experiments, that when 
 a piece of paper burns, the paper becomes 
 positively electrified, and the flame nega- 
 tively electrified. The combustion of al- 
 cohol gives similar results. 
 
 SOLUTIONS OF QUESTIONS. 
 
 Quest. 42, (page 256) answered by 
 C. N. F. 
 
 Let A C in the following figure, 
 
 B 
 
 represent the semi diameter of the earth = 
 3978-875 miles, and Eg-, the elevation 
 above the earth = 2-5 miles. By 36 and 
 37 Euclid 3d Book ^/Bg- x (Bg + 2AC) 
 (=V2 -5 X 7960-25) = 141-0695 = A B. 
 
 But the triangles B A C and A / C are si- 
 milar, therefore asBC : AC :: AC : / C,or 
 3981-375 : 3978*875 : : 3978 875 : 3976-369, 
 and consequently g/= A C — f c = 2-506 ; 
 now the convex surface of the segment of a 
 sphere being equal to the circumference of 
 the sphere multiplied by the height of the 
 segment, it will be 25000 (= the earth ’s 
 circumference) X 2*506 = 62650 square 
 miles = the area of the space in view at 
 the given height. 
 
 This question was also answered by Mr. 
 J. Johnston, Elm-street , Gray' s-inn-lane , 
 who makes the answer the same as the 
 above; by Mr. J. Barr, who would have 
 made it the same if he had taken the dia- 
 meter of the Earth the same; by the Pro- 
 poser, who makes it 46,876*6 square miles; 
 and by Mr. J. Holroyd, Oldham , who 
 makes it only 31,313-5 square miles. This 
 last we suppose ought to have been mul- 
 tiplied by 2. 
 
 Quest. 43, answered by A. B. ( the Pro- 
 poser. J 
 
 Let x = the height ’of the mercury in 
 the tube, and 30— a* = the inches of the 
 tube now occupied by the air. Then as the 
 elasticity of the air is inversely as the space 
 it occupies ; the elasticity was= 28 inches, 
 when it occupied 8 inches, and is now = 
 224 
 
 (30 — x) : 8 : : 28 : — — . But the mer- 
 
 oU — X 
 
 cury in the tube plus the elastic force of 
 the air in the top of it, being a counter- 
 balance to the pressure of the atmosphere, 
 may be expressed by the column of mercury 
 
 224 
 
 in the barometer. Therefore a -j- — 
 
 30— x 
 
 28, consequently x 2 — 58 a = — 616, or x 
 = 14 inches, the height required. 
 
 QUESTION FOR SOLUTION. 
 
 Quest. 46, proposed by W. J. Lombard- 
 street. 
 
 In what time will a sinking fund of 4 
 millions of pounds extinguish a debt of 
 600 millions of pounds, reckoning interest 
 at 3f per cent. 
 
 Errata in a few of our early impres- 
 sions. 
 
 For page 228, read 256. 
 
 In page 242, fig. 2, transpose the letters 
 B and G ; and A and F. 
 
 In page 304, col. 2, line 11, after water 
 read enters. 
 
- — — 
 

 THE ARTISAN. 
 
 PIEIMAmB, 
 
 321 
 
322 
 
 THE ARTISAN. 
 
 STEAM ENGINE. 
 
 r In treating of Pneumatics at page 289, 
 we gave a description, and two different 
 views of Mr. Maudslay’s portable Steam 
 Engine ; and we now present our readers 
 with a third view, or longitudinal section, 
 of that instrument, which could not be got 
 ready in time to accompany the others. In 
 doing this it may be necessary to state, 
 that the description given at page 290 and 
 291, as well as the capital letters employed 
 to denote the several parts, apply to each 
 of these views ; but the small letters re- 
 late only to the preceding section. 
 
 STEAM NAVIGATION. 
 
 The possibility of employing steam as a 
 moving power in the navigation of vessels, 
 was known early in the last century ; its 
 practical application, however, on a large 
 scale, has not been fully established above 
 twenty years. 
 
 In 1G98 Savery recommended the use of 
 paddle-wheels, similar to those now so 
 generally employed in steam vessels, though 
 without in the remotest degree alluding to 
 his engine as a prime mover ; and it is 
 probable that he intended to employ the 
 force of men or animals working at a winch 
 for that purpose* , About forty years after 
 the publication of this mode of propelling 
 vessels, Mr. Jonathan Hulls obtained a 
 patent for a vessel, in which the paddle- 
 wheels were driven by an atmospheric 
 engine of considerable power. 
 
 In describing his mode of producing a 
 force sufficient for towing of vessels and 
 other purposes, the ingenious patentee 
 says, “ In some convenient part of the tow- 
 boat, there is placed a vessel about titfo- 
 thirds full of water, with the top close shut; 
 this vessel being kept boiling, rarefies the 
 water into steam; this steam being convey- 
 ed through a large pipe into a cylindrical 
 vessel, and there condensed, makes a vacu- 
 um, which causes the weight of the atmos- 
 phere to press oh this vessel, and so presses 
 down a piston that is fitted into this cylin- 
 drical vessel, in the same manner as in Mr. 
 Newcomen's engine, with which he raises 
 water by fire. 
 
 “ It has been already demonstrated, that 
 when the air is driven out of a vessel oT 
 thirty inches diameter, (which is but two 
 feet and a half), the atmosphere presses on 
 it to the weight of 4 tons 16cwt. and up- 
 wards ; when proper instruments for this 
 work are applied to it, it must drive a ves- 
 sel with great force.” 
 
 Mr. Hull's patent is dated 1736, and he 
 employed a crank to produce a rotatory 
 motion of his paddle-wheels, and this in- 
 genious mode of converting a reciprocating 
 into a rotatory motion, was afterwards re- 
 
 commended by the Abbe Arnal, Canon of 
 Alais, in Lanquedoc, who, in 1781, pro- 
 posed the crank for the purpose of turning 
 paddle-wheels in the navigation of light- 
 ers. 
 
 After our countryman Hulls, the Mar- 
 quis de Jouffroy unquestionably holds the 
 most distinguished rank in the list of prac- 
 tical engineers, who have added to the 
 value of this invention. 
 
 It is evident from an article published in 
 the Journal des Debats, that in 1781 the 
 Marquis constructed a steam boat at Lyons, 
 of 140 feet in length. With this he made 
 several successful experiments on the 
 Soane, near that city. The events of the 
 revolution, which broke out a few years 
 afterwards, prevented M. de Jouffroy from 
 prosecuting this undertaking, or reaping 
 any advantage from it. On his return to 
 France after a long exile, in 1796, he 
 learned from the newspapers that M. de 
 Blanc, an artist of Trevoux, had obtained 
 a patent for the' construction of a steam- 
 boat, built probably from such information 
 as he could procure relative to the experi- 
 ments of the Marquis. The latter appealed 
 to the government, which was then too 
 much occupied with public affairs to attend 
 to those of individuals* Meanwhile Ful- 
 ton, who had gained the same information, 
 and was making similar experiments near 
 the Isle des Cygnes, alarmed M. de Blanc, 
 who knew that he had much more to fear 
 from the influence and mechanical skill of 
 an Anglo-American, than from that of an 
 emigrant. He accordingly alleged his 
 patent right, and requested the stoppage o{ 
 Mr. Fulton’s works, who returned for 
 answer, that his essays could not affect 
 France, as he had no intention to setup a 
 practical competition upon the rivers of 
 that country, but should soon return to 
 America, which he actually did, and com- 
 menced the erection of those engines, to 
 which he has since laid claim as exclusive 
 inventor. 
 
 Shortly after the first experiments were 
 made by the Marquis de Jouffroy, a gen- 
 tleman of the name of Miller, who resided 
 at Dalswinton, published a work, in which 
 he described the application of wheels to 
 the working of triple vessels on canals ; 
 and in 1794 he completed a model of a boat 
 on this construction, impelled by a steam 
 engine. 
 
 From this period till IS01, but little pro- 
 gress appears to have been made in this 
 species of navigation; in that year Mr. 
 Symington, who had been employed in the 
 construction of Miller’s vessel, tried a boat 
 propelled by steam on the Forth-and-Clyde 
 Inland Navigation : this, however, was 
 shortly laid aside, on account of the injury 
 with which it threatened the banks of the 
 
THE ARTISAN, 
 
 3*23 
 
 eaiial, from the violent agitation produced 
 by the paddle-wheqls. • ,The following 
 
 figure 
 
 boat. 
 
 exhibits a representation of the 
 
 A is the boiler, B the cylinder, C the 
 piston, D the .condensation pipe, E the air 
 pump, and F are stampers for breaking 
 ice. 
 
 The first really practicable, and we may 
 add profitable attempt at steam navigation 
 in Europe, appears to have been made on 
 the Clyde in the year 1812. This was a 
 vessel for the conveyance of passengers, 
 ivith an engine of only three horses’ power, 
 and which was of considerable draught. 
 On account, however, of the numerous 
 shallows in our rivers, it has been found 
 advisable to construct the vessels employed 
 in this species of navigation, so as to draw 
 as little water as possible. 
 
 Mr. Maudslay has lately constructed a 
 large engine for a steam boat, invented by 
 Mr. Brunei, which has two cylinders acting 
 alternately upon different cranks, formed 
 upon the same axis at right angles to each 
 other, so that the motion is continued 
 without the action of a fly-wheel. In this 
 engine, one boiler is placed between the 
 two cylinders, and one air-pump and con- 
 denser exhaust them both ; so that by these 
 means an engine of considerable power is 
 contained in the smallest possible space. 
 
 We shall now briefly notice the labours 
 of our Trans-atlantie brethren in this im- 
 portant branch of naval engineering. Pro- 
 fiting by the hints thrown out both by the 
 Marquis de JoulTroy and Mr. Miller, Ful- 
 ton, who had also seen Symington’s boat, 
 ordered an engine, as represented above, 
 capable of propelling a vessel, to be con- 
 structed by Messrs. Boulton and Watt. 
 This was sent out to America, and em- 
 barked on Hudson’s river in 1807 ; and such 
 was the ardour of the Americans in sup- 
 port of this apparently new discovery, that 
 the immense rivers of the new world, 
 whose great width gave them considerable 
 advantages over the canals and narrower 
 streams of Europe, were soon regularly 
 navigated by these vessels. 
 
 The city of New York alone possesses 
 eight steam boats, for commerce and pas- 
 sengers. One of those on the Mississippi 
 passes two thousand miles in twenty-one 
 
 days, and this too against the current 
 which is perpetually running down. This 
 boat is 126 feet in length, and carries 
 460 tons at a very shallow draft of water* 
 and conveys from New Orleans, whole 
 ships’ cargoes into the interior of the 
 country, as well as passengers. 
 
 The usual mode of applying this extra- 
 ordinary power to the propelling of ves- 
 sels, has been by means of the paddle , 
 which is k series of revolving oars on one 
 axis. 
 
 This possesses the great advantage of 
 admitting safely of any increase of velocity, 
 without endangering the connection of their 
 parts ; on the other hand, an alternate mo- 
 tion can hardly be produced of sufficient 
 rapidity, without having the effect of shak- 
 ing itself to pieces. 
 
 The increase of velocity is not limited as 
 in the common oar, where the application 
 of human power, and the difficulty of quick 
 re-percussion, obliges us, where great ve- 
 locity is wanted, to have recourse to oars 
 of great length, for the revolution of the 
 paddle wheel may be as rapid as we 
 please, or its diameter may be increased 
 in any degree, and by this last means the 
 loss arising from the obliquity of action at 
 the beginning and end of the stroke may 
 be lessened, and. the effect of back-water 
 on the wheel diminished by the increased 
 centrifugal force comma ni'cated to. the 
 water. Here, therefore, is a rich field for 
 the investigation of the mechanical philoso- 
 pher, or scientific engineer, but one which 
 we cannot enter into very deeply at pre- 
 sent. 
 
 We may however remark, that though 
 velocity in the propeller or oar be desira- 
 ble, yet it has its limits ; for, in the first 
 place, time must be given for the water to 
 fall in after the oar or paddle, before a 
 new stroke be given, and therefore the 
 paddles or oars should be as few as possi- 
 ble. A propeller of great radius will also 
 be found inconvenient, by occupying too 
 much space. The water should enter and 
 be discharged from the paddle, as nearly 
 as possible in a tangent to the circle ; and 
 Y 2 
 
324 
 
 THE ARTISAN. 
 
 where waves occur, they should be pre- 
 vented from rising against, and burying the 
 paddle. Where the vessel works both with 
 sails and paddles, the means of equalizing 
 the action of the paddles, as the vessel 
 heels, must be employed. For in heavy 
 gales of contrary wind, the machinery will 
 scarcely be able to force the vessel against 
 
 it, and the mode of beating to windward 
 with sails will be found of greater im- 
 portance. The propellers will destroy the 
 leeway ; and we know that if the vessel 
 can carry sail, she may, in such cases, run 
 on the obliqug course with a greater velo- 
 city than that of the wind. 
 
 OPTICS. 
 
 sir w. herschel’s large telescope. His telescope of forty feet will long remain 
 The Newtonian telescopes, which had a splendid example of royal munificence, 
 for a long time been thrown into the shade ana ^ an( * * n S enu ^y °f * ts inven- 
 
 by the fine Gregorian ones constructed by : ar * We 'shallnow attempt to convey an 
 Mr. Short, were revived, towards the end * dea °* lts appearance and construction 
 of the last century, by Sir W. Herschel. b y means of the following figure. 
 
 A B C is the path of a ray of light re- 
 flected by the min-or at B to the eye-glass 
 C. Da chair in which the observer sits. 
 E a moveable gallery on which several per- 
 sons may stand. F G a smooth surface on 
 which the bottom of the telescope is made 
 to roll along, while its opening is raised or 
 depressed by the pullies at H and I. K 
 one of two rooms for the accommodation of 
 the observer’s assistants. 
 
 It rests on a foundation of two concen- 
 tric circular brick walls, the outermost of 
 
 which is forty-two feet in diameter, and 
 the innermost twenty-one feet. These 
 walls are two feet six inches deep under- 
 ground; two feet three inches broad at the 
 bottom, and one foot two inches at the top, 
 and they are capped with paving stones, 
 about twelve and three-fourth inches 
 broad, and about three inches thick. Upon 
 these two walls, which were made uniform 
 on the surface, and horizontal, with the 
 greatest care, rests the bottom frame of the 
 whole apparatus, which moves e upon 
 
THE ARTISAN. 
 
 325 
 
 twenty concentric rollers, and is always 
 moveable upon a pivot, which gives a hori- 
 zontal motion to the whole apparatus. The 
 length of the ladders is forty-nine feet two 
 inches, and the flats and rounds are all 
 made of solid English split oak. The two 
 outside divisions of the ladders serve for 
 mounting into the gallery. The middle 
 top cross beam rests on the angle made by 
 the crossing of the two sets of ladders. 
 There is a small staircase, by which we 
 may ascend into the gallery without being 
 obliged to go up the ladders, and as the 
 gallery is strong enough to hold a company 
 of several persons, and can afterwards be 
 drawn up to any altitude, observations 
 may be made with the greatest facility and 
 conveniency. 
 
 The great tube, though of a very simple 
 form, was constructed with much difficulty. 
 It is thirty-nine feet four inches long, four 
 feet ten inches in diameter, and every part 
 of it is made of rolled or sheet iron, joined 
 together without rivets, by a kind of seal- 
 ing used in the manufacture of iron funnels 
 for stoves. The whole outside was thus 
 put together in all its length and breadth, 
 so as to make one sheet of nearly forty feet 
 long, and fifteen feet four inches broad. 
 Each sheet of iron was three feet ten inches 
 long, and about 23^ inches broad. Their 
 thickness was less than the 36th part of an 
 inch, and a square foot weighed about 
 fourteen ounces. Had the tube been made 
 of wood, its vreight would have exceeded 
 that of the iron one at least 3000 lbs. 
 
 The metat of the great mirror is 49§ 
 inches in diameter, but on the rim there is 
 an offset of three-fourths of an inch broad, 
 and one inch deep, which reduces the con- 
 cave face of it to a diameter of 48 inches of 
 polished surface. The thickness, which is 
 uniform throughout, is about 3| inches, 
 and its weight, when newly cast, was 
 2118 lbs. of which it must have lost a 
 small quantity in polishing. In order to 
 preserve the speculum from damp, a flat 
 cover of tin was soldered on a rim of iron, 
 about l|th broad, and l-8th thick, the 
 diameter of which is equal to that of the 
 iron ring which holds the speculum. On 
 the flat part of the rim, some close-grained 
 cloth, of an equal breadth with the rim, is 
 cemented all round, so that the rim of the 
 cover, when put over the speculum, fits 
 closely to the edge of the iron ring. 
 
 The method of observing with this teles- 
 cope, is what Sir W. Herschel calls the 
 front view, and for this purpose there is a 
 convenient seat D fixed to the end of the 
 tube, in which the observer sits with his 
 back towards the object he views. The 
 seat is moveable from the height of 
 one foot seven inches to two feet seven 
 inches, partly for the accommodation of 
 different observers, but chiefly for the al- 
 
 teration required at different altitudes. 
 This seat is brought to a horizontal posi- 
 tion by turning a handle attached to a bar, 
 carrying two pinions, which -work in two 
 strong toothed quadrants of iron at the 
 sides of the seat. The focus of the great 
 speculum is brought down by its proper 
 adjustment to within four inches of the 
 lower side of the mouth of the tube, and 
 comes forward into the air, and by this 
 arrangement there is room for that part of 
 the head which is above the eye, not to in- 
 terfere greatly with the rays that pass 
 from the object to the mirror ; the aperture 
 of the speculum being four feet, while the 
 diameter of the tube is four feet ten inches. 
 
 A slider on an adjustable foundation is 
 fixed at the mouth of the telescope, so as 
 to be directed to the centre of the specu- 
 lum. It carries a brass tube, into which 
 all the single eye-glasses are made to slide. 
 When they are nearly brought to the focus, 
 a milled head under the end of the tube 
 turns a bar, the motion of which adjusts 
 them completely, so that as there is no 
 small speculum, the eye-glasses are ap- 
 plied immediately to magnify the inverted 
 image in the focus of the great speculum. 
 
 From the mouth of the telescope a speak- 
 ing pipe descends to the bottom of the tube, 
 when it divides into two branches, one of 
 which enables the observer to communi- 
 cate with his assistant in the observatory 
 K, and the other withThe workman in ano- 
 ther room, who gives the instrument all its 
 movements. 
 
 A sidereal time-piece is placed in the 
 observatory, and close to it a polar dis- 
 tance-piece, which may be made to show 
 polar distances, declination, or altitude, by 
 setting it differently. The time and polar 
 distance-pieces are placed in such a man- 
 ner, that the assistants sit before them at a 
 table, the speaking pipe rising between 
 them, and in this manner observations may 
 be very conveniently made. 
 
 This splendid instrument magnifies above 
 6000 times, and Sir William has sometimes 
 employed a power of 6450 for the fixed 
 stars. These high powers are obtained 
 merely by using small double convex 
 lenses for eye-glasses. Some of these, 
 ground and polished with the utmost 
 care, are so small as one-fiftieth of an inch 
 in focal length. The existence of such 
 minute lenses we should have thought in- 
 credible, had we not been assured of the 
 fact, and found that others had of them 
 made by the same ingenious artist, (the 
 late Mr. Shuttleworth,) who ground them 
 for Sir William Herschel. 
 
 NEW REFLECTING TELESCOPE BY DR. 
 
 BREWSTER. 
 
 We believe it is generally admitted by 
 every person who has had much experi- 
 
THE ARTISAN. 
 
 ence in the construction and use of reflect- 
 ing telescopes, that the Newtonian form is 
 decidedly the best. Its construction is so 
 simple, and it is so little liable to derange- 
 ment from accidental causes, that for popu- 
 lar use, on a small scale, it is superior to 
 the Gregorian one, while, for instruments 
 of great size, it is the only form that is 
 practicable. But even when we consider 
 it in a scientific point of view, it has the 
 advantage of the Gregorian form. It is 
 more easy to give a perfect figure to an 
 uniform circular piece of metal than to a 
 perforated disc the spherical aberration 
 is less, in so far as it is not increased by a 
 second spherical mirror ; — and the quantity 
 of light reflected from the objique small 
 speculum is decidedly greater than when it 
 is reflected at a vertical incidence. 
 
 If we could dispense with tjie use of the 
 small specula in telescopes of moderate 
 length, by inclining the great speculum, 
 and using an oblique, and consequently a 
 distorted reflexion, as proposed first by 
 Le Maire, we should consider the New- 
 tonian telescope as perfect ; and on a large 
 scale, or when the instrument exceeds 
 twenty feet, it has undoubtedly this cha- 
 racter, as nothing can be more simple than 
 to magnify by a single eye-glass the image 
 formed by a single speculum. 
 
 As the front view is quite impracticable, 
 and indeed has never been attempted in 
 instruments of a small size, it becomes of 
 great practical consequence to remove as 
 much as possible the evils which arise 
 from the use of a small speculum. These 
 evils may be thus enumerated : 
 
 L. If we suppose the light reflected by 
 the large speculum to amount to 10000 rays, 
 then the light reflected by a well polished 
 plane speculum will not exceed 6666 at a 
 vertical incidence, and probably not above 
 6800 at an incidence of 45° ; consequently 
 8100 rays out of 10,000 are lost by the use 
 of the plane speculum. 
 
 2. Besides this great loss of light, we 
 have to encounter all the errors of a second 
 reflexion, arising from imperfection of 
 figure, and also from imperfections of sur- 
 face, as it is universally admitted that a 
 surface of glass is much superior to a me- 
 tallic surface ; and Newton has himself 
 remarked, “ that eyery irregularity in a 
 reflecting superficies makes the rays stray 
 jive or six times more out of their due 
 course than the like irregularities in a re- 
 fracting one. 
 
 The construction by which Dr. Brewster 
 proposes to remedy these disadvantages is 
 shown in the following figure, 
 
 A 
 
 J2— 
 
 where A B is the speculum, reflecting the 
 parallel rays R A, RB, to a focus at F. 
 The cone of rays A F B is intercepted by 
 an achromatic prism G H, which refracts 
 them to foci at /, where a distinct image 
 is formed in the anterior focus of the eye- 
 glass E, by which it is magnified. The 
 compound prism G H being composed of a 
 prism of crown glass, and a prism of flint 
 glass H, united by a cement of a mean re- 
 fractive power, the loss of light sustained 
 by the pencil in its transmission through 
 the two, will not exceed 600 rays out of 
 the 10,000, as the light transmitted through 
 a lens of glass is 9485 out of the 10,000 
 incident rays. Hence the light lost by 
 transmission through the prism is not one- 
 fifth part of the light lost by reflexion ; 
 and the errors of reflexion arising from 
 defect of surface and of figure are also in- 
 comparably less. As the refracting angle 
 of the prism G will require to be larger, 
 
 in order to produce a given deviation FH/, 
 when it is opposed by the refraction of the 
 flint-glass prism H, we may place the cor- 
 recting prism H nearer the focus/, and 
 make it of crown glass; or it might, 
 even be placed at A, beyond the focus, and 
 in contact with the lens E. If this should 
 be found advantageous, the prism and the 
 lens might be formed out of one piece of 
 glass, or a single hemisphere of glass 
 might be used, the eye-hole being placed 
 at such a point of the hemispherical sur- 
 face, as to obtain a variable prism of the 
 required angle united with a plano-convex 
 lens. 
 
 As Dr. Maskelyne found that the Green- 
 wich Newtonian telescope was greatly im- 
 proved by inclining the speculum, or its 
 axis, about 2£° to the axis of the tube, it 
 follows, that it performed best with oblique 
 pencils in a certain direction. Before 
 fitting up this telescope, therefore, or in- 
 
THE ARTISAN. 
 
 327 
 
 4e,ed .any Newtonion telescope, it should 
 he ascertained,, by turning the speculum in 
 its cell and giving its axis various degrees 
 of\obliquity, whether or not its performance 
 is improved. If this is found to be the 
 case, and that the angle of inclination is 
 2^°, we shall then require a less angle in 
 the prism G, as part of the deviation of 
 the pencil to the side of the tube is already 
 produced by the new position of the axis 
 of the speculum. 
 
 It is obvious that any rays incident on 
 the prism G H, parallel to the tube, will 
 be refracted upon the side of the tube, and 
 will have no effect upon the image ; but if 
 they should be thought injurious, we have 
 only to place an opaque screen, of the 
 same size as G H and its arm, somewhere 
 between GH and the mouth of the tube, 
 so as not to interfere with the cone of re- 
 fracted rays G H /. 
 
 In viewing eclipses of the sun, or the 
 lunar disc, or any other celestial phenome- 
 non, where there is either tpq much light, 
 or more than is necessary, a telescope 
 may be fitted up to permit more than one 
 person to see through it at the same time, 
 by allowing a portion of the cone of rays to 
 be refracted through another prism to an 
 eye-glass at the opposite side of the tube, 
 or even by having four prisms refracting 
 a fourth part of the cone to each of the 
 four sides of the tube. The same effect 
 might be produced in the common New- 
 tonian telescope, by using a pyramidal 
 small speculum with the planes meeting 
 at a vertex placed in the centre of the cone 
 of rays, and inclined to one another at 
 angles of 90°, and to the axis of the teles- 
 cope at angles of 45°. 
 
 CEEMISTEY, 
 
 OF THE METALS. 
 
 The metals are the next class of bodies 
 which fall to be described in the order 
 which we have laid down, for treating of 
 the various substances to be noticed in thus 
 part of the present work. 
 
 We shall therefore now enter upon the 
 description of these brilliant bodies so use- 
 ful to society ; which so highly influence 
 public and individual prosperity, not only 
 by their real properties, but by the ideal 
 value attached to them; which have on 
 the one hand rendered such eminent ser- 
 vices to humanity, and on the other pro- 
 duced so many evils; which at the same 
 time mark the industry of nations, and add 
 to the improvement of human reason, 
 while they so often become the instru- 
 ments, and almost the cause, of the depra- 
 vation, the misery, and all the evils which 
 
 afflict mankind. There are no productions 
 of nature which excite a higher degree of 
 interest in their study, or which have given 
 rise to so many discoveries : there are not, 
 consequently, any substances which de- 
 serve to be treated more fully, or with 
 greater care. 
 
 The multiplied uses to which the metals 
 are applicable, do not constitute the only 
 reason why they should be described with 
 accuracy, and studied with attention. The 
 vast influence which they have had on the 
 progress of chemistry, the discoveries which 
 relate to them, particularly in modern 
 times, and the perfection which they have 
 added to human reason, render them of the 
 greatest consequence to those who culti- 
 vate natural philosophy. On the proper- 
 ties of these bodies depend the mariners’ 
 compass, the arts of printing, of navigation 
 and astronomy, and every other science 
 which are most truly honourable to the 
 genius of man. There is, in truth, no art 
 which can be carried on without the metals. 
 They are the first movers and primary in- 
 struments of almost every workshop. 
 There is scarcely a single circumstance of 
 life in which we do not derive continual 
 services, or in which we are not subjected 
 to dangers from their energy. The metals 
 are friends which serve us, and which it is 
 desirable we should always have near us ; 
 or they are enemies pressed into our em- 
 ploy, which jt is consequently of import- 
 ance that we should know how to subdue, 
 and sometimes to coerce. 
 
 So sensible were the ancients of their 
 great importance, that they raised those 
 persons who first discovered the art of 
 working them to the rank of deities. In 
 Chemistry, they have always filled a con- 
 spicuous station : at one period the whole 
 science was confined to them ; and it may 
 be said to have owed its very existence to 
 a rage for making and transmuting metals. 
 
 Ojje of the most conspicuous properties 
 of the metals is a particular brilliancy 
 which they possess, and which has been 
 called the metallic lustrel There are other 
 bodies indeed (mica for instance) which 
 apparently possess this peculiar lustre ; 
 but in them it is confined to the surface, 
 and accordingly disappears when they are 
 scratched; whereas it pervades every part 
 of the metals. This lustre is_ occasioned 
 by their reflecting much more light than 
 any other bodies ; a property which seems 
 to depend partly on the closeness of their 
 texture. This renders them peculiarly 
 proper for mirrors, of which they always 
 form the basis. 
 
 They are perfectly opaque, or impervious 
 to light, even after they have been reduced 
 to very thin plates. Silver leaf, for in- 
 stance, tsootsu an * nc h does not 
 
 permit the smallest ray of light to pass 
 
328 
 
 THE ARTISAN. 
 
 through it. Gold, however, when very 
 thin, is not absolutely opaque ; for gold 
 leaf ss^uns °f an inch thick, when held be- 
 tween the eye and the light, appears of a 
 lively green, and must therefore, as New- 
 ton first remarked, transmit the green 
 coloured rays. It is not improbable that 
 all other metals, as the same philosopher 
 supposed, would also transmit light, if 
 they could be reduced to a sufficient de- 
 gree of thinness. It is to this opacity that 
 a part of the excellence of the metals, as 
 mirrors, is owing ; their brilliancy alone 
 would not qualify them for that purpose. 
 
 Most of them may be melted by the ap- 
 plication of heat, and even then still retain 
 their opacity. This property enables us to 
 cast them in moulds, and then to give 
 them any shape we please. In this man- 
 ner, many elegant iron utensils are formed. 
 Different metals differ exceedingly from 
 each other in their fusibility. Mercury is 
 so very fusible, that it is always fluid at 
 the ordinary temperature of the atmos- 
 phere; while other metals, as platinum, 
 cannot be melted except by the most vio- 
 lent heat which it is possible to produce. 
 
 In general, their specific gravity is much 
 greater than that of any other body at 
 present known. Potassium, one of the 
 lighest of them, is, however, lighter than 
 water ; and the specific gravity of plati- 
 num, the heaviest of all the metals, is 23. 
 This great density, no doubt, contributes 
 considerably to the reflection of that great 
 quantity of light which constitutes the 
 metallic lustre. 
 
 They are the best conductors of electri- 
 city of all the bodies hitherto tried. 
 
 None of the metals are very hard ; but 
 some of them may be hardened by art to 
 such a degree, as to exceed the hardness 
 of almost all other bodies. Hence the 
 numerous cutting instruments which the 
 moderns make of steel, and which the 
 ancients made of a combination of copper 
 and tin. 
 
 The elasticity of the malleable metals 
 ^depends upon their hardness ; and it may 
 be increased by the same process by which 
 4heir hardness is increased. Thus the 
 steel of which the balance springs of 
 watches is made is almost perfectly elastic, 
 though iron in its natural state possesses 
 but little elasticity. 
 
 But one of their most important pro- 
 perties is malleability , by which is meant 
 the capacity of being extended and flat- 
 tened when struck with a hammer. This 
 property, which is peculiar to metals, 
 enables us to give the metallic body any 
 form we think proper, and thus renders it 
 easy for us to convert them into the various 
 instruments for which we have occasion. 
 All metals do not possess this property ; 
 but almost all those which were known to 
 
 the ancients have it. Heat increases this 
 property considerably. Metals become 
 harder and denser by being hammered. 
 
 Another property, which is also wanting 
 in many of the metals, is ductility ; -by 
 which we mean the capacity of being drawn 
 out into wire, by being forced through 
 holes of various diameters. 
 
 Ductility depends, in some measure, on 
 another property which metals possess, 
 namely, tenacity ; by which is meant the 
 power which a metallic wire of a given 
 diameter has of resisting, without break- 
 ing, the action of a weight suspended from 
 its extremity. Metals differ exceedingly 
 from each other in their tenacity. An iron 
 wire, for instance, ^ of an inch in diame- 
 ter, will support, without breaking, about 
 5001b. weight; whereas a lead wire, of 
 the same diameter, will not support above 
 291b. 
 
 When metals are exposed to the action 
 of heat and air, most of them lose their 
 lustre, and are gradually converted into 
 earthy -like powders of different colours 
 and properties, according to the metal 
 and the degree of heat employed. ^Several 
 of them even take fire when exposed to a 
 strong heat; and after combustion, the re- 
 siduum is found to be the very same earthy- 
 like substance. 
 
 All metals, even the few that resist the 
 action of heat and air, undergo a similar 
 change, when exposed to acids, especially 
 the sulphuric, the nitric, and the muriatic, 
 or a mixture of the two last. All metals, 
 by these means, may be converted into 
 powders, which have no resemblance to 
 the metals from which they were obtained. 
 These powders were formerly called calces ; 
 but at present they are better known by 
 the name of oxides. They are of various 
 colours, according to the metal and the 
 treatment, and are frequently manufactured 
 in large quantities to serve as paints. 
 
 When these oxides are mixed with char- 
 coal powder, and heated in a crucible, 
 they lose their earthy appearance, and are 
 changed again into the metals from which 
 they were produced. Oil, tallow, hydro- 
 gen gas, and other combustible bodies, 
 may be often substituted for charcoal. By 
 this operation, which is called the reduc- 
 tion of the oxides, the combustible is dimi- 
 nished, and, indeed, undergoes the very 
 same change as when it is burned. 
 
 No metal can be converted into an oxide, 
 except some substance be present which 
 contains oxygen ; and, during the oxydize- 
 ment, a portion of that oxygen disappears. 
 
 There are some metallic oxides which 
 can be reduced by the application of heat in 
 close vessels. Now, whenever they are 
 reduced in that manner, they yield oxygen 
 gas : and the weight of the oxygen, toge- 
 ther with that of the metal obtained, is 
 
THE ARTISAN. 
 
 329 
 
 equal to the weight of the original oxide. 
 Thus, when the oxide of mercury is heated 
 in a retort, to which a pneumatic appara- 
 ratus is attached, to the temperature of 
 1000°, it is converted into pure mercury ; 
 and, at the same time, a quantity of oxygen 
 separates from it in a gaseous form. The 
 weights of the metal and the oxygen gas 
 are together equal to that of the oxide; 
 the calx of mercury, therefore, must be 
 composed of mercury and oxygen only. 
 Its calcination is merely the act of its 
 uniting with oxygen. Gold, platinum, 
 silver, nickel, and even lead, may be re- 
 duced in the same way, and w r ith the same 
 evolution of oxygen gas. Several other 
 oxides may be brought nearer the metallic 
 state, though they cannot be completely 
 reduced by heat, and this approach is ac- 
 companied by the escape of oxygen gas. 
 Manganese, zinc, and probably also iron, 
 are in this predicament. 
 
 All the oxides are reduced by means of 
 combustible bodies, and, during the com 
 bustion, the combustible unites to oxygen. 
 This is the reason that charcoal-powder is 
 so efficacious in reducing them ; and if they 
 are mixed with it, and heated in a proper 
 vessel furnished with a pneumatic appa- 
 ratus, it will be easy to discover what 
 passes. During the reduction, a great 
 deal of carbonic acid and carbonic oxide 
 comes over. These, together with the 
 metal, are equal to the weight of the oxide 
 and the charcoal : they must therefore con- 
 tain all the ingredients ; and we know that 
 they are composed of carbon and oxygen. 
 Therefore, during the process, the oxygen 
 of the oxide combines with the charcoal, 
 and the metal remains behind. In the 
 same manner, when oxide of iron is heated 
 sufficiently, in contact with hydrogen, the 
 iron is reduced, and water is formed, as 
 was first ascertained by the experiments of 
 Dr. Priestly. 
 
 It therefore cannot be doubted, that all 
 the metallic calces are composed of the 
 entire metals combined with oxygen ; and 
 that calcination, like combustion, is merely 
 the act of this combination. All metals, 
 then, in the present state of Chemistry, 
 must be considered as simple substances ; 
 for they have never yet been decom- 
 pounded. 
 
 The words calx and calcination being 
 evidently improper, because they convey 
 false ideas, the words oxide and oxidize- 
 ment, which were invented by the French 
 Chemists, are substituted for them. A 
 metallic oxide significes a metal united 
 with oxygen ; and oxidizement implies the 
 act of that union. 
 
 Metals, then, are all capable of combin- 
 ing with oxygen ; and this combination is 
 sometimes accompanied by combustion, 
 and sometimes not. The new compounds 
 
 formed’ are called metallic oxides, and in 
 some cases metallic acids. Like the two 
 last classes of bodies, they are capable of 
 combining with different doses of oxygen, 
 and of forming different species of oxides 
 or acids. These were formerly distin- 
 guished from each other by their colour. 
 One of the oxides of iron, for instance, was 
 called black oxide, another was termed red 
 oxide ; but it is now known that the same 
 oxide is capable of assuming different co- 
 lours, according to circumstances. The 
 mode of naming them from their colour, 
 therefore, wants precision, and is apt to 
 mislead ; especially as there occur different 
 examples of two distinct oxides of the 
 same metal having the same colour. 
 
 As it is absolutely necessary to be able 
 to distinguish the different oxides of the 
 same metal from each other with perfect 
 precision, and as the present chemical no- 
 menclature is defective in this respect, we 
 shall adopt the nomenclature of Dr. Thom- 
 son, and distinguish them from each other, 
 by prefixing to the word oxide the first 
 syllable of the Greek ordinal numerals. 
 Thus the protoxide of a metal will be em- 
 ployed to denote the metal combined with 
 a minimum of oxygen, or the first oxide 
 which the metal is capable of forming ; 
 deutoxide to denote the second oxide of a 
 metal, or the metal combined with two 
 doses of oxygen ;* and when a metal has 
 combined with as much oxygen as possi- 
 ble, the term peroxide will be employed to 
 signify that the metal is thoroughly oxi- 
 dized. 
 
 We shall therefore employ the term 
 oxide to denote the combination of metals 
 with oxygen in general ; the terms protoxide 
 and peroxide to denote the minimum and 
 maximum of oxidizement; and the terms 
 deutoxide, tritoxide, &c. to denote all the 
 intermediate states which are capable of 
 being formed. 
 
 Metals are capable of combining with 
 the simple combustibles. The compounds 
 thus formed are denoted by the simple com- 
 bustible which enters into the combination, 
 with the termination uret added to it. Thus 
 the combination of a metal with sulphur, 
 phosphorus, or carbon, is called the sul- 
 phuret, phosphuret, or carburet of the metal. 
 The compounds formed by the metals with 
 the three combustibles just mentioned are 
 usually solid ; but when hydrogen unites 
 with them, it still retains the elastic state. 
 These solutions of metals in hydrogen 
 have been but slightly examined. They 
 are usually distinguished by an epithet, 
 indicating the metal, prefixed to the word 
 hydrogen, as arsenical hydrogen. 
 
 * The same explanation v/iTI apply to tritoxide , 
 (third oxide), tetoxide (four tli oxide), &c. whenever 
 they become necessary. 
 
THE ARTISAN. 
 
 oSO 
 
 The metals in general unite very readily 
 ifrith one another, and form compounds, 
 some of which are extremely useful in the 
 manufacture of instruments and utensils. 
 Thus pewter is a compound of lead and 
 tin ; brass, a compound of copper and zinc; 
 bell-metal, a compound of copper and tin. 
 These metallic compounds are called by 
 Chemists alloys, except when one of the 
 combining metals is mercury. In that case, 
 the compound is called an amalgam. Thus 
 the compound of mercury and gold is called 
 the amalgam of gold. 
 
 When no other bodies were considered 
 as metals but those which possess ductility, 
 and when their number was confined to 
 six or seven, it was not necessary to seek 
 after many properties, nor to establish any 
 method for distinguishing and ascertaining 
 each of these bodies. The notion of form- 
 ing a classification must have scarcely 
 occupied the attention of chemists. 
 
 astronomy* 
 
 OF ECLIPSES. 
 
 Of all the various phenomena of the 
 heavens there are none which have created 
 so much curiosity, excited so much interest, 
 or caused so great terror throughout the 
 world, as eclipses of the sun and moon; 
 and to those who are unacquainted with 
 the principles of astronomy there is no- 
 thing perhaps which appears more extra- 
 ordinary than the accuracy with which 
 they can be predicted. 
 
 In the earlier ages of the world, before 
 science had enlightened the minds of men, 
 appearances of this kind were generally 
 regarded as alarming deviations from the 
 established laws of nature ; and but few, 
 even among philosophers themselves, were 
 able to account for these extraordinary ap- 
 pearances. At length, when men began 
 to apply themselves to observations, and 
 when the motions of the celestial bodies 
 were better understood, these phenomena 
 were not only found to depend upon a 
 regular cause, but to admit of a natural and 
 easy solution. There are, however, na- 
 tions that still entertain the most supersti- 
 tious notions respecting eclipses, particu- 
 larly the Mexicans and Chinese. 
 
 -Thus when the infant moon her circling sphere 
 Wheels o’er the sun’s broad disk, her shadow falls 
 On earth’s fair bosom ; darkness chills the fields, 
 And dreary night invests the face of heaven. 
 Reflected from the lake full many a star 
 Glimmers with feeble languour. India’s sons 
 Atfrighted in wild tumult rend the air. 
 
 Before his idol god with barb’rous shriek 
 TheBrachman* falls : when soon the eye of day 
 Darts his all-cheering radiance, from the gloom 
 
 * Although the Chinese perform the most ridicu- 
 lous and superstitious ceremonies during the time of 
 an eclipse, yet they can calculate them with tlie 
 greatest precision. 
 
 Emerging. Joy invades the Wond’fmg crowd, 
 
 And acclamation rushes from the tongues 
 Of thousands, that around their blazing pile 
 Riot in antic dance and dissonant song. ZoucU- 
 
 Many instances are to be found, not 
 only in ancient, but even in comparatively 
 modern history, where the superstition of 
 the times has continued to connect the 
 records of eclipses with the details of some 
 remarkable event, which either happens 
 soon after or during their continuance. But 
 these details being foreign to the nature of 
 the present work, we shall proceed to 
 give an account of the causes, and various 
 kinds of eclipses of the sun and moon. 
 
 As every planet belonging to the solar 
 system, both primary and secondary, de- 
 rives its light from the sun, it must cast a 
 shadow towards that part of the heavens 
 which is opposite to the sun. This shadow 
 is of course nothing but a privation of light 
 in the space hid from the sun by the opaque 
 body, and will always be proportionate to 
 the relative magnitudes of the sun and 
 planet. If the sun and planet were both 
 of the same size, the form of the shadow 
 cast by the planet would be that of a 
 cylinder, the diameter of which would be 
 the same as that of the sun or planet, and 
 it would never converge to a point. If the 
 planet were larger than the sun, the sha- 
 dow would continue to spread or diverge ; 
 but as the sun is much larger than the 
 greatest of the planets, the shadows cast 
 by any one of these bodies must converge 
 to a point, the distance of which from the 
 planet will be proportionate to the size and 
 distance of the planet from the sun. The 
 magnitude of the sun is such that the sha- 
 dow cast by each of the primary planets 
 always converges to a point before it reaches 
 any other planet ; so that not one of the 
 primary planets can eclipse another. The 
 shadow of any planet which is accom- 
 panied by satellites may, on certain occa- 
 sions, eclipse these satellites; butitisnot 
 long enough to eclipse any other body. The 
 shadow of a satellite or moon may also, on 
 certain occasions, fall on the primary and 
 eclipse it. 
 
 Eclipses of the sun and moon happen 
 when the moon is near her nodes, that is, 
 when she is either in the plane of the 
 ecliptic or very near it. Those of the sun 
 happen only at new moon, or when the 
 moon is in conjunction with the sun ; whilst 
 those of the moon happen at the time of full 
 moon, or when the moon is in opposition to 
 the sun. The sun, earth, and moon, must 
 therefore always be nearly in the same 
 straight line at the time of an eclipse ; and 
 conversely, when these three bodies are 
 nearly in a straight line, an eclipse must 
 take place. Hence it is evident, that an 
 eclipse happens in consequence of one of 
 the two opaque bodies, the earth and the 
 moon, being so placed as to prevent the 
 
THE ARTISAN. 
 
 331 
 
 &un’s light from falling on the other. — See 
 the following figure, which represents the 
 ipoon passing through the dark shadow of 
 
 the earth, as she moves in her orbit n z„ 
 while the earth moves in the ecliptic rq, 
 
 The interposition of t e moon between 
 |jhe sun and the earth produces an eclipse 
 of the sun ; and the interposition of the 
 earth between the moon and the sun, so 
 that its shadow falls on the moon, produces 
 an eclipse of the moon. On these princi- 
 ples the whole phenomena pf eclipses de- 
 pend, and adnjit of complete explanation. 
 
 If the moon’s orbit were coincident with 
 the plane of the ecliptic, the moon’s shadow 
 would fall upon the earth, and occasion a 
 central eclipse of the sun at every con- 
 junction, or newipoon; whilst the earth’s 
 shadow would fall on the moon, and occa- 
 sion a total eclipse of that body at every 
 opposition or full moon. For as the moon 
 would then always move in the ecliptic, 
 the centres of the sun, earth, and moon, 
 would all be in the same straight line at 
 both of these times. But the moon’s orbit 
 is inclined to the ecliptic, and forms with 
 it an angle of about 5° 10' ; and, therefore, 
 the moon is never in the ecliptic except 
 when she is in one of her nodes : hence, 
 there may be a considerable number of 
 conjunctions and oppositions of the sun 
 and mopn without any eclipse taking place. 
 
 The moop is always at some distance 
 from the ecliptic, except when she is in 
 one of her nodes; pnd this distance is 
 called her latitude , which is north or south, 
 according as the moon is on the north or 
 south side of the ecliptic. Now if the 
 moon has any latitude, there cannot be a 
 central eclipse, for this can only happen 
 when the moon is in one of her nodes at 
 the moment of conjunction, which is very 
 
 seldom the case ; and, of course, very few 
 central eclipses of the sun have taken place 
 since the creation of the world.* But the 
 section of the earth’s shadow (through 
 which the moon passes when she is 
 eclipsed) being much larger than the disc 
 of the moon, the moon may be totally 
 eclipsed, although she be at some distance 
 from her node at the time of opposition ; 
 but its duration will be the greater the 
 nearer she is to the node. An eclipse of 
 the sun may also happen, although the 
 moon be at some distance from her node at 
 the time of conjunction ; but its form, as 
 well as its duration, depend very much 
 upon that distance. This circumstance 
 has occasioned the division of eclipses into 
 central, total, annular, and partial. 
 
 As the meaning of these terms must be 
 obyious to the reader, it is almost unne- 
 cessary to give an explanation of them. 
 
 A central eclipse, is that in which the 
 centre pf the shadow falls on the centre of 
 the body which is eclipsed. 
 
 A total eclipse is the obscuration of the 
 whole body eclipsed. 
 
 An annular eclipse is that in which the 
 whole of the body eclipsed is hid, except 
 a ring round its edge, which remains lumi- 
 nous. 
 
 A partial eclipse is that in which part of 
 the eclipsed body is hid from view. 
 
 The following figure represents a partial 
 eclipse of the sun, which will be visible to 
 that tract of the earth marked npo, the 
 line m n marks the greatest obscura- 
 tion. 
 
 If the distance be very small, the eclipse 
 will be the greater and continue the longer; 
 but no eclipse of the sun can be either cen- 
 tral or total, except the moon be in the very 
 npde at the time of conjunction. But 
 
 should she be in this situation, when she is 
 
 * One of the most remarkable eclipses of this 
 kind which has ever happened, was visible in Bri- 
 tain and several other countries, on the 7th of Sep. 
 tember, 1820. 
 
332 
 
 THE ARTISAN. 
 
 at her least distance from the earth, aiid 
 the earth, at the same time, at its least 
 distance from the sun, then the eclipse will 
 not only be central but total , and continue 
 so for a few minutes. But if the moon 
 happens to be at her greatest distance from 
 the earth, and the earth at its greatest dis- 
 tance from the sun, the eclipse will be 
 annular, or a small space round the sun’s 
 centre only will be hid from view, and a 
 bright lucid ring round his edge will re- 
 main visible. 
 
 If the moon be less than 17| degrees 
 from either node at the time of conjunction, 
 her shadow will fall more or less ujpon the 
 earth, according as she is more or less 
 within this limit ; and, of course, the sun 
 will suffer a partial eclipse. And if she be 
 less than 12§ degrees from either node at 
 the time of opposition, she will pass 
 through more or less of the earth’s shadow, 
 according as she is more or less within 
 these lines, and of course she will suffer 
 an eclipse . 
 
 As these limits form but a small part of 
 the moon’s orbit, which is 360 degrees, 
 eclipses happen but seldom ; however, in 
 no year can there be fewer than two, and 
 there may be seven of the sun and moon 
 together — but taking one year with another, 
 there are about four each year. But as 
 the sun and moon spend as much time be- 
 low the horizon of any place as above it, 
 half the number of the eclipses will be in- 
 visible at any particular place, and con- 
 sequently there will be only two eclipses 
 visible in a year at that place, the one of 
 the sun and the other of the moon.'* 
 
 Every eclipse, whether of the sun or 
 moon, is visible at some place of the earth’s 
 surface, and invisible at others ; for the ra- 
 tional horizon of every place divides both 
 the earth and heavens into two equal por- 
 tions or hemispheres ; and as no celestial 
 body can be seen except it be above the 
 spectator’s horizon, it follows that any 
 eclipse which is visible in the one hemis- 
 phere cannot be visible in the other, because 
 the body which is eclipsed is below the ho- 
 rizon of that other. If a lunar eclipse, for ex- 
 amlpe, happens at any hour of the night, 
 between the time of sun-setting and sun- 
 rising, at any particular place, it will be 
 visible there and invisible to the inhabi- 
 tants of the opposite hemisphere, who have 
 the sun above their horizon at that time ; 
 for the sun and moon are in opposite parts 
 of the heavens at the time of a lunar 
 eclipse. And with respect to solar eclipses, 
 it is evident that they can only be seen at 
 any place when the sun is above the ho- 
 rizon of that place. There is, however, a 
 difference with regard to the visibility of a 
 solar and lunar eclipse ; for an eclipse of 
 
 the moon has the Same appearance to all 
 the inhabitants of that hemisphere to which 
 the moon is visible at the time, Owing, in 
 part, to the small distance of the moon from 
 the earth. But an eclipse of the sun may 
 be visible to some places and invisible to 
 others in the same hemisphere of the earth, 
 because the moon’s shadow is small in 
 comparison of the earth ; for its breadth, 
 excluding the penumbra, is only about 180 
 miles even in central eclipses.* Hence 
 those places which are considerably distant 
 from the path of the shadow will either 
 have no eclipse at all, or a very small one ; 
 while places near the middle of the shadow 
 will have the greatest possible. There is 
 also a difference in the absolute time at 
 which a solar eclipse happens at the va- 
 rious places where it is visible ; for it 
 appears more early to the western parts, 
 and later to the eastern, on account of the 
 motion of the moon ( and of course her 
 shadow) from west to east. 
 
 In most solar eclipses the moon’s disc 
 may be observed by a telescope to be 
 covered by a faint light, which is attri- 
 buted to the reflexion of light from the 
 illuminated part of the earth. When the 
 eclipses are total, the moon’s limb is sur- 
 rounded by a pale circle of light, which 
 some astronomers consider as an indication 
 of a lunar atmosphere, but others, as occa- 
 sioned by the atmosphere of the sun ; be- 
 cause it has been observed to move equally 
 with the sun and not with the moon. 
 
 Dr. Halley, in describing a central 
 eclipse of the sun, which happened at Lon- 
 don in April, 1715, says, that although the 
 disc of the sun was wholly covered by the 
 moon, a luminous ring of a faint pearly 
 light surrounded the body of the moon the 
 whole time ; and its breadth was nearly a 
 tenth of the moon’s diameter. 
 
 In lunar eclipses, the moon seldom dis- 
 appears entirely : and on some occasions, 
 even the spots may be distinguished 
 through the shade ; but this can only be 
 the case when the moon is at her greatest 
 distance from the earth at the time of the 
 eclipse, for the nearer the moon is to the 
 earth the darkness is the greater. In some 
 instances, the moon has disappeared en- 
 tirely ; and the celebrated astronomer, He- 
 raclius, has taken notice of one where the 
 moon could not be seen even with a tele- 
 scope, though the night was remarkably 
 clear. 
 
 Although eclipses of the sun and moon 
 were long considered by the ignorant and 
 superstitious as presages of evil, yet they 
 are of the greatest use in astronomy, and 
 may be employed to improve some of the 
 most important and useful of the sciences. 
 By eclipses of the moon the earth is proved 
 
 * If ithere be seven eclipses in any year, five of 
 them must be of the sun and two-of the moon. 
 
 * A penumbra is the faint shadow produced by 
 an opaqne body wheu opposed to a luminous one. 
 
THE ARTISAN.' 
 
 ass 
 
 to be of a globular form, the sun to be 
 I greater than the earth, and the earth greater 
 ! than the moon. When they are similar in 
 all their circumstances, and happen at con- 
 siderable intervals of time, they also serve, 
 to ascertain the real period of the moon’s 
 i motion. In geography, eclipses are of con- 
 siderable use in determining the longitude 
 ; of places, and particularly eclipses of the 
 ; moon, because they are oftener visible than 
 , I those of the sun, and the same eclipse is of 
 equal magnitude and duration at all places 
 where it is seen. In chronology, both 
 solar and lunar eclipses serve to determine 
 exactly the time of any past event. 
 
 For the purpose of finding the longitude 
 at places on the earth, eclipses of Jupiter’s 
 , I satellites are found much more useful than 
 eclipses of the moon ; not only on account 
 of their happening more frequently, but on 
 account of their instantaneous commence- 
 ment and termination. 
 
 When Jupiter and any of his satellites 
 | are in a line with the sun, and Jupiter be- 
 ; tween the satellite and the sun, it disap- 
 pears, being then eclipsed, or involved in 
 his shadow. When the satellite goes be- 
 hind the body of Jupiter, with respct to a 
 spectator on the earth, it is said to be oc- 
 culted, being hid from our sight by his 
 body, whether in his shadow or not. And 
 j when the satellite comes into a position 
 i between Jupiter and the sun, it casts a 
 shadow on the face of that planet, which 
 is seen by a spectator on the earth as an 
 obscure round spot. Lastly, when the sa- 
 tellite is in a line with Jupiter and the 
 earth, it appears on his disc as a round 
 black spot, which is termed a transit of the 
 | satellite. 
 
 As those phenomena appear at the same 
 moment of absolute time at all places on 
 the earth to which Jupiter is then visible, 
 but at different hours of relative time, ac- 
 g| cording to the distance between the meri- 
 t; dianof the places at which observations 
 are made, it follows that this difference of 
 1 time converted into degrees will be the 
 difference of longitude between those 
 places.* Suppose, for example, that a 
 person at London observed an eclipse to 
 begin at 11 o'clock in the evening, and that 
 a person at Barbadoes observed the same 
 at seven o’clock in the evening, it is certain 
 f the eclipse was seen by both persons at the 
 same moment of absolute time, although 
 I there is four hours difference in their man- 
 i ner of reckoning that time : and this con- 
 si verted into degrees (at the rate of 15 
 * I degrees to an hour) is the difference of 
 longitude between these two places — - 
 therefore Barbadoes is 60 degrees west 
 
 * Absolute time is that which is computed from 
 the same moment; relative is that which is com- 
 puted from different moments. 
 
 from London, the time not being so far 
 advanced there as at London. 
 
 Another phenomena, somewhat similar 
 to an eclipse, sometimes takes place, by 
 which the longitude of places may be de- 
 termined, although not quite so easily, nor 
 perhaps so accurately, as by the eclipses 
 of Jupiter’s satellites. This is the hiding 
 or obscuring of a fixed star or planet by the 
 moon or other planet, which takes place 
 when the moon or planet is in conjunction 
 with the star. Appearances of this kind 
 are termed occultations. They are very 
 little attended to except by practical astro- 
 nomers, who employ them for the correc- 
 tion of the lunar tables, and settling the 
 longitude of places, as already stated. 
 
 jTlt^eUatteous Subjects. 
 
 MEMOIR OF THE LIFE OF 
 HYPATIA. 
 
 Hypatia, a most beautiful, virtuous, and 
 learned lady of antiquity, was the daughter 
 of Theon, who governed the Platonic school 
 at Alexandria, the place of her birth and 
 education, in the latter part of the fourth 
 century. Theon was famous among his 
 contemporaries for his extensive knowledge 
 and learning ; but what has chiefly ren- 
 dered him so with posterity is, that he was 
 the father of Hypatia, who, encouraged by 
 her prodigious genius, he educated not 
 only in all the qualifications belonging to 
 her sex, but likewise in the most abstruse 
 sciences. She made an amazing progress 
 in every branch of learning, and the things 
 that are said of her almost surpass belief. 
 Socrates, the ecclesiastical historian, a 
 witness whose veracity cannot be doubted, 
 at least when he speaks in favour of a 
 heathen philosopher, tells us, that Hypatia 
 u arrived at such a pitch of learning, as 
 very far to exceed all the philosophers of 
 her time.” Philostorgius, a third historian 
 of the same stamp, affirms, that “ she was 
 much superior to her father and master, * 
 Theon, in what regards Astronomy and 
 Suidas, who mentions two books of her 
 writing, one “ On the Astronomical Canon 
 of Diophantus, and another on the Conics 
 of Apollonius,” avers, that “ she not only 
 exceeded her father in Astronomy, but also 
 that she understood all the other parts of 
 philosophy.” It is some confirmation of 
 these assertions, that she succeeded her 
 father in the government of the Alexan- 
 drian school : filling that chair, where 
 Ammonius, Hierocles, and many great and 
 celebrated philosophers had taught; and 
 this, at a time, when men of immense 
 learning abounded both at Alexandria, 
 and many other parts of the Roman em- 
 pire, Her fame was so extensive, and 
 
m 
 
 THE ARTISAN. 
 
 her worth so universally acknowledged, 
 that we cannot wonder if she had a crowded 
 auditory. “ She explained to her hearers,” 
 Says Socrates, “ the several sciences that 
 go under the general name of philosophy ; 
 for which reason there was a confluence to 
 her, from all parts, of those who made 
 philosophy their delight and study.” 
 
 Her scholars were as eminent as they 
 were numerous:- one of whom was the 
 celebrated Synesius, who was afterwards 
 Bishop of Ptolemais. This ancient Chris- 
 tian Platonist every where bears the 
 strongest, as well as the most grateful tes- 
 timony to the learning and virtue of his in- 
 structress ; and never mentions her without 
 the profoundest respect, and sometimes in 
 terms of affection coming little short of 
 adoration. In a letter to his brother 
 Euoptius, “ Salute,” says he “ the most 
 honoured and the most beloved of God, the 
 Philosopher ; and that happy society, 
 which enjoys the blessing of her divine 
 voice/’ In another, he mentions one 
 Egyptus, who “ sucked in the seeds of 
 wisdom from Hypatia.” In another, he 
 expresses himself thus : “ I suppose these 
 letters will be delivered by Peter, which 
 he will receive from that sacred hand.” 
 In a letter addressed to herself, he desires 
 her to direct a hydroscope to be made and 
 brought for him, which he there describes. 
 That famous silver astrolabe, which he 
 presented to Peonius, a man equally excel- 
 ling in philosophy and arms, he owns to 
 have been perfected by the directions of 
 Hypatia. In a long epistle, he acquaints 
 her with his reasons for writing two books, 
 which he sends her ; and asks her judg- 
 ment of one, resolving not to publish it 
 without her approbation. 
 
 But it was not Synesius only, 'and the 
 disciples of the Alexandrian school, who 
 admired Hypatia for her great virtue and 
 learning ; never woman was more caressed 
 by the public, and yet never woman had a 
 more unspotted character. She was held 
 as an oracle for her wisdom, which made 
 her consulted by the magistrates in all im- 
 portant cases ; and this frequently drew 
 her among the greatest concourse of men, 
 without the least censure of her manners. 
 “ On account of the confidence and autho- 
 rity,” says Socrates, “ which she had 
 acquired by her learning, she sometimes 
 came to the judges with singular modesty. 
 Nor was she any thing abashed to appear 
 thus among a crowd of men ; for all per- 
 sons, by reason of her extraordinary dis- 
 cretion, did at the same time both rever- 
 ence and admire her.’’ The same is con- 
 firmed by Nicephorus and other authors, 
 whom we have already cited. Damascius 
 and Suidas relate, that the governors and 
 magistrates of Alexandria regularly visited 
 her, and paid their court to her ; and when 
 Nicephorus intended to pass the highest 
 
 compliment on the Princess Eudbcia, h€ 
 thought he could not do it better, than by 
 calling her “ another Hypatia.” 
 
 While Hypatia thus reigned the bright- 
 est ornament of Alexandria, Orestes was 
 governor of the same place for the emperor 
 Theodosius, and Cyril bishop or patriarch. 
 Orestes, having had a liberal education, 
 admired Hypatia, and frequently con- 
 sulted her. This created an intimacy be- 
 tween them that was highly displeasing to 
 Cyril, who had a great aversion to Orestes: 
 which intimacy, as it is supposed, had 
 like to have proved fatal to Orestes, as we 
 may collect from the following account of 
 Socrates. “ Certain of the monks,” says 
 he, “ living in the Nitrian mountains, 
 leaving their monasteries to the number of 
 about five hundred, flocked to the city, and 
 spied the governor going abroad in his 
 chariot: whereupon approaching, they 
 
 called him by the names of Sacrificer and 
 Heathen, using many other scandalous ex- 
 pressions. The governor, suspecting that 
 this was a trick played him by Cyril, cried 
 out that he was a Christian, and that he 
 had been baptised at Constantinople by 
 Bishop Atticus. But the monks giving 
 no heed to what he said, one of them, 
 called Ammonius, threw a stone at Orestes, 
 which struck him on the head ; and being 
 all covered with blood from his wounds, 
 his guards, a few excepted, fled, some one 
 way and some another, hiding themselves 
 in the crowd, lest they should be stoned to 
 death. In the mean while, the people of 
 Alexandria ran to defend their governor 
 against the monks, and putting the rest to 
 flight, brought Ammonius, whom they ap- 
 prehended, to Orestes ; who, as the laws 
 prescribed, put him publicly to the torture, 
 and racked him till he expired. 
 
 But though Orestes escaped with his 
 life, Hypatia afterwards fell a sacrifice. 
 This lady, as we have observed, was pro- 
 foundly respected by Orestes, who much 
 frequented and consulted her : “ for which 
 reason,” says Socrates, “ she was not a 
 little traduced among the Christian mul- 
 titude, as if she obstructed a reconciliationr 
 between Cyril and Orestes. This occa- 
 sioned certain enthusiasts, headed by one 
 Peter, a lecturer, to enter into a conspiracy 
 against her; who, watching an opportu- 
 nity, when she was returning home from 
 some place, first dragged her out of her 
 chair, then hurried her to the church called 
 Caesar’s, and, stripping her naked, killed 
 her with, tiles. After this they tore her to 
 pieces ; and carrying her limbs to a place 
 called Cinaron, there burnt them to ashes.” 
 Cave endeavours to remove the imputation 
 of this horrid murder from Cyril, thinking 
 him too honest a man to have had any 
 hand in it; and lays it upon the Alexan- 
 drian mob in general, whom he calls “a 
 very trifliDg inconstant people,” But 
 
th& Artisan. 
 
 335 
 
 though dyril should foe allowed to have 
 been neither the perpetrator, nor even the 
 contriver of it, others have thought that he 
 did not discountenance it in the manner he 
 ought to have done : and was so far from 
 blaming the outrage committed by the 
 Nitrian monks upon the governor Orestes, 
 that . u he afterwards received the dead 
 body of Ammonius, whom Orestes had 
 punished with the rack ; made a panegyric 
 upon him, in the church where he was 
 laid, in which he extolled his courage and 
 constancy, as one that had contended fbr 
 the truth ; and, changing his name to 
 Thaumasius, or the Admirable, ordered 
 him to be considered as a* martyr. How- 
 ever,” continues Socrates, “ the wiser sort 
 of Christians did not approve the zeal 
 which Cyril showed on this man’s behalf, 
 being convinced, that Ammonius had justly 
 suffered for his desperate attempt.” We 
 learn from the same historian, that the 
 death of Hypatia happened in March, in 
 the 10th year of Honorius’s, and the 6th of 
 Theodosius’s, consulship ; that is, about 
 JLD. 415, , 
 
 IMPROVED HYDRAULIC RAM. 
 
 Amongst the various mathematical in- 
 struments and models of machines which 
 issue frorii the cabinet of M. A. F. L., and 
 are sold at Paris, in the Rue Castex, there 
 is to be seen an hydraulic ram, constructed 
 by Mr. Smith, under the superintendence 
 and direction of M. Montgolfier, jun., and 
 which we shall here describe. All its 
 parts are. extremely simple, but as well 
 adjusted, and as neatly executed, as the 
 most | finished philosophical instrument. 
 It is unquestionably the most complete and 
 perfect machine of the kind that has ever 
 been constructed. Its operations are per- 
 formed with great exactness, its action is 
 regular, and its effects are constant. 
 
 It is constructed so as to raise seven 
 pints of water in a minute to the height of 
 64 feet, at an expense of a stream of water 
 of 2| inches, and 30 inches fall ; the quan- 
 tity and height may, however, both be 
 augmented by elevating the fall. 
 
 Those parts which comprise the tubes of 
 the great pipe of 30 feet in length and 64 
 in height, are formed of copper, with ad- 
 mirable perfection. The tubes are of red 
 copper, without solder, every foot of which 
 is strengthened by strong brass rods, an 
 ihdispensible precaution for preserving 
 thOir stiffness. These tubes are formed in 
 parts of equal length, and each of the 
 length of five feet six inches, and fastened 
 together by means of brace s in brass work, 
 polished with emery, as the spigot of a 
 cask ; and when they are all mutually 
 connected with each other, the whole is 
 
 consolidated by a covering of the same 
 metal, screwed and locked with a key. 
 
 The apparatus is provided in several 
 parts with a number of valves, formed of 
 metal of different alloys, and of porcelain, 
 agate, or leather, &c. &c. ; which are em- 
 ployed in making interesting experiments 
 upon their relative duration and advantage, 
 in order that they may be replaced when 
 it is found necessary. 
 
 This excellent hydraulic ram may be 
 erected in a few hours, wherever its action 
 is requisite, without allowing a single drop 
 of water to escape. In fact, all the parts 
 which compose it may be taken to pieces 
 with equal facility, and packed into a case 
 of five feet eight inches in length, and only 
 16 inches in depth ; which may also serve 
 to contain any other philosophical instru- 
 ment. 
 
 There is an apparatus for the admission 
 or reception of air , which conforms exactly 
 to each stroke of the ram ; the purpose of 
 which is to keep in a constant level and a 
 permanent density the air which is con- 
 tained in the bell of the machine, or in the 
 compressing globe, which thus supplying 
 the loss of air which is absorbed in its 
 compression by the water, to maintain the 
 elasticity of the surrounding air, so neces- 
 sary to the operation of machines for raising 
 columns of water, to avert any sudden 
 jerks, prevent their fracture, and to regu- 
 late their movements. 
 
 The perfection of the hydraulic ram is 
 to be ascribed entirely to M. Montgolfier, 
 jun. In fact, the ram, deprived of this 
 latter improvement, would never move 
 with any regularity; it either bursts, or 
 stops suddenly, the moment the air in the 
 bell is absorbed. In this case, if the tubes 
 of ascension are brittle as those of cast 
 iron are, they split into a hundred pieces ; 
 if soft like lead, they tear ; and, lastly, if 
 they be elastic as copper, the machine af- 
 fords no further produce ; for the tubes di- 
 lating and contracting alternately the pul- 
 sations of the ram, proceed no further than 
 occasioning a movement, or rather an os- 
 cillation up and down, entirely useless in 
 the column of ascending water ; a capital 
 defect in this species of machinery, and 
 which was not considered by the original 
 inventors, but which the apparatus for the 
 inspiration of air occasions to be overcome. 
 
 This ram will perform its operations re- 
 gularly during three months without 
 stopping, if it is not touched or damaged ; 
 it isjrue, that great care must be taken to 
 place it in a proper position, and to shelter 
 or protect it from the weather. 
 
 It cannot be too strongly represented to 
 those persons who intend to employ the 
 powers of this hydraulic ram, that the 
 greater part of the defects in this ingenious 
 engine arise not from its construction, but 
 solely from the wretched economy observed 
 
THE ARTISAN. 
 
 336 ' 
 
 in its formation, and, above all, from the 
 negligence and carelessness of the work- 
 men who assist in fitting it up; who seldom 
 possess either the knowledge or the expe- 
 rience necessary to ensure its successful 
 operation. 
 
 All the parts of the hydraulic ram here 
 described were removed from the foundry, 
 a.s soon as it was possible, without running 
 the risk of having them too weak, or of en- 
 dangering their solidity; therefore there 
 is no superfluous metal attached to them. 
 The cost amounted to the sum of three 
 francs per pound, including the cost of 
 workmanship. The whole weight is 90 
 kilogr. (or 180 pounds de marc). All its 
 parts were put to the test, and were found 
 to be of sufficient strength. This ram is 
 provided with all the necessary jiltres , and 
 is complete in all its parts. The cost can- 
 not be estimated at less than five francs 
 per pound ; and the whole amount will be 
 about 900 francs, or £36 sterling. 
 
 Note. — There is attached to it a descrip- 
 tion of the method of raising it and putting 
 it in action. 
 
 SOLUTION OF QUESTIONS. 
 
 Quest. 43, answered by Mr. J. Taylor, 
 Clement's ■ lane y Lombard-street. 
 
 Let ABC denote the given elipsis, 
 
 D its centre, make D m ~ half n, and 
 make mn~c\ join D w, continuing it till 
 it cuts the arch E, draw E F parallel t© 
 m n , and E H parallel to G F ; lastly, draw 
 G H parallel E F, then is H G E F the rect- 
 angle required/ 
 
 Demon. The "triangles D win, andDEF 
 are similar, consequently as Dm : mn : : 
 DF : E F. Then, as twice Dm : mn : : 
 twice DP:EF. Q. E. D. 
 
 This problem was also solved by the 
 Proposer., nearly in a similar manner. 
 
 Quest. 44, ansivered by Mr. Whit- 
 combe, Mathematician , Cornhill. 
 
 Put 2 a~ £20, the sum of A and B’s 
 share ; m “ £602, the difference of the 
 cubes of their shares, and x~ half the 
 difference of their shares, then will a -J- x 
 
 ~ A’s share, and a . — x. — B’s share ; then, 
 per question 3 — a— x\ 3 Z= m; ex- 
 
 panded and reduced, we obtain 2 x 3 4-6 2 a x 
 ~ m, a cubic, which per Cardan we 
 find x — 1.-. a-fxzzlO + 1 — £11 “A’s 
 share, "and a — x — 10 — 1 — £9 n B’s 
 share as required. 
 
 This question was also solved by Mr, 
 J. Taylor; by Mr. J. Harding; by Mr. 
 J. Barr ; and we received an answer 
 from a Constant Reader, but without any 
 operation. The above is a very neat solu- 
 tion ; and though we have no room to in- 
 sert it, we have received another equally 
 neat from T. D. Bristol. Ed. 
 
 Quest. 45, answered by Mr. J. Stephens. 
 
 The circumference of a circle, whose 
 radius is 10 feet is 753*984 inches ; and as 
 the screw must sink 1 inch in one revolu- 
 tion as 1 : 753-984 : : 200 : 105796-8 pounds, 
 which is the pressure of the screw. 
 
 This question was also solved by a Con- 
 stant Reader ; by Mr. J. Johnston ; and 
 by the Proposer, who have mistaken the 
 radius for the circumference, by which 
 means they have made the answer only 
 half the above. 
 
 QUESTIONS FOR SOLUTION. 
 
 Quest. 47, proposed by T. D. Bristol. 
 
 It is required to find the distance (on a 
 horizontal plane) from the base of the 
 tower of Bristol Cathedral, to the image of 
 the sun, in a basin of water, which may be 
 observed by a person from the top of the 
 tower on the 29th of April, 1825, at 11 h. 
 5 m. 22 s. in the morning; the height of the 
 tower being 127*63 feet, and the observer's 
 eye 5*57 feet above the tower, in lat. 51° 
 27' 6". 3N, long. 2° 35' 28". 6 W. 
 
 Quest. 48, proposed by Mr. J. Whit- 
 combe, Cornhill. 
 
 In the equation 2*94327 lx — x 5 ~ 
 1*94353929, it is required to find the three 
 roots of x by a strict algebraic process, 
 without making use of conjecture, or fol- 
 lowing the methods of Newton, Ward, 
 Hutton, Emerson, or any of the modern 
 authors on Algebra. 
 
 We have inserted the above question at 
 the earnest request of the Proposer ; but 
 we wish it to be understood, that abstract 
 mathematical questions are not what we 
 wish. See our standing notice to Cor- 
 respondents on the Wrapper. Ed. 
 
 Errata.— For Quest. 42, page 320, read 41— 
 and for Quest. 43, read 42. 
 
THE ARTISAN. 
 
 337 
 
 GEOMETRY. 
 
 PROPOSITION XI. 
 
 Problem. — To divide a given straight line 
 into two parts , so that the rectangle con- 
 tained by the whole , and one of the parts, 
 shall be equal to the square of the other 
 part. 
 
 Let A B be the given straight line ; it is 
 required to divide it into two parts, so that 
 the rectangle contained by the whole, and 
 one of the parts, shall be equal to the 
 square of the other part. 
 
 Upon A B describe the square ABDC; 
 bisect A C in E, and join B E ; produce 
 C A to F, and make E F equal to E B, and 
 upon A F describe the square F G H A ; 
 A B is divided in H, so that the rectangle 
 A B, B H, is equal to the square of A H. 
 
 Produce G H to K : because the straight 
 line A C is bisected in E, and produced to 
 the point F, the rectangle C F, F A, to- 
 gether with the square of A E, is equal to 
 the square of E F : But E F is equal to 
 EB; therefore the rectangle C F, FA, to- 
 gether with the square of A E, is equal to 
 the square of EB: And the squares of 
 
 B A, A E are equal to the square of E B, 
 because the angle E A B is a right angle ; 
 therefore the rectangle CF, F A, together 
 with the square of A E, is equal to the 
 squares of BA, A E : Take away the 
 
 square of A E, w hich is“common to both, 
 therefore the remaining rectangle C F, FA, 
 is equal to the square of A B ; and the 
 figure F K is the rectangle contained by 
 C F, FA, for A F is equal to F G ; and 
 A D is the square of A B ; therefore F K 
 is equal to AD: Take away the common 
 part A K, and the remainder F H is equal 
 to the remainder H D : And H D is the 
 rectangle contained by A B, B H, for A B 
 is equal to BD; and F H is the square of 
 AH. Therefore the rectangle AB, BH 
 Vol. I.— No. 22. 
 
 is equal to the square of A H : Wherefore, 
 the straight line A B is divided in H, so 
 that the rectangle AB, BH, is equal to 
 the square of AH. Which was to be 
 done. 
 
 This proposition is one of those which 
 cannot be proved by numbers ; and shows 
 that Geometry is a more accurate branch 
 of the mathematics than arithmetic, at 
 least where it is applicable. 
 
 The solution by numbers may, however, 
 be approximated to sufficiently near for 
 any purpose that may be required, by 
 solving a quadratic equation in algebra ; 
 but as we are aware that comparatively 
 few can perform this operation, we shall 
 here give a very easy mode of approxima- 
 tion. 
 
 Assume the segments of the divided line 
 at first equal, and denote each by 1, then 
 their continued summation will produce 
 the following numbers : 1, 2, 3, 5, 8, 13, 
 21, 34, 55, 89, 144, &c. Now if the 
 divided line contained 89 equal parts, its 
 greater segment would contain 55, and its 
 lesser segment 34 of these parts, very 
 nearly ; and if the whole line contained 
 144 parts, its greater segment would con- 
 tain 89, and its lesser segment 34 of these 
 parts, which is an approximation still 
 nearer than the foregoing. 
 
 PROPOSITION XII. 
 
 Theorem. — In obtuse-angled friangles , if a 
 pei'pendicular be drawn front any of the 
 acute angles to the opposite side produced , 
 the square of the side subtending the ob- 
 tuse angle is greater than the squares of 
 the sides containing the obtuse angle, by 
 twice the rectangle contained by the side 
 upon which, when produced, the perpen- 
 dicular falls, and the straight line inter- 
 cepted without the triangle between the 
 perpendicular and the obtuse angle. 
 
 Let A B C be an obtuse angled triangle, 
 having the obtuse angle A C B, and from 
 the point A let AD be drawn perpendi- 
 cular to B C produced : The square of AB 
 is greater than the squares of A C, C B, 
 by twice the rectangle BC, CD. 
 
 Because the straight line B D is divided 
 into two parts in the point C, the square 
 
338 
 
 THE ARTISAN. 
 
 and twice the rectangle BC, CD: To 
 each of Ihese equals add the square of 
 DA; and the squares of B D, DA, are 
 equal to the squares of B C, CD, D A, 
 and twice the rectangle B C, CD: But 
 the"square of B A is equal to the squares 
 of B D, DA, because the angle at D is a 
 right angle ; and the square of C A is 
 equal to the squares of C D, D A : There- 
 fore the square of B A is equal to the 
 squares of B C, C A, and twice the rect- 
 angle B C, CD; that is, the square of 
 B A is greater than the squares of B C, 
 C A, by twice the rectangle B C, CD. 
 Therefore, in obtuse-angled triangles, 
 &c. Q. E. D. 
 
 & This and the following propositions 
 would be rendered more intricate, by any 
 attempt to illustrate them by numbers. i 
 
 PROPOSITION XIII. 
 
 Theorem. — In every triangle , the square of 
 the side subtending any of the acute 
 angles, is less than the squares of the 
 sides containing that angle, by twice the 
 rectangle contained by either of these 
 sides, and the straight line intercepted 
 between the perpendicular let fall upon it 
 from the opposite angle , and the acute 
 angle. 
 
 Let ABC be any triangle, and the 
 angle at B one of its acute angles, and 
 upon B C, one of the sides containing it, 
 let fall the perpendicular AD from the 
 opposite angle : the square of A C, oppo- 
 site to the angle B, is less than the squares 
 of C B, B A, by twice the rectangle C B, 
 B D. 
 
 First, let A D fall within the triangle 
 ABC; and because the straight line C B 
 
 A 
 
 is divided into two parts in the point D, 
 the squares of C B, B D are equal to twice 
 the rectangle contained by C B, B D, and 
 the square of D C : To each of these equals 
 add the square of AD; therefore the 
 squares of C B, B D, D A, are equal to 
 twice the rectangle C B, B D, and the 
 squares of A D, D C : Rut the square of 
 A B is equal to the Squares of B D, D A, 
 because the angle B D A is a right angle ; 
 and the square of AC is equal to the 
 squares of AD, DC: Therefore the 
 
 squares of C B, BA are equal to the 
 
 square of AC, and twice the rectangle 
 C B, B D ; that is, the square of A C alone 
 is less than the squares of C B, B A, by 
 twice the rectangle C B, BD. 
 
 Secondly, Let A D fall without the 
 triangle ABC; and because the straight 
 line B D is divided into two parts in C, 
 
 the squares of C B and B D are equal to 
 twice the rectangle contained by C B, B D, 
 and the square of D C : To each of these 
 equals add the square of A D ; therefore 
 the squares of C B, B D, D A, are equal to 
 twice the rectangle C B, B D, and the 
 squares of AD, DC: But the square of 
 A B is equal to the squares of B D, D A, 
 because the angle B D A is a right angle ; 
 and the square of AC is equal to the 
 squares of A D, DC: Therefore the squares 
 of C B, B A are equal to the square of 
 A C, and twice the rectangle C B, B D ; 
 that is, the square of A C alone is less than 
 the squares of C B, BA by twice the 
 rectangle C B, B D. 
 
 Lastly, let the side A C be perpendicular 
 to B C ; then is B C the straight line be- 
 tween the perpendicular and the acute 
 angle at B ; and it is manifest, that the 
 squares of A B, B C are equal to the square 
 of A C and twice the square of B C : There- 
 fore, in every triangle, &c. Q. E. D; 
 
 & 
 
 B C 
 
 PROPOSITION XIV. 
 
 Problem. — To describe a square that shall 
 be equal to a given rectilineal figure. 
 
 Let A be the given rectilineal figure ; it 
 is required to describe a square that shall 
 be equal to A. 
 
 Describe the rectangular parallelogram 
 B C D E equal to the rectiMheal figure A. 
 
THE ARTISAN. 
 
 3S9 
 
 If then the sides of it BE, ED are equal 
 
 to one another, it is a square, and what 
 was required is now done : But if they are 
 not equal, produce one of them B E to F, 
 and make E F equal to ED, and bisect 
 B F in G : and from the centre G, at the 
 distance G B, or G F, describe the semi- 
 circle B H F ; and produce D E to H, and 
 join G H : Therefore, because the straight 
 line B F is divided into two equal parts in 
 the point G, and into two unequal at E, 
 the rectangle BE, E F, together with the 
 square of E G, is equal to the square of 
 G F : But G F is equal to G H ; therefore 
 the rectangle B E, E F, together with the 
 square of E G, is equal to the square of 
 G H : But the squares of H E EG are 
 equal to the square of G H : Therefore the 
 rectangle BE, E F, together with the 
 square of EG, is equal to the squares of 
 H E, E G : take away the square of E G, 
 which is common to both ; and the remain- 
 ing rectangle BE, E F is equal to the 
 square of E H : but the rectangle contained 
 by B E, E F is the parallelogram B D, be- 
 cause E F is equal to E D ; therefore B D 
 is equal to the square of E H ; but B D is 
 equal to the rectilineal figure A ; therefore 
 the rectilineal figure A is equal to the 
 square of E H : Wherefore a square has 
 been made equal to the given rectilineal 
 figure A ; viz. the square described upon 
 E H. Which was to be done. 
 
 PROPOSITION A. 
 
 Theorem. — If one side of a triangle be bi- 
 sected , the swn of the squares of the other 
 two sides is double of the square of half 
 the side bisected , and of the square of the 
 line drawn from the point of bisection to 
 the opposite angle of the triangle. 
 
 Let A B C be a triangle, of which the 
 side B C is bisected in D, and D A drawn 
 to the opposte angle ; the squares of B A 
 and A C are together double of the squares 
 of B D and D A. 
 
 and because B C is divided equally in D, 
 and unequally in E, the squares of B E 
 and E C are together equal to twice the 
 square of B D, and twice the square of 
 D E, (II. 9) ; to each of these add twice 
 the square of A E, and the squares of B E 
 and E A are equal to the square of A B, 
 and the squares of C E and E A are equal 
 to the square of A C ; therefore the squares 
 of A B and A C are equal to twice the 
 square of B D, and twice the squares of 
 D E and A E ; but twice the squares of 
 D E and A E are equal to twice the square 
 of A D, therefore the squares ©f A B and 
 A C are equal to twice the square of BD 
 and of AD. 
 
 PROPOSITION B. 
 
 Theorem. — The sum of the squares of the 
 diagonals of any parallelogram, is equal 
 to the sum of the squares of the sides of 
 the parallelogram. 
 
 Let ABCD be a parallelogram, of 
 which the diameters are A C and B D ; the 
 sum of the squares of A C and B D is 
 equal to the sum of the squares of A B, 
 B C, C D, DA. 
 
 Let A C and B D intersect one another 
 in E : and because the vertical angles 
 A E D, C E B are equal, and also the alter- 
 nate angles E A D, E C B, the triangles 
 A D E, C E B have two angles in the one 
 equal to two angles in the other, each to 
 each : but the sides A D and B C, which 
 are opposite to equal angles in these tri- 
 angles, are also equal ; therefore the other 
 sides which are opposite to the equal 
 angles are also equal; viz. AE to EC, 
 and E D to E B. 
 
 A D 
 
THE ARTISAN. 
 
 $40 
 
 Since, therefore, B D is bisected in E, 
 the squares of A B and A D are equal to 
 twice the square of A E and twice the 
 square of B E ; and for the same reason 
 the squares of B C and C D are equal to 
 twice the square of C E and twice the 
 square of D E. Therefore the squares of 
 A B, AD, DC, and C B, are equal to four 
 times the square of B E, and four times 
 the square of A E. But four times the 
 square of B E is equal to the square of 
 B D, and four times the square of A E is 
 equal to the square of A C, because B D 
 and A C are both bisected in E ; therefore 
 the squares of A B, A D, D C, and C B, 
 are equal to the squares of A C and B D. 
 
 We have added the two last propositions 
 on account of their great Use in Geometry, 
 and their close connection with the proposi- 
 tions which precede them, in the second 
 book. Prop. A. is an extension of the 9th 
 and 10th of the same book ; and B is easily 
 proved, after the truth of A is established. 
 
 MBCHAN1CS. 
 
 atwood’s machine. 
 
 ( See page 809 . ) 
 
 If 4| oz. or 19 m. be included in either 
 box, this, with the weight of the box itself, 
 will be 25 m ; so that when the weights A 
 and B, each being 25 m, are balanced in 
 the manner represented in the figure, their 
 whole mass will be 50 m, which being 
 added to the inertia of the wheels 11m, 
 the sum will be 61 m. Besides these, 
 three circular weights are constructed, 
 each of which is equal to \ of an ounce, 
 or 6 m. If one of these be added to A and 
 one to B, the whole mass will now become 
 63 m, perfectly in equilibrio, and moveable 
 by the least weight added to either (setting 
 aside the effects of friction) in the same 
 manner precisely, as if the same weight or 
 force were applied to communicate motion 
 to the mass 63 m, existing in free space 
 and without gravity. 
 
 The moving force. Since the weight of 
 any substance is constant, and the exact 
 quantity of it easily estimated, it will be con- 
 venient here to apply a weight to the mass 
 A as a moving force. Thus, when the sys- 
 tem consists of a mass equal in Weight to 
 63 m, according to the preceding descrip- 
 tion, the whole being perfectly balanced, 
 let a weight of | oz. or m, be applied on the 
 mass A; this will communicate motion to the 
 whole system ; by adding a quantity of mat- 
 tter m to the former mass 63 m, the whole 
 quantity of matter moved will now become 
 64m, and the moving force being equal to 
 m, this will give the force which accele- 
 rates the descent of A, equal to g \th part 
 of the accelerating force of gravity. 
 
 In this way the moving force may be’ 
 altered without altering the mass moved ; 
 consequently, both the proportion and abso- 
 lute quantities of the moving force and 
 mass moved may be of any assigned mag- 
 nitude, according to the conditions of the 
 proposition to be illustrated. 
 
 Of the space described. The body A, fig. 
 1, descends in a vertical line ; and a scale 
 E F, about 64 inches in length, divided into 
 inches and tenths, is adjusted vertical, and 
 so placed, that the descending weight A 
 may fall in the middle of a square stage 
 Z, fixed to receive it at the end of the 
 descent; the beginning of the descent is 
 estimated from o. The descent of A is 
 terminated when the bottom of the box 
 strikes the stage Z, which may be fixed at 
 different distances from the point o; so 
 that by altering the position of the stage, 
 the space described from rest may be of 
 any given magnitude less than 64 inches. 
 
 The time of description is observed by the 
 pendulum X W vibrating seconds; and 
 the experiments intended to illustrate the 
 elementary propositions, may easily be so 
 constructed that the time of motion shall 
 be a whole number of seconds. The esti- 
 mation of the time, therefore, admits of 
 considerable exactness, provided the ob- 
 server takes care to let the bottom of the 
 box A begin its descent precisely at any 
 beat of the pendulum ; then the coincidence 
 of the stroke of the box against the stage, 
 and the beat of the pendulum at the end 
 of the time of motion, will show how 
 nearly the experiment and the theory agree. 
 There might be various devices for letting 
 the weight A begin its descent, at the in- 
 stant of a beat of the pendulum W ; for 
 instance, let the bottom of the box o, when 
 o on the scale, rest on a flat rod held in 
 the hand horizontally, its extremity being 
 coincident with o by attending to the 
 beats of the pendulum, and with a little 
 practice, the rod which supports the box A, 
 may be removed at the moment the pen- 
 dulum beats, so that the descent of A shall 
 commence at the same instant. 
 
 Of the velocity acquired. — It remains 
 only to describe in what manner the velo- 
 city acquired by the descending w r eight A, 
 at any given point of its path, is made evi- 
 dent to the senses. The velocity of A’s 
 descent being continually accelerated, will 
 be the same in two points of the space 
 described. This is occasioned by the con- 
 stant action of the moving force ; and, since 
 the velocity of A at any instant is mea- 
 sured by the space, which would be des- 
 cribed by it moving uniformly for a given 
 time, with the velocity it had acquired at 
 that instant, this measure cannot be expe- 
 rimentally obtained, except by removing 
 the force by which the descending body’s 
 acceleration was caused. But our limits 
 
THE ARTISAN. 
 
 341 
 
 will not permit us to state how this is 
 effected. 
 
 In the preceding description, as Mr. 
 Atwood remarks, two suppositions have 
 been assumed, neither of which is mathe- 
 matically true; but it might be easily 
 shown that they are so in a physical 
 sense, the error occasioned by them being 
 insensible in practice. 
 
 The force which communicates motion 
 to the system has been assumed constant; 
 which will be true, only on a supposition, 
 that the line at the extremities of which 
 the weights A and B, fig. 1. are affixed, is 
 without weight. 
 
 The bodies have also been supposed to 
 move in vacuo, whereas the resistance of 
 the air will have some effect in retarding 
 their motion ; but as the greatest velocity 
 communicated in these experiments, can- 
 not much exceed that of about 26 inches in 
 a second ; (suppose the limit of 26’2845, 
 and the cylindrical boxes If inches in 
 diameter,) the resistance of the air can 
 never increase the time of descent in so 
 great a proportion, as that of 240 to 241 ; 
 its effects will therefore be insensible in 
 experiment. 
 
 The effects of friction are almost wholly 
 Temoved by the friction wheels ; for when 
 the surfaces are well polished and free 
 from dust, &c. if the weights A and B be 
 balanced in perfect equlibrio, and the 
 whole mass consists of 63 m, according to 
 the example already described, a weight 
 of If grains, or at most 2 grains, being 
 added either to A or B, will communicate 
 motion to the whole, which shows that the 
 effects of friction will not be so great as a 
 weight of If or 2 grains. 
 
 In some cases, however, especially in 
 experiments relating to retarded motion, 
 the effects of friction become sensible, but 
 may be very readily and exactly removed, 
 by adding a mall weight of l\ r > or 2 
 grains to the descending body, taking care 
 that the weight added be such, as is in the 
 least degree smaller than that which is 
 just sufficient to put the whole in motion, 
 when A and B are equal, and balance 
 each other before the moving force is 
 applied. 
 
 ME. SMEATON’S MACHINE FOR EXPERIMENTS 
 ON ROTATORY MOTION. 
 
 The following ingenious apparatus was 
 employed by Mr. Smeaton, in his “ Expe- 
 rimental examination of the quantity and 
 proportion of mechanic power, necessary 
 to be employed in giving different degrees 
 of velocity to heavy bodies from a state of 
 rest, with the view of showing that the 
 same mechanic power is capable of pro- 
 ducing the same velocity as a given body, 
 whether it is applied, so as to produce it in 
 
 a greater or less time. The machine is 
 represented by the following figure. 
 
 A vertical axis is turned by a thread 
 passing over a pulley, and supporting a 
 scale with weights ; the thread may be 
 applied at different parts of the axis, 
 having different diameters, and the axis 
 supports two arms, on which two leaden 
 weights are fixed, at distances which may 
 be varied at pleasure. The same force 
 will then produce, in the same time, but 
 half the velocity, in the same situation of 
 the weights, when the thread is applied to 
 a part of the axis of half the diameter: 
 and if the weights are removed to a double 
 distance from the axis, a quadruple force 
 will be required, in order to produce an 
 equal angular velocity in a given time.* 
 
 Now having wound up a certain number 
 of turns of the thread on the barrel, and 
 having placed a weight in the scale, it is 
 obvious that it will cause the axis to turn 
 round and give motion to its arms, and to 
 the weights of lead placed on them, which 
 the heavy bodies to be put in motion by 
 are impulse of the weight in the scale ; and 
 when the line is wound off’, the scale falls 
 down, and the weight ceases to accele- 
 rate the motion of the heavy bodies, and 
 leaves them revolving equally forward 
 with the velocity they have regained ; ex- 
 cept so far as that velocity must be gra- 
 dually lessened by the friction of the ma- 
 chine, and the resistance of the air, which 
 being small, the bodies will revolve for 
 some time before their velocity is appa- 
 rently diminished. 
 
 When the bodies are at the smaller dis- 
 tance from the axis of rotation, they are 
 then in effect at half the greater distance 
 
 * In a circle, or any portion of a circle, turning 
 round its centre, the square of the distanoe of this 
 point from the centre, is half the square of the se- 
 midiameter; and the whole effect of the momentum 
 of the circle, upon an obstacle at its circumference, 
 is exactly half as great as that of an equal quantity 
 of matter, striking the obstacle with the velocity of 
 the circumference. 
 
312 
 
 THE ARTISAN. 
 
 from that axis ; for, since the axis itself, 
 and the cylindrical arms of wood, keep an 
 invariable distance from the centre of ro- 
 tation, the bodies themselves must be 
 moved nearer than half their former dis- 
 tance, that, by being compounded with 
 the invariable parts, they may be virtually 
 at the half distance. In order to find this 
 half distance nearly, Mr. Smeaton put in 
 an arm of the same wood, which only 
 passed through the axis, without extending 
 in the opposite direction; one of the 
 bodies being attached to the end of this 
 arm, at the distance of 8$ inches, the 
 whole machine was inclined, till the body 
 and arm became a kind of pendulum, 
 making 92 vibrations in the minute ; and 
 as a pendulum of the half length vibrates 
 quicker in the proportion of the square 
 root of 1 to the square root of 2 ; that is, 
 in the proportion, nearly of 92 to 130 ; 
 therefore, keeping the same inclination of 
 the machine, the weight was moved on the 
 arm, till it made 130 vibrations in the 
 minute, which was found to be as above 
 stated, when it was at 3*92 inches distant 
 
 from the centre ; which is about f 5 ths of an 
 inch nearer than the half distance. A 
 double arm was then put in, and marked 
 accordingly ; and the bodies being mounted 
 on it, the whole was adjusted ready for 
 use. 
 
 MACHINE FOR TRYING THE STRENGTH OF 
 MATERIALS. 
 
 In order to investigate the strength of 
 the various substances employed for the 
 purposes of the mechanical arts, it is most 
 convenient to use a machine furnished 
 with proper supports, and gripes, or vices, 
 for ; holding the materials, and with steel- 
 yards, for ascertaining the magnitude of 
 the force applied, while the extension or 
 compression is produced by a screw or a 
 winch, with the intervention of a wire, a 
 a chain, or a cord : provision ought also to 
 be made for varying the direction of the 
 force, when the flexure of the materials 
 renders such a change necessary. The 
 following figure represents a machiue pos- 
 sessed of these requisites. 
 
 r The force is applied by means of the 
 winch A, which winds up the rope B C, 
 passing over the first pulley, and under the 
 second, which is directly under the point 
 D, at which the force acts on the piece 
 E F to be broken ; the pulleys slide on two 
 parallel bars, fixed in a frame, which is 
 held down by a point projecting at G, from 
 the lever G H, which is graduated like a 
 steel-yard, and measures the force. The 
 piece to be broken is held by a double vice 
 
 I K, with four screws, two of them hiding 
 the other two in the figure : if a wire is to 
 be torn, it may be fixed to the cross bar 
 L M ; and a substance to be crushed must 
 be placed under the lever N O, the end N 
 receiving the rope, and the end O being 
 held down by the click, which acts on the 
 double ratchet O P. The lever is double 
 from O to Q, and acts on the substance by 
 a loop, fixed to it by a pin. 
 
THE ARTISAN. 
 
 313 
 
 H'SrUROSTATICS- 
 
 MACHINES FOR DISCHARGING A UNIFORM 
 QUANTITY OF WATER. 
 
 The discharge of a uniform quantity of 
 water from a vessel containing it, being a 
 matter of some importance, we shall give a 
 representation of several ingenious contri- 
 vances for this purpose. One of these is 
 exhibited by the following figure, 
 
 where M N O P is a vessel nearly full of 
 water, which consists of a tube B A moving 
 round a joint at B, and having its upper 
 end B connected with a hollow floating 
 ball C. The velocity with which the water 
 enters the extremity B, is that which is due 
 to the height B C, or the depth B below the 
 surface. As the surface M N descends, the 
 float C also descends, so that whatever be 
 the height of the water in the vessel, it will 
 always enter B with the same velocity. 
 The discharge at the other end A will not 
 be quite uniform, as the water will acquire 
 greater velocity in descending the tube BA 
 when it is much inclinedj than when it is 
 nearly horizontal. 
 
 A floating syphon produces the sameefiect, 
 but in a more correct manner. This instru- 
 ment is represented by the following figure, 
 
 where ABD is a syphon, with a hollow 
 floating ball at its shorter end. This sy- 
 phon is suspended by the chains EP, EP, 
 which pass over two pulleys PP upon a 
 horizontal axle P P, and suspend at their 
 other extremities counterweights W W . 
 As the water in the vessel MNOP sinks 
 by being discharged at D, the syphon 
 descends, and the counterweights rise, 
 and an uniform stream is obtained, till the 
 end A reaches the bottom of the vessel. 
 
 Another very ingenious contrivance for 
 the same purpose, is shown in the following 
 figure. 
 
 A cone A B, attached to a lenticular float 
 at C, and fixed upon the axis ef, rises and 
 falls in the aperture m n , by which the 
 water of the vessel MNOP is to be dis- 
 charged. It is kept in an upright position 
 by the horizontal axis op, rs. Now, when 
 the vessel is full of water, and the head 
 therefore great, the velocity at m n will 
 also be great ; but as the float C rises with 
 the surface MN, the aperture mn will be 
 partly filled by a thicker part of the cone 
 A B ; whereas, when the surface M N has 
 descended, the float AB will also descend, 
 and the aperture at mn will be widened, 
 in consequence of a smaller part of the 
 cone being included in it. In this way, 
 the varying diameter of the cone always 
 adjusts the aperture mn to the variable 
 head of water, so that the quantity dis- 
 charged through the tube mnop, is nearly 
 always the same. 
 
 WATER-BLOWING MACHINE, OR SHOWER 
 BELLOWS. 
 
 The water-blowing machine, called 
 trombe by the French, seems to have been 
 
344 
 
 THE ARTISAN., 
 
 first introduced in Italy about the year 
 1672, for the purpose of procuring a blast 
 of air by the descent of water. It is re- 
 presented by the following figure, 
 
 where M N is a reservoir of water, in the 
 bottom of which is inserted a long tube 
 A B, consisting of a conical part a 6, seen 
 upon an enlarged scale in the next fig. com- 
 municating with a cylindrical tube d B, 
 which enters the vessel C D E F. A num- 
 ber of openings c , d, &c. are made at the top 
 of the tube d B, so that when the water is 
 discharged at the conical aperture 6, it 
 drags along with it the adjacent air. This 
 mixture of air and water falls upon a stone 
 pedestal G, so as to separate the air from 
 the water. 
 
 ^The water descends to the bottom of the 
 vessel, while the air escapes through the 
 pipe C I K to supply the furnace. Another 
 form of the machine is represented by the 
 following figure, 
 
 where a/3 is the conical pipe, ahd the 
 water is supplied with air from the pipe 
 K0S0. 
 
 In the water blowing machines used in 
 Dauphiny, in the neighbourhood of' the 
 town of Alvar, the diameter of ab is 12 
 inches at a and 5 at b , the diameter of dB 
 is 10 inches. Only four holes are used at 
 c, d, and the end B enters If feet into the 
 vessel C D E F, which is 4 feet high and 4 
 feet broad. The water is discharged at an 
 aperture above F a foot in diameter, and 
 sometimes the admission of the water and 
 its discharge are regulated by sluices m 
 and n. A strong, equal, and continued 
 blast is obtained by this machine, but it is 
 thought to be too moist and too cold. 
 There is one of these machines in Switzer- 
 land, which works with great effect at the 
 lead works of M. Lenay, in the valley of 
 Servoz, near Chamouni. 
 
 Kircher appears to have been the first 
 who explained the production of wind by a 
 fall of water. Barthes long afterwards gave 
 another theory, and Dietrich and Fabri as- 
 cribed the wind to the decomposition of the 
 water. In 1791, the Academy of Thoulouse 
 invited philosophers to investigate this 
 phenomenon, and it was probably in con- 
 sequence of this that Venturi directed his 
 attention to the subject. This ingenious 
 philosopher has proved that the air is 
 dragged down upon the principle of the 
 lateral communication of motion in fluids ; 
 and he has pointed out the best mode of 
 constructing the machine, so as to produce 
 the greatest quantity of air. The diameter 
 of the tube d B should be at least double of 
 the aperture b. To a height about If feet 
 above C D, the tube should be completely 
 air tight, as well as the vessel C D E F ; 
 but above that part the tube d B may be 
 perforated in every part with holes. 
 
 If the pipe C I K does not discharge all 
 the air which is generated, the surface of 
 the water in the vessel will descend, and 
 part of the air will issue out of the lower 
 apertures of the tube d B. 
 
 Phenomena similar to those produced by 
 the water-blowing machine, have been ob- 
 served in nature, at the foot of the cas- 
 cades which fall from the glacier of Roche 
 Melon, on the naked rock of La Novalese, 
 towards Mount Cenis. Venturi found that 
 the force of the wind arising from the air 
 dragged down by the water could scarcely 
 be withstood. The ventaroli , or natural 
 blasts, which are most frequently found to 
 issue from volcanic mountains, arise from 
 the air carried down the hollows by the 
 falls of water ; and w hat are called the 
 rain ivinds have the same origin. 
 
THE ARTISAN* 
 
 345 
 
 j^feceltaneoua Subjects. 
 
 MEMOIR OF THE LIFE OF LEO- 
 NARD EULER. 
 
 ' Leonard Euler, a very eminent mathe- 
 matician, was born at Basil, on the 14th of 
 April, 1707, he was the son of Paul Euler 
 and of Margarat Brucker, (of a family 
 illustrious in literature,) and spent the 
 first years of his life at the village of 
 Richen, of which place his father was 
 Protestant minister. Being intended for 
 the church, his father, who had himself 
 studied under James Bernouilli, taught 
 him mathematics, as a ground-work of his 
 other studies, or at least a noble and use- 
 ful secondary occupation. But Euler, as- 
 sisted, and perhaps secretly encouraged, 
 by John Bernouilli, who easily discovered 
 that he would be the greatest scholar he 
 should ever educate, soon induced him to 
 declare his intention of devoting his life to 
 that pursuit. This intention the wise 
 father did not thwart; but the son did not 
 so blindly adhere to it, as not to connect 
 with it a more than common improvement 
 in every other kind of useful learning, inso- 
 much, that in his latter days men often won- 
 dered how, with such a superiority in 
 one branch, he could have been so near to 
 eminence in all the rest. Upon the found- 
 ation of the academy of sciences at St. 
 Petersburgh, in 1723, by Catherine I., 
 the two young Bernouillis, Nicholas 
 and Daniel, had gone thither, promising, 
 when they set out, to endeavour to procure 
 Euler a place in it. They accordingly 
 wrote to him soon after, to apply his ma- 
 thematics to physiology, which he did, 
 and studied under the best naturalists at 
 Basil, but at the same time ; i. e. in 1727, 
 published a dissertation on the nature and 
 propagation of sound ; and an answer to 
 the question on the masting of ships, 
 which the Academy of Sciences at Paris 
 judged worthy of the accessil. Soon after 
 this, he was called to St. Petersburgh, and 
 declared adjutant to the mathematical 
 class in the academy, a class in which, 
 from the circumstances of the times, (New- 
 ton, Leibnitz, and so many other eminent 
 scholars being just dead,) no easy laurels 
 were to be gathered. But notwithstanding 
 the great number of mathematicians that 
 flourished about this time, Euler soon took 
 his place among the number. He, indeed, 
 was much wanted ; the science of the 
 Integral Calculus , hardly come out of the 
 hands of its creators, was still too near 
 the stage of its infancy not to want to be 
 made more perfect. Mechanics, dynamics, 
 and especially hydrodynamics, and the 
 science of the motion of the heavenly 
 bodies, felt the imperfection. Engineering 
 
 and Navigation were only vague prin- 
 ciples, and founded on a number of iso- 
 lated facts and contradictory observations. 
 The irregularities in the motions of the 
 celestial bodies, and especially the com- 
 position of forces which influence the 
 motion of the moon, were still the disgrace 
 of geometers. Practical astronomy had 
 yet to wrestle with the imperfection of the 
 telescope, insomuch, that it could hardly 
 be said that any rule for making them 
 existed. Euler turned his thoughts to all 
 these objects ; he [perfected the Integral 
 Calculus ; he was the inventor of a new 
 kind of calculus, that of the arithmetic of 
 sines ; he simplified analytical operations ; 
 and, aided by these powerful helps, and 
 the astonishing facility with which he 
 knew how to subdue expressions the most 
 intractable, he threw a new light on all 
 the branches of the mathematics. But at 
 Catherine’s death the academy was threat- 
 ened with extinction, by men who knew 
 not the connection which arts and sciences 
 have with the happiness of a people Euler 
 was offered and accepted a lieutenancy on 
 board one of the Empress’s ships, with the 
 promise of speedy advancement. Luckily 
 things changed, and the learned captain 
 again found his own element, and was 
 named Professor of Natural Philosophy in 
 1733, in the room of his friend, John Ber- 
 nouilli. The number of memoirs which 
 Euler'produced is astonishing ; but what 
 he did in 1735 is almost incredible. An 
 important calculation was to be made, 
 without loss of time; the other Acade- 
 micians had demanded some months to do 
 it. Euler asked only three days — and in 
 that time he did it ; but the fatigue threw 
 him into a fever, in which he lost an eye, 
 an admonition which would have made an 
 ordinary man more sparing of the other. 
 The great revolution produced by the dis- 
 covery of fluxions, had entirely changed 
 the face of mechanics ; still, however, 
 there was no complete work on the science 
 of motion, two or three only excepted, of 
 which Euler felt the insufficiency. He 
 saw with pain, that the best works on the 
 subject ; viz. “ Newton’s Principia,” and 
 “ Herman’s Phoronomia,” concealed the 
 method by which these great men had 
 come at so many wonderful discoveries, 
 under a synthetic veil. In order to 're- 
 move this veil, Euler employed all the 
 resources of that analysis, which had 
 served him so well on so many other occa- 
 sions ; and thus uniting his own disco- 
 veries with those of other geometers, had 
 them published by the Academy in 1736. 
 To say that clearness, precision, and older, 
 are the characters of this work, would be 
 barely to say that it is, what without these 
 qualities no work can be, classical of its. 
 kind. It placed Euler in the rank of the 
 
346 
 
 THE ARTISAN. 
 
 first geometricians then existing, and this 
 at a time when John Bernoulli was still 
 living. Such labours demanded some 
 relaxation; the only one which Euler 
 admitted was music, but even to this he 
 could not go without the spirit of geome- 
 try with him. They produced together 
 the essay on a new theory of music, which 
 was published in 1739, but not very well 
 received, probably, because it contains too 
 much geometry for a musician. In 1740, 
 his genius was again called forth by 
 the Academy of Paris, to discuss the 
 nature of the tides. This prize Euler 
 did not gain alone ; but he divided it with 
 Maclaurin and D. Bernouilli, forming with 
 them a triumvirate of candidates, which 
 the realms of science had not often be- 
 held. The agreement of the several me- 
 moirs of Euler and Bernouilli, on this 
 occasion, is very remarkable. Though the 
 one philosopher had set out on the prin- 
 ciple of admitting vortices, which the 
 other rejected, they not only arrived at 
 the same end of the journey, but met seve- 
 ral times on the road ; for instance, in the 
 determination of the tides under the frozen 
 zone. Philosophy, indeed, led these two 
 great men by different paths ; Bernouilli, 
 who had more patience than his friend, 
 established every physical hypothesis he 
 was obliged to make, by painful and labo- 
 rious experiment. These Euler’s impe- 
 tuous genius scorned ; and, though his 
 natural sagacity did, not always supply 
 the loss, he made amends by his supe- 
 riority in analysis. In 1741, Euler re- 
 ceived some very advantageous propo- 
 sitions from Frederic the Second, to go 
 and assist him in forming an academy of 
 sciences, out of the wrecks of the Royal 
 Society founded by Leibnitz. With these 
 offers the tottering state of the St. Pe- 
 tersburgh academy under the regency, 
 made it necessary for the philosopher 
 to comply. In 1744, Euler published 
 a complete treatise of isoperimetrical 
 curves ; the theory of the motions of the 
 Planets and Comets ; the well known 
 theory of magnetism which gained the 
 Paris prize ; and the much improved 
 translation of Robins’s u Treatise on Gun- 
 nery.” Navigation was now the only 
 branch of useful knowledge, for which the 
 labours of analysis and geometry had done 
 nothing. The hydrographical part alone, 
 and that which relates to the direction of 
 the course of ships, had been treated by 
 geometricians conjointly with nautical 
 astronomy. Euler was the first who con- 
 ceived and executed the project of making 
 this a complete science. A memoir on the 
 motion of floating bodies communicated 
 to the academy of St. Fetersburgh, in 
 1735, by M. le Croix, first gave him this 
 idea. His researches on the ebuilibrium 
 
 of ships, furnished him with the means of 
 bringing the stability to a determined 
 measure. His success encouraged him to 
 go on, and produced the great work 
 which the academy published in 1749, in 
 which we find, in systematic order, the 
 most sublime notions on the theory of the 
 equilibrium and motion of floating bodies, 
 and on the resistance of fluids. This was 
 followed by a second part, which left 
 nothing to be desired on the subject, ex- 
 cept the turning it into a language easy of 
 access, and divesting it of the calculations 
 which prevented its being of general use. 
 Accordingly, in 1773, from a conversation 
 with Admiral Knowles, and other assist- 
 ance, out of the u Scientia Navalis,” 2 
 vols. 4to. was produced, the “ Complete 
 Theory of the Construction and Manage- 
 ment of Ships.” This work was instantly 
 translated into all languages, and the 
 author received a present of 6000 livres 
 from the French king ; previous to which 
 he received 300 pounds from the British 
 Parliament, for the Theorems , by which 
 Meyer computed his lunar tables.* 
 
 Few men of letters have written so much 
 as Euler ; no Geometrician has ever em- 
 braced so many objects at one time, or 
 has equalled him, either in the variety or 
 magnitude of his discoveries. When we 
 reflect on the good such men do to their 
 fellow-creatures, we cannot help indulging 
 a wish (vain, alas ! as it is) for their illus- 
 trious course to be prolonged beyond the 
 term allotted to mankind. Euler’s, though 
 it has had an end, was very long and very 
 honourable ; and it affords us some conso- 
 lation for his loss, to think that he enjoyed 
 it exempt from the ordinary consequences 
 of extraordinary application, and that his 
 last labours abounded in proofs of that 
 vigour of understanding which marked 
 his s early days, and which he preserved to 
 his 4 end. On the 7th of September he 
 talked with Mr. Lexell, who had come to 
 dine with him, of the new planet, and dis- 
 coursed with him upon other subjects, 
 with his usual penetration. He was play- 
 ing with one of his grand-children at tea 
 time, when he was seized with an apo- 
 
 * It was with great difficulty that 'this extraordi- 
 nary man, in 1766, obtained permission from the 
 King of Prussia to return to Petersburgh, where he 
 wished to ;pass the remainder of his days. Soon 
 after his return, which was graciously rewarded by 
 the munificence of Catherine II. he was seized with 
 a violent disorder, which ended in the total loss of 
 his sight. It was in this distressing situation that 
 he dictated to his servant, a taylor’s apprentice, 
 who was absolutely devoid of mathematical know- 
 ledge, his Elements of Algebra ; which, by its in- 
 trinsic merit in point of perspicuity and method, 
 has excited wonder and applause. This work, 
 though purely elementary, plainly discovers proofs 
 of an inventive genius; and it is perhaps here alone 
 that we meet with a complete theory of the analysis 
 of Diophantus. 
 
. THE ARTISAN. 
 
 347 
 
 plectic fit.^ “ I am dying,” said he, and 
 he ended his glorious life a few hours after, 
 aged seventy-six years. Euler possessed 
 to a great degree what is commonly called 
 erudition ; he had read all the Latin clas- 
 sics ; was perfect master of ancient mathe- 
 matical literature ; and had the history of 
 all ages and all nations, even to the minut- 
 est facts, ever present to his mind. Be- 
 sides this, he knew much more of physic, 
 botany, and chemistry, than could be ex- 
 pected from any man who had not made 
 these sciences his peculiar occupation. 
 
 Euler was twice married, and had thir- 
 teen children, four of whom only sur- 
 vived him. The eldest son was for 
 some time his father’s assistant and suc- 
 cessor ; the second, physician to the Em- 
 press ; and the third, a lieutenant-colonel 
 of artillery, and director of the armory at 
 Sesterbeck. The daughter married Major 
 Bell. From these children he had thirty- 
 eight grand children. “ Never have I 
 been present at a more touching sight than 
 that exhibited by this venerable old man, 
 surrounded, like a patriarch, by his nume- 
 rous offspring, all attentive to make his 
 old age agreeable, and enliven the re- 
 mainder of his days by every species of 
 kind solicitude and care.” 
 
 The catalogue of his works in the printed 
 edition makes 50 pages, 14 of which con- 
 tain the MS. works. The printed books 
 consist of works published separately, and 
 others to be found in the Peter sburgh and 
 Paris Acts, the Berlin Memoirs, and the 
 Transactions of several learned Societies. 
 
 OF GUNTER’S SCALE. 
 
 As this instrument is much employed in 
 constructing and solving mathematical 
 problems, and as we have frequent occa- 
 sion to mention the names of the lines 
 marked on that scale, we shall give a short 
 description of its construction, and the 
 various lines marked upon it. 
 
 The various lines on this instrument 
 were first laid down on a scale by Mr. 
 Edmund Gunter. The ruler to which 
 
 these lines are applied is commonly two 
 feet in length, and about an inch and a half 
 or two inches broad, both faces of it being 
 graduated. The lines on the one face are 
 employed for the construction and mea- 
 surement of figures, both plane and sphe- 
 rical ; and those on the other, for resolving, 
 with the help of a pair of compasses, the 
 various problems in trigonometry, and 
 some of the more common operations of 
 arithmetic. To distinguish the lines on 
 the two faces from each other, we shall 
 call the former natural lines, and the latter, 
 logarithmic , or artificial. 
 
 The natural lines are the following : 
 
 Lines of equal parts - 
 
 Marked.' 
 
 Chords - 
 
 CHO 
 
 Rhumbs - 
 
 RHU. 
 
 Sines - 
 
 SIN. 
 
 Secants - - - 
 
 SEC. 
 
 Tangents 
 
 TAN. 
 
 Semi-tangents - 
 
 S. T. 
 
 Longitude 
 
 M.L. 
 
 1. Lines of equal parts - 
 
 -The scales 1 
 
 which lines of equal parts are applied are 
 of two kinds, and are denominated simple 
 and diagonal. 
 
 The Simple Scale is formed by drawing 
 two parallel lines, and then dividing them 
 at right angles into such a number of equal 
 parts as the destined use of the scale may 
 require. An additional division on the 
 left hand is retained, to be afterwards 
 subdivided into 10 equal parts, for the con- 
 veniency of obtaining intermediate lengths 
 between the primary divisions. This scale 
 can only be used for laying off a line, the 
 dimension of which is expressed by two 
 digits, unless 10 of the primary divisions 
 be employed to represent an unit of the 
 next highest order. 
 
 The Diagonal Scale is constructed by 
 drawing 11 equidistant parallel lines, and 
 then dividing the upper line into as many 
 equal parts as may be thought proper. 
 Through each of the points of division lines 
 are then drawn, cutting the parallel lines 
 at right angles ; and the first division, both 
 above and below, is subdivided as before, 
 into 10 equal parts, as represented by the 
 following figure. 
 
 In this manner the primary and secondary 
 divisions of the scale are obtained. The 
 ternary or third order of divisions, which 
 must be a tenth of the scondary, are pro- 
 cured by drawing diagonal lines from the 
 9th of the secondary divisions above, to 
 the 10th of the same division below; from 
 the 8th above to the 9th below, and so on 
 in the case of each corresponding pair of 
 
 the secondary divisions. By halving each 
 of the primary divisions, and dividing the 
 last one at the other extremity of the scales 
 by diagonal lines, drawn in the same man- 
 ner, another scale is obtained of half the 
 dimensions. With either of these scales, 
 a line, whose dimension is expressed by 
 three digits, may be laid down or mea- 
 sured with the utmost precision. Thus, 
 
34S 
 
 THE ARTISAN. 
 
 let it be required to take from one of these 
 scales, a line, whose length is expressed 
 by 867 ; place one foot of the compasses 
 in the intersection of the sixth secondary 
 division and the seventh ternary one, and 
 then extend the other foot to the eighth 
 primary division. The extent will corres- 
 pond to 867. The same extent would also 
 answer to 86'7, 8-67, -867, &c. or to 8670, 
 86700, &c. according to the local value 
 assigned to the leading digit ; but whatever 
 
 value is attached to the primary divisions 
 in the measurement of any part of a figure, 
 the same value must be supposed to belong 
 to them in measuring all the other parts. 
 
 2. Line of Chords.— The line of 'chords, 
 and the other circular lines on the same 
 side of the scale, have a reference to one 
 another, and are all adapted to the same 
 radius, which is commonly two inches. 
 Let C A 
 
 represent that radius, and a circle beng 
 described with it about the centre C, draw 
 the diameters A B and DE at right angles 
 to each other. Divide one of the quadrants 
 as D A into 9 equal parts, and having 
 joined DA, transfer the chords of the 
 several arcs reckoned from A, to the 
 straight line DA, and DA will be a line 
 of chords, exhibiting every 10th division 
 of the scale. The intermediate divisions 
 are obtained by subdividing each of the 
 principal divisions of the quadrant into 10 
 equal parts, and transferring their chords 
 as before. The scale of chords is em- 
 ployed for laying down or measuring 
 angles, the chord of 60°, which is equal 
 
 to the radius, being always assumed as 
 the radius of the measuring arc. 
 
 3. Line of Rhumbs . — The line of rhumbs, 
 which is employed to lay down a ship’s 
 course when it is expressed in points, is 
 described in the same manner as the scale 
 of chords, only the quadrant is divided 
 into 8 equal parts in place of 9. Each of 
 the principal divisions is again subdivided 
 into 4 equal parts, and the chords of the 
 resulting arcs being transferred to the 
 straight line B D, the scale of rhumbs is 
 completed. 
 
 4. Line of Sines — The line of sines is 
 constructed by dividing one of the quad- 
 rants, as BE, into 90 equaljparts, as was 
 
THE ARTISAN, 
 
 349 
 
 i done for the scale of chords. Perpendi- 
 I; culars to the radius CE from every divi- 
 sion in the quadrant give the line of sines 
 reckoned from C towards E. This line 
 i is chiefly used in the orthographic projec- 
 c tion of the sphere. 
 
 5. Line of Secants. — Produce C E inde- 
 finitely to F, and through B draw B G 
 
 I parallel to C F and also of unlimited length, 
 i Through the centre C, and each division 
 ji of the quadrant B E, draw straight lines 
 I intersecting BG in the divisions 10, 20, 30, 
 I &c. The distance of each of these divisions 
 from C being transferred to the line C F, 
 i will form the line of secants, which com- 
 prehends in it the line of sines, the secant 
 of 0 being equal to the radius, or sine of 
 90°. 
 
 6. Line of Tangents — The construction 
 by which the line of secants is obtained, 
 gives at the same time the line of tangents, 
 along the line B G. This line, and the line 
 of secants, are chiefly employed in the ste- 
 reographic projection of the sphere. 
 
 7. Line of Semitangents. — The semitan- 
 gents of arcs are not, as the designation of 
 these lines would imply, the halves of the 
 tangents, but the tangents of half the cor- 
 responding arcs Thus the semitangent 
 of 40° is not half the tangent of the 40°, 
 but the tangent of 20°. Hence the scale 
 of semitangents may easily be obtained 
 from the scale of tangents. It may also be 
 obtained by joining the point B, and each 
 of the divisions in the quadrant A D; the 
 intersections of the lines, thus drawn, with 
 the line CD, will give along that line from 
 C, the scale of semitangents. This line, as 
 well as the two preceding, is used in the 
 stereographic projection of the sphere. 
 
 8. Line of Longitudes. — To construct the 
 line of longitudes, divide the radius AC 
 into 00 equal parts, and through each r of 
 the divisions draw straight lines parallel to 
 CE, and intersecting the quadrantal arc 
 A E. The chords of the resulting arcs, 
 reckoned trom A, being transferred to the 
 line A E, will give the line of longitudes. 
 
 The Buoy, with 
 
 This line being applied, in an inverted 
 order, to a corresponding line of chords 
 60 in the line of longitude being against 
 0° on the line of chords, and 0 on the former 
 line against 90° on the latter, if the divi- 
 sions on the line of chords be considered a 
 line of latitude, the opposite divisions on 
 the line of longitude will exhibit the cor- 
 responding number of miles belonging to a 
 degree of longitude, in each particular 
 latitude. This compound line is used to 
 show the convergency of the terrestrial 
 meridians, and to perform instrumentally 
 questions in parallel sailing. 
 
 To the Editor of the Artisan. 
 
 Sir, 
 
 As you have obliged me by publishing a 
 brief description of what I consider the 
 best plan yet invented, for getting a com- 
 munication with a stranded vessel from the 
 shore, I trust you will permit me to des- 
 cribe a simple plan lately invented, and 
 tried with success by a naval officer, for 
 the purpose of gaining the desired com- 
 munication from the wreck.* This inven- 
 tion is a buoy of the following description : 
 Let two small casks be connected by a 
 spar going through one head of each, 
 having its ends secured to the inner cen- 
 ters of the other heads, leaving a distance 
 between the casks of rather more than the 
 length of one of them. The spar will then 
 represent an axle, and the casks, two 
 wheels firmly fixed to it, and made water 
 tight. Upon this axle a line is to be reeled 
 in the manner of a log-line, and when 
 thrown overboard, with one end of the 
 line fast to the ship, the power of the wind 
 and sea will keep the casks in continual 
 revolution until the buoy reaches the shore; 
 and it will be found, that, as the line un- 
 reels only as the casks revolve, there Mull 
 be little danger of the bight getting far into 
 the under draught : this might be entirely 
 prevented by making the line buoyant f. 
 
 the Line reded. 
 
 A buoy of this description might be con- 
 stantly kept slung over the stern or quarter 
 of any vessel at sea, ready for cutting 
 away at a moment’s warning, either for 
 the purpose of saving the crew from a 
 wreck, or as a life buoy, in case of a man 
 falling overboard. And in the event of a 
 ship being stranded on a bar or bank at a 
 
 distance from land, where boats cannot 
 
 * Rockets have been recommended to be sup- 
 plied to ships, for the purpose of earning a line on 
 shore ; and I have no doubt they would in many 
 cases have tlje desired eftect. 
 
 t In the 32d vol. Trans. Soc. Arts, may be seen 
 an account of Mr. Cieghorn’s invention of a buoyant 
 iine and a life buoy or boat invented by Mr. T. 
 Boyce. 
 
55ft 
 
 THE ARTISAN. 
 
 get alongside the wreck, this buoy being 
 cut away, would carry a line from the 
 ship to a boat, by which means a commu- 
 nication would be formed, which might 
 ensure the safety of the crew. 
 
 The necessity of adopting some General 
 Plan, after a communication is established 
 between the shore and stranded vessel, 
 which should be understood, not only by 
 all persons having charge of mortars, but 
 also by the crews of all coasting and other 
 vessels, is so apparent, that I trust you 
 will still farther (oblige me, by making pub- 
 lic the following as an outline, to be im- 
 proved upon as circumstances may re- 
 quire. 
 
 The line thrown from the mortar should 
 not be less than 2-inch, which an 8-inch 
 mortar, within its chamber bored to con- 
 tain 20 ounces of powder, would throw 
 from 250 to 300 yards ; immediately this 
 is received on board, the crew should 
 reeve the end through a tail-block, and 
 haul off as much as will be sufficient for 
 the end and bight to go on shore again, in 
 which they may be guided by a seizing, or 
 stop seized on by the people on shore for 
 that purpose ; when this stop reaches the 
 block, the end is to be secured to it, and 
 both parts being hauled on shore, a single 
 whip purchase will be formed, by which 
 the people on shore may haul off, whatever 
 the situation of the wreck may render most 
 advisable for bringing the crew on shore.* 
 
 If time and the circumstances of the case 
 will admit, the end of a 3 and £ or 4-inch 
 hawser should now be hauled off, which 
 the crew must secure just above the tail- 
 block, and which should be either at the 
 mast-head, bowsprit-end, or most elevated 
 part of the Hull, as the master may deem 
 most advisable, in which he will be guided 
 by the state of the mast, bowsprit, &c. 
 always remembering that the higher it can 
 be placed, under the lower mast heads 
 with safety, the better. This hawser is to 
 be rove through a single block, strapped 
 with two grommets under it, just long 
 enough for a man to sit in each, holding on 
 below the block. When the end of the 
 hawser is fast on board, this block is to be 
 hauled off by one part of the whip, and 
 two men may get into the grommets, and 
 be hauled on shore by the other part. The 
 block, &c. being thus hauled to and fro, as 
 often as it may be necessary to bring the 
 whole crew on shore. At all stations 
 having a flat beach, a strong triangle 
 should accompany the apparatus, for the 
 purpose of raising the hawser on shore, 
 with a snatch-block for it to traverse in ; 
 when a party of men must keep the haw- 
 ser in hand, so as to ease it occasionally 
 to the motion of the vessel, and to keep 
 the crew as much out of the water as pos- 
 sible in their passage from the wreck. 
 
 The whole apparatus is represented by 
 the following figure : — 
 
 1. Represents the mast head, or any 
 other part to which the hawser, &c. is 
 
 # Various machines have been invented for the 
 purpose of bringing the people on shore from 
 stranded vessels. To particularize, or fully describe 
 any of these very praiseworthy inventions at pre- 
 sent would be trespassing too much on your valuable 
 miscellany ; but it may be right here to observe, 
 that whenever men are obliged to swim for their 
 lives, or be drawn through the water, they should 
 always endeavour to face the sea, that by so doing 
 they may be prepared to hold their breath, and 
 allow the heaviest to pass over them. And let them 
 bear in mind, that in the most apparently desperate 
 situations. 
 
 “ The brave man ne’er despairs — 
 
 And lives where cowards die l” 
 
 secured — 2, the tail-block/ through which 
 the whip or hauling line is rove — 3, 3, the 
 two parts of the whip — 4, the hawser — 5, 
 the block and grommets, or traveller — 6, 
 the triangle, with snatch-block on the 
 beach. 
 
 Permit me in conclusion to observe, that 
 this plan is not merely theoretical, it 
 having been invented in 1800, and since 
 put in practice with success, under some 
 of the most trying circumstances of ship- 
 wreck. X am, Sir, 
 
 Your obedient humble servant, 
 
 Navarchus. 
 
THE ARTISAN. 
 
 351 
 
 To the Editor qf the Artisan, 
 
 Sir, 
 
 As aerostation, or the practice of sailing 
 through air, has of late become a thing of 
 common occurrence in this country; and 
 perhaps, the art has arrived at a greater 
 state of perfection, than at any other period , 
 whether it will continue to afford only a 
 speculative amusement, or arrive at any 
 state of practical utility, time and the 
 developement of science can only deter- 
 mine. 
 
 As aeronauts are not always scientific 
 men and equal to the task they undertake, 
 it becomes the duty of philosophical minds 
 to suggest such improvements as shall, 
 from time to time, occur to them ; however, 
 in making the following suggestions, it is 
 but justice to myself to state, that I know 
 nothing of aerostation ; having never seen 
 a balloon otherwise than at a considerable 
 elevation. 
 
 Mr.] Graham, in his account of a late 
 ascension, tells us, “that owing to the 
 density of the atmosphere, he was compelled 
 to discharge the whole of his ballast, and 
 on arriving into lighter air , he ascended 
 with astonishing rapidity to the height of 
 2\ miles !” To return to a more rational 
 distance, from the earth : the only means 
 in the power of the aeronaut is, by a dis- 
 charge of the gas ; I am of opinion that 
 the gas and also the ballast, would be 
 much better (if possible) retained till the 
 balloon has nearly reached the earth. 
 
 Suppose a weight of several pounds, to 
 be suspended from a machine, through a 
 hole in the centre of the car, to be wound 
 up, or let down, at leisure; would not 
 such suspension have the two-fold effect, 
 of retarding its progress, and, by adding to 
 its specific gravity, cause it to descend ? If 
 so, it follows of course, that by winding 
 up the said weight, you accelerate its mo- 
 tion and consequently ascend. 
 
 I think it will be evident to every one, 
 that the balloon with its appendages can- 
 not possibly move so rapidly with a pendu- 
 lum suspended, at a considerable distance, 
 as if no such pendulum was attached. And 
 also that its elongation or contraction, must 
 add to, or diminish its specific gravity.* 
 
 If the balloon be sufficiently inflated, to 
 allow its ascension, with a considerable 
 portion of cord suspended; there would be 
 no necessity for so early a discharge of 
 ballast, which would be thus reserved for 
 the regulation of the decent, in my humble 
 opinion, a great desideratum : as all aerial 
 voyagers are agreed, that the descent is 
 the most dangerous part of the voyage. 
 
 To prevent a rotatory motion, I have 
 constructed a wheel or vertical fly on the 
 end of the car, which, I presume, if pro- 
 perly managed, would have the desired 
 effect. This apparatus is represented by 
 the following figure. 
 
 * We cannot see how the balloon can either as- 
 cend or descend by raising or lowering a weight 
 any distance, to which a balloon can ascend. Ed. 
 
352 
 
 THE ARTISAN. 
 
 Here A is the machine, B the weight 
 above alluded to, and C a section of the car. 
 
 F is a bowsprit fixed horizontally to the 
 end of [the car; on a spindle* affixed to 
 the perpendicular E, revolves (vertically) 
 the fly D ; should the balloon have a ten- 
 dency to veer round to the eastward, the 
 fly would be acted upon at 1, but the im- 
 pulse would be resisted at L. The equili- 
 brium of the fly being thus maintained, it 
 will continually revolve with a velocity in 
 proportion to the rate at which the balloon 
 passes through the air. 
 
 Knowing the estimation in which your 
 valuable pages are held by the lovers of 
 science generally, I shall not attempt to 
 till them by answering the many objections 
 that may possibly be urged against the 
 proposed fly, leaving it for the adoption, 
 improvement, or rejection, of those more 
 competent to the task than, 
 
 Sir, 
 
 Your most humble servant, 
 
 John Taylor. 
 
 Clement's Lane , Lombard Street. 
 
 ELECTROMAGNETIC AND GALVA- 
 NIC EXPERIMENTS. BY DR. HARE. 
 
 If a jet of mercury, in communication 
 with one pole of a very large calorimotor, 
 is made to fall on the poles of a very large 
 horse-shoe magnet communicating with the 
 other, the metallic stream will be curved 
 outwards or inwards, according as one or 
 the other side of the magnet may be ex- 
 posed to the jet, or as the pole communi- 
 cating with the mercury may be positive 
 or negative. When the jet of mercury is 
 made to fall just within the interstice 
 formed by a series of horse-shoe magnets, 
 mounted in the usual way, the stream will 
 be bent in the direction of the interstice, 
 and inwards or outwards, according as the 
 sides of the magnet, or the communication 
 with the galvanic poles, may be exchanged. 
 The result is analogous to those obtained 
 by Messrs. Barlow and Marsh with wires, 
 or wheels. 
 
 It is well kwown that a galvanic pair, 
 which will, on immersion in an acid, in- 
 tensely ignite a wire connecting the zinc 
 and copper surfaces, will cease to do so 
 after the acid has acted on the pair for some 
 moments, and that ignition cannot be re- 
 produced by the same apparatus, without 
 a temporary removal from the exciting 
 fluid. 
 
 I have ascertained that this recovery of 
 the igniting power does not take place, if, 
 during the removal from the acid, the 
 galvanic surfaces be surrounded either by 
 hydrogen gas, nitric oxide gas, or carbonic 
 acid gas. When surrounded by chlorine, 
 
 * The spindle should be somewhat inclined to 
 the horizon, that the fly, by its position and ten- 
 ujncy to fall upon the wind, may thereby ensure 
 its action. 
 
 or by oxygen gas, the surfaces regain 
 their igniting power in nearly the same 
 time as when exposed to the air. 
 
 The magnetic needle is nevertheless 
 much more powerfully affected by the gal- 
 vanic circuit, when the plates hav-e been 
 allowed repose, whether it take place in 
 the air, or in any of the other gases above 
 mentioned. ( American Journal of Science. ) 
 
 SOLUTIONS OF QUESTIONS. 
 Quest. 46, answered by A. Peacock, 
 St. George’s, East. 
 
 Let D denote the Debt, F the Fund, R 
 the Ratio, and T the required Time : then 
 
 the rule for finding T will be - — D -}- F 
 
 F 
 
 = R T ; therefore, §2°igg2’.g?g — 621000000 — 
 
 600000000 + 4000000 = 25000000, which 
 divided by 4*000000, gives 6*25 — ratio 
 involved to a power denoted by the time ; 
 now, as the successive divisions to obtain 
 this power by common arithmetic is very 
 prolix, it will be more convenient to em- 
 ploy logarithms. Thus, the log of 6*25 is 
 . 0*795880, which, divided by 0*01494, the 
 log of 1*035, gives 52*27175, or 52 years 3 
 months 1 week, the time required. 
 
 This question was solved in the same 
 manner, and the same answer obtained, 
 by the proposer. We also received two 
 other solutions from regular correspond- 
 ents; but they will perceive, by the above 
 solution, that they have mistaken the na- 
 ture of the question. 
 
 A sinking fund is very different from a 
 single sum of money improved at compound 
 interest, with which the two gentlemen 
 above alluded to have confounded it. 
 
 A sinking fund supposes that a sum 
 equal to the original amount of the fund is 
 added to the previous amount at the end of 
 every year, and the whole again put out 
 to interest. 
 
 QUESTIONS FOR SOLUTION. 
 
 Quest. 49, proposed by Q. Q. Portsea. 
 
 Given the apparent altitude of the sun’s 
 centre, with his declination, and the angle 
 at the zenith between the vertical circle 
 passing over the sun, and that passing over 
 a distant object in the horizon, together 
 with the declination of the object : to find 
 the latitude of the place of observation. 
 
 Quest. 50, proposed by Mr. J. M. Edney, 
 Clerkenwell. 
 
 The side of an equilateral triangle, (the 
 base of which falls on the diameter, and 
 its vertex in the middle of the arc of a 
 semi circle) may be found by multiplying 
 one third of the diameter by the square 
 root of 3. Required the analytical demon- 
 stration. 
 
THE ARTISAN. 
 
 353 
 
 PNEUMATICS. 
 
 STEAM ENGINE. 
 
 In our last article on Pneumatics, we 
 gave a short account of the progress of 
 steam navigation, and of the manner in 
 which steam is applied in this species of 
 navigation ; and having previously des- 
 cribed some of the ancient, as well as the 
 modern steam engines, and exhibited draw- 
 ings of them, as well as of their principal 
 parts, it only remains for us to give a des- 
 cription of that part of high-pressure en- 
 gines, termed the safety valve. This is 
 perhaps the more necessary, as the em- 
 ployment of engines of this kind has given 
 rise to much prejudice against the general 
 use of them, not only for propelling vessels 
 at sea, but for the movement of machinery 
 on land. 
 
 The safety-valve being therefore an 
 object of considerable importance, both as 
 regards the utility of the engine, and the 
 preservation of those connected with its 
 management, considerable attention has 
 been paid to its construction. 
 
 The first engine that was made by Cap- 
 tain Savery, had a steel-yard safety-valve, 
 to let the steam fly off when it arrived at a 
 dangerous degree of elasticity. The fol- 
 lowing figure will furnish a sufficiently 
 accurate idea of this simple apparatus. 
 
 A, the top of the boiler ; B, the safety- 
 valve or plug, made to fit air tight in the 
 tube or valve seat beneath ; C, the lever 
 working on an axis at D, and furnished 
 with a moveable weight E, adjusted to 
 balance the pressure of the steam. 
 
 When steam of considerable elasticity is 
 required, the weight is placed at the ex- 
 tremity of the lever, and as such acts 
 with greater force on the safety-valve, 
 than when removed to a point nearer to 
 the axis on which it revolves. So that 
 should low-pressure steam be required, it 
 will only be necessary to remove it nearer 
 the axis or centre, and vice versa. 
 
 Vol. I.— No. 23. 
 
 The lever and balance ball which form 
 this apparatus, would at all times be effect 
 tual, were they not liable to be fastened 
 by the corrosive nature of the materials of 
 which the valve is composed, and, what is 
 worse, their pressure altered by the addi- 
 tion of more weight. This, however, as 
 too frequent experience has shown, is con- 
 tinually the case, the engineer having 
 more regard for the full performance of 
 his machine, than for his own safety ; 
 and to the overloading of this valve, 
 accidents may be principally attributed. 
 
 To prevent a recurrence of those acci- 
 dents which first drew the attention of the 
 legislature to this important part of the 
 engine, and to which we have already re- 
 ferred, under the head of steam naviga- 
 tion, it appears advisable to inclose the 
 safety-valve in an iron box, and so put it 
 beyond the control of the engine-man. 
 
 The annexed figure represents an in- 
 accessible safety-valve, calculated to an- 
 swer all the purposes for which it is in- 
 tended ; namely, the preservation of those 
 employed in the neighbourhood of the 
 boiler, and economy in the use of steam. 
 
 .13 
 
 In this, as in the preceding diagram, A 
 represents the boiler, and B the safety- 
 valve, furnished with a small upright 
 staff, on which slide the additional weights 
 C C C. The whole is inclosed in a box D, 
 pierced with holes to allow the steam to 
 escape, fc after it has raised the valve B . 
 
 Should high pressure steam be wanted, 
 it is necessary only to increase the number 
 of weights, and the desired effect is pro- 
 duced ; or if, on the contrary, steam of 
 the usual atmospheric pressure be wanted, 
 the whole of the weights are taken off. 
 
 Another safety-valve, opening internally, 
 has, we believe, also been added by 
 Messrs. Boulton and Watt. This is of 
 great utility, more particularly in large 
 engines, as it prevents the sides of the 
 boiler being crushed in by the sudden in- 
 troduction of water, or any artificial con- 
 densation that may take place, from re- 
 ducing the heat of the boiler-head. 
 
 A A 
 
354 
 
 THE ARTISAN. 
 
 'The High-pressure Engine, in its most 
 simple form, may easily be understood by 
 reference to the following diagram. 
 
 four-way cock will be best understood hr 
 the section D ; in which E represents the 
 waste-pipe connected with the chimney , 
 while two other apertures serve to convey 
 the steam alternately to the upper and 
 under side of the piston, and a third com- 
 municates with the steam-boiler. So thaS 
 if we suppose the piston to be in au as- 
 cending direction, and the steam of course 
 entering the cylinder beneath, a communi- 
 cation will at the same time be formed be- 
 tween the upper side of the piston and the 
 atmosphere, while the steam that had pre- 
 viously been employed to depress the pis- 
 ton is now allowed to escape. When the 
 piston has reached the top of the cylinder, 
 the cock is turned, and its action reversed, 
 the steam now entering above the piston, 
 while a communication is formed for its 
 escape beneath. 
 
 With these observations we shall con- 
 clude the subject of the steam engine. 
 
 WIND-MILL. 
 
 The cylinder A is furnished with a pis- The internal structure of the wind-mill 
 ton and rod B, the latter being made to is much the same with that of water-mills, 
 fit air tight in a stuffing box. at the top of The difference between them lies chiefly in 
 the cylinder. A four-way cock O is also an external apparatus, for the application 
 provided for the admission of highly elas- of the power. 
 
 tic vapour, and its subsequent discharge This apparatus is represented by the 
 into the atmosphere. The action of the following figure, 
 
355 
 
 THE ARTISAN. 
 
 which consists of an axis’EF, with 
 two arms A B and C D passing through 
 it, and intersecting each other at right 
 angles in E, whose length is usually 
 about 32 feet : on these yards are formed 
 a kind of sails, vanes, or flights, in the 
 figure of trapeziums, with parallel bases ; 
 the greater whereof, H I, is about six feet ; 
 and the less, FG, determined by radii 
 drawn from the centre E, to I and H. 
 
 These sails are capable of being turned 
 always to the ivind, that they may receive 
 its impression : in order to which there 
 are two different contrivances, which con- 
 stitute the two different kinds of wind- 
 mills in use. 
 
 In the one the cover or roof only, with 
 the axis and sails, turn round ; and to 
 accomplish this more easily, the roof is 
 built in the shape of a turret or tower, as 
 in the foregoing figure. 
 
 This tower is encompassed by a wooden 
 
 ring, wherein is a groove, at the bottom of 
 which are placed, at certain distances, a 
 number of brass truclcels ; and within the 
 groove is another ring, upon which the 
 whole turret stands. To the moveable 
 ring are connected beams a b, and/c; 
 and to the beam a b is fastened a rope b , 
 which, at the other extreme thereof, is 
 fitted’ to a windlass or axis, in peritrochio: 
 this rope being drawn through the iron 
 hook G, and the windlass turned, the 
 sails will be moved round, and put in the 
 direction required. 
 
 In the other form of the machine, the 
 whole is sustained upon a moveable arbor, 
 or axis, perpendicular to the horizon, 
 on a stand or foot ; and by means of a 
 lever, may be turned as occasion may 
 require. 
 
 The following figure represents a ma- 
 chine of this kind, which is capable of 
 being turned so as to face any ■wind, by 
 
 having its top or dome sustained on fric- 
 tion rollers. The ease, therefore, with 
 which the sails, the axle, and cog-wheel, 
 contained in the dome a, can be turned to 
 the wind, depends on these, and the nu- 
 merous powers of the fly-wheel e. This 
 
 wheel consists of a number of triangular 
 thin boards, each forming an angle of 45° 
 with the plane of the wheel. On the axle 
 of this wheel is a thread or screw, which 
 fits into the teeth of the wheel o, and 
 gives motion to it ; this wheel turns on an 
 A A 2 
 
356 
 
 THE ARTISAN. 
 
 ! 
 
 axle, whose pivot is in the support, de- 
 noted by the dotted lines, and its other 
 end is in a socket fastened in the dome : 
 on this axle is the pinion 2 , which turns in 
 a fixed contrate wheel, on the wall plate 
 of the mill. When the wind changes 
 from the principal saris, it instantly puts 
 the fly-wheel e into motion ; this turns the 
 wheel 0 , whose pinion 2 , not being able to 
 turn the fixed wheel on the wall, is turned 
 itself, and with it the sails, the dome, and 
 all that it contains : this effect continues 
 till the fly-wheel gets into the lee of the 
 dome : it then ceases, and the sails being 
 brought to face the wind, are put into mo- 
 tion. Hence such a mill always turns 
 itself to the wind, preventing the care of 
 servants. The great sails produce an 
 equal motion in a high or low wind, by 
 being clothed with half-inch boards in- 
 stead of canvass : these little doors are 
 pushed open by a strong gale, and they 
 shut when the wind is weak ; so that by 
 playing with the momentary inequalities 
 of the wind, a [quantity of surface is 
 always presented in proportion to the im- 
 pulses of it. A pin is stuck into the 
 corner of each door, as at w, and all the 
 pins are united to a cord, which, passing 
 over the pulleys u, is fastened to a wire x f 
 going through the axle m: on the other 
 end of this wire is a nut, turning in the re- 
 sisting part of the crooked lever s; so 
 that the motion of the sails does not inter- 
 rupt the operation of the weight k, which 
 can be made greater or less, according to 
 the speed the mill should go with. That 
 the wind may have its full effect upon the 
 sails, one sail should not pass into the 
 place of another before the wind has re- 
 sumed its regular current; for, in acting 
 upon inclined planes, it is interrupted, and 
 obliged to push by, and give an impulse to 
 every sail in its passage ; hence it is found 
 that five sails are a maximum ; that is, 
 they are better than either four or five. 
 
 Horizontal wind-mills are weak, in com- 
 parison of those whose arms are inclined 
 planes; for, by giving way, or falling 
 back from the impulse of the wind, like 
 a ship, the power is not half what it is 
 against a plane that stands firm against 
 the wind. But the advantage of going 
 round always the same way, with every 
 wind without attendance, may, in some 
 cases, be thought adequate to the want of 
 power, the vast expense of building, and 
 the unsightly tower employed in the other 
 kinds. 
 
 In order to conceive how the wind ope- 
 rates upon the sails of a wind-mill, and 
 
 communicates motion to the machinery, it 
 is necessary to understand something of 
 the composition and resolution of forces.* 
 
 A body moving perpendicularly against 
 any surface, strikes it with all its force. 
 
 If it move parallel to the surface, it does 
 not strike it at all; and if it move obliquely, 
 its motion being compounded of the perpen- 
 dicular and parallel motion, only acts on 
 the surface, considered as it is perpendicu- 
 lar, and only drives it in the direction of 
 the perpendicular. So that every oblique 
 direction of a motion is the diagonal of a 
 parallelogram, whose perpendicular and 
 parallel directions are the two sides. The 
 angle which the sails ought to form with 
 their common axis, so that the wind may 
 have the greatest effect, is a matter of nice 
 enquiry, and has engaged the attention of 
 several eminent mathematicians. 
 
 Supposing the sail of a wind -mill to be a 
 plane, the effect of the wind to turn the 
 sail, in a plane at right angles to its axis, 
 will be the greatest when the plane or sail 
 makes an angle of 54° 44', with the direc- 
 tion of the wind ; consequently the incli- 
 nation of the sail to the plane of its mo- 
 tion, or what is called the angle of weather , 
 is 35° 16'. 
 
 This is true only when the sail is at rest, 
 or just beginning to move. When the sail 
 is in motion, and especially at the extre- 
 mity where the motion is quickest, the 
 wind strikes the sail under a far less 
 angle than at the centre, and therefore the 
 angle of weather must be less. Maclau- 
 rin has given a formula for calculating 
 this angle; which makes it vary from 26° 
 34 / at the point of the sail nearest the 
 centre, to 9° at its extremity. 
 
 From Mr. Smeaton’s experiments it ap- 
 pears, that a wind-mill works to the great- 
 est advantage when it is so constructed, 
 that the velocity of the sails, is to their 
 velocity when they go round without any 
 load, as a number between 6 and 7 is to 
 10; and also that the load, when the mill 
 works in this manner, is to the load that 
 would just keep it from moving, nearly as 
 8-5 to 10. 
 
 With the different velocities of wind, the 
 load that gives the maximum effect, varies 
 nearly as the square of the velocity of the 
 wind, and the effect itself as the cube. 
 
 The effect is always measured by the 
 product of the velocity of the load into its 
 weight. The velocity of the load varies 
 in the simple and direct ratio of the velo- 
 city of the wind. 
 
 * See pages 24 and 51. 
 
THE ARTISAN. 
 
 357 
 
 OPTICS. 
 
 *>N THE TREMORS OF REFLECTING TELE- 
 SCOPES. 
 
 Every person who has been in the prac- 
 tice of using Reflecting Telescopes of high 
 magnifying-powers, must have been struck 
 with the imperfection of vision arising 
 from the tremors with which they are 
 affected. During Dr. Maskelyne’s long 
 experience, he always found that the re- 
 flecting telescopes at Greenwich; viz. a 
 Gregorian of two feet, and a Newtonian of 
 six feet, showed the celestial objects in- 
 distinctly, and were considerably affected 
 with tremors, when the 48-inch triple 
 achromatic telescope showed them almost 
 entirely free from them, and generally 
 more distinct and better than even the six 
 feet reflector. He observed the same 
 effect in viewing land objects. Upon re- 
 questing the Rev. Mr. Edwards, however, 
 to investigate the cause of this great de- 
 fect, that ingenious individual undertook 
 the task, and completely succeeded, not 
 only in detecting the cause of these tre- 
 mors, but in discovering a remedy for 
 them. These causes were the springs which 
 were employed to press the telescope into 
 its cell, and the small eye-hole which was 
 always used in reflectors. By removing, 
 therefore, the springs at the back of the 
 great speculum, and supporting the spe- 
 culum on two pieces of card, wedged into 
 its cell, about 45° on each side of its low- 
 est point, and by taking away entirely the 
 eye-hole in the Greenwich Newtonian 
 reflector, Dr. Maskelyne found it so much 
 improved, as to show a printed paper 
 sensibly better and more distinct than the 
 46-inch achromatic telescope, which was 
 formerly so superior to it. 
 
 When the specula of reflectors are made 
 to rest on their lowest point, the weight of 
 the metal bends the speculum in a small 
 degree, and injures its figure. “ This,” 
 says Mr. Edwards, “ may appear strange ; 
 but I can at any time totally spoil the 
 figure of a metal, by wedging it only with 
 the thickness of a bit of common writing 
 paper.” Dr. Smith says, “ one thousandth 
 of an inch will spoil its figure. I am sure, 
 also, that quantity, if not less, will injure 
 it.” 
 
 From this observation we think it quite 
 
 evident, that if the speculum of a mode- 
 rate size was bent, by resting on its lower 
 point, a speculum of a larger size, must 
 also be bent when supported at the two 
 points above mentioned. We would, 
 therefore, strongly recommend to the 
 artist, not to allow the edge of his specula 
 to rest on any point at all, but to fix them 
 by their back, either to a plate of brass, 
 or a frame, so as to be suspended, as it 
 were, by every part of their posterior sur- 
 face. 
 
 ACHROMATIC TELESCOPE.* 
 
 As achromatic telescopes differ only from 
 those of the common refracting kind, in 
 the formation and combination of the 
 glasses employed in their construction ; 
 we did not think it necessary, in our defi- 
 nition of the different kinds of telescopes, 
 at page 265, to notice the varieties of the 
 two kinds there mentioned. But having 
 now described the form and construction 
 of the most approved instruments, both of 
 the refracting and reflecting kind, we shall 
 here endeavour to explain the nature and 
 properties of the achromatic telescope. 
 
 In viewing objects through a refracting 
 telescope, which is not furnished with an 
 achromatic object glass, a kind of aberra- 
 tion is produced, by the different refrangi- 
 bilities of the various coloured rays of 
 light which form an infinite number of 
 images, neither agreeing perfectly in situa- 
 tion nor in magnitude, so that the objects 
 are rendered indistinct, by an appearance 
 of colours at their edges : this imperfec- 
 tion, however, Mr. Dolland has in great 
 measure obviated, by his achromatic object 
 glasses : the construction of which depends 
 on the important discovery that some 
 kinds of glass separate the rays of differ- 
 ent colours from each other, much more 
 than others, while the whole deviation 
 produced in the pencil of light, is the same. 
 Mr. Dolland therefore combined a con- 
 cave lens of flint glass, with a convex lens 
 of crown glass, and sometimes with two 
 such lenses. 
 
 The following figure represents an achro- 
 matic telescope with a triple object glass, 
 and with Boscovich’s achromatic eye- 
 piece, consisting of two similar lenses, one 
 of which is every way three times as great 
 as the other, their distance being twice the 
 focal length of the smaller. 
 
 * A lens or prism is said to be achromatic , if it form an image free from colour, or if it refracts 
 all the rays of white light to one focus. A compound lens may be made achromatic, or nearly free 
 from colour, if it consists of two lenses formed of substances of different dispersive powers, the one 
 being convex and the other concave , and having their focal lengths proportional to their dispersive powers. 
 
358 
 
 THE ARTIS A Nr 
 
 The concave lens of flint glass was 
 sufficiently powerful to correct the whole 
 dispersion of coloured light produced 
 by the crown glass, but not enough 
 to destroy the effect of its refraction, 
 which was still sufficient to collect the 
 rays of light into a distant focus. For 
 this purpose it is necessary that the focal 
 lengths of the two lenses should be in the 
 same proportion as the dispersive powers 
 of the respective substances, when the 
 mean deviations of the pencils are equal ; 
 that is, in the case of the kinds of glass 
 commonly used nearly in the ratio of 7 to 
 10. Sometimes also the cromatic aber- 
 ration ; that is, the error arising from the 
 
 different refrangibilities of the different 
 rays, is particularly corrected in an eye 
 piece, by placing a field glass in such a 
 manner, as considerably to contract the 
 dimensions of the image formed by the 
 least refrangible rays, which is nearest to 
 the eye glass, and to cause it to subtend 
 an equal angle to the image formed by 
 the most refrangible rays, this image being 
 little affected by the glass. 
 
 The following figure represents one of 
 Mr. Dolland’s achromatic telescopes, sup- 
 ported in the centre of gravity, with its 
 rack work motions, and mounted on its 
 mahogany stand, 
 
 the three legs of which are made to close 
 up together by means of the brass frame 
 a a a, which is composed of three bars, 
 connected together in the centre pigce by 
 three joints, and also to the three legs of 
 
 the mahogany stand by three other joints, 
 so that the three bars of this frame may lie 
 xlose against the insides of the legs of the 
 mahogany stand when they are pressed 
 together, for convenience of carriage. 
 
THE ARTISAN. 
 
 359 
 
 The brass pin, under the rack work, is 
 made to move round in the brass socket b, 
 and may be tightened by means of the fin- 
 ger screw d, when the.telescope is directed 
 nearly to the object* intended to be ob- 
 served. This socket turns on two centres, 
 by which means it may be set perpendicu- 
 lar to the horizon, or to any angle re- 
 quired in respect to the horizon, the angle 
 may be ascertained by the divided arc, 
 and then made fast by the screw e. If 
 this socket be set to the latitude of the 
 place at which the telescope is used, and 
 the plane of this arc be turned on the top 
 'of the mahogany stand, so as to be in the 
 plane of the meridian, the socket b being 
 fixed to the inclination of the pole of the 
 earth, the telescope, when turned in this 
 socket, will have an equatorial motion, 
 which is always very convenient in making 
 astronomical observations. 
 
 Fig. 2 in the plate, represents a stand to 
 be used on a table, which may be more 
 convenient for many situations, than the 
 large mahogany stand. The telescope, 
 with its rack work, may be applied to 
 either of the two stands, as occasion may 
 require, the sockets on the top of both 
 being made exactly of the same size. The 
 sliding rods may be applied to the feet of 
 the brass stand, so that the telescope may 
 be used with the same advantages on one 
 as on the other. 
 
 The tube A A may be made either of 
 brass or mahogany, of three and half feet 
 long. The achromatic object glass of 
 three and half feet focal distance, has an 
 aperture of two inches and three quarters. 
 
 The larger size is with a tube five feet 
 long, and has an achromatic object glass 
 of three inches and one quarter aperture. 
 
 The eye tube, as represented by B, con- 
 tains four eye glasses to be used for day, 
 or any land objects. There are three eye 
 tubes, as C, which have two glasses in 
 «ach, to be used for astronomical pur- 
 poses. These eye tubes all screw into 
 the short brass tube at D. By turning 
 the button or milled head at/, this tube is 
 moved out of the larger, so as to adjust 
 the eye glasses to the proper distance 
 from the object glass, to render the object 
 distinct to any sight, with any of the dif- 
 ferent eye tubes. 
 
 The magnifying power of the three-and 
 half-feet Telescope, with the eye tube 
 for land objects, is forty-five times, and of 
 the five-feet lor land objects, sixty-five 
 times. With those for astronomical pur- 
 poses, with the three and-half-feet, the 
 magnifying powers are eighty, one hun- 
 dred and thirty, and one hundred and 
 eighty; and for the five feet, one hun- 
 dred and ten, one hundred and ninety, and 
 two hundred and fifty times. 
 
 Stained glasses, as g, are applied to ail 
 
 the different eye tubes, to guard the eye in 
 observing the spots on the sun. These 
 glasses are to be taken off when the eye 
 tubes are used for other purposes. 
 
 The rack work is intended to move the 
 telescope in any direction required, and is 
 worked by means of the two handles at li. 
 When the direction of the tube is required 
 to be considerably altered, the worm- 
 screws which act against the arc and the 
 circle must be discharged : then the screw 
 d being loosened, the pin of the rack 
 work will move easily round in the 
 socket b. 
 
 For the more readily finding or directing 
 the telescope to any object, particularly 
 astronomical objects, there is a small tube 
 or telescope, called the finder, fixed near 
 the eye-end of the large telescope. At the 
 focusof the object glass of this finder, there 
 are two wires, which intersect each other 
 in the axis of the tube, and as the magnify- 
 ing power is only about six times, the real 
 field of view is very large; therefore any 
 object will be readily found within it, 
 which being brought to the intersection of 
 the wires, it will then be within the field 
 of the telescope. 
 
 In viewing astronomical objects, (and 
 particularly when the greatest magnifying 
 powers are applied) it is very necessary 
 to render the telescope as steady as pos- 
 sible ; for that purpose there are two sets 
 of brass sliding rods, i i, as represented 
 in the figure. These rods connect the eye- 
 end of the telescope with two of the legs 
 of the stand, by which any vibrations of 
 the tube that might be occasioned by the 
 motion of the air or otherwise, will be 
 prevented, and the telescope rendered 
 sufficiently steady for using the greatest 
 powers. These sliding rods move within 
 one another with so much ease, as to 
 admit of the rack -work being used in the 
 same manner, as if they were not applied. 
 
 CHEMIST RTT- 
 
 OF THE METALS. 
 
 At the period when the existence of a 
 number of brittle metallic matters was as- 
 certained, and it was admitted, that all 
 their properties approach those of the duc- 
 tile metals, these began to be distinguished 
 by the terms, semi-metals, as if ductility 
 were the most essential character of these 
 bodies in nature, as it is in the uses of 
 art. Man, therefore, referring every thing 
 to himself, and his events, gave to these 
 bodies a determinate rank and place from 
 their utility to himself. Anothei idea, less 
 reasonable, no doubt, tended to confirm 
 this expression of the semi-metals. The 
 alchemists imagined that all the metals 
 
360 
 
 THE ARTISAN. 
 
 were only efforts of nature towards the 
 production of gold, considered as the most 
 perfect of metals, and that, by a subterra- 
 neous operation of nature, inimitable by 
 art, they were capable of arriving at a state 
 of maturity and perfection so as to become 
 gold ; and that all the metals were only 
 successive states from a less to a greater 
 degree of perfection, unto the last state, 
 namely, aurification. Now, as ductility is 
 one of the most prominent characters of 
 gold, and the metals properly so called 
 approach more or less to it by this charac- 
 ter ; those metals which did not possess it, 
 appeared to them to be the first essays of 
 nature, the embryos or metallic germs not 
 yet developed. Hence, the expression of 
 semi-metals to designate such bodies as 
 had not undergone more than a semi-me- 
 tallization. 
 
 But the slightest reflection is sufficient to 
 show, that the application of the same 
 idea must have led to the distinction of 
 third parts of metals, and metallic fractions 
 which might express the ratio or propor- 
 tion of metallic properties which each of 
 these bodies appeared comparatively to 
 possess. This supposition shows the falsity 
 of the expression of semi-metals, for it 
 shows, that while it is defective as a true 
 term of comparison to express the propor- 
 tion of the metallic properties, chemistry 
 would admit an erroneous and ridiculous 
 language, by supposing, that the metals 
 might in that manner pass from one to the 
 other conversion ; a conversion, which art 
 has never been able to effect, nor can it be 
 shown by any observation, to have been 
 effected in the processes of nature. 
 
 It is no less evident, that we may apply 
 the same remarks to the words imperfect 
 metals , which was adopted to denote such 
 metals as easily lose their metallic proper- 
 ties, and could not be again reduced to the 
 metallic state without the addition of some 
 combustible substance. The same may be 
 said of perfect metals , a name given to those 
 whose calces (oxides) were reducible by 
 the mere application of heat. This expres- 
 sion depends still more on the imaginary 
 transmutation, than the former term of 
 semi-metals ; since they affirm a pretended 
 perfection in the one, and an imperfection 
 in the other, which supposes a power of 
 coming to perfection, and arriving at the 
 state of the former. 
 
 Rejecting, therefore, these hypothetical 
 terms infected with the opinions of the al- 
 chemists, and aware of the necessity of 
 arranging the metals methodically, it be- 
 came requisite, that distinctions should be 
 admitted among them, derived from pro- 
 perties easily appreciated and compared 
 with each other. 
 
 This is, however, by no means an easy 
 task ; for the relations of these bodies to 
 
 the various objects of Chemisty are so 
 complex and diversified, that their classifi- 
 cation becomes a matter of considerable 
 difficulty ; and we may safely assert, that 
 no arrangement which has yet been made 
 of these interesting bodies is wholly free 
 from objection ; nor do we pretend to in- 
 troduce one, which has any peculiar claims 
 to superiority, in this respect, over those 
 that are generally received among the Che- 
 mists of the present day. 
 
 The celebrated French Chemist, Four- 
 croy, divides the metals into five orders or 
 classes. 1. The brittle and acidifiable , in- 
 cludes four species; viz. arsenic, tung- 
 sten, molybdena, and chrome. 2. The 
 brittle and simply oxydizable are seven; 
 titanium, uranium, cobalt, nickel, (since 
 shown by Richter not to belong to this 
 division,) manganese, bismuth, antimony, 
 and tellurium. 3. The metals that are 
 oxydizable and imperfectly ductile, are mer- 
 cury and zinc. 4. The ductile and easily 
 oxydizable, tin, lead, iron, and copper. 
 
 5 The very ductile, and difficult of oxy- 
 dizement, are silver, gold, and platina. 
 
 Another still more generally-followed 
 arrangement is that of Dr. Thomson, who 
 divides them into four classes. The first 
 class comprehends the malleable metals, 
 which are the following: gold, platina, 
 silver, mercury, palladium, rhodium, iri- 
 dium, osmium, copper, iron, nickel, tin, 
 lead, and zinc. The second class includes 
 the BRITTLE AND EASILY FUSED; viz. bis- 
 muth, antimony, tellurium, and arsenic. 
 The third class, metals that are brittle 
 and difficultly fused : these are cobalt, 
 manganese, chrome, molybdena, uranium, 
 and tungsten. The fourth class are termed 
 refractory metals, because they have 
 never yet been exhibited in a separate 
 form, but always in combination with oxy- 
 gen. These are titanium, columbium, 
 tantalium, cerium, and some others. 
 
 “ By arranging metals,” says Dr. Ure, 
 u according to the degree in which they 
 possess the obvious qualities of unalterabi- 
 lity, by common agents, tenacity, and lus- 
 tre, we also conciliate their most important 
 chemical relations ; namely, those to oxy- 
 gen, chlorine, and iodine ; since their 
 metallic pre-eminence is, popularly speak- 
 ing, inversely as their affinities for these 
 dissolvents. In a strictly scientific view, 
 their habitudes with oxygen should per- 
 haps be less regarded in their classifica- 
 tion, than with chlorine ; for this element 
 has the most energetic attractions for the 
 metals. But, on the other hand, oxygen, 
 which forms one-fifth of the atmospheric 
 volume, and eight-ninths of the aqueous 
 mass, operates to a much greater extent 
 among metallic bodies, and incessantly 
 modifies their form, both in nature and 
 art.” Now the arrangement we have 
 
THE ARTISAN. 
 
 361 
 
 adopted in the following list of these 
 bodies, will indicate very nearly their re- 
 lations to oxygen. As we progressively 
 descend, the influence of that beautiful 
 element progressively increases. Among 
 the bodies near the top of the table, its 
 powers are subjugated by the metallic 
 constitution ; but among those near the 
 bottom, it exercises an almost despotic 
 sway, which Volta’s magical pile, directed 
 by the genius of Davy, can only suspend 
 for a season. The emancipated metal soon 
 relapses under the dominion of oxygen. 
 
 The number of metals at present known 
 amount to thirty, if we except the bases of 
 the Alkalies and Earths, and one or two 
 other substances, which some individuals 
 wish to rank among these bodies ; but as 
 they are not generally acknowledged to 
 belong to this class of substances, we shall 
 not include them in the following table. 
 
 GENERAL TABLE OF THE METALS. 
 
 NAMES. 
 
 Spe.Gra. 
 
 Precipitants. 
 
 1 Platinum 
 
 2 Gold 
 
 3 Silver 
 
 4 Palladium 
 
 5 Mercury 
 
 6 Copper 
 
 7 Iron 
 
 8 Tin 
 
 9 Lead 
 
 10 Nickel 
 
 11 Cadmium 
 
 12 Zinc 
 
 13 Bismuth 
 
 14 Antimony 
 
 15 Manganese 
 
 16 Cobalt 
 
 IT Tellurium 
 
 18 Arsenic 
 
 19 Chromium 
 
 20 Molybdenum 
 
 21 Tungsten 
 
 22 Columbium 
 
 23 Selenium 
 
 24 Osmium 
 
 25 Rhodium 
 
 26 Iridium 
 
 27 Uranium 
 
 28 Titanium 
 
 29 Cerium 
 
 30 Wodanium 
 
 31 Potassium 
 
 32 Sodium 
 
 33 Lithium 
 
 34 Calcium 
 
 35 Barium 
 
 36 Strontium 
 
 37 Magnesium 
 
 38 Yttrium 
 
 39 Glucinum 
 
 40 Aluminum 
 
 41 Thorinum 
 
 42 Zirconium 
 
 43 Silicium 
 
 21*47 
 
 19-30 
 
 10- 45 
 11:8 
 13-6 
 
 8-9 
 
 7-7 
 
 7- 29 
 
 11- 35 
 
 8- 4 
 8-6 
 6-9 
 
 9- 88 
 
 6-70 
 
 8- 
 
 8-6 
 
 6*115 
 58-35 ? 
 \ 5'76 1 
 5-90 
 8-6 
 17-4 
 5-6? 
 
 4-3? 
 
 ? 
 
 10- 65 
 18*68 
 
 9-0 
 
 ? 
 
 ? 
 
 11- 47 
 0-865 
 0*972 
 
 Mar. ammon. 
 
 5 Sulph. iron 
 (Nitr mercury 
 Common salt 
 Prus. mercury 
 Common salt 
 Heat 
 Iron 
 
 Succin. soda, 
 with perox. 
 Corr. sublim. 
 Sulph. soda 
 Sulph. potash? 
 Zinc 
 
 Aik. carbonates 
 Water 
 5 Water 
 ( Zinc 
 Tartr. pot. 
 
 Aik. carbonates 
 f Water 
 \ Antimony 
 
 Nitr. lead 
 
 Do. 
 
 Do.? 
 
 Mur. lime? 
 
 Zinc, or inf. galls 
 5 Iron 
 
 l Sulphite amm. 
 Mercury 
 Zinc? 
 
 Do.? 
 
 Ferropr. pot. 
 
 Inf. galls 
 Oxal. amm. 
 
 Zinc 
 
 5 Mur. plat. 
 
 (Tart. acid. 
 
 The first 12 metals in the table are mal- 
 leable, as also the 31st, 32d, and 33d, in 
 their solid or congealed state. 
 
 The first 16 are capable of ’being con- 
 verted into oxides, which are neutral sali- 
 fiable bases. 
 
 Those marked 17, 18, 19, 20, 21, 22, 
 and 23, are capable of being acidified, by 
 combination with oxygen. 
 
 Of the oxides of the rest to the 31st, very 
 little is known. 
 
 The others form with oxygen, the alka- 
 line and earthy bases. 
 
 Having given as full a list of the metals 
 as it is possible to obtain, and having 
 stated pretty fully their general and cha- 
 racteristic properties, we shall now begin 
 to describe them individually, and to state 
 their particular properties. The malleable 
 metals, being the most valuable as well as 
 the most useful, we shall begin by des- 
 cribing them first. 
 
 OF GOLD. 
 
 Gold seems to have been known from 
 the very beginning of the world. Its pro- 
 perties and its scarcity have rendered it 
 more valuable than any other metal. 
 
 It is of an orange red, or reddish yel- 
 low colour, and has no perceptible taste or 
 smell. Its lustre is considerable, yield- 
 ing only to that of platinum, steel, silver, 
 and mercury. 
 
 Its specific gravity is 19*3. 
 
 No other substance is equal to it in duc- 
 tility and malleability. It may be beaten 
 out into leaves so thin, that one grain of 
 gold will cover 56f square inches. These 
 leaves are only of an inch thick. 
 
 But the gold leaf with which silver wire is 
 covered is only ^ of that thickness. An 
 ounce of gold, upon silver wire, is capable 
 of being extended more than 1300 miles in 
 length. 
 
 Its tenacity is considerable ; though in 
 this respect it yields to iron, copper, plati- 
 num, and silver. From the experiments 
 of Sickingen, it appears that a gold wire 
 0*078 inch in diameter, is capable of sup- 
 porting a weight of 150*07 lbs. avoirdu- 
 poise, without breaking. 
 
 It melts at 32° of Wedgewood’s pyro- 
 meter.* When melted, it assumes a bright 
 blueish green colour. It expands in the 
 act of fusion, and consequently contracts 
 while becoming solid more than most 
 metals ; a circumstance which renders it 
 less proper for casting into moulds. 
 
 It requires a very violent heat to volatil- 
 ize it; it is therefore, to use a chemical 
 term, exceedingly fixed. Gasto Claveus 
 
 * According to the calculation of the Dijon aca- 
 demicians, it melts at 1298° Fahrenheit ; according 
 to Mortimer, at 1301 p . 
 
362 
 
 THE ARTISAN. 
 
 informs us, that he put an ounce of pure 
 gold in an earthen vessel, into that part of 
 a glass-house furnace w here the glass is 
 kept constantly melted, and kept it in a 
 state of fusion for two months, yet it did 
 not lose the smallest portion of its weight. 
 Kunkel relates a similar experiment at- 
 tended with the same result ; neither did 
 gold lose any perceptible weight, after 
 being exposed for some hours to the ut- 
 most heat of Mr. Parker’s lens. Hom- 
 berg, however, observed, that when a very 
 small portion of gold is kept in a violent 
 heat, part of it is volatilized. This obser- 
 vation was confirmed by Macquer, who 
 observed the metal rising in fumes to the 
 height of five or six inches, and attaching 
 itself to a plate of silver, which it gilded 
 very sensibly ; and Mr. Lavoisier observed 
 the very same thing when a piece of silver 
 was held over gold melted by a fire blown 
 by oxygen gas, which produces a much 
 greater heat than common air. 
 
 After fusion, it is capable of assuming a 
 crystalline form. Tillet and Mongez ob- 
 tained it in short quadrangular pyramidal 
 crystals. 
 
 Gold is not in the least altered by being 
 kept exposed to the air ; it does not even 
 lose its lustre. Neither has water the 
 smallest action upon it. 
 
 It is capable, however, of combining 
 with oxygen, and even of undergoing com- 
 bustion in particular circumstances. The 
 resulting compound is an oxide of gold. 
 Gold must be raised to a very high tem- 
 perature before it is capable of abstracting 
 oxygen from common air. It may be kept 
 red hot almost any length of time without 
 any such change. Homberg, however, 
 observed, that when placed in the focus of 
 Tschirnhaus’s burning glass, a little of it 
 was converted into a purple-coloured 
 oxide ; and the truth of his observations 
 were confirmed by the subsequent experi- 
 ments of Macquer with the very same 
 burning-glass. But the portion of oxide 
 formed in these trials is too small to admit 
 of being examined. Electricity furnishes 
 a method of oxidizing it in greater quan- 
 tity. 
 
 ASTEOHOMY. 
 
 ON LIGHT. 
 
 'Fairest of beings! first created light! 
 
 Prime cause of beauty ! for from thee alone 
 The sparkling gem, the vegetable race, 
 
 The nobler worlds that live and breathe their charms, 
 The lovely hues peculiar to each tribe. 
 
 From thy unfading source of splendour draw 
 In thy pure shine, with transport I survey 
 This firmament, and these her rolling worlds, 
 
 Their magnitudes and motions. Mallet. 
 
 The nature of Light, has been the sub- 
 
 ject of speculation and conjecture among 
 philosophers, from the first dawnipgs of 
 philosophy to the present day. But of all 
 the conjectures which have been ad vanced 
 on this curious and interesting subject, 
 there is scarcely one supported by evi- 
 dence sufficient to entitle it to preference 
 over the other. There are, however, two 
 opinions on this subject, which have pre- 
 vailed more generally than any of the 
 others, and therefore, it may be proper to 
 notice them here, although the design of 
 the present work is rather to state what is 
 known respecting any phenomenon, than 
 to indulge in conjectures concerning it. 
 
 The celebrated Huygens considered 
 light as a subtle fluid filling space, and 
 rendering bodies visible bj/' the undulations 
 into which it was thrown. According to 
 this theory, when the sun rises it agitates 
 this fluid, the undtilaiiong gradually extend 
 themselves, and at last striking against 
 our eyes we see the sun. This opinion of 
 Huygens was adopted by Euler, one of 
 the best mathematicians that ever lived, 
 who exerted the whole of his consum- 
 mate mathematical skill in its defence. 
 
 Sir I. Newton and many other distin- 
 guished philosophers consider light as a 
 substance consisting of small particles, con- 
 stantly separating from luminous bodies, 
 moving in straight lines, and rendering 
 other bodies luminous by passing from 
 tlffim and entering the eye. Newton has 
 been at great pains to establish this theory, 
 and has certainly shown that all the phe- 
 nomena of light may be mathematically 
 deduced from it. 
 
 While Huygens and Euler have at- 
 tempted to support their hypothesis, 
 rather by starting objections to Newton’s, 
 than by bringing forward direct proofs, 
 Newton and his disciples, on the contrary, 
 have shown that the known phenomena of 
 light are inconsistent with the undulations 
 of a fluid, and that on such a supposition, 
 there can be no such thing as darkness at 
 all. They have also brought forward a 
 great number of direct arguments in sup- 
 port of their theory, which it has been 
 impossible to answer.* But without 
 giving a decided preference to any theory, 
 we shall proceed to state some of its pro- 
 perties. 
 
 Roemer, a Danish astronomer, while 
 engaged, in making observations on the 
 
 * M. Delavel maintains, that all light is reflected 
 by white particles, and coloured in its transmission. 
 No transparent medium reflects any light when 
 examined within a blackened bottle; this is shown 
 by experiments on 68 kinds of fluids, and on many 
 kinds of glasses, and other substances. For this, 
 and for the colours of the sea, M. Delaval pro- 
 poses a very singular theory ; but those who wish 
 to become particularly acquainted with it, must 
 consult his work on the permanent colours of opa- 
 que bodies. 
 
THE ARTISAN. 
 
 363 
 
 satellites of Jupiter, found that in eclipses 
 they emerged from the shadow at certain 
 times a few minutes later, and at others a 
 few minutes sooner than they ought to 
 have done according to the tables, which 
 had been previously constructed to show 
 the times of their revolutions, eclipses, 
 &c. On comparing these apparent irregu- 
 larities together, he found that the eclipses 
 happened before or after the computed 
 time, according as the earth was nearer to 
 or farther from Jupiter. Hence he formed 
 the ingenious conjecture, which was soon 
 demonstrated to be the case, that the 
 motion of light is not instantaneous, as 
 was then generally believed, but that it 
 required a certain portion of time, to pass 
 from the luminous body to the eye of the 
 observer. According to Roemer’s calcu- 
 lation, it was about seven minutes in tra- 
 versing the radius of the earth's orbit ; but 
 it has since been found, that when the 
 earth is exactly between Jupiter and the 
 sun, his satellities are eclipsed about 8^ 
 minutes sooner than the time found by the 
 tables ; but when the earth is nearly in 
 the opposite point, these eclipses happen 
 about minutes later than that determined 
 by the tables. It is therefore concluded 
 that light takes about 16£ minutes of time 
 to pass over a space equal to the diameter 
 of the earth’s orbit, which is at least one 
 hundred and ninety millions of miles ; it 
 therefore moves at the rate of nearly 
 200,000 miles per second, which is about 
 10,300 times faster than the earth in its 
 orbit, and 1,550,0000 times quicker than a 
 cannon ball.* 
 
 The velocity of light being known, it is 
 easy to know the time it requires to arrive 
 at the earth from any of the planets, or 
 even the fixed stars, if their distance be 
 known. For it has been ascertained, that 
 the reflected light of the planets and satel- 
 lites, travels with the same velocity as the 
 direct light of the sun or fixed stars ; and 
 that the velocity is the same from whatever 
 distance it comes. 
 
 The discovery of Roemer has been com- 
 pletely confirmed by another most im- 
 portant discovery made by our countryman, 
 Dr. Bradley, while engaged in making a 
 series of observations, with a view to de- 
 termine the annual parallax of the fixed 
 stars. This celebrated astronomer found 
 that the aberration or difference between 
 the true and apparent place of a fixed star, 
 is occasioned by the progressive motion of 
 light, combined with the motion of the 
 earth in its orbit ; and that this aberration , 
 when greatest, amounted to 20" , 232. Now 
 the earth describes an arc of 20"-232, in 
 8' 13", the time that light takes to pass 
 
 * The real time which light takes to pass from 
 the sun to the earth is 8 minutes 13 seconds. 
 
 over the semidiamer of the earth's orbit. 
 This circumstance, therefore, not only 
 affords one of the most convincing proofs 
 of the motion of the earth in its orbit, but 
 entirely overthrows both the Ptolemaic 
 and Tychonic systems, and completely 
 establishes the motion of the earth. 
 
 As the rays of light are known to pro- 
 ceed only in straight lines from luminous 
 bodies, and as the earth is constantly 
 moving forward in its orbit, it is evident 
 that a ray of light proceeding from any 
 celestial body, will impinge 'on the earth 
 at a different point from what it would 
 have done had the earth been stationary. 
 It is therefore necessary, in making astro, 
 nomical observations with nicety, to make 
 allowance for the aberration. When a 
 fixed star or planet, for example, is seen 
 through a tube or telescope, the tube does 
 not point exactly to the true place of the 
 star or planet, but to its apparent place, 
 which is always more advanced in the 
 direction we are moving than its true 
 place, by a quantity equal to the aberration 
 of the object.* But this will, perhaps, be 
 better understood by the following illus- 
 tration, which is given by M. Maupertuis 
 in his Elements of Geography. 
 
 “ The direction,” says he, “ in which 
 a gun must be pointed to strike a bird in 
 its flight, is not exactly that of the bird, 
 but of a point a little before it, in the path 
 of its flight ; and that so much the more 
 as the flight of the bird is more rapid, with 
 respect to the flight of the shot. In this 
 way of considering the matter, the flight of 
 the bird represents the motion of the 
 earth, and the flight of the shot the motion 
 of the light proceeding from the object.” 
 
 Many philosophers have attempted, not 
 only to compare the light of the stars with 
 that of the sun, but also to ascertain their 
 distances by comparisons of this kind. 
 
 The Rev. Mr. Mitchell, in an elaborate 
 and ingenious paper in the Transactions of 
 the Royal Society, states, that our sun 
 would still appear as luminous as the star 
 Sirius, although removed to 400,000 times 
 his present distance; and that the fixed 
 stars cannot be nearer than this, if they be 
 equal to the sun in lustre and magnitude, 
 and that they are so is the opinion of the 
 most celebrated astronomers of the pre- 
 sent day. Euler, who has already been 
 mentioned, makes the light of the sun 
 equal to 6,500 candles at one foot dis- 
 tance ; the moon equal to one candle at 7f 
 feet distance ; Venus to one at 421 feet; 
 and Jupiter to one at 1320 feet. From 
 this comparison it follows, the light of the 
 sun exceeds that of the moon 364,000 
 
 * The aberration not only affects the longitude 
 of a star or planet, but also its altitude, declination, 
 and right ascension. 
 
364 
 
 THE ARTISAN. 
 
 times. It is therefore no wonder that the 
 attempts which have been made by some 
 philosophers to condense the light of the 
 moon by lenses, have been attended with 
 so little success. For, should one of the 
 largest of these lenses even increase the 
 light of the moon one thousand times, still, 
 in this increased state, it will be three 
 hundred and sixty-four times less than the 
 intensity of the common light of the 
 sun. 
 
 The intensity of light has been found to 
 vary as the square of the distance ; for, if 
 an object be placed one foot distant from a 
 candle, it will receive four times more 
 light than when it is removed to double 
 the distance ; nine times more than when 
 it is removed to three times the distance, 
 and so on. 
 
 OF THE ATMOSPHERE, AND ASTRONOMICAL 
 REFRACTION. 
 
 The earth is surrounded by a thin fluid 
 mass of matter, called the Air or Atmos- 
 phere, which revolves with it in its diurnal 
 motion, and goes round the sun with it 
 every year. This fluid is both ponderous 
 and elastic. Its weight is known from the 
 Torricilian experiment, or that of the ba- 
 rometer; and its elasticity is proved by 
 simply inverting a vessel full of air in 
 water. 
 
 The atmosphere at the earth's surface 
 being pressed by the weight of all above 
 it, is there pressed the closest together ; 
 and therefore the atmosphere is densest of 
 all at the earth’s surface ; and its density 
 necessarily diminishes the higher up. For 
 each stratum of air is compressed only by 
 the weight of those above it ; the upper 
 strata are therefore less compressed, and 
 consequently less dense, than those below 
 them. 
 
 The pressure or weight of the atmos- 
 phere has been repeatedly determined, by 
 various experiments, to be about fourteen 
 pounds on every square inch of the earth’s 
 surface. Hence, the total pressure on the 
 whole surface of*the earth is 10,686,000,000 
 hundreds of millions of pounds avoirdu- 
 poise. 
 
 i From a number of experiments made on 
 the density of the atmosphere, at various 
 altitudes, by means of the barometer, it 
 has been ascertained, that if heights, 
 from the earth’s surface, be taken in arith- 
 metical progression, the density of the 
 corresponding strata of air decreases in 
 geometrical progression. Thus the den- 
 sity of the atmosphere is reduced one-half 
 for every 3§ miles of perpendicular ascent. 
 At seven miles in height, the correspond- 
 ing density is only one-fourth: at 10§ 
 
 miles, one eighth ; and 14 miles, one-six- 
 teenth : and t so on. Since the density of 
 the air decreases at this rapid rate, it is 
 evident that at a very moderate^ distance 
 
 from the surface of the earth, its density 
 would be so much diminished, as to ren- 
 der it incapable of sustaining animal life. 
 From observation and experiment, it is 
 pretty well known that 45 or 50 miles is 
 the utmost height at which the density is 
 capable of refracting a ray of light ; and, 
 therefore, this may be considered the alti- 
 tude corresponding to the least sensible 
 degree of density: for, according to the 
 law of its decrease, just stated, the den- 
 sity at this altitude is above 10,000 times 
 less than at the earth’s surface. 
 
 One of the most extraordinary and use- 
 ful properties of the atmosphere, is its re- 
 flective power, which causes the heavens 
 to appear luminous when the sun shines ; 
 for were it not for this power, the whole of 
 the heavens, and every thing on the earth, 
 would appear black, or completely dark, 
 except what the 'sun’s rays directly im- 
 pinged upon. The stars would be visible 
 by day as well as by night ; and we could 
 see nothing except what was fully exposed 
 to the sun. There could be no twilight, 
 and, consequently, the blackest darkness 
 would immediately succeed the brightest 
 sun-shine when the sun sets ; and the 
 transition would be equally sudden from 
 the blackest darkness to the brightest sun- 
 shine when the sun rose. But by means 
 of the atmosphere we enjoy the sun’s 
 light, reflected from the aerial particles 
 for some time before he rises, and also for 
 some time after he sets. For when the 
 earth, by its revolution on its axis, has 
 turned any particular place away from 
 the sun, the atmosphere above that place 
 will continue to be illuminated for some 
 time. However, as the sun gets farther 
 below the horizon, the less will the atmos- 
 phere be illuminated; and when he is 
 eighteen degrees under the horizon, it 
 ceases to be illuminated,' and then all that 
 part of the heavens which is over the place 
 will become dark : for the place will then 
 be turned too far from the sun, and his 
 rays will strike too high on the atmos- 
 phere to be refracted or bent downwards 
 at that place. In consequence of the re- 
 fractive power of the atmosphere, all the 
 heavenly bodies appear higher than they 
 really are : for, on account of the variation 
 in the density of the air, a ray of light in 
 passing through it will be refracted at 
 every instant, and consequently the path 
 of the ray will be a curve. And as an 
 object is always seen in the direction in 
 which the rays of light proceeding from it 
 enter the eye, it is evident every celestial 
 body will appear more elevated above the 
 horizon than it actually is, by a quantity 
 equal to the refraction which a ray of 
 light suffers in passing from it through the 
 atmosphere to the eye of the observer. 
 
 When the object is in the zenith, the re- 
 
THE ARTISAN. 
 
 365 
 
 fraction is quite insensible ; but it in- that situation, enter the atmosphere more 
 creases as the altitude of the object dimi- obliquely than in any other, and con- 
 nishes till it reaches the horizon, and sequently are more turned out of their 
 then the refraction is greatest; for the course. This will be evident from an m- 
 rays which proceed from the object, in spection of the following figure. „ 
 
 Where BOD represents the surface of served at Paris, on the 19th of July, 1750, 
 the earth, O the place of an observer, and when the moon appeared visibly eclipsed, 
 F G H the surrounding atmosphere. A while the sun was distinctly to be seen 
 ray of light proceeding from a body, Z, in above the horizon. 
 
 the zenith, is not refracted ; but if it pro- At some seasons of the year the sun 
 ceed from a body at A, it will enter the appears ten minutes sooner above the hori- 
 eye at O, and appear in the direction O a ; zon in the morning, and continues as much 
 if the body be in the horizon, as at E, the longer above it in the evening, than he 
 rays proceeding from it will enter the eye would do were there no refraction ; and 
 at O, and appear to come in the direction at a mean rate, about seven minutes on 
 eO. any day of the year. The refraction 
 
 On some accasions, the horizontal|refrac- varies, however, very much with the state 
 tion amounts to 36 or 37 minutes, and, of the atmosphere. In cold dry weather 
 generally, to about 33 minutes, which is the air is more dense than in warm 
 equal to the diameter of the sun or moon ; weather ; consequently the refraction is 
 and therefore the whole disc of the sun or greater in cold weather than in warm ; 
 moon will appear above the horizon, both and for the same reason, it is greater in 
 at rising and setting, although actually cold countries than in hot ones, 
 below. This is the reason that the full A remarkable instance of this is men- 
 moon has sometimes been seen above the tioned by Dr. Smith in his Optics, where 
 horizon before the sun was set. A re- he states, that some Hollanders who win- 
 markable instance^ of this kind was ob- tered in Nova Zembla, in the year 1596, 
 
365 
 
 THE ARTISAN. 
 
 were surprised to find that, after three 
 months’ constant darkness, the sun began 
 to appear seventeen days sooner than the 
 time by computation deduced from the 
 latitude, which was 76 degrees. Now this 
 phenomenon can only be accounted for by 
 the extraordinary refraction of the sun’s 
 rays in passing through the cold dense air 
 in that climate. 
 
 At the same altitudes, the sun, moon, 
 and stars, all undergo the same refraction; 
 for at equal altitudes, the rays which pro- 
 ceed from any of these bodies suffer the 
 same inclination. 
 
 The horizontal refraction being the 
 greatest, causes the sun and moon, at 
 rising and setting, to appear of an oval 
 form ; for the lower edge of each being 
 seen through denser atmosphere than the 
 upper edge, is more refracted ; conse- 
 quently, the perpendicular diameter must 
 appear shortened, while the horizontal 
 diameter, (which is not affected by refrac* 
 tion) remains the same, and in this way 
 the oval appearance is produced. For the 
 same reason, two fixed stars that are 
 near the horizon,' and right above each 
 other, appear nearer than when they are 
 high above the horizon ; and if they are 
 both in the horizon, but at some distance 
 from each other, then they will appear at 
 a less distance than they really are ; for 
 the refraction makes each of them higher, 
 and consequently must bring them into 
 parts of their respective vertical circles, 
 which are nearer to each other, because 
 all vertical circles converge and meet in 
 the zenith. Hence, in all astronomical 
 calculations allowance must be made for 
 refraction, before the true altitude of any 
 celestial body can be obtained. Tables, 
 containing this allowance for all altitudes, 
 are to be found in every work on practical 
 astronomy. 
 
 The atmosphere not only occasions ce- 
 lestial bodies to appear higher than they 
 really are, by bending the rays of light as 
 they pass through it, but it also affects 
 terrestrial bodies in the same way. The 
 quantity of this refraction is, however, 
 found to vary considerably with the differ- 
 ent states of the atmosphere, and is there- 
 fore very uncertain. But at a mean rate it 
 may be taken at one-fourteenth part of the 
 distance expressed in degrees in a great 
 circle : or, according to Professor Play- 
 fair, it is about one-seventh part of the 
 correction for the earth’s curvature, an- 
 swering to the distance between the ob- 
 server and the object.* 
 
 * For example, suppose the distance between a 
 person and any conspicuous object to be 5 English 
 miles, and he wishes to know how much it is 
 elevated by refraction. Tiie correction for the 
 earth’s curvature on this distance is 162 feet, one- 
 seventh part of which is 2 feet inches’ which it 
 is raised by refraction. 
 
 iHuscellfimeous Subjects. 
 
 MEMOIR OF DOCTOR FRANKLIN. 
 
 Benjamin Franklin, the celebrated Ame- 
 rican philosopher, was sprung, as he' him- 
 self informs us, from a family settled for a 
 long course of years in the village of Ecton, 
 in Northamptonshire ; where they had aug- 
 mented their income, arising from a small 
 patrimony of thirty acres of land, by adding 
 to it the profits of a blacksmith’s business. 
 His father, Josias, having been converted 
 by some nonconformist ministers, left Eng- 
 land for America in 16S2, and settled at 
 Boston, as a soap-boiler and tallow- 
 chandler. At this place, in 1706, Benja- 
 min, the youngest of his sons, was born. 
 It appeared at first to be his destiny to be- 
 come a tallow-chandler, like his father ; 
 but, as he manifested a particular dislike 
 to that occupation, different plans were 
 thought of, which ended in his becoming a 
 printer, in 1718, under one of his brothers, 
 who was settled at Boston, and in 1721 
 began to print a newspaper. This was a 
 business much more to his taste, and he 
 soon shewed a talent for reading, and occa - 
 sionally wrote verses, which were printed 
 in his brother’s newspaper, although un- 
 known to the latter. He wrote also in the 
 same some prose essays, and had the saga- 
 city to cultivate his style after the model 
 of the Spectator. With his brother he 
 continued as an apprentice, until their fre- 
 quent disagreements, and the harsh treat- 
 ment he experienced, induced him to leave 
 Boston privately, and take a conveyance 
 by sea to New York. This happened in 
 1723. From New York he immediately 
 proceeded, in quest of employment, to 
 Philadelphia, not without some distressing 
 adventures. His own description of his 
 first entrance into that city, where he was 
 afterwards in so high a situation, is too 
 curious to be omitted. 
 
 “ On my arrival at Philadelphia, I was 
 in my working dress, my best clothes being 
 to come by sea. I was covered with dirt ; 
 my pockets were filled with shirts and 
 stockings ; I was unacquainted with a 
 single soul in the place and knew not 
 where to seek for a lodging. Fatigued 
 with walking, rowing, and having passed 
 the night without sleep, I was extremely 
 hungry, and all my money consisted of a 
 Dutch dollar, and about a shilling’s worth 
 of coppers, which I gave to the boatmen 
 for my passage. As I had assisted them 
 in rowing, they refused it at first, but I in- 
 sisted on their taking it. A man is some- 
 times more generous when he has little, 
 than when he has much money ; probably 
 because,' in the first case, he is desirous, of 
 concealing his property. 
 
 I walked towards the top of the street, 
 looking eagerly on both sides till I oame 
 
THE ARTISAN, 
 
 367 
 
 to Market-street, where I met a child with 
 a loaf of bread. Often had 1 made my 
 dinner on dry bread. I enquired where 
 he bought it, and went straight to the 
 baker’s shop which he pointed out to me ; 
 l asked for some biscuits, expecting to find 
 such as we had at Boston, but they made, 
 it seems, none of that sort at Philadelphia. 
 I then asked for a threepenny loaf. They 
 made no loaves at that price. Finding 
 myself ignorant of the prices, as well as 
 of the different kinds of bread, I desired 
 him to let me have three pennyworth of 
 bread of some kind or other. He gave me 
 three large rolls. I was surprised at re- 
 ceiving so much. I took them, however, 
 and having no room in my pockets, I 
 walked on with a roll under each arm, 
 eating the third. In this manner I went 
 through Market-street to Fourth- street, 
 and passed the house of Mr. Read, the 
 father of my future wife. She was stand- 
 ing at the door, observed me, and thought, 
 with reason, that I made a very singular 
 and grotesque appearance.” 
 
 Notwithstanding this unpromising com- 
 mencement, Franklin soon met with em- 
 ployment in his business, working under 
 one Keimer, a very indifferent printer, 
 though at that time almost the only one in 
 Philadelphia. In 1724, encouraged by the 
 specious promises of Sir William Keith, 
 governor of the province, Franklin sailed 
 for England, with a view of purchasing 
 materials for setting up a press ; though 
 his father, to w r hom he had applied, pru- 
 dently declined encouraging the plan, on 
 account of his extreme youth, as he was 
 then only eighteen. On his arrival in 
 England, he had the mortification to find 
 that the governor, w ho had pretended to 
 give him letters of recommendation, and 
 of credit for the sum required for his pur- 
 chases, had only deceived him ; and he 
 w'as obliged to work at his trade in Lon- 
 don for a maintenance. The most exem- 
 plary industry, frugality, and ^temperance, 
 with great quickness and skill in his busi- 
 ness, both as a pressman and as a com- 
 positor, made this rather a lucrative situa- 
 tion. He reformed the workmen in the 
 houses where he was employed, "which 
 were, first, Mr. Palmer’s, afterwards Mr. 
 Watts’s, in Wild-street, Lincoln’s-Inn-fields, 
 by whom he was treated with a kindness 
 which he always remembered. Desirous, 
 however, of returning to Philadelphia, he 
 engaged himself as book-keeper to a mer- 
 chant, at fifty pounds a year ; “ which,” 
 says lie, “ was less than I earned as a 
 compositor.” He left England, July 23, 
 1726, and reached Philadelphia early in 
 October. In 1727, Mr. Denham, the mer- 
 chant, died, and Franklin returned to his 
 occupation as a printer, under Keimer, his 
 first master, with a handsome salary. But 
 
 it was not long before he setup for himself 
 in the same business, in concert with one 
 Meredith, a young man, whose father was 
 opulent, and supplied the money required . 
 
 A little before this, he had gradually 
 associated with a number of persons, like 
 himself, of an eager and inquisitive turn of 
 mind, and formed them into a club, or 
 society, to hold meetings for their mutual 
 improvement in all kinds of useful know- 
 ledge, which was in high repute for many 
 years after. Among many other useful 
 regulations, they agreed to bring such 
 books as they had into one place, to form 
 a common library ; but this furnishing only 
 a scanty supply, they resolved to contribute 
 a small sum monthly towards the purchase 
 of books for their use from London. In 
 this way their stock began to increase 
 rapidly ; and the inhabitants of Phila- 
 delphia, being desirous of profiting by their 
 library, proposed that the books should be 
 lent out on paying a small sum for this 
 indulgence. Thus, in a few years, the 
 society became rich, and possessed more 
 books than were perhaps to be found in all 
 the other colonies ; and the example began 
 to be followed in other places. * 
 
 About 1728 or 1729, Franklin set up a 
 newspaper, the second in Philadelphia, 
 which proved very profitable, and afforded 
 him an opportunity of making himself 
 known as a political writer, by his insert- 
 ing several attempts of that kind in it. He 
 also set up a shop for the sale of books and 
 articles of stationary, and in 1730 he mar- 
 ried a lady, whom lie had courted before 
 he went to England. He afterwards began 
 to have some leisure, both for reading 
 books, and writing them, of which he gave 
 many specimens from time to time. In 
 1732, he began to publish “ Poor Richard’s 
 Almanack,” w hich was continued for many 
 years, it was always remarkable for the 
 numerous and valuable concise maxims 
 which it contained, for the economy of 
 human life ; all tending to industry and 
 frugality ; and w hich were comprised in 
 a well-known address, entitled “ The way 
 to Wealth.” This has been translated 
 into various languages, and inserted in 
 almost every magazine and newspaper in 
 Great Britain or America. It has also 
 been printed on a large sheet, proper to be 
 framed, and hung up in conspicuous places 
 in all houses, as it very well deserves to be. 
 Mr. Franklin became gradually more 
 known for his political talents. In 1736, 
 he w r as “appointed clerk to the general 
 assembly of ! ennsylvania ; and was re- 
 elected by succeeding assemblies for sev eral 
 years, till he was chosen a representative 
 for the city of Philadelphia: and in 1737 
 he w as appointed post-master of that city. 
 In 1738, he formed the first fire-company 
 there, to extinguish and prevent fires, and 
 
368 
 
 THE ARTISAN. 
 
 the burning of houses ; an example which 
 was soon followed by other persons, and 
 other places. And soon after, he suggested 
 the plan of an association for insuring 
 houses and ships from losses by fire, which 
 was adopted; and the association con- 
 tinues to this day. In 1744, during a war 
 between France and Great Britain, some 
 French and Indians made inroads upon 
 the frontier inhabitants of the . province, 
 who were unprovided for such an attack ; 
 the situation of the province, was at this 
 time truly alarming, being destitute of 
 every means of defence. At this crisis 
 Franklin stepped forth, and proposed to a 
 meeting of the citizens of Philahelphia, a 
 plan of a voluntary association for the de- 
 fence of the province. This was approved 
 of, and signed by 1200 persons immediately. 
 Copies of it were circulated throughout the 
 province ; and in a short time the number 
 of signatures amounted to 10,000. Frank- 
 lin was chosen colonel of the Philadelphia 
 regiment, but he did not think proper to 
 accept of the honour. 
 
 Pursuits of a different nature now occu- 
 pied the greatest part of his attention for 
 some years. Being always much addicted 
 to the study of natural philosophy, and the 
 discovery of the Leyden experiment in elec- 
 tricity having rendered that science an 
 object of general curiosity, Mr. Franklin 
 applied himself to it, and soon began to 
 distinguish himself eminently in that way. 
 He engaged in g, course of electrical expe- 
 riments with al the ardour and thirst for 
 discovery which characterised the philo- 
 sophers of that day. By these he was 
 enabled to make a number of important 
 discoveries, and to propose theories to ac- 
 count for various phenomena ; which have 
 been generally adopted, and which will 
 probably endure for ages. His observa- 
 tions he communicated in a series of letters 
 to his friend Mr. Peter Collin son ; the first 
 of which is dated March 28, 1747. In these 
 he makes known the power of points in 
 drawing and throwing off the electric mat- 
 ter, which had hitherto escaped the notice 
 of electricians. He also made the discovery 
 of a plus and minus, or of a positive and 
 negative state of electricity ; from whence, 
 in a satisfactory manner he explained the 
 phenomena of the Leyden phial, first ob- 
 served by Cuneus, or Muschenbroeck, 
 which had much perplexed philosophers. 
 He shewed that the bottle when charged, 
 contained no more electricity than before, 
 but that as much was taken from one side 
 as was thrown on the other ; and that, to 
 discharge it, it was only necessary to make 
 a communication between the two sides, by 
 which the equilibrium might be restored, 
 and then no signs of electricity would 
 remain. 
 
 [ To be continued .] 
 
 SOLUTION OF QUESTIONS. 
 
 Quest. 48. answered by Mr. Whitcombe* 
 Cornhill. 
 
 Put a — 2-943271 and mzz 1*94353929. 
 then by substitution and transposition, we 
 have x 3 ■ — ax m~ o., and per Nicho- 
 las Tartalea’s method of solving cubics 
 which want their second term, we have x ~ 
 
 4 27 2 
 
 + j 
 
 /m 
 
 a 3 m 
 27 2 
 
 _ . m 2 a 3 
 
 But in the present instance ^ 
 
 W hence the eq uations 
 
 3 / /m* a 3 , , ,/ 
 
 v \/ — and -j- — 
 
 4 27 
 
 /m 2 a 3 
 
 ^ T~ 27 
 
 destroy each other ; Consequently, x — 
 8 m 
 
 — — \/ — 4 m .*. x — — s/ Am~ — 
 
 $ 7*77415716 = — 1*981 =z one of the 
 Roots. Now divide the given equation by 
 x -j- 1*981 and we have x 2 — 1*981 x ~ — 
 •98109 a quadratic ; then by completing the 
 square, and extracting the root, we obtain 
 x zz + *991 and — *99 which are the other 
 two roots of the given equation, and deter- 
 mined without a conjecture, approxima- 
 tion, or using either of the methods alluded 
 to in the question. 
 
 There appears to be nothing particular in 
 
 this question, except that n ~ is equal to 
 
 (when treated by Carden’s rule) ; conse- 
 quently two of the terms destroy each 
 other, as stated above; but we have^here 
 no new method of solving cubic equations, 
 nor any improvement on the old. Ed. 
 
 QUESTIONS FOR SOLUTION. 
 
 Quest. 51, proposed by Mr. J. M. Edney, 
 Clerkenwell. 
 
 There is a circular building of 40 feet 
 diameter, and 25 feet high to the ceiling, 
 which is covered with a saloon (dome), 
 the circular arch of which is 5 feet radius ; 
 required the whole content of the room in 
 cubic feet. 
 
 Quest. 52, proposed by Mr. Whitcomb, 
 Cornhill. 
 
 In a given quadrant of a circle to in- 
 scribe the greatest circle geometrically, and 
 to give the demonstration. 
 
 Quest. 53, proposed by Mr. J. Taylor, 
 Clement's Lane , Lombard Street. 
 
 Thomas and John put, monthly, into the 
 saving’s bank a certain sum of money each ; 
 the sum of their monthly deposits is £3^ 
 sterling, and the sum of their 5th powers 
 is £43*32933 ; I demand their respective 
 deposits, John’s being the greatest ? 
 
THE ARTISAN. 
 
 
 tt£OMETB/5T. 
 
 BOOK III. 
 
 DEFINITIONS. 
 
 The radius of a circle is the straight 
 line drawn from the centre to the circum- 
 ference. 
 
 I. A straight line is said to touch a cir- 
 cle, when it meets the circle, and being 
 produced does not cut it. 
 
 II. Circles are said to touch one ano- 
 ther, which meet, but do not cut one 
 another. 
 
 III. Straight lines are said to be equally 
 distant from the centre of a circle, when 
 the perpendiculars drawn to them from 
 the centre are equal. 
 
 IV. And the straight line on which the 
 greater perpendicular falls, is said to be 
 farther from the centre. 
 
 An arch of a circle is any part of the 
 circumference. 
 
 V. A segment of a circle is the figure 
 contained by a straight line, and the arch 
 which it cuts off. 
 
 VI. An angle in a segment is the angle 
 contained by two straight lines drawn 
 from any point in the circumference of the 
 segment, tq the extremities of the straight 
 Jine which is the base of the segment. 
 
 Vol. I.— No. 24. 
 
 VII. And an angle is said to insist or 
 stand upon the arch intercepted between 
 the straight lines that contain the angle. 
 
 VIII. The sector of a circle is the figure 
 contained by two straight lines drawn 
 from the centre, and the arch of the cir- 
 cumference between them. 
 
 IX. Similar segments of a circle, are 
 those in which the angles are equal, or 
 which contain equal angles. 
 
 PROPOSITION I. 
 
 Problem.-— T o find, the centre of a given 
 circle. 
 
 Let ABC be the given circle ; it is re- 
 quired to find its centre. 
 
 Draw within it any straight line A B, 
 and bisect it in D ; from the point D draw 
 D C at right angles to A B, and produce 
 it to E, and bisect C E in F : The point F 
 is the centre of the circle ABC. 
 
 For, if it be not, let, if possible, G be 
 the centre, and join G A, GD, GB : Then, 
 because DA is equal to DB, and DG 
 common to the two triangles ADG, BDG, 
 the two sides A D, D G are equal to the 
 two. B D, D G, each to each ; and the base 
 GA is equal to the base GB, because 
 they are radii of the same circle : there- 
 fore the angle ADG is equal to the angle 
 G D B : But when a straight line standing 
 8 B 
 
370 
 
 THE ARTISAN, 
 
 upon another straight line, makes the ad- 
 C 
 
 jacent angles equal to one another, each 
 of the angles is a right angle. Therefore 
 the angle GDB is a right angle: But 
 F D B is likewise a right angle ; where- 
 fore the angle F D B is equal to the angle 
 GDB, the greater to the less, which is 
 impossible : Therefore G is not the centre 
 of the circle ABC: In the same manner, 
 it can be shown, that no other point but 
 F is the centre ; that is, F is the centre of 
 the circle ABC: Which was to be found. 
 
 Cor. From this it is manifest, that if in 
 a circle a straight line bisect another at 
 right angles, the centre of the circle is in 
 the line which bisects the other. 
 
 PROPOSITION II. 
 
 Theorem. — If any two points be taken in 
 the circumference of a circle, the straight 
 line which joins them shall fall within the 
 circle. 
 
 Let A B C be a circle, and A B any two 
 points in the circumference ; the straight 
 line drawn from A to B shall fall within 
 the circle. 
 
 Take any point in A B as E ; find D the 
 centre of the circle ABC; join AD, DB 
 
 ahd D E, and let D E meet the circum- 
 ference in F. Then because DA is equal 
 to DB, the angle DAB is equal to the 
 angle D B A ; and because AE, a side of 
 the triangle DAE, is produced to B, the 
 angle DEB is greater than the angle 
 DAE; but DAE is equal to the angle 
 
 D BE ; therefore the angle DEB is 
 greater than the angle DBE: Now to 
 the greater angle the greater side is oppo- 
 site ; DB is therefore greater than DE: 
 but B D is equal to DF ; wherefore DF is 
 greater than D E, and the point E ^there- 
 fore within the circle. The same may be 
 demonstrated of any other point between 
 A and B, therefore A B is within the cir- 
 cle. Wherefore, if any two points, &c. 
 Q. E. D. 
 
 PROPOSITION III. 
 
 Theorem — If a straight line drawn through 
 the centre of a circle bisect a straight 
 line in the circle , which does not pass 
 through the centre , it will cut that line 
 at right angles ; and if it cut it at right 
 angles , it will bisect it. 
 
 Let ABC be a circle, and let C D, a 
 straight line drawn through the centre, 
 bisect any straight line A B, which does 
 not pass through the centre, in the point 
 F : It cuts it also at right angles. 
 
 Take E the centre of the circle, and 
 join E A, E B. Then, because A F is 
 equal to F B, and F E common to the two 
 triangles A F E, B F E, there are two 
 sides in the one equal to two sides in the 
 other; but the base EAis equal to the 
 
 equal to the angle BFE. And when a 
 straight line standing upon another makes 
 the adjacent angles equal to one another, 
 each of them is a right angle: Therefore 
 each of the angles A F E, B FE is a right 
 angle ; wherefore the straight line C D, 
 drawn through the centre, bisecting ano- 
 ther, A B, which does not pass through 
 the centre, cuts it at right angles. 
 
 Again, let CD cut AB at right angles ; 
 C D also bisects A B ; that is, A F is equal 
 toFR. 
 
 The same construction being made, be- 
 cause the radii EA, EB are equal to one 
 another, the angle E A F is equal to the 
 angle E B F ; and the right angle A F E is 
 equal to the right angle BFE: Therefore, 
 in the two triangles E A F, E B F, there 
 are two angles in one equal to two angles 
 
THE ARTISAN. 
 
 371 
 
 in the other ; and the side E F, which is 
 opposite to one of the equal angles in each, 
 is common to both ; therefore the other 
 sides are equal ; A F therefore is equal to 
 FB. Wherefore, if a straight line, &c. 
 Q. E. D. 
 
 PROPOSITION IV. 
 
 Theorem.— If in a circle two straight lines 
 cut one another, which do not both pass 
 through the centre , they do not bisect each 
 other. 
 
 Let A B C D be a circle, and AC, BD 
 two straight lines in it, which cut one 
 another in the point E, and do not both 
 pass through the centre : AC, BD do not 
 bisect one another. 
 
 3 For, if it is possible, let A E be equal to 
 E C, and B E to E D : If one of the lines 
 
 pass through the centre, it is plain that it 
 cannot be bisected by the other, which 
 does not pass through the centre. But if 
 neither of them pass through the centre, 
 take F the centre of the circle, and join 
 E F : and because F E, a straight line 
 through the centre, bisects another AC, 
 w'hich does not pass through the centre, it 
 must cut it at right angles ; wherefore 
 FEA is a right angle. Again, because 
 the straight line F E bisects the straight 
 line B D, which does not pass through the 
 centre, it must cut it at right angles ; 
 wherefore FEB is a right angle ; and 
 FEA was shown to be a right angle; 
 therefore FE A is equal to the angle FEB, 
 the less to the greater, which is impossi- 
 ble : therefore AC, B D do not bisect one 
 another. Wherefoi-e, if in a circle, &c. 
 Q. E. D. 
 
 PROPOSITION V. 
 
 Theorem. — If two circles cut one another , 
 
 they cannot have the same centre. 
 
 Let the two circles A B C, C D G cut 
 one another in the points B C ; tjiey have 
 not the same centre. 
 
 For, if it be possible, let E be their cen* 
 
 tre ; join E C, and draw any straight line 
 EFO meeting them in F and G : and be- 
 cause E is the centre of the circle ABC, 
 C E is equal to E F : Again, because E is 
 
 the centre of the circle C D G, C E is equal 
 to E G : but, C E was shown to be equal 
 to E F, therefore E F is equal to E G, the 
 less to t!he greater, which is impossible : 
 therefore E is not the centre of the circles 
 ABC, CDG. Wherefore, if two circles, 
 &c. Q. E. D. 
 
 PROPOSITION VI. 
 
 Theorem. — If two circles touch one another 
 internally , they cannot have the same cen- 
 tre. 
 
 Let the two circles A B C, C D E, touch 
 one another internally in the point C : 
 they have not the same centre. 
 
 For, if they have, let it be F : join F C, 
 and draw any straight line FEB meeting 
 them in E and B ; and because F is the 
 
 centre of the circle A B C, C F is equal to 
 FB; also, because F is the centre of the 
 circle C D E, C F is equal to F E : but 
 C s F was shown to be equal to F B ; there- 
 fore F E is equal to F B, the less to the 
 greater, which is impossible ; wherefore F 
 is not the centre of the circles ABC, 
 C D E. Therefore, if two circles, &c. 
 Q. E. D. 
 
 BB 2 
 
THE ARTISAN. 
 
 m 
 
 MECHANICS, 
 
 WIND-MILLS. 
 
 Previous to concluding our observations 
 on the subject of wind-mills, we shall add 
 a few of the most valuable maxims deduced 
 by Mr. Smeaton, from a number of experi- 
 ments which he made to determine their 
 greater effects. 
 
 Maxim 1. The velocity of wind-mill 
 sails, whether unloaded or loaded, so as 
 to produce a maximum effect, is nearly as 
 the velocity of the w r ind, their shape and 
 position being the same. 
 
 Maxim 2. The load at the maximum is 
 nearly, but somewhat less, than as the 
 square of the velocity of the wind, the 
 shape and position ofJ;he sails being the 
 same. 
 
 Maxim 3. The effects of the same sails 
 at a maximum, are nearly, but somewhat 
 less, than as the cubes of the velocity of 
 the wind. 
 
 Maxim 4. The load of the same sails at 
 the maximum, is nearly as the squares, 
 and their eflects as the cubes of their num- 
 ber of turns in a given time. 
 
 Maxim 5. When sails are loaded, so as 
 to produce a maximum at a given velocity, 
 and the velocity of the wind increases the 
 load, continuing the same : 1st. The in- 
 crease of effect, when the increase of the 
 velocity of the wind is small, will be 
 nearly as the squares of those velocities : 
 2dly, When the velocity of the wind is 
 double, the effects will be nearly as 
 10 : 274 ; but 3dly, W'hen the velocities 
 compared are more than double of that 
 where the given load produces a maxi- 
 mum, the effects increase nearly in the 
 simple ratio of the velocity of the wind. 
 
 Maxim 6. In sails where the figure and 
 positions are similar, and the velocity of 
 the wind the same, the number of turns in 
 a given time, will be reciprocally as the 
 radius or length of the sail. 
 
 Maxim 7. The load at a maximum, that 
 sails of a similar figure and position, will 
 overcome at a given distance from the cen- 
 tre of motion, will be as the cube of the 
 radius. 
 
 Maxim 8. The effects of sails of similar 
 figure and position, are as the square of 
 the radius. 
 
 Maxim 9. The velocity of the extremi- 
 ties of Dutch sails, as well as of the en- 
 larged sails in all their usual positions 
 when unloaded, or even loaded to a maxi- 
 mum, are considerably quicker than the 
 velocity of the wind. 
 
 MOTION OF MACHINES. 
 
 Machines either work with a variable or 
 a uniform velocity. If the moving power 
 is of the kind, that when the motion begins, 
 diminishes in the intensity of its action, 
 the machine, after a little time, will ac- 
 
 quire a uniform velocity. If, however, 
 the moving power be one that acts always 
 with the same force, and if the resistance 
 is also uniform, the machine will be con- 
 tinually accelerated. But as a motion 
 continually accelerated, is incompatible 
 with the purposes of machinery, it is either 
 contrived, that by an increased resistance, 
 the motion shall become uniform, or that 
 the moving power shall at intervals cease 
 altogether, or become a retarding force — 
 so that the velocity of the machine, though 
 continually changing, may be confined 
 within certain limits. 
 
 When the momentum of the power ap- 
 plied to a machine, is greater than the 
 momentum of the resistance, the machine 
 is put in motion, and if the power be one 
 that acts more forcibly on bodies at rest 
 than in motion, its action is of course di- 
 minished, and the acceleration of the ma- 
 chine in the second instant, is less than 
 in the first. This diminution of the acce- 
 lerating force continues to increase, till 
 the instant when that force becomes equal 
 to the resistance, or till the velocity gene- 
 rated every instant by the one, be just 
 equal to the velocity destroyed every in- 
 stant by the other. The acceleration then 
 ceases, and the motion of the machine be- 
 comes uniform. Now, this increase of re- 
 sistance may arise in many cases from an 
 increase of friction, which often, though 
 not always, accompanies an augmentation 
 of velocity ; or it may arise from the re- 
 sistance of the air, which must necessarily 
 increase with the velocity; and therefore 
 all machines are found soon to attain a 
 state of uniform motion. When an under- 
 shot wheel is driven by the impulse of 
 water, the uniformity of motion to which 
 it arrives, arises principally from the dimi- 
 nution of the power, which in this case 
 accompanies an increase of velocity. 
 When the mass of fluid strikes one of the 
 float-boards at rest, the impulse is then 
 a maximum. When the float-board is in 
 motion, it withdraws itself, as it were, 
 from the action of the power, and therefore 
 its mechanical effect will diminish as the 
 velocity increases, and if it were possible 
 that the velocity of the wheel should be- 
 come equal to that of the fluid, the float- 
 board would not be struck at all by the 
 moving water. Hence it follows, that the 
 power itself diminishes by an increase of 
 velocity, and therefore, that from this 
 cause alone, machines in general would 
 soon acquire a motion sensibly uniform. 
 This effect will be more easily understood, 
 if we suppose an axle to be put in motion 
 by two currents of water, moving with dif- 
 ferent velocities, and driving two w 7 heels, 
 one of which is placed at each extremity 
 of the axles. When the wheels have 
 begun to move, by the joint action of these 
 
THE ARTISAN. 375 
 
 falls of water, its motion will at first be 
 slow, and each fall of water will perform 
 its part in giving motion to the axle ; but 
 if the greater fall is capable, by the con- 
 tinuance of its action, of giving its wheel 
 a velocity either to a greater, than the ve- 
 locity of the smaller fall, then it is mani- 
 fest that the smaller fall ceases to impel 
 its wheel, and that the whole effect is pro- 
 duced by the action of the greater fall. 
 Hence it is easy to understand from this 
 statement, not only why a diminution of 
 
 the impelling power accompanies an in- 
 crease of velocity ; but why there is a 
 certain velocity of the machine, w hich is 
 necessary before we can gain all the use- 
 ful effect which we wish to have from the 
 powers which we employ. 
 
 In order to illustrate this in the case of a 
 real machine, let us suppose that the pow- 
 er of a man is to be employed in raising a 
 load, by means of the machine or walking 
 crane exhibited by the following figure. 
 
 Here the man walks at any required 
 distance from the axis of motion, and 
 pushes forward the lever A, which moves 
 the bar BC,, connected with the same 
 axis, and removes the break C D from the 
 circumference of the wheel. 
 
 From an attentive consideration of this 
 machine, it will soon be perceived, that as 
 the acceleration increases, the man must 
 walk with greater and greater velocity ; 
 but there is an obvious limit to this, for he 
 would soon be fatigued by the rapid walk- 
 ing, and therefore be rendered unfit to 
 continue his work. He must therefore 
 return to that distance from the axis, 
 
 where the wheel has such a velocity, as 
 he can continue to move with during the 
 period that his work is to last, there is 
 therefore a particular velocity with which 
 the man must walk, in order to perforin 
 the'greatest quantity of work ; and it would 
 be easy to find this velocity, if we knew the 
 law according to which his force diminish- 
 ed as his velocity increased. We may 
 suppose, however, that his force diminishes 
 in the same ratio as his velocity increases. 
 
 But previous to considering this more 
 particularly, we shall give a representa- 
 tion of an oblique ivalking wheel , for oxen, 
 or horses. 
 
374 THE ARTISAN. 
 
 We may, however, remark, that it is 
 advisable that walking wheels for quad- 
 rupeds should ^present to them a path 
 as little elevated as possible; and it 
 might probably be advantageous to har- 
 ness them, either to a fixed point, or to a 
 spring or weight, which would enable 
 them to exert a considerable force, even in 
 a horizontal direction ; but probably after 
 all, they might be more advantageously 
 employed in a circular mill walk. 
 
 In all machines the work done is to be 
 estimated, not merely from the quantity 
 of resistance overcome, but from the quan- 
 tity overcome in a given time; or, which 
 is the same, from the quantity of the re- 
 sistance multiplied into the velocity com- 
 municated. 
 
 The resistance is here supposed to be 
 expressed by weight, and the effect by 
 that weight multiplied , into the velocity 
 with which it is raised. 
 
 In all machines that work with a uni- 
 form motion, th6re is a certain velocity 
 and a certain load, that yield the greatest 
 effect, and which are therefore more ad- 
 vantageous than any other. 
 
 If the machine is loaded heavily, though 
 the resistance overcome may be great, it 
 may be overcome so slowly, that the total 
 effect shall be but small. And, again, if 
 the machine is loaded very lightly, it will 
 give great velocity to the load, though, 
 from the smallness of its quantity, the 
 effect will still be inconsiderable. Between 
 these two loads, there must be some in- 
 termediate one, that will make the effect 
 the greatest possible. 
 
 If the moving power observe the same 
 law that has been already ascribed to ani- 
 mal force, (see pages 276 and 277), then 
 the effect of the machine will be the great- 
 est possible, when the load is reduced to 
 four-ninths of the load or resistance, 
 which is just able to keep the machine at 
 rest, or prevent its motion altogether. 
 
 The moving power and the resistance 
 being both given, other things remaining 
 as above, if a machine be so constructed, 
 that the velocity of the point to which the 
 power is applied, be to the velocity of the 
 point to which the resistance is applied, 
 as 9 times the resistance to 4 times the 
 power, the machine will work to the 
 greatest possible advantage. 
 
 Under the name of the load, we suppose 
 the friction of the parts of the machine to 
 be comprehended, which must therefore 
 be determined by experiment. 
 
 Care should be taken to give to every 
 machine the greatest possible regularity 
 in its motion. 
 
 The contrivance known by the' name of 
 a fly, is one of the best adapted for this 
 purpose. When the impelling power is 
 subject to alternate intention and remis- 
 
 sion, the inertia of a heavy wheel, by 
 preserving the velocity it has acquired, 
 tends to lessen the irregularity resulting 
 from these causes. 
 
 The effect of a fly to remove irregularity 
 in the motion of a machine, its weight and 
 diameter being given, is proportional to 
 its velocity. 
 
 EnrDitAux.xcs» 
 
 HYDROSTATIC BELLOW8. 
 
 The Hydrostatic bellows being a ma- 
 chine much used in large founderies, for 
 producing a constant and equal blast of 
 air, we shall give a short description of it, 
 and endeavour to explain the principle 
 upon which it acts. 
 
 This machine is made of two strong 
 round boards united by strong leather, in 
 the manner of common bellows, but nailed 
 so tight to the edges of the boards as to 
 hold water. It is represented by the fol- 
 lowing figure. 
 
 Here a is a pipe of any height leading 
 into the insido of the bellows. If water 
 be poured into this pipe, the upper board 
 will soon begin to rise and lift the weight 
 w ; and if the pipe was tall, and that 
 board wide enough, it would lift the man 
 who poured* in the water. If, when the 
 bellows are full of water, weights are laid 
 on them till the water was forced up to 
 the top of the pipe a, those weights 
 would express the weight of a pillar of 
 water, whose base was equal to the area 
 of the under-board of the bellows, and 
 whose height was from that board to the 
 top of the pipe a ; which may be better 
 understood by the dotted line in the figure. 
 It is evident, that the returning pillar na 
 would press as forcibly against the bot- 
 tom n by re-action, as the tall pillar bn by 
 its weight, for the pressure against the 
 thumb a was equal to the weight of water 
 between b and c, and therefore the re-action 
 
THE ARTISAN, 
 
 375 
 
 ©f the short pillar upon n, would be equal 
 to the weight of the tall pillar. This rea- 
 soning applied to the bellows, will account 
 for the weight they lift; for the water 
 within the bellows is all returning pillars, 
 (like n a when the pipe a is full), each en- 
 deavouring to raise to the level e n, and 
 thrusting against the lid, with a force that 
 would bring them to that level, if they had 
 an opportunity. But if, instead of the 
 pillar of water e o, acting on the bellows 
 by its weight, that water was forced in by 
 a piston moving in eo f the bellows, if 
 
 strong enough, would lift a ship or a 
 house ! 
 
 It is on this principle that the pressure 
 of water has been applied by Mr. Bramah, 
 to the construction of a very convenient 
 press, «which will be described in another 
 part of this work. 
 
 blakey’s machine for raising water 
 
 FROM MINES, RIVERS, &C. 
 
 This machine is represented by the fol- 
 lowing figure. 
 
 A is a large, strong, close vessel, im- 
 mersed in water up to the cock 6, and 
 having a hole in the bottom, with a valve 
 a upon it, opening upward within the ves- 
 
 sel. B C is a pipe which rises from the 
 bottom of the vessel, and has a cock c in it 
 near the top, which is there very small, 
 for raising a jet d to a great height. L is 
 
376 
 
 THE ARTISAN. 
 
 a little boiler (not so large as a common 
 tea kettle) which is connected with the 
 vessel A by the steam pipe E ; and G is a 
 funnel, through which a little water must 
 be occasionally poured into the boiler, to 
 yield a proper quantity of steam. And a 
 small quantity of water will do for that 
 purpose, because steam occupies upwards 
 of 14,000 times as much space or bulk, as 
 the water does from which it proceeds. 
 
 The vessel A being immersed in water 
 up to the cock 6, open that cock, and the 
 water will rush in, through the bottom of 
 the vessel at a, and fill it as high up as 
 the water stands on its outside; and the 
 water, coming into the vessel, will drive 
 the air out of it (as high as the water 
 rises within it) through the cock b. When 
 the water has done rushing into the vessel, 
 shut the cock 6, and the valve a will fall 
 down, and hinder the water from being 
 pushed out that way, by any force that 
 presseth on its surface. All the part of 
 the vessel above b , will be full of common 
 air, when the water rises to b. 
 
 To set the machine to work, it is only 
 necessary to shut the cock c, and open the 
 cocks d and e; then pour as much water 
 into the boiler E (through the funnel G) 
 as will half fill the boiler ; and then shut 
 the cock d, and leave the cock e open. 
 
 This being done, a fire is to be made 
 under the boiler E, the heat of which will 
 raise steam from the water in the boiler, 
 which will make its way through the pipe 
 F, into the vessel A ; and the steam will 
 compress the air above b with a very great 
 force upon the surface of the water in A. 
 
 When the top of the vessel A feels very 
 hot by the steam under it, open the cock c 
 in the pipe C ; and the air being strongly 
 compressed in A, between the steam and 
 the water in it, will drive all the water 
 out of the vessel A, up the pipe BC, from 
 which it will fly up in a jet to a very great 
 height. Mr. Ferguson says, “ that he 
 made a machine of this kind, which, with 
 three tea-cups full of water in the boiler, 
 afforded steam enough to raise a jet 30 
 feet high.” 
 
 When all the water is out of the vessel 
 A, and the compressed air begins to follow 
 the jet, open the cocks b and d to let the 
 steam out of the boiler E and vessel A, 
 and shut the cock e to prevent any more 
 steam from getting into A ; and the air 
 will rush into the vessel A through the 
 cock ft, and the water through the valve 
 a ; and so the vessel will be filled up with 
 water to the cock b as before. Then shut 
 the cock by and the cocks c and d, and 
 open the cock e; and then, the next quan- 
 tity of steam that rises in the boiler, will 
 make its way into the vessel A again ; 
 and the operation will go on as above. 
 
 When all the water in the boiler E is 
 
 evaporated, and gone off into steam, pouf 
 a little more into the boiler, through the 
 funnel G. 
 
 In order to make this engine raise wafer 
 to supply a house, which is situated on the 
 bank of a river, the pipe B C may be' con- 
 tinued up to the intended height, in the 
 direction H I. Or, if the house be on the 
 side or top of a hill, at a distance from the 
 river, the pipe, through which the water is 
 forced up, may be laid along on the hill, 
 from the river or spring to the house. 
 
 The boiler may be fed by a small pipe 
 K, from the water that rises in the main 
 pipe B C H I ; the pipe K being of a very 
 small bore, so as to fill the funnel G with 
 water, in the time that the boiler E will 
 require a fresh supply. And then, by 
 turning the cock d, the water will fall 
 from the funnel into the boiler. The fun- 
 nel should hold as much water as will 
 about half fill the boiler. 
 
 When either of these methods of raising 
 water perpendicularly or obliquely, is 
 used, there will be no occasion for having 
 the cock c in the main pipe B C H I : for 
 such a cock is requisite only, when the 
 engine is used as a fountain. 
 
 A contrivance may be very easily made, 
 from a lever to the cocks b, d, and e ; so 
 that, by pulling the lever, the cocks b and 
 d may be opened, when the cock e must 
 be shut ; and the cock e be opened, when 
 b and d must be shut. 
 
 The boiler E should be inclosed in a 
 brick wall, at a little distance from it, all 
 around, to give liberty for the flames of 
 the fire under the boiler to ascend round 
 about it. By which means, (the wall not 
 covering the funnel G) the force of the 
 steam will be prodigiously increased by 
 the heat round the boiler ; and the funnel 
 and water in it will be heated from the 
 boiler; so that the boiler will not be 
 chilled by letting cold water into it ; and 
 the rising of the steam will be so much 
 the quicker. 
 
 This engine may be constructed at a 
 trifling expense, in comparison of the com- 
 mon steam engines now in use : it will 
 seldom need repairs, and will not consume 
 half so much fuel. And as it has no 
 pumps with pistons, it is clear of all their 
 friction: and the effect is equal to the 
 whole strength or compressive force of 
 the steam. 
 
 A MACHINE TO BE SUBSTITUTED FOR THE 
 HYDROSTATIC BELLOWS. 
 
 This machine is represented by the fol- 
 lowing figure. 
 
THE ARTISAN. 
 
 in 
 
 A B C D (fig. 1st.) is an oblong square 
 box, in one end of which is a round groove, 
 as at a, from top to bottom, for receiving the 
 upright glass tube I, which is bent to a 
 right angle at the lower end (as at i in 
 fig. 2,) and to that part is tied the end of a 
 large bladder K, (fig. 2) which lies in the 
 bottom of the box. Over this bladder is 
 laid the moveable board L, in which is 
 fixed an upright wire M; and leaden 
 weights N N, to the amount of 16 pounds, 
 with holes in their middle, are put upon 
 the wire, over the board, and press upon 
 it with all their force. 
 
 The cross bar p is then put on, to secure 
 the tube from falling, and keep it in an 
 upright position : And then the piece EFG 
 is to be put on, the part G sliding tight 
 into the dove-tailed groove H, to keep the 
 weights N N horizontal, and the wire M 
 upright ; there being a round hole e in the 
 part E F for receiving the wire. 
 
 There are four upright pins in the four 
 corners of the box within, each almost an 
 inch long, for the board L to rest upon ; 
 to keep it from pressing the sides of the 
 bladder below it, close together ai first. 
 
 The whole machine being thus put to» 
 gether, pour water into the tube at top, 
 and the water will run down the tube into 
 the bladder below the board; and after 
 the bladder has been filled up to the board, 
 continue pouring water into the tube, and 
 the upward pressure which it will excite 
 in the bladder, will raise the board with 
 all the weight upon it, even though the 
 bore of the tube should be so small, that 
 less than an ounce of water would fill it. 
 
 This machine acts upon the same prin- 
 ciple as the Hydrostatical paradox (see 
 page 9.) For the upward pressure 
 against every part of the board (which 
 the bladder touches) equal in area to the 
 area of the bore of the tube, will be pressed 
 upward with a force equal to the weight 
 of the water in the tube ; and the sum of 
 all these pressures, against so many areas 
 of the board, will be sufficient to raise it 
 with all the weights upon it. 
 
 This simple machine is well calculated 
 for showing the upward pressure of 
 fluids. 
 
378 
 
 THE ARTISAN. 
 
 fWisccllatteouss Subjects. 
 
 MEMOIR OF DR. FRANKLIN. 
 
 ( Continued from page 358. J 
 
 He afterwards demonstrated by experi- 
 ments, that the electricity did not reside 
 in the coating, as had been supposed, but 
 in the pores of the glass itself. After a 
 phial was charged, he removed the coat- 
 ing, and found that upon applying a new 
 coating, the shock might still be received. 
 In 1749, he first suggested the idea of ex- 
 plaining the phenomena of thunder-gusts, 
 and of the aurora borealis, upon electrical 
 principles. He points out many particu- 
 lars, in which lightning and electricity 
 agree; and he adduces many facts, and 
 reasonings from facts, in support of his po- 
 sitions. In the same year he conceived 
 the bold and grand idea of ascertaining 
 the truth of his doctrine, by actually draw- 
 ing down the forked lightning, by means 
 of sharp pointed iron rods raised into the 
 region of the clouds; from whence he de- 
 rived his method of securing buildings 
 and ships from being damaged by light- 
 ning. It was not until the summer of 
 1752, that he was enabled to complete his 
 grand discovery, the experiment of the 
 electrical kite, which being raised up into 
 the clouds, brought thence the electricity 
 or lightning down to the earth ; and M. 
 D'Alibard made the experiment about the 
 same time in France, by following the 
 track which Franklin had before pointed 
 out. The letters which he sent to Mr. 
 Collinson, it is said, were refused a place 
 among the papers of the Royal Society of 
 London; and Mr. Collinson published 
 them in a separate volume, under the 
 title of “ New Experiments and Observa- 
 tions on Electricity, made at Philadelphia, 
 in America, ” which were read with avi- 
 dity, and soon translated into different 
 languages. His theories were at first 
 opposed by several philosophers, and by 
 the members of the Royal Society of Lon- 
 don; but in 1755, when he returned to 
 that city, they voted him the gold medal, 
 which is annually given to the person who 
 presents the best paper on some interesting 
 subject. He was also admitted a member 
 of the Society, and had the degree of 
 LL.D. conferred upon him by different 
 Universities ; but at this time, by reason 
 of the war which broke out between 
 Britain and France, he returned to Ame- 
 rica, and interested himself in the public 
 affairs of that country. Indeed, he had 
 done this long before ; for although philo- 
 sophy was a principal object of Franklin’s 
 pursuit for several years, he did not con- 
 fine himself to it alone. In 1747, lie be- 
 
 came a member of the general assembly of 
 Pennsylvania, as a burgess for the city of 
 Philadelphia. Being a friend to the rights 
 of man from his infancy, he soon distin- 
 guished himself as a steady opponent of 
 the unjust schemes of the proprietaries. 
 He was soon looked up to as the head of 
 the opposition; and to him have been 
 attributed many of the spirited replies of 
 the assembly to the messages of the gover- 
 nors. His influence in the body was very 
 great, not from any superior powers of 
 eloquence ; he spoke but seldom, and he 
 never was known to make any thing like 
 an elaborate harangue ; but his speeches 
 generally consisting of a single sentence, 
 or of a well-told story, the moral was 
 always obviously to the point. He never 
 attempted the flowery fields of oratory. 
 His manner was plain and mild. His 
 style in speaking was, like that of his 
 writings, simple, unadorned, and remark- 
 ably concise. With this plain manner, 
 and his penetrating and solid judgment, 
 he was able to confound the most eloquent 
 and subtle of his adversaries, to confirm 
 the opinions of his friends, and to make 
 converts of the unprejudiced who had 
 opposed him. With a single observation 
 he has rendered of no avail a long and 
 elegant discourse, and determined the 
 fate of a question of importance. 
 
 In 1749 he proposed a plan of an aca- 
 demy to be erected in the city of Philadel- 
 phia, as a foundation for posterity to erect 
 a seminary of learning, more extensive 
 and suitable to future circumstances ; and 
 in the beginning of 1750, three of the 
 schools were opened ; namely, the Latin 
 and Greek school, the mathematical and 
 the English schools. This foundation 
 soon after gave rise to another more ex- 
 tensive college, incorporated by charter. 
 May 27, 1755, which still subsists, and in 
 a very flourishing condition. In 1752 he 
 was instrumental in the establishment of 
 the Pennsylvania hospital, for the cure and 
 relief of indigent invalids, which has 
 proved of the greatest use to that class of 
 persons. Having conducted himself so 
 well as post master of Philadelphia, he 
 was in 1753, appointed deputy post-master 
 general for the whole British colonies. 
 
 After the defeat of General Braddock, 
 in 1755, Franklin introduced into the as- 
 sembly a bill for organizing a militia, and 
 had the dexterity to get it passed. In 
 consequence of this act, a very respectable 
 militia was formed; and Franklin was 
 appointed colonel of a regiment in Phila- 
 delphia, which consisted of 1200 men ; and 
 in which capacity he acquitted himself 
 with much propriety, and was of singular 
 service, though this militia was soon after 
 disbanded by order of the English minis- 
 try. 
 
THE ARTISAN. 
 
 379 
 
 ' In 1757 he was sent to England, with a 
 petition to the king and council, against 
 \ the proprietaries, who refused to bear any 
 share in the public expenses and assess- 
 ments, which he got settled to the satis- 
 faction of the state. After the completion 
 of this business, Franklin remained at the 
 i court of Great Britain for some time, as 
 agent for the province of Pennsylvania ; 
 and also for those of Massachusetts, Mary- 
 land, and Georgia. Whilst here, he in- 
 vented the elegant musical instrument 
 called the Harmonica, formed of glasses 
 i, played on by the fingers. In the summer 
 ! of 1762 he returned to America, on the 
 passage to which he observed the singular 
 effect produced by the agitation of a vessel 
 containing oil, floating on water ; the 
 [ upper surface of the oil remained smooth 
 and undisturbed, whilst the water was 
 agitated with the utmost commotion. On 
 his return he received the thanks of the 
 assembly of Pensylvania ; which having 
 ci annually elected him a member in his ab- 
 sence, he again took his seat in this body, 
 and continued a steady defender of the 
 liberties of the people. In 1764, by the 
 intrigues of the proprietaries, Franklin 
 I lost his seat in the assembly, but was im- 
 mediately appointed provincial agent to 
 England. In 1766 he was examined be- 
 fore the Parliament relative to the stamp 
 $ act, which was soon after repealed. The 
 same year he made a journey into Holland 
 i\ and Germany, and another into France, 
 being every where received with the great- 
 est respect by the literati of all nations. 
 ( On the 29th January, 1774, he was ex- 
 
 i amined before the Privy Council, on a 
 ! petition which he had presented long be- 
 fore as agent for Massachusetts Bay 
 against Mr. Hutchinson: but this petition 
 ! being disagreeable to ministry, it was pre- 
 ; cipitately rejected, and he was soon after 
 removed from his office of postmaster- 
 ■ general for America Finding now all 
 i efforts to restore harmony between Great 
 | Britain and her Colonies useless, he re- 
 i turned to America in 1775, just after the 
 commencement of hostilities. Being named 
 one of the delegates to the Continental 
 Congress, he had a principal share in 
 bringing about the revolution and declara- 
 tion of independency on the part of the 
 Colonies. When it was determined by 
 Congress to open a public negotiation 
 with France, Dr. Franklin was fixed upon 
 | to go to ’that country ; and he brought 
 about the treaty of alliance offensive and 
 j defensive, which produced an immediate 
 war between England and France. 
 
 Dr. Franklin was one of the Commis- 
 sioners, who, on the part of the United 
 States, signed the provisional articles of 
 peace in 1782, and the definitive treaty in 
 
 the following year. Before he left Europe, 
 he concluded a treaty with Sweden and 
 Prussia. Having seen the accomplish- 
 ment of his wishes in the independence of 
 his country, he requested to be recalled, 
 and after repeated solicitations, Mr. Jeffer- 
 son was appointed in his stead On the 
 arrival of his successor, he repaired to 
 Havre de Grace, and crossing the English 
 channel, landed at Newport, in the Isle of 
 Wight, from whence, after a favourable 
 passage, he arrived safe at Philadelphia, 
 in September, 1785. Here he was received 
 amidst the acclamations of a vast and 
 almost innumerable multitude, who had 
 flocked from all parts to see him, and who 
 conducted him in triumph to his own 
 house, where in a few days he was visited 
 by the members of congress, and the prin- 
 cipal inhabitants of Philadelphia. He 
 was afterwards twice chosen president of 
 the assembly of Philadelphia; but in 
 1788, the increasing infirmities of his age 
 obliged him to ask and obtain permission 
 to retire, and spend the remainder of his 
 life in tranquillity; and on the 17th of April, 
 1790, he died at the great age of eighty- 
 four years and three months. He left be- 
 hind him one son, and a daughter married 
 to a merchant in Philadelphia. 
 
 Dr. Franklin was author of many tracts 
 on electricity, and other branches of natu- 
 ral philosophy, as well as on political and 
 miscellaneous subjects. Many of his 
 papers are inserted in the Philosophical 
 Transactions of London; and his essays 
 have been frequently reprinted in this 
 country as well as in America, and haye, 
 in common with his other works, been 
 translated into several modern languages. 
 A complete edition of all these was printed 
 in London in 1806, in 3 vols. 8vo. with 
 “ Memoirs of his early Life,” written by 
 himself, to which the preceding article is 
 in a considerable degree indebted. 
 
 As a philosopher, the distinguishing 
 characteristics of Franklin’s mind, as they 
 have been appreciated by a very judicious 
 writer, seem to have been a clearness of 
 apprehension, and a steady undeviating 
 common sense. We do not find him 
 taking unrestrained excursions into the 
 more . difficult labyrinths of philosophical 
 inquiry, or indulging in conjecture and 
 hypothesis. He is in the constant habit 
 of referring to acknowledged facts and 
 observations, and suggests the trials by 
 which his speculative opinions may be put 
 to the test. He does not seek for extraor- 
 dinary occasions of trying his philosophi- 
 cal acumen, nor sits down with the precon- 
 ceived intention of constructing a philoso- 
 phical system. It is in the course of his 
 familiar correspondence that he proposes 
 his new explanations of phenomena, and 
 
380 
 
 THE ARTISAN., 
 
 brings into notice his new discoveries. 
 If a mere hypothesis be proposed, the 
 author himself is the first to point its in- 
 sufficiency, and abandons it with more 
 facility than he had constructed it. Even 
 the letters on electricity, which are by far 
 the most finished of Franklin’s perform- 
 ances, are distinctly characterized by all 
 these peculiarities. The Doctor never be- 
 trays any exertion, nor displays an un- 
 warrantable partiality for his own specula- 
 tions ; he assumes no superiority over his 
 readers, nor seeks to elevate the import- 
 ance of his conceptions, by the adventitious 
 aid of declamation, or rhetorical flourishes. 
 He exhibits no false zeal, no enthusiasm, 
 but calmly and modestly seeks after truth ; 
 and if he fails to find it, has no desire to 
 impose a counterfeit in its stead. 
 
 DESCRIPTION OF GUNTER’S. 
 SCALE. 
 
 ( Continued from page 349 . ) 
 
 Having described the lines drawn upon 
 one side of this useful instrument at page 
 347, we shall here describe those upon the 
 other side, in order to render our descrip- 
 tion complete. 
 
 For the sake of distinction, we called the 
 lines on the one side natural lines, and 
 those on the other artificial , or logarithmic 
 lines ; the latter only remain to be noticed, 
 and are the following : 
 
 Sine Rhumbs - 
 
 Marked. 
 S. R. 
 
 Tangent Rhumbs 
 
 T. R. 
 
 Numbers 
 
 NUM. 
 
 Sines - 
 
 SIN. 
 
 Versed Sines - 
 
 V. S. 
 
 Tangents 
 
 TAN. 
 
 Meridional Parts 
 
 MER. 
 
 Equal Parts - 
 
 E. P. 
 
 1. The Line of Numbers — We begin with 
 the construction of this logarithmic line, 
 because all the other lines are constructed 
 with reference to it. The purposes to 
 which this line is usually applied do not 
 require that it should have numbers repre- 
 sented on it, such that the greatest should 
 exceed the least more than 100 times ; and 
 accordingly as the common logarithm of 
 100 is 2, and that of 10 is 1, the line of 
 numbers is made to consist of two equal 
 parts, the subordinate divisions in one of 
 which have a reference to an order of units, 
 ten times greater than those of the other. 
 Let an accurate scale of equal parts, there- 
 fore, be constructed of half the length of 
 the proposed line of numbers, and for the 
 sake of greater precision let it be a diago- 
 nal scale, with ten primary divisions. 
 Then, from this scale take the measure of 
 
 the logarithm of 2, and lay it off from the 
 beginning of the scale ; in like manner 
 take the length of the logarithms of 3, 4, 5, 
 &c. from the scale of equal parts, and lay 
 them off from the beginning ; lay off also 
 the intermediate divisions, and the first 
 half of the scale will be constructed. The 
 other half is constructed exactly in the 
 same manner. 
 
 It is scarcely necessary to observe, that 
 if the first unit, at the beginning of the 
 scale, be reckoned 1, the second unit is 10, 
 and the third 100 ; whereas, if the first 
 unit be accounted 10, the send is 100, and 
 the third 1000 ; and so on with regard to 
 any other value that may be attached to 
 the first unit. 
 
 2. The Line of Sine Rhumbs. — From the 
 same scale of equal parts which w r as em- 
 ployed in the construction of the line of 
 numbers, take the distances expressed by 
 the three first figures of the arithmetical 
 complement,* of the logarithmic sines of 
 7, 6, 5, points, &c. or the secants of 1, 2, 3, 
 points, &c. rejecting the indices, and lay 
 them off, towards the left hand succes- 
 sively from the point corresponding to the 
 sine of 90°, which is usually placed im- 
 mediately below the last unit on the right 
 hand of the line of numbers ; and thus the 
 scale of rhumbs will be obtained for the 
 several points. The quarter points are 
 laid down after the same manner. 
 
 3. The Line of Sines. — The construction 
 of the scale of logarithmic sines differs in 
 no respect from that of the rhumbs, only 
 degrees are employed in place of points. 
 
 4. The Line of Tangent Rhumbs. — This 
 scale, as far as 4 points, is constructed in the 
 same manner as the scale of log. sines, by 
 using the three first figures of arithmetical 
 complements of the logarithmic tangents of 
 3, 2, and 1 points, or of the logarithms of 
 the tangents of 5, 6, and 7 points, rejecting 
 the index. The tangent of 4 points being 
 equal to the radius, terminates the scale on 
 the right hand. The points above 4, if the 
 scale were extended from that point to- 
 wards the right hand, would be at the 
 same distance from 4, or the point cor- 
 responding to the radius, as the points as 
 much below 4 are from that point. Hence 
 the points corresponding to 3 and 5 points, 
 2 and 6 points, and 1 and 7 points, are 
 coincident on the scale, only the points 
 above 4, though actually laid down to the 
 left hand of the point corresponding to the 
 
 * The arithmetical complement of the sine, tan- 
 gent, &c. of an arc, is the remainder obtained by 
 subtracting it from 10-000000. 
 
THE ARTISAN. 
 
 SSI 
 
 adius, must be conceived, in the per- 
 formance of problems, to extend to the 
 right hand of it. 
 
 I 5. The Line of Tangents .— The scale of 
 |logarithmic tangents is constructed, like 
 that of logarithmic tangent rhumbs, by em- 
 ploying the three first figures of the arith- 
 metical complements of the log. tangents 
 ! of 40°, 30°, &c. or of the logarithms of the 
 tangents of 50°, 60°, rejecting their indices. 
 
 .i, 6. The Line of Versed Sines . — From the 
 scale of equal parts, employed in the con- 
 struction of all the preceding scales, take 
 the distances expressed by the three first 
 i figures of the arithmetical complements of 
 the logarithmic cosines of 5, 10, 15, &c. 
 j degrees, rejecting the indices, and lay off 
 the double of these distances, respectively, 
 i from right to left of the extended scale, 
 i The divisions, thus obtained, will corres- 
 pond to the log. versed sines of 10, 20, 30, 
 il &e. degrees. 
 
 7. Meridional Line . — Take the meridio- 
 nal parts for every 10° from a Table of meri- 
 dional parts, and having divided them by 
 60, lay off, by means of some convenient 
 j scale of equal parts, the distance expressed 
 by the several quotients. The line of equal 
 parts, which is placed immediately above 
 or below the meridional line, is divided into 
 19 principal divisions, marked from right 
 i to left 0, 10, 20, &c. each of these divisions 
 i, representing 10 degrees of the equator, or 
 ! 600 nautical miles. The first division on 
 the right from 0 to 10, is divided into 10 
 i equal parts, each of which, therefore, cor- 
 (i responds to a degree of the equator, or 60 
 miles ; and, consequently, the bisection of 
 i each of these equal parts reduces the ulti- 
 mate divisions to a distance representing 
 30 miles. The extent from the right hand ex- 
 ; tremity of the meridional line to any particu- 
 lar division, being applied, in like manner, 
 to the scale of equal parts, will indicate in 
 degrees the meridional parts belonging to 
 that division, reckoned from the equator. 
 Also the extent between any two divisions 
 in the meridional line being applied to the 
 line of equal parts, will give, in degrees, 
 the meridional difference of latitude be- 
 tween the two latitudes, expressed by the 
 J numbers at the extreme points of extent. 
 Hence the compound , scale may serve, in- 
 strumentally, the purposes of a table of 
 
 I meridional parts. 
 
 In using these logarithmic scales for the 
 solution of arithmetical problems, in trigo- 
 nometry or navigation, it follows from the 
 nature of logarithms, that the fourth term 
 of four proportional magnitudes being to 
 [ the third, as the second to the first, if 
 these magnitudes be A, B, C, and D, then 
 A divided by B, is equal to C, divided 
 
 by D ; and, consequently, the logarithm of 
 A, diminished by the logarithm of B, is 
 equal .to the logarithm of C, diminished 
 by the logarithm of JD. That is, the extent 
 from the log. A to the log. B, these two 
 quantities being of the same kind, will 
 reach from the log. C to the log J), always 
 carefully observing that the extent in the 
 second case must be taken in the same di- 
 rection as in the first. This circumstance, 
 which must never be lost sight of, requires 
 to be particularly observed in solving pro- 
 blems where the scale of logarithmic tan- 
 gents is employed, and the third term is 
 the tangent of 45° on the radius. In such 
 cases, when the extent is from the left to 
 the right, in respect of the two first terms, 
 the extent ought to be taken in the same 
 direction on the scale of tangents ; but the 
 manner of laying down the scale not ad- 
 mitting this, the extent is taken from right 
 to left, only the complement of the number 
 of degrees and minutes corresponding to it 
 is taken, in place of the numbers actually 
 marked on the scale. A similar precau- 
 tion is to be observed when either the first 
 or second term of an analogy is greater 
 than 45°, the extent in the second case 
 being always reckoned in the same direc- 
 tion of what it would have been, if the 
 line of logarithmic tangents had been con- 
 tinued to the right hand of 45°. 
 
 UNIFORMITY OF WEIGHTS AND 
 MEASURES. 
 
 A Bill having passed in the last session 
 of Parliament, for establishing a uniformity 
 of weights and measures throughout the 
 country, we consider that we shall render 
 a service to our readers, by making them 
 acquainted with the most important parts 
 of it. This we conceive will be best ac- 
 complished by making a few extracts from 
 the Act itself. 
 
 u I. That from and after the first day of 
 May, one thousand eight hundred and 
 twenty-five, the straight line or distance 
 between the centres of the two points in 
 the gold studs in the straight brass rod, 
 now in the custody of the clerk of the 
 House of Commons, whereon the words 
 and figures ‘ Standard Yard, 1760/ are 
 engraved, shall be and the same is hereby 
 declared to be the original and genuine 
 standard of that measure of length or lineal 
 extension called a yard ; and that the 
 same straight line or distance between the 
 centres of the said two points in the said 
 gold studs in the said brass rod, the brass 
 being at the temperature of sixty-two de- 
 grees by Fahrenheit's Thermometer, shall 
 
3£2 
 
 THE ARTISAN. 
 
 be and is hereby denominated the ‘ Im- 
 perial Standard Yard/ and shall be and 
 is hereby declared to be the unit or only 
 standard measure of extension, wherefrom 
 or whereby all other measures of exten- 
 sion whatsoever, whether the same be 
 lineal, superficial, or solid, shall be de- 
 rived, computed, and ascertained ; and 
 that all measures of length shall be taken 
 in parts or multiples, or certain propor- 
 tions of the said standard yard ; and that 
 one-third part of the said standard yard 
 shall be a foot, and the twelfth part of such 
 foot shall be an inch ; and that the pole 
 or perch in length shall contain five such 
 yards and a half, the furlong two hundred 
 and twenty such yards, and the mile one 
 thousand seven hundred and sixty such 
 yards. 
 
 a II. And be it further enacted, That 
 all superficial measure shall be computed 
 and ascertained by the said standard yard, 
 or by certain parts, multiples, or propor- 
 tions thereof; and that the Rood of land 
 shall contain one thousand two hundred 
 and ten square yards, according to the 
 said standard yard ; and that the Acre of 
 land shall contain four thousand eight 
 hundred and forty such square yards, being 
 one hundred and sixty square Perches, 
 Poles, or Rods. 
 
 « III. And whereas it is expedient that 
 the said standard yard, if lost, destroyed, 
 defaced, or otherwise injured, shall be re- 
 stored of the same length, by reference to 
 some invariable natural standard : And 
 whereas it has been ascertained by the 
 commissioners appointed by His Majesty 
 to inquire into the subject of weights and 
 measures, that the said yard hereby de- 
 clared to be the imperial standard yard, 
 when compared with a Pendulum vibrating 
 seconds of mean time, in the latitude of 
 London , in a vacuum at the level of the 
 sea, is in the proportion of thirty-six inches 
 to thirty-nine inches, and one thousand 
 three hundred and ninety-three ten-thou- 
 sandth parts of an inch; be it therefore 
 enacted and declared, That if at any time 
 hereafter the said imperial standard yard 
 shall be lost, or shall be in any manner de- 
 stroyed, defaced, or otherwise injured, it 
 shall and may be restored by making, un- 
 der the direction of the Lord High Trea- 
 surer, or the Commissioners of His Ma- 
 jesty’s Treasury of the United Kingdom of 
 Great Britain and Ireland, or any three of 
 them, for the time being, a new standard 
 yard, bearing the same proportion to such 
 pendulum as aforesaid, as the Said imperial 
 standard yard bears to such pendulum. 
 
 “ IV. And be it further enacted, That 
 from and after the first day of May, one thou- 
 
 sand eight hundred and twenty-five, the 
 standard brass weight of one Pound Troy 
 weight, made in the year one thousand 
 seven hundred and fifty-eight, now in the 
 custody of the Clerk of the House of Com- 
 mons, shall be and the same is hereby de- 
 clared to be the original and ^genuine 
 standard measure of weight, and that such 
 brass weight shall be and is hereby deno- 
 minated the imperial standard Troy pound, 
 and shall be and the same is hereby de- 
 clared to be the unit or only standard 
 measure of weight, from which all other 
 weights shall be derived, computed, and 
 ascertained ; and that one-twelfth part of 
 the said troy pound shall be an ounce ; 
 and that one-twentieth part of such ounce 
 shall be a penny-weight; and that one- 
 twenty-fourth part of such pennyweight 
 shall be a grain ; so that five thousand 
 seven hundred and sixty such grains shall 
 be a troy pound, and that seven thousand 
 such grains shall be and they are hereby 
 declared to be a pound avoirdupoise, and 
 that one-sixteenth part of the said pound 
 avoirdupois shall be an ounce avoirdupois, 
 and that one-sixteenth part of such ounce 
 shall be a dram. 
 
 “ V. And whereas it is expedient, that 
 the said standard troy pound, if lost, de- 
 stroyed, defaced, or otherwise injured, 
 should be restored of the same weight, by 
 reference to some invariable natural stand- 
 ard : And whereas it has been ascertained, 
 by the Commissioners appointed by His 
 Majesty to inquire into the subjects of 
 weights and measures, that a cubic inch of 
 distilled Water, weighed in air by brass 
 weights, aUthe temperature of sixty-two 
 degrees of Fahrenheit’s thermometer, the 
 barometer being at thirty inches, is equal 
 to two hundred and fifty-two grains, and 
 four hundred and fifty-eight thousandth 
 parts of a grain, of which, as aforesaid, 
 the imperial standard troy pound contains 
 five thousand seven hundred and sixty ; 
 be it therefore enacted, That if at any time 
 hereafter the said imperial standard troy 
 pound shall be lost, or shall be in any 
 manner destroyed, defaced, or otherwise 
 injured, it shall and may be restored by 
 making, under the directions of the Lord 
 High Treasurer, or the Commissioners of 
 His Majesty’s Treasury of the United 
 Kingdom of Great Britain and Ireland , or 
 any three of them for the time being, a 
 new standard troy pound, bearing the 
 same proportion to the weight of a cubic 
 inch of distilled water, as the said standard 
 pound hereby established bears to such 
 cubic inch of water. 
 
 {To be continued.) 
 
THE ARTISAN. 
 
 38 $ 
 
 To the Editor of the: Artisan . 
 
 Sir, 
 
 In Nicholson’s Philosophical Journal 
 for June 1803, I met with a letter from M. 
 Van Marum to M. Bertholet, containing 
 an account of some experiments, shewing 
 the method of extinguishing violent fires 
 with very small quantities of water, by 
 means of portable pumps ; and as this me- 
 thod appears to me, from its simplicity, 
 capable of being made extremely useful, 
 not only in crowded cities, but on board 
 ships, I request you will have the good- 
 ness to give it a more general circulation, 
 by inserting the following brief account of 
 it in the Artisan. 
 
 The Experiments of Van Aken, a Swede, 
 which were published in 1794, and which 
 gave rise to VanMarum’s, were performed 
 with a liquid of the following composition ; 
 viz. 40 lbs. of sulphate of iron, and 30 lbs. 
 of sulphate of allumine, mixed with 20 lbs. 
 of the red oxide of iron and 200 lbs. of clay. 
 By a series of experiments Van Marum 
 proved, that fire was always extinguished 
 more quickly by common water , used in the 
 same manner, than by this anti-incendiary 
 liquor ; and, “ I observed,” he says, “ at 
 the same time, that a very inconsiderable 
 quantity of water, if judiciously directed, 
 would extinguish a very violent fire.” The 
 result of his first experiment, was the ex- 
 tinguishing the fires of two casks covered 
 with pitch, their heads taken out, and 
 highly ignited, with only four ounces of 
 water. I shall give his instructions at 
 length as follow:- — “ According to these 
 experiments it appears, that the art of ex- 
 tinguishing a violent fire with a small 
 quantity of water, consists in this, that the 
 water be thrown on that part of the fire 
 which is most violent, so that the quantity 
 of steam produced, which suppresses the 
 flame, may be the greatest possible ; that 
 water be continued to be thrown on the 
 neighbouring inflamed parts as soon as the 
 fire has ceased in that on which the opera- 
 tion was began, and that all the burning 
 parts be visited in this way as quickly as 
 possible. By thus following the flames 
 regularly with streams of water they may 
 be every where suppressed, before the part 
 on which the operation was began shall 
 have entirely lost by evaporation the water 
 with which it was extinguished : this is 
 often necessary to prevent the parts from 
 breaking out a-fresh ; for, in the principle 
 above-mentioned, a burning body of which 
 the flames are suppressed, cannot be 
 again in flames until the water thrown on 
 it be totally extinguished. 
 
 In May, 1797, Van Marum prepared a 
 shell of dry wood, forming a room 24 feet 
 long, 23 feet wide, and 14 feet high, hav- 
 ing two doors on one side and two win- 
 
 dows on the other; the inside was strongly 
 pitched, and covered with twisted straw, 
 wood shavings, and cotton, soaked in tur- 
 pentine. u Very soon after lighting it,” 
 he says, u the flames being rendered more 
 brisk by the wind, were every where so 
 violent, that it was considered by my as- 
 sistants as impossible to extinguish them. 
 I succeeded, however, after the method 
 above directed, in little more than four 
 minutes, and with five buckets of water, 
 a part of which wqs wasted by the negli- 
 gence of my Assistant. This experiment 
 was repeated in the same month, and the 
 fire extinguished in 3 minutes, with less 
 than 5 gallons of water. A similar expe- 
 riment was repeated with equal success by 
 Dr. Van Marum, in the presence of the 
 Duke and Duchess of Gotha, at Gotha, in 
 July, 1798 ; an account of which was pub- 
 lished by the celebrated Astronomer Von 
 Zach, in a German periodical paper, en- 
 titled Reich’s Anrioger , 6th April, 1798, 
 No. 119, — where he assures us that the 
 fire was extinguished with 3 buckets of 
 water , in 3 minutes , with a small portable 
 pump. 
 
 Van Marum concludes with the following 
 observations. “ In operations of this kind, 
 particular attention must be paid to throw- 
 ing the water in such a way, that the en- 
 tire surface of the burning parts shall be 
 wetted and extinguished, and that in such 
 a way, that an extinguished part shall 
 never be left between two others which 
 are in flames ; for if attention be not paid 
 to this, the heat of the flames burning here 
 and Jhere, will quickly change the water 
 with which the part has been wetted into 
 steam, and the whole will again take fire. 
 In order then to extinguish a fire in all 
 cases, no more water must be thrown on 
 the burning part than is needful to wet the 
 surface ; and this I conceive to be all that 
 is requisite to extinguish a fire, whatever 
 may be the circumstances of its origin.” 
 
 In 1807, Mr. Hornblower, with whose 
 talents the world is so well acquainted, 
 constructed a fire engine which stood in 
 the compass of 14 inches square, and 2 
 feet high, and could be carried from one 
 room to another -with ease — he found by 
 experiments, that the 4 sides of a bed- 
 room all on fire, could be extinguished in 
 the space of a minute, by little more than 
 a pail of water. All that is required, is to 
 keep the engine filled in its proper place, 
 and to work it off every month or 6 weeks, 
 for the purpose of changing the water, and 
 ascertaining that it is in a proper working 
 state. 
 
 I am Sir, 
 
 Your very humble Servant, 
 Navarchus. 
 
 Nov. 30 th y 1824. 
 
884 
 
 THE ARTISAN. 
 
 SOLUTIONS OF QUESTIONS. 
 
 Quest. 39, solved Geometrically by A. 
 Mackinnon, Sheffield . (See page 288.) 
 
 ' Let A B be the height of the pillar, 
 and B D the height of the statue upon its 
 top. Bisect B D in C, and draw C H per- 
 pendicular to A C, and with the centre B 
 and distance A C, describe an arc cutting 
 C H in H ; then with the centre H and dis- 
 tance B H— A C, describe the circle DBK. 
 Join K B, K D, H B, H C, and H D, when 
 B K D, or B H C is the greatest possible, 
 it is evident that the angle HBC will be 
 the least possible ; and the line H C, as 
 also H B or H K, the radius of the circle, 
 will be the least possible when it is per- 
 pendicular to A K, in which case A K will 
 be a tangent to the circle at the point K ; 
 therefore when the angle BKDorBHC 
 is the greatest possible, B HzHK or A C, 
 and is therefore given. By (Euclid, 1 ft. 
 47) C H 2 = B H 2 -B C 2 orCHz 
 VBH 2 — BC *=V24000= 154-9161 ; and 
 the angle B H C or B K D is found to be 
 1° 50' 51". 
 
 This question was also solved geometri- 
 cally by Mr. Whitcombe, Cornhill, who 
 supplied the solution at page 288. 
 
 Quest. 47, answered by T. D. Bristol 
 ( the proposer ). 
 
 Having reduced the sun’s declination, 
 there are given in a spherical triangle, the 
 co-latitude, the co-declination, and the hour 
 angle, to find the sun’s true altitude— 
 51° 24' 8"*824, this corrected for semidia- 
 meter, refraction, and parallax, gives the 
 apparent altitude of the sun’s upper limb- 
 51 0 40' 42 ,/, 624. Now, by the laws of Op- 
 tics, the angle of incidence is equal to the 
 angle of reflection ; therefore there are in a 
 right angled plain triangle given the above 
 angle, and the height of the observer’s eye, 
 to find the horizontal distance— 105 27617 
 feet as required. 
 
 Quest. 49, answered by Q. Q. Portsea 
 ( the proposer). 
 
 Let N W S E represent the rational ho- 
 rizon, 
 
 N* 
 
 N S the celestial meridian, Z the zenith, 
 P the pole, S the sun, and y the object in 
 the horizon. Then, since the apparent al- 
 titude and declination of S are given, Z S, 
 P S the zenith, and polar distances, are 
 known ; also the zenith distance Z y of 
 y is known, being manifestly 90 and the 
 angle S Z y, and P y the polar distance of 
 y are given. Then the latitude may be 
 computed as follows : — In the first place, 
 with Z S, Z y and the angle S Zy find the 
 third side S y. 
 
 2. P S, S y , and P y, are given to find 
 the angle PS y, and with Z S, S y, and 
 Z y, compute the angle Z S y. The sum 
 or difference of the two angles; viz. the 
 angles PSy, ZSy (according to circum- 
 stances) is the angle Z S P, „ 
 
 Lastly, knowing Z S, P S, and the in- 
 cluded angle Z S P, the arc Z P may be 
 found, which is the colatitude ; the com- 
 plement of which is the latitude of the 
 place. 
 
 QUESTION FOR SOLUTION. 
 
 Quest. 54, proposed by Fr — d F— lk 
 
 — wo — TH. 
 
 I want to plan a hexagonal flower-gar- 
 den, so as to have walks from the middle 
 of the sides through the centre, and also 
 a walk round it, that the area of the 
 walks may be double that of the beds : 
 required the size of the garden, when all 
 the walks are 2 feet in breadth. 
 
THE ARTISAN. 
 
 385 
 
 PHBUMATICS. 
 
 In our last article on Pneumatics, we 
 gave a description of the most common 
 and approved wind-mills, with directions 
 for their construction and management ; in 
 the present article we shall give a short 
 
 account of several other machines which 
 have been constructed, with the view of 
 being moved by the same agent. Among 
 these may be mentioned the 
 
 SAILING CHARIOT. 
 
 The following figure represents a chariot 
 intended to be moved by the wind. 
 
 Here A B is the body of the chariot, 
 and C D E F horizontal sails, so contrived, 
 that the sails D facing the wind may ex- 
 pand, and those^oing from the wind may 
 contract. The sails are turned about by 
 the wind coming in any direction. These 
 sails turn the axis, and trundle G H, and 
 the trundle turns the wheel I L by the 
 cogs in it. Therefore the chariot may 
 move in any direction. R is a rudder to 
 steer with. 
 
 Suppose the chariot to go against the 
 wind. Let D be the centre of pressure of 
 tho two sails C D the wind blows on. And 
 let the power, (that is, the force of the 
 wind acting against the sails) be I, then 
 the force acting against the teeth in I L, 
 GD 
 
 is . . And this force being I, the force 
 OH 
 
 at L is also I ; therefore the power at D 
 G D 
 
 to the force at L, is as I to ; or as 
 OH 
 
 Vol. l,<s»No. 25. 
 
 O H to G D. Now, since the mast is 
 strained by the power falling on the sails, 
 therefore by this power O H, the chariot is 
 urged backward. And by the force at L 
 which is G D, it is urged forward. Let 
 R be the force of the wind upon the body 
 of the chariot, together with the friction 
 in moving. Therefore, if GD is greater 
 than the radius O H + R, the chariot will 
 move forward against the wind ; if less, 
 backward. But if they be equal, it will 
 stand still. 
 
 SAILING WAGGON. 
 
 Waggons have also been constructed 
 upon the same principle, with the intention 
 of making them sail against the wind. 
 One of these waggons is represented by 
 the following figure. 
 
 C C 
 
3SS 
 
 THE ARTISAN. 
 
 F G is the chariot, and S the sails of a 
 wind-mill, turning in the order 1, 2, 3. 
 As the sails go round, the pinion A moves 
 B, and the trundle C moves D, which has 
 both teeth and cogs. D by its teeth moves 
 E; and the trundle E fixed to the axle- 
 tree, carries round the wheels H I, which 
 move the waggon in the direction H G. 
 
 The sails are set at an angle of 45°, so the 
 force to turn them, and the force in the di- 
 
 rection of the axis, will be equal. This wag- 
 gon will always go against the wind, pro- 
 vided you give the sails power enough, by 
 the combination of the wheels. But then 
 its motion will be so much slower. 
 
 OF THE ANEMOSCOPE. 
 
 The Anemoscope is a machine for show- 
 ing the changes or turnings of the wind. 
 This machine is represented by the follow- 
 ing figure. 
 
 Here C,D is a weathercock of thin me- 
 tal, fixed fast to the long perpendicular 
 
 axis D F, which turns with the least wind 
 upon the foot F, and goes through the top 
 
THE ARTISAN. 
 
 387 
 
 of the house R S. To this axis is fixed the 
 pinion A, which works in the crown wheel 
 B, of an equal number of teeth. The 
 crown wheel is fixed on the axis P I, on 
 the end of which the index N S is fixed. 
 The axis P I goes through the wall L M, 
 against the wall is placed the circle 
 N E S W, with the points of the compass 
 round it. Then, if the vane C D be set to 
 the north, and at the same time the index 
 S N fixed on the axis P I, to point at S, 
 then, however, the wind varies, it will 
 turn the vane CD, and pinion A, and 
 also turn the wheel D with the index N ; so 
 that the index will always be directed to 
 the opposite point of the compass to the 
 vane D G, or to the same as the wind is in. 
 
 Having now noticed most of the ma- 
 chines moved by the wind, we shall here 
 make a few observations on a machine, 
 commonly employed to produce a blast of 
 wind, for purposes to which wind, as pro- 
 duced by nature, has never yet been ap- 
 plied. 
 
 WIND BELLOWS. 
 
 Bellows are commonly made of boards 
 connected by leather, so as to allow of 
 alternately increasing and diminishing the 
 magnitude of their cavities, the air being 
 supplied without by a valve. The blast 
 must be intermitted while the air is re- 
 plenished ; and in order to avoid this in- 
 convenience, a second cavity is sometimes 
 added, and loaded with a weight, which 
 preserves the continuity of the steam. If 
 great uniformity be required in the blast, it 
 will be necessary to take care that the cavity 
 be so formed, as \o be equally diminished, 
 while the weight descends through equal 
 spaces ; but notwithstanding this precau- 
 tion, there must always be an additional 
 velocity, while the new supply of air is 
 entering from the first cavity. 
 
 Bellows of this kind are represented by 
 the following figure A C I. 
 
 Where A L, B L, and C L are three 
 boards, the middle board B L dividing the 
 internal space into two parts. In the mid- 
 dle board is a valve S, opening into the 
 upper part; and in the lowest board is 
 another valve T opening into the under 
 part. The pipe P communicates only with 
 the upper cavity. D E a leaver moveable 
 
 about the axis G H. At I a weight is laid 
 upon the upper board to make it fall. The 
 bellows is fixed in the frame M K by two 
 iron pins, which are fast in the middle 
 board, and the pipe P lies upon the earth. 
 When the end E is pulled down by the 
 rope E F, the end D is raised, and the rope 
 or chain D R raises the lower board C h ; 
 CC 2 
 
38S 
 
 THE ARTISAN. 
 
 this shuts the valve T and opens S, and the 
 air is forced into the upper cavity, which 
 raises the upper board, and blows through 
 the pipe P. And when E is raised, the 
 boards A and C descend, and the valve S 
 shuts, and T opens. And the weight I 
 forces the air still out of the pipe, whilst 
 more air enters in at the valve T; which, 
 when C ascends, is forced again through 
 the valve S as before. And thus the bel- 
 lows have a continual blast. 
 
 OPTICS. 
 
 ON PHOTOMETRY, OR f HE 'MEASURE OF 
 LIGHT. 
 
 Photometry signifies the art of measuring 
 light; and though the term photometer has 
 been introduced as the name of an instru- 
 ment for accomplishing this object, yet we 
 can scarcely say that such an instrument 
 exists. In order to measure the quantity 
 of light lost by reflection, Bouguer placed 
 the reflecting surface to be tried at B, as 
 represented in the following figure, 
 
 and by means of a lamp or candle at P, he 
 illuminated two tablets, D E, parallel to 
 one another, and having precisely the same 
 degree of whiteness. He then placed 
 his eye at A, so that he could see at the 
 same time the tablet E directly , and the 
 image of the tablet D reflected from the 
 mirror B. When the direct and reflected 
 images were brought into contact, so that 
 the eye could compare together their de- 
 grees of illumination, he caused the candle 
 to be moved along the line E D, so as to 
 throw more or less light upon either of 
 them, till the intensity of their light ap- 
 peared perfectly equal. The square of 
 the distances E P, and D P, afforded an 
 expression of the diminution of the light 
 
 by reflection. An ingenious method 
 measuring; the comparative intensities o* 
 the light emitted by luminous bodies, was 
 proposed in the year 1794, by Count Rum- 
 ford. The two burning candles, or lamps,, 
 or any other two lights which were to be 
 compared, are placed at equal heights on 
 two moveable stands, in a darkened room. 
 A sheet of clean white paper, equally 
 spread out, is fastened on the wainscqt on 
 one side of the room, at the same height 
 from the floor as the lights ; and the lights 
 are placed over against this sheet of 
 paper, at the distance of six or eight feet 
 from it, and six or eight feet from each 
 other, in such a manner that a line drawn 
 from the centre of the paper, perpendicu- 
 lar to its surface, shall bisect the angle 
 formed by lines drawn from the lights to 
 that centre. In this case, the one light 
 will be in the line of reflection of the 
 other, the sheet of paper being considered 
 as a plane reflecting mirror. 
 
 When this adjustment is made, a cylin- 
 der of wood, about six inches long, and 
 one-fourth of an inch in diameter, is held 
 vertically about two or three inches before 
 the centre of the sheet of paper, so that 
 the two shadows of the cylinder produced 
 by the two lights may be distinctly seen. 
 If these shadows have unequal densities, 
 the light whose corresponding shadow is 
 the densest, must be removed farther oft', 
 or the other must be brought nearer to the 
 paper, till the densities of the shadows 
 appear exactly equal ; or, what is the 
 same thing, till the densities of the rays 
 diverging from the two lights, are equal 
 at the surface of the paper. When this 
 happens, the squares of the distances of 
 the lights will be to each other as the real 
 intensities of the lights. 
 
 In order to convert this instrument into 
 a photometer. Count Rumford received the 
 shadows of the cylinder on the back part 
 of a wooden box, open in front to receive 
 the light. Having found it inconvenient, 
 however, To compare two shadows pro- 
 jected by the same cylinder, he made use 
 of two cylinders fixed perpendicularly to 
 the bottom of the box, and distant from 
 the back of it 2^ths inches, while their 
 axes were placed at the distance of three 
 inches. These two cylinders projected 
 four shadows on the back of the box, 
 (called th e field of the instrument,) two of 
 which are in contact exactly in the middle 
 of the field, and are the two whose den- 
 sities are to be compared ; the two outer 
 ones being made to disappear, by falling 
 without the field on a blackened surface. 
 In one of Count Rumford’s instruments the 
 cylinders are ^ths of an inch in diameter, 
 and 2-^ths inches high, and the field is 
 2-^jth inches wide. In this instrument the 
 paper which forms the field is pasted on 
 
THE ARTISAN. 
 
 3 §9 
 
 a ’small frame of very fine ground glass, 
 and thg glass thus covered is let down 
 into a groove made to receive it in the back 
 of the box.. For the purpose of making 
 the shadows always of the same diameter, 
 which is not the case unless the lights 
 have the same diameter, the cylinders are 
 moveable about their axes, and to each is 
 added a vertical wing ^ths of an inch 
 wide, ^th of an inch thick, of the same 
 height with the part of the cylinder within 
 the box, and firmly fixed to it from the top 
 to the bottom. By means of these wings, 
 the widths of the shadows are augmented, 
 so as to fill the whole field of the photo- 
 meter. The cylinders, which are made of 
 brass, are turned round by taking hold of 
 the ends which project below the bottom 
 of the box. % 
 
 For a full account of this instrument, we 
 must refer the reader to the Philosophical 
 Transactions for 1794. 
 
 The celebrated M. Lambert first sug- 
 gested the thermometrical photometer, an 
 instrument which measures the intensity 
 of light, on the supposition that the quan- 
 tity of light and heat in any beam of the 
 solar or other rays, are invariably propor-" 1 
 tional to each other. He saw, however, 
 the imperfections of the instrument, and 
 remarked that its use was too circum- 
 scribed, as it was impossible to measure 
 with a thermometer the brightness of the 
 lunar rays. 
 
 The same principle was afterwards ap- 
 plied by Mr. Leslie to an air thermometer, 
 but for the reason assigned by Lambert, it 
 can never be considered as affording a mea- 
 sure of light. 
 
 DESCRIPTION OF THE OPTIGRAPH. 
 
 The optigraph is a telescope made for 
 the purpose of copying landscapes. It 
 was originally suggested by Dr. Darwin, 
 and improved by Mr. Watt, who put it 
 into the hands of the celebrated Mr. Rams 
 den, for the purpose of being constructed. 
 
 The optigraph, as constructed by Mr. 
 Ramsden, was afterwards improved by 
 Mr. Thomas Jones, who has given the 
 following description of it. 
 
 Fig. 1st, is a perspective view of the 
 optigraph. 
 
 A represents the drawing board, on the 
 outside frame of which is fixed the pillar 
 of the instrument B, by a clamp a; C is a 
 tube (sliding in the pillar) on the top of 
 which is fixed, by means of a screw c, the 
 frame D; at the end of this frame is a 
 plane mirror E, beneath which is sus- 
 pended, by a universal joint, the telescope 
 F, of which G is the eye-tube ; H are 
 sliding tubes, capable of being shortened 
 or lengthened in the same proportion as 
 the inside speculum c } as in the following 
 figure, 
 
 have all the freedom of a pen when held in 
 the hand for use. 
 
 Fig. 2d, represents a section of the 
 telescope, being the principal part of the 
 invention. The rays from an object en- 
 tering the plane mirror a, are reflected into 
 the telescope, passing through the object- 
 glass b , and entering the speculum c, are re- 
 flected through the eye-glass d , to the eye 
 at e: / is a piece of parallel glass, with a 
 small dot on its centre, exactly in the focus 
 of the eye-glass d. 
 
 Fix the drawing board to the table, (by 
 a clamp which is packed in the box) so 
 that the surface of the mirror E is nearly 
 parallel to the object ; then take hold of 
 the handle ft, and hold the pencil on that 
 part of the paper, where you would wish 
 the centre of your drawing, or any part of 
 it, to be. Then place your eye at the eye* 
 
390 
 
 THE ARTISAN. 
 
 tube G, and with your left hand alter the 
 inclination of the mirror E, until the small 
 dot described at / in Fig. 2d, is on some 
 particular part of the object that you wish 
 to begin with, adjusting the telescope to 
 distinct vision, by the milled head P. 
 Then by moving your hand (having the 
 pencil) you pass the dot seen in the field 
 of the telescope over the abject, the pencil 
 marking it at the same time on the paper. 
 
 To make your drawing larger, pull out 
 the tube of the pillar C, Fig. 1st, and fix it 
 with the screw e ; then pull out the sliding 
 tubes H, till the pencil is within half an 
 inch of the paper (in the middle of the 
 board,) and proceed as formerly. 
 
 To make the drawing smaller, shorten 
 the tubes c and H, by sliding them in, and 
 proceed as before. 
 
 CHEMISTRY,, 
 
 OF GOLD. 
 
 If a narrow slip of gold leaf be put, 
 with both ends hanging out a little, be- 
 tween two glass plates tied together, and 
 a strong electrical explosion be passed 
 through it, the gold leaf is missing in 
 several places, and the glass is tinged of a 
 purple colour by the portion of the metal 
 which has been oxidized. This curious 
 experiment was first made by Dr. Frank- 
 lin ; it was confirmed in 1773 by Camus. 
 The reality of the oxidizement of gold by 
 electricity was disputed by some philoso- 
 phers, but it has been put beyond the 
 reach of doubt by the experiments of Van 
 Marum. When he made electric sparks 
 from the powerful Teylerian machine pass 
 through a gold wire suspended in the air, 
 it took fire, burnt with a green-coloured 
 flame, and was completely dissipated in 
 fumes, which when collected proved to be 
 a purple-coloured oxide of gold. This 
 combustion, according to Van Marum, 
 succeeded not only in common air, but 
 also when the wire was suspended in hy- 
 drogen gas, and other gasses which are 
 not capable of supporting combustion. 
 The combustion of gold is now easily 
 effected by exposing gold-leaf to the action 
 of the galvanic battery. Dr. Thomson 
 made it burn with great brilliancy, by ex- 
 posing a gold wire to the action of a stream 
 of oxygen and hydrogen gas mixed toge- 
 ther and burning. Now in all cases of 
 combustion the gold is oxidized. We are 
 at present acquainted with two oxides of 
 gold : the protoxide has a purple or violet, 
 the peroxide a yellciv colour. 
 
 Of these the peroxide is most easily pro- 
 cured ; it is therefore best known. It may 
 be procured in the following manner : 
 equal parts of nitric and muriatic acids 
 
 are mixed together,* and poured upon 
 gold; an effervescence takes place, the 
 gold is gradually dissolved, and the liquid 
 assumes a yellow colour. It is easy to 
 see in what manner this solution is pro- 
 duced. For it is worthy of remark, that 
 no metal is soluble in acids till it has been 
 reduced to the state of an oxide. There is 
 a strong affinity between the oxide of gold 
 and muriatic acid. The nitric acid fur- 
 nishes oxygen to the gold, and the mu- 
 riatic acid dissolves the oxide as it forms. 
 When nitric acid is deprived of the greater 
 part of its oxygen, it assumes a gaseous 
 form, and flies off in the state of nitrous 
 gas. It is the emission of this gas which 
 causes the effervescence. The oxide of 
 gold may be precipitated from the nitro- 
 muriatic acid, by pouring in a little potash 
 dissolved in water, orjeven by lime water. 
 It subsides slowly, and has a yellowish 
 brown colour, and sometimes, indeed, 
 approaches to black. When carefully 
 washed and dried, it is insoluble in water 
 and tasteless. When this oxide is mode- 
 rately heated, it becomes purple. A 
 stronger heat expels the whole of the 
 oxygen, and reduces it to the metallic 
 state 
 
 The properties of the protoxide of gold 
 are but little known. It is formed when 
 the metal is subjected to combustion, or to 
 the action of electricity, and likewise by 
 exposing the peroxide to the proper degree 
 of heat, or even by placing it in the rays 
 of the sun. Its colour is purple. Various 
 preparations containing it are used in the 
 arts, which will be noticed afterwards. 
 
 Hitherto gold has been united arti- 
 ficially to none of the simple combustibles 
 except phosphorus. Hydrogen and char- 
 coal are said to precipitate it from its solu- 
 tions in the metallic state. 
 
 Sulphur, even when assisted by heat, 
 has no action on it whatever ; nor is it 
 ever found naturally combined with sul- 
 phur, as is the case with most of the 
 other metals ; — yet it can scarcely be 
 doubted that sulphur exercises some action 
 on gold, though but a small one : for when 
 an alkaline hydro-sulphuret is dropt into 'a 
 solution of gold, a black powder falls to 
 the bottom, which is found to consist of 
 g’old and sulphur, either combined or in- 
 timately mixed ; and when potash, sul- 
 phur, and gold, are heated together, and 
 the mixture boiled in water, a considerable 
 portion of gold is dissolved. Three parts 
 of sulphur, and three of potash, are suffi- 
 cient to dissolve one of gold. The solu- 
 tion has a yellow colour. When an acid 
 
 * This mixture, from its property of dissolving 
 gold, was formerly called aqua regia (for gold 
 among the alchymists, was the king of metals) , it is 
 now called nitro muriatic acid. 
 
THE ARTISAN. 
 
 391 
 
 is dropt into it, the gold falls down, united 
 to the sulphur in the state of a reddish 
 powder, which becomes gradually black. 
 
 Gold does not combine, as far as is 
 known, with either of the simple incom- 
 bustible bodies. 
 
 But gold combines readily with the 
 greater number of the metals, and forms 
 a variety of alloys. 
 
 This metal is so soft, that it is seldom 
 employed in a state of purity. It is almost 
 always mixed with small quantities of 
 copper and silver. Goldsmiths usually 
 announce the purity of the gold which 
 they sell in the following manner : Pure 
 gold they suppose divided into 24 parts, 
 called carats. Gold of 24 carats means 
 pure gold ; gold of 23 carats means an 
 alloy of 23 parts gold, and one of some 
 other metal ; gold of 22 carats means an 
 alloy of 22 parts of gold, and two of 
 another metal. The number of carats men- 
 tioned specifies the pure gold ; and what 
 that number wants of 24, indicates the quan- 
 tity of alloy. Thus gold of 12 carats 
 would be an alloy containing 12 parts 
 gold, and 12 of some other metal. In this 
 country, the carat is divided into four 
 grains; among the Germans into 12 ; and 
 by the French it was formerly divided into 
 32. 
 
 OF PLATINA. 
 
 Platina, or platinum, was not known by 
 Chemists till the middle of the eighteenth 
 century. Under this name, however, which 
 is of Spanish origin, and signifies little or 
 inferior silver , some white trinkets of little 
 estimation were sold, before the metal was 
 distinctly known. Antonio de Ulloa, a 
 Spanish mathematician, who accompanied 
 the members of the French academy, in 
 their famous voyage to Peru, for the pur- 
 pose of ascertaining the figure of the earth, 
 first gave something like a precise notion 
 of it, in the account of his voyage pub- 
 lished at Madrid in 1748. It is observed, 
 that Mr. Charles Wood, an English me- 
 tallurgist, brought some of it from Jamaica 
 in 1741. ;,This gentleman related some ex- 
 periments on this new metal in the Philo- 
 sophical Transactions for 1749 and 1750. 
 
 These first experiments, which announced 
 very extraordinary properties, made a great 
 noise in Europe, at a period when the dis- 
 covery of a metal, particularly one so sin- 
 gular as this appeared to be, was a phe- 
 nomenon beyond what any one had dared 
 to hope. The greatest Chemists of Europe 
 were then eager to examine platina, and 
 investigate its distinguishing characters. 
 Scheffer, a Swedish Chemist, gave the first 
 accurate series of experiments on this me- 
 tal, in the Memoirs of the Academy of 
 Stockholm, in 1752; in consequence of 
 which, he ranked this metal near gold for 
 its properties, ‘and called it white gold. 
 
 Lewis, an English Chemist, to whom we 
 are indebted, among other things, for a 
 history of silver and of gold, very complete 
 for the time, made a very extensive and 
 regular series of experiments on platina, 
 which he published in the Philosophical 
 Transactions for 1754. In the Memoirs 
 of the Academy of Berlin, for 1757, Mar- 
 graff gave an account of his experiments 
 on this metal. All these early labours 
 were collected and compared by Morin, in 
 a work he published in France, in 1758, 
 under the title of Platina , White Gold , or 
 the Eighth Metal. This is a methodical 
 compilation of all that had been done pre- 
 vious to that period. 
 
 After these researches, already very 
 numerous, Achard, Guyton, Lavoisier, and 
 Pelletier, successively published methods 
 of obtaining platina pure, and of fusing 
 it, and new information respecting its com- 
 binations. 
 
 From these combined labours, we have 
 acquired a considerable knowledge of the 
 properties of platina, though there are still 
 many things desirable for completing the 
 history of this metal. The Pneumatic sys- 
 tem has done nothing with regard to pla- 
 tina, except teaching us to place it on a level 
 with gold, in respect to its difficult oxida- 
 tion, its little affinity for oxygen, and its 
 consequent unalterability by the majority 
 of other substances. 
 
 Platina, when purified, is of a less 
 beautiful white than silver, and verging 
 a little towards the grey colour of iron. 
 When burnished, it has a blackish tint, 
 and not the white lustre of silver. Its un- 
 polished parts are somewhat grey and 
 dull. Its appearance is not so brilliant 
 and pleasing as that of silver, or gold : 
 and most men, though likely to confound 
 it with other metals, would not form from 
 the sight of it the same idea as of those 
 two precious metals, which attract their 
 eyes and excite their admiration, or attach 
 to it the same value. 
 
 This metal is the most dense and heavy 
 of all natural substances. When it is 
 slightly hammered or forged, its specific 
 gravity is 21*5, and after being well ham- 
 mered, it is 23. 
 
 The elasticity of platina appears to be 
 pretty considerable. Its ductility is great ; 
 though it is far from being easily wrought, 
 it is reduced to very slender wires, and 
 very thin leaves. Guyton gives it the 
 second rank in this respect, placing it 
 between gold and silver. It is easily 
 bended : and the resistance and cohesion 
 of the plates fabricated of it will, at some 
 future period, admit a great number of 
 uses to be made of it of high importance. 
 The same Chemist made the most accurate 
 experiments on its tenacity, or the cohesion 
 of its particles. In this point, he assigns 
 
392 
 
 THE ARTIS Aft. 
 
 it the third rank, after iron and copper, 
 and before silver and gold. 
 
 Platina, like all other metals, [heats quick- 
 ly, and is a very good conductor of caloric. 
 Borda found that its dilatation is to a 
 degree of Reaumur’s, and Ti^raa" to a degree 
 of the decimal thermometer. Of all me- 
 tals it is the most intractable in the fire, 
 and the most difficult to fuse. It goes be- 
 yond iron and manganese in this property. 
 Guyton estimates its fusibility at a degree 
 yet unknown, or beyond the utmost limit 
 of Wedgewood’s pyrometer. In fact, the 
 greatest fire produced by our furnaces 
 scarcely soften, perceptibly, the platina, in 
 grains. At the most extreme degrees of 
 heat, we can only agglutinate these grains 
 together, without imparting to them a true 
 or strong adhesion, since they may be 
 separated by hammering. Macquer and 
 Baume kept several in a continued line, 
 exposed to the constant and violent heat 
 of a glass-house furnace ; and these grains 
 only stuck slightly to each other, for they 
 were afterwards separated by the hand. 
 They perceived their colour become very 
 brilliant, when they were at a white heat. 
 On exposing the same grains of platina, 
 well purified, to the focus of the burning 
 lens of the Academy, the portions placed 
 in the centre of the focus smoked, melted 
 at the end of a minute, and formed an 
 homogeneous button, white and brilliant, 
 very ductile, and capable of being "cut 
 with a knife. Guyton likewise succeeded 
 in fusing small portions in a crucible, by 
 the help of his reducing flux, composed of 
 eight parts of pounded glass, one of cal- 
 cined borax, and half a part of charcoal, 
 and employing for this operation Mac- 
 quer’s wind-furnace. Lavoisier also fused 
 small portions of platina in a cavity on 
 charcoal with a blast of oxygen gas. After 
 all these trials, there is nothing more easy 
 than to procure little buttons of this metal 
 thus melted ; but they are in such small 
 masses, that it is impossible to employ 
 them in decisive experiments ; and we 
 may still say that no real and useful fu- 
 sion of platina has been obtained ; since, 
 when treated by the ordinary means, it is 
 impossible to fuse it in such a quantity as 
 allow us to examine its properties, and 
 employ it in experiments capable of ren- 
 dering us acquainted with them. Accord- 
 ingly it will appear farther on, that, to 
 apply it to the uses already made of it, 
 the fabrication of plates, bars, wires, ves- 
 sels, &c. it has been necessary to fuse it 
 by the help of some alloys, and separate 
 it afterwards by forging from the metals 
 united with it. 
 
 Platina is a very good conductor of the 
 electric fluid and of galvanism. Its power 
 in this respect has not been compared with 
 th.,t of other metals, but it appears to be 
 
 very great. It has neither smell nor taste* 
 in which it resembles silver and gold. 
 
 Platina has hitherto been found no 
 where except in the gold mines of America, 
 particularly in that of Santa Fe, near Car- 
 thagena, and in the bailiwick of Choco, in 
 Peru. It is collected in the form of little 
 grains, of a livid grey or white, the colour 
 of which partakes of those of silver and 
 iron. These grains are mixed with several 
 foreign substances ; among them are found 
 gold dust, blackish ferruginous sand, 
 grains that appear through the lens scori- 
 fied like the slag of iron, and some parti- 
 cles of mercury. 
 
 On examining the grains of platina with 
 a lens, some appear angular, and others 
 rounded or flattened like some pebbles. 
 They may be flattened under the hammer, 
 but some fly to pieces ; and these fre- 
 quently appear hollow within, and contain 
 portions of iron and a white powder. To 
 these small grains of iron must be ascribed 
 the property of being attracted by the mag- 
 net, observed in the grains of platina, 
 though well separated from the ferruginous 
 sand among them. To obtain the purest 
 aud largest grains of platina, they are 
 sorted by hand, and the gold dust, quartz, 
 sand, and iron, are separated from them. 
 
 It is probable that platina is not found 
 in the earth as it is brought to us, and as it 
 is seen in mineralogical collections. The 
 form of grains which it exhibits is owing 
 either to the motion of the water by which 
 it is carried dow n from the mountains into 
 the plains, or to the grinding of the mills, 
 through which the ores of gold with which 
 it is mingled in the native state are passed. 
 Sometimes pretty large pieces of it have 
 been found. No naturalist has yet de- 
 scribed the situations or varieties of ores of 
 platina. It is at present the least known 
 of all metals, and perhaps the only one 
 which, being found hitherto only in one 
 state, been likewise discovered but in one 
 single country. 
 
 Platina is very distinguishable by its 
 form, colour, and specific gravity. As it 
 is always mixed with sand and iron, and 
 frequently with gold and quicksilver, be- 
 side the sorting by hand already men- 
 tioned, by means of which Tillet found 
 some grains of this metal embedded in a 
 quartz gangue, different processes are em- 
 ployed for its purification. It is heated 
 red hot to volatilize the portion of mercury 
 left by the amalgamation, by means of 
 which gold w as obtained from it. Iron is 
 separated from it by the magnet, which 
 frequently takes up with this attractable 
 metal little fragments of platina. The 
 grains are also heated with muriatic acid, 
 which dissolves and takes up the iron, 
 Bergman has remarked, that platina loses 
 0*05 of its weight by this operation. After 
 
THE ARTISAN. 
 
 
 this, nothing remains but the platina and 
 the gold, both of which are to be dissolved 
 in nitro-muriatic acid ; and the propor- 
 tions of the two metals may be found by 
 precipitating the gold by sulphate of iron, 
 and carefully weighing the precipitate, 
 which, as we have before observed, is in a 
 metallic powder. 
 
 As to operations in the great way, there 
 is no one yet settled or practised. The 
 Spanish government, having found that its 
 miners debased gold with platina, and 
 that it was difficult to discover the fraud, 
 on account of the specific gravity and un- 
 alterableness of this compound, is said to 
 have shut up the mines of platina ; but 
 this is an improper expression, which re- 
 quires to be explained so as to leave no 
 ambiguity or uncertainty. It appears that 
 platina, being always found mixed with 
 gold ore, and both being disseminated in 
 the native state, in the same gangue, it is 
 impossible that the mines of platina can 
 have been shut ; but as fast as this metal, 
 which does not dissolve like gold in quick- 
 silver, is extracted and separated, it is 
 thrown away, or set apart, so that it is no 
 longer met with in trade as formerly. 
 Hence it is, that the mode of treating it in 
 the large way has made no progress, and 
 that no work in this new branch of metal- 
 lurgy has hitherto been erected. 
 
 Accordingly, what belongs to the metal- 
 lurgy of platina is nothing more than a 
 series of operations on a larger scale than 
 those of a simple assay, though on a much 
 less than the usual metallurgic operations. 
 It is by these that Carrochez, Jeannety, 
 Chabanon, Wollaston, and several others, 
 have accomplished the fusion, particularly 
 by the help of arsenious acid, or what is 
 called white arsenic, of some considerable 
 quantities of platina ; they have hammered 
 and forged it by repeatedly heating and 
 softening it, so as to deprive it by little 
 and little, and at length completely, of the 
 arsenic which rendered it fusible, and pre- 
 served its continuous and connected form, 
 so as to admit of its being flattened, 
 fashioned on moulds, and drawn into wire. 
 It is by a similar operation that it has been 
 brought to the greatest purity, reduced to 
 the common state of other metals, and 
 made to assume forms which may render 
 it useful for various purposes. 
 
 As the different processes employed by 
 most of the artists above-mentioned for 
 purifying, fusing, and forging platina, 
 have not yet been described, we shall here 
 state one of the simplest which has yet 
 been employed. Dissolve the grains in 
 diluted nitro-muriatic acid with as little 
 heat as possible. Decant the solution 
 from the black matter which resists the 
 action of the acid. Drop into it a solution 
 of sal ammoniac. An orange yellow co. 
 
 loured precipitate falls to the bottom. 
 Wash this precipitate ; and when dry, ex- 
 pose it to a heat slowly raised to redness 
 in a porcelain crucible. The powder which 
 remains is platinum nearly pure. By re- 
 dissolving it in nitro-muriatic acid, and 
 repeating the whole process, it may be 
 made still purer. When these grains are 
 wrapt up in a thin plate of platinum r 
 heated to redness, and cautiously ham- 
 mered, they unite, and the whole may be 
 formed into an ingot. 
 
 It cannot be combined with oxygen,, 
 and converted into an oxide, by the 
 strongest artificial heat of our furnaces. 
 Platinum, indeed, in the state in which it 
 is brought from America, may be par- 
 tially oxidized by exposure to a violent 
 heat, as numerous experiments have 
 proved ; but in that state it is not pure,, 
 but combined with a quantity of iron. It 
 cannot be doubted, however, that if we 
 could subject it to a sufficient heat, plati- 
 num would burn, and be oxidized like 
 other metals : for, wdien Van Marum ex- 
 posed a wire of platinum to the action of 
 his powerful electrical machine, it burnt 
 with a faint white flame, and was dissi- 
 pated into a species of dust, which proved 
 to be the oxide of platinum. By putting 
 a platinum wire into the flame produced 
 by the combustion of hydrogen gas mixed 
 with oxygen, he caused it to burn with all 
 the brilliancy of iron wire, and to emit 
 sparks in abundance. 
 
 To obtain the oxides of this metal, it is 
 necessary to have recourse to the action 
 of an acid. When the deep brown solu- 
 tion of platinum in nitro-muriatic acid is 
 treated with lime water, a yellowish brown 
 powder falls. Dissolve this pow-der in 
 nitric acid ; evaporate to dryness, and 
 apply a heat sufficient to drive off the acid. 
 The brown powder which remains is the 
 peroxide of platinum. It is tasteless and 
 insoluble in water. When heated to red- 
 ness, the oxygen is driven off, and the 
 oxide reduced to the metallic state. One 
 hundred and fifteen parts of oxide, by this 
 treatment, leave 100 parts of metal. 
 
 If the heat in this experiment be very 
 cautiously raised, the oxide, before it is 
 reduced, assumes a green colour. This 
 change is occasioned by the separation of 
 a portion of the oxygen. The green co- 
 loured powder is, according to Cheng vix, 
 a protoxide of platinum. 
 
 The action of the simple combustibles 
 on this metal is not more remarkable than 
 their action on gold. 
 
 Neither hydrogen nor carbon have been 
 hitherto combined with it. 
 
 Phosphorus unites with it easily, and 
 forms a phosphuret. By mixing together 
 an ounce of platinum, an ounce of phos- 
 phoric glass, and a dram of powdered 
 
394 
 
 THE ARTISAN. 
 
 charcoal, and applying a heat of about 32° 
 Wedgewood, Mr. Pelletier formed a phos- 
 phuret weighing more than an ounce. It 
 was partly in the form of a button, and 
 partly in cubic crystals. It was covered 
 above by a blackish glass. It was of a 
 silver white colour, very brittle, and hard 
 enough to strike fire with steel. When 
 exposed to a fire strong enough to melt it, 
 the phosphorus was disengaged, and burnt 
 on the surface. He found also, that when 
 phosphorus was projected on red hot pla- 
 tinum, the metal instantly fused and 
 formed a phosphuret. As heat expels the 
 phosphorus, Mr. Pelletier has proposed this 
 as an easy method of purifying platinum. 
 
 Platinum cannot be made to unite to 
 sulphur by heating them together. In this 
 respect it resembles gold ; yet there seems 
 to be an affinity between the two sub- 
 stances ; for when the metal is heated 
 with a mixture of potash and sulphur, it is 
 corroded and rendered partly soluble in 
 water, as was proved by the experiments 
 of Lewis and Margarf. And when sul- 
 phuretted hydrogen gas is passed into a 
 solution of platinum in an acid, the metal 
 is thrown down in dark brown flakes, 
 apparantly in combination with sulphur. 
 Indeed, if we believe Mr. Proust, a sul- 
 phuret of this metal occurs sometimes 
 mixed with native platina. 
 
 Platinum, as far as is known, does not 
 combine with the simple incombustibles. 
 
 It combines with most of the metals, 
 and forms alloys, which were first exa- 
 mined by Dr. Lewis. 
 
 OF THE CLOUDS. 
 
 Ye mists and exhalations that now rise 
 From hill or steaming lake, dusky or gray, 
 
 Till the sun paint your fleecy skirts with gold. 
 
 In honour to the world’s Great Author rise, 
 Whether to deck with clouds th’ uncoloured sky. 
 Or wash the thirsty^earth with falling showers. 
 Rising or falling, still advance his praise. 
 
 Milton. 
 
 Clouds are generally supposed to con- 
 sist of vapour, which has been raised from 
 the sea and land by means of heat. These 
 vapours ascend till they reach air of the 
 same specific gravity with themselves, 
 when they combine with each other, be- 
 come more dense and opaque, and then 
 become visible. 
 
 The thinner or rarer the clouds are, the 
 higher do they ascend in the air ; however, 
 it seldom happens that their height ex- 
 ceeds two miles. The greater number of 
 clouds are suspended at the height of one 
 mile ; and when they are highly electrified, 
 their height is not above eight or nine 
 hundred yards. 
 
 While Don Ulloa was in South America, 
 
 measuring a degree of the meridian, he 
 was for some time stationed on the summit 
 of Cotapaxi, a mountain about three miles 
 above the level of the sea, where he says — 
 the clouds could be seen at a great dis- 
 tance below, and that he could hear the 
 horrid noise of the thunder and tempests, 
 and even see the lightnings issue from the 
 clouds far below him. 
 
 The wonderful variety observable in the 
 colours of clouds, is owing to their parti- 
 cular position with respect to the sun, and 
 the different reflections of his light. The 
 various figures which they so readily as- 
 sume, is supposed to proceed from then- 
 loose and voluble texture, revolving in 
 any form, according to the direction and 
 force of the wind, or to the quantity of 
 electric matter which they contain. 
 
 About the tropics the clouds roll them- 
 selves into enormous masses, as white as 
 snow, turning their borders into the forms 
 of hills, piling themselves upon each other, 
 and exhibiting the shapes of mountains, 
 caverns, and rocks. “ There/’ says St. 
 Pierre, “may be perceived, amid endless 
 ridges, a multitude of valleys, whose 
 openings are distinguished by purple and 
 Vermillion.” These celestial valleys ex- 
 hibit, in their various colours, matchless 
 tints of white, melting into shades of dif- 
 ferent colours. Here and there may be 
 observed torrents of light issuing from the 
 dark sides of the mountains, and pouring 
 their streams, like ingots of gold and sil- 
 ver, over rocks of coral. These appear- 
 ances are not more to be admired for their 
 beauty than for their endless combinations, 
 for they vary every instant. What, a 
 moment before, was luminous, becomes 
 coloured ; what was coloured, mingles 
 into shade; forming singular and most 
 beautiful representations of islands and 
 hamlets, arched bridges stretched over 
 wide rivers, immense ruins, huge rocks, 
 and gigantic mountains. 
 
 Among the Highlands of Scotland the 
 clouds also display the finest outlines, and 
 assume the most beautiful figures; more 
 especially when viewed from their rugged 
 and lofty summits. 
 
 “ Clouds,” says Dr. Thompson, “ are 
 not formed in all parts of the horizon at 
 once ; the formation begins in one particu- 
 lar spot, while the rest of the air remains 
 clear as before ; and though the greatest 
 quantity of vapour exists in the lower 
 strata of the atmosphere, clouds never 
 begin to form there, but always at some 
 considerable height.” It is remarkable, 
 says the same author, that the part of the 
 atmosphere at which they form has not 
 arrived at the point of extreme moisture, 
 nor near that point, even a moment before 
 their formation. 
 
 They are not formed, then, because a 
 
THE ARTISAN, 
 
 395 
 
 greater quantity of vapour has got into the 
 air than could remain there without pass- 
 ing its maximum. It is still more remark- 
 able, that when clouds are formed, the 
 temperature of the spot does not always 
 suffer a diminution, although this may 
 sometimes be the case. On the contrary, 
 the heat of the clouds themselves is some- 
 times greater than that of the surrounding 
 air. Neither, then, is the formation of 
 the clouds owing to the capacity of air for 
 combining with moisture being lessened 
 by cold. So far from this being the case, 
 we often see clouds, which had remained 
 in the atmosphere during the heat of the 
 day, disappear in the night, after the heat 
 of the air was diminished. 
 
 The formation of clouds and rain, then, 
 cannot be accounted for by the principles 
 with which we are acquainted. It is 
 neither to the saturation of the atmosphere, 
 nor the diminution of heat, nor the mixture 
 of airs of different temperatures, as Dr. 
 Hutton supposed; for clouds are often 
 formed without any wind at all either above 
 or below them: and even if this mixture 
 constantly took place, the precipitation, 
 instead of accounting for rain, would be 
 almost imperceptible. 
 
 It is a well-known fact, that evaporation 
 goes on for a month or two together in hot 
 weather without any rain. This some- 
 times happens in the temperate zone ; and 
 every year in the torrid zone. At Cal- 
 cutta, during the month of January, in 
 the year 1785, it never rained at all: the 
 mean of the thermometer for the whole 
 month was 66! degrees : there were no 
 high winds, and, during the greater part 
 of the month, scarcely any wind at all. 
 
 As the moisture which is thus raised by 
 evaporation is not accumulated in the at- 
 mosphere, above the place from which it 
 was evaporated, it must be disposed of in 
 some other way ; but the manner in which 
 this is accomplished is not so well known. 
 If it be carried on daily through the differ- 
 ent strata of the atmosphere, and wafted 
 to other regions by superior currents of 
 air, it is impossible to account for the 
 different electrical states of the clouds, 
 situated between different strata, which 
 often produce the most violent thunder 
 storms. For vapours are conductors of 
 the electric fluid, and, of course, would 
 daily restore the equilibrium of the whole 
 atmosphere through which they passed. 
 There would, therefore, be no positive 
 and negative clouds, and consequently no 
 thunder storms. Clouds could not have 
 remained in the lower strata of the atmos- 
 phere, and been daily carried off by. winds 
 to other countries ; for there are often no 
 winds at all, during several days, to per- 
 form this office; nor would the dews 
 
 diminish as they are found to do when the 
 dry weather continues for a long time. 
 
 It is impossible for us to account for 
 this remarkable fact upon any principle 
 with which we are acquainted. The water 
 can neither remain in the atmosphere, nor 
 pass through it in the state of vapour. It 
 must, therefore, assume some other form ; 
 but what that form is, or how it assumes 
 it, we do not know. 
 
 In order to render the study of meteoro- 
 logy more systematic, Mr. Luke Howard 
 has lately introduced a scientific nomen- 
 clator, for distinguishing the various forms 
 or modifications of clouds, which promises 
 to be of great use in this important, but 
 hitherto neglected, branch of physical 
 science. 
 
 The simple forms, or modifications, are 
 three in number, and named Cirrus , Cu- 
 mulus, and Stratus. These are defined by 
 Mr. Haward as follows : — The Cirrus is 
 composed of parallel, flexuous, or diverg- 
 ing fibres, extensible in any or in all 
 directions. 
 
 The Cumulus, convex or conical, heaps, 
 increasing upwards from a horizontal base. 
 
 The Stratus , is a widely extended, con- 
 tinuous, horizontal sheet, increasing from 
 below. 
 
 The intermediate modifications are four 
 in number, each of which is formed from 
 various combinations of the simple modifi- 
 cations just mentioned. They are the 
 Cirro-cumulus , the Cirro-stratus , the Cu- 
 mulo-stratus , and the Cumulo-cirro-stratus , 
 or Nimbus ; and are defined as follows. 
 
 Cirro - cumulus. Small well-defined 
 roundish masses, in close horizontal ar- 
 rangement. 
 
 Cirro-stratus. Horizontal or slightly- 
 inclined masses, bent downward, or undu- 
 lated, separate, or in groups consisting of 
 a number of small clouds. 
 
 Cumulo-stratus. The cirro-stratus blended 
 with the cumulus, and either appearing 
 intermixed with the heaps of the latter, or 
 super-adding a wide-spread structure to 
 its base. 
 
 Cumulo-cirro-stratus. The rain cloud. 
 A cloud, or system of clouds, from which 
 rain is falling. It is a horizontal sheet, 
 above which the cirrus spreads, while the 
 cumulus enters it laterally, and from be- 
 neath. 
 
 OF THE CIRRUS. 
 
 Clouds in this modification appear to 
 have the least density, the greatest eleva- 
 tion, and the greatest variety of extent 
 and direction. They are the earliest ap- 
 pearance after serene weather. They are 
 first indicated by a few threads pencilled, 
 as it were, on the sky. These increase in 
 length, and new ones are in the mean time 
 added laterally. Often the first-formed 
 
$9Q 
 
 THE ARTISAN, 
 
 threads serve as stems to support numerous others. This modification is represented 
 branches, which in their turn give rise to by the following figure. 
 
 ' The increase is sometimes perfectly in- 
 determinate, at others it has a very decided 
 direction. Thus the first few threads 
 being once formed, the remainder shall be 
 propagated either in one, two, or more 
 directions laterally, or obliquely Tipward 
 or downward, the direction being often 
 the same in a great number of clouds 
 visible at the same time. 
 
 Their duration is uncertain, varying 
 from a few minutes after the first appear- 
 ance to an extent of many hours. It is 
 long when they appear alone and at great 
 heights, and shorter when they are formed 
 lower and in the vicinity of other clouds. 
 
 This modification, although in appear- 
 ance almost motionless, is intimately con- 
 nected with the variable motions of the 
 atmosphere. Considering that clouds of 
 this kind have long been deemed a prog- 
 nostic of wind, it is extraordinary that the 
 nature of this connection should not have 
 been more studied, as the knowledge of 
 it might have been productive of useful 
 results. 
 
 In fair weather, with light variable 
 breezes, the sky is seldom quite clear of 
 small groups of the oblique cirrus, which 
 frequently come on from the leeward, and 
 the direction of their increase is to wind- 
 
 ward. Continued wet weather is attended 
 with horizontal sheets of this cloud, which 
 subside quickly and pass to the cirrostra- 
 tus. 
 
 Before storms they appear lower and 
 denser, and usually in the quarter oppo- 
 site to that from which the storm arises. 
 Steady high winds are also preceded and 
 attended by streaks running quite across 
 the sky in the direction they blow in. 
 
 The relation of this modification with 
 the state of the barometer, thermometer, 
 hygrometer, and electrometer, have not 
 yet been attended to. 
 
 OF THE CUMULUS. 
 
 Clouds in this modification are com- 
 monly of the most dense structure : they 
 are formed in the lower atmosphere, and 
 move along with the current which is next 
 the earth. 
 
 A small irregular spot first appears, 
 and is, as it were, the nucleus on which 
 they increase. The lower surface con- 
 tinues irregularly plane, while the upper 
 rises into conical or hemispherical heaps ; 
 which may afterwards continue long 
 nearly of the same bulk, or rapidly rise to 
 mountains, as represented by the following 
 figure. 
 
THE ARTISAN. 
 
 397 
 
 In the former case they are usually nu- 
 merous and near together, in the latter 
 few and distant; but whether there are 
 few or many, their bases always lie nearly 
 in one horizontal plane, and their increase 
 upward is somewhat proportionate to the 
 extent of base, and nearly alike in many 
 that appear at once. 
 
 Their appearance, increase* and dis- 
 appearance, in fair weather, are often 
 periodical, and keep pace with the tem- 
 perature of the day. Thus they will begin 
 to form some hours after sun-rise, arrive 
 at their maximum in the hottest part of the 
 afternoon, then go on diminishing, and 
 totally disperse about sun-set. 
 
 But in changeable weather they partake 
 of the vicissitudes of the atmosphere ; 
 sometimes evaporating almost as soon as 
 formed, at others suddenly forming and 
 as quickly passing to the compound modi- 
 fications. 
 
 The cumulus of fair weather has a mo- 
 
 derate elevation and extent, and a well 
 defined rounded surface. Previous to 
 rain it increases more rapidly, appears 
 lower in the atmosphere, and with its sur- 
 face full of loose fleeces or protuberances. 
 
 Independently of the beauty and mag- 
 nificence it adds to the face of nature, the 
 cumulus serves to screen the earth from 
 the direct rays of the sun, by its multiplied 
 reflections, to diffuse, and, as it were, eco- 
 nomise the light, and also to convey the 
 product of evaporation to a distance from 
 the place of its origin. The relations of 
 the cumulus with the state of the barome- 
 ter, &c. have not yet been sufficiently at- 
 tended to. 
 
 The formation of large cumuli to lee- 
 ward in a strong wind, indicates the ap- 
 proach of a calm with rain. When they 
 do not disappear or subside about sun- 
 set, but continue to rise, thunder is to be 
 expected in the night. 
 
 fBtsicellaneous Subjects. 
 
 MEMOIR OF THE LIFE OF TOBIAS 
 JOHN MAYER. 
 
 Tobias John Mayer, a very eminent Ger- 
 man mathematician and astronomer, was 
 born at Marbach, a small town in the 
 duchy of Wirtemberg, on the 17th of Fe- 
 bruary, 1723. He did not enjoy the ad- 
 vantage of a regular academical education ; 
 but his genius and application enabled 
 him, at an early age, and without any as- 
 sistance, to become a proficient in the mathe- 
 matical and mechanical sciences, which he 
 afterwards cultivated with such success as 
 rendered his name celebrated throughout 
 Europe. Some essays which he published 
 in his twenty-second year attracted atten- 
 tion, and probably were the means of his 
 procuring an appointment, in 1746, in the 
 geographical establishment originally in- 
 
 stituted by Homann at Nuremberg, where 
 his talents were usefully employed in pre- 
 paring the maps which were published by 
 that company. £ His Critical Map of Ger- 
 many, in which |he corrected a multitude 
 of errors, was particularly esteemed. He 
 was, at the same time, admitted a member 
 of the Cosmographical Society of Nurem- 
 berg, and contributed several memoirs to 
 the collection published by that body 
 which may be considered as the precursors 
 ©f his larger works on the theory of the 
 lunar motions, and the determination of 
 the longitude. 
 
 The highly interesting train of investi- 
 gation, however, in which the genius of 
 Mayer was now engaged, would probably 
 never have been prosecuted to a success- 
 ful issue, had he not been placed in a si- 
 tuation more favourable to the cultivation 
 of science, by his appointment to the pro- 
 
398 
 
 THE ARTISAN. 
 
 fessorship of mathematics in the University 
 of Gottingen, in the year 1751. He avail- 
 ed himself, with indefatigable zeal and 
 industry, of the advantages which he now 
 enjoyed ; and he was still farther stimu- 
 lated to the prosecution of his astronomi- 
 cal labours, when, in 1754, the principal 
 charge of the observatory was committed 
 to him. His unremitted exertions, how- 
 ever, seem to have exhausted his frame ; 
 and his death is also supposed to have 
 been hastened by the sufferings to which 
 the town of Gottingen was exposed during 
 the seven-years’ war. He died on the 
 20th of February, 1762, at the age of 39. 
 
 The services of Mayer have long been 
 justly appreciated by men of science. His 
 reputation is chiefly founded on the Lunar 
 Tables , which he calculated with a degree 
 of exactness till then unknown, and which 
 he continued to improve until the day of his 
 death. He adopted the theory of Euler, 
 after having carefully investigated the cor- 
 rectness of its principles, and compared 
 them with the results of his own accurate 
 observations. About this period the atten- 
 tion of men of science in England had been 
 directed to the discovery of some means of 
 determining the longitude at sea, for 
 which a considerable reward had been 
 offered during the reign of Queen Anne. 
 As Mayer’s lunar tables seemed to afford 
 the means of attaining this object, he was 
 encouraged to lay claim to the reward, 
 and accordingly transmitted a copy of his 
 tables to the Lords of the Admiralty in 
 1755. He did not live, however, to reap 
 the reward of his services ; but the accu- 
 racy and utility of his labours were ac- 
 knowledged, and his widow received 
 £3000, being a part of the sum which had 
 been offered for the discovery of the longi- 
 tude. 
 
 The principles upon which Mayer pro- 
 ceeded in constructing these tables are 
 developed in the two following works : 
 Theoria Luncejuxta Sy sterna Newtonianum , 
 London, 1767, 4to. and Tabulce motuum So- 
 lis et Luna , ibid. 1770, 4to. These tables, 
 however, had been previously published in 
 the Memoirs of the Royal Society of Gottin- 
 gen during the author’s lifetime, and were 
 afterwards several times reprinted with 
 improvements. 
 
 Mayer also delineated, with great neat- 
 ness and accuracy, a new map of the 
 moon’s disc ; and he made some important 
 observations on the peculiar motions of 
 the fixed stars, besides constructing an 
 improved catalogue of 992 of these bodies. 
 His manuscripts, which, in addition to 
 the matters already mentioned, contained 
 some treatises on physical subjects, were 
 purchased by the government for the uni- 
 versity of Gottingen, and preserved in the 
 
 observatory. Lichtenberg began to col- 
 lect and to publish Mayer’s unprinted 
 treatises, but of this work only one volume 
 appeared, entitled Opera inedita. 
 
 UNIFORMITY OF WEIGHTS AND 
 MEASURES. 
 
 ( Continued from page 382.) 
 
 u VI. And be it further enacted, That 
 from and after the first day of May one 
 thousand eight hundred and twenty-five, 
 the standard measure of capacity, as well 
 for liquids as for dry goods not measured 
 by heaped measure, shall be the gallon, 
 containing ten pounds avoirdupois weight 
 of distilled water weighed in air, at the 
 temperature of sixty-two degrees of Fah- 
 renheit's thermometer, the.baremeter being 
 at thirty inches ; and that a measure shall 
 be forthwith made of brass, of such con- 
 tents as aforesaid, under the direction of 
 the Lord High Treasurer, or the Commis- 
 sioners of his Majesty’s Treasury of the 
 United Kingdom, or any three or more of 
 them for the time being ; and such brass 
 measure shall be and is hereby declared 
 to be the imperial standard gallon, and 
 shall be and is hereby declared to be the 
 unit and only standard measure of capa- 
 city, from which all other measures of 
 capacity to be used, as well for winre, 
 beer, ale, spirits, and all sorts of liquids, 
 as for dry goods not measured by heaped 
 measure, shall be derived, computed, and 
 ascertained; and that all measures shall 
 be taken in parts or multiplies, or certain 
 proportions of the said imperial standard 
 gallon; and that the quart shall be the 
 fourth part of such standard gallon, and 
 the pint shall be one-eighth of such 
 standard gallon, and that two such gallons 
 shall be a peck, and eight such gallons 
 shall be a bushel, and eight such bushels 
 a quarter of corn or other dry goods, not 
 measured by heaped measure. 
 
 “ VII. And be it further enacted. That 
 the standard measure of capacity for 
 coals, culm, lime, fish, potatoes, or fruit, 
 and all other goods and things commonly 
 sold by heaped measure, shall be the 
 aforesaid bushel, containing eighty pounds 
 avoirdupois of water as aforesaid, the 
 same being made round with a plain and 
 even bottom, and being nineteen inches 
 and a half from outside to outside of such 
 standard measure as aforesaid. 
 
 u VIII. And be it further enacted, That 
 in making use of such bushel, all coals 
 and other goods and things commonly sold 
 by heaped measure shall be duly heaped 
 up in such bushel, in the form of a cone, 
 such cone to be of the height of at least six 
 inches, and the outside of the bushel to be 
 
THE ARTISAN, 
 
 the extremity of the base of such cone ; 
 and that three bushels shall be a sack, 
 and that twelve such sacks shall be a 
 
 chaldron. 
 
 “ IX. Provided always, and be it en- 
 acted, That any contracts, bargains, sales, 
 and dealings, made or had for or with re- 
 spect to any coals, culm, lime, fish, pota- 
 toes, or fruit, and all other goods and things 
 commonly sold by heaped measure, sold, 
 delivered, done or agreed for, or to be 
 sold, delivered, done, or agreed for by 
 weight or measure, shall and may be 
 either according to the said standard of 
 weight, or the said standard of heaped 
 measure ; but all contracts, bargains, sales, 
 and dealings, made or had for any other 1 
 goods, wares, or merchandize, or other 
 thing done or agreed for, or to be sold, 
 delivered, done or agreed for by weight or 
 measure, shall be made and had according 
 to the said standard of weight, or to the 
 said gallon, or the parts, multiples, or 
 proportions thereof; and in using the 
 same the measures shall not be heaped, 
 but shall be stricken with a round stick or 
 roller, straight and of the same diameter 
 from end to end. 
 
 “ X. Provided always, and be it en- 
 acted, That nothing herein contained shall 
 authorize the selling in Ireland , by mea- 
 sure, of any articles, matters, or things 
 which by any law in force in Ireland are 
 required to be sold by weight only. 
 
 “ XI. And be it further enacted, That 
 copies and models of each of the s^id 
 standard yard, the said standard pound, 
 the said standard gallon, and the said 
 standard for heaped measure, and of such 
 parts and multiples thereof respectively, 
 as the Lord High Treasurer of the United 
 Kingdom of Great Britain and Ireland , or 
 the said Commissioners of His Majesty’s 
 Treasury, or any three of them for the 
 time being, shall judge expedient, shall, 
 within three calendar months next after 
 the passing of this Act, be carefully made 
 and verified under the direction of the said 
 Lord High Treasurer, or the Commis- 
 sioners of His Majesty’s Treasury, or any 
 three of them for the time being ; and that 
 the copies and models of the said standard 
 yard, of the said standard pound, of the 
 said standard gallon, and of the said 
 standard for heaped measure, and of parts 
 and multiples thereof, so forthwith to be 
 made and verified as aforesaid, shall, 
 within three calendar months after the 
 passing of this Act, be deposited in the 
 office of the Chamberlains of the Ex- 
 chequer at Westminster, and that copies 
 thereof, verified as aforesaid, shall be sent 
 to the Lord Mayor of London , and the 
 Chief Magistrate of Edinburgh and Dublin, 
 and of such other cities and places, and to 
 
 399 
 
 such other places and persons in His Ma- 
 jesty’s dominions or elsewhere, as the 
 Lord High Treasurer or Commissioners of 
 the Treasury may from time to time 
 direct. 
 
 SOLUTIONS OF QUESTIONS. 
 Quest. 50. ansivered by Mr. W hitcombe, 
 Cornhill. 
 
 Let A C R be the semicircle, and let 
 E C F be the triangle. 
 
 Then put x zz D E or D F half the base of 
 the triangle, then it is evident that 2 x z~ 
 E F zz E C or C F ; put also 3 m — C D, or 
 
 A B and by Euc. 47, and 1. Vi) E a -fB C 3 
 
 “CE, that is, s/x 2 -\- 9 m 2 in 2 x. Now 
 this squared becomes x 2 -j- 9 m 2 zz 4 x 2 , 
 or 3 x 2 — 9 m 2 , or x 2 “ 3 m 2 . Hence x 
 
 ~ mV 3, and 2#— 2m^/3; that is C E zz 
 
 ab r 
 TV 3 
 
 Q. E. I. 
 
 This question was also answered by 
 Mr. J. Holroyd, Oldham; and the pro- 
 poser. 
 
 Quest. 51, answered by I. C. S. Church 
 Row. 
 
 Here the diameter of the ceiling is 30 
 feet, x 3T416, gives the perimeter : and f 
 of the perimeter multiplied by 5, the height 
 of arch, and again by 5 the projection of 
 ditto, and by 3*1416, gives 1850*55498, call 
 this product A. Then the square of diffe- 
 rence of the diameter of the room and ceil- 
 ing x *7854, and again by § of the height of 
 the arch zz 261*79999, call this product B : 
 then square the diameter 30, multiply by 
 •7854 and again by the height of the arch, 
 gives 3534*3 call this product C — lastly 
 square the diameter of the room multiply by 
 •7854, and again by 20 the height of the 
 room to spring of the arch zz 21532*8, and 
 this added to the sum of A, B, and C, gives 
 the content in cubic feet zz: 30779*45947 as 
 required. 
 
 This question was also answered by 
 Mr. J. Taylor ; Mr. Geo. Fulvoye ; Mr. 
 Stephens ; and by the proposer, who ap- 
 pears to have taken the question from 
 Bonny castle’s Mensuration. 
 
400 
 
 THE ARTISAN. 
 
 Quest. 53, answeredby Mr. J. Harding, 
 Hart Street. 
 
 Put x -J- y and x — y for the respective 
 deposits. Then by question their sum 
 2#zz£3*3; hence xzz £1*65. Also by 
 the question x -f- y and x — y involved to 
 their 5th powers, become by addition 2 x 5 
 -f 20 x 3 y 2 + 10 x y* ~ £43*32933, or x 5 
 + 5 xy* -f- 10 x 3 y ~ zz £43*32933, which 
 by substituting the value of x or 1*65, di- 
 viding, and transposing, gives y* -f- 5*445 
 y 2 ~ 1*14361875 ; then by completing the 
 square and extracting the root y 2 -f- 2*7225 
 zz J 8*555625 zz 2*925. Whence y 2 zz 
 •2025 and y zz *45. Consequently John’s 
 or the greatest deposit is x -f- y zz £1*65 
 *45 zz £2 2. and x — y or Thomas’s de- 
 posit is 1*65— 45* £1 4. 
 
 This question was also correctly an- 
 swered by Mr. J. Whitcomb, Cornhill; 
 Mr. J. Taylor, Clement’s Lane ; J. C. S. 
 Church Row ; and by the proposer. 
 
 Quest. 54, answered by Fr — d F — lk, 
 — wo— th (the Proposer.) 
 
 Let the annexed figure represent Jhe 
 garden. 
 
 " Put ozzthe breadth of the walks zzKH, 
 e zz the tabular number for the hexagon— 
 2*598076, xzz the side of the garden zz 
 A R ; then, because in the hexagon CAzz 
 
 : CD z | 4he length of the 
 walks .*. the area of the centre walks, is 
 
 3ax*2 
 
 
 /3x 2 
 
 twice 
 
 formed by the crossing of the roads LM ; 
 the side of which may be found thus, be- 
 cause the least figure of which C is the 
 centre is a heptagon, the sides of which 
 being produced to the apex K, will form a 
 triangle equal, and equiangular to those 
 within, of which the figure is composed • 
 but they are equilateral, and their angles are 
 — 60 u .*. the angle RLH of the triangle 
 K L H, is zz 60°. Now by Trig. As the 
 natural sine of the Z K L Hzz60°zz 86603 ; 
 K Hzz2 : : the / HKL zz 90 zz 100000 ; 
 H L zz 2 30881J4, which let zz b ; then 
 
 /3x a 
 
 6 a J — 2 is the are * the centre 
 
 walks : Now to find the area of the outer 
 
 /§ x 2 . 
 
 walk, by similar triangle C 3) zz^/ — * 
 
 A D zz- : : A E zz a : E F or G F zz . 
 
 2 /3x j 
 
 •J 4 
 
 zz ~ now this multiplied into A E = a will 
 
 be zz the area of the figure A G F E, be- 
 cause the trian. A E F is zz the trian. A G F; 
 
 — now the outer walk is composed of 6 
 limes x a -f- 6 times the tig, A G F E .*. per 
 question, we have 6ax-j-3a a -i~6a. 
 
 /HZ — 2 a&zz 2 c* s — 12a. 
 v 4 v 4 
 
 — 4a ^ now by dividing by 2 and trans- 
 posing the terms, c x 2 — 3ax — 9a. 
 
 /‘Ax 
 
 s/ 
 
 3 
 
 — _ a 2 -j- a & from which x 8 — 
 
 2 
 
 1'ySi- 3 a\x =* ±. * + 8 
 
 
 c 
 
 /243 
 
 ') 
 
 Let 
 
 — 3 a zz d then is a zz 
 
 /%ab -f- 3 a 2 d 2 d 
 
 V —X + ~+ 3 = 4- 599 feet - 
 
 the side required. 
 
 This question was also answered by Mr. 
 Whitcombej but his answer was 5*575 
 feet. . 
 
 QUESTIONS FOR SOLUTION. 
 
 Quest. 55, proposed by Mr. J. Holroyd, 
 Oldham. 
 
 There are three towns A, B, C, the dis- 
 tance of the towns A, C is 20 miles, and 
 the roads from A, to B and C form a right 
 angle. Now two travellers set out at the 
 same time from the towns A and C, to go 
 to the town B; the traveller in the road 
 A B goes at the uniform rate of 4 miles an 
 hour, and the other at the uniform rate of 5 
 miles an hour, and the former arrives at 
 the town B just half an hour before the 
 other. Required the distance of the towns 
 A, and C, from the town B, geometrically. 
 
 Quest. 56, proposed by Mr. J. Taylor, 
 Clement’s Lane, Lombard Street. 
 
 Fig, the grocer, borrows of Premium a 
 certain sum, and per agreement, pays 
 Premium double the usual annual interest, 
 during Premium’s life : but at his death 
 the principal to be Fig’s. Quere how long 
 ought Premium to live so that Fig will be 
 neither a gainer nor lossr ? 
 

THE 
 
 ARTISAN; 
 
 OR, 
 
 MECHANIC’S INSTRUCTOR. : 
 
 CONTAINING 
 
 A POPULAR, COMPREHENSIVE, AND SYSTEMATIC VIEW OF THE FOLLOWING 
 
 SCIENCES : 
 
 GEOMETRY, 
 
 MECHANICS, 
 
 HYDRODYNAMICS, 
 
 PNEUMATICS, 
 
 OPTICS, 
 
 CHEMISTRY, 
 
 ASTRONOMY, 
 
 ARCHITECTURE, 
 
 PERSPECTIVE, 
 
 ELECTRICITY, 
 
 AND 
 
 MAGNETISM. 
 
 biographical Notices of eminent Scientific Jfttat, 
 
 ENRICHED BY PORTRAITS: 
 
 WITH MANY INTERESTING AND VALUABLE ARTICLES 
 
 * 
 
 RELATING TO 
 
 THE MECHANICAL AND USEFUL ARTS. 
 
 THE WHOLE INTENDED AS A 
 
 COMPANION TO THE INSTITUTES, 
 
 VOL. II. 
 
 LONDON : 
 
 PRINTED FOR WILLIAM COLE, 
 
 10, NEWGATE-STREET. 
 
INDEX 
 
 TO VOLUME THE SECOND, 
 
 GEOMETRY. 
 
 Page 
 
 Propositions, Book 3d. - 1, 33, 65, 97 
 
 MECHANICS, 
 
 Centre of Gyration 
 Forge for Iron 
 Glazier’s Vice ~ 
 Mechanics 
 
 - 5 
 
 - 103 
 
 - 102 
 4, 36, 69, 101 
 
 — — Sugar - - - - 10 
 
 Travelling 104 
 
 Pile Engine - - - - - 71 
 
 Rotation, of Bodies on a fixed Centre 4 
 — — on a moveable Centre - 5 
 
 Wheel Carriages 
 
 Work - 
 
 Wheels, Teeth of - 
 Whirling Table 
 
 - 38, 69 
 - 7 
 
 - 8, 36 
 
 PERSPECTIVE. 
 
 Page 
 
 Arches, Gothic - 131 
 
 Bridge in perspective - 114 
 
 Circles, how represented • - - 86 
 
 Cube, ditto - - - - 113 
 
 Cylinders, to regulate the height of - 130 
 Definitions - - 52 
 
 Hall, to put in perspective - - 129 
 
 Objects, their places determined - 53 
 
 Pavement, how represented - - 86 
 
 Perspective - 52, 85, 115, 129 
 
 — - Aerial - - - - 52 
 
 — Linear - - - 52 
 
 - — — Mechanical - - - 53 
 
 Pyramids, how represented - - 113 
 
 Squares - - - - =85 
 
 Walls, Columns, &c. - - - 113 
 
 Windows - - - - - 115 
 
 — — — — — Gothic - - - 130 
 
 ELECTRICITY. 
 
 Conductors, what 
 
 - 9 
 
 for Buildings - 
 
 - 107 
 
 Electrical Battery 
 
 - 41 
 
 Heat 
 
 - 72 
 
 — — Light 
 
 - 12 
 
 — — — - — Shock 
 
 - 40 
 
 Electricity 9, 
 
 39, 72, 105 
 
 — — Atmospherical 
 
 - 105 
 
 — Induced - 
 
 - 40 
 
 Nature of 
 
 - 9 
 
 _________ Negative 
 
 - 11 
 
 — — - Positive - 
 
 - 11 
 
 Resinous - 
 
 - 12 
 
 — — Vitreous 
 
 - 12 
 
 Electrics, what 
 
 - 9 
 
 Gymnotus, power of 
 
 - 74 
 
 Leyden Jar, what ~ 
 
 - 40 
 
 Lightning, to avoid the effects of - 107 
 
 Non-Conductors, what 
 
 - 9 
 
 — — - Electrics 
 
 - 9 
 
 PNEUMATICS. 
 
 
 Air, resistance of 
 
 - 17 
 
 the Vehicle of Heat, &c. 
 
 - 81 
 
 the Vehicle of Sound 
 
 - 18, 49 
 
 Pneumatics, 
 
 17, 49, 81 
 
 Rain, cause of - 
 
 - 83 
 
 Wind, cause of 
 
 - 51 
 
 MAGNETISM. 
 
 Aurora Borealis, Magnetic - 
 
 - 132 
 
 Dipping Needle ... 
 
 - 133 
 
 Magnetic effects of Iron - 
 
 - 131 
 
 Magnetism, Theory of 
 
 - 131 
 
 — — Positive and Negative 
 
 - 132 
 
 Magnets, Compound 
 
 - 132 
 
 Method of making 
 
 - 134 
 
 — Poles of - 
 
 - 132 
 
 Variation of the Needle - 
 
 - 133 
 
 CHEMISTRY. 
 
 Alkaline and Earthly Metals - - 140 
 
 Amalgam, what 
 
 - 89 
 
 Antimony 
 
 - 
 
 - 136 
 
 Arsenic 
 
 - 
 
 - 138 
 
 Bismuth 
 
 - 
 
 - 136 
 
 Cadmium 
 
 - 
 
 - 135 
 
 Cerium 
 
 
 - 140 
 
 Chemistry 
 
 - 
 
 - 25, 55, 88, 116, 134 
 
 Chromium 
 
 - 
 
 - 138 
 
 Cobalt 
 
 _ 
 
 - 137 
 
 Columbium 
 
 - 
 
 - 139 
 
 Copper 
 
 - 
 
 - 90, 116 
 
 Iridium - 
 
 - 
 
 - 139 
 
 Iron 
 
 
 - 117 
 
 Lead 
 
 _ 
 
 - 120 
 
 Manganese 
 
 - 
 
 - 137 
 
 Mercury 
 
 - 
 
 - 57, 88 
 
 Molybdenum 
 
 - 
 
 - 138 
 
 Nickel 
 
 - 
 
 - 134 
 
INDEX. 
 
 Osmium 
 
 Palladium 
 
 Platina 
 
 Plumbago 
 
 Rhodium 
 
 Selenium 
 
 Silver 
 
 Tellurium 
 
 Tin 
 
 Titanium 
 
 Tungsten 
 
 Uranium 
 
 Wodanium 
 
 Zinc 
 
 Page 
 
 - 139 
 
 - 56 
 
 - 25 
 
 - 118 
 
 - 139 
 
 - 139 
 
 - 25, 55 
 
 - 137 
 
 - 119 
 . 140 
 . 139 
 . 140 
 . 140 
 . 135 
 
 ASTRONOMY. 
 
 Astronomy . . 26, 59, 91, 121, 140 
 
 — — Systems of 141 
 
 Cartesian System .... 142 
 
 Clouds ...... 26 
 
 — Cirro-cumulus . . .27 
 
 — Cirro-stratus . . .27 
 
 — Cumulo-stratus . . .28 
 
 — Nimbus . . . .29 
 
 Earth, motions of the . . . 58 
 
 High Water, method of finding . 124 
 Quantity of matter in the Sun, &c. . 140 
 
 Tides, of the . . . . . - 121 
 
 - — -- Neap ..... 123 
 — — - Spring ..... 122 
 
 BIOGRAPHY. 
 
 Page 
 
 Life of Leibnitz, Godefroy - - 62 
 
 Pascal, Blaise - - - 13 
 
 Simson, Dr. Robert - - 109 
 
 Smeaton, John - - 93 
 
 Stone, Edmund - 127 
 
 Wallis, Dr. John - - 30, 42 
 
 — Wren, Sir Christopher - 74 
 
 MISCELLANEOUS. 
 
 Electricity by Chemical Action - 75 
 Floating Collimator - - - 45 
 
 Hadley’s Quadrant, Description of - 44 
 
 Lunar and Horary Tables - - 111 
 
 Moon, hypothesis respecting the - 78 
 
 Rail Roads - - - - - 46 
 
 Rhabdological Abacus - - - 47 
 
 Rope Bridges in India . - - 46 
 
 Shipwrecks, to save Seamen from - 63 
 Steel, method of softening - - 15 
 
 -, Tempering of - - - 43 
 
 Supports for Minerals . - - 77 
 
 Water, density of - - - 47 
 
 Weather, method of predicting - 76 
 
 Questions and Solutions 16, 32, 48, 
 
 64, 80, 96, 112, 128, 143 
 
 Printed toy W. Cole, 10, Newgate-street. 
 
artisan ; 
 
 MECHANIC’S INSTRUCTOR: 
 
 BEING 
 
 A COMPANION TO THE INSTITUTES. 
 
 ctieoMssTiiir. 
 
 PROPOSITION VII. the greatest, and FD the least of all the 
 
 Theorem. — -If any point be taken in the 
 diameter of a circle, which is not the cen- 
 tre, of all the straig ht lines which can be 
 drawn from it to the circumference, the 
 greatest is that in which the centre is, 
 and the other part of that diameter is the 
 least; and, of any others, that which is 
 nearer to the line passing through the cen- 
 tre is always greater than one more re- 
 mote from it: And from the same point 
 there can be drawn only two straight 
 lines that are equal to one another, one 
 upon each side of the shortest line. 
 
 Let A BCD be a circle, and AD its 
 diameter, in which let any point F be 
 taken which is not the centre : let the cen- 
 tre be E; of all the straight lines F B, FC, 
 F G, &c. that can be drawn from F to the 
 circumference, FA is the greatest, and 
 F D, the other part of the diameter A D, is 
 the least; and of the others, F B is greater 
 than FC, and FC than F G. 
 
 Join B'^E, C E, G E ; and because two 
 sides of a triangle are greater than the 
 third, BE, EF are greater than B F ; but 
 AE is equal to EB ; therefore A E, E F, 
 that is, AF is greater than BF: again, 
 because B E is equal to C E, and F E com- 
 mon to the triangles B EF, C EF, the two 
 sides B E, E F are equal to the two C E, 
 EF; but the angle BEF is greater than 
 the angle C E F ; therefore the base B F is 
 greater than the base F C ; for the same 
 reason, C F is greater than G F. Again, 
 because GF, FE are greater than EG, 
 and EG is equal to ED; GF, FE are 
 greater than E D : take away the common 
 part F E, and the remainder GF is greater 
 than the remainder F D ; therefore F A is 
 Vql. II.— No. 26. 
 
 straight lines from F to the circumference ; 
 and B F is greater than C F, and C F than 
 GF. 
 
 Also there can be drawn only two equal 
 straight lines from the point F to the cir- 
 cumference, one upon each side of the 
 shortest line F D : at the point E in the 
 straight line E F, make the angle FEH 
 equal to the angle GEF, and join FH : 
 Then, because G E is equal to E H, and 
 E F common to the two triangles GEF, 
 HEF; the two sides G E, E F are equal 
 to the two HE, EF; and the angle GEF 
 is equal to the angle HEF; therefore the 
 base F G is equal to the base F H : but 
 besides F H, no straight line can be drawn 
 from F to the circumference equal to F G : 
 for, if there can, let it be F K ; and be- 
 cause F K is equal to F G, and FG to 
 F H, F K is equal to F H ; that is, a line 
 nearer to that which passes through the 
 centre, is equal to one which is more re- 
 mote, which is impossible. Therefore, if 
 any point be taken, &c. Q. E. D. 
 
 B 
 
2 
 
 THE ARTISAN. 
 
 PROPOSITION VIII. 
 
 Theorem If any point be taken without 
 a circle , and straight lines be drawn from 
 it to the circumference, ivhereof one passes 
 through the centre; of those which fall 
 upon the concave circumference , the 
 greatest is that which passes through the 
 centre ; and of the rest , that which is 
 nearer to that through the centre is 
 always greater than the more remote: 
 But of those which fall upon the convex 
 circumference , the least is that between 
 the point without the circle , and the dia- 
 meter ; and of the rest, that which is 
 nearer to the least is always less than the 
 more remote : And only two equal straight 
 lines can be drawn from the point to 
 the circumference , one upon each side of 
 the least. 
 
 Let A B C be a circle, r and D any point 
 without it, from which let the straight 
 lines D A, D E, D F, D C be drawn to the 
 circumference, whereof DA passes through 
 the centre Of those which fall upon the 
 concave part of the circumference A EF C, 
 the greatest is A D which passes through 
 the centre ; and the nearer to it is always 
 greater than the more remote ; viz. D E 
 than D F, and D F than D C : but of those 
 which fall upon the convex circumference 
 HLEG, the least is D G between the 
 point D and the diameter A G ; and the 
 nearer to it is always less than the more 
 remote ; viz. D K than D L, and D L than 
 DH. 
 
 Take M the centre of the circle ABC, 
 and join M E, M F, M C, MK, M L, M H : 
 
 33 
 
 be added to each, A D is equal to EM 
 and M D ; but EM and M D are greater 
 than E D ; therefore also A D is greater 
 than E D. Again, because M E is equal 
 to M F, and M D common to the triangles 
 EMD, FMD: EM, MD are equal to 
 F M, MD ; but the angle EM D is greater 
 than the angle FMD; therefore the base 
 ED is greater than the base F D. In like 
 manner it may be shown, that F D is greater 
 than C D. Therefore D A is the greatest; 
 and D E greater than D F, and D F than 
 DC. 
 
 And because M K, K D are greater than 
 MD, and MK is equal to MG, the re- 
 mainder K D is greater than the remainder 
 G D; that is, G D is less than K D : And 
 because MK, DR are drawn to the point 
 K within the triangle M L D from M D, 
 the extremities of its side M D ; M K, K D 
 are less than ML, L D, whereof M K is 
 equal to ML; therefore the remainder 
 D K is less than the remainder D L : In 
 like manner, it may be shown that D L is 
 less than D H : Therefore D G is the least, 
 and D K less than D L, and D L less than 
 DH. 
 
 Also there can be drawn only two equal 
 straight lines from the point D to the cir - 
 cumference, one upon each side of the 
 least : at the point M, in the straight line 
 M D, make the angle D M B equal to the 
 angle D M K, and join D B ; and because 
 in the triangles KMD, BMD, the side 
 K M is equal to the side B M, and M D 
 common to both, and also the angle 
 KMD equal to the angle B M D, the base 
 DK is equal to the baseDB. But, be- 
 sides D B, no straight line can be drawn 
 from D to the circumference, equal to DK: 
 for, if there can, let it be D N ; then, be- 
 cause D N is equal to D K, and D K equal 
 to D B, D B is equal to D N ; that is, the 
 line nearer to D G, the least, equal to the 
 more remote, which has been shown to be 
 impossible. If, therefore any point, &c. 
 Q. E. D. 
 
 PROPOSITION IX. 
 
 Theorem. — If a point be taken within a cir- 
 cle, from which there fall more than two 
 
 equal straight lines upon the circumfer- 
 ence, that point is the centre of the circle. 
 
 Let the point D be taken within the cir- 
 cle ABC, from which there fall on the 
 circumference more than two equal straight 
 lines ; viz. D A, D B, D C, the point D is 
 the centre of the circle. 
 
 For, if not, let E be the centre, join D E 
 and produce it to the circumference in F, 
 G ; then F G is a diameter of the circle 
 ABC: And because in F G, the diameter 
 of the circle ABC, there is taken the 
 point D which is not the centre, D G shall 
 be the greatest line from it to the circum- 
 ference, and D C greater than D B, and 
 
THE ARTISAN. 
 
 equal, which is impossible : Therefore E 
 is not the centre of the circle ABC: In 
 like manner, it may be demonstrated, that 
 no other point but D is the centre ; D 
 therefore is the centre. Wherefore, if a 
 point be taken, &c. Q. E. D. 
 
 PROPOSITION X. 
 
 Theorem. — One circle cannot cut another 
 in more than two points. 
 
 If it be possible, let the circumference 
 F A B cut the circumference D E F in more 
 
 A 
 
 than two points ; viz. in B, G, F ; take the 
 centre K of the circle ABC, and join KB, 
 K G, K F : and because within the '^circle 
 DEF there is taken the point K, from 
 which more than two equal straight lines ; 
 viz. KB, KG, KF fall on the circum- 
 ference DEF, the point K is the centre 
 of the circle DEF; but K is also the cen- 
 tre of the circle ABC; therefore the same 
 point is the centre of two circles that cut 
 one another, which is impossible. There- 
 fore one circumference of a circle cannot 
 cut another in more than two points. 
 Q. E. D. 
 
 PROPOSITION XI. 
 
 Theorem. — If two circles touch each other 
 internally, the straight line which joins 
 their centres being produced , will pass 
 through the point of contact. 
 
 Let the two circles A B C, A D E, touch 
 
 & 
 
 each other internally in the point A, and 
 let F be the centre of the circle ABC, 
 and G the centre of the circle A D E ; the 
 straight line which joins the centres F, G, 
 being produced, passes through the point 
 A. 
 
 A 
 
 For, if not, let it fall otherwise, if pos- 
 sible, as F G D H, and join AF, A G : And 
 because AG, GF are greater than 'FA; 
 that is, than F H, for FA is equal to FH 
 being radii of the same circle ; take away 
 the common part F G, and the remainder 
 A G is greater than the remainder G H. 
 But A G is equal to G D, therefore G D is 
 greater than GH; and it is also less, 
 which is impossible. Therefore the 
 straight line which joins the points F and 
 and G, cannot fall otherwise than on the 
 point A ; that is, it must pass through A. 
 Therefore, if two circles, &c. Q. E. D. 
 
 PROPOSITION XII. 
 
 Theorem. — If two circles touch each other 
 externally, the straight line which joins 
 their centres will pass through the point 
 of contact. 
 
 Let the two circles ABC, A D E touch 
 each other externally in the point A ; and 
 let F be the centre of the circle ABC, 
 and G the centre of ADE: The straight 
 line which joins the points F, G shall 
 pass through the point of contact A. 
 
 For, if not, let it pass otherwise, if pos- 
 sible, as F C D G, and join FA, AG: 
 and because F is the centre of the circle 
 A B C, A F is equal to F C : Also because 
 
 C is the centre of the circle ADE, A G is 
 equal to GD. Therefore FA, AG are 
 
4 
 
 THE ARTISAN. 
 
 equal to F C, D G ; wherefore the whole 
 F G is greater than F A , A G ; but it is 
 also less, which is impossible : Therefore 
 the straight line which joins the points F, 
 G, cannot pass otherwise than through the 
 point of contact A ; that is, it passes 
 through A. Therefore, if two circles, &c. 
 Q. E. D. 
 
 PROPOSITION XIII. 
 
 Theorem. — One circle cannot touch another 
 in more points thanone 9 whether it touches 
 it on the inside or outside. 
 
 For, if be possible, let the circle E B F 
 
 D 
 
 G 
 
 G 
 
 on the outside in more than one point : For, 
 if it be possible, let the circle A C K touch 
 the circle A B C in the points A, C, and 
 join AC: Therefore, because the two 
 
 KL 
 
 touch the circle A B C in more points than 
 one, and first on the inside, in the points 
 B, D ; join B D, and draw G H, bisecting 
 B D at right angles: Therefore, because 
 the points B, D are in the circumference 
 of each of the circles, the straight line 
 B D falls within each of them ; and their 
 centres are in the straight line G H, 
 which bisects B D at right angles : There- 
 fore G H passes through the point of .con- 
 tact ; but it does not pass through it, be- 
 cause the points B, D are without the 
 straight line G H, which is absurd : There- 
 fore one circle cannot touch another in the 
 inside in more points than one. 
 
 Nor can two circles touch one another 
 
 points A, C are in the circumference of the 
 circle A C K, the straight line A C which 
 joins them shall fall within the circle 
 A C K : And the circle A C K is without 
 the circle ABC; and therefore the straight 
 line AC is without this last circle ; but, be- 
 cause the points A, C are in the circumfer- 
 ence of the circle A B C, the straight line 
 A C must be within the same circle, which 
 is absurd : Therefore a circle cannot touch 
 another on the outside in more than one 
 point ; and it has been shown, that a cir- 
 cle cannot touch another on the inside in 
 more than one point. Therefore, one cir- 
 cle, &c. Q. E. D. 
 
 MECHANICS. 
 
 ROTATION OFJ BODIES ABOUT A FIXED 
 CENTRE. 
 
 If a system of bodies in one plane, as 
 A, B, C, D, &c. in the following figure 
 
THE ARTISAN. 
 
 5 
 
 fee so connected, as to be immoveable with 
 respect to each other, but moveable about 
 an axis at right angles to the plane, and 
 passing through a given point S ; and if 
 a force act on one of the bodies A, such, 
 that if A were unconnected with the sys- 
 tem, it would receive a different velocity, 
 and move in a direction at right angles to 
 AS: then, if each body be multiplied into 
 the square of its distance from the axis of 
 rotation, the sum of all these products, is 
 to the product of A, into the square of its 
 distance from the same axis, as the velocity 
 Which A would have had if it had been 
 free to move by itself, to the velocity which 
 itthas as a part of the system. 
 
 Hence the momentum of the system re- 
 latively to S, is found, by multiplying each 
 body into the square of its distance from 
 S, and the sum into the velocity at A. 
 
 These propositions hold not only of a 
 system of bodies in one plane, but of a 
 system in different planes, if we suppose 
 perpendiculars drawn from them to the 
 axis of rotation. 
 
 Any system of bodies being given, a 
 -point may be found, in which, if all the 
 bodies were collected, a force applied at 
 any distance from the axis would commu- 
 nicate to the bodies, thus collected, the 
 same angular velocity that it would have 
 communicated to the system in its first 
 condition. 
 
 The point thus found is called the Centre 
 of Gyration. 
 
 As every body may be considered as a 
 system of physical points, it is evident that 
 the preceding propositions are of general 
 application. 
 
 ROTATION ON A MOVEABLE AXIS. 
 
 When the impulse communicated to a 
 body, is in aline passing through its cen- 
 tre of gravity, all the points of the body 
 move forward with the same velocity, and 
 in lines parallel to the direction of the im- 
 pulse communicated. But when the di- 
 rection of the impulse communicated does 
 not pass through the centre of gravity, the 
 body acquires a rotation on an axis, and 
 also a progressive motion, by which its 
 centre of gravity is carried forward in the 
 same straight line, and with the same ve- 
 locity, as if the direction of the impulse 
 had passed through the centre of gravity. 
 
 The progressive and rotatory motion are 
 independent of one another, each being the 
 same as if the other had no existence. 
 
 This is a consequence of the general law, 
 That the quantity of motion estimated in a 
 given direction, is not affected by the 
 action of the bodies on one another. The 
 revolution of a body on its axis arises 
 from an action of this kind, and can neither 
 increase nor diminish the progressive mo- 
 tion of the whole mass. 
 
 The progressive motion if the moving 
 force and the body moved are given, is 
 determined by the principles of Dyna- 
 mics, see page 21, vol. i, and the rotatory 
 motion is computed, as if it were about a 
 fixed axis, by the propositions just laid 
 down. 
 
 When one impulse only is communicated 
 to the body, the axis on which it begins to, 
 revolve, is a line drawn through its centre 
 of gravity, and perpendicular to the plane 
 that passes through that centre, and in the 
 direction of the impulse. 
 
 When a body revolves on an axis, and 
 a force is impressed, tending to make it 
 revolve on another, it will revolve on 
 neither, but on a line in the same plane 
 with them, dividing the angle which they 
 contain, so that the sines of the parts are in 
 the inverse ratio, of the angular velocities 
 with which the body would have revolved 
 about the said axis, separately. 
 
 If a force be impressed on any body, by 
 which it is made to revolve on an axis, the 
 quantity of its momentum, estimated by 
 collecting into one sum all the products of 
 the particles into their velocities, and their 
 distances from the axis of motion, is equal 
 to the momentum of the force impressed, 
 estimated in the same manner. 
 
 Hence, though, in consequence of the 
 rotation of a body on its axis, a change 
 may take place in its figure, or in its in- 
 ternal structure, the total quantity of its 
 momentum will continue the same. 
 
 A body may begin to revolve on any 
 line as an axis, that passes through its 
 centre of gravity ; but it will not continue 
 to revolve permanently about that axis, 
 unless the opposite centrifugal forces ex- 
 actly balance one another. 
 
 A homogeneous sphere may revolve 
 permanently on any diameter, because the 
 opposite parts of the solid, being in every 
 direction equal and similar, the opposite 
 centrifugal forces must be equal ; so that 
 no force tends to change the position of the 
 axis. 
 
 A homogeneous cylinder may revolve 
 permanently about the line which is its 
 geometric axis. It may also revolve per- 
 manently about any line that bisects that 
 axis at right angles ; but it can revolve 
 permanently about no other line, as the 
 centrifugal forces cannot be equal. The 
 same is true with respect to all solids of 
 revolution. 
 
 In every body, however irregular, there 
 are three axis of permanent rotation, at 
 right angles to one another, on any one of 
 which, when the body revolves, the oppo- 
 site centrifugal forces exactly balance one 
 another. These are called the principal 
 axis of rotation. 
 
 This singular theorem was first pro- 
 posed by Segner, in 1775, and first de- 
 
6 
 
 THE ARTISAN. 
 
 monstrated by Albert Euler, in a Memoir, 
 published at Paris in 1760. 
 
 These three axes have also this re- 
 markable property, that the momentum of 
 inertia, with respect to any of them, is 
 either a maximum or a minimum ; that is, 
 it is either greater or less, than if the body 
 revolved about any other axis. The mo- 
 mentum of inertia has already been de- 
 fined, to be the product of every particle 
 into the square of its distance from the 
 axis of rotation. 
 
 OF THE WHIRLING TABLE. 
 
 When a body is retained in a circular 
 orbit, by a force directed to its centre, its 
 velocity is every where equal to that 
 which it would acquire, in falling, by 
 means of the same force, if uniform, 
 through half the radius ; that is, through 
 one fourth of the diameter. This propo- 
 sition affords a very convenient method 
 of comparing the effects of central forces, 
 with those of simple accelerating forces, 
 and deserves to be retained in memory. 
 We may, in some measure, demonstrate 
 its truth, by means of the whirling table : 
 an apparatus, which is constructed for the 
 purpose of exhibiting the properties of cen- 
 tral forces, although it is more calculated 
 for showing their comparative, than their 
 absolute magnitude ; for accordingly as 
 we place the string on the pullies, the 
 
 two horizontal arms may be made to re- 
 volve, either with equal velocities, or one 
 twice as fast as the other. The sliding 
 stages, which may be placed at different 
 distances from the centres, and which are 
 made to move along the arms with as 
 little friction as possible, are in a certain 
 proportion to the weights which are to be 
 raised, by means of threads passing over 
 pullies in the centres, as soon as the centri- 
 fugal forces of the stages with their 
 weights are sufficiently great ; and the 
 experiment is to be so arranged, that when 
 the velocity, having been gradually in- 
 creased, produces a sufficient centrifugal 
 force, both stages may raise their weights, 
 and fly off at the same instant. But for 
 the present purpose, one of the stages 
 only is required, and the time of revolu- 
 tion may be measured by half a second 
 pendulum* We may make the force, or 
 the weight to be raised, equal to the 
 weight of the revolving body ; and we 
 shall find that this body will fly off, when 
 its velocity becomes equal to that, w r hich 
 would be acquired by any heavy body, in 
 falling through a height equal to half the 
 distance from the centre, and as much 
 greater, as is sufficient for overcoming the 
 friction of the machine. 
 
 The following figure represents a ma- 
 chine of this kind. 
 
 The arms A B and C D, are made to re- 
 volve on the axis EFandOH, by the 
 string passing over the wheel I, the upper 
 or under pulley of either axis being em- 
 ployed at pleasure ; the stages K and L, 
 with their weights, are placed at certain 
 distances from the centre, by means of the 
 racks or teeth below them ; they move 
 along the arms by means of friction wheels 
 resting on wires, and they raise the 
 weights M and N, by means of threads 
 passing each over two pullies. 
 
 It may also be demonstrated, that when 
 bodies revolve in equal circles, their cen- 
 trifugal forces are proportional to the 
 
 squares of their velocities. Thus, in the 
 whirling table, the two stages being equally 
 loaded, one of them, which is made to re- 
 volve w ith twice the velocity of the other, 
 will lift four equal weights, at the same 
 instant that the other raises a single one. 
 But when two bodies revolve with equal 
 velocities at different distances, the forces 
 are inversely as the distances; conse- 
 quently, the forces are, in all cases, di- 
 rectly as the squares of the velocities, and 
 inversely as the distances. 
 
 If two bodies revolve in equal times at 
 different distances, the forces by which 
 they are retained in their orbits, are simply 
 
THE ARTISAN. 
 
 t 
 
 as the distances. If one of the stages of 
 the whirling table De placed at twice the 
 distance of the other, it will raise twice as 
 great a weight, when the revolutions are 
 performed in the same time. 
 
 In general, the forces are as the dis- 
 tances directly , and as the squares of the 
 times of revolution inversely. Thus the 
 same weight revolving in a double time, at 
 the same distance, will have its effect re- 
 duced to one fourth ; but at a double dis- 
 tance, the effect will again be increased to 
 half of its original magnitude. 
 
 From these principles, may be deduced 
 the law discovered by Kepler, in the mo- 
 tions of the planetary bodies, and after- 
 wards demonstrated by Newton from me- 
 chanical considerations; but this subject 
 will be fully treated under the head of 
 Astronomy. 
 
 We may, however, state here, that ano- 
 ther important law, which was discovered 
 by Kepler, may, in some measure, be 
 shown by an experiment on the revolution 
 of a ball, suspended by a long thread, and 
 drawn towards a point, immediately under 
 the point of suspension, by another thread, 
 which may either be held in the hand, or 
 have a weight attached to it. 
 
 The law here alluded to is, that the 
 right line joining a revolving body, and its 
 centre of attraction, always describes equal 
 areas in equal times. 
 
 Thus, the bail A, revolving round B, 
 
 and being drawn towards it by means of 
 the thread B C, with a force variable at 
 pleasure, its velocity may be observed to 
 vary, according to its distance from the 
 point B, which must always be the case ; 
 otherwise, the areas described could not 
 be equal, in equal portions of time. 
 
 OF WHEEL WORK. 
 
 In treating of the simple mechanical 
 power, called the Wheel and Axle, (Vol. i. 
 p. 86), we stated that motion was communi- 
 cated from one wheel to another, either by 
 belts and straps passing over them, or by 
 teeth cut in the circumference of each, and 
 working in one another. We shall now 
 enter a little more fully into the subject, 
 and endeavour to explain some of the 
 most useful principles, upon which this 
 branch of practical mechanics depends, 
 and also to point out the various methods 
 of applying this mechanical power, in the 
 motion of different kinds of machinery. 
 
 Where a broad strap runs on a wheel, it 
 is usually confined to its situation, not by 
 causing the margin of the wheel to pro- 
 ject; but, on the contrary, by making the 
 middle prominent, as represented by the 
 following wheel or pulley, on which 
 
 a broad strap runs, the surface being 
 convex ; the wheel which drives it is of 
 a similar form ; but its upper part only 
 is shown in the figure. 
 
 The reason of the middle being made pro- 
 minent, may be understood, by examining 
 the manner in which a tight strap, running 
 on a cone, would tend to run towards its 
 thickest part. Sometimes also pins are 
 fixed in the wheels, and admitted into per- 
 forations in the straps; a mode only prac- 
 ticable, where the motion is slow and 
 steady. A smooth motion may also be ob- 
 tained, with considerable force, by form- 
 ing the surfaces of the wheels into brushes 
 of hair. More commonly, however, the cir- 
 cumferences of the contiguous wheels are 
 formed into teeth, impelling each other, as 
 with the extremities of so many levers, 
 either exactly, or nearly in the common 
 direction of the circumferences ; and some- 
 times an endless screw is substituted for 
 one of the wheels. 
 
THE ARTISAN. 
 
 In forming the teeth of wheels, it is of the opposite tooth, so as to produce'an 
 of consequence to determine the curva- equable angular motion in both wheels: 
 ture which will procure an equable com- the other method is, to form all the sur- 
 munication of motion, with the least pos- faces into portions of the involutes of cir- 
 sible friction. For the equable com- cles, or the curves described by a point of 
 munication of motion, two methods have a thread, which has been wound Tound 
 been recommended ; one, that the lower the wheel, while it is uncoiled ; and this 
 part of the face of each tooth should method appears to answer the purpose, in 
 be a straight line in the direction of an easier and simpler manner than the 
 the radius, and the upper, a portion of an former. The following figure represents 
 epicycloid ; that is, of a curve described the teeth, &c. of two wheels, formed into 
 by a point of a circle rolling on the wheel, involutes of circles, described by uncoil- 
 of which the diameter must be half that of ing a thread from the dotted circles; the 
 the opposite wheel ; and in this case it is point of contact of the teeth being always 
 demonstrable, that the plane surface of in the straight line, which touches both 
 each tooth will act on the curved surface circles. 
 
 It may be experimentally demonstrated, them to act on other teeth without friction, 
 that an equable motion is produced by the In order to diminish it as much as pos- 
 action of these curves on each other; if sible, the teeth must be as small and as 
 we cut two boards into forms, terminated numerous, as is consistent with strength 
 by them, divide the surfaces by lines into and durability; for the effect of friction 
 equal or proportional angular portions, always increases, with the distance of the 
 and fix them on any two centres, we shall point of contact, from the line joining the 
 find, that as they revolve, whatever parts centres of the wheels. In calculating the 
 of the surfaces may be in contact, the cor- quantity of the friction, the velocity with 
 Responding lines will always meet each which the parts slide over each other, has 
 other. generally been taken for its measure: this 
 
 Both of these methods may be derived is a slight inaccuracy of conception, for 
 from the general principle, that the teeth the actual resistance is not at all increased 
 of the one wheel must be of such a form, by increasing the relative velocity; but 
 that their outline may be described by the tbe effect of that resistance in retarding 
 revolution of a curve upon a given circle, the motion of the wheels, may be shown 
 while the outline of the teeth of the other fr° m the general laws of mechanics, to be 
 wheel, is described by the same curve re- proportional to the relative velocity thus 
 volving within the circle. It has been ascertained. 
 
 supposed by some of the best authors, that When it is possible to make one wheel 
 the epicycloidal tooth, has also the ad- act on teeth fixed in the concave surface of 
 vantage of completely avoiding friction ; another, the friction may be thus dimin- 
 fhis is, however, by no means true, and it ished in the proportion of the difference of 
 is e en impracticable to invent any form the diameters to their sum. 
 ior the teeth of a wheel, which will enable 
 
THE artisan: 
 
 ELECTRICITY. 
 
 r The phenomena of electricity are as 
 amusing and popular in their form and 
 appearances, as they are intricate and ab- 
 struse in their nature. 
 
 In examining these appearances, a phi- 
 losophical observer will not be content 
 with such exhibitions as dazzle the eye 
 for a moment, without leaving any impres- 
 sion that can be instructive to the mind, 
 but he will be anxious to trace the connec- 
 tion of the facts wdth their general causes, 
 and to compare them with the .theories 
 which have been proposed to account for 
 them ; and though the doctrine of electri- 
 city is, in many respects, yet in its infancy, 
 we shall find that some hypothesis may be 
 assumed, which are capable of explaining 
 the principal circumstances in a simple 
 and satisfactory manner, and which are 
 extremely useful, in connecting a multi- 
 tude of detatched facts into an intelligible 
 system. These hypotheses, founded on 
 the discoveries of Franklin, have been 
 gradually formed into a theory, by the 
 investigations of Aepinus, Cavendish, 
 Priestly, Cavallo, combined with the ex- 
 periments and inferences of Lord Stan- 
 hope, Coulomb, Robison, and others. 
 
 Some bodies acquire by friction, or rub- 
 bing, the power of attracting and repelling 
 certain other bodies. This power is called 
 electricity, and was discovered by the 
 ancients first in ( electrum ) amber. 
 
 The effects of this fluid are distinguished 
 from those of all other substances, by an 
 attractive or repulsive quality, which it 
 appears to communicate to different bodies ; 
 and which differs in general from other 
 attractions and repulsions, by its imme- 
 diate diminution or cession, when the 
 bodies, acting on each other, come into 
 contact, or when they are touched by other 
 bodies. 
 
 Many substances are possessed of this 
 property; such as glass, sealing wax, agate, 
 and almost all the precious stones. 
 
 These bodies attract others, which are 
 very light, as feathers, hairs, &c. The 
 sphere or extent of this attraction is several 
 feet ; but it varies with the state of the 
 weather, being greatest in hot dry weather: 
 in warm moist weather, it is very weak. 
 This virtue is excited by rubbing with the 
 hand, or with a piece of cloth ; but cannot 
 be produced by the warmth of fire. This 
 virtue exerts itself in vacuo, as well as in 
 air. 
 
 If a'glass rod be rubbed with the dry 
 hand, or with apiece of silk, in a short 
 
 time,' spark3 or flashes of light will dar 
 from its surface, and will attract ligh 
 substances in the same manner as sealing 
 wax. The metals possess none of these 
 properties. 
 
 The substances possessing these pro- 
 perties are termed Electrics; and those 
 incapable of being excited, or of producing 
 these effects, non electrics. 
 
 If an electric be under excitation, and 
 then a non electric brought near it, or in 
 contact with fit, the electricity in the 
 former will be carried off by the latter. 
 
 But if an electric be applied in the 
 same manner, to one that has been ex- 
 cited, it will not withdraw the electricity. 
 
 From this arises another distinction of 
 bodies into conductors, and non-con- 
 ductors. 
 
 The latter, or non-conductors, being the 
 same as electrics, and conductors the 
 same as non-electrics. 
 
 Glass, resinous substances, sulphur, 
 oils, hemp, silk, and the airs or gases, 
 are non-conductors. The principal con- 
 ductors or non-electrics, are metals, saline 
 and earthy substances, and water. 
 
 If the electric which is subjected to fric- 
 tion be insulated ; that is, supported on 
 another electric, or non-conductor, the 
 quantity of electricity evolved is incon- 
 siderable, and is soon limited. But if a 
 communication of it with the earth be 
 established, by the medium of a con- 
 ductor, it will afford electricity as long as 
 the friction is continued ; and a conductor 
 insulated, if placed before the electric, 
 will receive the electrical power, and re- 
 tain it till another conductor be applied 
 to it. 
 
 On another conductor being applied to 
 it, the accumulated electricity will be in- 
 stantly carried off, and in this way a 
 stream of electricity can be obtained. 
 
 On these principles the common elec- 
 trical machine is constructed. 
 
 It consists of a glass cylinder, which is 
 made to revolve against a cushion called 
 the rubber, supported on a glass pillar, 
 but connected with the earth by a metal 
 chain ; a large metallic tube, containing a 
 number of sharp pointed wires, named the 
 prime conductor, is placed before the 
 cylinder, and insulated, by being sup- 
 ported on a pillar of glass : the electricity 
 is produced by the friction of the cylinder 
 against the cushion or rubber, and is col- 
 lected by the prime conductor ; and on the 
 approach of any conducting substance, in- 
 stantly passes off under the form of a 
 spark. 
 
 The following figure represents an elec- 
 trical machine on Mr. Nairn’s construction. 
 
10 
 
 THE ARTISAN. 
 
 A is the cylinder of glass ; B the cushion 
 or rubber ; C the silk flap ; D the negative 
 conductor; E the positive conductor; F 
 a ball connected with the internal coating 
 of a glass jar, contained in the conductor. 
 
 The conductors are insulated by varnished 
 rods of glass. 
 
 The following figure represents a plate 
 machine. 
 
 Here A and B are the rubbers, which 
 are usually double ; CD are double flaps 
 of oiled silk, for confining the electricity ; 
 and E is the prime conductor. 
 
 The most convenient size of an electrical 
 machine, and one that is capable of pro- 
 ducing a sufficient quantity of electricity, 
 for exhibiting most of the properties and 
 effects of this wonderful fluid, consists of 
 a cylinder, about eighteen inches long and 
 fourteen in diameter. The two conductors 
 should be of copper or tin, very smooth, 
 round, and without points or edges, ex- 
 cept the points which are intended to take 
 off the electricity from the glass cylinder. 
 They should be as long as the cylinder, and 
 about eight or nine inches in diameter. The 
 cushion, which is fixed to the negative 
 conductor, should be of red leather, about 
 ten inches long, and stuffed evenly with 
 
 curled hair. It should be fixed, so as to 
 lie flat to the cylinder ; and on its under 
 side must be sewed a piece of the above 
 leather, ten inches wide, and five inches 
 long ; and at the same place a piece of 
 black silk, about ten inches wide and six- 
 teen long, to reach nearly over the cylin- 
 der to the prime conductor. A row of 
 points, eight or ten in number, must 
 project from the prime conductor, each 
 about the length of common pins, whose 
 points must be as near the glass cylinder 
 as possible, without touching it : both ends 
 of the cylinder, as well as the two con- 
 ductors, must be supported on solid glass 
 pillars, as already stated. The pillar 
 which supports the cushion or rubber, 
 should be fastened on a piece of board 
 that should slide in a groove, and be fixed 
 by a wooden screw to the board that sup- 
 
THE ARTISAN. 
 
 II 
 
 Electricity then, is excited by the friction These electrics also present the electric 
 of an electric ; but different electric, and light under different forms, 
 even the same electric under different cir- The appearance of the electrical light of 
 cumstances, exhibits different appearances a point enables us to distinguish the nature 
 under a state of excitation, and this gives 0 f the electricity with which it is charged ; 
 rise to the important distinction of two a pencil of light, streaming from the point, 
 forms of electricity, named positive and indicating that its electricity is positive, 
 negative. while a luminous star, with a few di- 
 
 If a glass rod be excited by friction with verging rays, shews that it is negative, 
 a woollen cloth, it will attract light sub- The sparks exhibited by small balls, 
 stances, as, a bit of cork ; the cork is first differently electrified, have also similar va= 
 attracted, but in a short time it is repelled, r i e ties in their forms according to the na- 
 and is not again attracted until it has ture of their charges. These appearances 
 touched some conducting substance. are we ll represented by the following 
 
 But if a rod of sealing-wax has been fig Ure ; 
 excited by friction, with the cloth, the 
 
12 
 
 TH£ ARTISAN. 
 
 Here A is a spark passing between a 
 negative and a neutral ball ; B, between a 
 neutral and positive ball ; C, between a 
 negative and a positive ball. D, two 
 sparks between a negative and a positive 
 cylinder, each of the same form as if it 
 were passing singly from the end of a 
 charged to the side of a neutral cylinder. 
 
 If a pointed conductor, as a needle, be 
 presented to the glass, a round lucid point 
 appears on its extremity in the dark ; but 
 if presented to the wax, a pencil of rays 
 seems to issue from the needle. 
 
 And if two bodies in these two different 
 states be brought into contact, or be made 
 to communicate by means of a conductor, 
 the electricity in the one appears to neu- 
 tralize that in the other, and the electrical 
 appearances cease. The one of these 
 electricities being first obtained from glass, 
 was named vitreous, and the other from 
 resinous bodies, such as wax, amber, &c. 
 was named resinous electricity : — and were 
 regarded as different. It was discovered 
 however, that, when two electrics are rub- 
 bed against each other,' the one always ac- 
 quires the one electricity, and the other 
 the other. Thus, in the common electrical 
 machine, when the cushion is insulated, 
 on friction being produced, it exhibits 
 what has been named the resinous electri- 
 city, while the glass yields the vitreous ; 
 and by certain management the same elec ■ 
 trie may be made to exhibit either electri- 
 city, glass the resinous, and sulphur or 
 sealing-wax the vitreous.* 
 
 From these facts Dr. Franklin was led 
 to deny that there was two different kinds 
 of electricity ; and stated that there exists 
 
 * This is by using a rubber of a different substance. 
 
 only one agent by which they are pro- 
 duced. To the two varieties just stated, 
 he gave the names of plus and minus, or 
 positive and negative. The vitreous he 
 called positive, and the resinous he called 
 negative electricity. This division ac- 
 counted so w ell for the discharge of the 
 Leyden phial, that electricians have, in 
 general, preferred it, on account of its 
 simplicity. These two electricities there- 
 fore are regarded as the opposite of each 
 other ; and when the equilibrium of these 
 forces is destroyed, the electric fluid is put 
 motion ; those bodies which allow the 
 fluids a free passage, are called perfect 
 conductors ; but those which impede its 
 motion, more or less, are imperfect con- 
 ductors For example : while the electric 
 fluid is received into the metallic cylinder 
 of the electrical machine, its accumulation 
 may be prevented,, by the application, of 
 the hand to the cylinder which receives it, 
 and it will pass off through the person 
 of the operator to the ground; hence the 
 human body is called a conductor. But 
 when the metallic cylinder, or prime con- 
 ductor, of the machine is surrounded only 
 by dry air, and supported by glass, the 
 electric fluid is retained, and its density 
 increased, until it becomes capable of 
 procuring itself a passage some inches in 
 length, through the air, which is a very 
 imperfect conductor. 
 
 If a person connected with the prime 
 conductor, be placed on a stool with glass 
 legs, the electricity will no longer pass 
 through him to the earth, but may be so 
 accumulated as to make its way to any 
 neighbouring substance which is capable 
 of receiving it, exhibiting a luminous ap- 
 pearance, called a spark ; and a person, 
 or any other substance, so placed as to be 
 in contact with non-conductors only, is 
 said to be insulated. When electricity is 
 abstracted from substances thus insulated, 
 it is said to be negatively electrified, but 
 the sensible effects are nearly the same, 
 except that in some cases the form of the 
 spark is a little different, as already ob- 
 served above. 
 
 Perfect conductors, when electrified, 
 are in general either overcharged or under- 
 charged with electricity in their most 
 distant parts at the same time ; but non- 
 conductors, although they have an equal 
 attraction for the electric fluid, are often 
 differently affected in different parts of 
 their substances : even when those parts 
 are similarly situated in every respect, 
 except that some of them have had their 
 electricity increased or diminished by a 
 foreign cause. This property of non- 
 conductors may be illustrated by means 
 of a cake of resin, or a plate of glass, to 
 which a local electricity may be commu- 
 nicated in any part of its surface, by the 
 
THE ARTISAN. 
 
 IS 
 
 contact of an electrified body ; and the 
 parts, thus electrified, may afterwards be 
 distinguished from the rest, by the at- 
 traction which they exert on " small 
 particles of dust or powder projected near 
 them : the manner in which the particles 
 arrange themselves on the surface, indica- 
 ting also, in some cases, the species of 
 electricity, whether positive or negative, 
 that has been employed ; positive electri- 
 city producing an appearance somewhat 
 resembling feathers ; and negative electri- 
 city an arangement more like spots. The 
 inequality in the distribution of the elec- 
 tric fluid in a non-conductor may remain 
 for some hours, or even some days, con- 
 tinually diminishing, till it becomes im- 
 perceptible. 
 
 fHiseellaneous Subjects. 
 
 MEMOIR OF THE LIFE OF BLAISE 
 PASCAL. 
 
 Blaise Pascal was born at Clermont, in 
 Auvergne, on the 19th of. June, 1623. 
 Etienne Pascal, the father, was first presi- 
 dent of the Cour-des-aides in Clermont, and 
 discharged the duties of his office with a 
 probity and discretion analogous to the 
 calm and amiable virtues of his private 
 character. 
 
 His son Blaise, discovered from his 
 earliest years a purity of disposition and a 
 power of understanding calculated to sa- 
 tisfy the fondest parent. Gifted with a re- 
 tentive memory and a surprising acuteness 
 of apprehension, he made rapid progress 
 in every species of polite literature to 
 which his faculties were applied. The 
 aptitude he showed for the exact sciences 
 was still more wonderful. The attention 
 of thinking men was now awakened to 
 those subjects by the discoveries of Galileo, 
 which had already begun to operate the 
 changes so sensibly felt before the century 
 was concluded. Roberval, Carcavi, with 
 a number of other scientific men at Paris, 
 among whom was Etienne Pascal, had 
 formed themselves into a kind of society 
 for discussing such matters ; they met at 
 each other’s houses, subject to no law 
 but the pleasure they felt in [usefully 
 communicating their discoveries or in- 
 formation ; a pleasure which they con- 
 tinued to enjoy in this natural and sim- 
 ple form, till a royal charter (in 1656) con- 
 verted this friendly club into the Academie 
 des Sciences. 
 
 Young Pascal listened with a boundless 
 curiosity to what passed when the meeting 
 was held at his father’s. The conversation 
 excited all his energies towards an object 
 fitted for his intellect, and recommended 
 to his imagination by the esteem it gained 
 
 from all whose opinion he honoured most 
 highly. A Treatise on Soujid , written at 
 the age of eleven, might have gratified his 
 father’s partiality, had it not been feared 
 that so ardent a devotion to mathematics 
 might cut off the hope of progress in other 
 branches of learning more suited to his age 
 and capacity. Blaise was therefore en- 
 joined to attend exclusively to language, as 
 a pursuit more profitable in its conse- 
 quences, and better fitted for one of his 
 years ; while, in order to sweeten the dis- 
 appointment, an assurance vvas given, that 
 if once Greek were mastered, he should 
 be allowed immediately to begin geometry, 
 concerning which it was enough for him 
 at present to know that its object lay 
 in examining the properties of figures, and 
 pointing out the various relations that sub- 
 sist among their several dimensions. But 
 the proffered hope was too distant for 
 soothing the boy’s impatience, which this 
 vague and general description now served 
 to direct and inflame. Blaise spent his 
 play-hours by himself in a remote room ; 
 he traced a variety of circles, triangles, 
 and squares, on the floor, with a piece of 
 charcoal ; he arranged and combined them 
 as fancy or judgment prompted ; and, 
 without the help of an instructor, of de- 
 finitions, or even of language, he is said to 
 have actually discovered the truth of 
 Euclid’s thirty-second proposition, that all 
 the angles of any triangle are measured by 
 arcs, which together amount to a semi- 
 circumference. His father detected the 
 circumstance, and consented with tears of 
 joy no longer to withstand the cultivation 
 of a talent, which his son had shown so 
 decided a disposition and so extraordinary 
 a power to improve. The study of mathe- 
 matics, commenced under such auspices, 
 was carried on with a corresponding suc- 
 cess. The young man read Euclid by his 
 own exertions without difficulty at the age 
 of twelve ; and, four years after, he com- 
 posed what was then considered an admi- 
 rable treatise on Conic Sections. But his 
 efforts were soon directed to higher objects 
 than learning, or even improving, what 
 others had discovered. Enjoying the sin- 
 gular advantage of being permitted to give 
 himself up without reserve to the prosecu- 
 tion of science, his ardent mind advanced 
 with gigantic steps in this career. He 
 profited by intercourse with the society 
 which had originally kindled his enthu- 
 siasm, and soon repaid them by investiga- 
 tions of his own. 
 
 In 1641, a change in his father’s circum- 
 stances caused young Pascal to change his 
 residence to Rouen, where he soon distin- 
 guished himself by the invention of his fa- 
 mous arithmetical machine. The present is 
 not a fit place for describing this curious 
 contrivance : its object was, to perform the 
 
14 
 
 THE ARTISAN. 
 
 operations of multiplying and dividing by 
 a combination of cylinders, marked with 
 certain columns of numbers, and turned by 
 wheel- work. The object was gained, 
 theoretically speaking ; but the complexity 
 of the instrument, and the facilities at- 
 tached to the use of logarithms, rendered 
 it inapplicable to practical purposes. — 
 Like the simpler calculating machine of 
 Leibnitz, it remains a wonderful but use- 
 less proof of its author’s ingenuity. 
 
 Pascal’s inventive powers were not long 
 after exhibited in a way as striking, and 
 far more beneficial to the cause of know- 
 ledge. We need not detail the circum- 
 stances which led Galileo to doubt the 
 truth of Nature’s abhorring a vacuum, or 
 Torricelli to maintain, that the ascent of 
 water in the sucking pump, or of mercury 
 in a glass tube free of air, is due to the 
 unbalanced weight of an atmospheric 
 column pressing on the external fluid. 
 Torricelli died in 1646, before the truth 
 of his conclusion could be firmly establish- 
 ed. The experiments, but not the in- 
 ference, were casually reported to Pascal, 
 who repeated them with important varia- 
 tions, and asserted the same opinion in a 
 small work published next year, under the 
 title of Experiences nouvelles touchant le 
 vuide. Yet the victory was not tamely 
 yielded. A subtle matter, aerian spirits, 
 every argument or hypothesis which the 
 bad philosophy of the time could furnish, 
 was employed to support the falling horror 
 of a vacuum ; the Jesuit Noel had pub- 
 lished his objections, when Pascal was 
 lucky enough to devise an experiment 
 which set the matter completely at rest. 
 If the mercury were suspended by the 
 weight of the superincumbent atmosphere, 
 it was evident that the quantity suspended 
 must diminish, as the weight, and conse- 
 quently as the height, of that atmosphere 
 diminished ; hence, if Torricelli’s view of 
 the subject were correct, the fluid must 
 sink as it approached a higher level and 
 carried less air above it : if the mercury 
 were not so suspended, or if the atmos- 
 phere were destitute of weight, no such 
 effect would follow ; and at the top of the 
 highest elevation, the fluid would rise 29 
 inches above its external level, exactly as 
 it \did at the bottom. Pascal fixed upon 
 his native mountain, the Puy-de-Dome, for 
 exemplifying those reasonings ; and being 
 confined by ill health, he committed the 
 execution of the project to M. Perier, his 
 brother-in-law. It was performed on the 
 19th of September, 1648 ; the mercury 
 rose and fell as he had predicted ; the 
 gravity of the air was proved, and Aris- 
 totle’s maxim destroyed for ever. 
 
 Pascal’s name is indelibly impressed'on 
 the history of the barometer ; it is also 
 closely united with many of the most im- 
 
 portant mathematical and physical in* 
 quiries, which during the next age occu- 
 pied the attention of scientific men. From 
 considering a particular case, he was 
 easily led to investigate the general prob- 
 lem relating to the equilibrium of fluids ; 
 his principle demonstrated in two different 
 ways, and the curious details which ac- 
 company it, were published after his 
 death, in the Traits sur Vequilibre des li- 
 queurs, and the Traite sur la pesanteur de 
 la masse de Vair. The solution of two 
 questions proposed by an ignorant game- 
 ster, the Count de Mere, laid a foundation 
 for the modern doctrine of probabilities : 
 his various geometrical tracts are unfortu- 
 nately lost ; but enough is known of his 
 Arithmetical triangle to show, that if his 
 purusits had been continued, the author of 
 so beautiful an invention might have an- 
 ticipated some of the most brilliant dis- 
 coveries of a subsequent age. 
 
 But the incessant application which pro- 
 duced results of such variety and extent, 
 produced another consequence equally in- 
 evitable, the loss of health, with all its 
 attendant evils. From his 19th year, 
 Pascal had laboured under the effects of 
 excessive study ; in 1647, he was seized 
 with a paralysis, which for three months 
 almost entirely took away the use of his 
 limbs. The family now returned to Paris, 
 and forced him in some degree to relax his 
 efforts. 
 
 One day in the month of October, 1654, 
 having gone out as usual to take the air in 
 a carriage, he was proceeding- over the 
 Seine by the bridge of Neuilly, when the 
 two foremost horses taking fright at a 
 spot where the parapet was wanting, 
 rushed furiously onward and plunged 
 headlong into the river. Providentially 
 their traces gave way ; the hindmost pair 
 stood shuddering on the verge, and were 
 led back unhurt. But the shock which 
 such an awful occurrence must have com- 
 municated to the feeble frame of Pascal, 
 may easily be conceived. He recovered with 
 difficulty from a long swoon ; the precipice 
 was for weeks continually present to his 
 imagination ; it haunted his dreams, and 
 occasioned waking visions, one of which, 
 in particular, made such an impression, 
 that he wrote an account of it, and wore 
 the paper ever after between the cloth and 
 the lining of his coat. By degrees, how- 
 ever, these alarming effects subsided ; they 
 were followed by others of a milder but 
 more permanent nature. He determined 
 to employ his remaining days in religious 
 meditation. The example of his sister 
 Jacqueline gave strength to this resolution, 
 and perhaps invited him to Port-Royal in 
 fulfilment of it. Here, in the company of 
 Arnaud, Saci, Nicole, and a few others of 
 similar habits, he spent most of his time 
 
THE ARTISAN. 
 
 IS 
 
 not indeed as a member of the establish- 
 ment, but as a visitor, whose stay was 
 sometimes lengthened to many months. 
 
 In this retreat, endeared by the sanctity 
 of its object, and enlivened by the society 
 of men imbued with kindred opinions, 
 Pascal gradually recovered some tran- 
 quillity ; he enjoyed intervals of compara- 
 tive health, during which fresh triumphs 
 in a new department gave farther proof 
 of the compass and versatility of his 
 powers. 
 
 His thoughts had long flowed exclu- 
 sively in the channel of devotion, and pre- 
 sent circumstances naturally contributed 
 to strengthen this tendency. Yet, before 
 his course was done, the speculations of 
 early life resumed their sway on one occa- 
 sion with a force and effect, which showed 
 that his mathematical powers were di- 
 verted, not destroyed. It was in 1658, 
 when an excruciating tooth-ache had kept 
 him long deprived of sleep, that he hap- 
 pened to recollect some properties formerly 
 discovered by him respecting the cycloid ; 
 and their beauty was such, that, to pro- 
 cure some abstraction from his suffering, 
 he determined to investigate their conse- 
 quences. The results which he obtained, 
 without the aid of modern analysis, are 
 still reckoned by mathematicians among 
 the finest exhibitions of their art. Pascal 
 was advised to publish them by way of 
 challenge, to show that the highest attain- 
 ments in a science of strict reasoning were 
 not incompatible with the humblest belief 
 in the principles of religion. His prob - 
 lems were accordingly announced under 
 the assumed name of Amos Dettonville ; 
 and a premium of forty pistoles was pro- 
 mised to whoever solved them first, of 
 twenty to whoever solved them next. The 
 competition, though graced by some of 
 the first names in Europe, was not success- 
 ful to any. Our countrymen, Wallis and 
 Wren, were among the number ; and the 
 former having failed of success by incor- 
 rectness of execution, rather than by error 
 of principle, accused Dettonville of in- 
 justice in not assigning him the prize. A 
 similar complaint was made, with far less 
 reason, and the very worst success, by 
 the Pere Lallouire, a Jesuit ; and Pascal, 
 to defend himself from such insinuations, 
 soon published his treatise on the cycloid, 
 containing the complete solution, which 
 none of the claimants had succeeded in 
 finding. 
 
 The character of Pascal, considered as 
 a moral or as an intellectual man, affords 
 a bright though unequal specimen of hu- 
 man nature. Uniting a saint-like purity 
 and tenderness of heart, with an under- 
 standing at once fine and capacious, his 
 short existence was marked by the practice 
 
 of benevolence and self-denial, no less than 
 by a series of brilliant discoveries • in the 
 highest regions of philosophy. Though 
 he lived but thirty-nine years, the longer, 
 and what is more important, the latter part 
 of which was spent in almost continual 
 ill-health ; yet such was the excellence of 
 his powers, and sxich the enthusiasm which 
 impelled them, that Pascal’s name is found 
 conspicuously engraven on all the most 
 important scientific achievements of his 
 time ; while, in the nobler parts of litera- 
 ture, he occupies a rank which few of his 
 countrymen have aimed at, and still fewer 
 reached. 
 
 METHOD OF SOFTENING STEEL. 
 
 It is well known that steel acquires 
 hardness from tempering only in proportion 
 as it has been heated red-hot before its 
 immersion in water ; but many persons are 
 not aware, that steel, heated a little above 
 the degree necessary to temper it, becomes 
 soft by that very operation of tempering , 
 and that this process, for nealing it, is 
 much superior to the ordinary methods, 
 since the metal is worked much more 
 easily with the file or burin, and is with- 
 out flaws or rough edges. This process in 
 no way deteriorates it, and it considerably 
 abridges the operation. Common springs 
 are tempered and nealed by two distinct 
 operations : first, they are heated to the de- 
 gree requisite, and then dipped in water or 
 oil, &c., and afterwards softened or nealed 
 by heating them by degrees, till their sur- 
 face when well cleaned, presents a series 
 of colours announcing different degrees of 
 hardness lost. Sometimes the nealing is 
 performed by burning upon the spring the 
 oil in which it has previously been tem- 
 pered. These two operations can be 
 effected at once, in the following manner. 
 
 To heat the steel to the degree required, 
 it must be plunged in a metallic bath, com- 
 posed of a mixture of lead and tin, resem- 
 bling very nearly the solder used by pump- 
 makers. This mixture is heated to the 
 degree required for tempering, by a stove, 
 in which it is placed in a vessel of cast 
 iron ; there is in this bath a pyrometer, to 
 indicate the temperature. Thus the steel 
 is at once tempered and nealed, without 
 any danger of its bending or cracking in 
 the process. 
 
 It would be advisable to heat the steel 
 to be tempered in a red-hot bath of lead, 
 before tempering it in the second metallic 
 bath intended for nealing it. It would 
 thus be heated more uniformly, and be 
 less exposed to oxidation. — ( Ann. de la 
 Soc. d * Agr.) 
 
IQ 
 
 THE ARTISAN. 
 
 SOLUTIONS OF QUESTIONS. 
 
 Quest. 52, answered by G. G. C. 
 
 Con. Let A BC be the given quadrant; 
 
 ■3> 
 
 bisect the angle A B C by the straight line 
 B F, and at the point F draw the indefinite 
 line D E, at right angles to B F ; produce 
 B A and B C to meet E D in the points D 
 and E ; bisect the angle BED, by the 
 straight line E I, then with the centre I 
 and radius I F, describe the circle F G H, 
 which is the circle required. 
 i Demon. Join l F, I G, and I H, and be- 
 cause they are radii of the circle they are 
 all equal ; and because D E is at right 
 angles to the diameter B F, it touches the 
 circle in that point. But the triangles 
 EFI and EGI are equal, for the two 
 sides F I and I E, are equal to the two GI 
 and I E, and the angle F E I is equal to 
 G E I, hence the angle E G I is equal to 
 E F I ; but E F I is a right angle, hence 
 E G I is also a right angle ; therefore EB 
 touches the circle in the point G. In the 
 same manner it may be shown, that the 
 angle I H B is equal to I G B, which is 
 also a right angle, hence the line B D 
 touches the circle in the point H; there- 
 fore a circle has been inscribed in the 
 given quadrant ABC. 
 
 The demonstration of this problem might 
 have been effected differently, by drawing 
 the lines I F, I G, and I H at right angles 
 to the sides of the triangle upon which 
 they fall, and then proving that they are 
 all equal to each other, in which case, a 
 circle described from the centre I. with 
 any of them as a radius, would pass 
 through the points F G H ; therefore the 
 lines B D, B E, and E D, touch the circle 
 in these points. 
 
 The Proposer .sent us a solution to this 
 question ; but though the construction was 
 
 good, the demonstration was not so: fo r 
 all that he attempts to prove is, that two* 
 radii (as I F and I G) are equal. Now it 
 is necessary to show, that three lines, going 
 from the centre to the circumference, are 
 equal ; and that the srtaight lines at their 
 extremities, touch the circle . 
 
 The Proposer’s demonstration would 
 have been inadmissible, had it even been 
 conclusive ; for the first part of it is geo - 
 metrcal and the latter algebraical. 
 
 Now Geometry and Algebra are quite 
 distinct branches of the Mathematics ; and 
 therefore Algebra must be completely ex- 
 cluded from a geometrical demonstration, 
 which was the species of proof required 
 in this problem, as the Proposer must 
 surely know ! 
 
 We received another solution ; but the 
 construction was too complex, and it was 
 unaccompanied by any thing like demon- 
 stration. Ed. 
 
 QUESTIONS FOR SOLUTION. 
 
 Quest. 56, proposed by D. T. Cheapside. 
 
 A grazier has 50 calves, value 21s. each ; 
 if he keep them 3 years, they will cost 10s. 
 the first year, 20s. the second, and 30s. the 
 third, for Summer’s grass; and 15s. the 
 first year, 25s. the second, and 40s. the 
 third, for Winter feeding, after which the 
 cattle will sell at 10 guineas each. Re- 
 quired his gain or loss by bringing them 
 up, supposing one to die each Summer, 
 another each Winter, and allowing simple 
 interest from the end of each year? 
 
 Quest. 57, proposed by G. G. C. Queen- 
 street. 
 
 A and B jointly perform a piece of 
 work in 12 days ; and if the sum of the 
 days in which they could each have sepa- 
 rately done the work, be multiplied by the 
 days in which A alone could have done it, 
 the product will be 1000. Required the 
 time in which each can do it ? 
 
 Quest. 58, proposed by J. D. Ironmonger 
 Lane. 
 
 If a cubic foot of brass were drawn out 
 into wire, ^th of an inch diameter ; re- 
 quired the length of the wire, supposing 
 no loss of the metal ? 
 
THE ARTISAN. 
 
 17 
 
 PNEUMATICS. 
 
 RESISTANCE OF THE AIR. 
 
 The resistance of fluids has long been 
 an important subject of consideration with 
 philosophers. The subject is highly in- 
 teresting, not as serving to show the ab- 
 surdity of exploded theories, but to ex- 
 plain the movements of bodies propelled 
 through the air. 
 
 The term “ resistance,” in regard to 
 retarded motions, is of similar import with 
 the expression “ moving force,” as applied 
 to accelerated motions. The moving 
 force is estimated by the product of the 
 “ tendency” of each particle in a mass, 
 into the number of particles which it may 
 contain, and is synonymous with the word 
 weight in common language. Resistance 
 to a body is measured by its loss of mo- 
 mentum, or is equal to the product of the 
 retardation of each particle into the num- 
 ber of particles. Thus, a body descending 
 in vacuo , its weight is the moving force ; 
 but to an ascending body, its weight is the 
 resistance. 
 
 To a body ascending or descending per- 
 pendicularly through the air, there is a 
 degree of velocity, such, that the retarda- 
 tion consequent upon it, is equal to the 
 accellerating force of gravity. It is, there- 
 fore, obvious, that when a descending 
 body has once acquired this velocity, it 
 can acquire no increase of velocity in its 
 future descent, as the retardation and ac- 
 celeration are equal; hence it has been 
 called the terminal velocity. 
 
 For an iron ball of I pound, the terminal 
 velocity has been found to be 244 feet ; for 
 one of 42 pounds, it is 456 feet. 
 
 In strictness, this velocity cannot be ac- 
 quired till after an infinite time, and a de- 
 scent infinitely long; but the time of acquir- 
 ing any given velocity can easily be 
 assigned. This will be shown in another 
 part of this work. 
 
 The resistance of the air is often many 
 times the weight of a body moving in it. 
 An iron ball, for example, 3 pounds in 
 weight, whose diameter is 2’8 inches, 
 when thrown with a velocity of 1800 feet 
 per second, is resisted by a force equal to 
 176 pounds, which is more than 58 times 
 its own weight. 
 
 The resistance of the air, like every 
 other arrangement of Nature, points out 
 to us the beneficent character, and un- 
 erring wisdom of its Creator. He has 
 formed it of such a density, as is the best 
 possible for supporting animal existence, 
 and at the same time for supplying a due 
 quantity of moisture to the vegetable crea- 
 tion. Had the air been much less dense 
 
 Vol. II.— No. 27. 
 
 than it is, the drops of rain would descend 
 “with such a velocity, as would completely 
 destroy that delicate organization, which 
 they are designed to refresh. The earth 
 would no longer grow green under the in- 
 fluence of the summer showers, but would 
 be converted into a barren waste, where 
 the most hardy plants could not flourish. 
 As at present constituted, even the hea- 
 viest drops of rain are so much retarded 
 in their descent, that they do not injure 
 the tenderest shoot. 
 
 It has been determined by calculation, 
 that the terminal velocity of a drop of 
 rain, whose diameter is T ^th of an inch, is 
 10-48 feet. 
 
 Now, were there no atmosphere, and 
 this particle to drop from the same height 
 as at present, its momentum would be in- 
 comparably greater, and could be sustained 
 by no object without the greatest injury. 
 
 AIR AS THE VEHICLE OF SOUND. 
 
 One of the most remarkable properties 
 of air in motion, is its capacity for trans- 
 mitting sound. The variety and delicacy 
 of the sensations, which are acquired 
 through this medium, are no less admira- 
 ble, than the wise and beautiful arrange- 
 ment by which they are communicated. 
 The first who apppears to have considered 
 this subject in a philosophical point of 
 view, was the illustrious Newton, who ex- 
 plained with very great precision the na- 
 ture of the phenomenon. The continental 
 writers, though they admit his conclusions, 
 have called in question the accuracy of his 
 demonstration. Euler, La Grange, and 
 several others, have engaged in the sub- 
 ject, but have added nothing new to our 
 information ; for they have been under the 
 necessity of restricting themselves to the 
 cases which Newton has supposed. We 
 shall therefore state them in a more detailed 
 manner, than that in which they are deli- 
 vered in the Principia. Sound is produced 
 by a sudden condensation of air, which 
 gradually extends itself in the form of a 
 pulse, or spherical shell, having its den- 
 sity greater than that of the surrounding 
 medium. The first proposition delivered 
 by Newton, concerning these pulses is, 
 that the particles of which they are com- 
 posed, advance from and recede to their 
 state of quiescence, under the influence of 
 a force, which varies as their distance 
 from the point of greatest condensation. 
 He assumes, however, in his reasoning, 
 that the greatest condensation differs only 
 by a very small quantity, from the conden- 
 sation of common air; an assumption 
 which will be found agreeable to fact, ex- 
 cept perhaps in the case of violent explo- 
 sions, where the condensation of the ad- 
 
18 
 
 THE ARTISAN. 
 
 jacent particles will be considerably 
 greater. 
 
 Sound is a motion capable of affecting 
 the ear with the sensation peculiar to that 
 organ. It is not simply a vibration or un- 
 dulation of the air, as it is sometimes 
 called ; for there are many sounds in 
 which the air is not concerned, as when a 
 tuning fork, or any other sounding body, is 
 held by the teeth : nor is sound always a 
 vibration, or alternation of any kind ; for 
 every noise is a sound, and a noise, as dis- 
 tinguished from a continued sound, con- 
 sists of a single impulse in one direction 
 only, sometimes without any alternation; 
 while a continued sound is a succession of 
 such impulses, which, in the organ of hear- 
 ing at least, cannot but be alternate. If 
 these successive impulses form a connected 
 series, following each other too rapidly to 
 be separately distinguished, they consti- 
 tute a continued sound, like that of the 
 voice in speaking ; and if they are equal 
 among themselves in duration, they pro- 
 duce a musical or equable sound, as that 
 of a vibrating chord or string, or of the 
 voice in singing. Thus, a quill striking 
 against a piece of wood causes a noise, 
 but against the teeth of a wheel or of a 
 comb, a continued sound ; and if the teeth 
 of the wheel are at equal distances, and 
 the velocity of the motion is constant, a 
 musical note is produced. 
 
 Sounds of all kinds are most usually 
 conveyed through the medium of the 
 air; and the necessity of the presence 
 of this, or of some other material sub- 
 stance, for its transmission is easily shown 
 by means of the air pump ; for the 
 sound of a bell struck in an exhausted re- 
 ceiver, is scarcely perceptible. The ex- 
 periment is most conveniently performed 
 in a moveable receiver or transferrer, 
 which may be shaken at pleasure, the 
 frame which suspends the bell being sup- 
 ported by some very soft substance, such 
 as cork or wool. As the air is gradually 
 admitted, the sound becomes stronger and 
 stronger, although it is still much weak- 
 ened by the interposition of the glass : not 
 that glass is in itself a bad conductor of 
 sound ; but the change of the medium of 
 communication from air to glass, and again 
 from glass to air, occasions a great diminu- 
 tion of its intensity. It is perhaps on ac- 
 count of the apparent facility with which 
 sound is transmitted by air, that the doc- 
 trine of acoustics has been usually con- 
 sidered as immediately dependant on 
 pneumatics, although it belongs as much 
 to the theory of the mechanics of solid 
 bodies, as to that of hydrodynamics. 
 
 A certain time is always required for the 
 transmission of an impulse through a ma- 
 terial substance, even through such sub- 
 
 stances, as appear to be the hardest and 
 the least compressible. It is demonstra- 
 ble, that all minute impulses are conveyed 
 through any homogeneous elastic medium, 
 whether solid or fluid, with a uniform ve- 
 locity, which is always equal to that which 
 a heavy body would acquire, by falling 
 through half the height of the atmosphere, 
 supposed to be of equal density ; so that 
 the velocity of sound passing through an 
 atmosphere of a uniform elastic fluid, must 
 be the same with that of a wave moving 
 on its surface. In order to form a distinct 
 idea of the manner in which sound is pro- 
 pagated through an elastic substance like 
 air, we must first consider the motion of a 
 single particle, which, in the case of a 
 noise, is pushed forwards, and then either 
 remains stationary, or returns back to its 
 original situation ; but in the case of a mu- 
 sical sound, is continually moved back- 
 wards and forwards, with a velocity 
 always varying, and varying by different 
 degrees, according to the nature or quality 
 of the tone; for instance, differently in the 
 notes of a bell and of a trumpet. We may 
 first suppose, for the sake of simplicity, a 
 single series of particles, to be placed only 
 in the same line with the direction of the 
 motion. It is obvious, that if these par- 
 ticles were sbsolutely incompressible, or 
 infinitely elastic, and were also retained in 
 contact with each other, by an infinite force 
 of cohesion or of compression, the whole 
 series must move precisely at the same 
 time, as well as in the same manner. But 
 in a substance, which is both compressible 
 and extensible, or expansible, the motion 
 must occupy a certain time, in being propa- 
 gated to the successive particles on either 
 side, by means of the impulse of the first 
 particle on those which are before it, and 
 by means of the diminution of its pressure 
 on those which are behind ; so that when 
 the sound consists of a series of alterna- 
 tions, the motion of some of the particles 
 will be always in a less advanced state, 
 than that of others nearer to its source ; 
 while at a greater distance forwards, the 
 particles will be in the opposite stage of 
 the undulation; and still further on, they 
 will again be moving in the same manner 
 with the first particle, in consequence of 
 the effect of a former vibration. 
 
 The situation of a particle at any time, 
 may be represented by supposing it to 
 mark its path, on a surface sliding uni- 
 formly along in a transverse direction. 
 Thus, if we fix a small pencil in a vibrat- 
 ing rod, and draw a sheet of paper along, 
 against the point of the pencil, an undu- 
 lated line will be marked on the paper, 
 and will correctly represent the progress 
 of the vibration. Whatever the nature of 
 the sound transmitted through any medium 
 
THE ARTISAN., 
 
 19 
 
 may be, it may be shown that the path thus 
 described will also indicate the situation 
 of the different particles at any one time. 
 The simplest case of the motion of the par- 
 ticles, is that in which they observe the 
 same law with the vibration of a pendu- 
 lum, which is always found opposite to a 
 point, supposed to move uniformly in a 
 circle: in this case the path described 
 will be the figure denominated a harmonic 
 curve ; and it may be demonstrated, that 
 the force impelling any particle backwards 
 or forwards, will always be represented, 
 by the distance of the particle before or 
 behind its natural place ; the greatest con- 
 densation and the greatest direct velocity, 
 as well as the greatest rarefaction and re- 
 trograde velocity, happening at the instant 
 when it passes through its natural place. 
 
 The least elastic substance that has been 
 examined, is perhaps carbonic acid gas, or 
 fixed air, which is considerably denser 
 than atmospheric air exposed to an equal 
 degree of pressure. The height of the at- 
 mosphere, supposed to be homogeneous, 
 is in ordinary circumstances, and at the 
 sea side, about 28,000 feet, and in falling 
 through half this height, a heavy body 
 would acquire a velocity of 946 feet in a 
 second. But from a comparison of the 
 accurate experiments of Derham, made in 
 the day time, with those of the French 
 Academicians, made chiefly at night, it 
 appears that the true velocity of sound is 
 about 11 BO feet in a second, which agrees 
 very nearly with some observations, made 
 with great care, by Professor Pictet. This 
 difference betweeu calculation and experi- 
 ment, has long occupied the attention of 
 natural philosophers; but the difficulty 
 appears to have been in a great measure 
 removed, by the happy suggestion of 
 Laplace, who has attributed the effect to 
 the elevation of temperature, which is 
 always found to accompany the action of 
 condensation, and to the depression pro- 
 duced by rarefaction. 
 
 This velocity remains unchanged by any 
 alternation of pressure, indicated by the 
 barometer; but it may be affected by a 
 change of temperature. 
 
 The Academicians del Cimento, en- 
 closed an organ pipe, with bellows worked 
 by a spring, in the receiver of an air pump 
 and of a condenser ; and they found that, 
 as long as the sound was audible, its pitch 
 remained unchanged. Papin screwed a 
 whistle on the orifice, which admits the air 
 into the receiver of the air pump; and Dr. 
 Young fixed an organpipein the same man- 
 ner, and the result agreed with the experi- 
 ments of the Academicians. But if the 
 density of the air is changed, while its 
 elasticity remains unaltered, which hap- 
 pens when it is expanded by heat, or con- 
 
 densed by cold, the height of the column, 
 and consequently the velocity, will also be 
 altered ; so that for each degree of Fahren- 
 heit’s thermometer, the velocity will vary 
 about one part in a thousand. 
 
 It does not appear that any direct expe- 
 riments have been made, on the velocity 
 with which an impulse is transmitted 
 through a liquid, although it is well known 
 that liquids are capable of conveying sound 
 without difficulty: Professor Robinson 
 
 informs us, for example, that he heard the 
 sound of a bell transmitted by water 1200 
 feet. It is, however, easy to calculate the 
 velocity with which sound must be propa- 
 gated in any liquid, of which the com- 
 pressibility has been measured. Mr. Can- 
 ton has ascertained, that the elasticity of 
 water is about 22,000 times as great as 
 that of air ; it is, therefore, measured by 
 the height of a column, which is in the 
 same proportion to 34 feet; that is, 750 
 thousand feet, and the velocity correspond- 
 ing to half this height, is 4900 feet in a 
 second. In mercury, also, it appears from 
 Mr. Canton’s experiments, that the velocity 
 must be nearly the same as in water, in 
 spirit of wine a little smaller. 
 
 We have hitherto considered the propa- 
 gation of sound in a single right line, or in 
 parallel lines only ; but it usually happens, 
 at least when a sound is transmitted 
 through a fluid, that the impulse spreads 
 in every direction, like a wave, so as to 
 occupy at any one time nearly the whole 
 of a spherical surface, as represented by 
 the following figure. 
 
 When any obstruction meets these waves 
 they rebound back and produce an echo. 
 
 When the waves strike obliquely upon a 
 reflecting surface, the echo may then be 
 heard, but not the original sound. 
 
 Thus, if a wave as ac in the following 
 figure, 
 
 B 2 
 
strike against the oblique wall d, the 
 sound will be reflected to an ear at m ; and 
 if a hill should intervene between the bell 
 at a, and the ear at m, then will the echo 
 be heard at m , and not the original sound 
 of the bell. We must, however, remark, 
 that it is necessary the reflecting object 
 be at a distance moderately great, other- 
 wise the returning sound will be confused 
 with the original one ; and it must either 
 have a smooth surface, or consist of a 
 number of surfaces, arranged in a suitable 
 form ; thus there is an echo, not only from 
 a distant wall or rock, but frequently from 
 the trees in a wood, and sometimes, as it 
 it is said, even from a cloud. 
 
 If a sound or wave proceed from one 
 focus of an ellipsis, and be reflected at its 
 circumference, it will be directed from 
 every part of the circumference towards 
 the other focus, as represented by the fol- 
 lowing figure. 
 
 The truth of this proposition may be 
 easily shown, by means of the apparatus 
 
 already described, for exhibiting the mo- 
 tions of the waves of water; we may also 
 confirm it by a simple experiment on a dish 
 of tea : the curvature of a circle differs so 
 little from that of an ellipsis of small eccen- 
 tricity, that if we let a drop fall into the cup 
 near its centre, the little wave which is ex- 
 cited will be made to converge to a point 
 at an equal distance on the other side of the 
 centre, see the annexed figure. 
 
 Sound is capable of being condensed in 
 a tube, or speaking trumpet, so as to pene- 
 trate through the air to a great distance, in 
 one line. For all the waves that fly off 
 globularly from a sounding body, are by 
 this trumpet condensed into one line, and, 
 therefore, its force becomes greater than 
 when left at liberty. The annexed figure 
 represents a section of a speaking trumpet, 
 and also of a hearing one ; the lines repre- 
 senting the direction of the sound before 
 and after its reflections. The trumpet has 
 
THE ARTISAN. 
 
 21 
 
 the effect of reflecting the Waves, both in of all the waves that coves the mouth of the 
 receiving and delivering sound ; for waves trumpet: hence its effect in assisting deaf- 
 striking the mouth of the trumpet, B, from ness. If two trumpets, as A and B, be 
 without, become condensed in the tube, and placed in the axis of each other, as in the an- 
 strike an ear at c with the compressed force nexed figure, at forty or fifty feet distance, 
 
 the smallest whisper at a would be heard 
 distinctly by an ear placed at c ; and vice 
 verscL : so that a person might ask a ques- 
 tion at a, and receive an answer from 
 The answers seemingly given by inanimate 
 figures, is a trick founded on this prin- 
 ciple. 
 
 In the case of a vibration, it is found 
 that every chord vibrates in the same man- 
 ner, as if it were a part of a longer chord, 
 composed of any number of such chords, 
 continually repeated in positions alter- 
 nately inverted ; consequently, if a long 
 chord be initially divided into any number 
 of such equal portions, its parts will con- 
 
 tinue to vibrate in the same manner as if 
 they were separate chords ; the points of 
 division only remaining always at rest. 
 Such subordinate sounds are called har- 
 monics: they are often produced in violins, 
 by lightly touching one of the points of 
 division with the finger, when the bow is 
 applied ; and in all such cases it may 1 be 
 shown, by putting small feathers or pieces 
 of paper on the string, that the remaining 
 points of division are also quiescent, while 
 the intervening portions are in motion. 
 This is very well represenied by the fol- 
 lowing figure. 
 
 Hence arise the wild and wonderful fifteenth, &c. A current of air is certainly 
 harmony of the Eolian harp ; for though a delicate fid dlebow, which affords a string 
 the instrument may have twenty strings, an opportunity of dividing itself into a 
 all tuned in unison to one another, yet do number of imaginary bridges, to which it 
 we hear not only the natural sound of each has a natural tendency. Thus, a and b f 
 string, but its octave, fifth, third, twelfth, in the following figure, 
 
 e ; the vibration of a e is thrice, while the 
 whole string is twice ; hence every third 
 wave of a e coincides with every second 
 wave of a b , and produces the concord 
 called a fifth. The remaining part of the 
 string e b, being half the length of a e, is, 
 
 bridges. 
 
 It is curious to observe by a microscope, 
 any luminous point on the surface of a vi- 
 brating chord ; for instance, the reflection 
 of a candle in the coil of a fine wire, wound 
 round it. The velocity of the motion is 
 
22 
 
 THE ARTISAN. 
 
 such, that the path of the luminous point 
 is marked by a line of light, in the same 
 manner as when a burning coal is whirled 
 round; and the figures thus described, 
 are not only different at different parts of 
 the same chord, but they often pass through 
 an amusing variety of forms, during the 
 progress of the vibration ; they also vary 
 considerably, according to the mode in 
 which that vibration is excited. The fol- 
 lowing figure represents a vibration, com- 
 pounded with another smaller vibration, 
 three times as frequent in a transverse 
 direction, the separate vibrations being 
 such, that the points may be always oppo- 
 site to a point moving uniformly in a cir- 
 cle. Thus, the vibrations in the lines A B 
 and A C, compose the complicated figure 
 DE. 
 
 The following figure exhibits a specimen 
 of the manner in which the vibrations of a 
 string are usually performed, when it is 
 struck with a bow. 
 
 OPTICS. 
 
 ON VISION. 
 
 Having given a comprehensive and po- 
 pular view of the general theory of Optics, 
 and also explained the construction and 
 use of optical instruments ; we shall con- 
 clude our observations on this interesting 
 and beautiful branch of Natural Philoso- 
 phy by making a few general remarks on 
 the sources of light and the nature of vi- 
 sion. 
 
 The sources from which light is com- 
 monly derived, are either the sun or stars, 
 or such terrestrial bodies as are under- 
 going those changes which constitute com- 
 bustion. The process of combustion im- 
 plies a change in which a considerable 
 emission of light or heat is produced ; but 
 it is not capable of a very correct defini- 
 tion : in general it requires an absorption, 
 or at least a transfer of a portion of 
 oxygen ; but there appears to be some 
 exceptions to the universality of this dis- 
 tinction; and it has been observed, that 
 both heat and light are often produced 
 
 where no transfer of oxygen takes place, 
 and sometimes by the effect of a mixture 
 which cannot be called combustion. 
 
 Light is also afforded, without any sen- 
 sible heat, by a number of vegetable and 
 animal substances, which appear to be un- 
 dergoing a slow decomposition, not wholly 
 unlike combustion. Thus decayed wood, 
 and animal substances slightly salted, often 
 afford spontaneously a faint light, without 
 any elevation of temperature ; and it is not 
 improbable that the light of the ignus 
 fatuus may proceed from a vapour of a 
 similar nature. 
 
 The effects which are commonly attribu- 
 ted to the motions of the electrical fluid, 
 are often attended by the production of 
 light ; and violent and rapid friction fre- 
 quently seems to be the immediate cause 
 of its appearance. But it is difficult to 
 ascertain whether friction may not be 
 partly concerned in the luminous pheno- 
 mena attributed to electricity, or electricity 
 in the apparent effects of friction. Light 
 is sometimes produced by friction with a 
 much lower degree of heat than is required 
 for combustion, and even when it is accom- 
 panied by combustion, the heat produced 
 by the union of these causes may be very 
 moderate : thus it is usual in some coal 
 mines, to obtain a train of light by the con- 
 tinual collision of flint and steel, effected 
 by the machine called a fire-wheel, in 
 order to avoid setting fire to the inflam- 
 mable gas emitted by the coal, which 
 would be made to explode if it came near 
 the flame of a candle. 
 
 There is a remarkable property, which 
 some substances possess in an eminent de- 
 gree, and of which few, except metals and 
 water, are entirely destitute. These sub- 
 stances are denominated solar phosphori ; 
 besides the light which they reflect and 
 refract, they appear to retain a certain 
 portion, and to emit it again by degrees till 
 it is exhausted, or till its emission is inter- 
 rupted by cold. The Bolognian phospho- 
 rus was one of the first of these substances 
 that attracted notice ; it is a sulphate 
 barytes, found in the state of a stone ; it is 
 prepared by an exposure to heat, and is 
 afterwards made up into cakes : these, 
 when first placed in a beam of the sun’s 
 light, and viewed afterwards in a dark 
 room, have nearly the appearance of a 
 burning coal, or a red hot iron. Burnt 
 oyster-shells and muriate of lime, have 
 also the same property, and some speci- 
 mens of the diamond possess it in a con- 
 siderable degree. From the different re- 
 sults of experiments, apparently accurate, 
 made by different persons, there is reason 
 to conclude that some of these phosphori 
 emit only the same kind of light as they 
 have received, while others exhibit the 
 same appearances, to whatever kind of 
 
THE ARTISAN. 
 
 25 
 
 light they may have been exposed. Some- 
 times it has even been found, that light of 
 a particular colour has been most effica- 
 cious in exciting in a diamond the appear- 
 ance of another kind of light, which it was 
 naturally most disposed to exhibit. The 
 application of heat to solar phosphori, in 
 general expedites the extrication of the 
 light which they have borrowed, and 
 hastens its exhaustion ; it also produces 
 in many substances, which are not remark- 
 able for their power of imbibing light, a 
 temporary scintillation, or flashing, at a 
 heat much below ignition. The most re- 
 markable of these are fluor spar in powder, 
 and some other chrystallized substances. 
 It appears that luminous bodies in general 
 emit light equally in every direction, not 
 from each point of any of their surfaces, as 
 some have supposed, but from the whole 
 surface taken together, so that the sur- 
 face, when viewed obliquely, appears 
 neither more nor less bright than when 
 viewed directly. 
 
 r The medium of communication, by which 
 we become acquainted with all the objects 
 that we have just been considering, is the 
 eye ; an organ that exhibits, to an atten- 
 tive observer, an arrangement of various 
 substances, so correctly and delicately 
 adapted to the purposes of the sense of 
 vision, that we cannot help admiring, at 
 every step, the wisdom by which each 
 part is adjusted to the rest, and made to 
 conspire in effects so remote from what the 
 mere external appearance promises, that 
 we have only been able to understand, by 
 means of a laborious investigation, the 
 nature and operations of this wonderful 
 structure, while its whole mechanism still 
 remains far beyond all rivalship of human 
 art. 
 
 Having already described the various 
 parts of this delicate and curious organ ; 
 at page 39, voL i., it is unnecessary to say 
 any thing here of the eye itself, we shall 
 therefore confine our remarks to the case 
 of objects viewed by that organ. 
 
 Opticians have often puzzled them- 
 selves, without the least necessity, in 
 order to account for our seeing objects in 
 their natural erect position, while the 
 image on the retina is in reality inverted : 
 but surely the situation of a focal point at 
 the upper part of the eye, could be no rea- 
 son for supposing the object corresponding 
 to it to be actually elevated. We call 
 that the lower end of an object which is 
 next the ground ; and the image of a trunk 
 of a tree being in contact with the image 
 of the ground on the retina, we may natu- 
 rally suppose the trunk itself to be in 
 contact with the actual ground : the image 
 of the branches being more remote from 
 that of the ground, we necessarily infer 
 that the branches are higher and the 
 
 trunk lower ; and it is much simpler that 
 we should compare the image of the floor 
 with the image of our feet, with which it 
 is in contact, than with the actual situation 
 of our forehead, to which the image of the 
 floor on the retina is only accidentally 
 near, and with which indeed it would 
 perhaps be impossible to compare it, as far 
 as we judge by the immediate sensations 
 only. 
 
 Wheivthe attention is not directed to any 
 particular object of sight, the refractive 
 powers of the eye are adapted to the for- 
 mation of an image of objects at a certain 
 distance only, which is different in differ- 
 ent individuals, and also generally in- 
 creases with increasing age. Thus, if we 
 open our eyelids suddenly, without parti- 
 cular preparation, we find that distant 
 objects only appear as distinct as we are 
 able to make them ; but by an exertion of 
 the will, the eye may be accommodated 
 to the distinct perception of nearer objects, 
 yet not of objects within certain limits. 
 Between the ages of 40 and 50, the refrac- 
 tive powers of the eye usually begin to 
 diminish, but it sometimes happens that 
 where they are already too great, the de- 
 fect continues unaltered to an advanced 
 age. 
 
 We estimate distances much less accu- 
 rately with one eye than with both, since 
 we are deprived of the assistance usually 
 afforded by the relative situation of the 
 optical axis ; thus we seldom succeed at 
 once in attempting to pass a finger or a 
 hooked rod sideways through a ring, with 
 one eye shut. Our idea of distance is also 
 usually regulated by a knowledge of the 
 real magnitude of an object, while we 
 observe its angular magnitude; and on the 
 other hand, a knowledge of the real or 
 imaginary distance of the object often 
 directs our judgment of its actual magni- 
 tude. The quantity of light intercepted 
 by the air interposed, and the intensity of 
 the blue tint which it occasions, are also 
 elements of our involuntary calculations : 
 hence, in a mist, the obscurity increases 
 the apparent distance, and consequently 
 the supposed magnitude of an unknown 
 object. We naturally observe, in estima- 
 ting a distance, the number and extent of 
 the intervening objects; so that a distant 
 church in a woody and hilly country, ap- 
 pears more remote than if it were situated 
 in a plain; and for a similar reason, the 
 apparent distance of an object seen at sea, 
 is smaller than its true distance. The city 
 of Loudon is unquestionably larger than 
 Paris ; but the difference appears at first 
 sight much greater than it really is ; and 
 the smoke produced by the coal fires of 
 London, is probably the principal cause of 
 the deception. 
 
 The syn, moon, and stars, are much less 
 
24 
 
 THE ARTISAN. 
 
 luminous when they are near the horizon, 
 than when they are more elevated, on ac- 
 count of the greater quantity of their light 
 that is intercepted in its longer passage 
 through the atmosphere : we also observe 
 a much greater yariety of nearer objects 
 almost in the same direction ; we cannot, 
 therefore, help imagining them to be more 
 distant when they rise or set, than at other 
 times : and since they subtend the same 
 angle, they appear to be actually larger. 
 
 For similar reasons the apparent figure of 
 the starry heavens, even when free from 
 clouds, is that of a flattened vault, its sum- 
 mit appearing to be much nearer to us 
 than its horizontal parts, and any of the 
 constellations seems to be considerably 
 larger when it is near the horizon,- than 
 when in the zenith. This will be under- 
 stood by a reference to the following 
 figure, where the curve ABC represents 
 the apparent form of the heavens, 
 
 therefore when the sun or moon is at A or 
 C, it will appear much larger than at B. 
 
 The faculty of judging of the actual dis- 
 tance of objects, is an impediment to the 
 deception, which it is partly the business 
 of a painter to produce. Some of the 
 effects of objects at different distances, 
 may, however, be imitated in painting on 
 a plane surface. Thus, supposing the eye 
 to be accommodated to a given distance, 
 objects at all other distances may be re- 
 presented with a certain indistinctness of 
 outline, which would accompany the 
 images of the objects themselves on the 
 retina : and this indistinctness is so gene- 
 rally necessary, that its absence has the 
 disagreeable effect called hardness. The 
 apparent magnitude of the subjects of our 
 design, and the relative situations of the 
 intervening objects, may be so imitated by 
 the rules of geometrical perspective, as to 
 agree perfectly with nature ; and we may 
 still further improve the representation of 
 distance, by attending* to the art of per- 
 spective, which' consists in a due observa- 
 tion of the loss of sight, and the bluish 
 tinge, occasioned by the interposition of a 
 greater or less depth of air between us, 
 and the different parts of the scenery. 
 
 In the panoramas now exhibiting in 
 London, and many other parts of Europe, 
 the effects of natural scenery are very 
 closely imitated ; the deception is favoured 
 by the absence of all other visible objects, 
 and by the faintness of the light, which 
 assists in concealing the defects of the re- 
 presentation, and for which the eye is 
 usually prepared, by being long detained 
 
 in the dark winding passages, which lead 
 to the place of exhibition. 
 
 The impressions of light on the retina, 
 appear to be always in a certain degree 
 permanent, and the more so as the light is 
 stronger ; but it is uncertain whether the 
 retina possesses this property, merely as a 
 solar phosphorus, or in consequence of 
 its peculiar organization. The duration 
 of the impression is generally from one 
 hundredth of a second, to half a second or 
 more ; hence a luminous object revolving 
 in a circle, makes a lucid ring ; and a 
 shooting star leaves a train of light behind 
 it, which is not always real. If the object 
 is painfully bright, it generally produces 
 a permanent spot, which continues to pass 
 through various changes of colour for 
 some time, without much regularity, and 
 gradually vanishes: this may, however, 
 be considered as a morbid effect. 
 
 When the eye has been fixed on a small 
 object of a bright colour, and is then turned 
 away to a white surface, a faint spot, re- 
 sembling in form and magnitude the object 
 first viewed, appears on the surface, of a 
 colour opposite to the first ; that is, of such 
 a colour as would be produed by with- 
 drawing it from white light ; thus, a red 
 object produces a bluish green spot; and a 
 bluish green object a red spot. The reason 
 of this appearance, is probably that the 
 portion of the retina, or of the sensorium, 
 that is affected, has lost a part of its sen- 
 sibility to the light of that colour with 
 which it has been impressed ; and is more 
 strongly affected by the other constituent 
 parts of the white light. 
 
THE ARTISAN. 
 
 2,f 
 
 CHEMSBTEY* 
 
 OF PLATINA. 
 
 Dr. Lewis found that gold united with 
 platinum when they were melted together 
 in a strong heat. He employed only 
 crude platina; but Vauquelin, Hatchett, 
 and Klaproth, have since examined the 
 properties of the alloy of pure platinum 
 and gold. To form the alloy, it, is neces- 
 sary to fuse the metals with a strong heat, 
 otherwise the platinum is only dispersed 
 through the gold. When gold is alloyed 
 with this metal, its colour is remarkably 
 injured ; the alloy having the appearance 
 of bell metal, or rather of tarnished silver. 
 Dr. Lewis found, that when the platinum 
 amounted only to -Jth, the alloy had nothing 
 of the colour of gold ; even ^d part of 
 platinum greatly injured the colour of the 
 gold. The alloy formed by Mr. Hatchett 
 of nearly eleven parts of gold to one of 
 platinum, had the colour of tarnished sil- 
 ver. It was very ductile and elastic. From 
 Klaproth we learn, that if the platinum 
 exceed ^th of the gold, the colour of the 
 alloy is much paler than gold ; but if it be 
 under ^th, the colour of the gold is not 
 sensibly altered. Neither is there any 
 alteration in the ductility of the gold. 
 Platinum may be alloyed with a conside- 
 rable proportion of gold, without sensibly 
 altering its colour. Thus an alloy of one 
 part of platinum with four parts of gold 
 can scarcely be distinguished in appear- 
 ance from pure platinum. The colour of 
 gold does not become predominant till it 
 constitutes eight-ninths of the alloy. 
 
 From these facts it follows, that gold 
 cannot be alloyed with ^th of its weight 
 of platinum, without easily detecting the 
 fraud by the debasement of the colour ; 
 and Vauquelin has shewn, that when the 
 platinum does not exceed T ^th, it may be 
 completely separated from gold by rolling 
 out the alloy into thin plates, and digest- 
 ing it in nitric acid. The platinum is 
 taken up by the acid, while the gold re- 
 mains. But if the quantity of platinum 
 exceeds gjjth, it cannot be separated com- 
 pletely by that method. 
 
 Some trinkets and utensils for the table 
 have already been made of platina ; but 
 though they have the advantage of being- 
 unalterable and infusible, they have the 
 real defect of not possessing a fine colour, 
 and are at the same time very ponderous. 
 Platina, therefore, can be employed only 
 for small and slender instruments, capable 
 of being exposed to several corrosive mat- 
 ters, and to the air, without being altered 
 by them ; but this use is confined within 
 narrow bounds. 
 
 By mixing it with copper and arsenic, in 
 various proportions, mirrors for telescopes 
 
 have been fabricated of it, which will 
 never experience any alteration in their 
 polish, and which unite with a bright and 
 perfectly uniform polish of surface, a com- 
 plete incapability of being altered by any 
 possible agent. 
 
 Platina also promises the greatest and 
 most important advantages in mechanics, 
 and particularly in the delicate art of 
 making time-pieces. The construction of a 
 great number of machines will gain by 
 the acquisition of this metal, which may 
 be substituted in numerous cases for cop- 
 per, iron, and even silver. 
 
 SILVER. 
 
 Silver was known to the nations of an- 
 tiquity. Its discovery is of an earlier date 
 than the most ancient records of mankind ; 
 and it soon became, by its scarcity, its 
 beauty, and its useful properties, the object 
 of the researches of a great number of 
 artists and men of science. It is not 
 astonishing that men, who had caused the 
 metallic substances to assume so many 
 different forms, and who so frequently 
 imitated by alloys the whiteness and seve- 
 ral of the properties of silver, harboured 
 from a very remote period the idea of 
 creating this precious metal by art. When 
 they compared it with the other white 
 metals, it seemed to them to differ from them 
 only in some qualities, and that it would 
 not be impossible to procure it free from 
 those qualities. Not discouraged by their 
 first unsuccessful attempts, in proportion 
 as this precious metal became amongst 
 mankind the representative of all other 
 objects, of all the productions of industry, 
 and even of those of genius, the alchemists 
 redoubled their efforts ; and though their 
 experiments and their laborious researches 
 have not had all the success which they 
 expected from them, they have not been 
 entirely lost. It is from these unfortunate 
 trials, accumulated by the labours of 
 ages, that Chemists have derived the facts 
 which they have employed in its history ; 
 and they have had, as it were, nothing- 
 more to do than to arrange, in a methodi- 
 cal order, and clearly to describe the phe- 
 nomena which this metal had presented, in 
 the tortures of every kind to which alche- 
 mists have subjected it. 
 
 Whilst the alchemists, who called silver 
 Luna or Diana , qualified it, even by the 
 sign which they consecrated to it, as a 
 kind of semi-gold, which they represented 
 by two semi-circular lines put together in 
 the same direction, with the horns turned 
 to the left ; so that nothing more was ne- 
 cessary than to turn back the interior 
 curve, and unite it with the exterior, in 
 order to form the circular figure, or cha- 
 racteristic sign of gold, to which they be- 
 lieved it to be in fact very nearly related, 
 
26 
 
 THE ARTISAN. 
 
 since it was only required to develope one 
 of its parts, in order to cause it to pass 
 into the state of gold, the last stage of me- 
 tallic perfection. The labours of the al- 
 chemists have extended its numerous uses, 
 and have been no less useful to the che- 
 mists in constructing the system of their 
 science. The pharmaceutical operations 
 themselves, though they have been much 
 Jess numerous upon silver than upon many 
 other metals, have served to increase the 
 stock of chemical knowledge concerning 
 this metal ; and it is from the whole of 
 these labours that the history of this im- 
 portant metal has gradually been formed. 
 
 Silver is of a fine white colour, and of an 
 extremely lively brilliancy. Whether bur- 
 nished or otherwise, this metal is the most 
 beautiful that is known, at least in the 
 opinion of most men. In general, it pleases 
 more than any other metallic substance. 
 There is no metal that approaches it in 
 lustre ; it holds only the fifth rank amongst 
 the metals with respect to density and 
 specific gravity ; it follows after platina, 
 gold, tungsten, mercury, and lead. Its 
 specific gravity is 10*474 when melted, 
 and 10*535 when hammered. 
 
 With respect to its hardness, it has been 
 placed between iron and gold ; this is, 
 however, augmented by the action of the 
 hammer, or by pressure. Its elasticity is 
 pretty considerable ; and in this respect it 
 is intermediate between gold and copper. 
 It is one of the most sonorous metals, and 
 when struck, it emits a very acute sound. 
 
 The ductility of silver is one of its 
 most marked properties ; it follows im- 
 mediately after gold and platina. It is 
 made into leaves so thin, that they are 
 easily wafted away by the wind, and into 
 
 wires of extreme tenuity. On this account 
 it is instanced in Natural Philosophy, to 
 prove the divisibility of matter. A grain 
 of silver may be sufficiently extended, and jj 
 at the same time sufficiently firm, to make 
 an hemispherical vessel to contain an 
 ounce of water, or a wire 400 feet in length. 
 
 It is upon this amazing malleability that 
 the art of gold and silver-beating is 
 founded. It holds the second rank after 
 gold with respect to tenacity, or resistance 
 against breaking. A wire of this metal, 
 one tenth of an inch in diameter, supports ! 
 a weight of 270 pounds before it breaks. 
 
 This wire is considerably lengthened be- : 
 fore it breaks. Silver is hardened by all i 
 kinds of pressure ; but it easily acquires | 
 its former ductility again by the action of 
 fire, or by annealing. 
 
 Silver is a very good conductor of calo- i 
 ric, and becomes heated very quickly. Its 
 expansion by heat is a little inferior to that j 
 of lead and tin, and superior to that of 
 iron. When silver has been expanded by 
 heat, and the fire urged till it is heated to 
 whiteness or incandescence, it softens and 
 runs. Its fusibility has been estimated by 
 Mortimer at 1000 degrees of Fahrenheit. 
 When silver has been fused and suffered 
 to cool slowly, it presents at its surface 
 figures similar to net work and fern-leaves, 
 which announce a very marked crystalliza- 
 bility. On breaking it we find a granu- J 
 lated texture, which possesses the same 
 property. Mongez and Tillet,by suffering 
 a liquid portion to run off from a large 
 mass of fused silver, have obtained it 
 crystallised in quadrangular or octahedral ij 
 prisms ; and it affects the same form in na- j 
 ture, as will be afterwards noticed. 
 
 iLSTHOMOMIT. 
 
 OF THE STRATUS. 
 
 This modification has a mean degree of 
 density. 
 
 It is the lowest of clouds, since its infe- 
 rior surface commonly rests on the earth 
 or water, as represented by the following 
 figure. 
 
27 
 
 THE ARTISAN. 
 
 Contrary to the last, which may be con- 
 sidered as belonging to the day, this is 
 properly the cloud of night; the time of 
 its first appearance being about sun-set. 
 It comprehends all those creeping mists 
 which in calm evenings ascend in spread- 
 ing sheets (like an inundation of wajer) 
 from the bottom of valleys and the surface 
 of lakes, rivers, &c. 
 
 Its duration is frequently through the 
 night. 
 
 On the return of tire sun the level sur- 
 face of this cloud begins to put on the 
 appearance of cumulus, the whole at the 
 same time separating from the ground. 
 The continuity is next destroyed, and the 
 Cloud ascends and evaporates, or passes 
 off with the appearance of the nascent 
 cumulus. 
 
 This has been long experienced as a 
 prognostic of fair weather, and indeed 
 
 there is none more serene than that which 
 is ushered in by it. The .relation of the” 
 stratus to the state of the atmosphere as 
 indicated by the barometer, &c. appears 
 notwithstanding to have passed hitherto 
 without much attention. 
 
 OF THE CIRRO-CUMULUS. 
 
 The cirrus having continued for some 
 time increasing or stationary, usually 
 passes either to the cirro-cumulus or the 
 cirro-stratus, at the same time descending 
 to a lower station in the atmosphere. 
 
 The cirro-cumulus is formed from a 
 cirrus, or from a number of small separate 
 cirri, by the fibres collapsing as it were, 
 and passing into small roundish masses, in 
 which the texture of the cirrus is no 
 longer discernible, although they still re- 
 tain somewhat of the same relative arrange- 
 ment, as exhibited by the following figure^ 
 
 This change takes place either through- 
 out the whole mass at once, or progres- 
 sively from one extremity to the other. In 
 either case, the same effect is produced on 
 a number of adjacent cirri at the same 
 time and in the same order. It appears in 
 some instances to be accelerated by the 
 approach of other elouds. 
 
 This modification forms a very beautiful 
 sky ; sometimes exhibiting numerous dis- 
 tinct beds of these small connected clouds, 
 .^floating at different altitudes. 
 
 The cirro-cumulus is frequent in sum- 
 mer, and is attendant on warm and dry 
 weather. It is also occasionally and more 
 sparingly seen in the intervals of showers, 
 and in winter. 
 
 It may either evaporate or pass to the" 
 cirrus or cirro-stratus. 
 
 OF THE CIRRO-STRATUS. 
 
 This cloud appears to result from the 
 subsidence of the fibres of the cirrus ton. 
 horizontal position, at the same time that 
 they approach towards each other late- 
 rally. The form and relative position, 
 when seen in the distance, frequently give 
 the idea of shoals of fish. Yet in this, as 
 in other instances, the structure must be 
 attended to rather than the form, which 
 varies much, presenting at other times the 
 appearance of parallel bars, interwoven 
 streaks like the grain of polished wood, 
 &c. It is always thickest in the middle, 
 or at one extremity, and extenuated to- 
 wards the edge, as represented by the 
 following figure. 
 
28 
 
 THE ARTISAN 
 
 The distinct appearance of a cirrus does 
 not always precede the production of this 
 and the last modification. 
 
 The cirro-stratus precedes wind and 
 rain, the near or distant approach of which 
 may sometimes be estimated from its 
 greater or less abundance and permanence. 
 It is almost always to be seen in the inter- 
 vals of storms. Sometimes this and the 
 cirro-cumulus 'appear together in the sky, 
 and even alternate with each other in the 
 same cloud, when the different evolutions 
 which ensue are a curious spectacle, and 
 a judgment may be formed of the weather 
 likely to ensue by observing which modi- 
 fication prevails at last. The cirro-stratus 
 is the modification which most frequently 
 and completely exhibits the phenomena of 
 the solar and lunar halo, and (as supposed 
 from a few observations) the parheliop 
 and paraselene also. Hence the reason of 
 the prognostic for foul weather, commonly 
 drawn from the appearance of the 
 halo. 
 
 OF THE CUMULO-STRATUS. 
 
 The different modifications which have 
 been just treated of, sometimes give place 
 to each other, at other times two or more 
 appear in the same sky ; but in this case 
 the clouds in the same modification lie 
 mostly in the same plane of elevation; 
 those which are more elevated appearing 
 through the intervals of the lower, or the 
 latter showing dark against the lighter 
 ones above them. When the cumulus in- 
 creases rapidly, a cirro-stratus is frequenty 
 seen to form around its summit, reposing 
 thereon as on a mountain, while the 
 former cloud continues discernible in some 
 degree through it. This state continues 
 but a short time. The cirro-stratus spee- 
 dily becomes denser and spreads, while 
 the superior part of the cumulus extends 
 itself and passes into it, the base continu- 
 ing as before, and the convex protube- 
 rances changing their position, till they 
 present themselves laterally and down- 
 ward. These are well represented by the 
 following figure. 
 
29 
 
 THE ARTISAN. 
 
 More rarely the cumulus alone performs 
 this evolution, and its superior part con- 
 stitutes the incumbent cirro-stratus. 
 
 In either case a large lofty dense cloud 
 is formed, which may be compared to a 
 mushroom with a very thick short stem. 
 But when a whole sky is crowded with 
 this modification, the appearances are 
 more indistinct. The cumulus rises 
 through the interstices of the superior 
 clouds, and the whole, seen as it passes off 
 in the distant horizon, presents to the fancy 
 mountains covered with snow, intersected 
 with darker ridges and lakes of water, 
 rocks and towers, &c. The distinct cumu- 
 lo-stratus is formed in the interval between 
 the first appearance of the fleecy cumulus 
 and the commencement of rain, while the 
 lower atmosphere is yet too dry; also 
 during the approach of thunder storms : 
 the indistinct appearance of it is chiefly in 
 the longer or shorter intervals of showers 
 of rain, snow, or hail. 
 
 The cumulo stratus chiefly affects a 
 mean state of the atmosphere as to pressure 
 
 and temperature; but in this respect, like 
 the other modifications, it affords much 
 room for future observation. 
 
 OF THE NIMBUS, OR CUMULO-CIRRO- 
 STRATUS. 
 
 Clouds, in any of the preceding modifi- 
 cations, at the same degree of elevation, 
 or in two or more of them, at different ele- 
 vations, may increase so as completely to 
 obscure the sky, and at times put on an 
 appearance of density^ which to the inex- 
 perienced observer indicates the speedy 
 commencement of rain. It is nevertheless 
 extremely probable, as well from attentive 
 observation as from a consideration of the 
 several modes of their production, that 
 the clouds, while in any one of these states, 
 do not at any time let fall rain. 
 
 Before this effect takes place, they have 
 been uniformly found to undergo a change, 
 attended with appearances sufficiently re- 
 markable to constitute a distinct modifica- 
 tion, which is represented by the following 
 figure, called the Nimbus, or Cumulo- 
 cirro-stratus cloud. 
 
 In this figure a shower is represented as tended uniform gloom of this modifica- 
 coming from behind an elevated point of tion. 
 
 land. The relations of rain, and of periodical 
 
 The nimbus, although in itself one of the showers more especially, with the varying 
 least beautiful clouds, is yet now and then temperature, density, and electricity of the 
 superbly decorated with its attendant the atmosphere, will probably now obtain a 
 rainbow ; which can only be seen in per- fuller investigation, and with a better 
 fection, when backed by the widely ex- prospect of success, than heretofore. 
 
30 
 
 THE ARTISAN. 
 
 jBtsreltoous ^ufyectss. 
 
 MEMOIR OF THE LIFE OF JOHN 
 WALLIS, D. D. 
 
 Dr. Wallis was the son of the Rev. John 
 Wallis, M. A. minister of Ashfold, in Kent, 
 and was born in November, 1616 : his 
 father dying when he was young, he was 
 indebted for his education to the care and 
 kindness of his mother, who sent him to 
 school, first to Tenterden, in his native 
 county, and afterwards to Felsted,in Essex, 
 where he became pretty well acquainted 
 with the Latin and Greek languages, and 
 also obtained some knowledge of Hebrew. 
 Being at home during the Christmas va- 
 cation, he learnt from a younger bro- 
 her the first rules of common arithme- 
 tic, which was his initiation into mathe- 
 matics, and all the teaching he had ; but 
 he afterwards prosecuted it as a pleasing 
 diversion at spare hours, for mathematics 
 was not at that time looked upon as 
 academical learning. In the year 1632, 
 he was sent to the university of Cambridge, 
 and there admitted in Emanuel college, 
 under the tuition of Mr. Anthony Burgess, 
 a pious, learned, and able scholar, a good 
 disputant, an eminent preacher, and after- 
 wards minister of Sutton Colefield, in 
 Warwickshire. Dr. Wallis proceeded 
 Bachelor of Arts in 1637, and Master of 
 Arts in 1640 : he entered into orders, and 
 was ordained by Bishop Curie. TJe was 
 afterwards Fellow of Queen’s college, 
 Cambridge, but quitted his fellowship on 
 his marriage in 1644. About this time he 
 was also appointed one of the secretaries 
 to the Assembly'of Divines at Westminster ; 
 and during his attendance on the assem- 
 bly, he was a minister in London, first in 
 Fenchurch-street, and afterwards in Iron- 
 monger-lane, where he continued till his 
 removal to Oxford. There the doctor pro- 
 secuted his studies ; till he at length 
 attained to such proficiency, as to be repu- 
 ted one of the first mathematicians of the 
 age in which he lived. “ He was (says 
 Mr. Scarborough,) one of the greatest 
 masters of geometry that hath appeared in 
 any of these later ages ; the honour of our 
 country, and the admiration of others/' — 
 Mr. Oughtred says, u he was a person 
 adorned with all ingenious and excellent 
 arts and sciences, pious and industrious, 
 of a deep and diffusive learning, an accu- 
 rate judgment in all mathematical studies, 
 and happy and successful to admiration in 
 decyphering the most difficult and intricate 
 writings ; which was indeed his peculiar 
 honour, and affords the greatest instance 
 ever known of the force and penetration 
 of the human understanding.” We shall 
 here give the reader the doctor’s own ac- 
 count of the first outset of this business, 
 
 “ About the beginning of our civil wars, a 
 chaplain of Sir William Waller showed 
 me, as a curiosity, an intercepted letter 
 written in cypher, (and it was indeed the 
 first thing I had ever seen of the kind); 
 and asked me, between jest and earnest, 
 if I could make any thing of it? and was 
 surprised, when I told him, perhaps I 
 might. It was about ten o’clock when we 
 rose from supper ; and I withdrew to my 
 chamber to consider of it. By the number 
 of different characters in it, I judged it 
 could be no more than a new alphabet ; 
 and before I went to bed I found it out ; 
 which was my first attempt upon decy- 
 phering : and I was soon pressed to at- 
 tempt one of a different character, consist- 
 ing of numerical figures, extending to four 
 or five hundred numbers, with other cha- 
 racters intermixed, which was a letter from 
 Secretary Windebank, (then in France,) to 
 his son in England ; and was a cypher 
 hard enough, not unbecoming a secretary 
 of state. And when, upon importuntiy, [ 
 had taken a great deal of pains with it 
 without success, I threw it by ; but after 
 some time I resumed it again, and had the 
 good hap to master it. 
 
 u Being encouraged by this success be- 
 yond expectation, I have ventured upon 
 many others and seldom failed of any that 
 I have attempted for many years ; though 
 of late the French methods of cyphers are 
 grown so extremely intricate, that I have 
 been obliged to quit many of them, without 
 having patience to go through with them/’ 
 The following extracts from the copies of 
 his letters are a convincing proof of his 
 labour and success in it ; and that he never 
 gave up a cypher while he had the least 
 hope of succeeding. In a letter to the 
 Earl of Nottingham, who was at that time 
 Secretary to William III. dated August 
 4th, 1689, he says, u From the time your 
 lordship’s servant brought me the letter 
 yesterday morning, I spent the whole day 
 upon it, (scarce giving myself time to eat,) 
 and most part of the night : and w r as at it 
 again early this morning, that I might not 
 make your messenger wait too long.” In 
 another : u I wrote to his lordship the 
 next day, on account of the difficulty I at 
 first apprehended, the papers being written 
 in a hard cypher, and in a language of 
 which I am not thorougly master ; but sit- 
 ting close to it in good earnest, I have 
 (notwithstanding that disadvantage) met 
 with better success, and with more speed 
 than I expected. I have therefore returned 
 to his lordship the papers which were 
 sent me, with an intelligible account of 
 what was there in cypher.” Being hard 
 pressed by the Earl of Nottingham, he thus 
 writes at the conclusion of one of his let- 
 ters : “ But, my lord, it is hard service, 
 and I am quite weary. If your honour 
 
THE ARTISAN. 
 
 81 
 
 were sensible liow much pains and study 
 it cost me, you would pity me ; and there 
 is a proverb of not riding a free horse too 
 I hard/’ The doctor, I suppose, thought it 
 | was now high time (after he had decy- 
 phered so many letters,) that some notice 
 \ were taken of his services ; he therefore 
 begins to give his lordship the hint: he 
 was a little more plain in his next, wherein 
 he says, 44 However I am neglected, I am 
 not willing to neglect their majesties’ ser- 
 vices ; and have therefore re-assumed the 
 letters which I had laid by, and which I 
 here send decyphered : perhaps it may be 
 thought worth little, after I have bestowed a 
 great deal of pains upon them, andbe valued 
 accordingly ; but it is not the first time 
 that the like pains have been taken to as 
 little purpose, by, my lord,” &c.— In ano- 
 ther appears the following postscript, dated 
 August 15, 1691 : 44 But, my lord, I do a 
 little wonder to receive so many fresh let- 
 ters from your lordship without taking any 
 notice of what I wrote in my last, which 
 I thought would have been too plain to 
 need a decypherer; certainly your other 
 clerks are better paid, or else they would 
 not serve you.” 
 
 In a letter to a friend, he says : 44 It is 
 true, I have had all along a great many 
 good words ; that he is my humble servant 
 - — my faithful servant — my very faithful 
 servant — that he will not fail to acquaint 
 the king with my diligence and success in 
 this difficult work,” &c. But he met with 
 a better master in Lord Arlington, for 
 whom he did not do the tenth part of what 
 he had done for the earl. And as the doc- 
 tor was thus treated by our own ministers, 
 so he was not used much better by those 
 of the elector of Brandenburgh, for whose 
 service he had decyphered some of the 
 French letters, the contents of which 
 were of great consequence ; the decypher- 
 ing of which quite broke the French king’s 
 measures in Poland for that time, and 
 caused his ambassadors to be thrust out 
 with disgrace, to their king’s great preju- 
 dice and disappointment. Take the doc- 
 tor’s own words : 44 Mr. Smettan, the elec- 
 tor’s envoy, entertained me all the while 
 with a great many fine words and great 
 promises, (which, when decyphered, I 
 found to be nulls,) telling me what im- 
 porant service it was to his master, and 
 how well accepted, and what presents I 
 was to receive from him ; and in particu- 
 lar, that I was to have a rich medal, with 
 an honourable inscription, and a gold 
 chain of great value, which (he said) he 
 expected by the next post : but after all, 
 he left England without making me the 
 least requital for all my pains and trouble, 
 save that once he invited me to dine with 
 him, which cost me more in coach hire 
 thither and back than would have paid for 
 
 as good a dinner at an ordinary. I believe 
 that the elector does not know how un- 
 handsomely I have been used ; and I take 
 it unkind of his envoy to treat me as a 
 child or as a fool, to be wheedled on to 
 hard services with fine words, and yet to 
 think me so weak as to be unable to un- 
 derstand him ; when I had decyphered 
 for them between two and three hundred 
 sheets of very difficult and very different 
 cyphers, they might, I think, at least have 
 offered me porter’s pay, if not that of a 
 scrivener. I did not contract with them, 
 but did it frankly ; for, having a prince to 
 deal with, I was to presume he would deal 
 like himself.” Whether it was in conse- 
 quence of the doctor’s letters, or that they 
 were ashamed of their own ingratitude, or 
 from whatever cause it proceeded, the 
 medal so long talked of, and so long ex--- 
 pected, was at last sent. However, though 
 they were so unwilling to reward his ser- 
 vices, yet they were desirous to prevent 
 his art of decyphering from dying with 
 him, for which purpose he was solicited 
 by Mr. Leibneitz, by order of George I. 
 then elector of Hanover, to instruct a 
 young gentleman whom he would send 
 over ; and desired the doctor to make his 
 own terms. But he excused himself by 
 saying, 44 that he should always be ready 
 to tserve his electoral highness, when- 
 ever there should be occasion ; but, as 
 his art of decyphering was a curiosity 
 that might be of further service to his own 
 country, he could not think of sending it 
 abroad without the consent of his sove- 
 reign.” 
 
 This was a great act of disinterestedness 
 in the doctor, and deserves the highest 
 commendation ; because it is certain he 
 might have made a very advantageous 
 bargain for himself, without the least im- 
 propriety of conduct, had he not preferred 
 the good of his country to his own private 
 emolument; and it was, no doubt, con- 
 sidered as such by King William, who 
 settled on him a pension of £100 a year,, 
 with survivorship to his grandson, whom 
 he had instructed in the art of decyphering 
 at the particular desire of his majesty* 
 We must now look back, and see the other 
 methods in which his useful pen was em- 
 ployed ; and we shall find it at no period 
 idle. About the year 1653 he published 
 his 44 Tractus de Loquela Grammatica- 
 physicus wherein he gives a particular 
 account of the physical or mechanical for- 
 mation of sounds used in speech, or ex- 
 pressed by the letters of several languages. 
 In the year 1692, he published at Oxford 
 three large folios upon mathematics, with 
 this title, 44 Mathesis Universalis.” Part 
 of the third volume of his 44 Opera Mathe- 
 matica,” is employed in preserving and 
 restoring divers ancient Greek authors, 
 
32 
 
 THE ARTISAN. 
 
 which were in clanger of being lost. In 
 the year 1642, he published a book, en- 
 titled, “ Truth Tried in answer to a 
 treatise written by Lord Brook, entitled 
 <( The Nature of Truth.” In the year 1653 
 was published, in Latin, his Grammar 
 of the English Tongue, for the use of 
 foreigners ; in which he has a curious 
 observation on words beginning with cr, 
 as if they took their meaning from the 
 cross. In his u Praxis Grammatica,” he 
 gives us the following jeu-d’esprit, which 
 shows him to have been so well acquainted 
 with the English tongue, as to be able to 
 translate extempore, from the French, an 
 example of joining kindred sound ( sensus) 
 with kindred words. In the above book 
 the doctor says, u A certain learned French 
 gentleman proposed to me the under- 
 written four chosen French verses, com- 
 posed on purpose ; boasting from it won- 
 derfully of the felicity of his French lan- 
 guage, which expressed kindred senses by 
 kindred words ; complaining, in the mean 
 while, of our English one, as very often 
 expressing kindred senses by words con- 
 joined by no relation : 
 
 Quand un cordier, cordant, veult corder une corde ; 
 Pour sa corde corder, trois cordons il accorde : 
 Mais, si un des cordons de la corde descorde, 
 
 Le cordon discordant fait descorder la corde. 
 
 But, that I might show that this felicity 
 of language was not wanting to our own, 
 immediately, without making choice of 
 fresh matter, I translated verbally the 
 same four verses into the English tongue, 
 retaining the same turn of words which he 
 had observed in his, only substituting the 
 word twist, purely English, for the exotic 
 word cord, which he expected me to use : 
 When a twister a-twisting, will twist him a twist, 
 For the twisting his twist, he three tiwines doth 
 entwist ; 
 
 But if one of the twines of the twist does untwist, 
 The twine that untwisteth, untwisteth the twist. 
 
 A nd to them these four others : 
 
 Untwirling the twine that untwisted between. 
 
 He twirls with his twister the two in a twine : 
 
 Then, twice having twisted the twines of the twine. 
 He twisteth the twine he hath twined in twain. 
 
 And these : 
 
 The twain that, in twaining before in the twine, 
 
 As twins were entwisted, he now doth untwine ; 
 ’I'wixt the twain intertwisting a twine more be- 
 tween. 
 
 He, twirling his twister, makes a twist of the twine. 
 
 {To be continued .) 
 
 SOLUTIONS OF QUESTIONS. 
 
 Quest. 55, answered by Mr. J. Holroyd. 
 ( the Proposer .) 
 
 Imagine CAB the right angled triangle; 
 then, (from the latter part of the question) 
 it is plain that the traveller in the road AB 
 will have finished his journey; when the 
 
 other is 2| miles distant from the town B, 
 
 (as suppose) at the point D ; draw the 
 line D E parallel to the given base A C ; 
 then the side C A of the triangle CAB, 
 and the side DB of the triangle DEB, 
 being both given, as well as the ratio of 
 C B to A B ; it follows (by Euclid v. 13), 
 that CB : AB : : DB : EBzz2, and by 
 Euclid i. 47, DE is found to be 1§ miles; 
 consequently, by similar triangles D E : 
 C A : : E B : A B zz 26§ miles, whence 
 CB is found to be 33| miles. 
 
 We received two other answers to this 
 question ; but they were both inaccurate, 
 and much more complex than the above. 
 We cannot, how ever, allow that this solu- 
 tion is a geometrical one. 
 
 Quest. 56, answered by Mr. Whitcombe, 
 Cornhill. 
 
 Let P denote the sum Fig receives from 
 Premium, R zz 1-05 the amount of £1, 
 with its interest for 1 year (considering 
 the interest to be 5 per cent.) and let t de- 
 note the required number of years Pre- 
 mium ought to live; then per the doctrine 
 of annuities, and per question, we obtain 
 this equation 2 P — PR* zr O; conse- 
 quently 2 P zz PR*; therefore R/ zz 2, 
 and per the nature of logarithms t x log. 
 R zz log. 2 ; hence it is manifest, that t ~ 
 loff 2 
 
 zz 14 years 75 days, the time Pre- 
 
 log. Iv 
 
 mium ought to live, as required. 
 
 This question was also correctly an- 
 swered by the Proposer. 
 
 QUESTION FOR SOLUTION. 
 
 Quest. 59, proposed by J. Anderson, 
 Brentford. 
 
 A cylindrical vessel, the diameter of 
 which is 60 inches, and the height 48, is 
 to be filled with water, in which there are 
 two holes, one at the bottom, and one in 
 the side close to the bottom. Supposing 
 these to be opened at the same time, it is 
 required to determine in what time the 
 vessel will be exhausted by the power of 
 gravity alone? 
 

 t // /rr J// 
 
 f // f/r Jt 
 
 JM? 1 
 
THE ARTISAN. 
 
 CTOMETEY. . 
 
 PROPOSITION XIV. 
 Theorem. — Equal straight lines in a circle 
 are equally distant from the centre ; and 
 those which are equally distant from the 
 centre , are equal to one another. 
 
 Let the straight lines A B, CD, in the 
 circle ABDC, be equal to one another; 
 they are equally distant from the centre. 
 
 Take E the centre of the circle ABDC, 
 and from it draw EF, E G perpendiculars 
 to A B, CD; join AE and EC. Then, 
 because the straight line EF passing 
 through the centre, cuts the straight line 
 
 A B, which does not pass through the cen- 
 tre at right angles, it also bisects it: 
 Wherefore A F is equal to F B, and A B 
 double of A F. For the same reason, C D 
 is double of CG: But AB is equal to 
 CD; therefore A F is equal to C G: And 
 because AE is equal to EC, the square 
 of A E is equal to the square of E C : Now 
 the squares of AF, FE are equal to the 
 square of A E, because the angle A F E is 
 a right angle ; and, for the like reason, the 
 squares of EG, GC are equal to the 
 square of EC: Therefore the squares of 
 A F, F E are equal to the squares of C G, 
 GE, of which the square of AF is equal 
 to the square of C G, because A F is equal 
 to C G ; therefore the remaining square of 
 FE is equal to the remaining square of 
 E G, and the straight line E F is therefore 
 equal to EG : But straight lines in a cir- 
 cle are said to be equally distant from the 
 centre, when the perpendiculars drawn to 
 them from the centre are equal : Therefore 
 AB, CD are equally distant from the 
 centre. 
 
 Next, if the straight lines A B, CD be 
 equally distant from the centre ; that is, if 
 F E be equal to E G, A B is equal to C D. 
 For, the same construction being made, it 
 may, as before, be demonstrated, that AB 
 is double of A F, and C D double of C G, 
 and that the squares of EF, F A are equal 
 to the squares of EG, G C ; of which the 
 square of F E is equal to the square of 
 E G, because F E is equal to E G ; there- 
 fore the remaining square of AFis equal 
 
 Vol. II — No, 28. 
 
 ?3 
 
 to the remaining square of C G ; and the 
 straight line A F is therefore equal to CG : 
 But A B is double of A F, and C D double 
 of C G ; wherefore A B is equal to C D, 
 Therefore equal straight lines, &c. Q. E. D. 
 
 PROPOSITION XV. 
 
 Theorem. — The diameter is the greatest 
 straight line in a circle ; and , of all others , 
 that which is nearer to the centre is always 
 greater than one more remote ; and th$ 
 greater is nearer to the centre than the 
 less. 
 
 Let AB C D be a circle, of which the 
 diameter is AD, and the centre f£; and 
 let B C be nearer to the centre than F G £ 
 
 AD is greater than any straight line BC, 
 which is not a diameter, and BC greater 
 than F G. 
 
 From the centre draw E H, E K perpen- 
 diculars to BC, FG, and join EB, EC, 
 EF; and because AE is equal to EB, 
 and ED to EC: AD is equal to EB, 
 E C : But EB, EC are greater than BC ; 
 wherefore, also A D is greater than BC. 
 
 And, because B C is nearer to the cen- 
 tre than FG, EH is less than EK: But, 
 as was demonstrated in the preceding, 
 B C is double of B H, and F G double of 
 F K, and the squares of EH, H B are 
 equal to the squares of E K, K F, of which 
 the square of EH is less than the square 
 of EK, because EH is less than EK; 
 therefore the square of B H is greater than 
 the square of F K, and the straight line 
 B H greater than F K : and therefore B C 
 is greater than F G. 
 
 Next, Let B C be greater than F G ; B C 
 is nearer to the centre than F G ; that is, 
 the same construction being made, EH 
 is less than EK: Because B C is greater 
 than F G, B H likewise is greater than 
 K F : but the squares of BH, HE are 
 equal to the squares of F K, K E, of which 
 the square of BH is greater than the 
 square of F K, because B H is greater 
 than FK; therefore the square of EH is 
 less than the square of E K, and the straight 
 line E H less than E K. Wherefore, the 
 diameter, &c. Q. E. D. 
 
34 
 
 THE ARTISAN. 
 
 PROPOSITION XVI. 
 
 Theorem. — The straight line drawn at right 
 angles to the diameter of a circle , from 
 the extremity of it , falls without the cir- 
 cle ; and no straight line can be drawn 
 between that straight line and the cir- 
 cumference, from the extremity of the 
 diameter , so as not to cut the circle . 
 
 Let A R C be a circle, the centre of 
 which is D, and the diameter A B : and 
 let A E be drawn from A perpendicular to 
 A B, A E shall fall without the circle. 
 
 In A E take any point F, join D F, and 
 let D F meet the circle in C. Because 
 
 angle D H A is a right angle, and the 
 angle D A H less than a right angle, the 
 side DH of the triangle DAH is less 
 than the side DA. The point H, there- 
 fore, is within the circle, and therefore the 
 straight line A G cuts the circle. 
 
 Cor. From this it is manifest, that the 
 straight line which is drawn at right angles 
 to the diameter of a circle from the ex- 
 tremity of it, touches the circle ; and that 
 it touches it only in one point; because, if 
 it did meet the circle in two, it would fall 
 within it. Also it is evident, that there 
 can be but one straight line which touches 
 the circle in the same point. 
 
 D A F is a right angle, it is greater than 
 the angle A F D ; but the greater angle of 
 any triangle is subtended by the greater 
 side, therefore D F is greater than D A ; 
 now D A is equal to D C, therefore D F is 
 greater than D C, and the point F is there- 
 fore without the circle. And F is any 
 point whatever in the line A E, therefore 
 A E falls without the circle. 
 
 Again, between the straight line AE 
 and the circumference, no straight line can 
 be drawn from the point A, which does 
 not cut the circle. Let A G be drawn, in 
 the angle DAE; from D draw D H at 
 
 PROPOSITION XVII. 
 
 Problem. — To draw a straight line from a 
 given point, either without or in the cir- 
 cumference, which shall touch a given 
 circle. 
 
 First, let A be a given point without the 
 given circle BCD; it is required to draw 
 a straight line from A, which shall touch 
 the circle. 
 
 Find the centre E of the circle, and join 
 AE; and from the centre E, at the distance 
 E A, describe the circle A FG ; from the 
 point D draw D F at right angles to E A, 
 and join EBF, and A B. AB touches 
 the circle BCD. 
 
 Because E is the centre of the circles 
 B C D, A F G, E A is equal to E F, and 
 E D to E B ; therefore the two sides A E, 
 
 E B are equal to the two FE, ED, and 
 they contain the angle at E common to 
 the two triangles A EB, F E D ; therefore 
 thejfbase D F is equal to the base A B, and 
 the triangle FED to the triangle A E B, 
 and the other angles to the other angles : 
 Therefore the angle E B A is equal to the 
 angle E D F ; but E D F is a right angle, 
 wherefore E B A is a right angle ; and 
 EBis drawn from the centre: but a 
 straight line drawn from the extremity of 
 a diameter, at right angles to it, touches 
 the circle : Therefore A B touches the cir- 
 cle; and is drawn from the given point 
 A. Which was to be done. 
 
THE ARTISAN. 
 
 3 5 
 
 Rut if the given point be in the circum- 
 ference of the circle, as the point D, draw 
 1) E to the centre E, and D F at right 
 angles to D E ; DF touches the circle. 
 
 PROPOSITION XVIII. 
 
 Theorem. — If a straight line touches a cir- 
 cle, the straight line drawn from the cen- 
 tre to the point of contact , is perpendicular 
 to the line touching the circle. 
 
 Let the straight line D E touch the circle 
 A B C in the point C ; take the centre F, 
 and draw the straight line F C : F C is 
 perpendicular to D E. 
 
 For, if it be not, from the point F draw 
 F B G perpendicular to D E ; and because 
 F G C is a right angle, G C F must be an 
 acute angle ; and to the greater angle the 
 
 greater side is opposite : Therefore F C is 
 greater than F G ; but F C is equal to F B ; 
 therefore F B is greater than F G, the less 
 than the greater, which is impossible ; 
 wherefore F G is not perpendicular to DE: 
 In the same manner it may bo shown, that 
 no other line but F C can be perpendicular 
 to D E ; F C is therefore perpendicular to 
 D E. Therefore, if a straight line, &c. 
 Q. E. D, 
 
 PROPOSITION XIX. 
 
 Theorem. — -If a straight line touches a cir- 
 cle, and from the point of contact a 
 straight line be drawn at right angles to 
 the touching line , the centre of the circle 
 is in that line . 
 
 Let the straight line D E touch the cir- 
 cle A B C, in C, and from C let C A be 
 drawn at right angles to D E ; the centre 
 of the circle is in C A. 
 
 For, if not, let F be the centre, if pos- 
 sible, and join C F : Because D E touches 
 the circle ABC, and F C is drawn from 
 the centre to the point of contact, F C is 
 perpendicular to D E ;~ therefore FCE is 
 a right angle : But A C E is also a right 
 angle ; therefore the angle F C E is equal 
 to the angle ACE, the less to the greater, 
 which is impossible ; Wherefore F is not 
 
 the centre of the circle ABC: In the same 
 
 A 
 
 manner it may be shown, that no other 
 point which is not in C A, is the centre j 
 that is, the centre is in C A. Therefore.) 
 if a straight line, &c. Q. E. D. 
 
 PROPOSITION XX. 
 
 Theorem.— The angle at the centre of a 
 circle is double of the angle at the circum- 
 ference , upon the same base ; that is, upon 
 the same part of the circumference. 
 
 Let ABC be a circle, and B D C an 
 angle at the Centre, and B A C an angle 
 at the circumference, which have the 
 same circumference B C for their base ; 
 the angle BDC is double of the angle 
 BA C. 
 
 First, let D, the centre of the circle, be 
 within the angle B A C, and join A D, and 
 produce it to E : Because D A is equal to 
 X> B, the angle D A B is equal to the angle 
 DBA; therefore the angles DAB, D BA 
 
 A 
 
 are double of the angle DAB; but the 
 angle B D E is equal to the angles DAB, 
 DBA; therefore also the angle B D E is 
 double of the angle DAB: For the same 
 reason, the angle E D C is double of the 
 angle D A C : Therefore the whole angle 
 B D C is double of the whole angle RAC* 
 Again, let D, the centre of the circle, be 
 without the angle B A C, and join A D and 
 C 2 
 
36 
 
 THE ARTISAN. 
 
 produce it. to E. It may be demonstrated, 
 
 as in the first case, that the angle E D C 
 is double of the angle D A C, and that 
 E 1) B, a part of the first, is double of 
 D A B, a part of the other ; therefore the 
 remaining angle B D C is double of the re- 
 maining angle BAG. Therefore the angle 
 at the centre, &c. Q. E. D. 
 
 order to support the more frequent recur- 
 rence of friction. It has been proposed, 
 for the coarser kinds of wheel-works, to 
 divide the distance between the middle 
 points of two adjoining teeth into 30 parts, 
 and to allot 16 to the tooth of the pinion, 
 and 13 to that of the wheel, allowing one 
 for freedom of motion. 
 
 The wheel and pinion may either be 
 situated in the same plane, both being 
 commonly of the kind denominated spur- 
 wheels, or their planes may form an angle : 
 in this case one of them may be a crown or 
 contrate wheel, as represented by the first 
 of the following figures, 
 
 A 
 
 
 
 
 i 
 
 
 Ui»sS ! Si 
 
 
 mnanRii 
 
 Miiiil 
 
 MECHA1ICS, 
 
 ON THE' TEETH OF WHEELS. 
 
 If the face of the teeth, where they are 
 in contact, is too much inclined to the 
 radius, their mutual friction is not much 
 affected, but a great pressure on their axis 
 is produced ; and this ©ccasions a strain 
 on the machinery, as well as an increase 
 of friction on the axis. 
 
 If it be desired to produce a great angu- 
 lar velocity, with the smallest possible 
 quantity of wheel-work, the diameter of 
 each wheel must be between three and 
 four times as great as that of the pinion on 
 which it acts, where the pinion impels the 
 wheel ; it is sometimes made with three or 
 four teeth only : but it is much better in 
 general to have at least six or eight ; and 
 considering the additional labour of in- 
 creasing the number of wheels, it may be 
 advisable to allot more teeth to each of 
 them, than the number resulting from the 
 calculation ; therefore we may allow 30 or 
 40 teeth to a wheel, acting on a pinion of 
 6 or 8. In works which do not require a 
 great degree of strength, the wheels have 
 sometimes a much greater number of teeth 
 than this ; and on the other hand, an end- 
 less screw or a spiral acts as a pinion of 
 one tooth, since it propels the wheel 
 through the breadth of one tooth only by 
 each revolution. For a pinion of six 
 teeth, it would be better to have a wheel 
 of 35 or 37 than 36 ; for each tooth of the 
 wheel would thus act in turn upon each 
 tooth of the pinion, and the work would be 
 more equally worn, than if the same teeth 
 continued to meet in each revolution. The 
 teeth of the pinion should also be some- 
 what stronger than those of the wheel, in 
 
 
 where A is a spur and B a crown-wheel, 
 or both of them may be bevilled, the 
 teeth being cut obliquely, as in the second 
 figure, where the wheel and pinion are 
 both bevilled, the faces of the teeth being 
 directed to the point A. According to the 
 relative magnitude of the wheels, the angle 
 of the be vil must be different, so that the 
 velocities of the wheels may be in the 
 same proportion at both ends of their 
 oblique faces ; for this purpose, the faces 
 of all the teeth must be directed to the 
 point where the axis would meet. 
 
 In cases where a motion not quite 
 equable is required, as it sometimes hap- 
 pens in the construction of clocks, but 
 more frequently in orreries, the wheels 
 may either be divided a little unequally, 
 or the axis may be placed a little out of 
 the centre ; and these eccentric wheels 
 may either act on other eccentric wheels, 
 or, if they are made as contrate wheels, 
 upon a lengthened pinion, as represented 
 by the annexed figure. 
 
THE ARTISAN. 
 
 37 
 
 An arrangement is sometimes made for 
 separating wheels, which are intended to 
 turn each other, and for replacing them 
 at pleasure; the wheels are said to be 
 thrown by these operations out of gear, 
 and into gear again. 
 
 When a wheel revolves round another, 
 and is so fixed as to remain nearly in a 
 parallel direction, and to cause the central 
 wheel to turn round its axis — the appa-. 
 ratus is called a sun -and- planet wheel, (see 
 page 227, vol. i.) In this case, the cir- 
 cumference of the central wheel moves as 
 fast as that of the revolving wheel, each 
 point of which describes a circle, equal in 
 diameter to the distance of the centres of 
 the two wdieels : consequently, w'hen the 
 wheels are equal, the central wdieel makes 
 two revolutions, every time that the ex- 
 terior wheel travels round it. If the cen- 
 tral wheel be fixed, and the exterior 
 wheel be caused to turn on its own centre 
 during its revolution, by the effect of the 
 contact of the teeth, it will make in every 
 
 revolution one turn more with respect to 
 the surrounding objects, than it would 
 make, if its centre were at rest, during 
 one turn of the wheel which is fixed : and 
 this circumstance must be recollected when 
 such wheels are employed in the construc- 
 tion of planetariums. 
 
 Wheels are usually made of wood, of 
 iron, either cast or wrought, of steel, or 
 of brass. The teeth of metal wdieels are 
 generally cut by means of a machine ; 
 the wheel is fixed on an axis, which also 
 carries a plate furnished with a variety of 
 circles, divided into different numbers of 
 equal parts, marked by small excavations ; 
 these are brought in succession under the 
 point of a spring, which holds the axis 
 firm, while the intervals between the teeth 
 are expeditiously cut out by a revolving 
 saw of steel. The . teeth are afterwards 
 finished by a file ; and a machine has also 
 been invented for holding and working the 
 file, 'i bis machine is represented by the 
 following figure : 
 
 A is the wheel, of which the teeth is 
 formed by the revolving saw B, turned by 
 the wheel and pinion C D, by means of 
 the handle E, while the frame, which 
 holds the saw', moving on hinges, and 
 resting on a spring, is depressed by the 
 handle F, its place having been previously 
 adjusted by the screw G. The large plate 
 H I contains a number of concentric cir- 
 cles, variously divided by points, into 
 which the end of the spring I sinks at each 
 step, so as to fix the apparatus in the re- 
 quired position. 
 
 Toothed wheels are employed in mecha- 
 nics, not only for increasing or diminishing 
 velocity, so as to adapt a given power to 
 the purpose of producing a certain effect, 
 as in a common mill, where the slow 
 motion of the water-wheel is made to pro- 
 duce the rapid motion of the mill -stone - r 
 but they are also employed for the purpose 
 of producing angular motions, that shall 
 obtain, with great precision, given ratios 
 to one another. This happens in clock 
 work, and it is there of importance to de- 
 termine, with accuracy, the number of 
 
38 
 
 THE ARTISAN. 
 
 wheels and the number of teeth in each ; 
 but this is a branch of mechanics, which 
 we considered too abstruse to be introduced 
 in a work like the present. We may, how- 
 ever, remark, that the number of teeth in a 
 wheel, and in a pinion which work toge- 
 ther, should be prime to one another, that 
 their coiifcidences may not recur in the 
 same order after every revolution. 
 
 The numbers expressing the ratio of the 
 angular velocity of the wheel to that of the 
 pinion, may sometimes be fractional, and 
 may consist of so many places, when the 
 fractions are taken away, that, to make 
 the motions exactly in their ratio, would 
 require more wheels, and a greater number 
 of teeth, than can conveniently be allowed. 
 It is then of consequence to find two num- 
 bers that will express the ratio, not ex- 
 actly, but more nearly, than can be done 
 by smaller numbers, The method of find- 
 ing such numbers is, however, too intricate 
 Jo be given here. 
 
 ON WHEEL CARRIAGES. 
 
 Though we have already treated pretty 
 fully of the friction of axles at page 215, 
 vol. i. yet the subject of wheel carriages 
 forms so important a part of mechanics, that 
 we shall devote a few pages to its considera- 
 tion. The wheels of carriages owe a great 
 part of their utility to the diminution of 
 friction, which is as much less in a car- 
 riage than a dray, as the diameter of the 
 axle is less than that of the wheel, even 
 supposing the dray to slide on a greased 
 surface of iron. The wheels also assist us 
 in drawing the carriage over an obstacle, 
 for the path which the axis of the wheel 
 describes, is always smoother and less 
 abrupt than the surface of a rough road on 
 which the wheel rolls. It is obvious, that 
 both these advantages are more completely 
 attained by large wheels than by smaller 
 ones : the dimensions of the axis not being 
 increased in the same proportion with 
 those of the wheel, and the path of the 
 axis to which that of the centre of gravity 
 is similar, consisting of portions of larger 
 circles, and consequently being less curved ; 
 and if the wheels are elastic, and rebound 
 from an obstacle, the difference is still in- 
 creased. It is, however, barely possible, 
 that the curvature of the obstacles to be 
 overcome, may be intermediate between 
 those of a larger and of a smaller wheel ; 
 and in this case the higher wheel will 
 touch a remoter part of the obstacle, so 
 that the path of the axis will form an 
 abrupt angle, while the smaller wheel fol- 
 lows the curve, and produces a more 
 equable motion. For example, the centre 
 pf the wheel A B, passing over the obstacle 
 describes the path DE; 
 
 and that of the larger wheel F G, the path 
 H I, which is less steep. 
 
 Again, the centre of the wheel A B des- 
 cribes the curved path CD, 
 
 in passing over the obstacle E, while that 
 of the larger wheel F G, has an angle at H, 
 The greater part of the resistance to the 
 motion of a carriage very frequently varies, 
 from the continual displacement of a por- 
 tion of the materials of the road, which do 
 not re-act on wheels with perfect elasticity, 
 but undergo a permanent change of form, 
 proportional to the loss of force. Hence, 
 in a soft sand, although the axles of the 
 wheels may move in a direction perfectly 
 horizontal, the draught becomes extremely 
 heavy. The more the wheel sinks, the 
 greater is the resistance ; and if we sup- 
 pose the degree of elasticity of the mate- 
 rials, and their immediate resistance at 
 different depths to be known, we may 
 calculate the effect of their re-action in re- 
 tarding the motion of the carriage. Thus, 
 if the materials were perfectly inelastic, 
 acting only on the preceding half of the 
 immersed portion of the wheel, and their 
 immediate pressure or resistance were 
 simply proportional to the depth, like 
 that of fluids or of other elastic substances, 
 the horizontal resistance would be to the 
 weight, nearly as the depth of the part 
 immersed to two thirds of its length ; but 
 if the pressure increased as the square of 
 the depth, which is a more probable sup- 
 position, the resistance would be to the 
 weight as the depth to about four-fifths 
 of the length ; the pressure may even vary 
 still more rapidly, and we may consider 
 the proportion of the resistance to the 
 weight, as no greater than that of the 
 depth of the part immersed to its length, 
 or of half this length to the diameter of 
 the wheel ; and if the materials are in apy 
 
THE ARTISAN. 
 
 39 
 
 degree elastic, the resistance will be les 
 sened accordingly. But on any of these 
 suppositions, it may be shown that the 
 resistance may be reduced to one half, 
 either by making a wheel a little less than 
 three times as high, or about eight times 
 as broad as the given wheel. This con- 
 sideration i3 of particular consequence in 
 soft and boggy soils, as well as in sandy 
 countries; thus, in moving timber in a 
 moist situation, it becomes extremely ad- 
 vantageous to employ very high wheels, 
 and they have the additional convenience, 
 that the timber may be suspended from 
 the axles by chains, without the labour of 
 raising it so high, as would be necessary 
 for placing it on a carriage of any kind. 
 
 But the magnitude of wheels is prac- 
 tically limited, by the strength or weight 
 of the materials of which they are made, 
 by the danger of overturning when the cen- 
 tre is raised too high, and in case of the 
 first pair of wheels of a four wheel car- 
 riage, by the inconvenience that would 
 arise in turning a corner, with a wheel 
 which might interfere with the body of the 
 carriage. It is also of advantage, that the 
 draught of a horse should be in a direction 
 somewhat ascending, partly on account of 
 the shape of the horse’s shoulder, and 
 partly because the principal force that he 
 exerts, is in the direction of a line passing 
 through the point of contact of his hind 
 feet with the ground. But a reason 
 equally strong, for having the draught in 
 this direction is, that a part of the force 
 may always be advantageously employed 
 in lessening the pressure on the ground : 
 and to answer this purpose the most effec- 
 tually, the inclination of the traces or 
 shafts, ought to be the same with that of 
 a road on which the carriage would begin 
 or continue to descend by its own weight 
 only. 
 
 In order to apply the force in this man- 
 ner to both pairs of wheels.where there are 
 four, the line of draught ought to be 
 directed to a point half way between them, 
 or rather to a point immediately under the 
 centre of gravity of the carriage ; and such 
 a line would always pass above the axis 
 of the fore wheels. If the line of draught 
 pass immediately through this axis, the 
 pressure on the hind wheels will remain 
 unaltered ; and if the traces or shafts be 
 fixed still lower, the pressure on the hind 
 wheels will even be somewhat increased 
 by the draught. It is evident, therefore, 
 that this advantage cannot be obtained if 
 the fore wheels are very high ; we may 
 also understand, that in some cases the 
 common opinion of the elegibility of placing 
 a load over the fore wheels, rather than 
 the hind wheels, may have some founda- 
 tion in truth. When several horses are 
 employed, the draught of all but the last 
 
 must be nearly horizontal ; in this case 
 the flexure of the chain brings it into a 
 position somewhat more favourable for the 
 action of the horses ; but the same cause 
 makes the direction of its attachment to 
 the waggon unfavourable; further than 
 this, there is no absolute loss of force, but 
 it appears to be advisable to cause the 
 shaft horse to draw in a direction as much 
 elevated as possible ; and on the whole it 
 is probable that horses drawing singly 
 have a material advantage, when they do 
 not require additional attendance from the 
 drivers. 
 
 The practice of making broad wheels 
 conical, has obviously the disadvantageous 
 effect of producing a friction at each edge 
 of the wheel, when the carriage is moving 
 in a straight line ; for such a wheel, if it 
 moved alone, would always describe a 
 circle round the vertex of the cone to 
 which it belongs. When the wheels are 
 narrow, a slight inclination of the spokes 
 appears to be of use in keeping them more 
 steady on the axles than if they were ex- 
 actly vertical ; and when, by an inclina- 
 tion of the body of the carriage, a greater 
 proportion of the load is thrown on the 
 lower wheel, its spokes, being then in a 
 vertical position, are able to exert all 
 their strength with advantage. The axles 
 being a little conical, in order that they 
 may not become loose, or may easily be 
 tightened as they wear, it is necessary 
 that they should be bent down, so that 
 their lower surfaces may be horizontal, 
 otherwise the wheels would press too 
 much on the linch pin. For this reason, 
 the distance between the wheels should be 
 a little greater above than below, and 
 their surfaces of course slightly conical. 
 
 EX.ECTRXCXT1T. 
 
 Having stated the fundamental proper- 
 ties of the electric fluid, and of the differ- 
 ent kinds of matter as connected with that 
 fluid, we shall now examine its distribu- 
 tion, and the attractive and repulsive 
 effects exhibited by it under different forms 
 and circumstances. The general effect of 
 electrified bodies on each other, if their 
 bulk is small in comparison with their 
 distance is, that they are mutually re- 
 pelled when in similar states of electricity, 
 and attracted when in dissimilar states. 
 This is a consequence immediately de- 
 ducible, from the mutual attraction of re- 
 dundant matter and redundant fluid, and 
 from the repulsion supposed to exist be- 
 tween any two portions, either of matter 
 or of fluid ; and it may also be easily con- 
 firmed by experimental proof. A neutral 
 body, if it were a perfect non-conductor, 
 
THE ARTISAN. 
 
 4# 
 
 Would not be affected either way by the 
 neighbourhood of an electrified body : for 
 while the whole matter contained in it re- 
 mains barely saturated with the electric 
 fluid, the attractions and repulsions 
 balance each other. But in general, a 
 neutral body appears to be attracted by an 
 electrified body, on account of a change of 
 the disposition of the fluid which it con- 
 tains, upon the approach of a body either 
 positively or negatively electrified. The 
 electrical affection produced in this man- 
 ner, without any actual transfer of the 
 fluid, is called induced electricity. 
 
 The stale of induced electricity may be 
 illustrated, by placing a long conductor at 
 a little distance from an electrified sub- 
 stance, and directed towards it : and by 
 suspending pith balls or other light bodies 
 from it, in pairs, at different parts of its 
 length : these will repel each other, from 
 being similarly electrified, at two ends, 
 which are in contrary states of electricity, 
 while at a certain point towards the mid- 
 dle they will remain at rest, the con- 
 ductor being here perfectly neutral. It 
 Was from the situation of this point, that 
 Lord Stanhope first inferred the true law 
 of the electric attractions and repulsions, 
 although Mr. Cavendish had before sug- 
 gested the same law as the most probable 
 supposition. 
 
 The attraction thus exerted by ah elec- 
 trified body upon neutral substances, is 
 strong enough, if they are sufficiently 
 light, to overcome their gravitation, and 
 to draw them up from a table at some 
 little distance : upon touching the electri- 
 fied body, if it is a conductor, they receive 
 a quantity of electricity from it, and are 
 again repelled, until they are deprived of 
 their electricity by contact with other sub- 
 stances, which, if sufficiently near to the 
 first, is usually in a contrary state, and 
 therefore renders them still more capable 
 of returning, when they have touched it, 
 to the first substance, in consequence of an 
 increased attraction, assisted also by a 
 hew repulsion. This alternation has been 
 applied to the construction of several 
 electrical toys ; a little hammer, for ex- 
 ample, has been made to play between 
 two bells ; and this instrument has been 
 employed for giving notice of any change 
 of the electrical state of the atmosphere. 
 The repulsion which takes place between 
 two bodies* in a similar state of electricity* 
 is the cause of the currents of air which 
 always accompany the discharge of elec- 
 tricity, whether negative or positive, from 
 pointed substances. 
 
 If two bodies approach each other, elec- 
 trified either positively or negatively in 
 different degrees, they will either repel or 
 attract each other, according to their dis- 
 tance ; when they are very remote, they 
 
 exhibit a repulsive force, but when they 
 are within a certain distance, the effects of 
 induced electricity overcome the repulsion, 
 which would necessarily take place, if 
 the distribution of the fluid remained un- 
 altered by their mutual influence. 
 
 When a quantity of electric fluid is ac- 
 cumulated on one side of a non-conducting 
 substance, it tends to drive off the fluid 
 from the other side ; and if this fluid is 
 suffered to escape, the remaining matter 
 exerts its attraction on the fluid, which 
 has been imparted to the first side, and 
 allows it to be accumulated in a much 
 greater quantity than could have existed 
 in an equal surface of a conducting sub- 
 stance. In this state, the body is said to 
 be charged ; and for producing it the 
 more readily, each surface is usually 
 coated with a conducting substance, which 
 serves to convey the fluid to and from its 
 different parts with convenience. The 
 thinner any substance is, the greater 
 quantity of the fluid is required for* charg- 
 ing it in this manner, so as to produce a 
 given tension, or tendency to escape : but 
 if it be made too thin, it will be liable to 
 break the attractive force of the fluid, for 
 the matter on the opposite side overcoming 
 the cohesion of the substance, and perhaps 
 forcing its way through the temporary 
 vacuum which is formed. 
 
 When a communication is made in any 
 manner by a conducting substance between 
 the two coatings of a charged plate' or 
 vessel, the equilibrium is restored, and 
 the effect is called a shock. If the coat- 
 ings be removed, the plate will still re- 
 main charged, and it may be gradually 
 discharged, by making a communication 
 between its several parts in succession, 
 but it cannot be discharged at once, for 
 want of a common connection; so that the 
 presence of the coating is not absolutely 
 essential to the charge ahd discharge of the 
 opposite surfaces. Such a coated substance 
 is most usually employed in the form of a 
 jar. Jars were formerly filled with water, 
 or with iron filings ; the instrument having 
 been principally made known frofn the ex- 
 periments of Musscheiibroek and others at 
 Leyden, it was called the Leyden jar or 
 phial ; but at present a coating of tin foil 
 is commonly applied on both sides of the 
 jar, leaving a sufficient space at its upper 
 part, to avoid the spontaneous discharge, 
 which w r ould often take place between the 
 coatings, if they approached too near to 
 each other; and a ball is fixed to the 
 cover, which has a communication with 
 the internal coating, and by means of 
 which the jar is charged, while the ex- 
 ternal coating is allowed to communicate 
 with the ground. This jar is represented 
 by the following figure : 
 
THE 
 
 A collection of such jars is called a 
 battery, and an apparatus of this kind 
 may be made so powerful, by increasing 
 the number of jars, as to exhibit many 
 striking effects by the motion of the electric 
 fluid, in its passage from one to the other 
 of the surfaces. The following figure re- 
 presents a battery, containing 16 jars. 
 
 The conducting powers of different sub- 
 stances are concerned, not only in the 
 facility with which the motions of the elec- 
 tric fluid are directed into a particular 
 channel, but also in many cases of its 
 equilibrium, and particularly in the pro- 
 perties of charged substances, which de- 
 pend on the resistance opposed by non- 
 conductors, to the ready transmission of 
 the fluid; These powers may be com- 
 pared, by ascertaining the greatest length 
 of each of the substances to be examined, 
 through which a spark or a shock will 
 take its course, in preference to a given 
 
 ARTISAN. 4l 
 
 length of air, or of any other standard of 
 comparison. 
 
 The progressive motion of the , electric 
 fluid through conducting substances is so 
 rapid, as to be performed in all cases with- 
 out a sensible interval of time. It has in- 
 deed been said, that when very weakly 
 excited, and obliged to pass to a very great 
 distance, a perceptible portion of time is 
 actually occupied in its passage ; but this 
 fact is somewhat doubtful, and attempts 
 have been .made in vain, to estimate the 
 interval, employed in the transmission of 
 a shock through several miles of wire. 
 We are not to imagine that the same par- 
 ticles of the fluid which enter at one part, 
 pass through the •whole "conducting sub- 
 stance, any more than that the same por- 
 tion of blood, which is thrown out of the 
 heart, in each pulsation, arrives at the' 
 wrist, at the instant that the pulse is felt 
 there. The velocity of the transmission of 
 a spark or shock far exceds the actual ve- 
 locity of each particle, in the same manner 
 as the velocity of a wave exceeds that of 
 the particles of water concerned in its pro- 
 pagation ; and this velocity must depend 
 both on the elasticity of the electric fluid, 
 and on the force with which it is confined 
 to the conducting substance. If this force. 
 were merely derived from the pressure of 
 the atmosphere, we might infer the den- 
 sity of the fluid from tlie velocity of a spark 
 or shock, compared with that of sound ; 
 or we might deduce its velocity from a de- 
 termination of its density. It has been 
 supposed, although perhaps somewhat 
 hastily, that the actual velocity is nearly 
 equal to that of light. 
 
 The manner in which the electric fluid 
 makes its way, through a more or less 
 perfect nonconductor, is not completely 
 understood : it is doubtful whether the 
 substance is forced away on each side, so 
 as to leave a vacuum for the passage of 
 the fluid, or whether the newly formed 
 surface helps to guide it in its way ; and 
 in some cases it has been supposed that 
 the gradual communication of electricity 
 has rendered the substance more capable 
 of conducting it, either immediately, or, 
 in the case of the air, by first rarefying it. 
 However this may be, the perforation of a 
 jar of glass by an overcharge, and that of 
 a plate of air by a spark, appear to be 
 effects of the same kind, although the 
 charge of the jar is principally contained 
 in the glass, while the plate of air is per- 
 haps little concerned in the distribution of 
 the electricity. 
 
 The actual direction of the electric cur- 
 rent has not in any instance been fully 
 ascertained, although there are some ap- 
 pearances which seem to justify the com- 
 mon denominations of positive, and nega- 
 tive. Thus, the fracture of a charged jar 
 
42 
 
 THE ARTISAN. 
 
 of glass, by spontaneous explosion, is well 
 defined on the positive, and splintered on 
 the negative side, as might be expected 
 from the passage of a foreign substance 
 from the former side to the latter ; and a 
 candle, held between a positive and a ne- 
 gative ball, although it apparently vi- 
 brates between them, is found to heat the 
 negative ball much more than the positive. 
 We cannot, however, place much depen- 
 dence on any circumstance of this kind, 
 for it is doubtful whether any current of 
 the fluid, which we can produce, pos- 
 sesses sufficient momentum to carry with 
 it a body of sensible magnitude. It is in 
 fact of little consequence to the theory, 
 whether the terms positive and negative 
 be correctly applied, provided that their 
 sense remain determined ; and that, like 
 positive and negative quantities in mathe- 
 matics, they be always understood of 
 states which neutralise each other. The 
 original opinion of Dufay, of the ex- 
 istence of two distinct fluids, a vitreous 
 and a resinous electricity, has at present 
 few advocates, although some have thought 
 such a supposition favoured by the pheno- 
 mena of the galvanic decomposition of 
 water. 
 
 When electricity is simply accumulated 
 without motion, it does not appear to have 
 any effect, either mechanical, chemical, 
 or physiological, by which its presence 
 can be discovered ; the acceleration of the 
 pulse, and the advancement of the growth 
 of plants, which have been sometimes 
 attributed to it, have not been confirmed 
 by the most accurate experiments. An 
 uninterrupted current of electricity, through 
 a perfect conductor, would perhaps be 
 also in every respect imperceptible, since 
 the best conductors appear to be the least 
 affected by it. Thus, if we place our 
 hand on the conductor of an electrical ma- 
 chine, the electricity will pass off continu- 
 ally through the body, without exciting 
 any sensation. 
 
 The most common effect of the motion 
 of the electric fluid is the production of 
 light. Light is probably never occasioned 
 by the passage of the fluid through a per- 
 fect conductor ; for when the discharge of 
 a large battery renders a small wire lu- 
 minous, the fluid is not wholly confined to 
 the wire, but overflows a little into the 
 neighbouring space. There is always an 
 appearance of light whenever the path of 
 the fluid is interrupted by an imperfect 
 conductor ; nor is the apparent contact of 
 conducting substances sufficient to prevent 
 it, unless they are held together by a con- 
 siderable force ; thus, a chain, conveying 
 a spark or shock, appears luminous at 
 each link, and the rapidity of the motion 
 is so great, that we can never observe any 
 difference in the times of the appearance 
 
 of the light in its different parts ; so that 
 a series of luminous points, formed by the 
 passage of the electric fluid, between a 
 string of conducting bodies, represents at 
 once a brilliant delineation of the whole 
 figure in which they are arranged. A 
 lump of sugar, a piece of wood, or an egg, 
 may easily be made luminous in this, man - 
 ner; and many substances, by means of 
 their properties as solar phosphori, retain 
 for some seconds the luminous appearance 
 thus acquired. Even water is so imper- 
 fect a conductor, that a strong shock may 
 be seen in its passage through it; and 
 when the air is sufficiently moistened or 
 rarefied to become a conductor, the track 
 of the fluid through it is indicated by 
 streams of light, which are perhaps de- 
 rived from a series of minute sparks pass- 
 ing between the particles of water or of 
 rarefied air. When the air is extremely 
 rare, the light is greenish ; as it becomes 
 more dense, the light becomes blue, and 
 then violet, until it no longer conducts. 
 
 iBisreKaneousi Subjects. 
 
 MEMOIR OF THE LIFE OF JOHN 
 WALLIS, D. D. 
 
 (Continued from page 32.) 
 
 In the year 1653, came out his, u Com- 
 mercium Epistolicum,” being an episto- 
 lary correspondence between Lord Brounc- 
 ker and Dr. Wallis, on one part, and 
 Messrs. Fermate and Frenicle, (two 
 French gentlemen,) on the other; occa- 
 sioned by a challenge given by Mr. Fer- 
 mate, to the English, Dutch, and French 
 mathematicians, to answer a numerical 
 question ; but this sort of questions were 
 not such as the Doctor was fond of; there- 
 fore, at first, he did not pay that attention 
 to it which it seemed to require ; but how 
 he succeeded afterwards may be learnt 
 from the following extracts. Sir Kenelm 
 Digby thus writes to the Doctor from 
 Paris : “ I beseech you to accept of the 
 profession I here make you, with all 
 truth and sincerity ; which is, that I 
 honour most highly your great parts and 
 worth, and the noble productions of your 
 large and knowing mind, which maketh 
 you the honour of our nation, and envy of 
 all others ; certainly you have had the sa- 
 tisfaction to have had the two greatest 
 men in France, (Messrs. Fermate and 
 Frenicle) to cope with ; and I doubt not 
 but your letter will make them, and all 
 the world, give as large and as full a de- 
 ference to you. This excellent production 
 of your single brain hath convinced our 
 mathematicians here, that, like Samson, 
 
THE artisan; 
 
 43 
 
 you can easily break and snap asunder 
 all the Philistines’ cords and snares, when 
 the assault cometh warmly upon you.” Mr. 
 Frenicle writes thus to Sir Renelm Digby : 
 £< I have read over the last letter of the 
 great Dr. Wallis, from which it appears 
 plain to me, how much he excels in ma- 
 thematical knowledge. I had given my 
 opinion of him dreaming, but now I will- 
 ingly give my judgment of him waking. 
 Before, 1 saw Hercules, but it was play- 
 ing with children; now 1 behold him 
 destroying monsters at last, going forth 
 in gigantic strength. Now must Holland 
 yield to England, and Paris to Oxford.” 
 Thus ended this learned dispute ; during 
 which many other ingenious problems 
 were started, and solved, equally to the 
 honour of the doctor. 
 
 In 1655, Mr. Thomas Hobbes published 
 (i Six Lessons to the Professors of Mathe- 
 matics in Oxford.” Upon this the Doctor 
 wrote an answer, entitled, “ Due Correc- 
 tion for Mr. Hobbes, or School Discipline 
 for not saying his Lesson right.” About 
 the year 1655 he published his Arithmetic 
 of Infinites, which was evidently the 
 ground work of Sir Isaac Newton’s 
 method of Fluxions. 
 
 In 1661, he wrote and published sundry 
 tracts, and a great variety of letters, on 
 philosophical, mathematical, and mecha- 
 nical, subjects. Upon the Restoration he 
 met with great respect ; and was not only 
 admitted one of the king’s chaplains in 
 ordinary, but likewise confirmed in his 
 two places of Savillian Professor, and 
 keeper of the archives, at Oxford. It does 
 not appear that Dr. Wallis had any con- 
 siderable church-preferment, nor that he 
 was desirous of it ; for, writing to a friend 
 upon that subject, he says, “ I have not 
 been fond of being a great man; studying 
 more to be serviceable, than to be great ; 
 and therefore have not sought after it.” 
 However, in the year 1692, the queen 
 made him the proffer of the deanery 
 of Hereford, which, being not quite agree- 
 able to his mind, he declined; probably 
 not thinking it worth his accepting : for, 
 he observes to a friend upon this occasion, 
 that “ It w as a proverb, when I was a 
 boy , 1 Better sit still than rise to fall.’ If 
 I have deserved no better, I shall doubt 
 whether I have deserved this; it being but 
 equivalent to what I have, and with which 
 I am contented : I am an old man, and am 
 not like to enjoy any place long.” Thus 
 did that great and good man give his la- 
 bours to his country, without seeking 
 those emoluments and rewards which 
 others, without the least degree of merit, 
 pursue with the greatest eagerness, and 
 think themselves injured if they do not 
 attain the in. 
 
 The Doctor lived to a good old age. 
 
 being upwards of eighty-seven when he 
 died. (October 28, 1703.) He was interred 
 in the choir of St. Mary’s church, in Ox- 
 ford, where a handsome monument is 
 erected to his memory, with a Latin in- 
 scription. 
 
 ON THE TEMPERING OF STEEL. ' 
 
 The processes invented for the tempering 
 of steel have been so various and so 
 inefficient, that it is of importance to 
 select such as appear to have been at- 
 tended with success. Among those which 
 have enabled us to give to this opera = 
 tion a degree of certainty previously 
 unknown, may be mentioned the baths of 
 oil, or of a fusible metallic alloy. 
 
 Chemists in this country have made re- 
 peated experiments for the purpose of 
 determining the degrees of temperature of 
 all the common oils in a state of ebullition, 
 as well as those of the fusion of many me- 
 tallic alloys composed of bismuth, lead, 
 and tin. 
 
 Those who adopt the use of metallic 
 baths for tempering cutting instruments, 
 ought to have them heated in vessels of cast 
 iron, of different sizes and forms, accord- 
 ing to the nature of the instruments to be 
 tempered. It would be well to have two 
 of them placed one against the other in the 
 body of a register stove, to intercept at 
 pleasure the communication of the fire, in 
 order to be able to heat the one while the 
 other is tempered. This method presents 
 many advantages. 
 
 1. There is, by this means, no uncer- 
 tainty as to the decree of temperature 
 which ought to be given ; for when once 
 the operator has ascertained which of the 
 metallic baths is adapted for the descrip- 
 tion of instruments that he wishes to tem- 
 per, he has only to arrange them in a row 
 upon the surface of the solid metal, and 
 kindle a fire to make it melt ; but great 
 attention must be paid to remove all the 
 instruments quickly, and to plunge them 
 in cold water the moment the surface of 
 the metal begins to liquefy, because they 
 will then have all equally acquired the 
 same temperature. 
 
 2. It is very difficult, not to say impos- 
 sible, by the ancient method, to give the 
 instruments an equal temperature through- 
 out, when they happen to have thick 
 backs ; for frequently the blade is too hot, 
 and even experiences alterations, before 
 the other parts are sufficiently and regu- 
 larly heated. The new process of metallic 
 baths is of incalculable advantage for tem- 
 pering large files and rasps, which must 
 be left a very long time in the fire before 
 they become equally heated in all their 
 parts. We are justified in saying that 
 
44 
 
 THE ARTISAN. 
 
 there are no instruments except the largest, 
 such as ploug'h-shares, planes, &C. that 
 cannot be tempered with much more cer- 
 tainty by means of metallic baths, than by 
 the methods formerly in use. 
 
 An opinion is pretty generally enter- 
 tained, that, in the -process of tempering, 
 if the steel has been too much heated be- 
 fore fmmersion, it is necessary to give it a 
 second time an excess of temperature, to 
 bring it back to its proper degree of hard- 
 ness, and that, unless this be done, a good 
 cutting instrument cannot be made. r I his 
 is, however, a very injudicious attempt to 
 rectify one inconvenience by another ; and 
 a very little reflection will convince a 
 thinking person that the method is alto- 
 gether vicious, and has produced a great 
 quantity of bad cutlery. It may be safely 
 affirmed, that tKe lowest possible tempera- 
 ture at which steel can be tempered, is in- 
 disputably the best ; and that to repeat the 
 operation in any manner, must essentially 
 affect its principal properties. 
 
 In fact, steel which has undergone too 
 strong a temperature, rarefies, and has 
 neither a fine nor a compact grain. It is 
 so susceptible of alteration at the least de- 
 gree of heat, that, if ever so slightly ex- 
 posed to it, its cutting qualities are injured. 
 
 It will be evident from these observations, 
 that no degree of temperature can restore 
 to steel which has once been over-heated, 
 the properties it has lost. Notwithstand- 
 ing this, many workmen perform this very 
 delicate operation without any attention, 
 with the idea that they can always repair 
 their negligence by the improper method 
 we have already mentioned . — ( Ann. de la 
 Soc. d'Agr.) 
 
 DESCRIPTION AND USE OF HAD- 
 LEY’S QUADRANT. 
 
 One of the most useful and convenient 
 instruments for measuring the altitude of a i 
 celestial object, is Hadley’s Quadrant, 
 which is represented by the following 
 figure : 
 
the artisan. 
 
 45 
 
 The form of the instrument is an octa- 
 gonal sector of a circle, and contains 4.T- ; 
 but, because of the double reflexion, the 
 limb is divided into 90°. 
 
 A B, and A C, are the two radii, and 
 B C the circle or limb, which, together 
 with the braces, P Q, form the octant, or 
 frame of the quadrant; A is the index 
 glass, H the fore horizon glass, and G the 
 back horizon glass, and E F the corres- 
 ponding sight vanes; I the coloured glass, 
 the stem of which is put into the hole K, 
 when the back . observation is used ; and 
 L is a pencil for writing down the obser- 
 vation. 
 
 The altitude of any object is determined 
 by the position of the index on the limb, 
 when, by reflection, that object appears in 
 contact with the horizon. 
 
 If the object whose altitude is to be ob 
 served be the sun, and if so bright that 
 its image may be seen in the transparent 
 part of the fore horizon glass, the eye is 
 then to be applied to the upper hole in the 
 sight vane ; otherwise, to the lower hole ; 
 and, in this case, the quadrant is to be held 
 so that the sun may be bisected by the line 
 joining the silvered and transparent parts 
 of the glass. The moon is to be kept as 
 nearly as possible in the same position, 
 and the image of a star is to be observed 
 in the silvered part of the glass, adjacent to 
 the line of separation of the two parts. 
 
 There are two different methods of 
 taking observations with the quadrant. In 
 the first of these the face of the observer 
 is directed towards that part of the hori- 
 zon immediately under the sun; and is 
 therefore called the fore observation. In 
 the other method, the observer’s face is 
 directed to the opposite part of the hori- 
 zon, and consequently his back is towards 
 the part under the sun, and is hence 
 called the back observation. This last 
 method of observation is to be used only 
 when the horizon under the sun is ob- 
 scured, or rendered indistinct by fog, or 
 any other impediment. 
 
 This quadrant was first proposed by 
 Newton, but improved, or perhaps re- 
 invented, by Hadley. Its operation de- 
 pends on the effect of two mirrors, which 
 bring both the objects of which the angular 
 distance is to be measured at once into the 
 field of view ; and the inclination of the 
 speculums by which this is performed 
 serves to determine the angle. The ray 
 proceeding from one of the objects is 
 made to coincide, after two reflections, 
 with the ray coming immediately from the 
 other, and since the inclination of the re- 
 flecting surfaces is then half the angular 
 distance of the objects, this inclination is 
 read off on a scale in which every aciual 
 degree represents two degrees of angular 
 distance, and is marked accordingly. 
 
 There is also a second fixed speculum 
 placed at right angles to the moveable 
 one, when in its remotest situation, which 
 then produces a deviation of two right 
 angles in the apparent place of one of the 
 objects, and which enables us, by moving 
 the index, to measure any angle between 
 80° and 90°. 
 
 This operation is called the back obser- 
 vation ; it is however seldom employed, 
 on account of the difficulty of adjusting 
 the speculum for it with accuracy. The 
 reflecting instrument, originally invented 
 by Hooke, was arranged in a manner 
 somewhat different. 
 
 FLOATING COLLIMATOR. 
 
 A paper by Capt. H. Kater, was read 
 on the 13th January, before the Royal 
 Society, entitled “ A Description of a 
 Floating’ Collimator. 
 
 This instrument is destined to supply 
 the place of a level or plumb-line in astro- 
 nomical observations, and to furnish a 
 ready *and perfectly exact method of de- 
 termining the position of the horizontal or 
 zenith point on the limb of a circle or ze- 
 nith sector. Its principle is the invaria- 
 bility, with respect to the horizon, of the 
 position assumed by any body of invari- 
 able figure and weight floating on a fluid. 
 It consists of a rectangular box containing 
 mercury, on which is floated a mass of cast 
 iron, about twelve inches long, four broad, 
 and half an inch thick, having two short 
 uprights or Y’s of equal height, cast in 
 one piece with the rest. On these is firmly 
 attached a small telescope, furnished with 
 cross wires, or, what is better, crossed 
 portions of the fine balance spring of a 
 watch, set flat-ways, and adjusted very 
 exactly in the sidereal focus of its object- 
 glass. The float is browned with nitric 
 acid to prevent the adhesion of the mer- 
 cury, and is prevented from moving late- 
 rally by two smoothly polished iron pins, 
 projecting from its sides in the middle of 
 its length, which play freely in vertical 
 grooves of polished iron in the sides of 
 the box. When this instrument is used, 
 it is placed at a short distance from the 
 circle whose horizontal point is to be 
 ascertained, on either side (suppose the 
 north) of its centre, and the telescopes of 
 the circle and of the collimator are so ad- 
 justed, as to look mutually at each other’s 
 cross wires (in the manner lately prac- 
 tised by Messrs. Gauss and Bessel), first 
 of all coarsely, by trial, applying the eye 
 to the eye-glasses of the two instruments 
 alternately, and finally by illuminating 
 the crosss wires of the collimator with a 
 lantern and oiled paper, (taking care to 
 exclude false light by a black screen 
 
46 
 
 THE ARTISAN* 
 
 having an appertttre eqtial to that of the 
 collimator,) and making the coincidence 
 in the manner of an astronomical observa- 
 tion, by the fine motion of the circle. The 
 microscopes on the limb are then read off*, 
 and thus the apparent zenith distance of 
 the collimating point (intersection of the 
 wires) is found. The collimator is then 
 transferred to the other (south) side of the 
 circle, and a corresponding observation 
 made without reversing the circle , but 
 merely by the motion of the telescope on 
 the limb. The difference of the two zenith 
 distances so read off is double the error of 
 the zenith or horizontal point of the gra- 
 duation, and their semi sum is the true 
 zenith distance of the collimating point, 
 or the co-inclination of the axis of the 
 collimating telescope to the horizon. 
 
 By the experiments detailed in Captain 
 Rater’s paper, it appears that the error to 
 he feared in the determination of the hori- 
 zontal point by this instrument, can rarely 
 amount to half a second if a mean of four 
 or five observations be taken. In a hun- 
 dred and fifty one single trials, two only 
 gave an error of two seconds, and one of 
 these was made with a wooden float. In 
 upwards of a hundred and twenty of these 
 observations, the error was not one se- 
 cond. 
 
 ROPE BRIDGES IN INDIA. 
 
 These bridges are called Portable Rustic 
 Bridges of Tension and Suspension, and 
 they are exactly what the name describes. 
 A few hackeries will carry the whole 
 materials, and the appearance of the 
 bridge is rustic and picturesque. They 
 are distinctly bridges of tension and sus- 
 pension, having no support whatever be- 
 tween the extreme points of suspension 
 independent of the standard piles, which 
 are placed about fifteen feet from the 
 banks of the nullah, or river, except 
 what they derive from the tension, which 
 is obtained by means of purchases applied 
 to a most ingenious combination of tarred 
 coir ropes of various sizes, lessening as 
 they approach the centre. These form 
 the foundation for the pathway, and are 
 overlaid with a light split bamboo frame- 
 work. The whole of this part of the 
 fabric is a fine specimen of ingenuity and 
 mathematical application. One great ad- 
 vantage it possesses is, that if by any ac- 
 cident one of the ropes should break, it 
 might be replaced in a quarter of an 
 hour, without any injury to the bridge. 
 It is impossible in this article to give so 
 particular a description as to render its 
 minute parts clear, nor in fact can any 
 description do so unaccompanied by the 
 plan. 
 
 The chief principle of its construction j 
 is the perpendicular action of its weight, a 
 principle obviously of paramount neces- I 
 sity in this country, where the soil is so 
 loose, and offers so little resistance — and 
 more particularly in relation to *the spe- 
 cific purpose for which they were invented* 
 The whole weight of the bridge, there- I 
 fore, resting on two single points, so far 
 separated, and unassisted either by pier- 
 head or abutment, rendered its construe- ' 
 tion a matter of extreme delicacy, and it 
 has been effected in a manner reflecting 
 the highest credit on the genius of the 
 inventor. The combination of lightness 
 with security, and the adaptation, to the 
 utmost nicety, of the required propor- 
 tionate strength to the parts, forms its 
 chief characteristics. The tension power I 
 is wholly independent of the suspension. 
 
 The bridge which was placed during 
 the last rains over the Berrai torrent was 
 160 feet between the points of suspension, 
 with a road-way of nine feet, and was 
 opened for unrestricted use, excepting 
 heavy loaded carts. The mails and bang- j 
 hees passed regularly over it, and were by | 
 its means forwarded when they would 
 otherwise have been detained for several 
 days. The last rainy season was the most 
 severe within the last fifty years, and yet 
 the bridge not only continued serviceable 
 throughout, but on taking it to pieces it 
 was found in a perfect state of repair. 
 The bridge intended for the Caramnassa j 
 is 320 feet span between the points of sus- 
 pension, with a clear width of eight feet. 
 
 It is in other respects the same a3 the 
 Berai torrent bridge. A six-pounder j 
 passes over with ease ; six horsemen also 
 passed over together, and at a round pace, 
 with perfect safety. 
 
 We have no doubt but that these bridges 
 will eventually become general. During 
 the rains there will be three of them on the j! 
 great military north-west road to Benares, 
 and We feel satisfied their utility will be 
 finally established at the conclusion of the 
 season. — Calcutta John Bull. 
 
 RAIL-ROADS— LOCOMOTIVE 
 STEAM ENGINES. 
 
 On the 17th instant, a grand experi- 
 ment as to the power of locomotive en- 
 gines was performed at Killingworth Col- 
 liery, near Newcastle-upon-Tyne, in 
 presence of several gentlemen from the 
 committees of the intended Manchester 
 and Liverpool and Birmingham and Liver- 
 pool rail-road companies — when the result 
 was as follows: The engine being one of j 
 eight-horse power, and weighing, with j 
 the tender (containing water and coal?), 
 
THE ARTISAN. 
 
 47 
 
 five tons and ten hundred weight, was 
 placed on a portion of rail- road, the incli- 
 nation of which, in one mile and a quarter, 
 was stated by the proprietor, Mr. Wood, to 
 be one inch in a chain, or one part in 792: 
 twelve waggons were placed on the rail- 
 road; each containing two tons, and be- 
 tween 13 and 14 hundred weight of coals— 
 making a total useful weight of 32 tons 
 and 8 cwt. The twelve waggons were 
 drawn one mile and a quarter each way, 
 making two miles and a half in the whole, 
 in forty minutes, or at the rate of 3| miles 
 an hour, consuming four pecks and a half 
 of coals. Eight waggons were then drawn 
 the same distance in thirty-six minutes, 
 consuming four pecks of coals; and six 
 waggons were drawn over the same ground 
 in thirty two minutes, consuming five pecks 
 of coals. Our correspondent also men- 
 tions, that the engine must be supplied 
 with hot or boiling, and not with cold 
 water; and that two hundred gallons of 
 water will take the engine 14 miles, at the 
 end of which the supply must be re- 
 newed. 
 
 RHABDOLOGICAL ABACUS. 
 
 A paper, drawn up by Dr. Gregory, was 
 lately read before the Astronomical So- 
 ciety of London, containing a description 
 of a box of rods, named the Rhabdological 
 Abacus , presented to the Society by the 
 family of the late Henry Goodwyn, Esq. 
 of Blackheath. It appears that these rods 
 were invented by Mr. Goodwyn for the 
 purpose of facilitating the multiplication of 
 long numbers of frequent occurrence : they 
 were probably suggested by Napier’s Rods, 
 and are, for the purposes which the inven- 
 tor had in view, a great improvement upon 
 them. The rods, which are square prisms, 
 contain on each side, successively, the pro- 
 posed number in a multiplicand, and its 
 several multiples up to nine times ; and 
 these in the several series of rods are re- 
 peated sufficiently often to serve for as ex- 
 tensive multiplications as are likely to 
 occur. Thus if the four faces of one rod 
 contain respectively, once, twice, three 
 times, and four times a proposed multipli- 
 cand ; another rod will exhibit in like 
 manner two, three, four, and five times the 
 same ; a third rod, three, four, five, and 
 six times the same ; and so on to nine ; and 
 in several cases, more rods. The numbers 
 are arranged uniformly upon equal and 
 equidistant compartments ; while at a small 
 constant distance to the left of each pro- 
 duct, stands the number two, three, four, 
 five, &c. which it represents. Hence, in 
 performing a multiplication, the operator 
 has only to select from the several faces of 
 the rods the distinct products which belong 
 
 to the respective digits in the multiplier, to 
 place them in due order above each other, 
 to add them up while they so stand, and 
 write down their sum, which is evidently 
 the entire product required, and obtained 
 without the labour of multiplying for each 
 separate product, or even of writing those 
 products down. For still greater conveni- 
 ence, the rods may be arranged upon a 
 board with two parallel projections placed 
 aslant at such an angle as of necessity 
 produces the right arrangement. There 
 are blank rods to place in those lines 
 which accord with a cypher in the multi- 
 plier ; and the arrangement may easily be 
 carried on from the bottom product up- 
 wards, by means of the indicating digits. 
 
 DENSITY OF WATER. 
 
 An elaborate memoir by Professor Hal- 
 lostrom, on the specific gravity of water at 
 different temperatures, and on the tempe- 
 rature of its maximum density, has ap- 
 peared in the Swedish Transactions for 
 1823. It is divided into two parts: The 
 first contains a critical discussion of the 
 results, and the methods employed by pre- 
 ceding experimenters : the second, a de- 
 tail of an extensive course of experiments, 
 instituted by himself, with a view to the 
 more accurate determination of this im- 
 portant but difficult inquiry. The method 
 of experimenting which he regarded as the 
 most accurate, and which he therefore 
 adopted, was to ascertain the weight of a 
 hollow glass globe, very little heavier than 
 water, and about inches in diameter, in 
 water of every degree of temperature be- 
 tween 0° and 32/5° cent. The errors aris- 
 ing from a dilatation or contraction of the 
 glass, the weight of the atmosphere, &c. 
 were all calculated, and a corresponding 
 correction made. The result was, that 
 water attains its greatest density at a 
 temperature of 4*108° cent. (39*394° 
 Fahr.) ; and the limits of uncertainty, 
 occasioned by the impossibility of ascer- 
 taining the dilatation of glass with perfect 
 accuracy, he estimates to be 0*238° (0*428° 
 Fahr.) on either side of this number. 
 
 PROF. OERSTED ON A METHOD 
 OF ACCELERATING THE DIS- 
 TILLATION OF LIQUIDS. 
 
 In Gehlen’s Journal fur Chemie und 
 Physik, i. 277 — 289, I have related a few 
 experiments which demonstrate that the 
 disengagement of gas in a fluid, resulting 
 from chemical decomposition, never takes 
 place except in contact with some solid 
 
4 S 
 
 THE ARTISAN. 
 
 body. This principle may without doubt 
 be applied to the disengagement of va- 
 pours. If a metallic wire be suspended in 
 a boiling fluid, it instantly becomes co- 
 vered with bubbles of vapour. Hence it 
 might be concluded, that a large number 
 of metallic wires, introduced into a fluid 
 which we wish to distil, wrnuld accele- 
 rate, the formation of vapours. To prove 
 this opinion, I introduced 10 pounds of 
 brass wire, of one-fifth of a line in diame- 
 ter, loosely rolled up, into a distillatory 
 vessel containing 20 measures (about 10 
 pints) of brandy : the result was, that 
 seven measures of brandy distilled over 
 with a heat, which, without the wire, 
 was capable of sending over only four 
 measures. 
 
 An expedient similar to this has been 
 long in common use in England. When a 
 steam-boiler has- become encrusted with so 
 much earthy matter, that the contained 
 water ceases to boil with rapidity, it is 
 customary to throw in a quantity of the 
 residue obtained from malt, by extracting 
 its soluble portion, and which consists 
 chiefly of small grains of fibres. Here the 
 disengagement of vapour is promoted by 
 the large number of thin and solid par- 
 ticles. — (Tidskrift for Naturvidenska- 
 berne.) 
 
 SOLUTIONS OF QUESTIONS. 
 Quest. 56, (page 16) answered by 
 
 G. G. C. 
 
 This question was, by mistake, numbered 
 the same as another at page 400, vol. i. 
 
 Present value of 50 
 
 calves at 21s. £52 
 
 10 0 
 
 
 Interest for 3 years 7 
 
 17 6 £ 
 
 s. d. 
 
 
 60 
 
 7 6 
 
 Grazing 50 cal. at 10s. 25 
 
 0 0 
 
 
 Wintering 49 cal. at 15s. 36 
 
 15 0 
 
 
 61 
 
 15 o 
 
 
 Interest for 2 years 6 
 
 3 6 
 
 
 
 67 
 
 18 6 
 
 Grazin g 48 cattle at 20s. 48 
 
 0 0 
 
 
 Wintering 47 do. at 25s. 58 
 
 15 0 
 
 
 106 
 
 15 0 
 
 
 Interest for 1 year 5 
 
 6 9 
 
 
 
 112 
 
 1 9 
 
 Grazing 46 cattle at 30s. 69 
 
 0 0 
 
 
 Wintering45do.at40s. 90 
 
 0 0 
 
 
 
 159 
 
 0 0 
 
 
 399 
 
 7 9 
 
 Amount of 44 cattle, at £10 10s is 462 
 
 0 0 
 
 Gain by bringing them up 
 
 £62 
 
 12 3 
 
 This question was also answered cor- 
 rectly by the Proposer ; but we received a 
 solution which was not correct. 
 
 Quest. 57, answered by J. D. Ironmon- 
 ger-lane. 
 
 Put x and y zz the days in which A and 
 B respectively could have done the work, 
 12 , 12 
 
 tuen— -j zz 1, and x 2 xy zz 1000. 
 
 x y 
 
 In the first, the value of «isz — ; 
 
 J x—12 
 
 12 x 2 
 
 consequently xy zz if this be sub- 
 
 x—12 
 
 stituted for xy in the second, and the re- 
 sult reduced, we obtain this equation 
 S 3 — 1000 * -j- 12000 zz 0 ; which being 
 resolved, gives xzzz20 days, and therefore 
 y zz 30 days, the time in which each could 
 have done the work. 
 
 This question was also answered by 
 Mr. Whitcombe. 
 
 Quest. 58, answered by Mr. W. Ander- 
 son, Strand. 
 
 1728 -f- (^) 2 zz 1728 X 1600zz2764800 x 
 •7854zz3520252 incheszz55 m. 4f. 104 yds. 
 2 ft. 4 inches. 
 
 This question was also correctly an- 
 swered by Mr. Harding, Mr. J. Stephens, 
 Mr. J. Taylor, Mr. Whitcombe, and Mr. 
 A. Copcake. 
 
 QUESTIONS FOR SOLUTION. 
 
 Quest. 60, proposed by Mr. W. Taylor, 
 Hackney. 
 
 A ball descending by the force of gra- 
 vity from the top of a tower, was observed 
 to fall half the way in the last second of 
 time ; required the tower’s height, and 
 the whole time of descent? 
 
 Quest. 61, proposed by Peter Plus, 
 Portpairick. 
 
 A hare starts 5 rods before a greyhound, 
 and is not perceived by him till she has 
 been up 34 seconds ; she scuds away at 
 the rate of 12 miles per hour, and the dog, 
 on view, makes after at the rate of 20 i 
 miles ; how long will the course hold, j 
 and how far will the dog have run when j 
 he overtakes the hare ? 
 
 To be solved without usingany algebraic j 
 characters. 
 
THE ARTISAN, 
 
 4-J 
 
 riEUHAms. 
 
 AIR AS THE VEHICLE OF SOUND. 
 
 The vibrations immediately dependent 
 on elasticity, are those of rods, plates, 
 rings, and some kinds of vessels, such as 
 drinking glasses. These admit of much 
 greater variety, but they are of more diffi- 
 cult investigation than the vibrations of 
 chords ; we shall therefore notice those 
 only, that seem to have something particu- 
 lar belonging to them. 
 
 The vibrations of plates may be traced 
 through wonderful varieties, by Professor 
 Chladni’s method of strewing dry sand on 
 the plates, which, when they are caused 
 to vibrate by the operation of a bow, is 
 collected into such lines as indicate those 
 parts, which remain either perfectly, or 
 very nearly at rest during the vibrations. 
 Dr. Hooke had employed a similar me- 
 thod, for showing the nature of the vibra- 
 tions of a bell ; and it has sometimes been 
 usual, in military mining, to strew sand 
 on a drum, and to judge by the form in 
 which it arranges itself, of the quarter 
 from which the tremours produced by 
 countermining proceed. The following 
 are specimens of the simplest manner in 
 which sand is collected into lines, on a 
 plate of glass or metal, which is made to 
 sound by means of the bow of a violin. 
 
 The following figure represents a round 
 plate performing some of its most com- 
 licated vibrations, the lines of division 
 eing indicated by the place of the sand. 
 
 The following is a representation of a 
 square plate, divided into a diversity of vi- 
 brating portions. 
 
 Vol. II.— No. 29. 
 
 The vibrations of rings and of vessels 
 are nearly connected with those of plates, 
 but they are modified in a manner which 
 has not yet been sufficiently investigated. 
 A glass or a bell divides in general into 
 four portions vibrating separately, and 
 sometimes into six or eight ; they may be 
 readily distinguished by means of the 
 agitations excited by them in a fluid con- 
 tained in the glass. It is almost unneces- 
 sary to observe, that the fluid thus applied, 
 by adding to the mass of matter to be 
 moved, makes the vibration slower, and 
 the sound more grave. 
 
 In some cases the vibrations of fluids 
 and solids are jointly concerned in the 
 production of sound : thus, in most of the 
 pipes of an organ denominated reed pipes, 
 the length of a tongue of metal is so ad- 
 justed, as to be capable of vibrating in the 
 same time with the air contained in the 
 pipe. Sometimes, however, the air only 
 serves to excite the motion of the solid, as 
 in some other organ pipes, which are 
 usually much shorter than would be re- 
 quired for producing the proper note alone, 
 and probably in the glottis, or organ of 
 the voice of animals. On the other hand, 
 the alternate opening and shutting of the 
 lips, in blowing the trumpet or French 
 horn, can scarcely be called a vibration, 
 and the pitch of the sound is here deter- 
 mined by the properties of the air in the 
 pipe only. The vibrations of a solid may 
 be excited by an undulation propagated 
 through a fluid ; thus, when a loud sound 
 strikes against a chord, capable of vibrat- 
 ing, either accurately, or very nearly, with 
 the same frequency, it causes a sympathe- 
 tic tone, resembling that from which it 
 originated ; and the chord may produce 
 such a sound, either by vibrating as a 
 whole, or by dividing itself into any num- 
 ber of equal parts. Thus, if the damper 
 be raised from any of the strings of a 
 harpsichord, it may be made to vibrate, by 
 striking or singing any note, of which the 
 sound corresponds, either to that of the 
 whole string, or to that of any of its ali- 
 quot parts. Sometimes also, two chords 
 that are very nearly alike, appear, when 
 sounding together, to produce precisely 
 the same note, which differs a little from 
 each of those which the chords would pro- 
 duce separately; and a similar circum- 
 stance has been observed with respect to 
 D 
 
so 
 
 THE ARTISAN. 
 
 two organ pipes placed near each other. 
 In these cases, the vibrating substances 
 must affect each other through the medium 
 of the air, nearly in the same manner as 
 two clocks, which rest on the same sup- 
 port, have been found to modify each 
 other’s motions, so as to exhibit a perfect 
 coincidence in all of them. 
 
 When sounds of different musical strings 
 are compared, a certain difference between 
 them is perceived by the ear, which is 
 called difference of tone ; and this differ- 
 ence is also expressed by saying, that the 
 one sound is graver, and the other more 
 acute ; the variations of tone are found to 
 have a constant or fixed relation to the 
 comparative celerities of vibration. 
 
 As the string performs more vibrations 
 in a given time, the sound it yields be- 
 comes more acute, and as it vibrates more 
 slowly, the sound is graver. This is 
 easily brought to the test of experiment. 
 The strings that vibrate faster, either from 
 the greater tension, or their smaller length 
 and weight, invariably produce sounds 
 that are more acute, &c. 
 
 If eight strings be such, that the num- 
 bers of the vibrations they perform in a 
 given time, are as the numbers 24, 27, 30, 
 32, 36, 40, 45, 48, the sounds of the first 
 seven will be perceived, as increasing in 
 acuteness one above another, from the first 
 to the last, and will yield the notes from 
 the combinations of which all musical 
 effects are produced. 
 
 The tone is not affected by the extent of 
 the vibrations, but merely by their time. 
 The loudness of the sound is supposed to 
 depend on the greater extent of the vibra- 
 tions. Noise and discordant sounds arise 
 from a want of isochronism of vibration. 
 When the vibrations are isochronous, or 
 all performed in the same time, the sounds 
 are always musical. 
 
 The last of the strings will sound what 
 is called the octave above the first, and the 
 same series may be repeated again between 
 the numbers 48 and its double 96, and 
 each note will be an octave above its cor- 
 responding note in the first interval; the 
 numbers of vibrations will be 54, 60, 64, 
 72, 80, 90, 96 ; and it is evident that this 
 series may be continued, either up or down, 
 without limit. 
 
 The musical scale thus formed, is called 
 the diatonic scale. 
 
 The pleasure derived from the succes- 
 sive or simultaneous perception of the 
 sounds of this series, appears to be an 
 ultimate fact that can be no farther ana- 
 lysed, but must be referred to the original 
 constitution of the mind. The selections of 
 the combinations of these notes, capable of 
 affording high degrees of pleasure, is the 
 object of the musical art. 
 
 The number of vibrations performed in 
 
 a given time by any sonorous body, may 
 be determined by comparing its sound 
 with the note that is sounded by a musical 
 string of a given length, weight, and 
 tension. The ear is sufficient to decide 
 what string in a harpsichord is in unison 
 with the given sound. The number, of vi- 
 brations performed in a given time by the 
 former, is equal to the number of those 
 performed in the same time by the latter. 
 
 All musical sounds are computed to be 
 contained within ten octaves ; so that the 
 number of vibrations in a given time that 
 yields the gravest note, is to that which 
 yields the most acute, as 1 to 2 10 , or as 
 1 to 1024. 
 
 OF WIND. 
 
 The principal cause of those currents of 
 air, to which we give the name of winds, 
 is the disturbance of the equilibrium of 
 the atmosphere, by the unequal distribu- 
 tion of heat. 
 
 The air or atmosphere which surrounds 
 the earth is a fluid, possessing, in a remark - 
 able degree, the property of being greatly 
 expanded or rarefied by heat, and con- 
 densed by cold. Therefore, when any 
 portion of the air is heated, whether by a 
 natural or artificial cause, it becomes rarer, 
 and consequently ascends to the higher 
 parts of the atmosphere: the cool and 
 dense air then rushes in to restore the 
 equilibrium, and the air at the surface 
 moves from the poles towards the equator. 
 The only supply for the air thus constantly 
 abstracted from the higher latitudes, must 
 be produced by a counter-current in the 
 upper regions of the atmosphere, carrying 
 back the air from the equator toward the 
 pole. The quantity of air tansported by 
 these opposite currents, is so nearly equal, 
 that the average weight of the air, as mea- 
 sured by the barometer, is the same in all 
 places of the earth. 
 
 If the surface of the earth were wholly 
 covered with water, so that there was no 
 part of it more disposed than another to 
 obstruct the motion of the air, or that had 
 a greater capacity than another, of acquir- 
 ing or communicating heat, the air would 
 probably circulate continually in this man- 
 ner from the poles to the equator, and back 
 again, without any irregularity whatso- 
 ever. 
 
 In consequence of the rotation of the 
 earth on its axis, another motion is com- 
 bined with that of the currents just des- 
 cribed. The air, which is constantly 
 moving from points where the earth's mo- 
 tion on its axis is slower, to those where it 
 is quicker, cannot have precisely the same 
 motion eastward with the part of the sur- 
 face over which it is passing, and there- 
 fore must, relatively to that surface, des- 
 cribe a curve, having its convexity turned 
 
THE ARTISAN, 
 
 51 
 
 to the east. The two currents, therefore, 
 from the opposite hemispheres, when they 
 meet toward the middle of the earth, have 
 each acquired an apparent motion west- 
 ward, and as their opposite motions from 
 south and north must destroy one another, 
 nothing will remain but this motion, by 
 which they will go on together, and form 
 a wind blowing directly from the east. 
 
 This is the cause of the trade wind , 
 which, {with certain exceptions} blows 
 continually between the tropics, or rathef 
 between 30° on the one side of the equator, 
 and 30° on the other. 
 
 The trade wind declines somewhat from 
 due east toward the parallel to which the 
 sun is vertical at different seasons of the 
 year. As the sun approaches the southern 
 tropic, the trade wind is directed some- 
 what to the south ; and as he approaches 
 the northern, somewhat to the north. 
 
 The cause usually assigned for the trade 
 wind, is the constant motion toward the 
 west of the spot to which the sun is verti- 
 cal, and where of course the rarefaction is 
 greatest. This, it is supposed, draws along 
 with it the air from the east. This, how- 
 ever, is by no means satisfactory ; and it 
 seems certain, that if the trade wind were 
 produced in this way, it must have a great 
 rapidity, in place of being a gentle breeze, 
 at the rate of seven or eight miles an hour. 
 
 The opinion that the trade wind is pro- 
 duced by the air in its motion southward, 
 falling back toward the west, is mentioned, 
 but rejected, by Halley. It has since been 
 espoused by Franklin and La Place, and 
 is, on the whole, less objectionable than 
 any other. 
 
 The matter is here stated somewhat 
 differently from what is done by those 
 authors, particularly the effect of the cur- 
 rents from the opposite hemispheres, in 
 determining the motion to be wholly from 
 the east. 
 
 The attractions of the sun and moon 
 have sometimes been considered as among 
 the general causes of the winds. They 
 have, no doubt, a tendency to produce in 
 the atmosphere an undulation backwards 
 and forwards, like the tides which they 
 cause in the ocean. It does not appear, 
 however, that they could produce any 
 continued progressive motion of the air, 
 similar to that of the trade winds. Their 
 effects also are too minute to be perceived, 
 amid the action of so many more powerful 
 causes. 
 
 The superior current above described 
 restores the air carried from the higher 
 latitudes to the lower with such a degree 
 of equality, that the average weight of the 
 atmosphere, as measured by the barometer, 
 is nearly the same in all climates. This 
 restoration is, however, subject to great 
 local and temporary irregularities, from 
 
 the different degrees of resistance that the 
 air meets with in passing over the surface, 
 and the different capacities of that surface 
 for receiving and communicating heat. 
 
 The motion of the inferior and superior 
 currents may be seen exemplified on open- 
 ing a door between two apartments of dif- 
 ferent temperatures. The flame of a can- 
 dle near the ground will show the stream 
 that sets from the colder room to the 
 warmer ; near the top it will indicate a 
 stream in the opposite direction. As the 
 average quantities of the air carried by 
 these opposite currents are equal, the sur- 
 face that separates them is probably not far 
 different from that at which the barometer 
 would stand at 15 inches, or half its me- 
 dium height, at the surface. 
 
 If we suppose the mean temperature to 
 be 32°, this elevation will be found zz 3010 
 fathoms, or 18,060 feet zz 3*425 miles ; 
 which is not so high as the summits of the 
 Cordilleras. 
 
 The upper stream in each hemisphere 
 being directed to one point, namely, the 
 pole of that hemisphere, there must arise a 
 considerable condensation and acceleration 
 of the air, as the currents approach that 
 point ; and hence the causes of irregular 
 winds must be increased on approaching 
 the poles. 
 
 The general direction of the upper cur- 
 rent must be to the westward ; for the same 
 reason that that of the lower was toward 
 the east. 
 
 The trade wind itself is subject to cer- 
 tain irregularities. As the sun advances 
 into the northern hemisphere, the trade 
 wind becomes irregular; and about the 
 middle of April, in all the tract between 
 Africa and the Peninsula of India, and 
 much beyond, changes from north-east to 
 south-west, and continues to blow in that 
 direction till the sun returns to the south- 
 ern hemisphere. 
 
 The cause of this change is difficult to 
 be assigned. It seems probable that, by 
 the sun’s entry into the northern hemis- 
 phere, he communicates great heat to the 
 sandy deserts of Africa, which lie to the 
 west or south-west of the seas just men- 
 tioned. The great heat acquired by the 
 sand of those deserts produces a rarefac- 
 tion in the columns of air incumbent upon 
 them, and consequently a tendency, in the 
 columns that are near them, and more mo- 
 derately heated, to flow in and displace 
 the heated air. The air of the Atlantic is 
 most likely to do this ; and in passing over 
 Nigritia, &c., to acquire a velocity that 
 carries it on eastward through the Indian 
 ocean. 
 
 These periodical winds are called Mon- 
 soons. 
 
 The change, or the setting in of the 
 monsoons, does not happen all at once. 
 
 D 2 
 
52 
 
 THE ARTISAN. 
 
 In some places the shifting of the wind is 
 accompanied with calms ; in others, with 
 variable winds, heavy rains, thunder, and 
 violent storms. 
 
 The tract from the parallel of 30° to the 
 pole, in each hemisphere, is the region of 
 variable winds ; and their unsteadiness 
 and violence seem to increase the nearer 
 they approach the polar circles. 
 
 The irregularity of winds proceeds from 
 inequalities in the motion of the general 
 currents above-mentioned, and from a va- 
 riety of local causes ; also from the che- 
 mical changes that are carried on in the 
 air ; such as the solution and precipitation 
 of moisture, and the action of the electric 
 fluid on the different gases which compose 
 the atmosphere. 
 
 Sudden and strong gales of wind appear 
 most always to arise from a diminution of 
 the weight of the air in the tract where the 
 wind prevails ; and are accompanied or 
 preceded by a fall of the barometer. 
 
 Notwithstanding these irregularities, 
 there is in most countries a tendency to 
 periodical winds more or less remarkable, 
 
 according to the steadiness of the climate. 
 Even with us, where an insular situation, 
 with a great continent on one side, and a 
 great ocean on the other, unites all the 
 causes of a variable climate, the east wind 
 usually prevails in the spring, from the 
 vernal equinox to the summer solstice, and 
 beyond it ; during the rest of the year, the 
 westerly winds prevail, though not with- 
 out frequent incursions of the east ; by 
 which our most unpleasant weather is 
 always produced. 
 
 The Etesian , or northerly wind, prevails 
 very much in summer all over Europe. 
 Pliny describes it as blowing regularly in 
 Italy for forty days after the summer sol- 
 stice, lib. ii. cap. 47. It is part of the 
 great current that carries the atmosphere 
 of the higher latitudes down to the tropical 
 regions. 
 
 The velocity of the wind varies from one 
 that is hardly sensible to one of 100 miles 
 in an hour. 
 
 The velocity of wind may be estimated 
 by the velocity of clouds, or of light bodies 
 carried by it. 
 
 PERSPECTIVE. 
 
 Having given a comprehensive and po- 
 pular view of the beautiful and interesting 
 science of Optics, we shall now introduce 
 an equally beautiful and useful branch of 
 natural philosophy — that is, Perspective. 
 This may be considered as a continuation 
 of Optics, its fundamental principles being 
 derived from that science, while its appli- 
 cation is regulated by laws purely geome- 
 trical. 
 
 But though a correct knowledge of geo- 
 metry is indispensably necessary to the 
 acquirement of a complete knowledge of 
 the practical part of perspective, we shall 
 endeavour to convey a knowledge of the 
 elementary and most useful part of this 
 art, to those who have made but small pro- 
 gress in the study of Geometry. 
 
 Perspective is the art of delineating 
 visible objects upon a plane surface, so 
 
 that the figure drawn may represent the 
 same form and position, w hich the object 
 holds in nature, or, as it would be found 
 to be represented upon the retina, in the 
 bottom of the eye. 
 
 Perspective is usually divided into two 
 blanches, linear and aerial. 
 
 Linear Perspective regards the position, 
 magnitude, form, &c. of the several lines 
 or colours of objects, and the manner of 
 exhibiting their diminution. It is, there- 
 fore, the mathematical part of perspec- 
 tive. 
 
 Aerial Perspective is that which regards 
 the colour, lustre, strength, boldness, &c. 
 of distant objects, considered as viewed 
 through a column of air ; it therefore forms 
 an important part of the art of painting. 
 
 Linear Perspective > suppose a glass 
 plane, as 
 
THE ARTISAN. 
 
 53 
 
 H I raised perpendicular on an horizontal 
 plane; and the spectator S directing his 
 eye O, to the triangle ABC: if now we 
 conceive the rays AO, OB. OC, &c. in 
 their passage through the plane, to leave 
 their traces or vestigia, in a, b, c, &c. on 
 the plane ; there will appear the triangle 
 a b c, which, as it strikes the eye by the 
 rays a O, b O, c O, by which the species 
 of the triangle A B C is carried to the 
 same ; it will exhibit the true appearance 
 of the triangle A B C, though the object 
 should be removed; the same distance 
 and height of the eye being preserved. 
 The business of perspective , then, is to 
 show by what certain rules the points 
 a b c, &c. may be found geometrically : 
 and hence also, we have a mechanical 
 method of delineating any object very 
 accurately. 
 
 In delivering the general laws of this 
 branch of study, it is necessary to premise 
 the following properties of a right line; 
 namely, That the appearance of a right 
 line is ever a right line, whence the two 
 extremes being given, the whole line is 
 given. That if a line F G, as represented 
 in the following figure, 
 
 be perpendicular to any right line NI 
 drawn on a plane, it will be perpendicular 
 to every other right line through the same 
 point G, drawn on the same plane. That 
 the height of the point appearing on a 
 plane, is to the height of the eye, as the 
 distance from the objective point from the 
 plane, to the aggregate of that distance, 
 and the distance of the eye. 
 
 Besides these elementary observations, 
 it is necessary we should subjoin the fol- 
 lowing definitions , respecting the various 
 planes, &c. referred to when treating of 
 Perspective. 
 
 DEFINITIONS. 
 
 1 . The plane on which the representa- 
 tion, projection, or picture of any object 
 is drawn, is called the perspective plane , 
 and also the plane of the picture. It is 
 supposed to be placed between the eye and 
 the object. 
 
 2. The point of sight is that point from 
 which the picture ought to be viewed. 
 This point is also called the point of view. 
 
 3. If from the point of sight, a line be 
 drawn at right angles to the picture or 
 perspective plane, the point in which it 
 meets that plane is called the centre of the 
 picture; and the distance between that 
 centre and the point of sight, or the per- 
 pendicular above mentioned, is called the 
 distance of the picture. 
 
 4. By original object, is meant the real 
 object placed in the situation it is repre- 
 sented to have by the picture. 
 
 5. By original plane, is meant the plane 
 on which any original point, line, or plane 
 figure, is situated. 
 
 6. The point in which any original line, 
 or any original line produced, cuts the 
 perspective plane, is called the intersection 
 of that line. 
 
 7. The line in which any original plane 
 cuts the perspective plane, is called the 
 intersection of that original plane. If the 
 original plane be that of the horizon, its 
 intersection with the picture, or the line 
 above mentioned, is called the ground 
 line. 
 
 8. The point in which a straight line 
 drawn through the point of sight parallel 
 to any original line cuts the picture, is 
 called the vanishing point of that ori- 
 ginal line. And the distance between 
 that point and the point of sight, is simply 
 called the distance of that vanishing point. 
 
 9. The line in which a plane drawn 
 through the point of sight parallel to any 
 original plane cuts the perspective plane, 
 is called the vanishing line of that original 
 plane. If from the point of sight there be 
 drawn a line cutting that vanishing line at 
 right angles, the point of intersection is 
 called the centre of the vanishing line. 
 And the distance between the point of 
 sight and that point or centre, is called 
 simply the distance of the vanishing line. 
 
 10. If from a given point, a straight 
 line be drawn at right angles to any plane, 
 the point of intersection is called the seat 
 or orthographic projection of the given 
 point on that plane. And if from all the 
 points of any line or plane figure perpendi- 
 culars be drawn to any plane, the line or 
 figure formed by their intersections with 
 it, is called the seat or orthographic pro- 
 jection of the given line or figure on that 
 plane. 
 
 Previous to giving rules for delineating 
 objects according to the established laws 
 of perspective, we shall shov.' how this may 
 be done in a mechanical manner, by means 
 of a frame with cross threads or wires, in- 
 terposed between the eye and the object. 
 The eye is to be applied to an aperture, 
 which must be fixed, in order to preserve 
 the proportions of the picture ; and which 
 must be small, in order that the threads 
 and the more distant objects may be viewed 
 at the same time with sufficient distinct- 
 
54 
 
 THE ARTISAN. 
 
 ness. The paper being furnished with 
 corresponding lines, we may observe in 
 what division of the frame any conspicu- 
 ous point of the object appears, and may 
 then represent its image by a point simi- 
 larly situated among the lines drawn on 
 our paper; and having obtained in this 
 manner a sufficient number of points, we 
 may complete the figures by the addition 
 of proper outlines. 
 
 Sometimes, for the delineation ^f large 
 objects requiring close inspection, it has 
 been found useful to employ two similar 
 
 frames, the one a little smaller than the 
 other, and placed a certain distance from 
 it, so that every part of the object, when 
 seen through the corresponding divisions 
 of both frames, appears in the same man- 
 ner as if the eye were situated at a very 
 remote point. 
 
 The following figure represents an in- 
 strument of this kind. The dotted lines 
 show how a second frame may be applied 
 instead of the sight, so as to answer the 
 same purpose. 
 
 Having now shown the nature of per- attempt to illustrate the principles of thi& 
 spective drawing, and given a number of art, by showing how any object may be 
 definitions, in order to render the subject represented upon a plane, as it actually 
 as intelligible as possible, we shall next appears in nature. 
 
 A being the place of the eye, and BC point, and EL, IL their whole images: 
 the plane of projection, if AD be parallel and A O being parallel to P Q, O will be 
 to E F, G H, and I K, D will be their its vanishing point. 
 
 vanishing point, and ED, GD, and ID, Let A be the centre of the picture re- 
 their whole images : A L being parallel to presented by the following figure. 
 
 E M and I N, L will be their vanishing 
 
THE ARTISAN. 
 
 AB the horizontal vanishing line, AC species that can be distinguished amongst 
 the vertical line, and D the point of dis- the ores of this metal is infinitely more 
 tance, if a ground plane EFGH of any limited than those which are admitted in 
 figure on the horizontal plane be placed in most of the other metals. The mine- 
 .its true position with respect to IK, the ralogists, who have hitherto considered 
 bottom of the picture, the vanishing point its varieties as species, have moreover 
 of all its lines will be found, by drawing committed another error ; namely, that of 
 I> L, DM, D N, and D O parallel to those having too closely followed the errors and 
 lines respectively ; and the whole images prejudices of the miners. These, consider- 
 of the lines will be P L, Q M, K N, and ing as ores of silver all those ores that are 
 
 I O, determining by their intersections 
 the figure R S T U, which will be the pro- 
 jection of E F G H. The plan may also be 
 drawn in an inverted position, below the 
 line I K, and the point of distance taken 
 above A, instead of below it. 
 
 In order to find the position of the image 
 of a given point of a line, we must divide 
 the whole image in such a manner, that 
 its parts may be to each other, in the same 
 proportion as the distance of the given 
 point, and of the eye, from the plane of 
 projection. This may be readily done, 
 when a ground plan has been first made, 
 by drawing a line from any point in the 
 plan, to the point of distance, which will 
 cut the whole image of the line in the 
 point required, as in the following figure : 
 A B, being the whole image of the line re- 
 presented by A C as a ground plan, and D 
 
 the point of distance, we may find E the 
 image of the point C, by drawing C D ; or 
 we may make B F — B D, and A G~ AC, 
 F G will then also cut A B in the point E. 
 
 CHEMISTRY. 
 
 SILVER. 
 
 Silver is a very good conductor of elec- 
 tricity and galvanism. It has no sensible 
 taste nor smell ; neither does it produce 
 any effect upon the animal economy ; and 
 though it cannot be considered as dan- 
 gerous to the health, it must, nevertheless, 
 be reckoned amongst the number of per- 
 fectly inert substances, destitute of any 
 medicinal property. 
 
 Nature presents silver neither in such 
 abundance, nor in so many places, nor in 
 such large masses, as most of the other 
 metallic substances. Even the number of 
 
 capable of affording this precious metal, 
 of whatever nature they may be, which 
 have very much obscured the natural 
 history of this metal. 
 
 Pure silver, when exposed to the air, 
 remains in it without alteration, except 
 with respect to its polish and brilliancy ; 
 it becomes less shining and a little tar- 
 nished at its surface, but without being, 
 oxidized. We ought not, however, ta 
 confound the kind of covering or stratum 
 of a deep blue colour, which is formed 
 upon old silver plate exposed for a long 
 time to the contact of several gases mixed 
 with the air; with a stratum which, accord- 
 ing to the examination of it instituted by 
 Mr. Proust, as merely a sulphuret of this 
 metal. Silver has long been believed to 
 he perfectly indestructible by the contact 
 of the air, even when aided by a very in- 
 tense heat; and on this account it was 
 ranked amongst the perfect metals. Se- 
 veral Chemists, and especially Junker, 
 had advanced, that by treating silver by 
 a long reverberation, and in a furnace 
 where the flame circulated above the 
 metal, the silver was at last converted into 
 a vitriform oxide. It has even been added, 
 that when united with mercury, and di- 
 vided by this liquid metal, it was oxidized 
 by the processes which are usually em- 
 ployed for converting mercury into red 
 oxide,, and which is not improbable. 
 
 Many experiments made since the asser- 
 tion of Junker, and by different pro- 
 cesses, have proved that silver is really 
 oxidizable, but only that it is much less 
 so, and with much greater difficulty, than 
 the other metals. Macquer was the first 
 who remarked this oxidation, by exposing 
 silver in a crucible to the intense heat of 
 the furnace of Sevres twenty successive 
 times. At the last time, very sensible 
 traces of oxidation were perceived, and a 
 vitrification of an olive colour. Macquer 
 never failed to observe, when treating 
 silver in the focus of a burning glass, 
 that after a long incandescence, it be- 
 came covered with a white powder, 
 which formed a stratum upon the support 
 of the silver. Homberg, in the first expe- 
 riments with the burning glass of Tchirs- 
 hausen, had made the same observations 
 upon silver and upon gold. It cannot be 
 doubted that these facts indicate a marked 
 oxidation of the silver, and that they be- 
 come more strong and conclusive when 
 
THE ARTISAN. 
 
 &3 
 
 joined with the experiments which we 
 shall mention. 
 
 Van Marum made many valuable re- 
 searches respecting the effects of electri- 
 city with the grand machine of Teyler, 
 and found that it took fire and burned. 
 By passing the electric shock from a 
 battery through a wire of this metal, the 
 wire is suddenly reduced, asdt were, into 
 powder, with a greenish white flame, 
 which passes with the rapidity of light- 
 ning, and the oxide manifestly formed in 
 this operation is dissipated in smoke. If 
 we perform the same operation by w rap- 
 ping up the wire, or fixing it upon white 
 paper, it attaches itself to it in a very fine 
 powder of a greenish grey colour, so fine 
 and so adherent, that it resembles smoke, 
 or a light covering which cannot be sepa- 
 rated from it again. It is impossible here 
 to doubt either of the state of oxidation of 
 the silver, or of its combustiblity ; because 
 the phenomenon is constantly accompanied 
 with flame. We may attribute this effect, 
 which is not produced by ordinary fire, 
 however intense it may be, to the extreme 
 division of the metal by the electric shock, 
 and to the high temperature produced by 
 the electric composition in the body which 
 is exposed to it. A stroke of lightning 
 upon silver wires and silver furniture, 
 produces exactly the same phenomena, and 
 is followed by the same results. 
 
 The oxide of silver formed by these 
 different processes, and which is so diffi- 
 cult to be obtained, is likewise extremely 
 easy of reduction, because the silver ad- 
 heres to the oxygen very weakly. Though 
 the presence of this body augments its 
 weight, changes its properties, and espe- 
 cially renders it acrid and caustic, nothing 
 more is required than to expose these 
 greenish or yellowish grey oxides to the 
 contact of the solar rays, in order to make 
 them assume a darker colour, become 
 black, and approach to the metallic state. 
 When we heat them in close vessels, and 
 with the pneumatic apparatus, we obtain 
 from them pure oxygen gas, and easily 
 convert them into the brilliant and ductile 
 metal, by fusing them in a crucible. 
 
 Neither carbon nor hydrogen have been 
 combined with silver ; but it combines 
 readily with sulphur and phosphorus. 
 
 It is well known, that when silver is 
 long exposed to the air, especially in 
 frequented places, as churches, theatres, 
 &c. it acquires a covering of a violet 
 colour, which deprives it of its lustre and 
 malleability. This covering, which forms 
 a thin layer, can only be detatched from 
 the silver by bending it, or breaking it in 
 pieces with a hammer. It was examined 
 by Mr. Proust, and found to be sulphuret 
 of silver . 
 
 Silver does not combine with the simple 
 
 incombustibles. 
 
 Silver combines readily with the greater 
 number of metallic bodies. 
 
 When silver and gold are kept melted 
 together, they combine, and form an alloy, 
 composed, as Homberg ascertained, of one 
 part of silver and five of gold. He kept 
 equal parts of gold and silver in gentle 
 fusion for a quarter of an hour, and found, 
 on breaking the crucible, two masses, the 
 uppermost of which was pure silver, the 
 undermost the whole gold combined with 
 | of silver. Silver, however, may be 
 melted with gold in almost any proportion ; 
 and if the proper precautions be employed, 
 the two metals remain combined together. 
 
 The alloy of gold and silver is harder 
 and more sonorous than gold. Its hard- 
 ness is a maximum when the alloy contains 
 two parts of gold and one of silver. The 
 density of these metals is a little ’dimin- 
 ished, and the colour of the gold is much 
 altered, even when the proportion of the 
 silver is small ; one part of silver produces 
 a sensible change in twenty parts of gold. 
 The colour is not only pale, but it has also 
 a very sensible greenish tinge, as if the 
 light reflected by the silver passed through 
 a very thin covering of gold. This alloy, 
 being more fusible than gold, is employed 
 to solder pieces of that metal together. 
 
 When silver and platinum are fused to- 
 gether, (for which a very strong heat is 
 necessary,) they form a mixture, not so 
 ductile as silver, but harder and less 
 white. The two metals are separated by 
 keeping them for some time in the state of 
 fusion ; the platinum sinking to the bottom 
 from its weight. This circumstance would 
 induce one to suppose, that there is very 
 little affinity between them. Indeed, Dr. 
 Lewis found, that when the two metals 
 were melted together, they sputtered up 
 as if there were a kind of repugnance be- 
 tween them. The difficulty of uniting 
 them was noticed also by Scheffer. 
 
 OF PALLADIUM. 
 
 This metal was first found by Dr. Wol- 
 laston combined with platina, among the 
 grains of which he supposes its ore to 
 exist, or an alloy of it with iridium and 
 osmium, scarcely distinguishable from the 
 crude platina, though it is harder and 
 heavier.. 
 
 Palladium is of a greyish white colour, 
 scarcely distinguishable from platina, and 
 takes a good polish. It is ductile and 
 very malleable; and being reduced into 
 thin slips, is flexible, but not very elastic. 
 Its fracture is fibrous, and in diverging 
 striae, showing a kind of crystalline ar- 
 rangement. In hardness it is superior to 
 wrought iron. Its specific gravity is from 
 10’9 to 11*8. It is a less perfect conductor 
 of caloric than most metals, and less ex- 
 pansible, though in this it exceeds platina. 
 
THE ARTISAN. 
 
 57 
 
 On exposure to a strong heat, its surface 
 tarnishes a little, and becomes blue; but 
 an increased heat brightens it again. It 
 is reducible per se. Its fusion requires a 
 much higher heat than that of gold ; but if 
 touched while hot with a small bit of sul- 
 phur, it runs like zinc. The sulphuret is 
 whiter than the metal itself, and extremely 
 brittle. 
 
 Nitric acid soon acquires a fine red 
 colour from palladium, but the quantity it 
 dissolves is small. Nitrous acid acts on 
 it more quickly and powerfully. Sulphu- 
 ric acid, by boiling, acquires a similar co- 
 lour dissolving a small portion. Muriatic 
 acid acts much in the same manner. Nitro- 
 muriatic acid dissolves it rapidly, and 
 assumes a deep red. 
 
 Alkalis and earths throw down a preci- 
 pitate from its solutions generally of a fine 
 orange colour ; but it is partly re-dissolved 
 in an excess of alkali. Some of the neutral 
 salts, particularly those of potash, form 
 with it triple compounds, much more solu- 
 ble in water than those of platina, but 
 insoluble in alcohol. 
 
 Alkalis acts on palladium even in the 
 metallic state ; the contact of air, however, 
 promotes their action. 
 
 A neutralized solution of palladium is 
 precipitated of a dark orange or brown 
 colour by recent muriate of tin ; but if it 
 be in such proportions as to remain trans- 
 parent, it is changed to a beautiful eme- 
 rald green. Green sulphate of iron pre- 
 cipitates the palladium in a metallic state. 
 Sulphuretted hydrogen produces a dark 
 brown precipitate ; prussiate of potash an 
 olive coloured: and prussiate of mercury 
 a yellowish white. As the last does not 
 precipitate platina, it is an excellent test 
 of palladium. This precipitate is from a 
 neutral solution in nitric acid, and deto- 
 nates at about 500° of Fahr., in a manner 
 similar to gunpowder. Fluoric, arsenic, 
 phosphoric, oxalic, tartaric, citric, and 
 some other acids, with their salts, precipi- 
 tate some of the solutions of palladium. 
 
 When strongly heated, its surface as- 
 sumes a blue colour; but by increasing 
 the temperature, the original lustre is 
 again restored. This blue colour is doubt- 
 less a commencement of oxidizement ; but 
 neither the properties of the oxides of this 
 metal, nor the proportion of oxygen with 
 which it combines, have been ascertained. 
 
 The effect of hydrogen upon palladium 
 has scarcely been tried. Chenevix melted 
 the metal in a charcoal crucible, but it 
 was not in the least altered. 
 
 Palladium unites very readily to sul- 
 phur. When it is strongly heated, the 
 addition of a little sulphur causes it to 
 run into fusion immediately, and the sul- 
 phuret continues in a liquid state till it be 
 only obscurely red hot. Sulphuret of pal- 
 ladium is rather paler than the pure metal, 
 
 and is extremely brittle. By means of heat 
 and air, the sulphur may be gradually 
 dissipated, and the metal obtained in a 
 state of purity. 
 
 Azote has probably no effect upon it; 
 but muriatic acid promotes its oxidize- 
 ment, and forms a red solution with the 
 oxide. 
 
 OF MERCURY. 
 
 Mercury, like some other metals, ap- 
 pears to have received its name from the 
 planet, with which it was compared by 
 the Persians, on account of its nature, 
 which was supposed to approach to that of 
 gold, as this planet is nearest to the sun, 
 and has been known since the most re- 
 mote ages of antiquity. From a compari- 
 son of its properties with those of silver, 
 it was long ago termed quicksilver , hydrar- 
 gyrum. In the species of hieroglyphics 
 that were formerly employed for repre- 
 senting bodies, mercury was represented 
 by the combined signs of the sun and 
 moon, or of gold and silver, linked toge- 
 ther, and supported upon a cross. 
 
 The alchemists have laboured much 
 upon this metal. They considered it as 
 very much resembling gold and silver, and 
 differing but very little from them ; they 
 imagined that it wanted but very little to 
 become either the one or the other, and 
 they always hoped to discover the means 
 of transmuting it into these metals. Some 
 of them have even affirmed, that they had 
 succeeded in effecting this transmutation. 
 These adepts agree •with each other, that 
 it is much more easy to convert it into 
 silver than into gold. According to them, 
 in order to convert it into silver, nothing 
 more is required than to fix it. It was, 
 therefore, in this fixation of mercury that 
 they made all the art of their opus mag- 
 num, all the marvellous part of their sci- 
 ence to consist; this was the grand object 
 of their attention, and the scope of all 
 their wishes. All these pretensions, how- 
 ever, are not supported by a single well- 
 attested fact : and the more we advance in 
 the study of the properties of mercury, the 
 more differences we find between it and 
 the metals to which it has been supposed 
 to approach the nearest. 
 
 The most celebrated philosophers, and 
 the most able chemists, have all succes- 
 sively occupied themselves with this metal : 
 they have endeavoured to ascertain all its 
 properties with more or less precision ; 
 and the use which has been made of it since 
 the end of the last century, or since the 
 time of Boyle, in the construction of a 
 great number of philosophical instru- 
 ments, has afforded frequent occasion for 
 investigating and examining its different 
 characters. It is in this manner that its 
 weight, its phosphorescence, its dilatibi- 
 
§8 
 
 THE ARTISAN, 
 
 lity, its volatility, its alterability, its along the shore ; fancies that every thing 
 mobility, &o. have been successively ascer- which the carriage or vessel passes is in 
 tained. motion, and that he is himself at rest. 
 
 The application of the pneumatic che- An appearance still more deceiving 
 mistry has connected together all the takes place, when a person looks out of 
 known facts relative to the chemical pro- the cabin window of a ship, in a dark 
 perties of mercury ; it has given rise to night, at a distant light apparently in 
 the discovery of a considerable number of motion. For the change of place in the 
 
 new ones ; it has elucidated a great num- 
 ber of facts which before could not be ex- 
 plained ; it has drawn from oblivion seve- 
 ral which were neglected, or in a manner 
 abandoned; it has dissipated all the ob- 
 scurity, ambiguity, or uncertainty that re- 
 mained in the enunciation of its proper- 
 ties ; it has conducted Chemists to several 
 important discoveries : such as the mutual 
 differences between the greater part of the 
 metallic or mercurial salts ; the compara- 
 tive state of the different oxides of mer- 
 cury ; the action of each oxide upon this 
 metal or its oxides ; the formation of seve- 
 ral triple salts ; the cause of the energy 
 and causticity of the mercurial salts or 
 oxides ; the spontaneous reduction of these 
 oxides; their decompositions by some of 
 the metals ; the nature and characters of 
 several precipitates ; the different states of 
 some of its solutions; the extinction of 
 mercury in a number of substances, which 
 had always been considered as a simple 
 division, but which, in reality, is a true 
 oxidation. Mercury being one of the most 
 useful of metallic substances for medical 
 purposes, for the arts, and for all those 
 branches of knowledge which extend our 
 views of nature, we shall give a full de- 
 tail of its properties. 
 
 4STEOHOMY, 
 
 MOTIONS OF THE EARTH. 
 
 When we consider the apparent diurnal 
 motion of all the celestial bodies, we can- 
 not but recognise the existence of one ge- 
 neral cause, which produces this appear- 
 ance. But when we consider that these 
 bodies are not only at different distances 
 from the earth, but at different distances 
 from each other, and that these distances 
 are not always the same, we shall find it 
 difficult to conceive that it is the same 
 cause that produces this appearance on all 
 of them. 
 
 The difficulty, however, becomes con- 
 siderably less when it is recollected, that 
 a person in motion, looking at an object at 
 rest, perceives the same change of position 
 in the object as if he were himself at rest, 
 and the object in motion in the opposite 
 direction. Every one who has looked, for 
 the first time, from the window of a car- 
 riage moving quickly along the road ; or 
 from the deck of a ship sailing smoothly 
 
 light may arise either from its being really 
 in motion, or on board of another vessel, 
 while the vessel, in which the spectator is, 
 is placed at anchor ; or the light may be 
 stationary, and its apparent motion occa- 
 sioned by the motion of the ship which 
 carries the spectator ; or it may even be 
 occasioned by the motion of the vessel 
 which carries the light being quicker or 
 slower than the one which carries the 
 spectator. The difficulty in determining 
 to which of these causes the motion of the 
 light is to be attributed, arises from the 
 want of some intervening object whose 
 state is known, and by which the apparent 
 motion may be compared. Now this 
 is precisely the situation in which we 
 stand with regard to the heavenly bodies. 
 For the motion of the earth on its axis, if 
 it really has such a motion, must be in- 
 comparably smoother than any vessel or 
 machine made by human art; and as there 
 is no fixed intermediate object between it 
 and the heavenly bodies, no direct proof 
 of this motion can be obtained. 
 
 As far, then, as appearances enable us 
 to judge, either the earth may be at rest, 
 and the heavens carried round it every 
 twenty-four hours* or the heavens may be 
 at rest, and the earth revolve round its 
 axis, in the same time. For the rising and 
 setting of the sun and stars, with all the 
 other celestial phenomena, will be pre- 
 sented in the same order whether the hea- 
 vens revolve round the earth, or the earth 
 round its axis. 
 
 However, on comparing these appear- 
 ances with others which are more within 
 our reach, and with the established laws 
 of motion, we shall find it is much more 
 probable they are occasioned by the revo- 
 lution of the earth on its axis, than the re- 
 volution of the whole heavens. For as the 
 heavenly bodies present the same appear- 
 ances to us, whether the firmament carries 
 them round the earth, or the earth itself 
 revolves in a contrary direction, it seems 
 much more natural to admit the latter hy- 
 pothesis than the former, and to regard 
 the motion of the heavens as only ap- 
 parent. 
 
 The semidiameter of the earth is only 
 about 4000 miles, and consequently its cir- 
 cumference is about 25,000 miles. 
 
 This is, therefore, the space every point 
 of its equator must pass through, if the 
 earth revolves on its axis, which is little 
 more than 1000 miles per hour, or about 
 17 miles per minute, This velocity is cer- 
 
THE ARTISAN. 
 
 59 
 
 aj tainly very considerable, being nearly 
 equal to that of a cannon-ball when it 
 ij leaves the mouth of a cannon; but it be- 
 comes totally insignificant when compared 
 of with the motion of some of the heavenly 
 rk bodies, required on the other supposition, 
 in The distance of the sun from the earth is 
 is about ninety-five millions of miles; and 
 ly therefore if he revolves round the earth in 
 1 twenty-four hours, he must pass over more 
 ij j than six times this space in the same time, 
 be | and consequently must move at the rate 
 a. of about 25,000,000 miles per hour, which 
 :h is more than 20,000 times quicker than a 
 e { cannon-ball. The planet Uranus is about 
 el twenty times farther distant from the earth 
 or than the sun, and consequently the velo- 
 ie city of its daily motion must be twenty 
 ijj times greater. But although these velo- 
 ie cities are sufficient to startle the imagina- 
 ie tion, they are really nothing when com- 
 ie pared to the rapidity with which the fixed 
 at stars must movedo accomplish a revolution 
 is round the earth in twenty-four hours. If 
 ;e the distance of the fixed stars be assumed 
 s, at 200,000 times the distance of the sun 
 if from the earth, they must move over the 
 ], space of 1,400,000,000 miles per second, 
 ir in order to complete a revolution round 
 e the earth in twenty-four hours ! This is a 
 it | degree of velocity of which we can have 
 if J no kind of conception ; and yet, if we con- 
 
 I sider the velocity which those stars must 
 have that are many thousands of times 
 more distant from the earth, it must be 
 y almost infinitely greater. If we, there - 
 i 0 ij fore, take into consideration the number of 
 is bodies that must move, and the prodigious 
 d rapidity of their motions, to produce the 
 P same appearances which the revolution of 
 : one body, with a comparatively moderate 
 velocity, can produce, we shall scarcely 
 b ! hesitate a moment in concluding that the 
 motion of this one body is the true cause 
 of these appearances. 
 
 n This conclusion must appear still more 
 s j obvious when we attend to the compara- 
 e tive bulk of these different bodies. Of the 
 ' planets which belong to the solar system, 
 3 three of them are known to be much 
 e I greater than the earth ; Jupiter being 
 j nearly fifteen hundred times ; Saturn nine 
 s & hundred times ; and Uranus eighty times, 
 f But the sun exceeds them all in magnitude, 
 s being considerably more than a million of 
 0 times greater than the earth. Our igno- 
 j ranee of the' real distances of the fixed 
 j stars prevents us from ascertaining cor- 
 I rectly their real magnitudes ; but, from 
 y what we know of their distances, we are 
 l entitled to conclude that they are at least 
 j equal in size to the largest of the planets. 
 \ If such, therefore, be the magnitude of 
 these bodies, how inconsistent would it be 
 with every idea of order and arrangement 
 it to suppose, that such a vast number of im- 
 
 mense bodies daily revolve round such a 
 little and comparatively insignificant body 
 as the earth ! What extraordinary power 
 would be necessary to retain them in their 
 orbits, and counterbalance the amazing 
 centrifugal force which they must possess! 
 The idea, too, of so many immense and in- 
 dependent bodies, so vastly distant from 
 the earth and from each other, performing 
 their revolutions round this little ball, ex- 
 actly in the same number of seconds, is 
 scarcely to be entertained for a single mo- 
 ment : all the phenomena, especially when 
 supposed to arise from these revolutions, 
 can be satisfactorily and easily accounted 
 for, by supposing the earth to revolve on 
 its axis. 
 
 If we suppose the planets to be carried 
 round the earth, from east to west, every 
 twenty-four hours, and also allow them a 
 motion peculiar to themselves from west to 
 east, (which they are observed to have,) 
 we produce such a combination of opposite 
 motions, as has never yet been observed 
 in any of the heavenly bodies, and which 
 it would be impossible to ^reconcile with 
 any of the known principles of mechanics. 
 But the rotation of a body on its axis, 
 combined with a motion in its curvilineal 
 orbit, is what we are quite familiar with, 
 and what is exhibited by a school-boy by 
 spinning his top. 
 
 But one of the strongest proofs of the ro- 
 tation of the earth is its figure. For it is 
 now well known that the earth is not a 
 perfect sphere: its polar diameter being 
 considerably less than its equatorial.* It 
 is also known that this is the shape which 
 a spherical body would in time assume, if 
 it revolved on a fixed axis ; and therefore 
 it is reasonable to conclude that the sphe- 
 roidical figure of the earth is occasioned 
 by its rotatory motion. This conclusion is 
 supported by the extraordinary fact, that 
 the difference between the polar and equa- 
 torial axis of the earth, as deduced from 
 theory alone, is nearly the same as from 
 actual measurement of various arcs of me- 
 ridian circles. — The same conclusion is 
 farther supported by analogy. 
 
 A rotatory motion has been observed in 
 several of the other planets, and from west 
 to east, the direction in which the earth 
 must resolve in order to occasion the ap- 
 parent diurnal motion of the heavens from 
 east to west. Jupiter, a much larger 
 body than the earth, turns round his axis 
 in less than twelve hours. Now both the 
 earth and Jupiter are known to be flattened 
 at the poles. All these facts, therefore, 
 lead us to conclude, that the earth has 
 really a motion of rotation, and that the 
 
 * Some of the objections which have been stated 
 against the rotation of the earth will be noticed in 
 treating of the Ptolemaic and Tychonic systems. 
 
m 
 
 THE ARTISAN. 
 
 diurnal motion of the heavens is only an 
 illusion produced by this rotation. 
 
 The diurnal rotation of the earth being 
 assented to, its annual motion will scarcely 
 be denied ; for its similarity to the other 
 planets is considerably strengthened by 
 this circumstance. For the planets being 
 found to revolve on their axis, and to be 
 flattened at the poles like the earth ; and 
 being found to have periodical revolutions 
 from west to east, we are led to suppose, 
 that the earth has a similar revolution, in 
 order to render the analogy between it and 
 the rest of the planets complete. But the 
 appearances afford us as little assistance 
 in ascertaining the truth of this supposi- 
 tion, as in the case of the diurnal motion ; 
 for, whether we suppose the earth to be at 
 rest and the sun to move round it in the 
 ecliptic in the course of a year, or the sun 
 to be at rest and the earth to describe this 
 path in the same time ; the phenomena of 
 the seasons, eclipses, and all other appear- 
 ances connected with the sun’s annual mo- 
 tion, may be explained on either hypothe- 
 sis. But, although this be the case, it is 
 much more probable that these appear- 
 ances are produced by the annual motion 
 of the earth round the sun, than by the 
 motion of the sun round the earth. For by 
 supposing the earth to move round the sun, 
 we not only give order and simplicity to 
 the solar system, and preserve the analogy, 
 which is so conspicuous among the other 
 bodies which compose that system, but we 
 remove several difficulties which unavoid- 
 ably attend the opposite hypothesis. — It 
 has already been remarked, that the earth 
 is considerably smaller than several of the 
 other planets, and that it is about fourteen 
 hundred thousand times less than the sun ; 
 it is therefore quite inconsistent with every 
 idea of order and arrangement to suppose, 
 that bodies of such extraordinary size 
 should revolve round one of comparatively 
 small magnitude. For, independent of the 
 complication of the planetary motions 
 which such a supposition would introduce, 
 it would overthrow one of the best estab- 
 lished principles of mechanics,! and is 
 quite inconsistent with the law which is 
 known to subsist between the times of the 
 revolutions of the planets, and their dis- 
 tance from the sun. For the farther they 
 are from the sun, their motion is the slower. 
 Their periodic times of revolution being to 
 each other as the cubes of their mean dis- 
 tances from the sun. Now, according to 
 this remarkable law, the length of a revo- 
 lution of the earth round the sun, should 
 be exactly a sidereal year. This is there- 
 fore an incontestible proof that the earth 
 moves round the sun, like the other pla- 
 nets, and is subject to the same laws. To 
 this we may add, that the aspects of in- 
 crease and decrease of the planets, the 
 
 times of their seeming to stand still, and 
 move direct and retrograde, answer pre- 
 cisely with the motion of the earth: but 
 cannot be reconciled with that of the sun, 
 without introducing the most absurd and 
 monstrous suppositions, which would 
 destroy all order, harmony, and simplicity, 
 in the system. 
 
 But the most direct proof of the earth’s 
 annual motion is derived from the aberra- 
 tion of light. For during the time which 
 light takes to pass over the semidiameter 
 of the earth’s orbit, which is 8' 13", the 
 earth ought to move 20" , 232 in its orbit, and 
 this is found by observations to be actually 
 the case. 
 
 The annual as well as the diurnal motion 
 of the earth may, therefore, be considered 
 as completely established. The objections 
 which have been urged against these mo- 
 tions, by the supporters of the Ptolemaic 
 and Tychonic systems of the heavens, will 
 be noticed when treating of these systems. 
 
 To the texts of Scripture which seem to 
 contradict the motions of the earth, the 
 following reply may be made to them all. 
 That it is plain from many instances, that 
 the Scriptures were never designed to in- 
 struct men in philosophy, but in matters 
 of religion, and are not always to be taken 
 in the literal sense. For Job describes 
 the earth as being supported upon pillars , 
 and in another place as being hung upon 
 nothing ; and Moses calls the moonja great 
 luminary, although it is well known to be 
 an opaque body, which shines only by re- 
 flecting the light of the sun. 
 
 It is perfectly certain these expressions 
 were not meant to convey any astronomical 
 opinion; but employed because they ■would 
 be easily understood by those to whom 
 they were immediately addressed. In 
 familiar discourse, astronomers them- 
 selves speak of the sun’s place in the 
 ecliptic, of his rising and setting, &c. ; for 
 if they did not, they would be under the 
 necessity of explainining their meaning 
 every time they had occasion to mention 
 those appearances. 
 
 ON THE CHANGE OF SEASONS.* 
 
 The alternate succession of day and 
 night, as well as the variety of seasons, 
 depend entirely on the motions of the 
 earth. For if the sun and the earth were 
 perfectly at rest with respect to each 
 other, it is evident that one half of the 
 earth would always be in the light, and 
 the other half in darkness, as the sun can 
 only enlighten one half of its surface at a 
 
 * If a terrestrial globe be placed in the various 
 positions mentioned in this article, it will contribute 
 very much to impress the mind with the true cause 
 of the change of the seasons. 
 
THE ARTISAN. 
 
 61 
 
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 time. But as the earth turns round its 
 axis once in twenty-four hours, any par- 
 ticular place on its surface will pass 
 through light and darkness alternately. 
 As long as it continues in the enlightened 
 hemisphere, it will be day at that place ; 
 but while it passes through the opposite 
 hemisphere, it will be night. But although 
 the regular succession of day and night be 
 occasioned by the diurnal revolution of the 
 earth on its axis, yet this motion is not of 
 itself sufficient to produce that variety in 
 the lengths of days and nights, which the 
 various places of the earth experience in 
 the course of a year. 
 
 For should it revolve on its axis, with 
 one of its poles always pointed exactly to 
 the sun, one half of the earth would be 
 constantly in the light and the other half 
 in darkness, notwithstanding its rotation. 
 Again, if we suppose the earth to turn on 
 its axis, with its equator directly pointed 
 to the sun, then the light would just reach 
 both poles, consequently all places would 
 be in light and darkness alternately, and 
 the days and nights would be exactly 
 twelve hours each at every part of the 
 globe. 
 
 If either extremities of the earth’s axis, 
 suppose the northern, were to make an 
 acute angle with an imaginary line joining 
 the centre of the sun with any point of 
 the earth’s equator, it would follow that 
 the north pole, and a certain tract round 
 it, would remain always in the light, not- 
 
 withstanding the revolution of the earth 
 on its axis. Even those places in the 
 northern hemisphere to which the sun ap- 
 peared to rise and set, would have their 
 days always longer than their nights ; at 
 the equator the days and nights would be 
 equal ; but in the southern hemisphere the 
 reverse would happen to what took place 
 in the northern. For those places to 
 which the sun appeared to rise and set 
 would have their nights longer than their 
 days ; and the south pole would be con- 
 stantly in darkness, with a tract around it 
 equal to what was constantly in the light 
 round the north pole. It is evident, also, 
 that in this case the sun would be always 
 on the north side of the equator, and ver- 
 tical to a certain circle parallel to it, which 
 would be as many degrees from the equa- 
 tor, as the angle contained between the 
 earth’s axis and the imaginary line wanted 
 of a right angle. 
 
 This last supposition is in some degree 
 similar to what actually takes place in na- 
 ture; for the axis of the earth makes an 
 angle of 23§ degrees, with a perpendicular 
 to its orbit ; and as the axis always re- 
 mains parallel to itself, or points in the 
 same direction, this angle must be con- 
 stantly changing as the earth moves for- 
 ward in its orbit.* 
 
 This is well represented by the follow- 
 ing figure, which shows the earth at twelve 
 different times of the year. 
 
 The line a b is the equator, n the north 
 pole, and s the south. The signs of £ . 
 
 &c. denote the points of the ecliptic in 
 which the earth is when it has the positions 
 in the figure. 
 
 As the position of the poles of the earth, 
 with respect to the sun, depends entirely 
 on this angle, their position must always 
 be changing; and, of course, every point 
 on the earth’s surface must also alter its 
 
 position with respect to the sun. About 
 the 20th of March, when the sun, as 
 seen from the earth, enters the sign Aries, 
 the line supposed to join the centres of the 
 earth and sun is perpendicular to the 
 earth’s axis ; consequently both poles are 
 
 # Or, what amounts to the same thing, the axis 
 of the earth makes an angle with the plane of the 
 ecliptic of 66| degrees. 
 
62 
 
 THE ARTISAN. 
 
 similarly situated with respect to the sun, 
 as he is then directly over the equator, and 
 the days and nights are equal at every 
 place on the globe. This time of the year 
 is called the vernal equinox, because 
 spring commences to the inhabitants of the 
 northern hemisphere, while autumn begins 
 to those of the southern. 
 
 fHtsceHancous Subjects. 
 
 MEMOIR OF THE LTFE OF GODE- 
 
 FROY WILLIAM DE LEIBNITZ. 
 
 Godefroy William de Leibnitz, an emi- 
 nent mathematician and philosopher in the 
 17 th century, was born at Leipsic in 
 Saxony, in 1646. He soon made a prodi- 
 gious progress in polite literature ; and at 
 the age of fifteen years he applied himself 
 to mathematics at Leipsic and Jena ; and 
 upon his return to Leipsic in 1663, he 
 maintained a thesis de Principiis Indivi- 
 duationis. The year following he was 
 admitted master of arts. About this time 
 he read with great attention the Greek 
 philosophers ; and endeavoured to recon- 
 cile Plato with Aristotle, as he afterwards 
 did Aristotle with Des Cartes. But the 
 study of the law was his principal view ; 
 in which faculty he was admitted bache- 
 lor in 1665. The year following he would 
 have taken the degree of doctor, but was 
 refused it on pretence that he was too 
 young, but in reality because he had 
 raised himself several enemies, by reject- 
 ing the principles of Aristotle and the 
 schoolmen. Upon this he went to Altorf, 
 where he maintained a thesis de Casibus 
 Perplexis with such applause, that he had 
 the degree of doctor conferred on him, 
 and was offered a professorship extraordi- 
 nary in law, which he refused. Thence 
 he went to Nuremberg to visit the learned 
 men there, and was introduced into the 
 acquaintance of several persons engaged 
 in the pursuit of the philosopher’s stone. 
 In 1672 he went to Paris, and there con- 
 tracted a friendship with the learned men, 
 and applied himself with vigour to the 
 mathematics. Having observed some de- 
 fects in the arithmetical machine of Mr. 
 Pascal, he invented a new one, which was 
 so approved by Mr. Colbert and the aca- 
 demy of sciences, that they offered him 
 the place of pensionary-member. He 
 might have settled to great advantage at 
 Paris ; but as it would have been neces- 
 sary to have embraced the Roman Catholic 
 religion, he refused all offers. In 1673 
 he went to England, where he became ac- 
 quainted with Mr. Oldenburg, secretary 
 of the Royal Society, and Mr. John Col- 
 lins, fellow of that, society. Soon after 
 
 the elector of Mentz died, by which he lost 
 his pension. He returned to France, 
 whence he wrote a letter to the Duke of 
 Brunswick, to inform him of his circum- 
 stances. The prince returned him a kind 
 answer ; and, as a pledge of his future 
 favour, appointed him counsellor of his 
 court, with a stipend, and gave him leave 
 to continue at Paris till his arithmetical 
 machine should be completed. In 1676 he 
 returned to England, and thence went into 
 Holland, in order to proceed to Hanover, 
 where he proposed to settle. Upon his 
 arrival there, he applied himself to enrich 
 the duke’s library with the best books of 
 all kinds. The duke dying in 1679, his 
 successor, Ernest Augustus, then bishop 
 of Osnabrug, shewed our author the same 
 favour as his predecessor had done, and 
 ordered him to write the history of the 
 house of Brunswick. He undertook it, 
 and travelled over Germany and Italy in 
 order to collect materials, and returned to 
 Hanover in 1690. In 1700 be was ad- 
 mitted a member of the Royal Academy at 
 Paris. The elector of Brandenburg, after- 
 wards king of Prussia, founded an aca- 
 demy the same year at Berlin by his ad- 
 vice ; and he was appointed perpetual 
 president, though his affairs would not 
 permit him to reside constantly at Berlin. 
 However, he furnished their memoirs with 
 several curious pieces in geometry, polite 
 literature, natural philosophy, and even 
 physic. He projected an academy of the 
 same kind at Dresden, and communicated 
 the plan to the king of Poland in 1703; 
 and this design would have been executed, 
 if it had not been prevented by the confu- 
 sions in Poland. He was engaged like- 
 wise in a scheme for an universal lan- 
 guage. His writings had long before made 
 him famous over all Europe. Besides the 
 office of privy-counsellor of justice, which 
 the elector of Hanover had given him, the 
 emperor appointed him in 1711 Aulic 
 counsellor ; and the czar made him his 
 privy-counsellor of justice, with a pension 
 of a thousand ducats, after a conversation 
 with him at Torgaw, at the time of the 
 marriage of the princess of Wolfenbuttel 
 with the son of that prince. He under- 
 took at the same time the establishment of 
 an academy of the sciences at Vienna ; but 
 the plague prevented the execution of it. 
 However, the emperor, as a mark of his 
 favour, settled a pension on him of two 
 thousand florins, and promised him another 
 of four thousand, if he would come and 
 reside at Vienna. He would have com- 
 plied with this offer, but he was prevented 
 by death. Upon his return to Hanover in 
 1714, he found that the elector, who was 
 then raised to the throne of Great Britain, 
 had appointed Mr. Eckhard his colleague 
 in writing the history of Brunswick. — 
 
THE ARTISAN. 
 
 6& 
 
 This work was interrupted by others 
 which he wrote occasionally. The last 
 affair he was engaged in was his dispute 
 with Mr. Samuel Clarke ; which was put 
 an end to by Mr. Leibnitz’s death, occa- 
 sioned by the gout and stone, November 
 14th, 1716, aged 70. His memory was 
 so strong, that, in order to fix any thing in 
 it, he had no more to do but to write it 
 once, and never read it again ; and he 
 could, even in his old age, repeat Virgil 
 exactly. He was of a warm temper, and 
 was very sensible of the honour of being 
 considered as one of the greatest men in 
 Europe. He made use of the favour of 
 princes for learning as well as himself. 
 He professed the Lutheran religion, but 
 never went to sermon ; and upon his death- 
 bed, his coachman, who was his favourite 
 servant, desiring him to send for a minis- 
 ter, he refused, saying, he had no need of 
 one. Mr. Locke and Mr. Molyneux plainly 
 seem to think he was not so great a man 
 as he had the reputation of being ; and, in 
 truth, many of his metaphysical notions 
 are quite unintelligible. In his Theodicte 
 he seems to have had a confused idea of 
 the true philosophy ; but it is not well 
 digested, nor did he seem to perceive all 
 ; the consequences of it. However, he was 
 certainly a great genius, but dissipated by 
 too great ambition to excel in every thing. 
 
 | Foreigners did for some time ascribe to 
 him the honour of an invention, of which 
 be received the first hints from Sir Isaac 
 ! Newton’s letters, who had discovered the 
 method of fluxions in 1664 and 1665. It 
 would be tedious to give the reader a de- 
 tail of the dispute concerning the right to 
 that invention. The method of fluxions 
 and the Calculus Differ entialis are the 
 same method of analysis under two dif- 
 ferent names. Sir Isaac Newton and the 
 English call it the method of fluxions ; but 
 Leibnitz gave it the name of Calculus 
 Diff er entialis , in which he has been fol- 
 lowed by all the mathematicians abroad. 
 The Marquis de l’Hospital published the 
 elements of it under the title of The Ana- 
 lysis of Infinitely Small Quantities . The 
 very learned and ingenious Dr. Berkely, 
 bishop of Cloyn in Ireland, has given rise 
 to many pamphlets in defence of this 
 highly-boasted of science. Many’ways of 
 speaking, at least, in it were very excep- 
 tionable. But Mr. Maclauran, professor 
 of the mathematics in the university of 
 Edinburgh, X published a treatise of flux- 
 ions ; in which he proceeds with the 
 preciseness of the ancient geometricians, 
 has set the first principles of that science 
 in [a clear light, and carried it to a vast 
 height of perfection. By so doing, he has 
 put an end to verbal disputes, which had 
 | got into that science, as well as others, 
 
 | that had^ been long plagued and incum- 
 
 bered by them, and was like to have ob- 
 structed its progress, and employed men 
 of genius in jangling more than invention. 
 With regard to the disputes between him 
 and Dr. Clarke about space, none of them 
 express themselves clearly or philosophi- 
 cally enough. Nothing hath been reckon- 
 ed by philosophers so obscure as time and 
 place, or space ; yet the vulgar, and they 
 themselves, too, in the affairs of life, un- 
 derstand it very well. And yet I think 
 every body would understand this propo- 
 sition : a body would go on in the same 
 line of direction for ever, did it meet with 
 nothing to obstruct or retard its motion. 
 Yet if this be understood, it is not diffi- 
 cult, one would imagine, to comprehend in 
 what sense space may be said to be infi- 
 nite, and wherein it differs from body or 
 matter. 
 
 To the Editor of the Artisan. 
 
 Sir, 
 
 As it not unfrequently happens in cases 
 of shipwreck, that various insurmountable 
 obstacles prevent the possibility of either 
 the people on shore or those in the stran- 
 ded vessel, pursuing the whole of the plan 
 given in your 22d No. p. 350, when the 
 first part might be practised with success ; 
 permit me to point out two methods, either 
 of which may at any time be resorted to, 
 whenever a rope communication can by 
 any means be attained between the shore 
 and the wreck, and the single whip pur- 
 chase is established. 
 
 A close net or canvas bag, invented by 
 Mr. A. Bosquet in Feb. 1802, which I 
 shall first describe, would be found a very 
 useful accompaniment to the mortar appa- 
 ratus, as it could be hauled to and fro 
 by the whip in less time, perhaps, than any 
 other machine of equal utility. This net, 
 or canvas collar, should be made of dimen- 
 sions, when stuffed with cork shavings, 
 equal to about that of a small bed bolster, 
 coiled or formed in this manner, like a 
 
 collar, and sufficiently wide for the head 
 and shoulders to pass through, or be put 
 
64 
 
 THE ARTISAN. 
 
 on and off by straps and buckles, so that 
 it may occupy the space between the arm- 
 pits and the loins ; this will sustain the 
 person who has it on in an erect posture, 
 and always high above the water, and 
 most essentially protect him from those 
 bruises on rocks which frequently prove 
 fatal. It could be put on in a minute, and 
 would not prevent the use of the limbs 
 whenever ground was felt. 
 
 The following description of a wicker 
 boat, which was also invented by Mr. 
 Bosquet, and published at the same time 
 with the above, is given in the Naval 
 Chronicle , Vol. vii. p. 137 ; and as I am 
 thoroughly convinced that most of the ad- 
 vantages mentioned by him would be 
 gained by its use, I shall describe it in 
 his own words : — “ First, the figure may be 
 either oval or round, the latter I would 
 prefer ; its form resembling a basin, com- 
 posed of two frames of similar forms, con- 
 structed of wickerwork, but of different 
 diameters : the one laying within the 
 other. The diameter of the inner frame at 
 the mouth may be from five to six feet; 
 the depth from the gunwale to the bottom, 
 about three ; the internal diameter at the 
 bottom, which is to be flat, a third less 
 than at the mouth ; the space between the 
 outer and inner frame, all round, and to 
 its entire depth, may be about eighteen 
 inches : this space to be closely filled with 
 cork shavings, and closed with wicker 
 work, or a light wooden gunwale. The 
 bottom or area is to be furnished with two 
 false lattice, or grated bottoms, of strong 
 basket work, through which the water 
 may have free egress and regress ; the 
 ground bottom may be on a plane with the 
 lower extremes of the sides, which may be 
 furnished with a wooden seat; and the 
 inner or upper bottom placed at from nine 
 to twelve inches higher within the boat, 
 and sufficiently firm to bear the required 
 pressure to which it must be subject; it 
 therefore may be composed of a grated 
 wooden frame. This boat, by its own 
 weight, will not draw more than from five 
 to six inches, and with the additional 
 weight of eight men within, the water 
 would not rise to the second bottom ; and 
 supposing that the boat might contain 
 twenty men, which I think it might, yet 
 the water would be found not to rise twelve 
 inches internally above the second bottom. 
 There should be a seat of wicker-work, 
 all round stuffed like the sides, and about 
 nine or ten inches high from the upper 
 bottom. 
 
 “ The advantages which would pertain 
 to such a boat are — First, its cheapness 
 and simplicity; it may cost about £5. 
 Secondly, Any basket maker, with proper 
 instructions, could make it. Thirdly , That 
 
 of being conveniently portable ; half a 
 dozen men could carry it. — Fourthly, It 
 would not upset. — Fifthly, The utmost 
 number of persons that could force them 
 selves into it, could not cause it to founder, 
 or the water to rise internally more than 
 twelve or fourteen. inches. Sixthly, Though 
 it might be filled for a moment, yet it would 
 as suddenly free itself through its grated 
 bottom. — Seventhly, Such a boat cannot go 
 to pieces by any shock, nor can the most 
 violent concussions against rocks, or the 
 sides of a ship, do it any injury, as it will 
 both yield and rebound by its elastic 
 quality.” 
 
 This last qualification mentioned by Mr. 
 Bosquet, gives the wicker boat a decided 
 superiority over every other, as it might 
 without danger be hauled off through any 
 sea without a man on board, which to 
 another boat would be certain destruction. 
 It might be hauled to and fro by the whip 
 alone, or with both the whip and hawser, 
 by reeving the hawser through two rollers 
 fixed at opposite sides on her gunwale; 
 this latter method would keep her more 
 steady and better under command. When- 
 ever the hawser is used, its in-shore end 
 should be rove through the ring of a small 
 anchor through which it can be veered, 
 and hauled according to the motion of the 
 wreck. 
 
 I am Sir, 
 
 Your obedient humble Servant, 
 Navarchus. 
 
 January 2 1st, 1825. 
 
 SOLUTION OF QUESTIONS. 
 
 Quest. 59, answered by J. Anderson, 
 ( the Proposer. ) 
 
 Put 16 ^ feet — m, *7854 ~ n, the area 
 of each aperture, azz 48 inches, and b zz 
 60 in. Then by hydrost. Ijm :2m:: >ja : 
 2sfam~ the velocity of the water through 
 the aperture at the bottom, and 2 am - m 
 = the velocity through the one in the side. 
 2 n sj am + 2n *fam — in zz the quantity 
 discharged by both in the first second of 
 b *X *7854 X a X 2 
 
 time. Hence ■ - — x § — 
 
 ^ v^a»i + 2 n^/am—m 
 24* 9" the time required. 
 
 QUESTION FOR SOLUTION. 
 
 Quest. 62, proposed by J. D. 
 
 If 9 oxen eat up 3 acres of grass in 5 
 weeks, and 20 oxen eat up 10 acres of the 
 same in 1 0 weeks ; how many oxen will 
 eat up 30 acres of the same in 25 weeks, 
 if the grass grow uniformly during that 
 time ? 
 
THE ARTISAN. 
 
 65 
 
 ®@MITEY a 
 
 PROPOSITION XXI. 
 Theorem. — The angles in the same segment 
 of a circle are equal to one another . 
 
 Let ABCD be a circle, and RAD, 
 RED angles in the same segment R AED : 
 The angles R A D, R E D are equal to one 
 another. 
 
 Take F the centre of the circle A R CD : 
 And, first, let the segment RAED be 
 greater than a semicircle, and join R F, 
 F D : And because the angle R F D is at 
 the centre, and the angle R A D at the 
 circumference, and that they have the 
 same part of the circumference ; viz. RCD 
 for their base ; therefore the angle B F D 
 is double of the angle RAD: For the 
 same reason, the angle R F D is double of 
 the angle BED: Therefore the angle 
 
 B A D is equal to the angle RED. 
 
 Rut, if the segment RAED be not 
 greater than a semicircle, let BAD, BED 
 be angles in it; these also are equal to one 
 another : Draw A F to the centre, and 
 produce it to C, and join C E : Therefore 
 the segment BADC is greater than a 
 semicircle; and the angles in it RAC, 
 R E C are equal, by the first case : For 
 the same reason, because C R E D is 
 
 greater than a semicircle, the angles 
 CAD, CED are equal : Therefore the 
 whole angle R A D is equal to the whole 
 Vol. II.— No. 30. 
 
 angle BED. Wherefore the angles in the 
 same segment, &c. Q. E. D. 
 
 PROPOSITION XXII. 
 
 Theorem. — The opposite angles of any quad- 
 rilateral figure described in a circle , are 
 together equal to two right angles. 
 
 Let A R C D be a quadrilateral figure in 
 the circle ABCD; any two of its opposite 
 angles are together equal to two right 
 angles. 
 
 Join AC, B D ; and because the three 
 angles of every triangle are equal to two 
 riget angles, the three angles of the tri- 
 angle CAB; viz. the angles C A B, 
 A B C, B C A, are equal to two right 
 angles : But the angle C A B is equal to 
 the angle C D B, because they are in the 
 same segment BADC, and the angle 
 ACB is equal to the angle ADB, be- 
 cause they are in the same segment 
 ADCB: Therefore the whole angle 
 
 A D C is equal to the angles CAB, ACB: 
 To each of these equals add the angle 
 ABC; therefore the angles A B C, C A B,, 
 
 33 
 
 RCA, are equal to the angles ABC, 
 ADC: But ABC, C A B, B C A, are equal 
 to two right angles; therefore also the 
 angles ABC, ADC are equal to two 
 right angles : In the same manner the 
 angles B A D, D A B, D C B, may be shown 
 to be equal to two right angles. There- 
 fore, the opposite angles, &c. Q. E. D. 
 
 PROPOSITION XXIII. 
 
 THEOREM.—Upon the same straight line , 
 and upon the same side of it , there cannot 
 be two similar segments of circles , not co- 
 inciding with another. 
 
 If it be possible, let the two similar seg- 
 ments of circles; viz. ACB, ADB, be 
 
 E 
 
66 
 
 THE ARTISAN. 
 
 line A B, not coinciding with one another : 
 then, because the circle ACB cuts the 
 circle A D B in the two points A, B, they 
 cannot cut one another in any other point : 
 one of the segments must therefore fall 
 within the other: let ACB fall within 
 ADB, and draw the straight line BCD, and 
 join C A, DA: and because the segment 
 A C B is similar to the segment ADB, and 
 that similar segments of circles contain 
 equal angles, the angle AC B is equal to the 
 angle ADB, the exterior to the interior 
 opposite, which is impossible. Therefore, 
 there cannot be two similar segments of 
 circles upon the same side of the same 
 line, which do not coincide. Q. E. D. 
 
 PROPOSITION XXIV. 
 
 Theorem* — Similar segments of circles upon 
 equal straight lines , are equal to one 
 another. 
 
 Let AEB, C FD be similar segments of 
 circles upon the equal straight lines A B, 
 CD; the segment AEB is equal to the 
 segment C F D. 
 
 For, if the segment A E B be applied to 
 
 :e 
 
 C “D 
 
 the segment C F D, so as the point A be on 
 C, and the straight line AB upon C D, the 
 point B shall coincide with the point D, 
 because AB is equal to CD: Therefore 
 the straight line A B coinciding with C D, 
 the segment AEB must coincide with the 
 segment CFD, and therefore is equal to 
 it. Wherefore, similar segments, &c. 
 Q. E. D. 
 
 PROPOSITION XXV. 
 
 Problem. — A segment of a circle being 
 given , to describe the circle of which it is 
 the segment . 
 
 Let A B C be the given segment of a cir- 
 cle; it is required to describe the circle of 
 which it is the segment. 
 
 Bisect A C in D, and from the point D 
 draw D B at right angies to A C, and join 
 A B : first, let the angles A B D, B A D be 
 
 equal to one another; then the straight 
 line B D is equal to D A, and therefore to 
 D C ; and because the three straight lines 
 DA, DB, DC, are all equal; D is the 
 centre of the circle : from the centre D, at 
 the distance of any of the three D A, D B, 
 D C, describe a circle ; this shall pass 
 through the other points; and the circle 
 of which A B C is a segment is described : 
 and because the centre D is in A C, the 
 segment A B C is a semicircle. But if the 
 angles A B D, B A D are not equal to one 
 another, at the point A, in the straight 
 line A B, make the angle B A E equal to the 
 angle A B D, and produce B D, if neces- 
 sary, to E, and join E C : and because the 
 
 B 
 
 13 
 
 angle A P» E is equal to the angle B A E, 
 th.e straight line B E is equal to E A : and 
 because A D is equal to D C, and D E 
 compidn to the triangles A D E, C D E, 
 the two sides AD, DE are equal to the 
 two CD, D E, each to each; and the 
 angle ADE is equal to the angle C D E, 
 for each of them is a right angle; there- 
 fore the base A E is equal to the base 
 E C : but A E was shown to be equal to 
 E B, wherefore also B E is equal to E C : 
 
THE ARTISAN. 
 
 67 
 
 and the three straight Unes A E, E B, E C 
 are therefore equal to one another; where- 
 fore E is the centre of the circle. From 
 the centre E, at the distance of any of the 
 three A E, EB, EC, describe a circle, 
 this shall pass through the other points ; 
 and the circle of which A B C is a segment 
 is described : also it is evident, that if the 
 angle ABD be greater than the angle 
 BAD, the centre E falls without the seg- 
 ment ABC, which therefore is less than a 
 semicircle: butif the angle A BD be less 
 than B A D, the centre E falls within the 
 segment ABC, which is therefore greater 
 than a semicircle : Wherefore, a segment 
 of a circle being given, the circle is des- 
 cribed of which it is a segment. Which 
 was to be done. 
 
 PROPOSITION XXVI. 
 
 Theorem. — In equal circles, equal angles 
 stand upon equal arches, whether they be 
 at the centres or circumferences. 
 
 Let ABC, DE F be equal circles, and 
 the equal angles BGC, EHF at their 
 centers, and BAC, EDF, at their cir- 
 cumferences: the arch B K C is equal to 
 the arch ELF. 
 
 Join B C, E F ; and because the circles 
 A B C, D E F are equal, the straight lines 
 drawn from their centres are equal : there- 
 
 the two EH, H F ; and the angle at G is 
 equal to the angle at H; therefore the 
 base B C is equal to the base E F : and be- 
 cause the angle at A is equal to the angle 
 at D, the segment B A C is similar to the 
 segment EDF; and they are upon equal 
 straight lines BC,EF; but similar seg- 
 ments of circles upon equal straight lines 
 are equal to one another, therefore the 
 segment BAC is equal to the segment 
 EDF: but the whole circle A B C is equal 
 to the whole D E F ; therefore the remain- 
 ing segment B K C is equal to the remain- 
 ing segment ELF, and the arch B K C to 
 the arch ELF. Wherefore in equal cir- 
 cles, &c. Q. E. D. 
 
 PROPOSITION XXVII. 
 
 Theorem. — In equal circles, the angles 
 which stand upon equal arches are equal 
 to one another, whether they be at the 
 centres or circumferences. 
 
 Let the angles B G C, E H F at the cen- 
 tres, and BAC, EDF at the circumferen .. 
 ces of the equal circles ABC, D E F 
 stand upon the equal arches B C, E F : the 
 angle B GC is equal to the angle E H F, 
 and the angle B A C to the angle EDF. 
 
 If the angle B G C be equal to the angle 
 EHF, it is manifest that the angle BAC 
 is also equal to EDF. But, if not, one 
 of them is the greater : let B G C be the 
 
 A 
 
68 
 
 THE ARTISAN. 
 
 greater, and at the point G, in the straight 
 line B G, make the angle BGK equal to 
 the angle E H F. And because equal 
 angles stand upon equal arches, when 
 they are at the centre, the arch B K is 
 equal to the arch E F : but E F is equal to 
 B C ; therefore also B K is equal to B C, 
 the less to the greater, which is impossible. 
 Therefore the angle B G C is not unequal 
 to the angle E H F ; that is, it is equal to 
 it : and the angle at A is half of the angle 
 B G C, and the angle at D half of the angle 
 EHF: therefore the angle at A is equal 
 to the angle at D. Wherefore, in equal 
 circles, &c. Q. E. D. 
 
 PROPOSITION XXVIII. 
 
 Theorem. — In equal circles , equal straight 
 lines cut off equal arches, the greater 
 equal to the greater , and the less to the 
 less . 
 
 Let ABC,DEF be equal circles, and 
 BC, EF equal straight lines in them, 
 which cut off the two greater arches 
 BAG, EDF, and the two less BGC, 
 EHF: the greater B A C is equal to the 
 greater E D F, and the less B G C to the 
 less EHF. 
 
 Take K, L, the centres of the circles, 
 and join B K, K C, E L, L F : and because 
 
 A 
 
 D 
 
 the circles are equal, the straight 
 
 from their centres are equal; therefore 
 B K, K C are equal to B L, L F ; but the 
 base B C is also equal to the base E F ; 
 therefore the angle B K C is equal to the 
 angle ELF: and equal angles stand 
 
 upon equal arches, when they are at 
 the centres ; therefore the arch B G C is 
 equal to the arch E H F. But the whole 
 circle A B C is equal to the whole EDF; 
 the remaining part, therefore, of the cir- 
 cumference ; viz. B A C, is equal to the 
 remaining part EDF. Therefore, in equal 
 circles, &c. Q. E. D. 
 
 PROPOSITION XXIX. 
 
 Theorem. — In equal circles equal arches 
 are subtended by equal straight lines. 
 
 Let A B C, D E F be equal circles, and 
 let the arches BGC, EHF also be equal, 
 and join B C, E F : the straight line B C is 
 equal to the straight line E F. 
 
 Take K, L, the centres of the circles, 
 join BR, RC, EL, L F : and because 
 the arch B G C is equal to the arch EHF, 
 the angle BKC is equal to the angle 
 ELF: also because the circles ABC, 
 DEFare equal, their radii are equal: 
 therefore B K, K C are equal to E L, 
 
 A 
 
 3 > 
 
 L F, and they contain equal angles : there- 
 fore the base B C is equal to the base EF , 
 Therefore, in equal circles, &c. Q. E. D. 
 
THE ARTISAN* 
 
 G9 
 
 PROPOSITION XXX. 
 
 Problem . — To bisect a given arch ; that is, 
 to divide it into two equal parts. 
 
 Let A D B be the given arch ; it is re- 
 quired to bisect it. 
 
 Join A B, and bisect it in C ; from the 
 point C draw CD at right angles to A B 
 
 D 
 
 and join AD,DB: the arch A D B is bi- 
 sected in the point D. 
 
 Because A C is equal to CB, and CD 
 common to the triangles ACD,BCD, the 
 two sides AC, CD are equal to the two 
 B C, C D ; and the angle AC D is equal to 
 the angle BCD, because each of them is a 
 right angle ; therefore the base A D is 
 equal to the base B D. But equal straight 
 lines cut off equal arches, the greater 
 equal to the greater, and the less to the 
 less; and A D, D B are each of them less 
 than a semicircle, because D C passes 
 through the centre : Wherefore the arch 
 A D is equal to the arch D B ; and there- 
 fore the given arch A D B is bisected in 
 D. Which was to be done. 
 
 mecbanxcs. 
 
 on Wheel carriages. 
 
 The effect of the suspension of a car- 
 riage on springs, is to equalize its motion, 
 by causing every change to be more gra- 
 dually communicating to it, by means of 
 the flexibility of the springs, and by con- 
 suming a certain portion of every sudden 
 impulse, in generating a degree of rotatory 
 motion. This rotatory motion depends on 
 the oblique position of the straps suspend- 
 ing the carriage, which prevents its swing- 
 ing in a parallel direction ; such a vibra- 
 tion as would take place, if the straps 
 were parallel, would be too extensive, un- 
 less they were very short, and then the 
 motion would be somewhat rougher. The 
 obliquity of the straps tends also in some 
 measure to retain the carriage in a hori- 
 zontal position: for if they were parallel, 
 both being vertical, the lower one would 
 have to support the greater portion of the 
 weight, at least according to the common 
 mode of fixing them to the bottom of the 
 carriage ; the spring, therefore, being 
 flexible, it would be still further depressed. 
 But when the straps are oblique, the upper 
 one assumes always the more vertical 
 position, and consequently bears more of 
 the load ; for when a body of any kind is 
 
 supported by two oblique forces, their 
 horizontal thrusts must be equal, other- 
 wise the body would move more laterally ; 
 and in order that the horizontal portions 
 of the forces may be equal, the more in- 
 clined to the horizon must be the greater : 
 the upper string will, therefore, be a little 
 depressed, and tire carriage will remain 
 more nearly horizontal than if the springs 
 were parallel. The reason for dividing 
 the springs into separate plates, has 
 already been explained : the beam of the 
 carriage that unites the wheels, supplies 
 the strength necessary for forming the 
 communication between the axles ; if the 
 body of the carriage itself was to perform 
 this office, the springs would require to 
 be so strong, that they could have little or 
 no effect in equalizing the motion, and we 
 should have a waggon instead of a coach. 
 The ease with which a carriage moves, 
 depends not only on the elasticity of the 
 springs, but also on the small degree of 
 stability of the equilibrium, of which we 
 may judge in some measure, by tracing 
 the path which the centre of gravity must 
 describe, when the carriage swings. 
 
 In the following figure A B and C D re- 
 present the straps or braces by which a 
 
70 
 
 THE ARTISAN. 
 
 coach is suspended, if the centre of gravity 
 be at E, F, or G, it must move, when the 
 carriage swings in the curve passing 
 through the respective point. 
 
 The modes of attaching horses and oxen 
 to carriages are different in different coun- 
 tries, nor is it easy to determine the most 
 eligible method. When horses are har- 
 nessed to draw side by side, they are 
 usually attached to the opposite ends of a 
 bar or lever; and if their strength is very 
 unequal, the bar is sometimes unequally 
 divided by the fulcrum, the weaker horse 
 being made to act on the longer bar, and 
 being thus enabled to counteract the 
 greater force of his companion. But even 
 without this inequality, a compensation 
 
 takes place, for the centre on which the 
 bar moves, is always considerably behind 
 the points of attachment of the horses; 
 and when one of them falls back a little, 
 the effective arm of the lever becomes 
 more perpendicular to the direction of his 
 force, and gives him a greater power, 
 while the opposite arm becomes more 
 oblique, and causes the other horse to act 
 at a disadvantage, so that there is a kind 
 of stability in the equilibrium. If the ful- 
 crum were farther forwards than the ex- 
 tremity of the bar, the two horses could 
 never draw together with convenience. 
 The following figure represents the mode 
 of harnessing two horses, so as to make 
 them draw conveniently together : 
 
 When either horse ad vances so far that the 
 bar A B assumes the position C D, the 
 foremost horse has the disadvantage of 
 acting on a lever, equivalent only to EF, 
 while the other horse acts on EC. 
 
 In mining countries, and in collieries, it 
 is usual for facilitating the motion of the 
 carriages, employed in moving the ore or 
 the coals, to lay wheel-ways of wood or 
 iron along the road on which they are to 
 pass ; and this practice has of late been 
 extended in some cases, as a substitute for 
 the construction of navigable canals. 
 Where there is a turning, the carriages 
 are usually received on a frame supported 
 by a pivot, which allows them to be 
 turned with great ease. In particular 
 situations these waggons are loaded by 
 little carts, rolling without direction down 
 inclined planes, and emptying themselves; 
 they are also provided with similar con- 
 trivances for being readily unloaded, when 
 they arrive at the place of their destina- 
 tion. The carriages used for drawing 
 loaded boats over inclined planes, where 
 they have to ascend and again to descend, 
 are made to preserve their level, by having 
 at one end four wheels instead of two, on 
 the same transverse line; the outer one as 
 much higher than the pair at the other 
 end, as the inner ones are lower : and the 
 wheel-way being so laid, that either the 
 largest or the smallest act on it; according 
 
 as the corresponding part of the plane is 
 lower or higher than the opposite end. 
 
 It is probable that roads paved with 
 iron, or what is termed rail roads, may 
 hereafter be employed for the purpose of 
 expeditious travelling, since there is 
 scarcely any resistance to be overcome, 
 except that of the air ; consequently such 
 roads would allow the velocity to be in- 
 creased almost without limit. On this 
 interesting subject we have just learned 
 the result of a grand experiment, per- 
 formed at Killingworth Colliery, near 
 Newcastle-upon-Tyne, in presence of seve- 
 ral gentlemen from the committees ap- 
 pointed to manage the intended Manches- 
 ter and Liverpool, and the Birmingham 
 and Liverpool rail-roads about to be made. 
 The experiment was made with a locomo- 
 tive steam engine of eight horse power, and 
 weighing, with the tender (containing water 
 and coals), five tons and ten hundred weight, 
 was placed ou a portion of rail-rood, the 
 inclination of which, in one mile and a 
 quarter, was stated by the proprietor Mr. 
 Wood, to be one inch in a chain, or one 
 part in 792 : twelve waggons were placed 
 on the rail-road, each containing two tons 
 and between 13 and 14 hundred weight of 
 coals — making a total useful weight of 
 32 tons and 8 cwt. The twelve waggons 
 were drawn one mile and a quarter each 
 way, making two miles and a half in the 
 
THE ARTISAN. 
 
 71 
 
 whole, in forty minutes, or at the rate of 
 3g- miles an hour, consuming four pecks 
 and a half of coals. Eight waggons were 
 then drawn the same distance in thirty- 
 six minutes, consuming four pecks of 
 coals ; and six waggons were drawn over 
 the same ground in thirty-two minutes, 
 consuming five pecks of coals. We under- 
 stand that the engine must be supplied 
 with hot or boiling, and not with cold 
 water ; and that two hundred gallons of 
 water will take the engine 14 miles, at the 
 end of which the supply must be renewed. 
 
 ENGINE FOR DRIVING PILES. 
 
 In the engine for driving piles or up- 
 right beams, used for the foundations of 
 buildings in water, or in soft ground, the 
 weight is raised slowly to a considerable 
 height, in order that, in falling, it may 
 acquire sufficient energy to propel the pile 
 with efficacy. The same force, if applied 
 by very powerful machinery immediately 
 to the pile, would perhaps produce an 
 equal effect in driving it ; but it would be 
 absolutely impossible in practice to con- 
 struct machinery strong enough for the 
 purpose, and if it were possible, there 
 
 would be an immense loss of force from 
 the friction. For example: supposing a 
 weight of 500 pounds, falling from a 
 height of 50 feet, to drive the pile 2 inches 
 at each stroke ; then, if the resistance be 
 considered as nearly uniform, its magni- 
 tude must be about 150 thousand pounds, 
 and the same moving power, with a me- 
 chanical advantage of 300 to 1, would per- 
 form the work in the same time. But for 
 this purpose, some parts of the machinery 
 must be able to support a strain equivalent 
 to the draught of 600 horses. In the 
 pile-driving engine, the forceps or tongs, 
 sometimes called the monkey or follower, 
 is opened as soon as the weight arrives at 
 its greatest height ; and at the same time 
 a lever detaches the drum employed for 
 raising the weight, from the axis or wind- 
 lass at which the horses are drawing ; the 
 follower then descends after the weight, 
 uncoiling the rope from the drum, and the 
 force of the horses is employed in turning 
 a fly-wheel, until the connection with the 
 weight is again restored. The following 
 figure represents an engine of this kind on 
 Yauloue’s construction. 
 
 The horses drawing at AB, raise the 
 weight C, held by the tongs D, fixed in 
 the follower E, which are opened when 
 they reach the summit, by being pressed 
 between the inclined planes F G, so as to 
 let the weight fall. At the same time the 
 lever H is raised by the rope I, and 
 presses on the pin K L, so as to depress 
 the lever M N, and draw the pin out of 
 the drum P Q ; the follower then descends 
 and uncoils the rope, its too rapid motion 
 being prevented by the counterpoise R, 
 acting on the spiral barrel Q. The motion 
 is regulated by the fly S, the pinion of 
 which is turned by the great wheel T. 
 
 Having described the construction and 
 operation of the pile engine, we shall here 
 
 make a few remarks on the manner of re- 
 gulating forces. 
 
 If a machine were constructed for raising 
 a solid weight, and so arranged, as to per- 
 form its office in the shortest possible time 
 With a given expense of power, the weight 
 would still possess, when it arrived at the 
 place of its destination, a considerable 
 and still increasing velocity : in order that 
 it might retain its situation, it would be 
 necessary that this velocity should be des- 
 troyed ; if it were suddenly destroyed, 
 the machinery would undergo a strain 
 which might be very injurious to it : and 
 if the velocity were gradually diminished, 
 the time would no longer be the same. In 
 the second place; the forces generally em- 
 
72 
 
 fHE ARTISAN. 
 
 played are by no means uniformly accele- 
 rating forces, like that of gravitation : 
 they are not only less active when a cer- 
 tain velocity has once been attained* but 
 they are often capable of a temporary in- 
 crease or diminution of intensity at plea- 
 sure. We have mentioned the inconve- 
 nience of producing a great final velocity, 
 on account of its endangering the struc- 
 ture of the machine ; if, therefore our per- 
 manent force be calculated according to 
 the common rule, so as to be able to 
 maintain the equilibrium, and overcome 
 the friction, the momentum or inertia of 
 the weights, when once set in motion, will 
 be able to sustain that motion equably ; 
 and it will not be difficult to give them a 
 sufficient momentum, by a greater exertion 
 of the moving force, for a short space of 
 time, at the beginning : and this is in fact 
 the true mode of operation of many ma- 
 chines where animal strength is employed. 
 Other forces, for instance those of wind 
 and water, regulate themselves in some 
 measure, at least with respect to the rela- 
 tive velocity of the sails and the wind, or 
 the floatboards and the water ; for we may 
 easily increase the resistance, until the 
 most advantageous effect is produced. If 
 we compare the greatest velocity with 
 which a man or a horse can run or walk 
 without fatigue, to the velocity of a stream 
 of water, and the actual velocity of that 
 part of the machine to which the force is 
 applied, to the velocity of the float-boards 
 of a water wheel, the strength which can 
 be exerted may be represented, according 
 to the experiments of some authors, by the 
 impulse of the stream, as supposed to be 
 proportional to the square of the relative 
 velocity ; consequently the same velocity 
 would be most advantageous in both cases, 
 and the man or horse ought, according to 
 these experiments, to move, when his force 
 is applied to a machine, with one third of 
 the velocity with which he could walk or 
 run when at liberty. This, for a man, 
 would be about a mile and a half an hour; 
 for a horse, two or three miles : but in 
 general both men and horses appear to 
 work most advantageously with a velocity 
 somewhat greater than this.* 
 
 Where a uniformly accelerating force, 
 like that of gravitation, is employed in 
 machines, it might often be of advantage 
 to regulate its operation, so that it might 
 act nearly in the same manner as the forces 
 that we have been considering ; at first 
 with greater intensity, and afterwards with 
 sufficient power to sustain the equilibrium, 
 and overcome the friction only. This 
 might be done, by means of a spiral barrel, 
 like the fusee of a watch ; and a similar 
 
 See page 276, vol. i. 
 
 modification has sometimes been applied, 
 by causing the ascending weight, when it 
 arrives near the place of its destination, 
 to act on a counterpoise, which resists it 
 with a force continually increasing, by 
 the operation of a barrel of the same kind, 
 so as to prevent the effect of the shock 
 which too rapid a motion would occasion. 
 
 On the whole, we may conclude, that 
 on account of the limited velocity which is 
 usually admissible in the operation of ma- 
 chines, a very small portion of the moving 
 force is expended in producing momentum • 
 the velocity of 3 miles an hour, would be 
 generated in a heavy body, descending by 
 its own weight, in one seventh of a se- 
 cond, and a very short time is generally 
 sufficient for obtaining as rapid a motion 
 as the machine or the nature of the force 
 will allow ; and when this has been 
 effected, the whole force is employed in 
 maintaining the equilibrium, and over- 
 coming the resistance. 
 
 ESiECXK,ICZT-Z-. 
 
 The production of heat by electricity 
 frequently accompanies that of light, and 
 appears to depend in some measure on 
 the same circumstances. A fine wire may 
 be fused and dissipated by the discharge 
 of a battery ; and without being perfectly 
 melted, it may sometimes be shortened or 
 lengthened, accordingly as it is loose or 
 stretched during the experiment. The 
 more readily a metal conducts, the shorter 
 is the portion of it which the same shock 
 can destroy ; and it has sometimes been 
 found, that a double charge of a battery 
 has been capable of melting a quadruple 
 length of wire of the same kind. 
 
 The powerful effect of a battery may be 
 very readily illustrated by the following- 
 experiment. Let two or three pieces of 
 gold leaf be put at the distance of jjjth of 
 an inch from each other, between two thin 
 slips of window-glass, on the ivory table 
 a in the foilowing figure, 
 
THE ARTISAN. 
 
 73 
 
 and be held fast to the table by the rods c 
 and b , turning on the stiff joints e and d , 
 and insulated by the glass legs g g . If 
 the battery, (page 41,) be charged, and a 
 wire or chain from the hook e join the rod 
 c, and the knob z of the discharging rod 
 touch the rod b, at the same time that its 
 other knob a touches the knob c of the 
 battery, the discharge will pass between 
 the glass slips, break them in its passage, 
 melt or rather oxydize the gold leaf, and 
 enamel or incorporate it with the pieces of 
 broken glass. If a small weight be placed 
 on the glass slips, the experiment will 
 succeed still better. 
 
 The mechanical effects of electricity are 
 probably in many cases the consequences 
 of the rarefac tion produced by the heat 
 which is excited; thus, the explosion, 
 attending the transmission of a shock or 
 spark through the air, may easily be sup- 
 posed to be derived from the expansion 
 caused by heat ; and the destruction of a 
 glass tube, which contains a fluid in a 
 capillary bore, when a spark is caused to 
 pass through it, is the natural consequence 
 of the conversion of some particles of the 
 fluid into vapour. But when a glass jar 
 is perforated, this rarefaction cannot be 
 supposed to be adequate to the effect. It 
 is remarkable that such a perforation may 
 be made by a very moderate discharge, 
 when the glass is in contact with oil or 
 with sealing wax ; and no sufficient ex- 
 planation of this circumstance has yet been 
 given. 
 
 A strong current of electricity, or a suc- 
 cession of shocks or sparks, transmitted 
 through a substance, by means of fine 
 wires, is capable of producing many che- 
 mical combinations and decompositions, 
 some of which may be attributed merely 
 to the heat which it occasions, but others 
 are wholly different. Of these the most 
 remarkable is the production of oxygen 
 and hydrogen gas from common water, 
 which are usually extricated at once, in 
 such quantities, as, when again combined, 
 will reproduce the water which has dis- 
 appeared ; but in some cases the oxygen 
 appears to be disengaged most copiously 
 at the positive wire, and the hydrogen at 
 the negative. 
 
 When the ^park is received by the 
 tongue, it has generally a subacid taste ; 
 and an explosion of any kind is usually 
 accompanied by a smell somewhat like 
 that of sulphur, or rather of fired gun- 
 powder. The peculiar sensation, which 
 the electric fluid occasions in the human 
 frame, appears in general to be derived 
 from the spasmodic contractions of the mus- 
 cles through which it passes ; although 
 in some cases it produces pain of a differ- 
 ent kind; thus, the spark of a conductor 
 occasions a disagreeable sensation in the 
 
 skin, and when an excoriated surface is 
 placed in the galvanic current, a sense of 
 smarting, mixed with burning, is expe- 
 rienced. Sometimes the effect of a shock 
 is felt most powerfully at the joints, on 
 account of the difficulty which the fluid 
 finds in passing the articulating surfaces 
 which form the cavity of the joints. The 
 sudden death of an animal, in consequence 
 of a violent shock, is probably owing 
 to the immediate exhaustion of the whole 
 energy of the nervous system. It is re- 
 markable that a very minute tremor, com- 
 municated to the most elastic parts of the 
 body, in particular to the chest, produces 
 an agitation of the nerves, which is not 
 wholly unlike the effect of a weak elec- 
 tricity. 
 
 The electricity produced by the simple 
 contact of any two substances is extremely 
 weak, and can only be detected by very 
 delicate experiments : in general it appears 
 that the substance, which conducts the 
 more readily, acquires a slight degree of 
 negative electricity, while the other sub- 
 stance is positively electrified in an equal 
 degree. The same disposition of the fluid 
 is also usually produced by friction, the 
 one substance always losing as much as 
 the other gains ; and commonly, although 
 not always, the worst conductor becomes 
 positive. At the instant in which the fric- 
 tion is applied, the capacities or attractions 
 of the bodies for electricity appear to be 
 altered, and a greater or less quantity is 
 required for saturating them ; and upon 
 the cessation of the temporary change, this 
 redundancy or deficiency is rendered sen- 
 sible. When two substances of the same 
 kind are rubbed together, the smaller or 
 the rougher becomes negatively electrified; 
 perhaps because the smaller surface is 
 more heated, in consequence of its under- 
 going more friction than an equal portion 
 of the larger, and hence becomes a better 
 conductor ; and because the rougher is in 
 itself a better conductor than the smoother, 
 and may possibly have its conducting 
 powers increased by the greater agitation 
 of its parts which the friction produces. 
 The back of a live cat becomes positively 
 electrified, with whatever substance it is 
 rubbed ; glass is positive in most cases, 
 but not when rubbed with mercury in a 
 vacuum, although sealing wax, which is 
 generally negative, is rendered positive by 
 immersion in a trough of mercury. When 
 a white and a black silk stocking are 
 rubbed together, the white stocking ac- 
 quires positive electricity, and the black 
 negative, perhaps because the black dye 
 renders the silk both rougher and a better 
 conductor. 
 
 Vapours are generally in a negative 
 state; but if they rise from metallic sub- 
 stances, or even from some kinds of heated 
 
74 
 
 THE ARTISAN. 
 
 glass, the effect is uncertain, probably on 
 account of some chemical actions which 
 interfere with it. Sulphur becomes elec- 
 trical in cooling, and wax candles are 
 said to be sometimes found in a state so 
 electrical, when they are taken out of 
 their moulds, as to attract the particles of 
 dust which are floating near them. The 
 tourmalin, and several other crystallized 
 stones, become electrical when heated or 
 cooled, and it is found that the disposition, 
 assumed by the fluid, bears a certain rela- 
 tion to the direction in which the stone 
 transmits the light most readily; some 
 parts of the crystal being rendered always 
 positively and others negatively electrical, 
 by an increase of temperature. 
 
 If a piece of window-glass be laid on a 
 warm poker, and the tourmalin on the 
 glass, the glass will become negative, and 
 the side of the stone touching it will be 
 positive. The heat excites the tourmalin, 
 and qualifies it to absorb electricity from 
 the glass ; the glass of course becomes 
 negative, while the fossil is in a state of 
 condensation. 
 
 Electricity does not appear over the 
 whole surface of the stone, but only on 
 two opposite sides, like the poles of a 
 loadstone ; so that its virtue lies in the 
 direction of its strata, and, therefore, is 
 capable of being forced, or drawn, to or 
 from one pole towards the other, by heat- 
 ing, cooling, or friction. When put in the 
 fire, it becomes covered with ashes ; when 
 rubbed with silk it emits strong flashes ; 
 and is luminous when warmed in the 
 dark : so that changing the degree of heat, 
 is what excites the stone. 
 
 That the animal nerve is a vehicle for 
 electricity, and perhaps the cause of sen- 
 sation, many experiments make more than 
 probable. In the torpedo, we find an 
 electrical battery, abstracted from the ves- 
 sels appropriated to the animal functions ; 
 it consists of a great number of vessels like 
 an honey-comb, standing across the fish, 
 from its belly to its back; so that if one 
 hand touches the belly, and the other the 
 back, an electric shock is instantly felt, 
 and the fish is convulsed. If the fish be 
 touched with a stick, a numbness seizes 
 the hand that holds the stick. The same 
 effect takes place, if a charged battery be 
 touched with a stick, because the stick is 
 a bad conductor, and the electric matter 
 can only pass through it in a stream, be- 
 numbing the hand in its passage ; but a 
 regular conducting power from its positive 
 and negative sides, would be a shock. 
 The electric eel, or gymnotus, has a 
 stronger electrical power than the torpedo: 
 the head and shoulders of this fish contain 
 the animal functions ; the rest seems all 
 electrical : and electrical by volition, for 
 the creature has the power of exerting or 
 
 withholding the shock. If one hand be 
 put in the water, and the other touch the 
 eel, a violent shock takes place. Mr. 
 Walker says he electrified thirty people at 
 once with this eel ; and that sparks have 
 been produced by an electric circuit of 
 this kind. How these two species of 
 fish collect and retain their electricity, in 
 a conducting medium, is an inexplicable 
 wonder ; they were no doubt endowed 
 with this power for defence, and catching 
 their prey ; and have organs to secrete it 
 from the water as other animals secrete 
 nutrition from the heterogeneous contents 
 of the stomach. 
 
 JHtSfellattemts subjects. 
 
 MEMOIR OF THE LIFE OF SIR 
 CHRISTOPHER WREN. 
 
 Sir Christopher Wren was one of the 
 greatest philosophers and mathematicians, 
 as well as one of the most learned and emi- 
 nent architects, of his age. He was the son 
 of the Rev. Christopher Wren, Dean of 
 Windsor, and was born at Knoyle, in 
 Wiltshire, in 1632. He studied at Wad- 
 ham College, Oxford, where he took the 
 degree of Master of Arts in 1653, and was 
 chosen Fellow of All Souls’ College there. 
 Soon after he became one of that ingenious 
 and learned society, who then met at Ox- 
 ford, for the improvement of natural and 
 experimental philosophy, and which at 
 length produced the Royal Society. 
 
 When very young, he discovered a sur- 
 prising genius for the mathematics ; in 
 which science he made great advances be- 
 fore he was sixteen years of age. In 1657 
 he was made Professor of Astronomy in 
 Gresham College, London ; and his lec- 
 tures, which were much frequented, tend- 
 ed greatly to the promotion of real know- 
 ledge. He proposed several methods by 
 which to account for the shadows return- 
 ing backward ten degrees on the dial of 
 King Ahaz, by the laws of nature. One 
 subject of his lectures was upon telescopes, 
 to the improvement of which he had greatly 
 contributed ; another was on certain pro- 
 perties of the air, and the barometer. In 
 the year 1658 he read a description of the 
 body and different phases of the planet 
 Saturn ; which subject he proposed to in- 
 vestigate, while his colleague, Mr. Rooke, 
 then professor of geometry, was carrying 
 on his observations upon the satellites of 
 Jupiter. The same year he communicated 
 some demonstrations concerning cycloids 
 to Dr. Wallis, which were afterwards 
 
THE ARTISAN. 
 
 7 5 
 
 published by the Doctor at the end of his 
 treatise upon that subject. About that 
 i time also he resolved the problem pro- 
 posed by Pascal, under the feigned name 
 of John de Montford, to all the English 
 mathematicians ; and returned another to 
 the mathematicians in France, formerly 
 proposed by Kepler, and then resolved 
 likewise by himself, to which they never 
 g’ave any solution. In 1660 he invented 
 a method for the construction of solar 
 eclipses ; and in the latter part of the same 
 year he, with ten other gentlemen, formed 
 themselves into a society, to meet weekly, 
 for the improvement of natural and expe- 
 rimental philosophy ; being the foundation 
 of the Royal Society. In the beginning of 
 t 1661 he was chosen Savilian Professor of 
 Astronomy at Oxford, in the room of Dr. 
 Seth Ward ; where he was the same year 
 i created Doctor of Laws. 
 
 Among his other accomplishments, Dr. 
 Wren had gained so considerable a skill 
 in architecture, that he was sent for the 
 ! same year from Oxford, by order of King 
 Charles the Second, to assist Sir John 
 Denham, surveyor-general of the works. 
 In 1663 he was chosen Fellow of the 
 Royal Society, being one of those who 
 were first appointed by the council after 
 the grant of their charter. Not long after, 
 it being expected that the King would 
 make the society a visit, the Lord Broun- 
 ker, then president, by a letter, requested 
 I the advice of Dr. Wren, concerning the 
 . experiments which might be most proper 
 on that occasion. To whom the Doctor 
 recommended principally the Torricellian 
 experiment, and the weather needle, as 
 being not mere amusements, but useful, 
 
 i and also neat in their operation. 
 
 In 1665 he travelled into France, to 
 examine the most beautiful edifices and 
 
 ii curious mechanical works there, when he 
 made many useful observations. Upon 
 his return home, he was appointed archi- 
 tect, and one of the commissioners for re- 
 pairing St. Paul’s cathedral. Within a 
 
 1 few days after the fire of London, 1666, he 
 drew a plan for a new city, and presented 
 i it to the king ; but it was not approved by 
 
 i the parliament. In this model the chief 
 t streets were to cross each other at right 
 t angles, with lesser streets between them ; 
 ij the churches, public buildings, &c. so 
 !ii disposed, as not to interfere with the 
 
 streets, and four piazzas placed at proper 
 i] distances. Upon the death of Sir John 
 
 * Denham, in 1668, he succeeded him in 
 
 ii the office of surveyor-general of the king’s 
 'i works ; and from this time he had the di- 
 
 * rection of a great many public edifices, by 
 ,: i which he acquired the highest reputation. 
 Ij He build the magnificent theatre at Ox- 
 ford, St. Paul’s Cathedral, the Monument, 
 
 ; the modern partof Hampton Court, Chelsea 
 
 College, one of the wings of Greenwich 
 Hospital, the churches of St. Stephen Wal- 
 brook and St. Mary-le-Bow, with upwards 
 of sixty other churches and public works, 
 which that dreadful fire made necessary. 
 In the management of which business he 
 was assisted in the measurements, and 
 laying out of private property, by the in- 
 genious Dr. Robert Hook. The variety 
 of business in which he was by this means 
 engaged, requiring his constant attend® 
 ance and concern, he resigned his Savilian 
 Professorship at Oxford in 1673 ; and the 
 year following he received from the king 
 the honour of knighthood. He was one 
 of the commissioners who, on the motion 
 of Sir Jonas Moore, surveyor-general of 
 the ordnance, had been appointed to find 
 out a proper place for erecting an observa- 
 tory ; and he proposed Greenwich, which 
 was approved of ; the foundation stone of 
 which was laid the 10th of August, 1675, 
 and the building was afterwards finished, 
 under the direction of Sir Jonas, with the 
 advice and assistance of Sir Christopher. 
 
 In 1680 he was chosen President of the 
 Royal Society; afterwards appointed ar- 
 chitect and commissioner of Chelsea Col- 
 lege ; and in 1684, principal officer or 
 comptroller of the works in Windsor Cas- 
 tle. Sir Christopher sat twice in Parlia- 
 ment, as a representative for two different 
 boroughs. While he continued surveyor- 
 general, his residence was in Scotland- 
 yard; but after his removal from that 
 office, in 1718, he lived in St. James’s- 
 street, Westminster. He died the 25th of 
 February, 1723, at 91 years of age; and 
 he was interred with great solemnity in 
 St. Paul’s Cathedral, in the vault under 
 the south wing of the choir, near the east 
 end. 
 
 OF ELECTRICITY DEVELOPED 
 DURING CHEMICAL ACTION. 
 
 Mr. Becquerel, of the Royal Academy 
 of Sciences in France, has just pub- 
 lished some important remarks upon the 
 above subject. In the first place, he has 
 demonstrated that the electricity developed 
 in chemical action was not appreciable by 
 the apparatus at present in use. In order 
 to prove this, the following experiment 
 was made Since, in the action of an acid 
 upon a metal, the acid takes the positive, 
 and the metal the negative electricity, an 
 attempt was made to form a battery with 
 couples, each composed of a metal and an 
 acid ; a slip of copper was then bent, and 
 one of its extremities plunged into an acid, 
 and the other in a concentrated solution of 
 a hydrate of potash. Supposing an elec- 
 tric tension, the acid would keep the posi- 
 
76 
 
 THE ARTISAN, 
 
 tive electricity, and transmit the negative 
 electricity to the alkaline solution. A 
 dozen of these plates were afterwards 
 united by means of curved platina wires ; 
 one of the ends of each being plunged into 
 the acid, and the other into the neighbour- 
 ing alkaline solution. This disposition 
 was really that which was proper for an 
 electric battery, and the distribution of 
 the electricity ought to take place in it 
 conformably to the theory of Volta, in the 
 case in which each couple would have had 
 an electric tension, however slight. 
 
 This kind of battery being in action, the 
 two ends of the galvanometrical wire were 
 plunged into the two extreme liquids, 
 where the tension was expected to be the 
 strongest ; and it was immediately per- 
 ceived that the variation of the magnetic 
 needle was less than that which would 
 have been obtained with a single couple. 
 It was then demonstrated, that the elec- 
 tricity developed during chemical action 
 had no sensible tension ; and hence it is 
 sufficiently clear why Sir H. Davy could 
 not obtain electricity with a condensator, 
 during the action of the sulphuric acid 
 upon the potash. 
 
 Mr. Becquerel has likewise directed his 
 attention to the measure of chemical ac- 
 tion, by means of electro-chemical effects. 
 The experiment which led him to this was 
 as follows — In plunging unequally the 
 two ends of a metallic wire into an acid 
 capable of attacking it, he observed a cur- 
 rent of electricity pass from the end the 
 most attacked to tlie other. He began by 
 analysing this phenomenon, and afterwards 
 discovered an apparatus, by the assistance 
 of which, chemical action may be mea- 
 sured. This apparatus is composed of 
 two platina vases reposing upon a wire of 
 the same metal. If the object is to ascer- 
 tain which of the substances acts the most 
 strongly upon an acid, two platina wires 
 are to be taken, and the ends fixed in two 
 cups filled with mercury, themselves com- 
 municating with the extremities of the 
 galvanometrical wire ; afterwards, by 
 means of hooks, likewise of platina, two 
 small fragments of different substances, 
 neither of which exercises any electromo- 
 tive action upon the metal, are attached to 
 the extremity of these wires ; these sub- 
 stances are made to touch the acid at the 
 same time, so that the number of points of 
 contact may be nearly the same ; the elec- 
 tric current that will then manifest itself 
 will pass from that substance which has 
 experienced the stronger action on the part 
 of the acid to the other. 
 
 When the chemical actions of metals 
 upon an acid are to be compared, small 
 wires of these metals are substituted for 
 those of platina; and, instead of the mer- 
 cury, the cups are filled with an alkaline 
 
 solution. By operating in this manner, it | 
 has already been discovered that nitric 
 acid acts more powerfully upon potash ij 
 than upon soda ; that soda was more at- 
 tacked than zinc, &c. 
 
 If the relation between the chemical ac- 
 tions of two acids upon one base is sought, I 
 these acids are put into the two small pla- 
 tina vases above-mentioned, into which 
 two fragments of the same substance, each 
 suspended to one end of the platina wire, 
 must be plunged at the same time, and 
 equally. The direction of the current in | 
 this instance also will determine which 
 of the acids has acted with the greater 
 energy. 
 
 The question, however, whether the 
 energy with which an acid attacks a base 
 can serve to measure their reciprocal affi- 
 nity, cannot yet be satisfactorily resolved ; 
 but there is reason to think that a relation 
 must exist between these two effects, since 
 the greater the affinity of one body for 
 another, the more rapidly these bodies 
 must approximate when in combination. 
 
 It may, therefore, be reasonably supposed, 
 that the relations between chemical ac- 
 tions, found as above, do not differ greatly 
 from those which would result from a 
 comparison of their affinities. 
 
 ON PREDICTING THE WEATHER. 
 
 From a very great number of meteorolo- 
 gical observations, made in England be- 
 tween the years 1677 and 17S9, Mr. Kir • 
 wan has deduced the following probable 
 conjectures of the weather : — 
 
 1. That when there has been no storm 
 before or after the vernal equinox, the en- 
 suing summer is generally dry , at least 
 five times in six. 
 
 2. That when a storm happens from any 
 easterly point, either on the 19th, 20th, or 
 21st of March, the succeeding summer is 
 generally dry, four times in fiv§. 
 
 8. That when a storm arises on the 25th, 
 26th, or 27th of March, and not before, in 
 any point, the succeeding summer is ge- 
 nerally dry, four times in five. 
 
 4. If there be a storm at S. W., or 
 W. S. W., on the 19th, 20th, 21st, or 22d 
 of March, the succeeding summer is gene- 
 rally wet, four times in five. 
 
 To the above we shall add the follow- 
 ing observations from the Encyclopedia 
 Britannica. 
 
 1. A moist autumn, with a mild winter, 
 is generally followed by a cold and dry 
 spring, which greatly retards vegetation. 
 
 2. If the summer be remarkably rainy, 
 
THE ARTISAN. 
 
 77 
 
 ii is probable that the ensuing winter will 
 be severe; for the unusual evaporation 
 will have carried olf the heat of the earth. 
 W et summers are generally attended with 
 an unusual quantity of seed on the white 
 thorn and dog-rose bushes. Hence the 
 unusual fruitfulness of these shrubs is a 
 sign of a severe winter. 
 
 3. The appearance of cranes, and birds 
 of passage, early in autumn, announces a 
 very 'severe winter; for it is a sign that it 
 has already begun in the northern coun- 
 tries. 
 
 4. When it rains plentifully in May, it 
 will rain but little in September, and vice 
 versa. 
 
 5. When the wind is S.W. during sum- 
 mer or autumn, and the temperature of the 
 air unusually cold for the season, both to 
 the feeling and the thermometer, with a 
 low barometer, much rain is to be ex- 
 pected. 
 
 C. Violent temperatures, as storms or 
 great rains, produce a sort of crisis in the 
 atmosphere, which produces a constant 
 temperature, good or bad, for some 
 months. 
 
 7. A rainy winter predicts a sterile 
 year; a severe autumn announces a windy 
 winter. 
 
 By the Barometer. 
 
 It is now a considerable time since the 
 barometer was proposed as a proper in- 
 strument for predicting the weather ; and 
 hence it obtained the name of weather 
 glass. Accordingly, rules for this pur- 
 pose have been given by Dr. Halley, Dr. 
 Hutton, Messrs. Pascal, Patrick, Rown- 
 ing, Changeux, de Luc, Clarke, Dalton, 
 and many others, from whose writings we 
 have collected the following rules. 
 
 When the mercury in the barometer 
 rises, it is a sign of fair weather, attended 
 with heat, if in summer; but frost in win- 
 ter. If the mercury falls, it denotes rain, 
 or wind, or perhaps both. 
 
 If the mercury rises suddenly during the 
 time of rain, the ensuing fair weather 
 will not continue long; but if the rise is 
 gradual, and continues for several days, 
 a continuance of fair weather may be ex- 
 pected. 
 
 If the mercury falls suddenly several 
 divisions, it is a sign that the succeeding 
 rain will not be of long duration. But if 
 the mercury continues to fall regularly for 
 several days, rain or wind, or perhaps 
 both, will be of considerable duration. 
 
 The mercury falling considerably in 
 autumn, winter, or spring, indicates gales 
 of wind, commonly attended with rain, 
 snow, or sleet ; but, in summer, it denotes 
 rain, and probably thunder. The mer- 
 
 cury is low with high winds, and still 
 lower if accompanied with rain. If the 
 mercury falls quickly in very Warm wea- 
 ther, thunder showers may be expected 
 soon after. 
 
 If the mercury be in an unsettled and 
 fluctuating state, the weather has the ap- 
 pearance of being very changeable. 
 
 If the mercury has been stationary 
 during several days, its surface must be 
 carefully observed, to ascertain whether 
 it is rising or falling. For this purpose, 
 let the exact figure of the surface of the 
 mercury be observed; then shake the tube a 
 little, and observe if the mercury is more 
 or less convex or concave. If it is more 
 convex, it is a sign the mercury is rising; 
 if the same as before, it is stationary ; but 
 if less, that it has attained its greatest 
 altitude at that time, and will fall soon. 
 If the mercury was concave before the 
 tube was shaken, and more concave after- 
 wards, the mercury is falling ; if of the 
 same concavity, or nearly so, it is sta- 
 tionary ; but if less concave it is rising. 
 
 Between the tropics, there is little varia- 
 tion in the height of the mercury in the 
 barometer ; and the more distant any place 
 is from the equator, the greater is the 
 range of the mercury. Thus, at St. He- 
 lena, the extreme variation is very little ; 
 at Jamaica it is only about three tenths of 
 an inch ; at Naples it seldom exceeds an 
 inch. In England the extreme range 
 amounts to about 2f inches ; and at Peters- 
 burgh to 3^ inches nearly. 
 
 SUPPORTS FOR MINERALS BE- 
 FORE THE BLOW PIPE. 
 
 Some time ago, Mr. Smithson published 
 an interesting paper on this subject, in 
 the Annals of Philosophy, in which he re- 
 commends the use of a mixture of water 
 and clay, instead of water, saliva, or gum- 
 water, generally used. A little of the 
 moist clay is to be taken up on the end of 
 the splinter of sappare ; and the particle 
 to be heated being touched by it adheres, 
 the whole is laid aside for a few minutes, 
 and is then dry, and may be heated. Mr. 
 Smithson also recommends small triangles, 
 or slender slips of baked clay, in lieu of 
 sappare, which is not always to be had. 
 Another more recent process is, to file the 
 very end of a platina wire flat, place the 
 minutest portion of the moist clay on it, 
 and then touch the particle to be heated. 
 In a few moments it is dry, and may be 
 put into the flame without flying off, un- 
 less too much clay has been taken. 
 
 Lieut.-Col. Totten, of the United States, 
 has lately published some experiments on 
 
78 
 
 THE ARTISAN. 
 
 the same subject. His process is a modi- 
 fication of that adopted by Mr. Smithson. 
 
 “ Not being able,” says he, “ to obtain 
 any clay sufficiently refractory for my 
 purpose, though I tried the German and 
 the English (Stourbridge) clay, used for 
 crucibles by glass-blowers, and two or 
 three specimens called pipe-clay, I had 
 recourse to the minerals which I designed 
 to expose to the action of the flame : this 
 is Mr. Smithson’s third process. Instead, 
 however, of taking upon the point of the 
 wire a very minute portion of the paste 
 made of the powdered mineral, according 
 to Mr. Smithson’s method, I formed a 
 paste by mixing the powder with very 
 thick gum- water, and rolling a little of it 
 under the finger, formed a very acute cone, 
 sometimes nearly an inch in length, and 
 generally about a twentieth of an inch in 
 diameter at the base. These cones, being 
 held by the forceps, or attached to the end 
 of a wire, or even of a splinter of wood, 
 may be directed accurately upon the mi- 
 nutest visible particle ; and being a little 
 moistened at the point with saliva, the 
 particle will adhere to the very apex under 
 the strongest blast of the blow-pipe. 
 
 u I conceived, that when a very small 
 quantity of paste was used, the extremity 
 of the wire or forceps must necessarily 
 abstract much heat from the fragment 
 under examination, because it must itself 
 be often within the limits of the blue flame ; 
 and my object was, as much as possible, 
 to insulate the fragment. These cones 
 need not, in fact, be more than one-quar- 
 ter or one-fifth of an inch in length ; for so 
 effectually is the conducting property of 
 the mineral substance destroyed, by des- 
 troying the continuity of its particles, that 
 one of these cones, of the length of half an 
 inch, may be held at the base by the fingers 
 with impunity, while the apex is in the 
 focus of heat. 
 
 “ One great advantage of this method 
 over the others is, that if fusion ensues, it 
 is owing entirely to the nature of the sub- 
 stance experimented upon, and not in any 
 degree to the agency of foreign substances 
 acting as fluxes.” 
 
 ( Annals of the Lyceum of Natural His- 
 tory, New York.) 
 
 REMARKS ON DIFFERENT HYPO- 
 THESIS RESPECTING THE MOON, 
 AND VARIOUS PHENOMENA OF 
 THAT PLANET. 
 
 We make no apology for submitting to 
 our readers the subjoined extracts from a 
 highly ingenious and interesting work, 
 entitled Selenognostic Fragments, pub- 
 
 lished by Dr. Gruithuisen, whose name 
 ranks deservedly high in the list of foreign 
 astronomers. 
 
 No body in the starry heavens, observes 
 the Doctor, in his introduction, excites 
 more general interest than the faithful 
 satellite of the earth : in fact, its surface 
 presents, even to the naked eye; objects 
 so varied, that it instantly inspires the 
 spectator with a wish to inspect this un- 
 known world, with the aid of a powerful 
 telescope. But what especially prompts 
 us to study the physical properties and 
 constitution of the moon, is the expectation 
 of discovering an analogy common to all 
 the great bodies of the universe, with res- 
 pect to their organization. This, he adds, 
 is what has hitherto been the foundation 
 of my celestial observations, being myself 
 convinced that we shall never attain to any 
 excellence in the study of geognosy, till 
 we have discovered this analogy. It is 
 with this intention that the auther has sur- 
 veyed, examined, and studied many 
 chains of terrestrial mountains ; and it is 
 with this view that he publishes the par- 
 ticular appearances, which eight years 
 observations have enabled him to remark 
 upon the surface of the moon. 
 
 To render his work more intelligible to 
 his readers, the Doctor has inserted a 
 lithographic general map of this planet; 
 for which purpose he has consulted Mayer’s 
 draught of the moon, and the special maps 
 given by Schroeter in his Selenographic 
 Fragments. Nor has he neglected to avail 
 himself of his own observations. He like- 
 wise cites the lunar map of Lambert, and 
 refers to a memoir of that philosopher in 
 the first volume of the Berlin astronomical 
 almanack. 
 
 Atmosphere of the Moon. Cassini, Lou- 
 ville, Bianchini, Carbone, Euler, Kruger, 
 Boscovich, Ulloa, Dusejour, Wolf, and 
 Halle, maintain the existence of a lunar 
 atmosphere; while Mayer, Grandjean de 
 Fouchy, De l’Isle, and De la Hire, deny 
 it. Without dwelling upon the reasons 
 and observations which, before the inven- 
 tion of achromatic telescopes have been 
 alleged on both sides of the question, 
 Doctor Gruithuisen confines himself to the 
 direct proofs drawn from the discoveries 
 of Schroeter. The latter has calculated 
 the elevation of the twilight observed by 
 him in repeated observations on the in- 
 creasing moon. This elevation agrees in 
 a surprising manner with the theorem of 
 Melanderhielm; namely, that on the sur- 
 face of planets the density of their atmos- 
 phere is in proportion to the squares of the 
 weight of the bodies. This proportion 
 had been suggested to Newton by that of 
 the squares of weights on the surface of 
 the moon, and the surface of the earth. 
 
THE ARTISAN, 
 
 79 
 
 In fact, this latter proportion being as 1 to 
 28*40, is almost equal to the result of 
 Schroeter, who found that the lunar at- 
 mosphere is 28-94 times less dense than 
 our own. Hevelius, De Luc, and many 
 other philosophers, have thought that the 
 air on the surface of planets was only ether 
 condensed, and have considered ether, in 
 its turn, as rarefied air, an opinion, which, 
 in a theoretical point of view, confirms the 
 theorem ©f Melanderhielm. 
 
 To attempt to combat this theory, adds 
 our author, would have the effect of en- 
 tangling us in a multitude of inextricable 
 difficulties ; for we must then affirm that 
 ether and air have no communication to- 
 gether; that, consequently, they cannot 
 mix, and that there is between them a 
 kind of barrier, as if our earth was en- 
 closed in a globe of hollow glass : yet we 
 know that all gases mingle together, which, 
 moreover, must happen from the pressure 
 of our air upon ether, and, reciprocally, 
 on account of the rapid motion of the 
 earth. It is to this pressure that M. de 
 Zach attributes the diurnal oscillations of 
 the barometer, observed at the equator by 
 Humboldt. We should likewise be obliged 
 to affirm, that as the air of planets is es- 
 sentially different from ether, there can be 
 no affinity between them, and consequently 
 that no body can burn in ether for want of 
 oxygen, a conclusion not warranted by ob- 
 servations, since shooting stars and me- 
 teors burn and shine at a height at which 
 in general the presence of atmospheric 
 air is not supposed. For example, in 
 1795, Schroeter saw, with his reflecting 
 telescope of 20 feet long, a shooting star, 
 the height of which he estimated at more 
 than four millions of miles. If then it be 
 admitted that each body of the universe, 
 by the influence of a weight proportioned 
 to its bulk, forms out of ether, the atmos- 
 phere by which it is surrounded, then the 
 moon must also borrow from ether its por- 
 tion, which becomes condensed and forms 
 its atmosphere. The existence of water in 
 the lunar atmosphere can no longer be 
 questioned, for clouds have been seen 
 upon its surface, as is proved by the al- 
 most innumerable observations of Schroeter, 
 to whose work the Doctor refers for more 
 extensive details. 
 
 Organised Beings in the Moon. It is a 
 remarkable circumstance, observes M. 
 Gruithuisen, that all those who can take 
 what may be termed a cursory survey of 
 the moon through a telescope, consider it 
 as a desert and globe, upon which nothing 
 lives or grows : on the contrary, others, 
 who have explored its surface for many 
 years, speak of it, as if organised beings 
 could not fail to exist there. 
 
 Shroeter conjectures the existence of a 
 town towards the north of murius (a lunar 
 spot), and the canals which are observa- 
 ble towards hyginus (another spot), and 
 which, after disappearing in some places* 
 are again perceived in others (a thing, 
 says Dr. G. of which I have convinced 
 myself), appear to him very advantageous 
 for the commerce of the Selenites : finally, 
 he represents a part of the spot named 
 mare imbrium to be as fertile as Cam- 
 pania. 
 
 The ancients supposed the moon to be 
 inhabited. Orpheus, Anaxagoras, Zeno- 
 phon, and Pythagoras, are of this opinion. 
 Their strength of reasoning compensated, 
 in this instance, for their want of teles- 
 copes : even Plutarch entertained the 
 
 idea, that the obscure places on the moon’s 
 surface were seas, which could not reflect 
 the light of the sun. More recently, 
 Kepler, Duhamel, and many others have 
 been of the same way of thinking respect- 
 ing the existence of the Selenites. Indeed, 
 so general has this sentiment been, that 
 even the American savages have believed 
 the moon to be inhabited. 
 
 In latter times, some persons have con- 
 sidered the too great rarefaction of the 
 air as an insuperable obstacle to peopling 
 the moon. Without doubt, says our 
 author, this circumstance would not fail 
 to alarm more than one philosopher of a 
 delicate constitution, particularly when he 
 knows that neither raisins nor apricots 
 are to be found even on Chimboraqo. 
 Others, on the contrary, have not forgotten 
 that M. Guy-Lussac ascended, with his 
 balloon, to a height greater by 2000 feet 
 than the height of that mountain. So that 
 an inhabitant of our globe, if placed in 
 the lowest regions of the moon, might find 
 himself very ill at his ease, but not so 
 much so as to cause his death. 
 
 While speaking of the inhabitants of the 
 moon, we may observe, that some theorists 
 have affirmed that no animated beings 
 could exist on that planet, but such as 
 were capable of eating stones, doing with- 
 out drink, living on a scanty supply of 
 air, and supporting the extremes of heat 
 and cold. These particulars, adds Mr. 
 Gruithuisen, may be considered as a sum- 
 ming up of all the doubts that have arisen 
 on the question whether the planets are 
 habitable or not. He then discusses each 
 of these points. He thinks he can con- 
 fidently affirm that the moon has vegeta- 
 bles and animals to serve for food to its in- 
 habitants: he even goes so far as to indi- 
 cate some of their genera and species. In 
 the absence of wine, he continues, the Se- 
 lenites have water, so that they possess 
 the means of quenching their thirst. They 
 are likewise supplied with air in more 
 
5S 
 
 THE ARTISAN. 
 
 than sufficient quantity, only that this 
 air is extremely rarefied. If we admit of 
 lakes and seas in the moon, why should 
 they not contain shell and other fish, and 
 amphibious beings ? And that man can ac- 
 custom himself to a highly rarefied atmos- 
 phere, has been shown by the aerial ascent 
 of M. Guy-Lussac, already referred to. 
 According to Humboldt, the atmosphere 
 supports a column of quicksilver of only 
 twenty inches at Quito ; of eighteen inches 
 at Micuipampa, and of seventeen inches in 
 the latitude of Antisana, all inhabited 
 places upon the earth, notwithstanding 
 this rarefaction. Lastly, the Selenites can 
 face the cold and heat with the assistance 
 of fire, which they have the means of pro- 
 curing in the former case; and in the 
 latter, by means of the deep caverns, in 
 whose coolness they can obtain refuge 
 from the heat. 
 
 SOLUTIONS OF QUESTIONS. 
 
 Quest. 61, answered by an anonymous 
 Correspondent. 
 
 As 1 h. : 12m. :: 34s. : 36 T 4 s r. +5 = 
 41 t |, then the hound gains 8 miles per 
 hour: as 8m. : 1 h. :: 41-jtr. :.58^ 2 s. 
 the time the hound would be in catching the 
 hare. And as 1 h. : 20 m. •: : 58 g k s. : 
 103| r. the distance. Then 58 g L s. ~ time, 
 and 103| rods ~ distance. 
 
 This question was accurately solved by 
 Mr. J. Harding and Mr. Philip Munis; 
 but we prefer the above on account of its 
 arrangement. 
 
 Quest. 60 , answered by Mr. W, Taylor 
 ( the Proposer ). 
 
 Waters in the Moon. By these, says 
 our author, I understand all the springs, 
 rivers, lakes, and seas. After having col- 
 lected and discussed at great length all 
 the facts calculated to illustrate the sub- 
 ject, he thinks he has a right to ask, who 
 can now bring forward any probable ar- 
 gument against the existence of lakes in 
 the moon ? But, he adds, lakes presuppose 
 rivers, or at least simple rivulets or 
 springs, their existence is then sufficiently 
 demonstrated. 
 
 Of the Lunar Structure. The interior 
 structure of the moon is probably not dif- 
 ferent from that which is common to all 
 the bodies of the universe ; namely, con- 
 centric beds formed by the accumulation 
 of successive strata. 
 
 Of the Exterior Structure or Constitution. 
 This consists properly in the chains of 
 mountains; the caverns, the declivities 
 and the acclivities are immediate con- 
 sequences of this disposition. 
 
 We shall only add a few words relative 
 to the lithographical map which Doctor 
 Gruithuisen has attached to his work, for 
 the purpose of facilitating the discovery of 
 the points, which he more particularly 
 wishes to designate upon the face of the 
 moon. To accomplish this, he indicates 
 their situation by their distance from two 
 lines, which may be said to represent the 
 equator and the first meridian of the moon, 
 which we consider to be a felicitous and 
 useful imitation of terrestrial longitudes 
 and latitudes. 
 
 Let t equal the whole time of the des- 
 cent, then will t - 1 be the time of descent 
 through the first half of the tower’s height, 
 and therefore we have t 2 : (t — 1) 2 : : 2 : 1, 
 t 2 
 
 whence t 2 - 2 t -f 1 — — , which re- 
 
 duced, gives t~2 -f x/ 2 — 3*414 seconds 
 for the time, and the tower’s height is 
 187*48 feet. 
 
 We received two other solutions to this 
 question from intelligent and old Corres- 
 pondents; but they were both erroneous. 
 
 QUESTION FOR SOLUTION. 
 
 Quest. 63, proposed by Mr. Whitcombe, 
 Cornhill. 
 
 In a given quadrant of a circle to in- 
 scribe geometrically a rectangle, whose 
 length and breadth shall be in the ratio of 
 mton; and to give a geometrical demon- 
 stration. 
 
 Quest. 64, proposed by Mr. J. Taylor, 
 Clement' s-lane. 
 
 John goes with a message from Charing 
 Cross to the India House, and Peter with 
 a message from the India House to Charing 
 Cross: they start at the same instant of 
 time ; both travel uniformly, and in such 
 proportion, that John, 20 minutes after 
 their meeting, arrives at the India House ; 
 and Peter, in 45 minutes after their meet- 
 ing, arrives at Charing Cross. From this 
 data I demand the respective times occu- 
 pied in the journies of John and Peter? 
 
THE ARTISAN. 
 
 81 
 
 ttlUMATOS. 
 
 AIR AS THE VEHICLE OF HEAT AND 
 MOISTURE. 
 
 The earth and the atmosphere, taken 
 generally, receive at all times nearly the 
 same quantity of heat and light from the 
 sun. 
 
 As the whole of one side of the earth is 
 constantly turned to the sun, the only dif- 
 ference in the quantity of heat and light 
 which the earth receives in a given time, 
 must arise from the changes which take 
 place in its distance from the sun at differ- 
 ent seasons of the year. In consequence 
 of these changes, the quantities of light 
 and heat received by the earth are not 
 proportional to the times, but to the angles 
 described by the earth round the sun in 
 those times. These variations, however, 
 are but inconsiderable; and as they are 
 annual, they do not produce any inequa- 
 lity in the whole heat or light of one year, 
 compared w r ith those of another. 
 
 Though the earth is thus receiving heat 
 continually, and nearly at the same rate, 
 its average temperature appears to remain 
 invariable; as much heat as comes from 
 the solar rays, flying off* continually into 
 the fields of vacuity or of ether. 
 
 While the general temperature of the 
 earth remains invariable, the distribution 
 of heat over its surface is extremely un- 
 equal, being different in different places, 
 and in the same place subject to variations, 
 both regular and irregular. 
 
 The causes that determine the distribu- 
 tion of heat over the earth’s surface, are 
 either the direct influence of the solar 
 rays, or the communication of heat by the 
 air from one part of the earth’s surface to 
 another. 
 
 The first of these depends on the lati- 
 tude of the place, or its distance from the 
 equator, by which the intensity of the heat 
 and light from the sun, and also the length 
 of the day, are determined for different 
 seasons of the year. 
 
 The intensity of the sun’s rays, when 
 they strike on any plane, is as the quan- 
 tity that falls on a given space, or as the 
 sine of the sun’s elevation above the plane. 
 The nearer the sun is to the zenith of any 
 place, at a given moment, the greater the 
 intensity of heat produced by his rays. 
 
 The heat for an entire day depends also 
 on the length of the day ; and as the day 
 is longer where the distance from the ze- 
 nith is greater, the inequality in the dis- 
 tribution of heat arising from the one of 
 these causes, compensates that proceeding 
 from the other, and brings their combined 
 effects nearer to an equality than might be 
 imagined. Fontana has shown, that the 
 heat of the day of the summer solstice at 
 
 Yql. II — No. 31. 
 
 Pavia, is greater than the heat of the same 
 day at Petersburg only in the ratio of 63 u 
 to 62°, though the latitude of the former 
 be 45° ll', and of the latter 59° 5b'. 
 
 The same author finds, that when the 
 sun’s declination exceeds 18°, or from 
 about the 10th of May to the 30th of July, 
 the heat in twenty-four hours proceeding 
 from the sun’s rays, is greater at the north 
 pole than at the equator. 
 
 The distribution of heat, therefore, if 
 only the direct influence of the sun were 
 to act, would be very different from that 
 which takes place in nature. 
 
 The intensity of the solar heat is less in 
 low elevations than is here supposed, on 
 account of, the rays coming through a 
 larger mass of air, and of air more loaded 
 with vapour, so that a great quantity of 
 them is intercepted. 
 
 The effects of the direct influence of the 
 sun, are greatly modified by the transpor- 
 tation of the temperature of one region 
 into another, in consequence of that dis- 
 turbance in the equilibrium of the atmos- 
 phere, which the action of those rays ne- 
 cessarily produces. 
 
 In order that there may be an equili- 
 brium in a fluid like the air, every stratum 
 of air that is level or horizontal all round, 
 ought to be of the same density, it ought, 
 therefore, also to be everywhere of the 
 same temperature, which not being the 
 case, the constant motion of the air is the 
 necessary consequence of heat being un- 
 equally distributed. The columns of air 
 that are lighter, are displaced by those 
 that are heavier, and hence a general ten- 
 dency in the air to move from the poles 
 toward the equator. This general ten- 
 dency, which is calculated to moderate 
 the extremes of temperature, is also greatly 
 modified by local circumstances. 
 
 The sea is preserved of a moderate tem- 
 perature, by the statical principle that 
 makes the heavier columns of a fluid dis- 
 place the lighter. A more uniform tem- 
 perature is thus given to the sea, which 
 communicates itself to the air incumbent 
 on it, and to that on every side. 
 
 Conversely, the effect of great and un- 
 broken continents is favourable to the ex- 
 tremes of heat or of cold. 
 
 The constitution of the surface may tend 
 to increase and sometimes to diminish this 
 effect. High mountains especially, if 
 covered with snow, may enforce the 
 rigour of a cold climate, or temper the 
 heats of a warm one. 
 
 Forests tend to increase the cold, by 
 preventing the sun’s rays from striking 
 the ground. Evaporation produces cold ; 
 and marshes and lakes are therefore fa- 
 vourable to the severity of the weather. 
 The congelation of w r ater produces heat, 
 and moderates the cold ; the melting of 
 F 
 
82 
 
 THE ARTISAN. 
 
 jce, on the other hand, increases the capa- 
 city for heat, and so produces cold. 
 
 Height above the level of the sea, 
 causes a diminution of heat, at the con- 
 stant rate of about 1° for 270 feet nearly, 
 when not far from the surface of the 
 earth. 
 
 It has already been remarked, that this 
 decrease seems to be somewhat slower as 
 we ascend, but not very considerably, as 
 far as our observations have extended. 
 
 The combination of these causes gives 
 to every place a mean temperature, which 
 remains always nearly the same, and which 
 decreases from the equator to either pole, 
 according to a law that has been deter- 
 mined by observation. 
 
 This mean temperature may be deter- 
 mined by a geometrical construction, as 
 follows : Divide the line A C into equal 
 parts numbered from A, so as to represent 
 the scale of a thermometer, let A C be 
 made equal to 85, and A B to 58 of those 
 parts. Then from the centre B with the 
 
 distance B C or 27, describe the semi- 
 circle C H ; take the arch C G equal to 
 the double latitude of any parallel ; and 
 from G draw G O perpendicular to AC; 
 then is A O the mean temperature of that 
 parallel, according to Fahrenheit's scale. 
 
 The mean temperatures thus found, 
 agree very well with observation. Springs, 
 in which the water does not considerably 
 change its heat from one season of the 
 
 year ta another, afford an expeditious and 
 accurate way of ascertaining the mean 
 temperature. 
 
 On ascending into the atmosphere at a 
 certain height in every latitude, a point is 
 found where it always freezes, or where it 
 freezes more than it thaws, so that the 
 mean temperature is below 82°. The 
 curve joining all these points frotn the 
 equator to the pole, is called the line of 
 perpetual congelation. (See page 110, 
 vol. i.) 
 
 The temperature of the latter end of 
 April is observed, at least in the tempe- 
 rate zone, to be nearly the mean tem- 
 perature of the year. From the time the 
 heat increases, and is at its maximum 
 about the 21st of July, it goes on decreas- 
 ing from that time till it come to the mean 
 in the end of October, and passes from 
 thence to the greatest cold about the 21st 
 of January. 
 
 As we go eastward from the shores of 
 the Atlantic, the mean temperature of any 
 parallel becomes lower at a rate that may 
 perhaps, for the north part of the tempe- 
 rate zone, be estimated at a degree for 
 150 miles. 
 
 At St. Petersburg!!, lat. 59° 56', about 
 750 miles from what may be accounted the 
 shores of the Atlantic, the temperature is 
 5° 5' below the standard. The medium 
 temperature of January is no more than 
 10°. By computation, it ought to be 
 greater than 32°. The winter lasts from 
 October to April, and the cold is some- 
 times as great as the freezing point of 
 mercury, or — 39°. From a mean of seve- 
 ral years, the mean of the winter cold is 
 —25°. 
 
 It was at Krasnojark, lat. 56° 30', long. 
 93° E, that mercury was first known to 
 freeze by natural cold. 
 
 At Irkutz, lat. 52° 15', long. 105°east, 
 the mean temperature from October to 
 April has been known to be as low as 
 - — 6° 8', a temperature which for severity 
 and duration, exceeds any thing that has 
 yet been observed elsewhere. 
 
 This increase of the severity of the 
 winter, and the consequent diminution of 
 the mean temperature on going eastward, 
 holds in all the latitudes north of the 
 parallel of 30°; but the diminution is 
 slower as we approach that parallel ; to 
 the south of 30°. the mean heat increases 
 on retiring from the ocean. 
 
 This diminution takes place all the way 
 to the shores of the Pacific, or very near 
 them. The climate of Pekin is vastly 
 more severe than that of the same parallel 
 (39° 54') in Europe. 
 
 In the new Continent also, at least in 
 the part of it to the north of the Tropic of 
 Cancer, the mean temperature is much be- 
 low the standard, and the severity of the 
 
THE ARTISAN. 
 
 S3 
 
 winter much greater than in the same 
 latitudes in Europe. 
 
 At Prince of Wales’ Fort, Hudson’s 
 Bay, lat. 59° long. 92° west, the mean 
 temperature is 20° under the standard ; at 
 Nain, in Labrador, 16°; at Cambridge, in 
 New England, (lat. 42° 25 ) 10 degrees. 
 Mercury has been supposed to be frozen 
 by the natural cold as far south as Quebec, 
 lat. 47°. 
 
 A very low mean temperature, and ex- 
 treme cold in winter, are characteristic of 
 the climate of North America. 
 
 In the higher latitudes of the southern 
 hemisphere, the temperature is lower than 
 in the same latitudes of the northern he- 
 misphere. 
 
 The south pole is surrounded to the 
 distance of 18 or 19 degrees with a barrier 
 of solid ice, through which even the skill 
 and intrepidity of Captain Cook could not 
 force a passage. 
 
 It is known also, that detached masses 
 of ice float down in that hemisphere, as 
 low as the latitude of 46°. The cause of 
 this phenomenon is by no means suffi- 
 ciently understood. The varieties of tem- 
 perature to be met with on the surface of 
 the earth, appear to be confined within the 
 limits of 100° and — 40°. 
 
 No degree of cold much below — 40° has 
 ever been observed in nature, even when 
 thermometers have been employed, con- 
 taining a fluid not liable to congelation. 
 
 The heat of 100° is rare; but a heat 
 approaching to 90°, is found in the sum- 
 mer of most countries within the limits of 
 the temperate zones. 
 
 There is hardly any climate, even in the 
 frigid zone, where a temperature between 
 60° and 50° is not occasionally experi- 
 enced. 
 
 The greatest heat is much less above 
 the mean temperature, than the greatest 
 cold is below it. The mean temperature 
 for the whole surface may be taken at 58° ; 
 the greatest summer heat is only 42° above 
 this ; the greatest winter cold is 98° under 
 it. 
 
 There is reason to think that the climates 
 of Europe were more severe in ancient 
 times than they are at present; and the 
 change that has taken place, may with 
 great probability be ascribed to the better 
 and more extensive cultivation of the 
 ground. 
 
 Caesar says, a that the vine could not 
 be cultivated in Gaul, on account of the 
 severity of the winter.” The rein-deer 
 was then an inhabitant of the Pyrenees. 
 The Tiber was sometimes frozen over, and 
 the ground about Rome covered with snow 
 for several weeks together. 
 
 Cultivation may improve a climate. 1st, 
 By the draining of marshes and lessening 
 the evaporation, which is so great a cause 
 
 of cold. 2d. By turning up the soil and 
 exposing it to the rays of the sun. 3d. 
 By thinning or cutting down forests, which 
 by their shade prevented the penetration 
 of the sun’s rays. The improvement which 
 is continually taking place in the climate 
 of North America, proves that the power 
 of man extends to the phenomena, which, 
 from the magnitude and variety of their 
 causes, seemed most superior to his con- 
 troul. At Guiana, in South America, the 
 rainy season has been shortened by the 
 clearing of the country, and the warmth 
 greatly increased. It thunders continually 
 in the woods; rarely in the cultivated 
 parts. 
 
 OF RAIN. 
 
 The vapour that rises from water uniting 
 itself to the air, ascends into the higher 
 regions of the atmosphere, and is carried 
 by the winds to great distances. 
 
 It cannot be doubted, that the humidity 
 raised in this manner, is chemically dis- 
 solved in the air. 
 
 The humidity does not lessen, but in- 
 creases the transparency of the air, and 
 cannot be withdrawn from it, but by sub- 
 stances that attract it powerfully. 
 
 The power of air to dissolve humidity, 
 increases in a greater ratio, than that in 
 which its temperature increases. 
 
 It appears from Saussure's experiments, 
 that while the temperature increases in 
 arithmetical progression, the humidity 
 which the air is able to contain, increases 
 in geometric progression. A cubic foot 
 of air, of the temperature 66°, is able to 
 hold in solution 11 or 12 grains of water: 
 the air itself weighs 570 grains ; to that 
 air of the temperature 66°, dissolves about 
 a 50th of its own weight of water. 
 
 Hence, if two portions of air, of different 
 temperatures, and both saturated with 
 humidity, be mixed together, a precipita- 
 tion of humidity must necessarily take 
 place. 
 
 If, therefore, large portions of the at- 
 mosphere, of different temperatures, and 
 saturated, or nearly saturated, with humi- 
 dity, be driven against one another by 
 contrary winds, the consequence must be 
 a precipitation of humidity, or the forma- 
 tion of clouds. 
 
 The mixture of different portions of air is 
 likely to take place most frequently, when 
 the two opposite currents already men- 
 tioned, come in contact with each other. 
 This is at the height of 18000 feet and 
 upwards, which argees very well with the 
 medium height of the clouds. 
 
 The clouds thus formed have their par- 
 ticles united into larger masses or drops 
 by different causes, such as the mutual 
 attraction of aqueous particles, the force 
 of the wind, or the operation of electricity, 
 F 2 
 
84 
 
 THE ARTISAN. 
 
 and so fall down in rain on the surface of 
 the earth. 
 
 The intimate connection between rain 
 and the existence of different currents of 
 air, is evident from many appearances. 
 Some of which we shall state. 
 
 1. When the trade winds blow uni- 
 formly, hardly any rain falls ; but when 
 the monsoon changes, heavy falls of rain 
 seldom fail to take place. 
 
 2. In the tropical climates, the rainy 
 season is always on the sun’s approach to 
 the zenith, at which time also the winds 
 are most variable. 
 
 3. There are some spots of continual 
 rain, which seem to be where opposite 
 streams of air constantly meet one another. 
 
 4. There are several tracts on the earth’s 
 surface where it hardly ever rains. They 
 are usually far inland, and have extensive 
 plains, without any of those inequalities 
 of surface that promote the mixture of 
 air. 
 
 5. In the midst of those desarts, where 
 mountains occur, moisture is precipitated 
 sometimes in the form of rain, but most 
 frequently of dew, so that there are springs 
 of fresh water, and great fertility pro- 
 duced. 
 
 6. There is in our climate hardly any 
 instance of rain without a change of wind, 
 and very rarely a change of wind without 
 rain in a greater or smaller quantity. 
 
 7. The lowness of the mercury in the 
 barometer is a sign of rain. It is a certain 
 indication of the subversion of the equili- 
 brium of the atmosphere ; and makes it 
 probable, that before the equilibrium of 
 the atmosphere is restored, winds from 
 different quarters, and of different tem- 
 peratures, must come into collision with 
 one another. 
 
 The vapour raised up into the air, is of 
 a quantity sufficient to afford all the rain 
 that falls, or to supply all the springs, and 
 of consequence all the rivers derived from 
 them on the surface of the earth. 
 
 Dr. Halley shewed, that the evaporation 
 from the sea alone is a sufficient supply for 
 all the waters that the rivers carry into it. 
 His calculation was founded on a very 
 complex view of the subject, and liable to 
 several objections. BufFon took a more 
 simple view of the matter, by selecting 
 one of those lakes that sends out no stream 
 to the ocean, and shewing that the pro- 
 bable evaporation from the surface of the 
 lake, is equal to all the water carried into it. 
 
 A simpler view still may be taken, by 
 showing that all the water annually emp- 
 tied by a river into the sea, is less than 
 the rain that falls on the surface drained 
 by it. Thus, according to Dr. Halley’s 
 computation, the water which the Thames 
 carries down through Kingston Bridge, to 
 which the tide does not reach, is 25344000 
 
 cubic yards, or 684288000 cubic feet pet 
 day, which gives 249765120000 cubic feet, 
 for the quantity of water which the Thames 
 discharges annually into the sea. Now, 
 the surface drained by the Thames and its 
 branches, appears to be about equal to a 
 circle of 40' miles radius; that is, nearly 
 to 5036 square miles, or 140395622400 
 square feet. But if we suppose that the 
 depth of rain that falls annually, at an 
 average over this surface, is two feet, we 
 have a quantity which exceeds that carried 
 down by the Thames by 31026124800, or 
 nearly an eighth part of the whole, which 
 is therefore left to be taken up by the 
 evaporation. 
 
 The disputes that prevailed so long con- 
 cerning the origin of fountains and rivers, 
 chiefly arose from the difficulty of conceiv- 
 ing how a precarious and accidental supply 
 could be rendered equal to a regular and 
 great expenditure. 
 
 The quantity of rain that falls in differ- 
 ent places in the same year, and in the 
 same place in different years, is extremely 
 various ; and even in the temperate zone, 
 runs between the extremes of 18 and 100 
 inches. 
 
 In places not very distant from one 
 another, the difference in the quantity of 
 rain is often very great. The neighbour- 
 hood of the sea on one hand and moun- 
 tains on the other, is most favourable to 
 the production of rain ; from the first is 
 derived a humid atmosphere, and from the 
 second the prevalence of winds of different 
 temperatures. 
 
 The region of the air in which the pre- 
 cipitation of humidity takes place, is fre- 
 quently one where the temperature is 
 below freezing ; the frozen particles then 
 uniting, as in the case of melted vapour, 
 form flakes of snow, which reach the sur- 
 face in that same state, when the cold of 
 freezing continues down to the surface. 
 
 When the aqueous particles first form a 
 drop, and are afterwards frozen in their 
 descent, they become hail, which is some- 
 times found crystallized with some degree 
 of regularity. The whiteness and opacity 
 of the hail, is probably owing to the con- 
 gelation being performed where the air is 
 very rare. 
 
 Professor Leslie has remarked, in the 
 curious experiments he has made on the 
 production of ice by evaporation, in a re- 
 ceiver where the air was considerably 
 rarefied, that the ice is more porous and 
 less transparent, than that which is formed 
 under the ordinary pressure of the atmos- 
 phere. 
 
 Dew is a precipitation of humidity from 
 the lower strata of the atmosphere, which 
 does not disturb the transparency of the 
 ah', and to which the mixture of different 
 streams of air does not seem necessary. 
 
THE ARTISAN. 
 
 85 
 
 Dew is only formed in calm weather, 
 and in the evening or daring the night. 
 The resting of the globules of dew on the 
 points of grass and other plants, seems to 
 indicate the presence of some electrical 
 influence. Bruce has remarked, that 
 during the dry season no dew falls in 
 Egypt, but that it is usually observed in 
 the Delta five or six days before the inun- 
 dation. 
 
 Besides these deposits from the atmos- 
 
 phere, which are all of one substance, 
 there are others that cannot be traced to 
 the same origin. These are the stones 
 which have often been said, and have of 
 late years been ascertained beyond all 
 doubt, to fall down from the air : on ex- 
 amination, they are found to contain cer- 
 tain metallic ores, in many respects un- 
 like to any thing that is found, either on 
 the surface or in the bowels of the earth. 
 
 ^EESFECT IVE. 
 
 To exhibit the Perspective Appearance of a 
 Square seen obliquely, and having one of 
 its , Sides in the fundamental Line. 
 
 Let A BCD be the square, having the 
 side AB in the fundamental line; 
 
 distance of the eye. Transfer the perpen- 
 diculars A C and B D to the fundamental 
 line D E ; and draw the right lines K B, 
 K D, as also A V, Y C. Then will A and 
 B be their own appearances; and c and 
 d the appearances of the points C and D. 
 Consequently A c d B is the appearance of 
 the square A B C D. If the square ACBD 
 should be at a distance from the fun- 
 damental line DE; which rarely hap- 
 pens in practice, the distances of the 
 angles A and B must likewise be trans- 
 ferred to the fundamental line, as is evi- 
 dent from the preceding problem. And 
 since even the oblique view is not very 
 common ; in what follows we shall always 
 suppose the figure to be posited directly 
 opposite to the eye, unless where the con- 
 trary is expressly mentioned. 
 
 the square being viewed obliquely, assume To exhibit the appearance of a square , 
 the principal point V in the horizontal line whose diagonal is perpendicular to the 
 H R, in such a manner as that a perpendi- fundamental line. 
 
 cular to the fundamental line may fall Let A B C D be the square, having its 
 without the side of the square A B ; at diagonal A C perpendicular to the funda- 
 least, may not bisect it ; and make VK the mental line. 
 
86 
 
 THE ARTISAN. 
 
 Continue the sides DC and CB till 
 they meet the fundamental line in 1 and 2, 
 From the principal point V set off' the dis- 
 tance of the eye to K and L. From K to 
 A and 1, draw right lines K A and K 1 ; 
 and from L to A and 2, the right lines 
 LA, L2. The intersections of these lines 
 will exhibit the appearances of the square 
 A BCD viewed angle-wise. 
 
 To exhibit the appearance of a square , having 
 another inscribed in it. , 
 
 Let the square ABCD, which inscribes 
 the square I M G H, have its side A B in 
 the fundamental line, and the diagonal of 
 the less perpendicular to it. 
 
 From the principal point V, set off, each 
 way, on the horizontal line HR, the dis- 
 tances Y L and V K ; draw V A and VB ; 
 and KA and L B ; then will A c d B be the 
 appearance of the square A C DB. Pro- 
 duce the side of the inscribed square I H, 
 till it meet the fundamental line in 1 ; and 
 draw the right lines K 1, and KM ; then 
 
 will i h g M be the representation of the 
 inscribed square I H G M. Hence is 
 easily conceived the projection of any 
 figure inscribed in another. 
 
 To exhibit the perspective of a pavement, 
 consisting of square stones viewed di- 
 rectly. 
 
 Divide the side A B transferred to the 
 
 fundamental line D E into as many equal 
 parts as there are square stones in one 
 row. From the several points of division, 
 draw right lines to the principal point Y ; 
 and from A to the point of distance K, 
 draw a right line A K ; and from B to the 
 other point of distance L, draw another 
 LB. Through the points of the intersec- 
 tions of the corresponding lines, draw right 
 lines on each side, to be produced to the 
 right lines AY and BV. Then will Afg B 
 be the appearance of the pavement 
 AFG B. 
 
 To exhibit the perspective of a circle. 
 
 If the circle be small, circumscribe it by 
 a square. Draw diagonals and diameters 
 h a and d e, 
 
THE ARTISAN. 
 
 57 
 
 intersecting each other at right angles ; 
 and draw the right lines/g’ and b c paral- 
 lel to the diameter de through b and/; 
 as also through c and g draw right lines, 
 meeting the fundamental line D E in the 
 points 3 and 4. To the principal point V 
 draw right lines V 1, V 3, V 4, V 2 ; and 
 to the points of distance L and K, draw 
 
 the right lines L2 and K 1. Lastly, con- 
 nect the points of intersection a, b, d,f 7 h, 
 g, e, c, with arches a b,bd,df, &c. Thus, 
 will abdfhg eca, be the appearance of 
 the circle. 
 
 If the circle be large, on the middle of 
 the fundamental line A B, 
 
 describe a semicircle ; and from the seve- 
 ral points of the periphery, C, F, G, H, I, &c. 
 to the fundamental line, let fall perpendi- 
 culars Cl, F2, G 3, H4, I 5, &c. From 
 the points A, 1, 2, 3, 4, 5, &c. draw right 
 lines to the principal point V, as also a 
 right line from B to the point of distance 
 L; and another from A to the point of 
 distance K. Through the common inter- 
 sections, draw right lines as in the pro- 
 ceeding problem ; thus shall we have the 
 points e , f, g, h, i, which are the represen- 
 tations of these, A, C, F, G, H, I ; and these 
 being connected as before, give the pro- 
 jection of the circle. 
 
 Hence appears, not only how any curvi- 
 linear figure may be projected on a plane ; 
 but also how any pavement, consisting of 
 any kind of stones, may be delineated in 
 perspective. 
 
 Hence also appears what use the square 
 is of in perspective ; for even in the second 
 case we use a square divided into certain 
 areolae, and circumscribed about the circle ; 
 though it be not delineated on the geome- 
 trical plane in the diagram. 
 
 We may here observe, that if the mag- 
 nitudes of the several parts of an object 
 be given in numbers, together with the 
 height and distance of the eye, the figures 
 of the object is first to be constructed by 
 a scale geometrically ; and the fundamen- 
 tal point, with the point of distance to 
 be determined by the same scale. We 
 may also observe, that it is not necessary 
 that the object be delineated under the 
 fundamental line: in the projection of 
 squares and pavements, it is best not. 
 But where it is necessary and space is 
 wanting, draw it apart; find the divisions 
 in it, and transfer them to the fundamental 
 line in the plane. 
 
 Threads being hung on the principal 
 point, and the point of distance, and thence 
 stretched to the points of the divisions of 
 the fundamental line ; the common inter- 
 sections of the threads, will give the pro- 
 jection of the several points without con- 
 fusion ; a thing much to be feared from 
 the multiplicity of lines to be drawn. 
 
THE ARTISAN. 
 
 ss 
 
 CHEMISTHY a 
 
 Mercury is always fluid when in a pure 
 state, and is one of the most brilliant and 
 shining of all known metals. When its 
 surface is sufficiently clear, it forms a very 
 line mirror. Its colour is as beautiful as 
 that of silver, with which it has always 
 been compared. After platina and gold, 
 it is considered as the heaviest of all 
 known bodies. Its specific gravity is 
 13-568,* taking water at 1-000. — Authors 
 were formerly very particular in observ- 
 ing, that all the most ponderous substances 
 swam upon its surface, whilst gold alone 
 sunk in it; at the present day we have to 
 add to this, platina and tungsten 
 
 Boerhaave asserted, in his Elements of 
 Chemistry, that mercury could not be ren- 
 dered solid by any degree of cold, though 
 he admits a condensation of of its pri- 
 mitive volume; a circumstance which 
 cannot take place in its real congelation. 
 This assertion of Boerhaave, and other 
 philosophers who have followed him, w as 
 proved to be false in the year 1759; in 
 which year the academicians of Peters- 
 burg, availing themselves of an intense 
 degree of natural cold, augmented it still 
 further by a mixture of snow- and fuming 
 nitrous acid ; the mercurial thermometer 
 which they used descended to 213 degrees 
 of De Lisle’s scale, which corresponds 
 with 46 below 0 of that of Fahrenheit. As 
 the mercury did not descend any lower, 
 but seemed stationai-y, the academicians 
 broke the glass bulb of their instrument, 
 in which they found congealed mercury, 
 that formed a solid substance susceptible 
 of being extended by the hammer. They 
 thus discovered that mercury might become 
 solid, and that in this state it possessed a 
 certain degree of ductility. They re- 
 marked, that at every stroke of the ham- 
 mer, the pressui-e, developing the caloric 
 in the interior of the metal, fused it, and 
 that it ran into globules. 
 
 This first experiment was, in some mea- 
 sure, nothing more than a hint to philoso- 
 phers concerning a property unknown, 
 and till then even denied, in mercury ; it 
 has since been often repeated, -and of late 
 it has become as easy and simple an expe- 
 riment as most of those that are made in 
 Chemistry. In the year J772, Pallas 
 caused mercury to congeal, at Krasnejark, 
 by a natural cold of — 55f deg. of Fahren- 
 heit’s scale. It was observed that it then 
 resembled soft tin ; that it could be flat- 
 tened ; that it broke easily ; and that its 
 fragments, when brought into contact, 
 were glued or soldered together, as hap- 
 pens in all other softened metals. How- 
 ever, it is evident that he did not obtain 
 if§ real conversion into a solid, or complete 
 
 concretion, as the mercury was still soft, 
 and only in a state of semi-congelation. 
 In the year 1775, Mr. Hutchins observed 
 the same congelation at Albany Fort, and 
 Mr. Bicker at Rotterdam, in 1776, at 56 
 deg. below 0. In the year 1783, the con- 
 gelation of mercury was effected in Eng- 
 land with a less degree of cold ; and Mr. 
 Cavendish has proved 31| below 0 of 
 Reaumur’s, or 40 below r Fahrenheit’s ther- 
 mometer, to be the real degree at which it 
 takes place. 
 
 As a metal always fused, always liquid 
 at fee temperature of our climate, mer- 
 cury constantly affects the form of perfect 
 globules when it is divided. When in- 
 closed in a glass phial or tube, its surface 
 is convex, which depends upon the small 
 attraction which it has for the glass; in 
 fact, if we pour it into a vessel or tube of 
 some metal with which it is able to com- 
 bine, instead of remaining convex, its sur- 
 face becomes concave. As this round, 
 curved, and convex surface may give rise 
 to some errors in barometrical observa- 
 tions, especially in those which are made 
 with tubes of a fine bore, in which the 
 elevation of the mercury ought to be an 
 exact measure of the height of the places 
 which we wish to determine, attempts 
 have been made to obviate this source of 
 error, by rendering the mercurial surface 
 flat. Cassebois succeeded by boiling the 
 mercury for a long time in the barometrical 
 tubes ; by which means a surface almost 
 perfectly horizontal was obtained, espe- 
 cially in tubes of a wide bore. 
 
 The expansion of mercury by the action 
 of fire has not yet been very accurately de- 
 termined ; it is known to be a very good 
 conductor of caloric, on which account it 
 appears very cold to the hand when im- 
 mersed in it ; and it is also owing to this 
 conducting property that a red hot iron, 
 when plunged into mercury, instantane- 
 ously loses its redness, which it would 
 have retained for some time in the air, and 
 even in water. Its expansion by heat pro- 
 ceeds in a very uniform manner ; and it is 
 on this account that it is employed in the 
 construction of thermometers. When it is 
 penetrated with a quantity of caloric, 
 which has not yet been well ascertained, 
 but which is estimated at 656 degrees of 
 Farhenheit’s thermometer, the mercury 
 swells, is reduced to the state of vapour, 
 and volatilized. When this experiment is 
 performed in the air, the mercury presently 
 condenses into a white smoke, which is 
 capable of producing very injurious effects 
 upon animals. If it be performed in close 
 vessels, in such a manner that the metal 
 may speedily become fixed and liquefied, 
 this becomes a means of distillation, in 
 which the habitudes of the volatile metal 
 are the same as those of every other dis- 
 
THE ARTISAN. 
 
 89 
 
 tilled liquid. In this operation, which is 
 often employed for the purpose of purify- 
 ing the mercury, it is customary to adapt 
 to the neck of the retort of iron or stone- 
 ware which is used a tube of linen, the 
 extremity of which is immersed in the 
 water with which the receiver is filled. 
 By means of this apparatus, the mercury 
 is speedily condensed into the liquid form, 
 and collected entire under the water, from 
 which it is afterwards separated by rub- 
 bing it with paper manufactured without 
 size, drying it in a gentle heat, passing it 
 through a skin, agitating it with very dry 
 bread-crumbs, bran, and other desiccating 
 means of a like nature. It is on account 
 of this easy process of distillation that 
 Chemists have considered mercury as the 
 most volatile of all metals. 
 
 Mercury is a very good conductor of 
 electricity and galvanism. Its electrical 
 property is probably the cause of the phos- 
 phorescence, and the considerably bright 
 light which it emits, when it is agitated in 
 a vacuum. It has been discovered that 
 this phosphorescence is an electrical phe- 
 nomenon, which takes place only in con- 
 sequence of the friction of the mercury- 
 against the sides of the tube, and that the 
 mercury does not thereby suffer any sen- 
 sible alteration. 
 
 Mercury is not altered by being kept 
 under water. When exposed to the air, 
 its surface is gradually tarnished, and 
 covered with a black powder, owing to its 
 combining with the oxygen of the atmos- 
 phere. But this change goes on very 
 slowly, unless the mercury be either 
 heated or agitated ; by shaking it, for in- 
 stance, in a large bottle full of air. By 
 either of these processes, the metal is con- 
 verted into an oxide : by the last, into a 
 black oxide ; and by the first, into a red 
 coloured oxide. This metal does not seem 
 to be capable of combustion ; at least, no 
 method which has hitherto been tried to 
 burn it has succeeded. It is the only 
 metal which may not, by peculiar manage- 
 ment, be made to burn. 
 
 Native mercury, which has been termed 
 virgin mercury, is found in the form of 
 liquid globules, which are very easily re- 
 cognised by their brilliancy and liquidity. 
 It is commonly found in tender and friable 
 earths and stones, and frequently inter- 
 posed between the fissures and the cavities 
 of its own orbs, especially of its sulphuret. 
 It is seldom perfectly pure, and frequently 
 contains some other metal with which it is 
 alloyed; but when it is sufficiently liquid, 
 it is considered as pure, or really native. 
 At Ydria, and in Spain, and America, it is 
 collected in the cavities and clefts of the 
 rocks, into which it filtrates from all sides. 
 It is found liquid in argil at Almaden, and 
 ip the beds of chalk in Sicily. It is also 
 
 found in the ores of silver ana lead, and 
 even mixed with the arsenious acid, or 
 white arsenic. 
 
 Mercury does not combine with the sim- 
 ple incombustibles ; but it combines with 
 the greater number of metals. These com- 
 binations are known in Chemistry by the 
 name of amalgams. 
 
 The amalgam of gold is formed very 
 readily, because there is a very strong 
 affinity between the two metals. If a bit 
 of gold be dipped into mercury, its sur- 
 face, by combining with mercury, becomes 
 as white as silver. The easiest way of 
 forming this amalgam is to throw small 
 pieces of red hot gold into mercury heated 
 till it begins to smoke. The proportions 
 of the ingredients are not determinable, 
 because they combine in any proportion. 
 This amalgam is of a silvery w hiteness. By 
 squeezing it through leather, the excess of 
 mercury may be separated, and a soft 
 white amalgam obtained, which gradually 
 becomes solid, and consists of about one 
 part of mercury to two of gold. It melts 
 at a moderate temperature ; and in a heat 
 below redness the mercury evaporates, 
 and leaves the gold in a state of purity. It 
 is much used in gilding. The amalgam 
 is spread upon the metal which is to be 
 gilt; and then, by the application of a 
 gentle and equal heat the mercury is 
 driven off, and the gold left adhering to 
 the metallic surface ; this surface is then 
 rubbed with a brass wire brush under 
 water, and afterwards burnished. 
 
 Dr. Lewis attempted to form an amal- 
 gam of platinum, but succeeded only im- 
 perfeotly, as was the case also with 
 Scheffer. Morveau succeeded by means 
 of heat. He fixed a small cylinder of pla- 
 tinum at the bottom of a tall glass vessel, 
 and covered it with mercury. The vessel 
 was then placed in a sand-bath, and the 
 mercury kept constantly boiling. The 
 mercury gradually combined with the pla- 
 tinum ; the weight of the cylinders was 
 doubled, and it became brittle. When 
 heated strongly, the mercury evaporated, 
 and left the platinum partly oxidized. 
 It is remarkable that the platinum, not- 
 withstanding its superior specific gravity, 
 always swam upon the surface of the mer- 
 cury, so that Morveau was under the ne- 
 cessity of fixing it down. 
 
 There are few metallic substances that 
 exceed mercury in utility. In physics, it 
 is employed in its metallic form; in the 
 construction of meteorological instru- 
 ments, and a great number of machines in 
 the arts ; it is employed in the same form 
 for gilding, silvering of glass mirrors, and 
 in metallurgical operations; its solutions 
 are used in dyeing. 
 
 In chemistry, it is applied to a great 
 variety of uses, all equally important. 
 
90 
 
 THE ARTISAN. 
 
 Besides the experiments in which it is 
 employed for demonstrating the principal 
 truths of this science, it has become of in- 
 dispensible necessity for furnishing the 
 vessels destined to collect, preserve and 
 combine many of the gases. 
 
 It is of equal importance for medicinal 
 purposes. 
 
 OF COPPER. 
 
 Copper is one of those metals which 
 were known in the most early ages of the 
 world, and has at all times been one of the 
 most easy to extract and manufacture. 
 The Egyptians employed it for a variety 
 of uses, and made of it cast figures, re- 
 markable for their elegant form, in the re- 
 motest times of their history. The Greeks 
 manufactured it, melted it, cast it, and 
 employed it in various arts. With them it 
 made the base of the celebrated compounds 
 called Corinthian Brass. The Romans 
 likewise manufactured it in great quan- 
 tity ; and it has even been imagined, that 
 the greater number of their utensils were 
 always made with this metal, and very 
 rarely with iron. This circumstance has 
 been urged as a valid proof that they 
 knew little of iron, and were unskilful in 
 manufacturing it. 
 
 The alchemists employed themselves 
 much about copper. They called it Venus , 
 on account of the great facility it possesses 
 of combining with many substances, par- 
 ticularly with other metals, and because 
 of the sort of adulteration it makes in 
 these compounds. 
 
 By representing it by the emblem ap- 
 propriated to gold, terminated at bottom 
 by the sign of a cross, they considered it 
 as formed chiefly of gold, but disguised 
 and altered by something acrid and cor- 
 rosive, which rendered it crude. Though, 
 in the different periods of the great revolu- 
 tion, which has changed the face of Che- 
 mistry, we cannot find any researches con- 
 cerning copper that are immediately con- 
 nected with the annals of this revolution, 
 or have served to lay the foundation of it, 
 yet this metal holds a rank among those 
 substances, of which the properties are 
 better known, and the modifications have 
 been more accurately determined since the 
 establishment of the pneumatic doctrine. 
 In this class of properties, accurately ex- 
 plained by the modern theory, we ought 
 particularly to place its different degrees 
 of oxidation, its solutions in acids and in 
 ammonia, its precipitates from the metallic 
 state to its highest degree of oxidation, 
 and its reduction by various processes. 
 The labours of Berthollet, Guyton, and 
 Proust, have particularly contributed to 
 the accurate knowledge of these last men- 
 tioned facts. Our knowledge of this 
 metal has also become much more com- 
 
 plete, and the facts concerning it by far 
 more simple, since the discoveries which 
 have been lately made in experimental 
 Chemistry. It holds almost the third 
 rank among metals in this respect. With 
 regard to its elasticity, it holds nearly the 
 same rank. Its ductility has led Guyton 
 to place it in the sixth rank of metals, be- 
 tween tin and lead. It may be reduced 
 into laminae, or leaves extremely thin, 
 which the wind will blow away. Its tena- 
 city likewise is pretty considerable : a 
 copper wire, one-tenth of an inch in dia- 
 meter, supports a weight of 299^ pounds, 
 without breaking. Its strength or re- 
 sistance to being broken is estimated by 
 Wallerius as nearly equal to that of iron. 
 Its sonorous quality is superior to that of 
 iron, as may be proved by wires of the 
 two metals of equal length and thickness. 
 
 This metal is of a fine red colour, and 
 has a great deal of brilliancy. Its taste is 
 styptic and nauseous; and the hands, 
 when rubbed for some time on it, acquires 
 a peculiar and disagreeable odour. 
 
 The density of copper is such, that its 
 specific gravity is to that of water as 
 7*788 to 1*000. This gravity, however, 
 varies according to the state of the metal : 
 when it has only been melted and cast, it 
 is less than when it has been hammered 
 and forged; but after having passed 
 through the mill, and been drawn into 
 wire, it has the specific gravity of 8'878, 
 which is an increase of about one- 
 seventh. 
 
 Its power of conducting caloric has not 
 been accurately ascertained, though it is 
 known to be very great. It does not 
 melt till it is very red. Its fusibility has 
 been estimated by Mortimer at 1450° of 
 Fahrenheit’s thermometer, and by Guyton 
 at 27° of the pyrometer of Wedgwood. 
 When it is melted and cast into ingot- 
 moulds, that it may cool quickly, it as- 
 sumes a granulous and porous texture, 
 which shows like a kind of crumb in its 
 fracture, and is liable to exhibit many ca- 
 vities and flaws in its interior parts. If it 
 be cooled slowly, it yields crystals in quad- 
 rangular pyramids, or in octahedrons, 
 which arise from the cube, its primitive 
 form. At a temperature above what is re- 
 quired for its fusion, it rises in vapour, and 
 in a visible smoke, as is observed in places 
 where this metal is cast in the large way, 
 and in the chimneys over the furnaces. 
 
 Copper is a very good conductor of elec- 
 tricity and galvanism ; but its order and 
 power in this respect, compared with that 
 of other metallic substances, has not yet 
 been determined with precision. The 
 acrid and somewhat fetid smell which 
 pretty sensibly characterises and distin- 
 guishes copper, is well known to every 
 one. Rubbing the hand a little time on it 
 
THE ARTISAN. 
 
 91 
 
 is sufficient to impart this coppery odour, 
 
 [ to which some other phenomena of the 
 organ of smell have even been compared, 
 particularly that of a cold in the head. 
 
 Copper is pretty abundantly diffused 
 throughout nature. Germany, Sweden, 
 
 | and Siberia, however, are the three coun- 
 ts tries, where it has hitherto been found in 
 the largest quantity, and which furnish 
 the most to commerce and the arts. The 
 1 states of this metal in the earth are so 
 various in their appearance, and in their 
 physical properties, that mineralogists 
 have singularly multiplied the species of 
 it : some have admitted fifteen or twenty, 
 though it is difficult to reckon nine or ten 
 really different from each other in their 
 nature. What they have taken for species 
 are only varieties. 
 
 Native copper is met with, pretty fre- 
 quently in the interior parts of the earth, 
 where it is even found very pure. It is 
 known by its brilliancy, its red colour, 
 its ductility, and its specific gravity. Most 
 commonly its surface is of an obscure dull 
 and brown red, on account of the slight 
 oxidation it has experienced. Sometimes 
 it is found shining, and as if it had been 
 burnished or polished ; but this is much 
 more rare than the preceding. Its form is 
 ! frequently crystalline and regular ; that of 
 Siberia distinctly exhibits the cubic figure. 
 
 The places where native copper is most 
 frequently observed, are Siberia, Norberg 
 in Sweden, Newsol in Hungary, and 
 Saint-Bel, near Lyons. 
 
 Copper exposed to cold air, and par- 
 ticularly to damp air, soon loses its lustre ; 
 it tarnishes, becomes of a dull brown, 
 grows gradually darker, acquires what is 
 called the colour of antique bronze, and 
 at last becomes covered with a sort of 
 green tint, tolerably bright, known to 
 every one by the name of verdigris , or 
 verdet gris , as the modern French Che- 
 mists will have it. 
 
 The atmospheric oxygen begins by con- 
 verting the surface of the metal into brown 
 oxide ; this oxidation is favoured and ac- 
 celerated by water. The carbonic acid 
 soon unites itself with the copper thus 
 oxidized ; so that the kind of varnish of 
 antique medals, statues, and utensils of 
 various kinds, which antiquaries prize in 
 them, and which they callpatine, is nothing 
 but a true super-oxygenated carbonate of 
 copper, very analogous to malachite or 
 mountain green. 
 
 This alteration of copper is much more 
 powerful and rapid, if the temperature of 
 the metal be increased. Every one may 
 have observed how quickly the copper 
 tunnels, used for carrying off the smoke of 
 stoves, change their colour from the mo- 
 ment they are first heated, even slightly, 
 in contact with the air: they speedily as- 
 
 sume a blueish, orange, yellowish, or 
 brown tinge, which at length becomes 
 wholly of an uniform deep brown over all 
 the surface. These different and very 
 beautiful hues are obtained even by cau- 
 tiously exposing on burning coals thin 
 plates or laminse of copper, as well as that 
 which is in light leaves. By this process, 
 leaves of a sort oifoil are made of various 
 colours, which are chiefly used, after being- 
 cut into small pieces, for covering chil- 
 dren’s toys, to which they are fastened by 
 a kind of mordant or cement, previously 
 applied on them. In fabricating these, 
 the succession of blue, yellow, violet, and 
 brown, may be observed ; the last colour 
 too is that which remains, and is perma- 
 nent. 
 
 When the action of fire on copper is 
 strongly urged ; when it is thrown, for 
 instance, in the form of fine filings, into a 
 very strong fire, or when it is heated in a 
 crucible to a white heat after having been 
 melted, it burns much more rapidly than 
 in the former cases ; it experiences a real 
 conflagration ; it even yields a very bril- 
 liant green flame. Accordingly, it is em- 
 ployed in the composition of the coloured 
 fires of the smaller kinds of fireworks, par- 
 ticularly those which are called table fire- 
 works. The same effect w\hich is per- 
 ceptible at the surface of the crucible in 
 which copper, thoroughly fused and very 
 red, if melted and stirred, is produced by 
 sending through this metal, in a small 
 piece, or in wire, or in thin leaves, an 
 electric discharge. It instantly emits a 
 greenish flame, breaks with decrepitation, 
 and is dispersed in smoke or dust in the 
 air. It may be collected on paper, and 
 will be found covered with a reddish 
 brown oxide. It is to this property like- 
 wise we are indebted for the green colour 
 which we so frequently see in the flame of 
 various combustible substances, but par- 
 ticularly alcohol, when cupreous salts 
 have been dissolved in it. Notwithstanding 
 the activity of this sort of combustion, and 
 its difference from the slow oxidation 
 already described, the oxide resulting 
 from it uniformly contains but twenty-five 
 parts of oxygen to a hundred of the metal, 
 and completely resembles that which is 
 obtained by the former kind of combus- 
 tion. 
 
 After the 20th of March the sun appears 
 to rise every day sensibly more to the 
 northward than he did the day before, to 
 be more elevated at mid-day, and to con- 
 tinue longer above the horizon, till the 
 21st of June, which is the longest day at 
 all places in the northern hemisphere. 
 
m 
 
 THE ARTISAN. 
 
 At this time the angle formed by the 
 northern half of the earth’s axis, and the 
 line joining the centre of the earth and 
 sun is then at the least, which is 69| 
 degrees. The sun will then appear to 
 touch the tropic of Cancer, and be vertical 
 to all places 23| degrees north of the equa- 
 tor. This time of the year is called the 
 summer solstice , because it is the middle 
 of summer, and the sun seems to remain 
 stationary for a few days. 
 
 After the 21st of June, the angle joining 
 the centres of the earth and sun gradually 
 increases, and the sun appears to recede 
 from the tropic of Cancer, in the same 
 manner as he advanced to it, rising every 
 day a little farther to the south than he 
 did the day before, till the 23d of Septem- 
 ber, when the axis has a similar position 
 to what it had on the 20th of March, being 
 again at right angles to the line just men- 
 tioned, consequently the days and nights 
 are again equal all over the globe, which 
 constitutes the autumnal equinox. 
 
 The sun now appears to cross the equi- 
 noctial; and the south pole, which, during 
 the last six months, was in the dark, 
 begins to turn towards the sun ; and pre- 
 cisely the same phenomena are exhibited 
 
 to the southern hemisphere, as those 
 already described in the case of the north- 
 ern half of the earth. On the 22d of 
 December the sun appears to touch the 
 tropic of Capricorn, and is vertical to all 
 those places on the earth that are 23§ 
 degrees south of the equator. The days 
 are then longest at all places in thd south- 
 ern hemisphere, but at the shortest in the 
 northern. This time of the year is termed 
 the winter solstice. 
 
 From the tropic of Capricorn the sun 
 appears to move forward, and to arrive at 
 the equinoctial on the 20th of March. 
 
 Thus by a combination of the annual 
 and diurnal motions of the earth, with the 
 parallelism of its axis, and the obliquity of 
 its orbit to the plane of its equator, the 
 various seasons are produced, and the 
 same quantity of light and darkness, in 
 the space of a year, are distributed to 
 every region of the globe. 
 
 The manner in which the sun enlightens 
 the earth, the parallelism of its axis, and 
 the increase and decrease of the days 
 and nights, may be well illustrated by a 
 small terrestrial globe, suspended by a 
 string fastened to its north pole, as repre- 
 sented by the following figure. 
 
 A circle of wire a b , representing the 
 plane of the earth’s equator, may be held 
 parallel to a table, and equal in height 
 with the flame of a candle standing upon 
 it. If the string be twisted a little towards 
 the left hand, and the globe suspended 
 within the circle, with its equator at the 
 same height, the globe will begin to turn 
 on its axis from west to east, and day and 
 night will be represented by the light and 
 shade produced by the candle on its sur- 
 face. But if the globe be carried round 
 
 the wire, to represent a year, the candle 
 will illuminate both poles, and every spot 
 on its surface will describe half a circle in 
 the enlightened part, and half in the dark 
 part, and make equality of day and night 
 through the year. This is, however, not 
 the case in nature, as has already been 
 fully explained. If then the wire be in- 
 clined to the table at an angle of 23| 
 degrees, as represented by the circle abed , 
 and the globe be carried gently round it, 
 the seasons, and increase of day and 
 
THE ARTISAN. 
 
 93 
 
 and night, will appear as they are in 
 nature ; i. e. when the globe is at a, the 
 candle enlightens it no farther northward 
 than the arctic circle no; all within 
 which, in the middle of our winter, is de- 
 prived of a sight of the sun ; while all 
 places within the antarctic, or opposite 
 circle, have perpetual day : at this time 
 the candle shines vertically on the tropic 
 of Capricorn. As the earth moves towards 
 b (the vernal equinox), if a small patch be 
 laid on latitude 5I|° north, it will show 
 how the days increase at London, and how 
 the nights decrease. When it has arrived 
 at b , the candle will then be perpendicu- 
 larly over the equator, and, shining to 
 both poles, equality of day and night will 
 take place': as it proceeds towards c (the 
 summer solstice), the days increase, and 
 the candle shines more and more over the 
 north pole : when it has arrived at c, the 
 whole arctic circle, and the countries it 
 includes, will revolve in continual sight of 
 the sun ; and all within the antarctic cir- 
 cle will be deprived of that sight. At 
 this time the candle shines vertically on 
 the tropic of Cancer. Moving from mid- 
 summer towards d (the autumnal equinox), 
 the days will be found to decrease, and 
 the nights to increase in length, till they 
 come again to equality at d , and thence to 
 the winter solstice, and so on. 
 
 The particular temperature which dis- 
 tinguishes each of the seasons, at any par- 
 ticular place, is owing to a difference in 
 the sun’s altitude, and the time of his con- 
 tinuance above the horizon of that place. 
 In winter, the rays of the sun fall so ob- 
 liquely, and the sun is such a short time 
 above the horizon, that his influence in 
 heating the earth is but very little, com- 
 pared with what it is in summer. For at 
 this season, the sun is so much higher than 
 in winter, that his rays not only fall more 
 perpendicularly, but more of them fall on 
 any given space; and as the day is also much 
 longer than the night, the temperature of 
 the earth and the surrounding atmosphere 
 must be much greater than in winter. 
 
 Since the power of the sun is greater in 
 heating the earth at any particular place, 
 when his rays fall most directly, and when 
 the days are longest at that place, it may 
 be asked, how does it happen that the 
 heat is greatest about the end of July, 
 when the sun is highest and the day 
 longest about the 21st of June ? The rea- 
 son of this may easily be discovered, by 
 attending a little to the manner in which 
 bodies are heated. The heat which the 
 earth receives is not transient, but is re- 
 tained by it for some time. For, like other 
 solid bodies, it receives heat and parts 
 with it gradually. Now as the earth con - 
 tinues to receive more heat in the day than 
 it gives out in the night, for a considerable 
 
 time after the 21st of June, its tempera- 
 ture will continue to increase, till the days 
 and nights begin to approach to an equa- 
 lity. But this is not the case till the end of 
 July, at least; the earth goes on increas- 
 ing in temperature, till about this time, 
 when it is found to be much greater than 
 about the 21st of June, although the sun 
 be then higher at mid-day, and the day 
 longer than at any other time of the year 
 in the northern hemisphere.* The heat in 
 July would be still greater were the sun 
 at his mean distance from the earth ; but 
 this is not the case, for he is then at his 
 greatest distance. However, the difference 
 between his distance at this time and the 
 mean distance being only ^th part of the 
 whole, it could not make a great altera- 
 tion in the heating power of the rays. 
 But if it does operate in any degree in 
 diminishing the heat in the northern hemis- 
 phere in July, the same cause must ope- 
 rate in increasing the heat, but in a double 
 degree, in the southern hemisphere in 
 January. For the sun is s \th part nearer 
 the earth than his mean distance on the 
 1st of January. Consequently the heat 
 must be greater in the southern hemis- 
 phere in January than in the northern in 
 July, all other circumstances being the 
 same. The effect of the direct influence 
 of the sun are, however, greatly modified 
 by the transportation of the temperature 
 of one region into another, in consequence 
 of that disturbance in the equilibrium of 
 the atmosphere, which the action of the 
 sun’s rays necessarily produce. 
 
 Thus we see by what simple means the 
 whole variety of the seasons are produced ; 
 and also how admirably fitted the means 
 are to accomplish the end. 
 
 fferellancous snorts. 
 
 MEMOIR OF THE LIFE OF JOHN 
 SMEATON. 
 
 John Smeaton was born the 28th of May, 
 1724, O. S. at Austhorpe, near Leeds, in a 
 house built by his grandfather, and where 
 his family have resided ever since. The 
 strength of his understanding, and the 
 originality of his genius, appeared at an 
 early age ; his playthings were not the 
 playthings of children, but the tools which 
 men employ ; and he appeared to have 
 greater entertainment in seeing the men in 
 the neighbourhood work, and asking them 
 questions, than in any thing else. One 
 day he was seen, to the distress of his fa- 
 mily, on the top of his father’s barn, fixing 
 
 * The same phenomena take place in the southern 
 hemisphere in a reverse order, or at six months* 
 difference of time. 
 
94 
 
 THE ARTISAN. 
 
 up something like a windmill. Another 
 time he attended some men fixing a pump 
 at a neighbouring -village ; and observing 
 them cut oft’ a piece of bored pipe, he was 
 so lucky as to procure it, and he actually 
 made with it a working pump that raised 
 water. These anecdotes refer to circum- 
 stances that are said to have happened 
 while he was in petticoats, and most likely 
 before he attained his sixth year. 
 
 About his fourteenth and fifteenth year 
 he had made for himself an engine for 
 turning, and wrought several presents to 
 his friends of boxes in ivory or wood, very 
 neatly turned. He forged his iron and 
 steel, and melted his metal ; he had tools 
 of every sort for working in wood, ivory, 
 and metals. He had made a lathe, by 
 which he had cut a perpetual screw in 
 brass ; a thing little known at that day, 
 which was the invention of Mr. Henry 
 Hindley,of York, with whom Mr. Smeaton 
 soon became acquainted, and they spent 
 many a night at Mr. Hindley’s house till 
 day -light, conversing on those subjects. 
 Thus had Mr. Smeaton, by the strength of 
 his genius and indefatigable industry, ac- 
 quired, at the age of 18, an extensive set 
 of tools, and the art of working in most of 
 the mechanical trades, without the assist- 
 ance of any master. A part of every day 
 was generally occupied in forming some 
 ingenious piece of mechanism. 
 
 Mr. Smeaton’s father was an attorney, 
 and desirous of bringing him up to the 
 same profession. Mr. Smeaton therefore 
 came up to London in 1T42, and attended 
 the courts in Westminster Hall ; but find- 
 ing, as his common expression was, that 
 the law did not suit the bent of his genius, 
 he wrote a strong memorial to his father 
 on that subject; whose good sense from 
 that moment left Mr. Smeaton to pursue 
 the dictates of his genius in his own way. 
 
 In 1751 he began a course of experi- 
 ments, to try a machine of his invention to 
 measure a ship’s way at sea, and also made 
 two voyages, in company with Dr. Knight, 
 to try it, and a compass of his own inven- 
 tion and making, which was made magne- 
 tical by Dr. Knight’s artificial magnets. 
 The second voyage was made in the For- 
 tune sloop of war, commanded at that time 
 by Captain Alexander Campbell. 
 
 In 1753 he was elected member of the 
 Royal Society ; the number of papers 
 published in their Transactions will show 
 the universality of his genius and know- 
 ledge. 
 
 In 1759 he was honoured by an unani- 
 mous vote with their gold medal, for his 
 paper intitled, u An Experimental Inquiry 
 concerning the Natural Powers of Water 
 and Wind to turn Mills, and other Ma- 
 chines, depending on a circular Motion.” 
 This paper, he says, was the result of ex- 
 
 periments made on working models in the 
 year 1752 and 1753, but not communicated 
 to the Society till 1759 ; before which time 
 he had an opportunity of putting the effect 
 of these experiments into real practice, in 
 a variety of cases, and for various pur- 
 poses, so as to assure the Society he had 
 found them to answer. 
 
 In December, 1755, the Eddystone Light- 
 house was burnt down. Mr. Weston, the 
 chief proprietor, and the others, being de- 
 sirous of rebuilding it in the most substan- 
 tial manner, inquired of the Earl of Mac- 
 clesfield, then President of the Royal So- 
 ciety, whom he thought the most proper to 
 rebuild it ; his Lordship recommended Mr. 
 Smeaton. Mr. Smeaton undertook the 
 
 work, and completed it in the’ summer of 
 1759. Of this Mr. Smeaton gives an am- 
 ple description in the volume he published 
 in 1791. 
 
 Though Mr. Smeaton completed the 
 building of the Eddystone Lighthouse in 
 1759, a work that does him so much cre- 
 dit, yet it appears he did not soon get into 
 full business as a civil engineer; for in 
 1764, while in Yorkshire, he offered him- 
 self a candidate for one of the receivers of 
 the Derwentwater estate ; and on the 31st 
 of December in that year, he was ap- 
 pointed, at a full board of Greenwich Hos- 
 pital, in a manner highly flattering to him- 
 self, when two other persons strongly re- 
 commended and powerfully supported 
 were candidates for the employment. In 
 this appointment he was very happy, by 
 the assistance and abilities of his partner, 
 Mr. Walton, one of the receivers ; who, 
 taking upon himself the management and 
 accounts, left Mr. Smeaton leisure and op- 
 portunity to exert his abilities on public 
 works, as well as to make any improve- 
 ments in the mills and in the estates of 
 Greenwich Hospital. By the year 1775, 
 he had so much business as a civil engi- 
 neer, that he wished to resign this appoint- 
 ment, and would have done it then, had not 
 his friends, the late Mr. Stuart, the hos- 
 pital surveyor, and Mr. Ibbetson, their se- 
 cretary, prevailed upon him to continue in 
 the office about two years longer. 
 
 Mr. Smeaton having now got into full 
 business as a civil engineer, performed 
 many works of general utility. Fie made 
 the river Calder navigable ; a work that 
 required great skill and judgment, owing 
 to the very impetuous floods in that river. 
 He planned and attended the execution of 
 the great canal in Scotland, for conveying 
 the trade of the country either to the At- 
 lantic or German Ocean ; and having 
 brought it to the place originally intended, 
 he declined a handsome yearly salary, in 
 order that he might attend to the multipli- 
 city of his other business. 
 
 On the opening of the great arch at Lon- 
 
THE ARTISAN. 
 
 95 
 
 don bridge, the excavation around and un- 
 der the starlings was so considerable, that 
 the bridge was thought to be in great dan- 
 ger of falling. He was then in Yorkshire, 
 and was sent for by express, and arrived 
 with the utmost dispatch. “ I think,” 
 says Mr. Holmes, the author of his Life, 
 “ it was on a Saturday morning, when the 
 apprehension of the bridge was so general, 
 that few would pass over or under it. He 
 applied himself immediately to examine it, 
 and to sound about the starlings as mi- 
 nutely as he could ; and the committee 
 being called together, adopted his advice, 
 which was to re-purchase the stones that 
 had been taken from the middle pier, then 
 lying in Moorfields, and to throw them 
 into the river to guard the starlings” — 
 Nothing shows the apprehensions concern- 
 ing the falling of the bridge more than the 
 alacrity with which this advice was pur- 
 sued; the stones were re-purchased that 
 day, horses, carts, and barges, were got 
 ready, and they began the work on Sunday 
 morning. Thus Mr. Smeaton, in all human 
 probability, saved London bridge from 
 falling, and secured it till more effectual 
 methods could be taken. 
 
 The vast variety of mills which Mr. 
 Smeaton constructed, so greatly to the sa- 
 tisfaction and advantage of the owners, 
 will show the great use which he made of 
 his experiments in 1752 and 1753 ; for he 
 never trusted to theory in any case where 
 he could have an opportunity to investigate 
 it by experiment. He built a steam-engine 
 at Austhorpe, and made experiments there- 
 on, purposely to ascertain the power of 
 Newcomen’s steam-engine, which he im- 
 proved, and brought to a far greater de- 
 gree of perfection, both in its construction 
 and powers, than it was before. 
 
 Mr. Smeaton, during many years of his 
 life, was a frequent attendant on parlia- 
 ment, his opinion being continually called 
 for. And here his strength of judgment 
 and perspicuity of expression had its full 
 display. It was his constant custom, 
 when applied to plan or support any 
 measure, to make himself fully acquainted 
 with it, to see its merits, before he would 
 engage in it. By this caution, added to 
 the clearness of his description and the 
 integrity of his heart, he seldom failed to 
 obtain for the bill which he supported an 
 act of parliament. No one was heard 
 with more attention, nor had any one ever 
 more confidence placed in his testimony. 
 In the courts of law he had several com- 
 pliments paid him from the bench by Lord 
 Mansfield and others, for the new light 
 which he threw on difficult subjects. 
 
 About the year 1785, Mr. Smeaton’s 
 health began to decline; and he then took 
 the resolution to endeavour to avoid all the 
 business he could, so that he might have 
 
 leisure to publish an account of his inven- 
 tions and works, which was certainly the 
 first wish of his heart ; for lie has often 
 been heard to say, that u he thought he 
 could not render so much service to his 
 country as by doing that.” He got only 
 his account of the Eddystone Lighthouse 
 completed, and some preparations to his 
 intended Treatise on Mills ; for he could 
 not resist the solicitations of his friends in 
 various Avorks ; and Mr. Aubert, whom 
 he greatly loved and respected, being 
 chosen chairman of Ramsgate harbour, 
 prevailed upon him to accept the place of 
 engineer to that harbour ; and to their 
 joint efforts the public is chiefly indebted 
 for the improvements that have been made 
 there within the last 30 years ; which fully 
 appears in a report that Mr. Smeaton gave 
 in to the Board of Trustees in 1791, which 
 they immediately published. 
 
 Mr. Smeaton being at Austhorpe, walk 
 ing in his garden, on the 16th of Septem- 
 ber, 1792, was struck with the palsy, and 
 died the 28th of October. u In his illness,” 
 says Mr. Holmes, “ I had several letters 
 from him, signed with his name, but writ- 
 ten and signed by another’s pen ; the dic- 
 tion of them shewed that the strength of 
 his mind had not left him. In one written 
 the 26th of September, after minutely des- 
 cribing his health and feelings, he says, 
 * In consequence of the foregoing, I con- 
 clude myself nine-tenths dead ; and the 
 greatest favour the Almighty can do me, 
 as I think, will be to complete the other 
 part; but as it is likely to be a lingering 
 illness, it is only in his power to say when 
 that is likely to happen/ ” 
 
 Mr. Smeaton had a warmth of expression 
 that might appear to those who did not 
 know him well to border on harshness ; 
 but those more intimately acquainted with 
 him knew that it arose from the intense 
 application of his mind, which was always 
 in the pursuit of truth, or engaged in inves- 
 tigating difficult subjects. He would some- 
 times break out hastily, when any thing 
 was said that did not tally with his ideas ; 
 and he would not give up any thing he ar- 
 gued for, till his mind was convinced by 
 sound reasoning. In all the social duties 
 of life he was exemplary; he was a most 
 affectionate husband, a good father, a 
 warm, zealous, and sincere friend, always 
 ready to assist those he respected, and 
 often before it was pointed out to him in 
 what way he could serve them. He was 
 a lover and encourager of merit wherever 
 he found it ; and many men are, in a great 
 measure, indebted to his assistance and 
 advice for their present situations. As a 
 companion, he was always entertaining and 
 instructive; and none could spend any 
 time in his presence without improvement. 
 
 As a civil engineer, he was perhaps un- 
 
THE ARTISAN. 
 
 SMS 
 
 rivalled, certainly not excelled by any one, 
 either of the present or former times. His 
 building the Eddystone Lighthouse, were 
 there no other monument of his fame, would 
 establish his character. The Eddystone 
 rocks have obtained their name from the 
 great variety of contrary sets of the tide 
 or current in their vicinity. They are si- 
 tuated nearly S.S.W. from the middle of 
 Plymouth Sound ; their distance from the 
 port of Plymouth is about 14 miles. They 
 are almost in the line which joins the Start 
 and the Lizard Points ; and as they lie 
 nearly in the direction of vessels coasting 
 up and down the Channel, they were un- 
 avoidably, before the establishment of a 
 Lighthouse there, very dangerous, and 
 often fatal to ships. Their situation with 
 regard to the Bay of Biscay and the At- 
 lantic is such, that they lie open to the 
 swells of the bay and ocean, from all the 
 south-western points of the compass ; so 
 that all the heavy seas from the south-west 
 quarter come uncontrolled upon the Eddy- 
 stone rocks, and break upon them with the 
 utmost fury. Sometimes, when the sea 
 is to all appearance smooth and even, and 
 its surface unruffled by the slightest 
 breeze, the ground swell, meeting the slope 
 of the rocks, the sea beats upon them in a 
 frightful manner, so as not only to obstruct 
 any work being done on the rock, or even 
 landing upon it, when, figuratively speak- 
 ing, you might go to sea in a walnut-shell. 
 That circumstances fraught with danger 
 surrounding it should excite mariners to 
 wish for a Lighthouse, is not wonderful ; 
 but the danger attending the erection leads 
 us to wonder that any one could be found 
 hardy enough to undertake it. Such a 
 man was first found in the person of Mr. 
 H. Winstanley, who, in the year 1696, was 
 furnished by the Trinity House with the 
 necessary powers. In 1700 it was finished ; 
 but in the great storm of November, 1703, 
 it was destroyed, and the projector pe- 
 rished in the ruins. In 1709, another, 
 upon a different construction, was erected 
 by a Mr. Rudyerd, which, in 1755, was 
 unfortunately consumed by fire. The next 
 building was, as we have seen, under the 
 direction of Mr. Smeaton ; who, having 
 considered the errors of the former con- 
 structions, has judiciously guarded against 
 them, and erected a building, the demoli- 
 tion of which seems little to be dreaded, 
 unless the rock on which it is erected 
 should perish with it. Of his works, in 
 constructing bridges, harbours, mills, en- 
 gines, &c. &c. it were endless to speak. 
 Of his inventions and improvements of 
 philosophical instruments, as the air- 
 pump, the pyrometer, hygrometer, &c. &c. 
 some idea may be formed from the list of 
 tils writings. See Hutton’s Diet. 
 
 SOLUTIONS OF QUESTIONS. 
 
 Quest, 62, answered by J. D. (the Pro- 
 poser ). 
 
 Here 10 acres would have fed 15 oxen 
 for 10 weeks, or 30 acres 18 oxen for 25 
 weeks, if the grass had not grown after 
 the first 5 weeks ; for 
 
 A. A. Ox. 
 
 3 : 
 
 W. 
 10 
 A. 
 3 : 
 W. 
 25 
 
 10 : 
 W. 
 
 : 5 
 A. 
 30 : 
 W. 
 5 
 
 : 9 ? 10 X 9 X 5 
 j 10 X 3 
 Ox. 
 
 : 9 >30 x 9 x 5 
 
 5 
 
 3 X 25 
 
 15 oxen. 
 
 ~ 18 oxen. 
 
 But, as 10 acres fed 20 oxen for 10 weeks, 
 20 — 15 ~ 5 oxen must have been fed for 
 10 weeks, by the grass which grew on 
 these 10 acres during the second 5 weeks. 
 Now, at the same rate of growth, 24 oxen 
 may be fed for 25 weeks, by the grass 
 which will grow on 30 acres during the 
 20 weeks, which remain after the first 5 
 weeks; for 
 
 W. W. Ox. 
 
 25 : 10 : : 5") 
 
 I’ 2o' 1*0 X20X30X5 
 
 A. A f 10X5X25 
 
 10 : 30 J 
 
 ~ 24 oxen. 
 
 Thus, the grass which 
 grows during the last 
 20 weeks, will feed - 24 oxen, 
 and that which was on 
 the field at the beginning 
 of the 25 weeks, to- 
 gether with its growth 
 during the first five 
 weeks, will feed - - 18 oxen. 
 
 Sum 42 oxen, Ans. 
 We received several solutions of this 
 intricate question ; but none of them was 
 correct, except Mr. Harding’s. Ed. 
 
 QUESTION FOR SOLUTION. 
 
 Quest. 65, proposed by Master Thomas 
 Morris, Liverpool. 
 
 , A reservoir for water has two cocks to 
 supply* it : by the first alone it may be 
 filled in 40 minutes, by the second in 50 
 minutes : and it has also two discharging 
 cocks ; the first will empty three such re- 
 servoirs in 100 minutes, and the latter two 
 such in 180 minutes. Now supposing 
 these four cocks are all left open, and the 
 water comes in, in what time will the cis- 
 tern be filled, supposing the influx and 
 efflux of the water to be always the same? 
 
 We insert the above question, as we are 
 assured the Proposer is only 10 years of 
 age. We are sorry that his solution of the 
 61st question came too late for insertion. 
 
THE ARTISAN. 
 
 97 
 
 CTOMETEY. 
 
 PROPOSITION XXXI. 
 
 Theorem. — In a circle, the angle in asemi- 
 cirle is a right angle; but the angle in a 
 segment greater than a semicircle is less 
 than a right angle : and the angle in a 
 segment less than a semicircle is greater 
 than a right angle. 
 
 Let ABC9 be a circle, of which the 
 diameter is BC, and centre E; and draw 
 CA, dividing the circle into the segments 
 ABC, ADC, and join BA, AD, DC; 
 the angle in the semicircle B A C is a right 
 angle; and the angle in the segment 
 ABC, which is greater than a semicircle, 
 is less than a right angle ; and the angle 
 in the segment ADC, which is less than a 
 semicircle, is greater than a right angle. 
 
 Join A E, and produce BA to F; and 
 because BE is equal to EA, the angle 
 E A B is equal to E B A ; also, because 
 A E is equal to E C, the angle E A C is 
 
 IT 
 
 equal to EGA; wherefore the whole 
 angle BAC is equal to the two angles 
 ABC, ACB: But FAC, the exterior 
 
 angle of the triangle A B C, is equal to the 
 two angles ABC, ACB; therefore the 
 angle BA C is equal to the angle FAC, 
 and each of them is therefore a right angle : 
 Wherefore the angle B A C in a semicircle 
 is a right angle. 
 
 And because the two angles ABC, 
 BAC of the triangle ABC are together 
 less than two right angles, and that BAC 
 is a right angle, ABC must be less than a 
 right angle; and therefore the angle in a 
 segment ABC greater than a semicircle, 
 is less than a right angle. 
 
 And because A B C D is a quadrilateral 
 figure in a circle, any two of its opposite 
 angles are equal to two right angles; 
 therefore the angles ABC, ADC are 
 equal to two right angles ; and A B C is 
 less than a right angle; wherefore the 
 other A D C is greater than a right angle. 
 
 Vol. II, — No. 32. 
 
 Besides, it is manifest, that the circum- 
 ference of the greater segment ABC falls 
 without the right angle CAB; but the 
 circumference of the less segment ADC 
 falls within the right angle C A F. And 
 this is all that is meant, when in the Greek 
 text, and the translations from it, the angle 
 of the greater segment is said to be 
 greater, and the angle of the less segment 
 is said to be less, than a right angle. 
 
 Cor. From this it is manifest, that if one 
 angle of a triangle be equal to the other 
 two, it is a right angle, because the angle 
 adjacent to it is equal to the same two ; 
 and when the adjacent angles are equal, 
 they are right angles. 
 
 PROPOSITION XXXII. 
 
 Theorem.— If a straight line touches a cir- 
 cle , and from the point of contact a 
 straight line be drawn cutting the circle , 
 the angles made by this line with the 
 line touching the circle , shall be equal to 
 the angles which are in the alternate seg- 
 ments of the circle. 
 
 Let the straight line E F touch the cir- 
 cle A BCD in B, and from the point B 
 let the straight line B D be drawn, cutting 
 the circle : The angles which B D makes 
 with the touching line E F, shall be equal 
 to the angles in the alternate segments of 
 the circle : that is, the angle F B D is equal 
 to the angle which is in the segment DAB, 
 and the angle DBE to the angle in the 
 segment BCD. 
 
 From the point B draw B A at right 
 angles to E F, and take any point C in the 
 circumference B D, and join A D, D C, 
 C B ; and because the straight line E F 
 touches the circle ABC D in the point B, 
 and B A is drawn at right angles to the 
 
 touching line from the point of contact B, 
 the centre of the circle is in B A; there- 
 fore the angle A D B in a semicircle is a 
 right angle, and consequently the other 
 two angles B A D, A B D are equal to a 
 right angle : But A B F is likewise a right 
 angle ; therefore the angle A B F is equal 
 to the angles BAD, A B D : Take from 
 
98 
 
 THE ARTISAN. 
 
 these equals the common angle ABD; 
 therefore the remaining angle D B F is 
 equal to the angle BAD, which is in the 
 alternate segment of the circle ; and be- 
 cause A B C D is a quadrilateral figure in 
 a circle, the opposite angles BAD, BCD 
 are equal to two right angles ; therefore 
 the angles DBF, D B E, being likewise 
 equal to right angles, are equal to the 
 angles B A D, B C D ; and D B F has been 
 proved equal to B A 1) : Therefore the re- 
 maining angle D B E is equal to the angle 
 B C D in the alternate segment of the cir- 
 cle. Wherefore, if a straight line, &c. 
 Q. E. D. 
 
 PROPOSITION XXXIII. 
 
 Problem.— Upon a given straight line to 
 describe a segment of a circle , containing 
 an angle equal to a given rectilineal 
 angle. , 
 
 Let A B be the given straight line, and 
 the angle at C the given rectilineal angle ; 
 it is required to describe upon the given 
 straight line A B a segment of a circle, 
 containing an angle equal to the angle C. 
 
 First, let the angle at C be a right angle, 
 and bisect A B in F, and from the centre 
 F, at the distance F B, describe the semi- 
 circle A H B ; therefore the angle A H B 
 in a semicircle is equal to the right angle 
 at C. 
 
 But, if the angle C be not a right angle, 
 at the point A, in the straight line AB, 
 make the angle BAD equal to the angle 
 C, and from the point A draw A E at 
 
 right angles to A D ; bisect AB in F, and 
 from F draw F G at right angles to A B, 
 and join G B : And because A F is equal 
 to F B, and F G common to the triangles 
 AFG,BFG, the two sides A F, F G are 
 equal to the two B F, F G ; and the angle 
 
 A F G is equal to the angle B F G ; there- 
 fore the base A G is equal to the base GB: 
 and the circle described from the centre G, 
 at the distance G A, shall pass through the 
 point B; let this be the circle AHB : 
 And because from the point A the extre- 
 mity of the diameter A E, A D is drawn at 
 right angles to AE, therefore A D touches 
 the circle; and because A B drawn from 
 the point of contact A cuts the circle, the 
 
 
 angle D A B is equal to the angle in the 
 alternate segment AHB: But the angle 
 D A B is equal to the angle C, therefore 
 also the angle C is equal to the angle in 
 the segment AHB: Wherefore, upon the 
 given straight line A B the segment AHB 
 of a circle is described, which contains an 
 angle equal to the given angle at C. Which 
 was to be done. 
 
 PROPOSITION XXXIV. 
 
 Problem.— T o cut off a segment from a 
 given circle , ivhich shall contain an angle 
 equal to a given rectilineal angle. 
 
 Let A B C be the given circle, and D the 
 given rectilineal angle ; it is required to 
 cut off a segment from the circle ABC, 
 that shall contain an angle equal to the 
 given angle D. 
 
 Draw the straight line E F touching 
 the circle A B C in the point B, and at the 
 
THE A SiTIS AN. 
 
 90 
 
 angle F B C equal to the angle D : There- 
 fore, because the straight line E F touches 
 the circle ABC, and B C is drawn from 
 the point of contact B, the angle F B C is 
 equal to the angle in the alternate segment 
 B A C of the circle : But the angle FBC 
 is equal to the angle D; therefore the 
 angle in the segment B A C is equal to the 
 angle D : Wherefore the segment B A C is 
 cut off from the given circle ABC, con- 
 taining an angle equal to the given angle 
 D. Which was to be done. 
 
 PROPOSITION XXXV. 
 Theorem. — If two straight lines within a 
 circle cut one another , the rectangle con . 
 tabled by the segments of one of them , is 
 equal to the rectangle contained by the 
 segments of the other. 
 
 Let the two straight lines A C, B D, 
 within the circle A B C D, cut one another 
 in the point E : the rectangle contained by 
 A E, E C is equal to the rectangle con- 
 tained by BE, E D 
 
 If A C, B D pass each of them through 
 the centre, so that E is the centre ; it is 
 evident, that A E, E C, B E, ED, being 
 all equal, the rectangle AE, EC, is like- 
 wise equal to the rectangle B E, E D. 
 
 But let one of them B D pass through 
 the centre, and cut the other A C which 
 does not pass through the centre, at right 
 angles, in the point E : Then, if B D be 
 
 
 bisected in F, F is the centre of the circle 
 ABCD; join A F: And because BD, 
 which passes through the centre, cuts the 
 straight line A C, which does not pass 
 through the centre, at right angles in E, 
 A E, E C are equal to one another : And 
 because the straight line B D is cut into 
 two equal parts in the point F, and into 
 two unequal in the point E, the rectangle 
 B E, E U, together with the square of 
 E F, is equal to the square of F B : that is, 
 to the square of F A ; but the squares of 
 AE, EFare equal to the square of FA; 
 therefore the rectangle BE, ED, together 
 with the square of E F, is equal to the 
 squares of A E, E F : Take away the com- 
 mon square of EF, and the remaining 
 rectangle B E, E D is equal to the remain- 
 ing square of A E ; that is, to the rectangle 
 AE, EC. 
 
 Next, let B D, which passes through the 
 centre, cut the other A C, which does not 
 pass through the centre, in E, but not at 
 right angles : Then, as before, if B D be 
 bisected in F, F is the centre of the circle. 
 Join A F, and from F draw F G perpen- 
 dicular to A C ; therefore A G is equal to 
 G C ; wherefore the rectangle A E, E C, 
 together with the square of E G, is equal 
 to the square of A G : To each of these 
 equals add the square of GF : therefore 
 
 the rectangle A E, E C, together with the 
 squares of E G, G F, is equal to the squares 
 of A G, G F : But the squares of E G, G F 
 are equal to the square of EF; and the 
 squares of AG, GF are equal to the 
 square of A F : Therefore the rectangle 
 A E, E C, together with the square of E F, 
 is equal to the square of A F ; that is, to 
 the square of F B : But the square of F B 
 is equal to the rectangle B E, ED, together 
 with the square of E F ; therefore the 
 rectangle A E, EC, together with the 
 square of EF, is equal to the rectangle 
 BE, ED, together with the square of 
 EF. Take away the common square of 
 EF, and the remaining rectangle AE, 
 EC, is therefore equal to the remaining 
 rectaugle BE, ED. 
 
 Lastly, let neither of the straight lines 
 G2 
 
100 
 
 THE ARTISAN. 
 
 AC, BD pass through the centre : Take 
 
 the diameter G E F H : And because the 
 rectangle AE, EC is equal, as has been 
 shewn, to the rectangle GE, EH; and, 
 for the same reason, the rectangle BE, 
 ED is equal to the same rectangle GE, 
 E H ; therefore the rectangle A E, E C is 
 equal to the rectangle BE, ED. Where- 
 fore, if two straight lines, &c. Q. E. D. 
 
 PROPOSITION XXXVI. 
 Theorem. — If from any point without a 
 circle two straight lines he drawn , one of 
 which cuts the circle , and the other 
 touches it ; the rectangle contained hy the 
 whole line which cuts the circle , and the 
 part of it without the circle , shall be equal 
 to the square of the line which touches it. 
 Let D be any point without the circle 
 ABC, and D C A, D B two straight lines 
 drawn from it, of which D C A cuts the 
 circle, and DB touches the same: The 
 rectangle A D, D C is equal to the square 
 of DB. 
 
 Either D C A passes through the centre, 
 
 3 * 
 
 or it does not : first, let it pass through the 
 centre E, and join E B ; therefore the 
 angle E B D is a right angle : And because 
 the straight line A C is bisected in E, and 
 produced to the point D, the rectangle 
 A D, D C, together with the square of E C, 
 is equal to the square of E D, and C E is 
 equal to EB. Therefore the rectangle 
 AD, DC, together with the square of 
 E B, is equal to the square of E D : But 
 the square of ED is equal to the squares 
 of EB, B D, because EBD is a right 
 angle : Therefore the rectangle A D, 
 
 D C, together with the square of E B, 
 is equal to the squares of E B, B D : Take 
 away the common square of E B ; there- 
 fore the remaining rectangle A D, D C is 
 equal to the square of the tangent D B. 
 
 But if D C A does not pass through the 
 centre of the circle ABC, take the centre 
 E, and draw EF perpendicular to AC, 
 and join EB, E C, E D : And because the 
 straight line EF, which passes through 
 the centre, cuts the straight line A C, 
 which does not pass through the centre, 
 
 D 
 
 cause the straight line A C is bisected in 
 F, and produced to D, the rectangle 
 AD, DC, together with the square of FC, 
 is equal to the square of F D : To each of 
 these equals add the square of F E ; there- 
 fore the rectangle A D, D C, together with 
 the squares of C F, F E, is equal to the 
 squares of D F, F E : But the square of 
 ED is equal to the squares of DF, FE, 
 because E F D is a right angle : and the 
 square of E C is equal to the squares of 
 C F, FE; therefore the rectangle AD, 
 D C, together with the square of E C, is 
 equal to the square of E D : And C E is 
 equal to E B ; therefore the rectangle AD, 
 D C, together with the square of E B, is 
 
tHE ARTISAN. 
 
 101 
 
 equal to the square of E D : But the 
 squares of E B, B D are equal to the square 
 of ED, because EBD is a right angle; 
 therefore the rectangle AD, DC, together 
 with the square of EB, is equal to the 
 squares of E B, B D : Take away the com- 
 mon square of E B ; therefore the remain- 
 ing rectangle, A D, D C is equal to the 
 square of DB. Wherefore, if from any 
 point, &c. Q. E. D. 
 
 Cor. If from any point without a circle, 
 there be drawn two straight lines cutting 
 it, as A B, A C, the rectangle^ contained 
 by the whole lines and the parts of them 
 
 A 
 
 without the circle, are equal to one another; 
 viz. the rectangle B A, A E to the rect- 
 angle C A, A F : For each of them is equal 
 to the square of the straight line AD 
 which touches the circle. 
 
 PROPOSITION XXXVII. 
 
 Theorem.— If from a point without a cir- 
 cle there be drawn two straight lines , one 
 of which cuts the circle, and the other 
 meets it; if the rectangle contained by 
 the whole line which cuts the circle, and 
 the part of it without the circle be equal to 
 the square of the line which meets it, 
 the line which meets shall touch the 
 circle. 
 
 Let any point D be taken without the 
 circle ABC, and from it let two straight 
 lines D C A and D B be drawn, of which 
 DCA cuts the circle, and D B meets it ; if 
 the rectangle AD, D C be equal to the 
 square of D B ; DB touches the circle. 
 
 Draw the straight line D E, touching 
 the circle ABC, find its centre F, and 
 join F E, F B, F D ; then F E D is a right 
 angle : And because D E touches the circle 
 A B C, and DCA cuts it, the rectangle 
 A D, D C is equal to the square of DE: 
 But the rectangle A D, DC is, by hypo- 
 
 thesis, equal to the square of D B : There- 
 fore the square of DE is equal to the 
 square of D B ; aud the straight line D E 
 equal to the straight line D B, And F E 
 is equal to F B, wherefore D E, E F are 
 equal to D B, B F ; and the base F D is 
 common to the 
 
 I> 
 
 two triangles D EF, DBF; therefore the 
 angle D E F is equal to the angle DBF; 
 but D E F is a right angle, therefore also 
 D B F is a right angle : And FB, if pro- 
 duced, is a diameter, and the straight line 
 which is drawn at right angles to a diame- 
 ter, from the extremity of it, touches the 
 circle : Therefore D B touches the circle 
 ABC. Wherefore, if from a point, &c. 
 Q. E, D. 
 
 MECHJLlflCS* 
 
 OF MILLS. 
 
 Machines, by which the larger masses 
 of matter are crushed, broken, or ground, 
 are generally comprehended under the 
 name of mills. After the pestle and mor- 
 tar, the simplest machine of this kind 
 appears to be the stamping mill ; the 
 stampers resemble the hammers of the 
 mill employed in the extraction of oils 
 from seeds, and the machine is used for 
 reducing to powder the ores of metals, and 
 sometimes also barks and linseed ; the sur- 
 face of the stampers being armed with 
 iron or steel. But barks and seeds are 
 more usually ground by the repeated pres- 
 sure of two wheels of stone, rolling on an 
 axis, which is forced in a horizontal direc- 
 tion round a fixed point. 
 
 The materials for making gunpowder, 
 are also ground by a wheel revolving in a 
 
102 
 
 THE ARTISAN 
 
 trough : in order to corn them, they are 
 moistened, and put into boxes with a num- 
 ber of holes in their bottoms, and these 
 boxes being placed side by side, in a cir- 
 cular frame, suspended by cords, the frame 
 js agitated by a crank revolving horizon- 
 tally, and the paste shaken through the 
 holes : the corns are polished, by causing 
 them to revolve rapidly within a barrel. 
 
 The rollers by which sugar canes are 
 pressed, are in general situated vertically, 
 the middle one of these being turned by 
 horses, by mules, or by water, and the 
 canes being made to turn round it, so as to 
 pass through both interstices in succes- 
 
 sion. It appears to be of some advantage 
 in presses of this kind, that all the rollers 
 should be turned, independently of their 
 action, on the materials interposed, since 
 the friction of two rollers may tend to draw 
 the materials into the space between them, 
 with more regularity and greater force, 
 than the action of a single roller would do. 
 For this reason, it may be advisable to 
 retain the toothed wheels turning the 
 rollers, even when their axis are not firmly 
 fixed, but held together by an elastic 
 hoop. 
 
 In the following figure the axis A is 
 turned either by animal force or by water. 
 
 The liquor is collected in the trough B, and 
 runs off in the channel C. The openings 
 D are for the purpose of adjusting the axis 
 of the rollers. The canes are supplied by 
 the hands of the workmen. 
 
 Substances are seldom extended or flat- 
 tened by forces that tend immediately to 
 increase the dimensions of the substance 
 only : this is generally performed by re- 
 ducing the magnitude of the substance in 
 another direction, sometimes by means of 
 pressure, but more effectually by percus- 
 sion. The rollers of the press employed 
 for laminating metals are turned by ma- 
 chinery, and are capable of being moved 
 backwards and forwards, in order to re- 
 peat the operation on the same substance ; 
 their distance is adjusted by screws, which 
 are turned at once by pinions fixed on the 
 same axis, in order that they may be 
 always parallel. In this manner lead, 
 copper, and silver, are rolled into plates ; 
 and a thin plate of silver being soldered to 
 a thicker one of copper, the compound 
 plate is submitted again to the action of 
 the press, and made so thin as to be 
 afforded at a moderate expense. The gla- 
 zier’s vice is a machine of the same nature, 
 fqr forming window lead: the softness of 
 
 the lead enables it to assume the required 
 shape, in consequence of the pressure of 
 the rollers or wheels; and the circum- 
 ference of these wheels is indented, in 
 order to draw the lead along by the cor- 
 responding elevations. 
 
 The following figure represents a ma- 
 chine of this kind : 
 
 The vacuity in the middle shows the 
 form of the section of the lead, which is 
 draw n through it. 
 
 In drawing wire, the force is originally 
 applied in the direction of the extension ; 
 but it produces a much stronger lateral 
 
THE ARTISAN. 
 
 305 
 
 compression, by means of the conical 
 apertures through which the wire is suc- 
 cessively drawn. For holding the large 
 "wire, pincers are at first used, which em- 
 brace it strongly while they pull, and open 
 when they advance to a new position, the 
 interruption being perhaps of use, by 
 enabling the pincers to acquire a certain 
 momentum before they begin to extend the 
 wire; but afterwards, when the wire is 
 finer, it is simply drawn through the aper- 
 ture from one wheel or drum to another. 
 During the operation, it requires frequent 
 annealing, which causes a scale to form 
 on its surface; and this must be removed 
 by rolling it in a barrel with proper ma- 
 terials ; for the application of an acid is 
 said to injure the temper of the metal. 
 Copper is sometimes drawn into wire so 
 large, as to serve for the bolts used in 
 shipbuilding, especially for sheathing 
 ships’ bottoms. Silver wire thinly covered 
 with gold, is rendered extremely fine, and 
 then flattened, in order to be fit for making 
 gold thread : the thickness of the gold is 
 inconceivably small, much less than the 
 millionth part of an inch, and sometimes 
 only a ten millionth part. 
 
 The operation of coining depends also 
 in a great degree on an extension of the 
 metal, for the bars are taken out of the 
 moulds, and scraped, brushed, flattened 
 in a mill, and brought to the proper thick- 
 ness of the pieces to be coined ; the plates 
 thus reduced are then cut into a round 
 form, called blanks or planchets, with an 
 instrument fastened to the lower end of an 
 arbor, whose upper end is formed into a 
 screw, which being turned by an iron 
 handle turns the arbor, and lets the steel, 
 well sharpened in form of a punch cutter, 
 fall on the plates ; and thus a piece is 
 punched out 
 
 In forges the hammers are raised by 
 machinery, and thrown forcibly against a 
 spring, so as to recoil with great velocity. 
 With the help of this spring the hammer 
 sometimes makes 500 strokes in a minute, 
 its force being many times greater than 
 the weight of the hammer. Such forges 
 are used in making malleable iron, in 
 forming copper plates, and in manufactur- 
 ing steel. 
 
 The following figure represents a ham- 
 mer of this kind elevatad by the plugs, 
 projecting from an axis, either at A , or 
 
 more conveniently at B, and thrown forci- 
 bly against the wooden spring C. 
 
 OF CORN MILLS. 
 
 Some kinds of grain are occasionally 
 ground in mills of iron or steel, which con- 
 sist of a solid cylinder or cone turning 
 with a hollow one, both the surfaces being 
 cut obliquely into teeth. 
 
 The common mill for grinding corn is 
 composed of two circular stones of sili- 
 cious grit, placed horizontally ; the upper 
 one revolves with considerable velocity, 
 and is supported by an axis passing 
 through the lower one, at a distance va- 
 riable at pleasure. When the diameter is 
 five feet, the stone usually makes about 
 90 revolutions in a minute ; if the velocity 
 were greater, the flour would be too much 
 heated. The corn is shaken out of a fun- 
 nel or hopper, by means of projections 
 from the revolving axis, which strikes 
 against the orifice ; it passes through the 
 middle of the upper mill-stone, and is 
 readily admitted between the stones ; the 
 lower stone is slightly convex, and the 
 upper one somewhat more concave, so that 
 the corn passes over more than half the 
 radius of the stone before it begins to be 
 ground : after being reduced to powder, it 
 is discharged at the circumference, its 
 escape being favoured by the convexity of 
 the lower stone, as well as by the centri- 
 fugal force. The surface of the stones is 
 cut into grooves, in order to make them 
 act more readily and effectually on the 
 corn. The resistance in grinding wheat 
 has been estimated at about a thirty-fifth 
 of the weight of the mill-stone. The stones 
 have sometimes been placed vertically, 
 and the axis supported upon friction 
 wheels : but the common position appears 
 to be more eligible for mills on a large 
 scale. It is said that a man and a boy 
 may grind by a hand mill a bushel of 
 wheat in an hour ; in a water mill, the 
 grinding and dressing of a bushel of wheat, 
 is equivalent to the effect of 201G0 pounds 
 of water falling through a height of 10 
 feet, which is about as much as the work 
 of a labourer, for little more than half an 
 hour. In a wind-mill, when the velocity 
 is increased by the irregular action of the 
 wind, the corn is sometimes forced rapidly 
 through the mill without being sufficiently 
 ground. There is an elegant method of 
 preventing this by means of the centrifugal 
 force of two balls, which fly out as soon 
 as the velocity is augmented ; and as they 
 rise in the arc of a circle, allow the end of 
 a lever to rise with them, while the oppo- 
 site end of the lever descends with the 
 upper mill-stone, and brings it a little 
 nearer to the lower one.* The bran or 
 
 * See page 226 , vol. i. 
 
104 
 
 THE ARTISAN. 
 
 husk is seperated from the flour, by sifting presented by the letter E in the following 
 it in the bolting mill, which consists of a figure, which exhibits a corn mill, with 
 cylindrical sieve, placed in an inclined some of the improvements made in Ame- 
 position, and turned by machinery, as re- rica by Mr. Ellicott and Mr. Evans. 
 
 The corn, being poured into the funnel 
 A, is conveyed by the revolutions of a 
 spiral B C to C, whence it is raised by the 
 chain of buckets to C 1), to be cleaned by 
 the revolving sieve E and the fan F ; it is 
 then deposited in the granary G, which 
 supplies the funnel or mill hopper H ; this 
 being perpetually agitated by the iron 
 axis of the upper mill-stone, shakes it by 
 degrees into the perforation of the stone ; 
 it escapes, when ground, at I, and is con- 
 veyed by means of the carrier K L, and 
 the elevator LM, to the cooler N, where 
 it is spread on a large surface : it passes 
 
 afterwards to the bolter O, and is received 
 into the binn P from w 7 hence it is taken, 
 to be packed in sacks or barrels. Q re- 
 presents the surface of a mill-stone cut 
 into furrows, in order to make it act more 
 readily on the corn. 
 
 A TRAVELLING CORN-MILL. 
 
 The following figure represents a mill, 
 which depends on the draught of a horse 
 and the friction of the road for its motion. 
 It is meant to move round a green, or any 
 smooth road, and to travel from one house 
 or village to another. 
 
 ab is a square frame of scantling, fixed 
 on the shafts of a common cart : in this 
 frame is fixed the case c, which contains 
 the iron mill-stones d; the upper stone, as 
 usual, turned and supported by the trundle 
 
 or pinion e (the support of which, and its 
 regulator, cannot be represented in the 
 drawing, but are the same as in a com- 
 mon mill). The iron part of the spindle 
 that is fixed into the stone is supported on 
 
THE ARTISAN. 
 
 105 
 
 three or four friction-wheels, to keep the 
 stone steady when any inequalities are in 
 the road ; and which can, by screws, raise 
 or depress the stone according to the fine- 
 ness of the flour required, or the grain to 
 be ground. A cog-wheel, A, is fixed on a 
 square part of the axle of the cart-wheels, 
 and is about a foot less in diameter. This 
 cog-wheel can be easily separated from 
 the trundle e, when the mill travels from 
 one place to another. Inclining under the 
 stones is the bolting sieve z z, represented 
 by dotted lines, with teeth that act i# the 
 trundle e. The flour is ejected from the 
 stones into this circulating sieve, and falls 
 through it into a close case that deposits it 
 in the bag o ; while the bran flowing 
 through the length of the sieve, is re- 
 ceived in another bag. The stones should 
 be about three feet in diameter (if of cast 
 iron, so much the better), and the whole 
 machine covered. It is conceived, one 
 horse will draw the mill and a miller, and 
 grind a bushel of wheat in travelling about 
 one mile and a half. 
 
 
 OF ATMOSPHERICAL ELECTRICITY. 
 
 Air is one of those bodies which have 
 received the name of electrics , because 
 they are capable of being positively or ne- 
 gatively charged with electric matter. It 
 not only contains that portion of electri- 
 city which seems necessary to the consti- 
 tution of all terrestrial bodies, but it is 
 liable also to be charged negatively or 
 positively when electricity is abstracted 
 or introduced by means of conducting 
 bodies. These different states must occa- 
 sion a variety of phenomena, and in all 
 probability contribute very considerably 
 to the various combinations and decom- 
 positions which are continually going on 
 in the air. The electrical state of the at- 
 mosphere, then, is a point of considerable 
 importance, and has with great propriety 
 occupied the attention of philosophers ever 
 since Dr. Franklin demonstrated that thun- 
 der is occasioned by the agency of elec- 
 tricity. 
 
 The most complete set of observations 
 on the electricity of the atmosphere were 
 made by Professor Beccaria of Turin. He 
 found the air almost always positively 
 electrical, especially in the day-time and 
 in dry weather. When dark or wet 
 weather clears up, the electricity is al- 
 ways negative. Low thick fogs rising 
 into dry air carry up a great deal of elec- 
 tric matter. 
 
 In the morning, when the hygrometer 
 indicates dryness equal to that of the pre- 
 
 ceding day, positive electricity obtains 
 even before sunrise. As the sun gets up, 
 this electricity increases more remarkably 
 if the dryness increases. It diminishes in 
 the evening. 
 
 The mid-day electricity of days equally 
 dry is proportional to the heat. 
 
 Winds always lessen the electricity of a 
 clear day, especially if damp. 
 
 For the most part, when there is a clear 
 sky and little wind, a considerable elec- 
 tricity arises after sunset at dew falling. 
 
 Considerable light has lately been thrown 
 upon the sources of atmospherical electri- 
 city by the experiments of Saussure, Hum- 
 boldt, and other philosophers. Air is not 
 only electrified by friction like other elec- 
 tric bodies, but the state of its electricity 
 is changed by various chemical opera- 
 tions which often go on in the atmosphere. 
 Evaporation seems in all cases to convey 
 electric matter into the atmosphere; and 
 Saussure has ascertained that the quan- 
 tity of electricity is much increased when 
 water is decomposed, as when water is 
 dropt on a red hot iron. On the other 
 hand, when steam is condensed into vesi- 
 cular vapour, or into water, the air be- 
 comes negatively electric. Hence it would 
 seem that electricity enters as a compo- 
 nent part . into water ; that it separates 
 when water is decomposed or expanded 
 into steam, and is re-united when the 
 steam is condensed again into water. 
 
 Mr. Canton has ascertained that dry air, 
 when heated, becomes negatively electric, 
 and positive when cooled, even when it is 
 not permitted to expand or contract : and 
 the expansion and contraction of air also 
 occasions changes in its electric state. 
 
 Thus there appears to be at least four 
 sources of atmospheric electricity known ; 
 namely, Friction ; Evaporation ; Heat and 
 cold ; Expansion and Contraction : not to 
 mention the electricity evolved by the 
 melting, freezing, solution, &c. of various 
 bodies in contact with air. 
 
 As air is an electric, the matter of elec- 
 tricity, when accumulated in any particu- 
 lar strata, wall not immediately make its 
 way to the neighbouring strata, but will 
 induce in them changes similar to what is 
 induced upon plates of glass or similar 
 bodies piled upon each other, Therefore 
 if a stratum of air be electrified positively, 
 the stratum immediately above it will be 
 negative, the stratum above that positive, 
 and so on. Suppose now that an imper- 
 fect conductor were to come into contact 
 with each of these strata, we know, from 
 the principles of electricity, that the equi- 
 librium would be restored, and that this 
 would be attended with a loud noise, and 
 with a flash of light. Clouds which con- 
 sist of vesicular vapours mixed with par- 
 ticles of air are imperfect conductors ; if 
 
106 
 
 THE ARTISAN. 
 
 a cloud therefore come into contact with 
 two such strata, a thunder-clap would fol- 
 low. If a positive stratum be situated 
 near the earth, the intervention of a cloud 
 will serve to bring the stratum within the 
 striking distance, and a thunder-clap will 
 be heard while the electrical fluid is dis- 
 charging itself into the earth. If the stra- 
 tum be negative, the contrary effects will 
 take place. 
 
 It has been proved by Mr. Canton that 
 dry air, when heated, becomes negatively 
 electrified, but that it assumes the positive 
 state when cooled. He has also shewn that 
 it undergoes changes in its electrical con- 
 dition as it is exposed to various degrees of 
 pressure ; and Beccaria, Cavallo, Achard, 
 and other experimental enquirers, have 
 ascertained that these changes are con- 
 nected with meteorological phenomena. 
 
 On. this subject we quote the following 
 observations from Humboldt, which that 
 illustrious traveller made in the valleys of 
 Aragua : “ Being sufficiently habituated 
 to the climate,” says he, “ not to fear the 
 effects of tropical rains, we remained on 
 the shore to observe the electrometer. I 
 held it more than twenty minutes in my 
 hand, six feet above the ground, and ob- 
 served that, in general, the pith balls 
 separated only a few seconds before the 
 lightning was seen. The separation was 
 four lines. The electric discharge remained 
 the same during several minutes ; and hav- 
 ing time to determine the nature of the 
 electricity, by approaching a stick of seal- 
 ing wax, I saw here on the plain what 
 I have often observed on the back of the 
 Andes, during a storm, that the electricity 
 of the atmosphere was first positive, then 
 null, and then negative. These oscilla- 
 tions from the positive to the negative 
 state were often repeated. We had al- 
 ready observed,” he adds, “ in valleys 
 of Aragua, from the 18th and 19th of 
 February, clouds forming at the com- 
 mencement of the night. In the beginning 
 of the month of March the accumulation 
 of the vesicular vapours became visible to 
 the eye, and with them signs of atmosphe- 
 ric electricity augmented daily. We saw 
 flashes of lightning to the South, and the 
 electrometer of Volta displayed constantly 
 at sun set positive electricity. The separa- 
 tion of the little pith balls null during the 
 rectof the day, was from three to four lines 
 at the commencement of the night; which is 
 triple what I generally observed in Europe 
 with the same instrument in calm weather.” 
 Again he remarks, “ about the end of 
 February and the beginning of March, the 
 blue of the sky is less intense, the hygro- 
 meter indicates by degrees greater hu- 
 midity, the stars are sometimes veiled by 
 a thin stratum of vapours, and their light 
 is no longer steady and planetary; they 
 
 are seen twinkling from time to time 20° 
 above the horizon. The breeze at this 
 period, becomes less strong, less regular, 
 and is often interrupted by dead calms.” 
 For guarding against accidents from 
 lightning, Dr. Franklin’s great invention 
 of metallic conductors may be very advan- 
 tageously employed; for, when properly 
 fixed, they afford a degree of security, 
 which leaves very little room for appre- 
 hension. A conductor ought to be con- 
 tinued deep into the earth, or connected 
 with some well or drain; it should be 
 of ample dimensions, and where smallest, 
 of copper, since copper conducts electri- 
 city more readily than iron. In one in- 
 stance a conductor of iron, four inches 
 wide, and half an inch thick, appears to 
 have been made red hot by a stroke of 
 lightning. It seems to be of some advan- 
 tage that a conductor should be pointed, 
 but the circumstance is of less consequence 
 than has often been supposed. Mr. Wil- 
 son exhibited some experiments in which 
 a point was struck at a greater distance 
 than a ball, and therefore argued against 
 the employment of pointed conductors. 
 Mr. Nairne, on the contrary, showed that 
 a ball is often struck in preference to a 
 point. But it has been observed, that if 
 a point attracts the lightning from a greater 
 distance, it must protect a greater extent 
 of building. It is easy to show, by hang- 
 ing cotton or wool on a conductor, that a 
 point repels light electrical bodies, and 
 that a pointed conductor may, therefore, 
 drive away some fleecy clouds; but this 
 effect is principally derived from a current 
 of air repelled by the point ; and such a 
 current could scarcely be supposed to 
 have any perceptible effect upon clouds 
 so distant as those which are concerned in 
 thunder storms. 
 
 A small quantity of metal is found to 
 conduct a great quantity of this fluid. A 
 wire no bigger than a goose-quill, has 
 been known to conduct (with safety to the 
 building, as far as the wire was conti- 
 nued,) a quantity of lightning that did 
 prodigious damage both above and below 
 it ; and probably larger rods are not ne- 
 cessary, though it is common in America, 
 to make them of half an inch, and some 
 of three quarters, or an inch in diameter. 
 
 The rod may be fastened to the wall, 
 chimney, &c. with staples of iron. The 
 lightning will not leave the rod (a good 
 conductor,) to pass into the wall, (a bad 
 conductor,) through those staples. — It 
 would rather, if any were in the wall, 
 pass out of it into the rod to get more 
 readily by that conductor into the earth. 
 
 If the building be very large and ex- 
 tensive, two or more rods may be placed 
 at different parts for greater security. 
 
 Small ragged parts of clouds suspended 
 
THE ARTISAN. 
 
 107 
 
 in the air, between the great body of 
 clouds and the earth, (like leaf gold in 
 electrical experiments,) often serve as par- 
 tial conductors for the lightning, which 
 proceeds from one of them to another, 
 and by their help comes within the strik- 
 ing distance to the earth or a building. 
 It therefore strikes through those parts of 
 a building that would otherwise be out of 
 the striking distance. 
 
 It is therefore proper to elevate the 
 upper end of the rod six or eight feet above 
 the highest part of the building, tapering 
 it gradually to a fine sharp point, which 
 should be gilt to prevent its rusting. 
 
 The pointed rod will thus either pre- 
 vent a stroke from the cloud, or, if a 
 stroke takes place, will conduct it to the 
 earth with safety to the building. 
 
 A person apprehensive of danger from 
 lightning, happening, during the time of 
 thunder, to be in a house not so secured, 
 will do well to avoid sitting near the chim- 
 ney, looking-glass, gilt pictures, or wains- 
 cot 5 the safest place is in the middle of 
 the room, (if not under a metal lustre, 
 suspended by a chain,) sitting on one 
 chair and laying the feet on another. 
 It is still safer to bring two or three mat- 
 trasses or beds into the middle of the 
 room, and folding them up double, place 
 the chair upon them ; for they not being 
 so good conductors as the walls, the light- 
 ning will not chuse an interrupted course 
 through the air of the room and the bed- 
 ding, when it can go through a continued 
 better conductor, the wall. But where it 
 can be had, a hammock or swinging bed, 
 suspended by silk cords equally distant 
 from the walls on every side, and from the 
 ceiling and floor above and below, affords 
 the safest situation a person can have in 
 any room whatever; and what indeed may 
 be deemed quite free from danger of any 
 stroke by lightning. 
 
 ASTEOMOMYs ' 
 
 ON THE REGULATION OF TIME 
 BY THE HEAVENLY BODIES. 
 
 Though time, considered in an abstract 
 and philosophical point of view, was cer- 
 tainly coeval with the Deity, since nothing 
 can possibly exist but in some portion of it, 
 yet the measuring of time is a matter of a 
 very different nature ; and though various 
 nations have differed on this subject, it is, 
 nevertheless, a subject of the utmost im- 
 portance to every human being. For the 
 opposite and contradictory methods of 
 calculating time have often been produc- 
 tive of very great mischief in the w orld ; 
 while chronologers, sometimes from igno- 
 rance, and as often from prejudice, have 
 
 misrepresented events, which, however 
 trifling they might appear to them, may 
 nevertheless affect the happiness of future 
 ages. During the general chaos, or that 
 period when the materials of which the 
 beautiful fabric of the universe was what 
 Ovid calls rudis indig estaque moles, a rude 
 and indigested heap, there were no human 
 beings, and consequently no occasion for 
 any method of measuring or regulating 
 time. But as soon as the world was made 
 a fit habitation for man, the measurement 
 of time became necessary on many ac- 
 counts : our pleasure, as well as our inte- 
 rests, require that this object should be 
 accomplished ; but it is only an acquaint- 
 ance with astronomy that can furnish the 
 means of doing it correctly. For time has 
 always been measured and defined by the 
 motions of the heavenly bodies, and parti- 
 cularly by the sun, as being the most re- 
 gular and constant in his apparent revo- 
 lutions.* 
 
 The principal divisions of time are the 
 year and the day, which are measured by 
 the annual and diurnal revolution of the 
 sun. The day, or the time in which the 
 sun appears to go round the earth, has 
 been divided into twenty-four equal parts, 
 which are called hours, and these again 
 subdivided into minutes, &c. This divi- 
 sion is, however, merely arbitrary ; there 
 being no astronomical appearance to war- 
 rant or regulate such a division of the day, 
 more than a division into twenty-two, 
 forty-eight, or any other number of equal 
 parts. 
 
 The length of the tropical year, or the 
 time the sun is in going from any point of 
 the ecliptic to the same again, is 365 days, 
 5 hours, 48 minutes, 49 seconds. But the 
 sidereal year, or the time which intervenes 
 between the conjunction of the sun and 
 any fixed star, and his next conjunction 
 with the same star, is 365 days, 6 hours, 9 
 minutes, 11^ seconds. The difference be- 
 tween these two periods, which amounts 
 to 20 22%', is occasioned by the recession 
 of the equinoxes, or the falling back of the 
 equinoctial points 50|; seconds of a degree 
 every year. This retrograde motion of 
 the equinoctial points is caused by the 
 joint attraction of the sun and moon upon 
 the earth, in consequence of its spheroi- 
 dical figure.t 
 
 Time is distinguished according to the 
 manner of measuring the day, into appa- 
 rent, mean, and sidereal. Apparent time, 
 which is also called true, solar, and astro- 
 
 * As it may contribute to perspicuity in treating 
 of this important subject, we shall consider the ap- 
 parent motions of the sun as real. 
 
 t These variations are computed and inserted in a 
 table, which is called a Table of the Equation of 
 Time. 
 
108 
 
 THE ARTISAN. 
 
 nomical time, is derived from observations 
 made on the sun. Mean, or mean solar 
 time, sometimes called equated time, is a 
 mean or average of apparent time, which 
 is not always equal ; for the intervals be- 
 tween two successive transits of the sun 
 over the meridian are not always the same. 
 This is owing to the eccentricity of the 
 earth’s orbit, and its obliquity to the plane 
 of the equinoctial. If the earth’s orbit 
 were an exact circle, and coincident with 
 the equinoctial, the sun would always re- 
 turn to the meridian of any place at equal 
 intervals of time, and apparent and mean 
 solar time would bedhe same. But as this 
 is not the case, mean time is deduced from 
 apparent by adding or subtracting the dif- 
 ference between them, which is usually 
 called the equation of time. 
 
 Mean solar days are all equal, being 
 twenty-four hours each ; but apparent 
 solar days are sometimes more than twenty- 
 four hours, and sometimes less. A sidereal 
 day is the interval between two successive 
 transits of a star over the same meridian, 
 and is always of the same length ; for all 
 the fixed stars make their revolutions in 
 equal times, owing to the uniformity of the 
 earth’s diurnal rotation about its axis. The 
 sidereal day is, however, shorter than the 
 mean solar day by S' 56£". This difference 
 arises from the sun’s apparent annual mo- 
 tion from west to ea9t, by which he leaves 
 the star, as it were, behind him. Thus, if 
 the sun and a star be observed on any day 
 to pass the meridian at the same instant, 
 the next day, when the star passes the me- 
 ridian, the sun will have advanced nearly 
 a degree to the eastward ; and, as the 
 earth’s diurnal rotation on its axis is from 
 west to east, the star will come to the me- 
 ridian before the sun ; and in the course 
 of a year the star will have gained a whole 
 day on the sun ; that is, it will have passed 
 the meridian 366 times, while the sun will 
 only have passed it 365 times. Now as 
 the sun appears to perform the whole of 
 the ecliptic in 365 days, 5 hours, 48 mi- 
 nutes, 49 seconds, he describes 59' 8*3", 
 or nearly one degree of it per day, at a 
 mean rate ; and this space reduced to time 
 is exactly 3' 56§", the excess of a mean 
 solar day above a sidereal day.* 
 
 The equation of time, or the difference 
 between mean and apparent time, as al- 
 ready mentioned, arises from two causes; 
 namely, the obliquity of the ecliptic to the 
 plane of the equinoctial, and the eccentri- 
 city of the earth’s orbit. There are, how- 
 ever, four days in the year when the equa- 
 tion of time is nothing, or when the mean 
 and apparent time coincide ; these days 
 are, at present, the 15th of April, the 15th 
 
 * This excess is sometimes called the acceleration 
 ot the fixed stars. 
 
 of June, the 1st of September, and the 
 24th of December. From the first of these 
 days to the second, the apparent time is 
 before the mean ; from the second to the 
 third, the mean time is before the appa- 
 rent ; from the third to the fourth, the ap- 
 parent is before the mean ; and from the 
 last of those days to the first, the mean is 
 again before the apparent, and so on al- 
 ternately.* 
 
 If the revolution of the sun consisted of 
 an entire number of days, for instance 365, 
 the year would naturally be made to do 
 the same ; and there would be no difficulty 
 in the formation of the calendar , or in ad- 
 justing the reckoning in years and in days 
 to one another. 
 
 All the years would thus contain pre- 
 cisely the same number of days, and would 
 also begin and end with the sun in the 
 same point of the ecliptic. But the sun’s 
 revolution includes a fraction of a day, 
 and therefore a year and a revolution of 
 the sun cannot be precisely completed at 
 the same moment. However, as this frac- 
 tion makes a whole day in four revolutions, 
 one day is added every four years, in order 
 to make this number of years equal to the 
 same number of revolutions. The year to 
 which this day is added therefore contains 
 366 days. 
 
 This is the arrangement of what is called 
 the Julian Calendar; and the year thus 
 computed is termed the Julian year, from 
 Julius Caesar, by whom it was introduced 
 at Rome.f But as the real length of the 
 year is 365 days, 5 hours, 49 minutes, 
 nearly, the manner of reckoning adopted 
 by Julius Caesar was not sufficiently exact 
 to preserve the seasons in the same time of 
 the year : for in four years, the difference 
 between the year thus regulated and the 
 true solar year amounted to about 44 mi- 
 nutes, and in 132 years to one entire day. 
 The Julian year must, therefore, have be- 
 gun one day earlier than the solar year at 
 the end of this period. Consequently, the 
 continuance of this erroneous mode of rec- 
 koning would have made the seasons 
 change their places altogether in the course 
 of twenty-four thousand years. 
 
 At the time of the Council of Nice , in 
 the year 325 of the Christian era, the Ju- 
 lian calendar was introduced into the 
 Church ; and at that time the vernal equi- 
 nox fell on the 21st of March ; but on ac- 
 
 * Clocks and watches ought to he regulated by 
 mean time, as none of them can shew apparent 
 time, because they are all constructed on the prin- 
 ciple of uniform and equable motion. 
 
 t The intercalary day, or the day which was 
 added every fourth year, was accounted the 24th of 
 February, and called by the Romans the 6th of the 
 Kalends of March ; on this account there were every 
 fourth year two 6ths of the Kalends of March, and 
 therefore they called this year Bissextile. With us 
 it is called Leap Year. 
 
THE ARTISAN. 
 
 109 
 
 count of the imperfection of the mode of 
 reckoning just noticed, the reckoning fell 
 constantly behind the true time : so that 
 in the year 1582, the Julian year had fallen 
 nearly ten days behind the sun ; and the 
 equinox, instead of falling on the 21st of 
 March, fell on the 11th of March. 
 
 The defects of the calendar were disco- 
 vered long before the year 1582 ; but all 
 attempts made to reform it proved in vain. 
 At last Pope Gregory, who was desirous 
 of rendering his pontificate illustrious by 
 bringing about a reformation, which his 
 predecessors had failed to accomplish, in- 
 vited all the astronomers in Chistendom to 
 give their opinions on this important affair. 
 This invitation had the effect of bringing 
 forth many ingenious plans ; but the one 
 which he ordered to be adopted was af- 
 forded by an astronomer of Verona, named 
 Lilius. 
 
 The first step was to allow for the loss 
 of the ten days ; which was done by count- 
 ing the 5th of October, 1582, the 15th of 
 that month. By this means, the vernal 
 equinox was again brought to-the 21st of 
 March, as it was at the time of the Coun- 
 cil of Nice ; and to prevent the like incon- 
 venience in future, it was decreed that the 
 last year of every century, not divisible by 
 four , should be accounted a common year, 
 which, according to the Julian reckoning, 
 should be leap year ; but that those hun- 
 dreds which were divisible by four, such 
 as 1600, 2000, 2400, &c. should still be 
 accounted leap year. Although this cor- 
 rection be sufficiently exact to keep the 
 seasons to the same time of the year, yet it 
 does not altogether correspond with the 
 real length of the year ; for the time that 
 the Julian year exceeds the true will 
 amount to 3 days in 390 years. If, there- 
 fore, at the end of 390 years, three days 
 were expunged, the equinox would very 
 nearly keep to the same day of the month ; 
 but by suppressing 3 days only in 400 
 years, as in the Gregorian account, a small 
 deviation will take place in the course of 
 twelve or sixteen centuries, but so trifling 
 as scarcely to deserve notice. 
 
 As this reformation of the calendar was 
 brought about under the auspices of Pope 
 Gregory, it is called the Gregorian Calen- 
 dar, and sometimes the New Style , to dis- 
 tinguish it from the Julian account. This 
 new calendar was immediately adopted in 
 all Catholic countries; but it was not 
 adopted in this country till the year 1752. 
 In Russia, Prussia, and some other coun- 
 tries, the Julian account is still used. 
 
 iBisrellfitteous J?ithjertfs. 
 
 MEMOIR OF THE LIFE OF DR. 
 
 ROBERT SIMSON. 
 
 Dr. Robert Simson was born in the 
 year 1687 of a respectable family, which 
 had held a small estate in the county of 
 Lanark for some generations. He was, 
 we think, the second son of the family. A 
 younger brother was professor of medicine 
 in the university of St. Andrew, and is 
 known by some works of reputation, par- 
 ticularly u A Dissertation on the Nervous 
 System,” occasioned by the dissection of 
 a brain completely ossified. 
 
 Dr. Simson was educated in the univer- 
 sity of Glasgow under the eye of some of 
 his relations who were professors. Eager 
 after knowledge, he made great progress 
 in all his studies ; and as his mind did 
 not, at the very first openings of science, 
 strike into that path which afterwards so 
 strongly attracted him, and in which he 
 proceeded so far almost without a com- 
 panion, he acquired in every walk of 
 science a stock of information, which, 
 though it had never been much augmented 
 afterwards, would have done credit to a 
 professional man in any of his studies. He 
 became, at a very early period, an adept 
 in the philosophy and theology of the 
 schools, was able to supply the place of a 
 sick relation in the class of oriental lan- 
 guages, was noted for historical know- 
 ledge, and one of the most knowing bota- 
 nists of his time. As a relief to other 
 studies, he turned his attention to mathe- 
 matics. Perspicuity and elegance he 
 thought were more attainable, and more 
 discernible in pure geometry, than in any 
 other branch of the science. To this there- 
 fore he chiefly devoted himself; for the 
 same reason he preferred the ancient me- 
 thod of studying pure geometry. He con- 
 sidered algebraic analysis as little better 
 than a kind of mechanical knack, in which 
 we proceed without ideas, and obtain a re- 
 sult without meaning, and without being 
 conscious of any process of reasoning, and 
 therefore without any conviction of its 
 truth. Such was the ground of the strong 
 bias of Dr. Simson’s mind to the analysis 
 of the ancient geometers. It increased as 
 he advanced, and his veneration for the an- 
 cient geometry was carried to a degree of 
 idolatry. His chief labours were exerted 
 in efforts to restore the works of the an- 
 cient geometers. The inventions of flux- 
 ions and logarithms attracted the notice of 
 Dr. Simson, but he has contented himself 
 with demonstrating their truth on the ge- 
 nuine principles of ancient geometry. 
 
 About the age of twenty-five, Dr. Sim- 
 son was chosen Regius Professor of Ma- 
 thematics in the University of Glasgow. 
 
no 
 
 THE ARTISAN. 
 
 He went to London immediately after his 
 appoiniment, and there formed an acquaint- 
 ance with the most - eminent men of that 
 bright era of British science. Among 
 these he always mentioned Captain Halley 
 (the celebrated Dr. Edmund Halley) with 
 particular respect; saying, that he had 
 the most acute penetration, and the most 
 just taste in that science, of any man he 
 had ever known. And, indeed, Dr. Hal- 
 ley has strongly exemplified both of these 
 in his divination of the work of “ Apollo- 
 nius de Sectione Spatii,” and the eighth 
 book of his “ Conics,” and in some of the 
 most beautiful theorems of Sir Isaac New- 
 ton’s “ Principia.” Dr. Simson also ad- 
 mired the wide and masterly steps which 
 Newton was accustomed to take in his in- 
 vestigations, and his manner of substitut- 
 ing geometrical figures for the quantities 
 which are observed in the phenomena of 
 nature. It was from Dr. Simpson that his 
 biographer, to whom we are indebted for 
 this article, learnt, u That the thirty-ninth 
 proposition of the first book of the Prin- 
 cipia was the most important proposition 
 that had ever been exhibited to the phy- 
 sico -mathematical philosopher;” and he 
 used always to illustrate to his more ad- 
 vanced scholars the superiority of the geo- 
 metrical over the algebraic analysis, by 
 comparing the solution given by Newton 
 of the inverse problem of centripetal 
 forces, in the forty-second proposition of 
 that book, with the one given by John 
 Bernoulli in the Memoirs of the Academy 
 of Sciences at Paris for 1713. He had 
 heard him say, that to his own knowledge 
 Newton frequently investigated his propo- 
 sitions in the symbolical way ; and that it 
 was owing chiefly to Dr. Halley that they 
 did not finally appear in that dress. But 
 if Dr. Simson was well informed, we think 
 it a great argument in favour of the sym- 
 bolic analysis when this most successful 
 practical artist (for so we must call New- 
 ton when engaged in a task of discovery) 
 found it conducive either to despatch or 
 perhaps to his very progress. Returning 
 to his academical chair, Dr. Simson dis- 
 charged the duties of a professor for more 
 than fifty years with great honour to the 
 university and to himself. It is almost 
 needless to say, that in his prelections he 
 followed strictly the Euclidian method in 
 elementary geometry. He made use of 
 Theodosius as an introduction to spherical 
 trigonometry. In the higher geometry he 
 lectured from his own Conics : and he 
 gave a small specimen of the linear prob- 
 lems of the ancients, by explaining the 
 properties, sometimes of the conchoid, 
 sometimes of the cissoid, with their appli- 
 cation to the solution of such problems. 
 In the more advanced class he was accus- 
 tomed to give Napier’s mode of conceiv- 
 
 ing logarithms ; i. e. quantities as gene- 
 rated by motion ; and Mr. Cotes’s view of 
 them, as the sums of ratiunculae; and to 
 demonstrate Newton’s lemmas concerning 
 the limits of ratios ; and then to give the 
 elements of the fluxionary calculus ; and to 
 finish his course with a select set of propo- 
 sitions in optics, gnomonics, and central 
 forces. His method of teaching was -sim- 
 ple and perspicuous, his elocution clear, 
 and his manner easy and impressive. He 
 had the respect, and still more the affec- 
 tion, of his scholars. 
 
 It was chiefly owing to the celebrated 
 Halley that Dr. Simson so early directed 
 his efforts to the restoration of the ancient 
 geometers. He had recommended this to 
 him, as the most certain way for him, at 
 that time very young, both to acquire re- 
 putation, and to improve his own know- 
 ledge and taste ; and he presented him 
 with a copy of Pappus’s Mathematical 
 Collections, enriched with his own notes. 
 Hence he undertook the restoration of 
 Euclid’s porisms,awork of some difficulty, 
 that his biographer says nothing but suc- 
 cess could justify in so young an adven- 
 turer. From this he proceeded to other 
 works of importance, which he executed 
 with so much skill, as to obtain the repu- 
 tation of being one of the most elegant 
 geometers of the age. His edition of Eu- 
 clid’s u Elements” has long been reckoned 
 the very best that exists. Another work, 
 on which Dr. Simson bestowed much la- 
 bour, was the u Sectio Determinata,” 
 which was published after his death, by 
 the late Earl Stanhope, with the great 
 work, “ The Porisms of Euclid.” This 
 nobleman had kept up a correspondence 
 with Dr. Simson till his death in 1768, 
 when he engaged Mr. Clow, to whose care 
 the Doctor had left his papers, to make a 
 selection of such as would serve to support 
 and increase his reputation, as the restorer 
 of ancient geometry. This selection Lord 
 Stanhope printed at his own expense. 
 
 “ The life of a literary man rarely teems 
 with anecdote ; and a mathematician, de- 
 voted to his studies, is perhaps more ab- 
 stracted than any other person from the 
 ordinary occurrences of life, and even the 
 ordinary topics of conversation. Dr. Sim- 
 son was of this class ; and, having never 
 married, lived entirely a college life. — 
 Having no occasion for the commodious 
 house to which his place in the university 
 entitled him, he contented himself with 
 chambers, good indeed, and spacious 
 enough for his sober accommodation, and 
 for receiving his choice collection of mathe- 
 matical writers, but without any decoration 
 or commodious furniture. His official 
 servant sufficed for valet, footman, and 
 chambermaid. As this retirement was en- 
 tirely devoted to study, he entertained no 
 
THE ARTISAN. 
 
 Ill 
 
 company in his chambers, but in a neigh- 
 bouring house, where his apartment was 
 sacred to him and his guests. Having in 
 early life devoted himself to the restoration 
 of the works of the ancient geometers, he 
 studied them with unremitting attention ; 
 and, retiring from the promiscuous inter- 
 course of the world, he contented himself 
 with a small society of intimate friends, 
 with whom he could lay aside every re- 
 straint of ceremony or reserve, and in- 
 dulge in all the innocent frivolities of life. 
 Every Friday evening was spent in a party 
 at whist, in which he excelled, and took 
 delight in instructing others, till increasing 
 years made him less patient with the dull- 
 ness of a scholar. The card-party was 
 followed by an hour or two dedicated 
 solely to playful conversation. In like 
 manner, every Saturday he had a less se- 
 lect party to dinner at a house about a mile 
 from town. The Doctor’s long life gave 
 him occasion to see the dramatis personae 
 of this little theatre several times com- 
 pletely changed, while he continued to 
 give it a personal identity ; so that, with- 
 out any design or wish of his own, it be- 
 came, as it were, his own house and his 
 own family, and went by his name. Dr. 
 Simson was of an advantageous stature, 
 with a fine countenance ; and even in his 
 old age had a graceful carriage and man- 
 ner, and always, except when in mourn- 
 ing, dressed in white cloth. He was of a 
 cheerful disposition ; and though he did 
 not make the first advances to acquaint- 
 ance, had the most affable manner, and 
 strangers were at perfect ease in his com- 
 pany. He enjoyed a long course of unin- 
 terrupted health ; but towards the close 
 of life suffered from an acute disease, and 
 was obliged to employ an assistant in his 
 professional labours for a few years pre- 
 ceding his death, which happened in 1768, 
 at the age of 81. He left to the university 
 his valuable library, which is now arranged 
 apart from the rest of the books, and the 
 public use of it is limited by particular 
 rules. It is considered as the most choice 
 collection of mathematical books and ma- 
 nuscripts in the kingdom ; and many of 
 them are rendered doubly valuable by Dr. 
 Simson’s notes.” For a more particular 
 account of the life and writings of this 
 great man, the reader is referred to the 
 article in the Encyclopedia Britannica, 
 vol. xvih 
 
 NEW LUNAR AND HORARY TA- 
 BLES.— By David Thomson. 
 
 As it has been our practice from the 
 commencement of the present work to no- 
 tice any discovery or improvement made 
 in the physical sciences or useful arts, 
 
 during the progress of the present work, 
 we consider that we shall render an essen- 
 tial service to the cause of navigation, by 
 giving a short account of a work just pub- 
 lished, containing tables for facilitating 
 the computation of the longitude at sea. 
 
 The importance of the subject is such as 
 to interest all who attach any value either 
 to science or commerce ; we shall there- 
 fore endeavour to point out the great im- 
 provement which the author of these ta- 
 bles has accomplished in the calculation of 
 this laborious and important problem. 
 
 Though chronometers, or time-keepers, 
 are now pretty generally used on board of 
 ships, and afford the readiest and most di- 
 rect method of determining the longitude 
 at sea ; yet they are so apt to change their 
 rates of going, and to get deranged, that 
 it not only becomes necessary to correct 
 them at sea, but even to determine the 
 longitude without placing the least de- 
 pendence upon them. The only accurate 
 and practical method of accomplishing 
 this at sea is, by what is termed the Lunar 
 method; which is, to measure the distance 
 between the sun and the moon, or the moon 
 and a star, with a sextant ; and from this 
 distance, and the altitudes of the objects, 
 to deduce the true distance between them, 
 as the measured distance is seldom or never 
 the same as the true. Now, though some 
 of the best mathematicians and astronomers 
 in Europe have endeavoured to shorten 
 the process of calculation, and various 
 methods have been devised by means of 
 particular sets of tables ; yet still it ap- 
 pears so formidable and laborious, that, 
 comparatively speaking, few seamen can 
 be induced to employ this mode of deter- 
 mining the longitude ; but will rather 
 trust to the precarious and uncertain one 
 by dead-reckoning •, which is often one hun- 
 dred leagues from the truth. And some 
 captains, who have chronometers on board 
 of their vessels, have paid so little atten- 
 tion to the Lunar method, on account of 
 the necessary calculation, that they are 
 under the necessity of making the land for 
 the sole purpose of correcting their chro- 
 nometers, though it should be many miles 
 out of the direct course they ought to steer. 
 
 These are facts that are too well known 
 to admit of dispute or contradiction ; and 
 appear to have led the ingenious author of 
 the work before us to think intensely on 
 the nature of this most useful problem ; the 
 result of which has been the construction 
 of a small set of tables, by which the true 
 distance between the sun and moon, or the 
 moon and a star, may be computed by the 
 addition of a few figures. But, in order 
 to show the shortness and simplicity 
 of the process, we shall give an exam- 
 ple, which may be compared with the 
 
112 
 
 THE ARTISAN. 
 
 methods of calculation given in any other sun’s apparent altitude 26° 3', that of the 
 work which treats on the same subject. moon 66° 38', and the moon’s horizontal 
 
 Suppose the apparent distance between parallax 55' 47" : required the true dis- 
 the sun and moon to be 86° 19 10", the tance ? 
 
 Moon’s hor. par. 0°55'47" Log. 0 0488 ........ Log. 0 0488 
 
 Sun’s app. alt. 26° 3' 0" Log. 0*8174 Moon’s ap. alt. 66° 38' Log. 0-4972 
 
 App. dist. 86° 19' 10" Log. S 0-9991 ...... Log. T 2-1913 
 
 First correc. 4° 35 ; 27" Log. 1*8653 
 
 Second correc. 5° 3' 18" Log. 2 7373 
 
 Third correc. 0° 2 ' 10" 
 
 gum — lOmTrue Dist. 86° O' 5" 
 
 The numbers here called Logs, are di- 
 rectly obtained from the tables, which are 
 so arranged as to admit of the quantities 
 being taken out nearly at one opening of 
 the book. 
 
 The manner of computing the true dis- 
 tance between the moon and a star being 
 exactly similar to the above, it is unneces- 
 sary to give any example. 
 
 The manner of finding the time as well 
 as the altitudes of the objects, are also very 
 easily performed by the precepts and ta- 
 bles contained in this work. But what we 
 consider next in importance to the simple 
 and concise method here given of com- 
 puting the true distance , is the full and 
 lucid manner in which the method of as- 
 
 certaining the longitude by Chronometers 
 is illustrated and explained ; and we have 
 no hesitation in saying, that the observa- 
 tions on the method of managing and de- 
 termining the rate of these delicate ma- 
 chines at sea, are such as display an inti- 
 mate acquaintance both with the theory 
 and practice of navigation. 
 
 To the practical seaman this must there- 
 fore prove a very valuable work ; and as 
 it is of a moderate price, the humblest in- 
 dividual who goes to sea may procure it. 
 
 We may add, that the typographical 
 execution and appearance of this work is 
 superior to any book of figures we have 
 ever seen. 
 
 SOLUTIONS OF QUESTIONS. 
 Quest. 63, answered by Mr. Whitcombe, 
 Cornhill ( the Proposer). 
 
 Let A O D be the given quadrant, then 
 in A D take DC to D E, as m to «, and 
 
 draw CV parallel to DO and equal to 
 D E ; join E V, also D V, and continue it 
 till it cuts AO inH; then draw H B pa- 
 rallel to DO, and HI to AD; then 
 H B D I will be the rectangle required. 
 
 Demon. Because H B, V C, and D I are 
 parallel ; also H I, V E, and B D, the tri- 
 angles HBD and VCD are similar; 
 
 therefore CD : CV :: BD : BH; but 
 C D : C V or D E : : m : n; consequently 
 B D : B H : : m : w. Hence B H I D is the 
 rectangle required. 
 
 Though this is a very beautiful and 
 simple problem, yet the above is the only 
 solution of it which we have received. 
 We are sorry that Geometry should be so 
 little studied by our mathematical corres- 
 pondents, as it appears to us to be ; for we 
 have observed during the progress of the 
 present work, that few of our correspon- 
 dents have paid much attention to this 
 elegant and beautiful branch of the Mathe- 
 matics. Ed. 
 
 QUESTION FOR SOLUTION. 
 
 Quest. 65, proposed by Mr. J. Taylor, 
 Clement’s -lane, Lombard-street. 
 
 Two ladies subscribe to a certain charity 
 certain sums of money, in the ratio of 4 to 
 5 ; now the sum of the squares of each per- 
 son’s subscription amounted to 69/. 5s. 9^d. 
 I demand the sum subscribed by each 
 lady ? 
 
THE ARTISAN, 
 
 113 
 
 PERSPECTIVE. 
 
 To exhibit the perspective of a cube with 
 one of its angles presented to the eye. 
 
 As the basis of a cube, with one of its 
 angles presented to the eye, and standing 
 on a geometrical plane, is a square with 
 one of its angles presented to the eye ; 
 draw a square, viewed angular-wise, on 
 the perspective to b b, or plaue. Raise 
 the side H I of the square perpendicularly 
 
 on each point of the terrestrial line DE; 
 and to any point, as Y/, of the horizontal 
 line HR, draw the right lines VI and 
 V K. From the angles d, b , and c, draw 
 cl, d2, &c. parallel to the terrestrial line 
 D E. From the points 1 and 2, raise L 1 
 and M 2, perpendicular to the same. 
 Lastly, since K I is the height to be 
 raised in a, L I in c and b, and M 2 in d ; 
 in a raise the line fa perpendicular to a E ; 
 in b and c, raise bg and c e perpendicular 
 to bcli and lastly, raise dh perpendicu- 
 lar to d 2 ; and make af equal to HI, bg 
 equal to e c, and also LI, and h equal 
 tod M2: if, then, the points g, h,e,f be 
 connected by right lines, the perspective 
 will be complete. 
 
 To exhibit the perspective of a pyramid 
 standing on its base. 
 
 Suppose it were required to delineate 
 a quadrangular pyramid, with one of its 
 angles presented to the eye since the 
 base of such a . pyramid is a square, pre- 
 senting one of its angles to the eye, con- 
 struct such a square. To find the vertex 
 of the pyramid ; that is, a perpendicular 
 let fall from the vertex to the base, draw 
 diagonals mutually intersecting each other 
 in e. 
 
 ii v JEL 
 
 On any point, as H, of the terrestrial 
 line D E, raise the altitude of the pyramid 
 HI; and, drawing the right lines HV 
 and IY, to each point of the horizontal 
 line H R, produce the diagonal a b, till it 
 meet the line V H in h. Lastly, from h 
 draw h i parallel to H I. This being 
 raised on the point e, will give the vertex 
 of the pyramid K ; consequently, the lines 
 d k , k a, and k b , will be determined at the 
 same time. 
 
 To exhibit the perspective of walls, columns , 
 fyc. or to raise them on the pavement. 
 
 Suppose a pavement AFHI repre- 
 sented in a plan, together with the basis of 
 
 C 
 
 BA N I LMR T 5 4 I 3 1 I 
 
 the columns, &c. if there be any. Upon point V, by the right lines D V and G V. 
 the terrestrial line set off the thickness of Upon F and H raise perpendiculars HG 
 the wall BA and 1, 3. Upon A and B, and E F. Thus will all the walls be de- 
 as also upon 3 and 1, raise perpendiculars lineated. Now to raise the pillars, &c. there 
 A D and B C ; as also 3, 6, and 1, 7. Con- needs nothing but, from their several bases 
 nect the points D and 6 with the principal (whether square or circular) projected on 
 Vol. II.— No. 33. H 
 
114 
 
 THE ARTISAN. 
 
 the perspective plan, to raise indefinite 
 perpendiculars ; and on the fundamental 
 line, where intersected by the radius F A 
 passing through the base, raise the true 
 altitude A 1) : for D Y being drawn as be- 
 fore, the perspective altitudes will be de- 
 termined. 
 
 To exhibit the perspective of a door in a 
 building. (See last figure.) 
 
 Suppose a door required to be delineated 
 in a wall DEFA: upon the fundamental 
 line set off its distance A N from the angle 
 A, together with the breadths of the posts 
 N I and LM, and the breadth of the gate 
 itself LI. To the point of distance K, 
 from the several points N, I, L, M, draw 
 right lines R N, KI, KL, KM, which 
 will determine the breadth oi the door li, 
 and the breadths of the posts i n and m l. 
 From A to O, set off the height of the gate 
 A O, and from A to P, the height of the 
 posts A P. Join O and P with the prin- 
 cipal point, by the right lines PV and 
 O V. Then, from n, i, l , m, raise perpen- 
 diculars, the middle ones whereof are 
 cut by the right line O V in o, and the ex- 
 tremes, by the right line V P in p. Thus 
 will the door be delineated, with its posts. 
 If the door were to have been exhibited 
 in the wall E F G H, the method would 
 have been nearly the same. For, upon 
 the terrestrial line, set off the distance of 
 the door from the angle, and thence also 
 the breadth of the door RT. From R and 
 T draw right lines to the principal point 
 Y, which give the breadth r t in the per- 
 spective plan. From r and t raise indefi- 
 nite perpendiculars to FH. From A to 
 O, set off the true height A O. Lastly, 
 from O to the principal point V, draw r the 
 right line O Y, intersecting EF in Z, and 
 make r r and 1 1 equal to F Z. Thus is the 
 door rr, 1 1, drawn ; and the posts are 
 easily added, as before. 
 
 To exhibit the perspective of ivindows in a 
 wall. (See last figure.) 
 
 When it is known how to represent 
 doors, there will be no difficulty in adding 
 windows ; all that is further required, 
 being to set off the height of the window 
 from the ground : the whole operation is 
 as follows : — From 1 to 2 set off the thick- 
 ness of the w r all at the window ; from 3 to 
 4, its distance from the angle 3 ; and from 
 4 to 5 its breadth. From 4 and 5, to the 
 point of distance L, draw r the right lines 
 L 5 and L 4, which will give the perspec- 
 tive breadth 10, 9 of the window. From 
 
 10 and 9 raise lines perpendicular to the 
 pavement ; that is, draw indefinite paral- 
 lels to 6 and 3. From 3 to 11 set off' the 
 distance of the window from the pavement 
 3 and 11 ; and from 11 to 12, its height 
 
 11 and 12. Lastly, from 11 and 12, to the 
 principal point V, draw lines V 11 and 
 V 12 ; which intersecting the perpendicu- 
 lars 10, 13, and 9, 14, in 13 and 14, as also 
 in 15 and 16, will exhibit the appearance 
 of the window. 
 
 From these examples, which are all no 
 more than applications of the first grand 
 or general rule, it will be easily perceived 
 what method to take to delineate any other 
 object, and at any height from the pave- 
 ment. 
 
 When it is required to determine a point 
 in a line parallel to the picture, we may 
 suppose a line to be drawn through it per- 
 pendicular to the picture, and, by finding 
 the image of this line, we may intersect 
 the former image in the point required. 
 It is thus, that any number of columns or 
 figures, at different distances, may be 
 readily determined. Thus, the heights of 
 the houses, windows, doors, and figures in 
 the following representation of a street, 
 are determined by lines directed to the 
 centre of the picture ; the true height being 
 measured on the lines A B, CD, where 
 the objects are supposed to touch the plane 
 of projection. 
 
THE ARTISAN. 
 
 115 
 
 The distance EF, and all other parts of 
 lines perpendicular to the picture, are 
 measured by laying off the lengths of the 
 originals, as G H, on the line A C, and 
 drawing I E G I E H from I, the point of 
 distance; which, in most cases, will be 
 more remote from the centre of the picture 
 than is here made. The line KL, and 
 others parallel to A C, may be measured 
 by the assistance of any point M in the 
 horizontal line, the distances N O, O P, 
 being laid off on A C, or simply by reduc- 
 ing the scale in the proportion of M P to 
 ML. 
 
 To form a bridge in perspective, a front 
 vieiv. 
 
 Let the station of the observer be oppor 
 site the centre of the nearest arch, his eye 
 elevated 15 feet above the water, or plane 
 of the base, and viewed under an angle of 
 60 degrees. 
 
 Let the length of the bridge be 181 feet, 
 
 and consist of 3 arches ; the first arch to 
 the left hand 50 feet; the second TO; and 
 the third 35 ; the piers 13 feet each, about 
 one-fifth of the opening of the 70 feet arch 
 being the ordinary thickness of them, 
 although much less is sufficient; but this 
 is not a place for discussion. The height 
 of the pier to the spring of the arch, 20 
 feet, and the arches semicircles ; the width 
 of the bridge, including the parapets of 
 the road-way, 40 feet ; the height of the 
 road- way may be about 62 feet, if a semi- 
 circle ; if an ellipse upon the greater dia- 
 meter, or if a segment of a circle, the 
 height may be much less ; and if Gothic 
 arches are used, they may be considerably 
 greater, which circumstances must regu- 
 late. 
 
 Tn form the bridge, and parts, from a 
 one-fourth inch scale. 
 
 Let A B be the ground line, of an inde- 
 finite length. 
 
 With the span of the arch 50, and width 
 40, describe the perspective parallelogram 
 A B b a, by prob. 4 ; at the point A, draw 
 A C perpendicular to the ground line, and 
 equal to the height of the pier, and radius 
 of the circle, which is 45 feet ; draw C D 
 equal and parallel to A B ; upon C P, and 
 with the same breadth 40, describe the 
 perspective parallelogram C D d c ; set off 
 A F, B G, each equal 20 feet, the height 
 of the spring of the arch ; join F G, and 
 upon F G describe the parallelogram 
 F G gf; bisect / g in the points E, e ; with 
 the centre E, e, and distances EG, eg, 
 describe the semicircles FHG , fhg; 
 which represent the front and opposite 
 opening of the arch. 
 
 To form the arch on the right hand of 
 the front opening. Upon the ground line 
 A B, set off' from B the thickness of the 
 pier 13 feet to A 7 ; from A 7 setoff A'B 7 
 equal to 70 feet; upon A'B 7 70, with the 
 width 40, describe the parallelogram 
 A 7 B 7 b a' ; raise the perpendiculars A 7 C , 
 B'D 7 , equal 55 feet; mark off A'F 7 , B'G 7 
 20 feet, for the spring of the arch, as be- 
 fore ; join C 7 B 7 , and upon C 7 D 7 , F 7 G 7 , with 
 the width 40, describe the parallelograms 
 G'F g'f, C 7 D'd'c; find the centres E, e, 
 as in the last; with the centres E, e, and 
 
 distance E F, ef, describe the semicircle, 
 GHFjg' hf; G H F representing the front 
 of the opening of the arch, and ghf the 
 back opening, of which part is hid by the 
 pier. In the same manner, any number of 
 similar arches may be formed, either upon 
 the right or left hand ; and the opening of 
 the arches will decrease in the same man- 
 ner, and for the same reasons, as were 
 shewm in forming windows. 
 
 To form the arch stones. These are 
 here measured 3 feet, in the 50 feet arch, 
 and 4 feet in the 70, and 1 foot thick ; in 
 the 50 feet arch, the measure of one foot is 
 from the outside of the architrave ; and in 
 the 70 feet arch, the measure of 1 foot is 
 taken from the inside of the architrave. In 
 drawing the arch stones, the lines are all 
 directed to the centre of curvature ; but in 
 forming the perspective of the inside of the 
 arch, the lines are all directed to the point 
 of sight, whether they proceed from the 
 curvature of the arch, or from the inside of 
 the piers. 
 
 If the curvature is represented in the 
 circular part of the arch, the distance of 
 the centres E, e, being divided into as 
 many parts as there are stones in the 
 width of the bridge ; or into so niany parts 
 as would render the circles distinct, each 
 H 2 
 
116 
 
 THE ARTISAN. 
 
 of these points would be centres of the 
 different circles, which might be drawn 
 till intercepted by the side of the pier and 
 arch. The opposite bank of the river is in 
 the direction i ar; such objects as come in 
 view upon it may be represented. 
 
 The abutments, or land-stools, may be 
 formed at pleasure, the situation of the 
 banks of the river must regulate the form 
 of the arch, as to its height; and the situa- 
 tion of the observer, must be regulated by 
 what is intended for the view ; if his sta- 
 tion is on a level with the road-way, a con- 
 siderable part of the field may come into 
 view, but most of the inner part of the 
 arch will be hid. 
 
 To form the cut-water of the pier. This 
 may be angular, or rounded off at plea- 
 sure ; suppose it to be formed by an equi- 
 lateral triangle, described upon the breadth 
 of the pier 13 feet, the perpendicular 
 height of that triangle is 11 feet nearly; 
 which set off on the ground line A B ; from 
 the point A draw the radials i A, ill, and 
 from the distance point z, draw z 1 1 , till it 
 cut the radial A i produced in r ; draw r s 
 parallel to AB; bisect the piers B A', 
 draw radials through the points of section, 
 till they cut the parallel rs; then these 
 points of section will give the vertexes of 
 the cut-water ; join the vertex and sides 
 of the piers, which will give the true re- 
 presentation of the cut-water. In the same 
 manner form the top. 
 
 CHEMISTRY. 
 
 We are yet ignorant of the union of cop- 
 per with the first combustible substances ; 
 particularly with azote, hydrogen, and 
 carbon, with which it is even believed to 
 be incapable of combining. All we know 
 is, that hydrogen and carbon decompose 
 the oxide of this metal, take from it its 
 oxygen, and reduce it to the metallic state, 
 at a red heat. 
 
 Copper is capable of combining with 
 most of the metals ; and some of its alloys 
 are of very great utility. 
 
 The alloy of gold and copper is easily 
 formed by melting the two metals together. 
 This alloy is much used, because copper 
 has the property of increasing the hard- 
 ness of gold, without injuring its colour. 
 Indeed, a little copper heightens the co- 
 lour of gold, without diminishing its duc- 
 tility. This alloy is more fusible than 
 gold, and is therefore used as a solder for 
 that precious metal. Copper increases 
 likewise the hardness of gold. According 
 to Muschenbroek, the hardness of this 
 alloy is a maximum, when it is composed 
 of seven parts of gold, and one of copper. 
 Gold alloyed with ^th of pure copper, by 
 
 Mr. Hatchett, was perfectly ductile, and 
 of a fine yellow colour, inclining to red. Its 
 specific gravity was 17*157. This was be- 
 low the mean. Hence the metals have suf- 
 fered an expansion. Their bulk before 
 union was 2732, after union 2798. So that 
 916§ of gold, and 83§ of copper, when 
 united, instead of occupying the space of 
 1000, as would happen were there no ex- 
 pansion, become 1024. 
 
 Gold coin, sterling or standard gold, 
 consists of pure gold alloyed with ^ of 
 some other metal. The metal used is 
 always either copper or silver, or a mix- 
 ture of both, as is most common in British 
 coin. Now it appears, that when gold is 
 made standard by a mixture of equal 
 weights of silver and copper, that the ex- 
 pansion is greater than when the copper 
 alone is used, though the specific gravity 
 of gold alloyed with silver differs but little 
 from the mean. The specific gravity of 
 gold alloyed with 5 \th of silver and 5 \th of 
 copper was 17*344. The bulk of the metals 
 before combination was 2700, after it 2767.* 
 We learn from the experiments of Mr. 
 Hatchett, that our standard gold suffers 
 less from friction than pure gold, or gold 
 made standard by any other metal besides 
 silver and copper ; and that the stamp is 
 not so liable to be obliterated as in pare 
 gold. It therefore answers better for coin. 
 A pound of standard gold is coined into 
 44§ guineas, or 46^ g sovereigns. 
 
 Platinum may be alloyed with copper 
 by fusion, but a strong heat is necessary. 
 The alloy is ductile, hard, takes a fine 
 polish, and is not liable to tarnish. This 
 alloy has been employed with advantage 
 for composing the mirrors of reflecting 
 telescopes. The platinum dilutes the co- 
 lour of the copper very much, and even 
 destroys it, unless it be used sparingly. For 
 the experiments made upon it we are in- 
 debted to Dr. Lewis. Strauss has lately 
 proposed a method of coating copper ves- 
 sels with platinum instead of tin ; it con- 
 sists in rubbing an amalgam of platinum 
 over the copper, and then exposing it to 
 the proper heat. 
 
 Silver is easily alloyed with copper by 
 fusion. The compound is harder and more 
 sonorous than silver, and retains its white 
 colour even when the proportion of cop- 
 per exceeds one-half. The hardness is a 
 maximum when the copper amounts to 
 one-fifth of the silver. The standard or 
 sterling silver of Britain, of which coin is 
 made, is a compound of 12| silver and one 
 copper. Its specific gravity after simple 
 
 * The first guineas coined were made standard by 
 silver; afterwards copper was added to make up 
 for the deficiency of the alloy ; and as the propor- 
 tion of the silver and copper varies, the specific gra- 
 vity of our gold coin is various also. 
 
THE ARTISAN. 
 
 117 
 
 fusion is 10 200. By calculation it should 
 be H’33. Hence it follows that the alloy 
 expands, as is the case with gold when 
 united to copper. A pound of standard 
 silver is coined into 66 shillings. 
 
 Mercury acts but feebly upon copper, 
 and does not dissolve it while cold ; but if 
 a small stream of melted copper be cau- 
 tiously poured into mercury, heated nearly 
 to the boiling point, the two metals com- 
 bine, and form a soft white amalgam. 
 
 There is no metal more useful than cop- 
 per, excepting iron, to which it yields the 
 superiority. Every one knows that a great 
 number of instruments and utensils are 
 made of copper for various purposes. 
 Those vessels which are to be placed upon 
 the fire are generally made of it, as it is 
 much less liable to alteration than iron, 
 and at the same time much more easy to 
 be wrought. Its alloys with zinc and tin 
 are employed for a great number of pur- 
 poses in the arts, and in common life. But, 
 unfortunately, this metal acts as a poison 
 upon the animal economy ; and it is one of 
 the bodies that most threaten our existence. 
 It is therefore much to be wished that it 
 were prescribed, at least for economical 
 and domestic uses. Cisterns, reservoirs, 
 pipes, and cocks, made of this metal, or 
 its alloys, are no less dangerous than cop- 
 per-pans; and frequently they are even 
 more pernicious, as they are not kept with 
 the same care as the vessels, the whole of 
 which is exposed to view at once, and 
 which are employed several times a day. 
 Too much care, attention, and prudence, 
 cannot be employed in the use of all uten- 
 sils made of copper, as all its oxides are 
 extremely susceptible of dissolving in fat, 
 oils, and most of the unctuous substances 
 that are employed in the preparation of 
 food. Frequent tinning is the most cer- 
 tain defence against this terrible evil. 
 
 Besides the varied and multiplied uses 
 of copper in the metallic form, several ores 
 and preparations of this metal are em- 
 ployed in a great number of the arts. The 
 pyrites sulphurets serve for the preparation 
 of the sulphate of copper, by their spon- 
 taneous efflorescence and their lixiviation ; 
 it is also prepared by burning a mixture 
 of sulphur and copper. The malachites 
 are cut and polished for trinkets ; copper 
 is continually alloyed with zinc and tin 
 for making brass, casting statues, bells, 
 pieces of artillery, &c. Its different salts 
 and oxides enter into the preparation of 
 colours for painting ; of the baths ; the 
 preparations and mordants for dyeing ; of 
 enamels and glazings for pottery and 
 porcelain ; and of coloured glasses. 
 
 OF IRON. 
 
 Iron is the most important and most use- 
 ful of all metallic substances. Without 
 
 this metal no art could have arisen ; man 
 had remained in the savage state, and dis- 
 puted for his food by brute strength with 
 the other animals. Without this metal, 
 agriculture could not have existed, nor 
 could the plough have rendered the earth 
 fertile. Without iron, all the other metals 
 would have been of no utility ; for it is by 
 means of this agent that they receive their 
 varied forms and dimensions. Iron alone 
 may be considered as the representative 
 of every other metal ; it may be substituted 
 in the place of any of them, but no metal 
 can afford a substitute for iron. Though 
 the scarcity, the brilliancy, and durability 
 of gold and silver may place them in a 
 higher rank in these respects, yet the ser- 
 vice which iron renders to society en- 
 titles it to a higher degree of estimation in 
 the minds of men, who are accustomed to 
 think with justice and propriety. It is 
 true, that it does not shine with a splen- 
 dour equally strong ; nature has not de- 
 corated it with so beautiful a colour, but 
 its intimate properties are much more 
 precious. All the other metals might, in 
 truth, be dispensed with ; but iron, on the 
 contrary, is indispensible and necessary. 
 The condition of humanity would be truly 
 miserable without this metal, as is proved 
 by the history of those people with whom 
 the art of working it is still unknown, and 
 who, with joy and exultation, exchange 
 the gold with which their country is en- 
 riched for morsels of iron, which happier 
 and more cultivated nations bring to them 
 in exchange. Iron composes the first in- 
 strument of machines, and the first mover 
 of mechanics. In the hands of men it go- 
 verns, and, as it were, subdues all the pro- 
 ducts of nature. In successive obedience 
 to his power, we behold it change the form 
 and properties of other bodies, by the per- 
 petual influence it exercises upon them. 
 In a word, it is the soul of all the arts, 
 and the source of almost every beneficial 
 product. 
 
 Though a thousand facts in history prove 
 that the ancients were not acquainted with 
 the art of working iron like the modern 
 nations, the historians of Chemistry have 
 nevertheless placed the infancy of their 
 science among the first operators at the 
 forge, whose existence they have ad- 
 mitted almost in the first ages of the world. 
 
 The Alchemists qualified iron with the 
 name of Mars, by consecrating it to the 
 god of war, in whose service it has been 
 much employed. From the denomination 
 of Mars given to iron, naturally flowed the 
 appellation martial , which has been suc- 
 cessively attributed to numerous prepara- 
 tions made with this metal. 
 
 Iron possesses a peculiar metallic bril- 
 liancy. When we wish to describe its co- 
 lour, we are obliged to say that it is white, 
 
118 
 
 THE ARTISAN. 
 
 rather livid, inclined to grey and to blue. 
 In its texture it is formed of small fibrous 
 threads, or small grains and small plates 
 very pointed. When examined with the 
 microscope, it presents a great number of 
 pores or small cavities, more perceptible 
 than in copper. It appears that its in- 
 terior texture, as shewn in its fracture, 
 which is more or less fibrous, granulated 
 or lamellated, depends much on the me- 
 thod of its cooling, the pressure it has un- 
 dergone, the manner of treatment, and the 
 heat under which it has been forged or 
 struck. 
 
 The specific gravity of iron varies from 
 7-600 to 7*800. Its hardness exceeds that 
 of any other metal, and on this account it 
 is used to grind, cut, fashion, engrave, 
 and file most natural bodies, stones, wood, 
 and particularly the other metals. It is 
 also the most elastic of metals, and is 
 therefore preferred to all the others for 
 springs of every description. 
 
 The ductility of iron is also very con- 
 siderable ; but it is in some sort of a par- 
 ticular kind, or rather it is limited by its 
 excessive hardness, or the cohesion of its 
 particles. Though these adhere much more 
 strongly than most of the other metallic 
 substances, it cannot be made into plates 
 as thin as are formed of several other of 
 the latter; the thinnest sheet iron is in 
 fact much thicker than very coarse leaves 
 of lead or tin. For this reason iron is com- 
 monly placed in the fourth rank among 
 metals as to its ductility, and this place is 
 given on account of its ductility in the 
 wire-drawers’ plates. Its malleability is 
 very limited, on account of its firmness, so 
 that its ductility is much more eminent and 
 remarkable. A wire of this metal, of one- 
 tenth of an inch in diameter, supports a 
 weight of four hundred and fifty pounds 
 before it breaks, which cannot be done 
 with any other metal, not even copper and 
 platina, which approach the nearest to it. 
 Muschenbroeck, by examining a paralel- 
 lopipedon of iron, of one-tenth of an inch 
 in diameter, was obliged to use a force of 
 seven hundred and forty pounds to break 
 it ; and he remarks on this occasion, that 
 a similar piece of iron, forged of horse- 
 shoe nails, which had remained for some 
 time in the hoof of a horse, did not exhibit 
 a greater tenacity. This opinion is there- 
 fore, a prejudice which arises only from the 
 goodness and purity of iron made use of 
 for forging those nails. When heated to 
 about 158 u of Wedgewood’s pyrometer, as 
 Sir George M‘Kenzie has ascertained, it 
 melts. This temperature being nearly the 
 highest to which it can be raised ; it has 
 been impossible to ascertain the point at 
 which this melted metal begins to boil and 
 evaporate. Neither has the form of its 
 crystals been examined : but it is well 
 
 known that the texture of iron is fibrous; 
 that is, it appears when broken to be com- 
 posed of a number of fibres or strings, 
 bundled together. 
 
 Iron is rapidly penetrated by the elec- 
 tric fluid ; it is one of the best conductors 
 of electricity ; and accordingly, since the 
 discoveries of Franklin on the identity of 
 atmospheric thunder and electric spark, it 
 is employed with great success to fabri- 
 cate those elevated conductors, which are 
 appropriated by their gilded and unaltera- 
 ble terminations in a point, to attract with- 
 out noise, and rapidly to transport the 
 electric matter into the earth or into water, 
 where their inferior extremities terminate. 
 It has been long observed, that iron, thus 
 vertically placed in an elevated situation 
 of the atmosphere, if it remains a long 
 time, or be struck with the electric fluid of 
 lightning, it assumes the properties of a 
 magnet. It iron be struck in the air by the 
 electric shock, it takes fire ; but as this 
 phenomenon belongs to the history of its 
 combustion, we shall speak of it in another 
 place. 
 
 Magnetism is one of the most charac- 
 teristic, and, at the same time, most sin- 
 gular of the properties of iron. It was 
 long supposed to be peculiar to this metal ; 
 but it is now well known, that cobalt and 
 nickel also possess it. Nevertheless, all 
 the experiments relative to the magnetism 
 of these two last metals not having been 
 made either with the same accuracy, or to 
 the same extent, as upon iron, the princi- 
 pal phenomena of this force have been well 
 observed only in the latter metal. 
 
 The taste and smell are also two very 
 distinct and very evident properties in 
 iron. If we hold a piece of iron for some 
 time in the hand, and afterwards hold it a 
 little distance from the nose, we may dis- 
 cern its odour and quality. 
 
 When exposed to the air, its surface is 
 soon tarnished, and it is gradually changed 
 into a brown or yellow powder, well known 
 under the name of rust. This change 
 takes place more rapidly if the atmosphere 
 be moist. It is occasioned by the gradual 
 combination of the iron with the oxygen 
 of the atmosphere, for which it has a very 
 strong affinity. 
 
 Carburet of iron is found native, and has 
 been long known under the names of plum- 
 bago and black lead . It is of a dark iron 
 grey or blue colour, and has something of 
 a metallic lustre. It has a greasy feel, 
 is soft, and blackens the fingers, or any 
 other substance to which it is applied It 
 is found in many parts of the world, espe- 
 cially in Britain,* where it is manufactured 
 into pencils. It is not affected by the 
 
 * The chief mines are at Keswick in Cumberland, 
 ancl in Airshire. 
 
THE ARTISAN. 
 
 I ID 
 
 most violent heat as long as air is ex- 
 cluded, nor is it in the least altered by 
 simple exposure to the air or to water. A 
 moderate heat produces no effect upon it, 
 and occasions but little change in its bulk. 
 It is used, therefore, in making the cruci- 
 bles called black lead . It was long sup- 
 posed to be incombustible. 
 
 OF TIN. 
 
 Tin is one of the metals which was 
 earliest known, and of which the discovery 
 must have been among the first which was 
 made by men ; at least, its discovery ap- 
 pears to be hidden in the darkness of 
 ancient times, even beyond those of fabu- 
 lous history. The Egyptians made great 
 use of it in their arts; and the Greeks 
 alloyed it with other metals. Pliny, with- 
 out composing an accurate history, or pre- 
 cisely comparing its qualities with other 
 metals, speaks of it as a metal well known, 
 and much employed in the arts, and even 
 applied to a great number of the orna- 
 ments of luxury. He often calls it white 
 lead, and points out its frequent and frau- 
 dulent contamination with black lead, or 
 lead properly so called. 
 
 The alchemists attended greatly to tin ; 
 they named it Jupiter, and have distin- 
 guished its various preparations by the 
 name of Jovial. 
 
 Pure tin is of a white colour, equal in 
 beauty and brilliancy to that of silver ; 
 and if this colour were not changeable, it 
 would be as valuable as silver. It was 
 formerly considered as the lightest of me- 
 tals, when a distinct and particular class 
 was made of the semi-metals. Its specific 
 gravity varies from 7*291 to 7 500, accord- 
 ing as it is hammered or not. 
 
 It is one of the softest of metals. It may 
 be easily scratched with the nail; and 
 there is scarcely any other metal which 
 cannot injure its surface by pressure or by 
 friction. A knife readily cuts it ; it may 
 be easily bended, and when bended, affords 
 a peculiar crackling noise. In this property 
 it has been compared to zinc; but~the 
 noise is very different, or much weaker, in 
 zinc than in tin. 
 
 This phenomenon appears to depend on 
 a separation of its parts, and the sudden 
 fracture which they suffer by the bending, 
 though tin is not easily broken. Its so- 
 norous quality is feeble; its ductility is 
 sufficient to admit of its being reduced by 
 the hammer, or laminating cylinder, into 
 very thin leaves, which are of great use in 
 the arts. It holds the fifth rank among 
 metals in this property. It has little elas- 
 ticity or tenacity ; a wire of this metal of 
 ■jq of an inch in diameter supports, with- 
 out breaking, a weight of 50 pounds. 
 
 Tin is one of the most dilatable of metals 
 
 by caloric, according to the experiments o 
 Muschenbroeck. 
 
 It is also a good conductor of heat. 
 After mercury, it is the most fusible of all 
 the metals. It comes immediately before 
 bismuth and lead in this respect ; its melt- 
 ing point is 440° of Fahrenheits’s scale. 
 When fused, it does not rise in vapour, but 
 at a very elevated temperature ; it has 
 ever been considered as one of the most 
 fixed of metals ; on which account the 
 alchemists thought it considerably resem- 
 bled silver. If it be suffered to cool slowly, 
 and when its surface is congealed it be 
 pierced, and the part which is still fluid be 
 carefully poured out, the interior presents 
 crystals in rhombs of considerable size, 
 formed by the assemblage of a great num- 
 ber of small needles longitudinally united. 
 
 Tin is a very good conductor of elec- 
 tricity and galvanism, and is frequently 
 used for covering conductors, and for Ley- 
 den bottles. It has a very remarkable 
 odour, with which it impregnates the hands 
 and bodies rubbed with it. Its taste is also 
 very sensible, and it also possesses very 
 powerful medicinal properties. 
 
 Tin is not very abundant in the bowels 
 of the earth, at least in Europe. The most 
 abundant mines are in Cornwall, Bohemia, 
 and Saxony. The most skilful mineralo- 
 gists have hitherto distinguished only three 
 species of tin ores ; namely, native tin, its 
 oxide, and its sulphurated oxide. 
 
 Tin is not easily oxidized in the air 
 without heat, but it soon loses its bright 
 and beautiful white colour. When cut, it 
 is as brilliant and as clear as silver ; but in 
 a few hours this fine colour changes, be- 
 comes dull, and in a few days becomes 
 tarnished. Long exposure to the air con- 
 siderably increases this alteration, though 
 it takes place only at the surface ; so that 
 at last it becomes of a dirty grey, without 
 any brilliancy, and is covered with a light 
 stratum of grey oxide. It is, therefore, 
 necessary that vessels of tin should be fre- 
 quently cleaned and brightened to renew 
 their surface and retain their beauty. But 
 this weak oxidation never penetrates so 
 deeply as to justify the assertion that tin, 
 like other metals, rusts in the air. 
 
 When tin is fused with the contact of the 
 air, the metal, when scarcely liquefied, 
 becomes covered with a dull grey pellicle, 
 which becomes wrinkled, and separates 
 from the portion of fused tin. When this 
 pellicle is detached, another is formed ; 
 and by proceeding in the same manner, 
 the whole of the tin may be converted into 
 pellicles. 
 
 In the art of casting and purifying tin 
 vessels, this oxidized matter, formed at 
 the surface of the metal in fusion, was 
 called dross ; and it is very evident that it 
 
120 
 
 THE ARTISAN. 
 
 is in the power of the founder, to convert 
 all the tin into dross ; he consequently did 
 not lose this pretended impurity, but knew 
 very well how to recover it again in its 
 metallic form, by heating it with tallow or 
 resin. This crust is, therefore, a true grey 
 oxide of tin; the metal contains from eight 
 to ten per cent, of oxygen, and it is easily 
 reduced. If tin be continually heated with 
 the contact of air, particularly with agita- 
 tion, it become divided, attenuated, and 
 is changed into a powder, which gradually 
 becomes white, with increase of weight, is 
 more oxidized, and constitutes what is 
 called putty of tin in the arts. 
 
 OF LEAD. 
 
 The alchemists compared lead to Saturn, 
 not only because they suppose this metal 
 to be the oldest, and, as it were, the father 
 of all the others, but also because it was 
 considered as very cold, and possessing 
 the property of absorbing and apparently 
 destroying almost all the other metals ; in 
 the same manner as fabulous history affirms 
 that Saturn, the father of the gods, de- 
 voured his children. 
 
 Lead is of a blueish white colour, and 
 when newly melted is very bright ; but it 
 soon becomes tarnished by exposure to 
 the air. It has scarcely any taste, but 
 emits on friction a peculiar smell. It stains 
 paper or the fingers of a blueish colour. 
 When taken internally, it acts as a poison. 
 
 Its specific gravity is 11*3523, but it is 
 not increased by hammering; so far from 
 it, that Muschenbroeck found lead when 
 drawn out into a wire, or long hammered, 
 to be diminished in its specific gravity. A 
 specimen at first of the specific gravity 
 11*479 being drawn out into a fine wire, 
 was of the specific gravity 11-3 IT ; and on 
 being hammered, it became 11*2187 ; yet 
 its tenacity was nearly tripled. 
 
 It is very malleable, and may be reduced 
 to very thin plates by the hammer ; it may 
 be also drawn out into a wire, but its ducti- 
 lity is not great. Its tenacity is such, that a 
 lead wire ^ of an inch diameter is capable 
 of supporting only 29| pounds without 
 breaking. 
 
 Lead is a very good conductor of caloric, 
 though it is not extremely dilatable. It 
 melts at a low heat, and immediately after 
 mercury, tin, and bismuth ; it holds the 
 fourth rank in the order of fusibility. Mr. 
 Crichton, of Glasgow, estimates it at 612 
 degrees of Fahrenheit’s thermometer. 
 When it is kept long red hot, it sublimes, 
 and emits fumes in the air ; but for this 
 purpose a very elevated temperature is re- 
 quired. If it be slowly cooled, it crystal- 
 lizes in quadrangular pyramids, all formed, 
 as it would appear, of octahedrons. Thus 
 it was that Mongez, the younger, obtained 
 
 it. It is observable that when this opera- 
 tion is performed, it succeeds best (as tin 
 likewise does) when the lead has been 
 fused several times successively. 
 
 This metal is a conductor of electricity 
 and galvanism ; but it appears that it pos- 
 sesses these properties only in a weak de- 
 gree. It has a particular and rather fetid 
 smell ; its taste is also somewhat acrid and 
 disagreeable ; in consequence of this pro- 
 perty, it would seem that it acts upon the 
 animal economy, and produces the dead- 
 ening and paralysing action which is so- 
 well known. 
 
 The ores of lead are very abundant in 
 nature, particularly in France, Germany, 
 England, &c. It is also a metal of which 
 the ores are the most varied. 
 
 The treatment of the ores of lead in the 
 large way is one of the most important of 
 metallurgical operations, and one of those 
 which have the greatest as well as the 
 most intimate connection with the know- 
 ledge and accurate processes of Chemistry* 
 The sulphurous ores containing silver are 
 wrought by pounding them in a stamping 
 engine, and carefully washing them on 
 platforms, and then carrying them to the 
 blast-furnace, where they are first roasted 
 by a gentle heat, and afterwards fused by 
 increase of temperature. The fused lead is 
 drawn off from the furnace by opening a 
 hole on one of the sides of its hearth, 
 which, during the fusion, is kept closed 
 with loam. The lead is first cast into pigs, 
 which are called work-lead, because it is 
 intended to be used in subsequent opera- 
 tions to separate the silver which it contains. 
 
 Lead exposed to the air becomes speedily 
 tarnished, soon looses the slight brilliancy 
 which characterises it, becomes of a dirty 
 grey colour, and afterwards of a light grey, 
 which constitutes a true rust at its surface. 
 
 When thin plates of lead are exposed to 
 the vapour of warm vinegar, they are gra- 
 dually corroded, and converted into a 
 heavy white powder, used as a paint, and 
 called white lead. This powder was for- 
 merly considered to be a peculiar oxide of 
 lead ; but it is now known that it is a com- 
 pound of the yellow oxide and carbonic 
 acid. 
 
 The grey oxide of lead, when strongly 
 heated for a considerable time in contact 
 with the air, soon becomes yellow by a 
 new absorption of oxygen. In this state 
 of yellow oxide it is called massicot in the 
 arts ; it appears that it contains from six 
 to nine parts of oxygen in the hundred. It 
 is distinguished into two kinds in com- 
 merce on account of its colour : the one is 
 called white massicot, and the other yelloiv 
 massicot . It is a pigment of a dull hue, 
 without any beauty ; sometimes inclining 
 to green, which nevertheless is prepared in 
 
THE ARTISAN. 
 
 121 
 
 the large way in certain manufactories, on 
 account of the uses to which it is applied 
 in the arts. The method of producing it 
 consists simply in perpetually agitating 
 the lead in contact with the air, without 
 using a violent heat. 
 
 If massicot, ground to a fine powder, be 
 put into a furnace, and constantly stirred 
 while the flame of the burning coals plays 
 against its surface, in about 48 hours it is 
 converted into a beautiful red powder, 
 known by the name of minium or red lead. 
 This powder, which is likewise used as a 
 paint, and for various other purposes, is 
 the tritoxide, or red oxide of lead. 
 
 Lead and tin may be combined in any 
 proportion by fusion. This alloy is harder, 
 and possesses much more tenacity than 
 tin. Muschenbroeck informs us that these 
 qualities are a maximum when the alloy is 
 composed of three parts of tin and one of 
 lead. The increased hardness seems to 
 prevent in a great measure the noxious 
 qualities of the lead from becoming sensi- 
 ble when food is dressed in vessels of this 
 mixture. What is called ley pewter in this 
 country is often scarcely any thing else 
 than this alloy.* Tinfoil is also a com- 
 pound of tin and lead. 
 
 ASTRONOMY. 
 
 OF THE TIDES. 
 
 The tides have always been found to 
 follow, periodically, the course of the sun 
 and moon ; and hence it has been sus- 
 pected, in all ages, that the tides were, 
 some way or other, produced by these 
 bodies. 
 
 The celebrated Kepler was the first per- 
 son who formed any conjectures respecting 
 their true cause. But what Kepler only 
 hinted, has been completely developed and 
 demonstrated by Sir Isaac Newton. 
 
 After his great discovery of the law of 
 gravitation, he found it an easy matter to 
 account for the whole phenomena of the 
 tides : for, according to this law of nature, 
 all the particles of matter which compose 
 the universe, however remote from one 
 another, have a continual tendency to ap- 
 proach each other, with a force directly 
 proportional to the quantity of matter they 
 contain, and inversely proportional to the 
 square of their distance asunder. It is 
 therefore evident, from this, that the earth 
 will be attracted both by the sun and 
 
 * There are three kinds of pewter in common 
 use in this country ; namely, plate, trifle, and ley. 
 The plate pewter is used for plates and dishes; the 
 trifle chiefly for pint and quart pots ; and the ley 
 metal for wine measures, &c. Their specific gravi- 
 ties are as follows: plate, 7*248 ; trifle, 7*359; ley, 
 7*963. 
 
 moon. But although the attraction of the 
 sun greatly exceeds that of the moon, yet 
 the sun being nearly four hundred times 
 more distant from the earth than the 
 moon, the difference of his attraction upon 
 different parts of the earth is not nearly so 
 great as that of the moon ; and therefore 
 the moon is the principal cause of the 
 tides. 
 
 If all parts of the earth were equally 
 attracted by the moon, it would always 
 retain its spherical form, and there would 
 be no tides at all. But the action of the 
 moon being unequal on different parts of 
 the earth, those parts being most attracted 
 that are nearest the moon, and those at the 
 greatest distance least, the spherical figure 
 must suffer some change from the moon’s 
 action. Now as the waters of the ocean 
 directly under the moon are nearer to her 
 than the central parts of the earth, they 
 will be more attracted by her than the cen- 
 tral parts. For the same reason, the cen- 
 tral parts will be more attracted than the 
 waters on the opposite side of the earth ? 
 and therefore the distance between the 
 earth’s centre and the waters on its sur- 
 face, both under the moon and on the op- 
 posite side, will be increased ; or the 
 waters will rise higher, and it will then be 
 flood, or high water, at those places. But 
 this is not the only cause that produces 
 the rise of the waters at these two points ; 
 for those parts of the ocean which are 90° 
 from them will be attracted with nearly 
 the same force as the centres of the earth, 
 the effect of which will be a small increase 
 of their gravity towards the centre of the 
 earth. Hence, the waters at those places 
 will press towards the zenith and nadir , or 
 the points where the gravity of the waters 
 is diminished, to restore equilibrium, and 
 thus occasion a greater rise at those points. 
 But in order to know the real effect of the 
 moon on the ocean, the motion of the earth 
 on its axis must be taken into account. 
 For if it were not for this motion, the 
 longest diameter of the watery spheroid 
 would point directly to the moon’s centre ; 
 but by reason of the motion of the whole 
 mass of the earth on its axis, from west to 
 east, the most elevated parts of the water 
 no longer answer precisely to the moon, 
 but are carried considerably to the east- 
 ward in the direction of the rotation. 
 The waters also continue to rise after they 
 have passed directly under the moon, 
 though the immediate action to the moon 
 begins there to decrease ; and they do not 
 reach their greatest height till they have 
 got about 45° farther. After they have 
 passed the point which is 90° distant 
 from the point below the moon, they con- 
 tinue to descend, although the force which 
 the moon adds to their gravity begins there 
 to decrease. For still the action of the 
 
122 
 
 THE ARTISAN. 
 
 moon adds to their gravity, and makes 
 them descend till they have got about 45° 
 farther; the greatest elevations, therefore, 
 do not take place at the points which are 
 in a line with the centres of the earth and 
 moon, but about half a quadrant to the 
 
 east of these points, in the direction of the 
 motion of rotation. 
 
 Thus it appears, if the earth were en- 
 tirely covered by the ocean, as represented 
 by the circle b d e c in the following 
 figure — 
 
 that the spheroidical form which it would 
 assume, would be so situated, that its 
 longest diameter would point to the east 
 of the moon, or the moon would always 
 be to the west of the meridian of the parts 
 of greatest elevation. And as the moon 
 apparently shifts her position from east to 
 west in going round the earth every day, 
 the longer diameter of the spheroid follow- 
 ing her motions will occasion two floods 
 and two ebbs in the space of a lunar day, 
 or 24 hours 48 min. 
 
 These are the effects produced by the 
 action of the moon only ; but the sun has 
 also a considerable effect on the waters of 
 the ocean. Rut it is not the action of 
 these bodies on the earth, but the inequa- 
 lities of their actions w hich produce these 
 effects. The sun’s action on the whole 
 mass of the earth is much greater than of 
 the moon’s ; but his distance is so great, 
 that the diameter of the earth is a mere 
 
 point compared with it ; and, therefore, 
 the difference between his effects on the 
 nearest and farthest side of the earth, be- 
 comes on this account vastly less than it 
 w r ould be if the sun were as near as the 
 moon. How r ever, the immense bulk of 
 the sun makes the effect still sensible, even 
 at so vast a distance; and although the 
 action of the moon has the greatest share 
 in producing the tides, yet the action of 
 the sun adds sensibly to this effect, when 
 his action is exerted in the same direction, 
 as at the time of new and full moon, when 
 these two bodies are nearly in the same 
 straight line with the centre of the earth. 
 When this is the case, the effects of these 
 two bodies are united, so that the tides 
 rise higher than at any other time, and 
 are called spring tides; as represented by 
 the following figure, where S denotes the 
 sun, dnez the moon, and c the earth. 
 
THE ARTISAN. 
 
 m 
 
 The action of the sun diminishes that of 
 the moon in the quarters , because his 
 action is opposed to that of the moon; 
 consequently, the effect must be to depress 
 the waters where the moon’s action has a 
 tendency to raise them. These tides are 
 considerably lower than at any other 
 time, and are called neap tides. 
 
 The sring tides do not take place on the 
 very day of the new and full moon, nor 
 the neap tides on the very day of the quad- 
 ratures, but a day or two after ; because 
 in this case, as in some others, the effect is 
 neither the greatest nor least when the 
 immediate influence of the cause is great- 
 est or least : as the greatest heat, for ex- 
 ample, is not on the solstitial day, when 
 the immediate action of the sun is greatest, 
 but some time after it. And although the 
 action of the sun and moon were to cease, 
 yet the ocean would continue to ebb and 
 flow for some time, as its waves continue 
 in violent motion for some time after a 
 storm. 
 
 The high water at a given place does 
 not always answer to the same situation 
 of the moon, but happens sometimes sooner 
 and sometimes later than if the moon alone 
 acted on the ocean. This proceeds from 
 the action of the sun not conspiring with 
 that of the moon. The different distances 
 of the moon from the earth also occasions 
 a sensible variation in the tides. 
 
 When the moon approaches the earth, 
 her action in every part increases, and the 
 difference in that action, upon which the 
 tides depend, likewise increases. For the 
 attraction of any body is in the inverse 
 ratio of the square of its distance ; the 
 nearer, therefore, the moon is to the earth 
 the greater is her attraction, and the more 
 remote, the less. Hence, her action on the 
 nearest parts increases more quickly than 
 it does on the more remote parts, and 
 therefore the tides increase in a higher 
 proportion as the distance of the moon 
 diminishes. 
 
 Sir Isaac Newton has shown that the 
 tides increase as the cube of the distances 
 decrease, so that the moon, at half her 
 present distance, would produce a tide 
 eight times greater. Now the moon des- 
 cribes an ellipse about the earth, and, of 
 course, must be once in every revolution 
 nearer the earth than in any other part of 
 her orbit ; consequently, she must produce 
 a much higher tide when in this point of 
 her orbit than in the opposite point. 
 
 This is the reason that two great spring 
 tides never take place immediately after 
 each other; for if the moon be at her least 
 distance at the time of new moon, she must 
 be at her greatest distance at the time of 
 full moon , having performed half a revo- 
 lution in the intervening time, and there- 
 fore the spring tide at the full will be 
 
 much less than that at the preceding 
 change. For the same reason, if a great 
 spring tide happens at the time of full 
 moon , the tide at the following change will 
 be less. 
 
 The spring tides are highest and the 
 neap tides lowest about the beginning of 
 the year ; for the earth being nearest the 
 sun about the 1st of January, must be 
 more strongly attracted by that body than 
 at any other time of the year : hence, the 
 spring tides which happen about that time 
 will be greater than at any other time. 
 And should the moon be new or full in 
 that part of her orbit which is nearest to 
 the earth, at the same time the tides will 
 be considerably higher than at any other 
 time of the year. 
 
 The tide which happens at any time, 
 while the moon is above the horizon, is 
 called the superior tide , and the other the 
 inferior tide. When the moon is in the 
 equinoctial, other things remaining the 
 same, the superior and inferior tides are of 
 the same height ; but when the moon de- 
 clines towards the elevated pole, the 
 superior tide is higher than the inferior r 
 If the latitude of the place and the decli- 
 nation of the moon are of contrary names, 
 the inferior tide will be the highest. But 
 the highest tide at any particular place, is 
 when the moon’s declination is equal to 
 the latitude of the place, and of the same 
 name ; and the height of the tide dimi- 
 nishes, as the difference between the lati- 
 tude and declination increases; therefore, 
 the nearer any place is to that parallel 
 whose latitude is equal to the moon’s de- 
 clination and of the same name, the higher 
 will the tide be at that place.* 
 
 Such would the tides regularly be if the 
 earth were all covered over with the 
 ocean to a great depth ; but as this is not 
 the case, it is only at places situated on 
 the shores of large oceans where such 
 tides, as above described, take place. 
 
 The tides are also subject to very great 
 irregularities from local circumstances ; 
 such as meeting with islands, shoals, 
 headlands, passing through straits, &c. 
 In order that they may have their full mo- 
 tion, the ocean in which they are produced 
 ought to extend 90° from east to west, be- 
 cause that is the distance between the 
 greatest elevation and the greatest depres- 
 sion produced in the waters by the moon. 
 Hence it is, that the tides in the Pacific 
 Ocean exceed those of the Atlantic, and 
 that they are less in that part of the 
 Atlantic which is within the torrid zone 
 
 * In comparing the height of the tides at differ- 
 ent places, it is supposed that the sun and moon are 
 at the same distance from the earth, and in the same 
 position with respect to the meridian of these 
 places. 
 
124 
 
 THE ARTISAN. 
 
 between Africa and America, than in the 
 temperate zones, on either side of it where 
 the ocean is much broader. 
 
 In the Baltic, the Mediterranean, and 
 the Black seas, there are no sensible tides ; 
 for they communicate with the ocean by 
 so narrow inlets, and are of so great ex- 
 tent, that they cannot speedily receive and 
 let out water enough to raise or depress 
 their surfaces in any sensible degree. 
 
 The power of the moon to raise the 
 waters, Sir I. Newton has shown to be 
 about 4 ^ times that of the sun, and that 
 the moon raises the waters 8 feet 7 inches, 
 while the sun and moon together raise 
 them lOf feet, when at their mean dis- 
 tances from the earth, and about 12 feet 
 when the moon is at her least distance. 
 These heights are found to agree very 
 well with observations on the coasts of 
 open and deep oceans, but not well on the 
 coasts of small seas, and where the water 
 is shallow. 
 
 The mean retardation of the tides, or of 
 the moon^s coming to the meridian in 24 
 hours, is 48' 45"*7, and the mean interval 
 between two successive tides is 12 h 25' 
 14" 2 ; hence, the mean daily retardation 
 of high water is 50' 28" *4. 
 
 About the time of new and full moon the 
 interval is least, being only 12 h 19' 28"; 
 and at the quadratures the interval is the 
 greatest, being 12 h 80' 7". 
 
 The common method of calculating the 
 time of high water at any place, is to 
 multiply 50' 28", or the mean daily retar- 
 dation of the tides, by the moon’s age, and 
 then to divide the product by 60, which 
 gives the mean time of the moon coming to 
 the meridian on that day, in hours ; to this 
 is added the time of high water on the 
 days of full and change at the given place, 
 and the sum is the time of high water at 
 that place on the afternoon of the given 
 day, if the sum be less than 12 hours; but 
 if greater, 12 hours 25 minutes must be 
 subtracted, in order to have the time on 
 the afternoon of the given day; and 25 
 minutes subtracted from this time will give 
 the time of high water on the mqrning of 
 the given day.* 
 
 The following figure exhibits the pro- 
 gress of the tides from the Atlantic through 
 the channels surrounding the British 
 islands ; the lunar tides happening in any 
 part of the shaded lines nearly at the 
 hour after the moon’s southing, which is 
 indicated by the figure annexed to it. 
 
 * This 
 
 method is far from being exact; but affords an approximation, which may be! useful on some 
 occasions. When accuracy is wanted recourse must be had to other methods. 
 
THE ARTISAN. 
 
 125 
 
 OF THE FORCES WHICH RETAIN 
 
 THE PLANETS IN THEIR ORBITS. 
 
 Before the time of Kepler, who flou- 
 rished about the end of the 16th century, 
 the planets were supposed to move in cir- 
 cular orbits; but since his great discovery 
 of the laws which regulate the motions of 
 these bodies, astronomers have been ena- 
 bled to determine their periods, and the 
 figure of their orbits, with the greatest 
 exactness. 
 
 The laws of Kepler are, 
 
 1. That all the planets move round the 
 sun, in such a manner, that the Radius 
 Vector, or a line joining the sun and 
 planet, passes over equal areas or spaces 
 of the orbit in equal portions of time. 
 
 2. That each of the primary planets des- 
 cribes an ellipse, having the sun in one of 
 its foci. 
 
 3. That the squares of the periodic 
 times of the planets are to each other as 
 the cubes of their mean distances from the 
 sun. 
 
 These three laws are the basis of all 
 physical astronomy. But in a popular 
 work like the present, it would be impro- 
 per to enter upon any demonstrations of 
 them. However, as it may, perhaps, gra- 
 tify the reader to see an illustration of the 
 third law, we shall give an example, by 
 comparing the distance and periodic time 
 of Mercury with those of the earth. 
 
 Suppose the distance of Mercury were 
 given, and it was required to find the 
 time it required to perform a revolution 
 round the sun, having the distance of the 
 earth from the sun and the length of the 
 year given. By the third law of Kepler 
 it would be determined thus : — As the 
 cube of the earth’s distance (95 3 millions 
 of miles) is to the cube of Mercury’s dis- 
 tance (36| 3 millions), so is the square of 
 the earth’s periodic time (365|; 2 days) to 
 the square of Mercury’s year (88 2 days 
 nearly). 
 
 The distance may also be found by the 
 same law, if the periodic time be known. 
 Let it be required to find the distance of 
 Mercury, having its periodic time given ; 
 then it would be determined thus : as the 
 square of 365£ days is to the square of 88 
 days, so is the cube of 95 millions of miles 
 to the cube of 36| millions of miles, the 
 distance of Mercury from the sun. In the 
 same way, the distance of any other planet 
 may be determined, if its period be known, 
 or its period if its distance be known.* 
 
 After the laws of gravitation were 
 known, it was demonstrated by Sir Isaac 
 Newton, d priori, that the laws of Kepler 
 
 * In order to perform the calculation in this ex- 
 ample, it is necessary to be acquainted with propor- 
 tion, and the method of extracting the square and 
 cube roots. 
 
 must be those that regulate the system of 
 the world. 
 
 This extraordinary man found that the 
 laws of motion, and even the general pro- 
 perties of matter, are the same in the hea- 
 vens as on the earth. That the elliptical 
 figure of the orbits described both by the 
 primary and secondary planets ; the small 
 deviations in the form and position of their 
 orbits, as well as in the place of the 
 planets ; the facts which concern the 
 shape, rotation, and position of their axis ; 
 and the oscillation of the waters which sur- 
 round the earth, are all explained by one 
 principle ; namely, that of the mutual gra- 
 vitation of all bodies with forces directly 
 as their quantities of matter, and inversely 
 as the squares of their distances. 
 
 But as we cannot follow this celebrated 
 philosopher in all his demonstrations on 
 this important subject, in a work of this 
 kind, we shall endeavour to give as clear 
 and comprehensive a view of the doctrine 
 of gravitation, as our limits will permit, at 
 the same time avoiding every thing ab- 
 struse. 
 
 Thus, if one body contain double the 
 quantity of matter that another contains, 
 its attractive power will also be double ; if 
 it contain ten times the quantity of matter, 
 its attractive power will be ten times 
 greater, and so on. 
 
 But if a body be placed at any distance 
 from another body, and then removed to 
 double the distance, it will attract it only 
 with a fourth part of the force it did be- 
 fore ; at three times the distance, with a 
 ninth part of the force ; and at four times 
 the distance only with a sixteenth part, 
 and so on. 
 
 These are termed the laws of gravita- 
 tion; and are known to affect every 
 species of matter, and to connect the most 
 distant bodies in the universe. But what 
 the power or principle is which causes 
 bodies to affect each other according to 
 these laws, we shall not attempt to en- 
 quire. Because any enquiry of this kind 
 is not likely to be attended with much 
 success ; nor is it necessary to know the 
 cause which produces these effects : for 
 all that the astronomer is concerned to 
 know is, whether such a power or force is 
 exerted by one body on another, and if it 
 is, what are the laws of its action. Now 
 both of these important facts have been 
 determined with the greatest precision, 
 not only by calculation, but by observation 
 and experiment. 
 
 Every person knows that a heavy body 
 dropped from any height above the earth’s 
 surface descends in a straight line towards 
 the centre of the earth, where the whole 
 force of gravity seems to be accumulated. 
 And although it be difficult to discover 
 any sensible change in the intensity of this 
 
THE ARTISAN. 
 
 |26 
 
 force by a direct experiment on the weight 
 of a body, on account of the distances to 
 which we can either ascend or descend 
 from the earth’s surface being so small ; 
 yet the experiments which have been made 
 with the pendulum, lead us to infer, that 
 the force of gravity diminishes as we re- 
 cede from the centre of the earth, at the 
 rate we have stated above; namely, as 
 the square of the distance increases. The 
 effect of terrestrial gravity, as exhibited in 
 descent of falling bodies, has been accu- 
 rately measured, and the law which it ob- 
 serves fully ascertained and confirmed. It 
 had been long known that falling bodies 
 acquire an increase of velocity as they 
 approach the earth; arid consequently that 
 they pass over a greater space in any given 
 time. But Galileo was the first person 
 who made known the law which regulates 
 their descent, which is as follows. When 
 a body falls freely from a state of rest, it 
 passes through the space of sixteen feet 
 one inch in the first second of time ; and at 
 the end of the first second it will have 
 acquired such a degree of velocity as 
 would carry it thirty-two feet two inches 
 in the next second, though it should ac- 
 quire no new impulse from gravity. But 
 as the same accelerating cause continues 
 constantly to act, it will move sixteen feet 
 and one inch more the next second ; con- 
 sequently at the end of two seconds it will 
 have fallen sixty-four feet four inches, and 
 acquired such a velocity as would, in the 
 next second, carry it over forty-eight feet, 
 although it received no new impulse, and 
 so on. If a body be projected perpendicu- 
 larly upwards, its motion is continually 
 retarded by the same cause which accele- 
 rates it in descending. But if it be pro- 
 jected in a direction different from the 
 vertical line, that direction will be con- 
 tinually varying, and a curved line will 
 be described in consequence of the inces- 
 sant power of gravity, which, in such 
 cases, is measured by the degree of curva- 
 ture of the line described by the body. 
 
 This phenomenon affords a very good 
 illustration of the theory of the planetary 
 motions; for the effect produced is per- 
 fectly analogous to the motion of a planet 
 in its orbit. Every person knows that the 
 greater the velocity with which any body 
 is thrown, in a horizontal direction, from 
 an engine, the further will it range before 
 it falls. And though a body cannot be 
 thrown to a very great distance on the 
 earth, yet we can conceive a body pro- 
 jected with such a velocity as to carry 
 it quite round the earth without touching 
 it, and to continue to circulate round it in 
 the same path w ith undiminished velocity, 
 in every respect as the moon does. By 
 reasoning in this manner, Sir Isaac New- 
 ton conceived, that the force that produces 
 
 pressure in a body that is supported, or 
 that causes a heavy body to fall to the 
 ground, or a body thrown obliquely in the 
 air, to describe a curvilineal path, might 
 perhaps be the same that retains the moon 
 in her orbit ; and makes the planets and 
 comets revolve round the sun. Though 
 this was at first only a plausible conjec- 
 ture, yet, upon an appeal to the pheno- 
 mena exhibited by these bodies, he was 
 enabled to verify this conjecture. 
 
 It was, however, a fortunate circum- 
 stance for science, as well as for Newton, 
 that the real motions of the heavenly 
 bodies, as well as the laws of Kepler, 
 were known before he undertook the in- 
 vestigation of this subject. For these 
 laws were not only the basis upon which 
 he founded his investigations, but they 
 suggested to him the manner of conducting 
 them. 
 
 The first law, for example, led him to 
 the important discovery, that the action of 
 a force always directed towards the sun 
 bends the path of each planet into a curve ; 
 and the second law not only led him to the 
 knowledge of the changes produced in the 
 intensity of this force, by distance, but to 
 the law which regulates the intensity. 
 
 And as it was previously known that 
 the planets move round the sun in ellipti- 
 cal orbits, he was enabled to establish this 
 important law, that the force by which a 
 planet describes areas proportional to the 
 times round the focus of its elliptical orbit, 
 is inversely as the square of the distance 
 from that focus. Hence it follows, that 
 each planet is under the influence of a 
 force directed towards the sun, and urging 
 it in that direction, and that the intensity 
 of this force is inversely proportional to 
 the square of the planet’s distance from the 
 sun. 
 
 This power or force is sometimes called 
 the centripetal force ; because it urges the 
 planet in the direction of the centre of its 
 orbit, and prevents it from flying off in a 
 straight line, which every body moving in 
 a curve has a tendency to do ; and that 
 force by w hich it is urged in a straight 
 line, or endeavours to fly off from the cen- 
 tre, is called the centrifugal force. It is 
 by the nice combination of these two 
 forces, that the whole solar system is pre- 
 served in the order in which we behold it, 
 and that every body which forms any part 
 of the whole, performs its revolution 
 round the common centre of the system. 
 
 If the projectile or centrifugal force that 
 urges the planets forward in their orbits 
 were destroyed, each of them would fall to 
 the sun, by the force of gravity, just as a 
 stone descends to the earth. 
 
 The time in which the different planets 
 would fall to the sun, from a state of rest, 
 by the action of the centripetal force, or 
 
THE ARTISAN. 
 
 127 
 
 the power of gravity, is as follows: — Mer- 
 cury, in 15 days 13 hours ; Venus, 39 
 days 17 hours; the Earth, 64 days 13 
 hours; Mars, 121 days 10 hours; Jupiter, 
 765 days 19 hours; Saturn, 1901 days; 
 Uranus, 5425 days ; and the Moon to the 
 earth, in 4 days 20 hours. 
 
 As the centripetal force or attractive 
 power of the sun increases , as the square 
 of the distance decreases , it is obvious that 
 the nearer any body is to the sun, the 
 more powerfully will it be attracted by 
 him. This not only accounts for the 
 planets which are nearest the sun moving 
 faster in their orbits than those that are 
 most remote from him ; but also for the 
 motion of a planet being quickest in that 
 part of its orbit which is nearest the sun, 
 and slowest in that part which is farthest 
 distant from him. For the centrifugal 
 force must always be equal to the centri- 
 petal, in order that the planet may con- 
 tinue to revolve in the same orbit. In this 
 manner, all the bodies which compose the 
 solar system are attracted by the sun, and 
 made to perform their revolutions round 
 him ; and as action and re-action are equal, 
 and in opposite directions, the sun is 
 equally attracted by all the bodies that 
 revolve round him. Hence the order and 
 regularity of the whole system is pre- 
 served. 
 
 As neither our limits nor the nature of 
 the present work will permit us to give a 
 particular account of the planetary dis- 
 turbances, or the effect which they have 
 on each other, we shall conclude the 
 present article by mentioning the disco- 
 veries which have been the result of the 
 investigations of astronomers on this intri- 
 cate subject. These maybe reduced to the 
 two following ; viz. 1st. That all the in- 
 equalities produced by the mutual action 
 of the planets are periodical ; that is, after 
 a certain time they all run through the 
 whole series of changes to which they are 
 subject. 2d. That amid all these changes, 
 two of their elements remain the same — 
 the greater axis of the orbit, and the peri- 
 odic time. Hence, the mean motion of a 
 planet, and its mean distance are constant 
 quantities. For these important disco- 
 veries we are indebted to the celebrated 
 French mathematicians, La Grange and 
 La Place. And, as the late Professor 
 Playfair has observed, they have made 
 known to us one of the most important 
 truths in Physical Astronomy; namely, 
 that the system is stable ; that it does not 
 involve any principle of destruction in it- 
 self ; but is calculated to endure for ever, 
 unless the action of an external power be 
 introduced. 
 
 fEtsreHaneous subjects. 
 
 MEMOTR OF THE LIFE OF 
 EDMUND STONE. 
 
 Edmund Stone, a distinguished self- 
 taught mathematician, was born in Scot- 
 land; but neither the place nor time of his 
 birth are well known; nor have we any 
 memoirs of his life, except a letter from 
 the Chevalier de Ramsay, author of the 
 “ Travels of Cyrus/’ in a letter to Father 
 Castel, a Jesuit at Paris, and published in 
 the 44 Memoirs de Trevoux,” p. 109, as 
 follows : 44 True genius overcomes all the 
 disadvantages of birth, fortune, and edu- 
 cation ; of which Mr. Stone is a rare ex- 
 ample. Bom the son of a gardener of the 
 Duke of Argyle, he arrived at eight years 
 of age before he learned to read. By 
 chance a servant having taught young 
 Stone the letters of the alphabet, there 
 needed nothing more to discover and ex- 
 pand his genius. He applied himself to 
 study, and he arrived at the knowledge of 
 the most sublime geometry and analysis 
 without a conductor, without any other 
 guide but pure genius. 
 
 At eighteen years of age he had made 
 these considerable advances without being 
 known, and without knowing himself the 
 prodigies of his acquisition. The Duke of 
 Argyle, who joined to his military talents 
 a general knowledge of every science that 
 adorns the mind of a man of his rank, 
 walking one day in his garden, saw lying 
 on the grass a Latin copy of Sir Isaac 
 Newton’s celebrated 44 Principia.” He 
 called some one to him to take and carry 
 it back to his library. Our young gar- 
 dener told him that the book belonged to 
 him. 4 To you!’ replied the Duke. 1 Do 
 you understand geometry, Latin,' Newton?” 
 4 1 know a little of them,’ replied the young 
 man, with an air of simplicity arising from 
 a profound ignorance of his own know- 
 ledge and talents. The Duke was sur- 
 prised ; and having a taste for the sci- 
 ences, he entered into conversation with 
 the young mathematician : he asked him 
 several questions, and was astonished at 
 the force, the accuracy, and the candour 
 of his answers. 4 But how,’ said the Duke, 
 
 4 came you by the knowledge of all these 
 things?’ 4 Stone replied, 4 A servant 
 taught me, ten years since, to read : does 
 one need to know any thing more than the 
 twenty-four letters in order to learn every 
 thing that one wishes ? ’ The Duke's cu- 
 riosity redoubled; he sat down upon a 
 bank, and requested a detail of all his 
 proceedings in becoming so learned. 4 I 
 first learned to read,’ said Stone: 4 the 
 masons were then at work upon your 
 house : I went near them one day, and I 
 saw that the architect used a rule, com- 
 
128 
 
 THE ARTISAN. 
 
 passes, and that he made calculations* 
 I enquired what might be the meaning 
 and use of these things; and I was in- 
 formed that there was a science called 
 arithmetic : 1 purchased a book of arith- 
 metic, and I learned it. I was told there 
 was another science called geometry : I 
 bought the books, and I learned geometry. 
 By reading I found that there were good 
 books on these two sciences in Latin: I 
 bought a dictionary, and I learned Latin. 
 
 I understood also that there were good 
 books of the same kind in French : I 
 
 bought a dictionary, and I learned French. 
 And this, my Lord, is what I have done : 
 it seems to me that we may learn every 
 thing when we know the twenty-four 
 letters of the alphabet.’ This account 
 charmed the Duke. He drew this won- 
 derful genius out of his obscurity; and he 
 provided him with an employment which 
 left him plenty of time to apply himself to 
 the sciences. He discovered in him also 
 the same genius for music, for painting, 
 for architecture, for all the sciences which 
 depend on calculations and proportions. 
 
 “ I have seen Mr. Stone. He is a man 
 of great simplicity. He is at present sen- 
 sible of his own knowledge ; but he is not 
 puffed up with it. He is possessed with a 
 pure and disinterested love for the mathe- 
 matics ; though he is not solicitous to pass 
 for a mathematician; vanity having no 
 part in the great labour he sustains to ex- 
 cel in that science. He despises fortune 
 also; and he has solicited me twenty 
 times to request the Duke to give him less 
 employment, which may not be worth the 
 half of that he now has, in order to be 
 more retired, and less taken off from his 
 favourite studies. He discovers some- 
 times, by methods of his own, truths 
 which others have discovered before him. 
 He is charmed to find on these occasions 
 that he is not a first inventor, and that 
 others have made a greater progress than 
 he thought. Far from being a plagiary, 
 he attributes ingenious solutions, which 
 he gives to certain problems, to the hints 
 which he has found in others, although 
 the connections is but very distant,” &c. 
 
 Mr. Stone was author and translator of 
 several useful works; viz. 1. “ A new 
 Mathematical Dictionary,” in 1 vol. 8vo. 
 first printed in 1726. 2. ei Fluxions,” in 
 
 1 vol. 8vo. 1730. The Direct Method is a 
 translation from the French of Hospital s 
 “ Analyse des Infiniments Petis ;” and the 
 Inverse Method was supplied by Stone 
 himself. 3. u The Elements of Euclid,” 
 in 2 vols. Svo. 1731. A neat and useful 
 edition of these Elements, with an account 
 of the life and writings of Euclid, and a 
 defence of his Elements against modern 
 objectors. Beside other smaller works. 
 Stone was a fellow of the Royal Society, 
 
 and had inserted in the “ Philosophical 
 Transactions,” (vol. xii. p. 218) an “ Ac- 
 count of two species of Lines of the third 
 Order, not mentioned by Sir Isaac Newton 
 or Mr. Stirling.” 
 
 SOLUTIONS OF QUESTIONS. 
 
 Quest. 64, answered by Mr. J. Hoarding. 
 
 Let C denote Charing Cross, and I 
 the India House, and m the place of 
 
 meeting; C ™ 1 put 
 
 a “ 20 min., b ~ 45 min., and x ~ the 
 minutes they travel before meeting. Then, 
 as the distances gone over with the same 
 uniform motion are to each other as the 
 times in which they are described, it will 
 be as C m : m I : : x (the time in which 
 John goes the distance Cm) : a (the time 
 in which he goes over m I. And, for the 
 same reason, as Cm : ml : : b (Peter’s 
 time in going the distance Cm) : x (the 
 time in which he goes the distance m 1.) 
 Consequently, as x is to a in the ratio of 
 Cratoml, and Ho a: also in the same 
 ratio, we have x : a : : b : x ; whence x ~ 
 sju~u~ 30. Then 30 + 20 n 50 min. 
 will be John’s, and 30 H- 45 ~ 75 min. 
 Peter’s time. 
 
 This question was also solved correctly 
 by Mr. Whitcombe, Teacher , Lothbury, 
 and Mr. John Stanley, Lambeth , and 
 the Proposer. We received another solu- 
 tion, but it was inaccurate. 
 
 Quest. 65, answered by Master Thomas 
 Morris ( the Proposer ). 
 
 m. Cist. m. what the two cocks 
 
 If 40 : 1 : : 1 : y w in fill 0 f the cis- 
 
 50 : 1 : : 1 : y tern j n a m inute. 
 
 m. Cist. m. what of the cistern, 
 
 If 100 : 3 :: 1 : ^ f the two cocks will 
 
 180 : 2 : : 1 : ^ y empty in a minute. 
 
 Then (^ + ^) — ( T §g + 9 ^) 205 - §00 — 
 
 the parts gained by the filling cocks in 
 a minute. 
 
 Therefore, if T ^g :1m. : : 1 ' : 4 h. 17 m. 
 8^ sec. the time the cistern will be filled. 
 
 This question was accurately answered 
 by Mr. J. Harding, but his solution was 
 too late for insertion ; it was also solved 
 by H. W. S., but the arrangement was not 
 so clear as the above. We likewise re- 
 ceived a solution signed Philip Minus; 
 but it was performed according to no rule, 
 and of course the result was erroneous. 
 
 QUESTION FOR SOLUTION. 
 
 Quest. 66, proposed by Mr. Whitcombe, 
 Teacher of Mathematics , Lothbury. 
 
 In a given semicircle to inscribe a paral- 
 lelogram that shall be the greatest pos- 
 sible ; and to give a geometrical demon- 
 stration. 
 
THE ARTISAN. 
 
 129 
 
 PERSPECTIVE. 
 
 To put a hall into perspective, with paved 
 floor , two ranges of pyramids , a range of 
 cylinders , a range of square solids, of the 
 same diameter and height with the cy- 
 linders ? and let the hall be lighted from 
 a large Gothic window in the end . 
 
 Suppose the hall to be 16 feet wide, 22 
 in length, and 14 feet in height. 
 
 Let A B in the following figure be the 
 ground line, and that the parts of the figure 
 may appear, as viewed from the different 
 heights of the eye. Let the height of the 
 eye, fig. 1, be 12 feet; and because the 
 base of the room, in breadth, is less than 
 6 inches, the figure must be viewed under 
 
 an angle less than 60 degrees. Let the 
 distance point be z, a distance greater than 
 what the equilateral triangle on the base 
 A B would ,give. Upon the ground line 
 A B, from any scale, suppose of one fourth 
 of an inch, set off 16 divisions, which can 
 represent 16 feet; draw from each of 
 these divisions to the point of sight i; 
 and A z to the distance point, cutting the 
 radial B i in b ; draw b a parallel to A B ; 
 then AB&a is a square of 16 feet; but 
 the length required was 22 feet. From 
 b, on the right line a b, set off 6 feet at b' ; 
 draw b'z cutting the radial B i in d ; draw 
 d c parallel to A B ; then A B d c is the di- 
 mensions, 16 feet by 22, as was required. 
 Through the points where the distance 
 lines b'z , Az, cuts the several radials, 
 draw right lines parallel to A B ; then 
 the whole floor will be divided into 352 
 square feet, which may represent the pave- 
 ment. To find the height of the roof, draw 
 Vol. II — No. 34. 
 
 A K perpendicular to A B, at the height 
 of 14 feet, through K draw K L equal and 
 parallel to A B ; draw the radials K i, 
 Li; from the points d, c , in the right line 
 d c , draw the perpendiculars c k, d l, cutting 
 the radials K i, L i , in the points k, l ; join 
 k l, then A K k c is one side of the room, 
 equal to its opposite side BLic; ABdc 
 is the floor, K L l k is the roof, and kcdl 
 is the end of the room fronting the observer. 
 
 2. To raise the pyramids. Let the base 
 be two feet square, and 5 feet distance ; 
 from the centre of the base, draw a line at 
 right angles to the ground line, and of 
 length equal to the height of the roof ; 
 and draw right lines from each angle of 
 the pyramid to the vertex. 
 
 To ascertain the point in which this 
 vertex shall touch the roof. Observe, 
 that the centre of the pyramid is one foot 
 from the ground line A B, and one foot 
 from A i , the ground line of the perpend U 
 l 
 
130 
 
 THE ARTISAN. 
 
 cular plane, which forms the side of the light, with a circular arch above, width 
 wall, therefore from the point K, upon the of the inside of 'the window 10 feet, the 
 line K L, set off K o, equal to one foot ; lower lintel of the window 2 feet above 
 draw the radial o i. and distance line o z. the floor. Let the thickness of the wall. 
 
 cutting the radial o i in v ; then v is the 
 point of the roof which the vertex of the 
 pyramid touches; and the radial ovi , 
 regulates the height and position of the 
 whole range. In the same manner, the 
 vetex on the other side may be found. Or, 
 from L set off Lo equal to K o; draw the 
 radial o i through v ; draw*;..'*? parallel to 
 K L, cutting oi in i/ ; then v is the place 
 of the vertex of the pyramid in the roof, 
 and the radial oi regulates the whole range 
 on that side. The distance the pyramids 
 are placed from one another, is at pleasure ; 
 in this example the distance is taken 5 
 feet. N.B. The side of pyramids of the 
 left hand, ought to have been light, as 
 those on the right hand are. 
 
 3. To draw the range of cylinders. Let 
 the diameter of each be 1 foot, the height 
 2 feet, the distance from the base of the 
 pyramid 3 feet, and their distance from 
 one another 8 feet. 
 
 To regulate the height of the cylinder. 
 Upon the perpendicular A K set off A P 
 equal to 2 feet; draw the radials Pi, 
 which regulates all objects of that height, 
 from the station of the observer, to the point 
 of sight. 
 
 From P draw the indefinite right line 
 P p parallel to the ground line A B ; at 
 the points 1, 1, of the perspective square, 
 draw the right lines 1 .2, perpendicular to 
 the ground line, and cutting the indefi- 
 nite right line Pp in .2 2 ; in the perspec- 
 tive squares at 1*1,2, 2, inscribe the per- 
 spective circles, by prob. 12, and join their 
 diameters, which gives the cylinder re- 
 quired. 
 
 To find the height of the second cylinder 
 in the range, whose base is the side of the 
 square 3. .3; produce 3.3 to the radial A i, 
 cutting it in q ; draw q r parallel to A P, 
 cutting the radial P i in r ; through r draw 
 the indefinite right line rr parallel to A B ; 
 from 3.3, draw right lines perpendicular to 
 the ground line, to the height of r r ; form 
 the square, inscribe the circle, and join the 
 diameters, as in the last. In the same 
 manner, from each of the bases of the re- 
 maining cylinders in the range; produce 
 their bases to the radials A i ; draw lines 
 parallel to A p, where these cut the pa- 
 rallel P i, draw lines parallel to the ground 
 line, gives the respective heights of 2 feet. 
 
 After the above description, an inspec- 
 tion of the square figures will be sufficient, 
 as the squares are described in the same 
 manner as those in which the cylinder 
 were inscribed ; and their heights are ob- 
 tained in the same manner. 
 
 4. To form the Gothic window in a front 
 view, 7 feet by 12, for the opening of the 
 
 from the inside to the frame of the win- 
 dow, be 3 feet, and from thence to the out- 
 side of the wall be 1 foot. Set off’ 3 feet 
 for the thickness of the wall to the inside 
 of the frame, in the same manner as the 
 floor was extended. Tf it is to be open from 
 the floor upwards, upon the ground line 
 c d set off d s equal to 3 feet, or B S upon 
 the ground line ; draw the radial S i cutting 
 dc in s ; draw s z cutting the radial d i in 
 g ; draw g g parallel to d c. And because 
 the window is to be 10 feet wide within, 
 set off the distance of the inner corner of 
 the window from B, upon the ground line, 
 which, in this example, is 3 feet at S ; but 
 if more or less, another letter and distance 
 must be taken ; and the window being 7 
 feet wide at the glass frame, measure off 
 1| from S to t, and 7 feet from t to l, and If 
 feet from l to x ; draw the radial ti cutting 
 the line ggin t ; li cutting gg in u; xi 
 cutting gg in x ; join st, xu. Draw the 
 right lines s s, th,u u, xx, perpendicular 
 to the ground line, and extending to the 
 height of the impost, which cannot in this 
 figure exceed 7 or 8 feet, as the height of 
 the room is only 14 feet. 
 
 But if below the window is to be solid 
 wall to the height of 2 feet from the floor, 
 draw c y parallel to A P, cutting the radial 
 Pi in y ; draw y y parallel to c d ; from 
 the point in which y y cuts the radial s i, 
 draw to the distance point, cutting the 
 radial Bi in 3; draw the right line 3-3 
 parallel to yy ; then the right line 3-3 
 gives the lower part of the frame of the 
 window on the inside ; and being below 
 the eye, the sole of the window without 
 will likewise be in view. 
 
 The height of the room being only 14 
 feet, the height of the spring of the arch 
 cannot exceed 8 feet ; but to allow greater 
 scope for the arch stone, part of the roof 
 is formed a cove. 
 
 At the height of the impost, which is, by 
 the rules of architecture, one eighth part 
 of the opening, and its projection from one 
 third to four ninths of its height, according 
 to the order to which it belongs. With a 
 radius of 5 feet describe a semicircle, 
 meeting the impost in x..s; and with a 
 radius of G feet for the architrave, describe 
 the outer semicircle. Let this arch be di- 
 vided as in the figure, and the radii of the 
 architrave directed to the centre of the 
 semicircle. With the radius of 3§ feet, 
 describe the inner semicircle, meeting the 
 impost in u.Ji. Form the inner part of the 
 window, by drawing radials from each of 
 the divisions, on the corner of the archi- 
 trave, to the point of sight, both in the 
 plain and arched part of the window. 
 
THE ARTISAN. 
 
 131 
 
 The window being a front view, the 
 panes are at equal distances, and are 
 formed by dividing the base according to 
 the number of panes intended ; the dif- 
 ferent heights are measured off upon the 
 perpendicular A K, from the scale as laid 
 down upon the ground line. The form of 
 the bars are regulated, as to their rise 
 above the glass, or the depth of the glass 
 below them, in the same manner as the 
 depth of the window ; but being here so 
 small, they may be formed by the hand, 
 and regulated hy the eye of the artist. 
 
 The Gothic arches are described accord- 
 ing to the number of the panes they con- 
 tain, with a radius of 3| feet from the centre 
 1, 2, &c. on each side. 
 
 Observe.— That the height being taken 
 off, upon the perpendicular A K, from the 
 same scale upon which the other parts of 
 the figure were measured ; A P, in this 
 example, is 2 feet, and any line bounded by 
 the radials A i, P i, drawn parallel to A P, 
 is of the same measure with A P. There- 
 fore, to obtain the height of any object, 
 that stands upon the plane AB dc, and 
 from dc continued to the point of sight: 
 as, the object standing upon 3-3, the line 
 3 ..q drawn from the base 3-3 to q, in the 
 radial A i; and from the point of section 
 q, the right line q r, be drawn perpendicu- 
 lar to the ground line, cutting P i in r ; 
 then r q is the height of the object at that 
 distance from the ground line. In the same 
 manner c y is the given height at its dis- 
 tance from the ground line, or from the 
 point of sight. 
 
 And, if the object is nearer the observer 
 than the ground line A B, the radials, A i, 
 P i, being produced, then the line drawn 
 through the base of the object parallel to 
 the ground line, till it cut A i ; the per- 
 pendicular raised from that point in which 
 it cuts the radial P 2 , is the height of the 
 object; which will be greater than AP, 
 and the object will appear of greater mag- 
 nitude than if placed upon A B, in the re- 
 ciprocal proportion of its distance from the 
 observer ; or, in the direct proportion of its 
 distance from the point of sight. 
 
 For, because the triangles AiP, qir , 
 ciy , have their sides q r , and c y, each pa- 
 rallel to AP; and have the angle at i 
 common, the triangles are similar; and the 
 perpendiculars AP, q r, cy , are to one 
 another in the direct proportion of the side 
 2 c, iq, and d i, their respective distances 
 from i ; or, in the reciprocal proportion of 
 their several distances from the station of 
 the observer ; and the same proportions 
 will hold, if the object is nearer to the ob- 
 server than the ground line A B. 
 
 OF MAGNETISM. 
 
 The theory of magnetism, bearing a 
 strong resemblance to that of electricity, 
 naturally falls to be considered after it. 
 We shall, therefore, devote a few pages to 
 the consideration of this interesting sub- 
 ject, having now finished that of electri- 
 city. 
 
 We have seen that the electric fluid not 
 only exerts attractions and repulsions, and 
 causes a peculiar distribution of neigh- 
 bouring portions of a fluid similar to itself, 
 but we have also seen it excited in one 
 body and transferred to another, in such a 
 manner as to be perceptible to the senses, 
 or at least to cause sensible effects in its 
 passage. The attraction and repulsion, 
 and the peculiar distribution of the neigh- 
 bouring fluid, are found in the phenomena 
 of magnetism ; but we do not perceive that 
 there is ever any actual excitation, or any 
 perceptible transfer of the magnetic fluid 
 from one body to another distinct body ; 
 and it has also this striking peculiarity, 
 that metallic iron is very nearly, if not 
 absolutely, the only substance capable of 
 exhibiting any indications of its presence 
 or activity. 
 
 In order to explain the phenomena of 
 magnetism, the particles of a fluid are sup- 
 posed to repel each other, and to attract 
 the particles of metallic iron with equal 
 forces, diminishing as the square of the 
 distance increases ; and the particles of 
 such iron must also be imagined to repel 
 each other in a similar manner. Iron and 
 steel, when soft, are conductors of the mag- 
 netic fluid, and become less and less per- 
 vious to it as their hardness increases. 
 
 A strong degree of heat appears from 
 the experiments of Gilbert and of Mr. 
 Cavallo, to destroy completely all mag- 
 netic action. 
 
 It is perfectly certain that magnetic 
 effects are produced by quantities of iron 
 incapable of being detected, either by 
 their weight or by any chemical tests. 
 Mr. Cavello found that a few particles of 
 steel, adhering to a hone on which the 
 point of a needle was slightly rubbed, 
 imparted to it magnetic properties; and 
 Mr. Coulomb has observed, “ that there 
 are scarcely any bodies in nature which 
 do not exhibit some marks of being sub- 
 jected to the influence of magnetism, 
 although its force is always proportional 
 to the quantity of iron which they contain, 
 as far as that quantity can be ascertained: 
 a single grain being sufficient to make 20 
 pounds of another metal sensibly magnetic. 
 A combination with a large portion of 
 oxygen, deprives iron of the whole or the 
 greater part of its magnetic properties ; 
 finery cinder is still considerably mag- 
 netic, but the more perfect oxides and the 
 I 2 
 
132 
 
 THE ARTISAN. 
 
 salts of iron only in a slight degree ; it is 
 also said that antimony renders iron in- 
 capable of being attracted by the magnet. 
 Nickel, when freed from arsenic and from 
 cobalt, is decidedly magnetic, and the 
 more so as it contains less iron. 
 
 The aurora borealis is certainly in some 
 measure a magnetical phenomenon ; and if 
 iron were the only substance capable 
 of exhibiting magnetic effects, it would 
 follow that some ferruginous particles 
 must exist in the upper regions of the 
 atmosphere. The light usually attending 
 this magnetic meteor may possibly be de- 
 rived from electricity, which may be the 
 immediate cause of a change of the distri- 
 bution of the magnetic fluid contained in 
 the ferruginous vapours, that are imagined 
 to float in the air. 
 
 We are still less capable of distinguish- 
 ing with certainty in magnetism than in 
 electricity, a positive from a negative 
 -state, or a real redundancy of the fluid 
 from a deficiency. The north pole of a 
 magnet may be considered as the part in 
 which the magnetic fluid is either redund- 
 ant or deficient, provided that the south 
 pole be understood in a contrary sense: 
 thus, if the north pole of a magnet be sup- 
 posed to be positively charged, the south 
 pole must be imagined to be negative ; and 
 in hard iron or steel, these poles may be 
 considered as unchangeable. 
 
 A north pole, therefore, always repels a 
 north pole, and attracts a south pole. And 
 in a neutral piece of soft iron, near to the 
 north pole of a magnet, the fluid becomes 
 so distributed by induction, as to form a 
 temporary south pole next to the magnet, 
 and the whole piece is of course attracted, 
 from the greater proximity of the attract- 
 ing pole. If the bar is sufficiently soft, 
 and not too long, the remoter end becomes 
 a north pole, and the whole bar a perfect 
 temporary magnet. But when the bar is 
 of hard steel, the state of induction is im- 
 perfect, from the resistance opposed to the 
 motion of the fluid ; hence the attraction 
 is less powerful, and an opposite pole is 
 formed, at a certain distance, within the 
 bar ; and beyond this another pole, similar 
 to the first, the alternation being some- 
 times repeated more than once. 
 
 The polarity of magnets, or their dispo- 
 sition to assume a certain direction, is of 
 still greater importance than their attrac- 
 tive power. If a small magnet, or simply 
 a soft wire, be poised on a centre, it will 
 arrange itself in such a direction, as will 
 produce an equilibrium of the attractions 
 and repulsions of the poles of a larger 
 magnet ; being a tangent to a certain oval 
 figure passing through those poles* of 
 which the properties have been calculated 
 by various mathematicians. 
 
 The same effect is observable in iron 
 
 filings placed near a magnet, and they ad- 
 here to each other in curved lines, by vir- 
 tue of their induced magnetism, the north 
 pole of each particle being attached to the 
 south pole of the particle next it. This 
 arrangement is represented by the follow- 
 ing figure, and may be actually produced, 
 
 by placing the filings either on mercury, 
 or on any surface that can be agitated ; it 
 may also be imitated by strewing powder 
 on a plate of glass, supported by two balls, 
 which are contrarily electrified. 
 
 The polarity of a needle may often be 
 observed, when it exhibits no sensible at- 
 traction or repulsion as a whole ; and this 
 may easily be understood by considering, 
 that when one end of a needle is repelled 
 from a given point, and the other is 
 attracted towards it, the two forces, if 
 equal, will tend to turn it round its centre, 
 but will wholly destroy each other’s effects, 
 with respect to any progressive motion of 
 the whole needle. Thus, when the end of 
 a magnet is placed under a surface on 
 which iron filings are spread, and the sur- 
 face is shaken, so as to leave the particles 
 for a moment in the air, they are not drawn 
 sensibly towards the magnet, but their 
 ends, which are nearest to the point over 
 the magnet, are turned a little downwards, 
 so that they strike the paper further and 
 further from the magnet, and then fall 
 outwards, as if they were repelled by it. 
 
 The magnets, which we have hitherto 
 considered, are such as have a simple and 
 well determined form ; but the great com- 
 pound magnet, which directs the mariner’s 
 compass, and which appears to consist 
 principally of the metallic and slightly 
 oxidized iron, contained in the internal 
 parts of the earth, is probably of a far more 
 intricate structure, and we can only judge 
 of its nature, from the various phenomena 
 derived from its influence. 
 
 The accumulation and the deficiency of 
 the magnetic fluid, which determine the 
 place of the poles of this magnet, are pro- 
 bably in fact considerably diffused, but 
 they may generally be imagined, without 
 much error in the result, to centre in two 
 points, one of them nearer to the north 
 pole of the earth, the other to the south 
 pole. In consequence of their attractions 
 and repulsions, a needle, whether pre- 
 viously magnetic or not, assumes always, 
 
THE ARTISAN. 
 
 1331 
 
 if freely poised, the direction necessary 
 for its equilibrium ; which, in various parts 
 of the globe, is variously inclined to the 
 meridian and to the horizon. Hence 
 arises the use of the compass in naviga- 
 tion and surveying; for a needle (which is 
 poised with the liberty of a horizontal 
 motion) always assumes the direction of 
 the magnetic meridian, which, for a cer- 
 tain time, remains almost invariable for the 
 same place ; and as the true meridian can 
 easily be determined, the variation is thus 
 ascertained. 
 
 Though the dipping needle is only 
 moveable in a vertical plane, yet it evinces 
 a similar property to that of the horizontal 
 needle; for when the vertical plane in 
 which it is at liberty to move, is placed in 
 the magnetic meridian, the needle acquires 
 an inclination to the horizon, which varies 
 according to the place with respect to the 
 magnetic poles. The dip of the north pole 
 of the needle in the neighbourhood of Lon- 
 don, is at present about 72 degrees- 
 
 The following figure represents the dip- 
 ping needle. 
 
 The piece A B is brought into such a 
 situation, that the line drawn on it coin- 
 cides with the middle of the vibrations of 
 the needle. The position of the needle 
 may be changed, either by turning the 
 stand half round, or by turning the needle 
 within the stand. 
 
 A bar of soft iron, placed in the situation 
 of the dipping needle, acquires from the 
 earth a temporary state of magnetism, 
 which may be reversed at pleasure by re- 
 versing its direction ; but bars of iron, 
 which have remained long in or near this 
 direction, assume a permanent polarity; 
 for iron, even when it has been at first 
 quite soft, becomes in time a little harder. 
 A natural magnet, or loadstone, is no more 
 than a heavy iron ore, which, in the' course 
 of ages, has acquired a strong polarity 
 from the great primitive magnet. It must 
 have lain in some degree detached, and 
 must possess but little conducting power, 
 in order to have received and to retain its 
 magnetism. 
 
 We cannot, from any assumed situation 
 of two or more magnetic poles, calculate 
 the true position of the needle for all 
 places ; and even in the same place, its 
 direction is observed to change in the 
 course of years, according to a law which 
 has never yet been generally determined, 
 although the variation which has been ob- 
 served at any one place, since the dis- 
 covery of the compass, may perhaps be 
 comprehended in some very intricate ex- 
 pressions ; but the less dependence can be 
 placed on any calculations of this kind, as 
 there is reason to think that the change 
 depends rather on a chemical than on phy- 
 sical causes. Dr. Halley, indeed, con- 
 jectured, that the earth contained a nuc- 
 leus, or seperate sphere, revolving freely 
 within it, or rather floating in a fluid con- 
 tained in the intermediate space, and 
 causing the variation of the magnetic me- 
 ridian ; and others have attributed the 
 effect to the motions of the celestial bodies: 
 but in either case, the changes produced 
 would have been much more regular and 
 universal than those which have been ac- 
 tually observed. Temporary changes of 
 the terrestrial magnetism, have certainly 
 been sometimes occasioned by other causes ; 
 such causes are, therefore, most likely to 
 be concerned in the more permanent 
 effects. Thus, the eruption of Mount 
 Hecla was found to derange the position 
 of the needle considerably ; the aurora 
 borealis has been observed to cause its 
 north pole to move six or seven degrees to 
 the westward of its usual position ; and a 
 still more remarkable change occurs con- 
 tinually in the diurnal variation. 
 
 The line of no variation passed in 1657 
 through London, and in 1666 through 
 Paris: its northern extremity appears to 
 have moved continually eastwards, and 
 its southern parts westwards : and it now 
 passes through the middle of Asia. The 
 opposite portion seems to have moved more 
 uniformly westwards; it now runs from 
 North America to the middle of the South 
 Atlantic. On the European side of these 
 lines, the declination is westerly ; on the 
 South American side, it is easterly. The 
 variation in London has been for several 
 years a little more than 25°. In the West 
 Indies it changes but slowly ; for instance, it 
 was 5° near the island of Barbadoes, from 
 1700 to 1756. 
 
 The art of making magnets consists in a 
 proper application of the attractions and 
 repulsions of the magnetic fluid, by means 
 of the different conducting powers of dif- 
 ferent kinds of iron and steel, to the pro- 
 duction and preservation of such a distri- 
 bution of the fluid in a magnet, as is the 
 best fitted to the exhibition of its peculiar 
 properties. 
 
 We may begin with any bar of iron that 
 
134 
 
 THE ARTISAN. 
 
 has long stood in a vertical position ; but 
 it is more common to employ an artificial 
 magnet of greater strength. When one 
 pole of such a magnet touches the end of a 
 bar of hard iron or steel ; that end assumes, 
 in some degree, the opposite character, 
 and the opposite end the same character : 
 but in drawing the pole along the bar, the 
 first end becomes neutral, and afterwards 
 has the opposite polarity; while the se- 
 cond end has its force at first a little in- 
 creased, then becomes neutral, and after- 
 wards is opposite to what it first was. 
 When the operation is repeated, the effect 
 is at first in some measure destroyed, and 
 it is difficult to understand why the repe- 
 tition adds materially to the inequality of 
 the distribution of the fluid ; but the fact 
 is certain, and the strength of the new 
 magnet is for some time increased at each 
 stroke, until it has acquired all that it is ca- 
 pable of receiving. Several magnets, made 
 in this manner, may be placed side by side, 
 and each of them being nearly equal in 
 strength to the first, the whole collection 
 will produce together a much stronger 
 effect ; and in this manner we may obtain 
 from a weak magnet others continually 
 stronger, until we arrive at the greatest 
 degree of polarity, of which the metal is 
 capable. It is, however, more usual to 
 employ the process called the double 
 touch : placing two magnets, with their 
 opposite poles near to each other, or the 
 opposite poles of a single magnet, bent 
 in the following form, 
 
 with the middle of the bar : the opposite 
 actions of these poles then conspire in 
 their effort to displace the magnetic fluid, 
 and the magnets having been drawn back- 
 wards and forwards repeatedly, in equal 
 number of times to and from each end of 
 the bar, with a considerable pressure, they 
 are at last withdrawn in the middle, in 
 order to keep the poles at equal distances. 
 
 CHUMISTHir. 
 
 OF NICKEL. 
 
 Hierne was the first person who men- 
 tioned the particular ore which contains 
 nickel, in a work on the art of discovering 
 metals, published in 1694. The ore was 
 named kupfernickel by the Germans, which 
 signifies false copper. Henckel considered 
 it as a species of cobalt, or arsenic mixed 
 with copper. Cramer referred it also to 
 the copper and arsenical ores, though he 
 did not obtain copper from it ; which is also 
 confessed by Henckel. 
 
 In its highest state of purity, it is of a 
 yellowish or reddish white, of variable 
 brilliancy and granulated texture. This 
 texture is lamellated only in the case of 
 impurity. 
 
 Its specific gravity, according to Richter, 
 after being melted, is 8 279; but when 
 hammered, it becomes 8’666. 
 
 It is malleable both cold and hot ; and 
 may without difficulty be hammered out 
 into plates not exceeding the hundredth 
 part of an inch in thickness. 
 
 It is attracted by the magnet at least as 
 strongly as iron. Like that metal, it may 
 be converted into a magnet; and in that 
 state points to the north, when freely sus- 
 pended, in the same manner as a common 
 magnetic needle. 
 
 There are three ores of nickel, very dis- 
 tinct and very easy to be distinguished ; 
 these are the sulphuret of nickel, ferrugi- 
 nous nickel, and native oxide of nickel. 
 
 Rinman also affirms, that nickel has 
 been found a native of Hesse ; it is heavy, 
 of a deep red, forming a kind of product 
 of the furnaces among the materials from 
 which nickel may extracted. It is con- 
 sidered as an alloy of cobalt and bismuth, 
 by the medium of nickel. 
 
 Nickel is very difficult to be oxidized by 
 the action of caloric and of the air. When 
 it is heated under a muffle, and constantly 
 agitated, it only assumes a dark colour. 
 However, by long exposure to moist and 
 cold air, it becomes covered with an ef- 
 florescence of a clear green colour, of a 
 very particular and distinct tinge. It is 
 this efflorescence which is found upon the 
 surface of the sulphurous ores of nickel, 
 the tinge of which being very remarkable 
 and very different from that of copper, 
 enables us to distinguish them with ease 
 and certainty. 
 
 The alloys of this metal are but very im- 
 perfectly known. 
 
 Mr. Hatchett melted a mixture of 11 parts 
 gold and one nickel, and obtained an alloy 
 of the colour of fine brass. It was brittle, 
 and broke with a coarse-grained earthy 
 fracture. The specific gravity of the gold 
 was 19- 172 ; of the nickel 7’S ; that of the 
 
THE ARTISAN. 
 
 135 
 
 alloy 17*068. The bulk of the metals before 
 fusion was 2792, after fusion 2812 ; hence 
 they suffered an expansion. Had their 
 bulk before fusion been 1000, after fusion 
 it would have become 1007. When the 
 proportion of nickel is diminished, and 
 copper substituted for it, the brittleness of 
 the alloy gradually diminishes, and its 
 colour approaches to that of gold. The 
 expansion, as was to be expected, in- 
 creases with the proportion of copper in- 
 troduced. 
 
 Nickel has hitherto been applied to 
 little or no use. It cannot, however, be 
 doubted that it may be employed with 
 great advantage in the manufacture of 
 enamels, glass, porcelain, and pottery. It 
 is even probable that it may be an ingre- 
 dient in the secret processes of some ma- 
 nufactures, as large portions of it are 
 frequently found with the druggests of 
 Paris, who procure it from Saxony only 
 in proportion to the demand which is 
 made for it. 
 
 OF CADMIUM. 
 
 Cadmium was first discovered by M. 
 Stromeyer, in the autumn of 1817, in car- 
 bonate of zinc, which he was examining in 
 Hanover. It has been since found in the 
 Derbyshire silicates of zinc. 
 
 The following is Dr. Wollaston’s pro- 
 cess of procuring cadmium. From the so- 
 lution of the salt of zinc supposed to con- 
 tain cadmium, precipitate all the other 
 metallic impurities by iron ; filter, and im- 
 merse a cylinder of zinc into the clear 
 solution. If cadmium be present it will 
 be thrown down in the metallic state, and 
 when redissolved in muriatic acid, will 
 exhibit its peculiar character on the appli- 
 cation of the proper tests. 
 
 The colour of cadmium is a fine white, 
 with a slight shade of blueish-grey, ap- 
 proaching much to that of tin, which it 
 resembles in lustre and susceptibility of 
 polish. Its texture is compact, and its 
 fracture hackly. It crystallizes easily in 
 octahedrons, and presents on its surface, 
 when cooling, the appearance of leaves of 
 fern. It is flexible, and yields readily to 
 the knife. It is harder and more tenacious 
 than tin ; and, like it, stains paper, or the 
 fingers. It is ductile and malleable, but 
 when long hammered, it scales off in dif- 
 ferent places. Its specific gravity, before 
 hammering, is 8-6, and when hammered, 
 it is 8-69. It melts, and is volatilized 
 under a red heat. Its vapour, which has 
 no smell, may be condensed in drops like 
 mercury, which, on congealing, present 
 distinct traces of crystallization. 
 
 Cadmium is as little altered by exposure 
 to the air as tin. When heated in the open 
 air, it burns like that metal, passing into a 
 smoke which falls and forms a very fixed 
 oxide, of a brownish-yellow colour. Ni- 
 
 tric acid readily dissolves it cold; dilute 
 sulphuric, muriatic, and even acetic acids 
 act feebly on it with the disengagement of 
 hydrogen. The solutions are colourless, 
 and are not precipitated by water. 
 
 Cadmium unites easily with most of the 
 metals, when heated along with them and 
 the air excluded ; but most of its alloys 
 are brittle and without colour. That of 
 copper and cadmium is white, with a slight 
 tinge of yellow. Its texture is composed 
 of very fine plates. A very small portion 
 of cadmium communicates a good deal of 
 brittleness to copper ; but at a strong heat 
 cadmium flies oft'. 
 
 Cadmium unites with several other me- 
 tals; particularly with cobalt, platinum, 
 and mercury. W ith the last metal it forms 
 an amalgam, the specific gravity of which 
 exceeds that of mercury itself. 
 
 OF ZINC. 
 
 It is believed that zinc was not known 
 to the ancients. Paracelsus is the first 
 Chemist who has treated of it, and who 
 gave it the name which it bears. Agricola 
 has since termed it contre-feyne, and Boyle 
 speltrum. Albertus Magnus, who died in 
 the year 1280, makes very distinct mention 
 of it; he knew that it was combustible and 
 inflammable, and that it coloured metals. 
 It appears that zinc has for a long period 
 back been extracted from its ores in the 
 East Indies, as was first discovered by 
 Jungius, in the year 1647. It was brought 
 from those parts under the name of tuten- 
 ague. Without being particularly ac- 
 quainted with it, and distinguishing it 
 accurately from other metals, the Greeks 
 seem also to have employed it, as it is said 
 to have constituted a part of the famous 
 Corinthian brass. 
 
 It is not known by what process the 
 Chinese obtain this metal, which they em- 
 ploy in a great number of alloys ; it is, 
 however, believed that they extract it by 
 distillation. Henckel asserted, in 1721, 
 in his Pyritologia, that zinc might be ex- 
 tracted from calamine. 
 
 Zinc is of a brilliant white colour, with 
 a shade of blue, and is composed of a num- 
 ber of thin plates adhering together. 
 When this metal is rubbed for some time 
 between the fingers, they acquire a pecu- 
 liar taste, and emit a very perceptible 
 smell. 
 
 When rubbed upon the fingers, it tinges 
 them of a black colour. The specific gra- 
 vity of melted zinc varies from 6*861 to 
 7*1; the lightest being esteemed the purest. 
 When hammered it becomes as high as 
 7*1908. 
 
 This metal forms, as it were, the limit 
 between the brittle and the malleable 
 metals. When struck with a hammer it 
 does not break, but yields, and becomes 
 
136 
 
 THE ARTISAN. 
 
 somewhat flatter ; and by a cautious and 
 equal pressure, it may be reduced to pretty 
 thin plates, which are supple and elastic, 
 but cannot be folded without breaking. 
 This property of zinc was first ascertained 
 by Mr. Sage. When heated somewhat 
 above 212°, it becomes very malleable. It 
 may be beat at pleasure without breaking, 
 and hammered out into thin plates. When 
 carefully annealed, it may be passed 
 through rollers. It may also be very 
 readily turned on the lathe. When heated 
 to about 400°, it becomes so brittle, that it 
 may be reduced to powder in a mortar. 
 
 Jt possesses a certain degree of ductility, 
 and may with care be drawn out into wire. 
 Its tenacity, from the experiments of Mus- 
 chenbroeck, is such, that a wire, whose 
 diameter is equal to -/ 0 th of an inch, is ca- 
 pable of supporting a weight of about 
 26 lbs. 
 
 When heated to the temperature of about 
 680®, it melts ; and if the heat be increased, 
 it evaporates, and may be easily distilled 
 over in close vessels. When allowed to 
 cool slowly, it crystallizes in small bundles 
 of quadrangular prisms, disposed in all 
 directions. If they are exposed to the 
 air while hot, they assume a blue change- 
 able colour. 
 
 Zinc is applied to uses no less numerous 
 than important in many of the arts. It 
 forms a part of a number of hard and 
 white alloys. It is particularly employed 
 in the fabrication of tombac and brass. 
 The eastern nations, and especially the 
 Chinese, make use of it, as has already 
 been observed, much more frequently than 
 the Europeans; perhaps because they 
 possess it in greater abundance than we 
 do, and perhaps because they are better 
 acquainted with its useful properties. 
 
 Zinc and its chemical preparations have 
 already been applied to medicinal pur- 
 poses. Its property of conducting so 
 great a degree of galvanism, may hereafter 
 render it much more valuable to the heal- 
 ing art. 
 
 OF BISMUTH. 
 
 Bismuth is of a reddish white colour, 
 and almost destitute both of taste and 
 smell. It is composed of broad brilliant 
 plates adhering to each other. The figure 
 of its particles, according to Haiiy, is an 
 octahedron, or two four-sided pyramids, 
 applied base to base. 
 
 Its specific gravity is 9-822 ; but when 
 hammered cautiously, its density, as Mus- 
 chenbroeck ascertained, is considerably 
 increased. It is not therefore very brittle; 
 it breaks however, when struck smartly 
 by a hammer, and consequently is not 
 malleable. Neither can it be drawn out 
 into wire. Its tenacity, from the trials of 
 Muschenbroeck, appears to be such, that 
 
 a rod one-tenth of an inch in diameter, is 
 capable of sustaining a weight of nearly 
 29 lbs. 
 
 When heated to the temperature of 476°, 
 it melts; and if the heat be much in- 
 creased, it evaporates, and may be dis- 
 tilled over in close vessels. When allowed 
 to cool slowly, and when the liquid 
 metal is withdrawn as soon as the surface 
 congeals, it crystallizes in parallelopipeds, 
 which cross each other at right angles. 
 
 When exposed to the air, it soon loses 
 its lustre, but scarcely undergoes any 
 other change. It is not altered when kept 
 under water. 
 
 Bismuth is alloyed with several metals, 
 in order to give them hardness, rigidity, 
 or consistence ; it is particularly useful to 
 the pewterers, and all those who employ 
 white and hard alloys. It is generally 
 believed that it acts upon the animal eco- 
 nomy in the same manner as lead, though 
 this opinion is yet supported by no deci- 
 sive facts. 
 
 The utility of its oxides is very con- 
 siderable. It is employed in this form by 
 the manufacturers of porcelain in the pre- 
 paration of some yellow enamels ; it is 
 mixed with other oxides, in order to tinge 
 the colour of glazes and paintings. It is 
 sometimes used in the manufacture of co- 
 loured glass, and to give a yellow tinge 
 approaching to green. The white paint or 
 focus made from the oxide of bismuth is 
 often used by females to paint the face ; 
 but it injures the skin very much, and is 
 converted to a black by sulphuretted hy- 
 drogen gas. 
 
 OF ANTIMONY. 
 
 Antimony is of a greyish white colour,^ 
 and has a good deal of brilliancy. Its 
 texture is laminated, and exhibits plates 
 crossing each other in every direction, and 
 sometimes assuming the appearance of 
 imperfect crystals. Haiiy has with great 
 labour ascertained, that the primitive form 
 of these crystals is an octahedron, and 
 that the integrant particles of antimony 
 have the figure of tetrahedrons. 
 
 When rubbed upon the fingers, it com- 
 municates to them a peculiar taste and 
 smell. 
 
 Its specific gravity is, according to 
 Brisson, 6-702 ; according to Bergman, 
 6-86. Hatchett found it 6-712. 
 
 It is very brittle, and may be easily re- 
 duced in a mortar to a fine powder. Its 
 tenacity, from the experiments of Mus- 
 chenbroeck, appears to be such, that a rod 
 of -^th of an inch in diameter is capable of 
 supporting about 10 pounds weight. 
 
 When heated to 810° Fahrenheit, or just 
 to redness, it melts. If after this the heat 
 be increased, the metal evaporates. 
 
 Antimony is the base of the alloy which 
 
THE ARTISAN, 
 
 137 
 
 Is employed for casting printing-types, to 
 which it communicates hardness. It is 
 often made to enter, with lead and tin, 
 into rigid hard alloys, which are very use- 
 ful for a variety of purposes. The oxide 
 of antimony is used in the fabrication of 
 coloured glass, enamels, the glazing and 
 painting upon porcelain ; it is the basis of 
 the yellow, brownish, and orange colours, 
 which resemble the amethyst. It is mixed 
 with several other oxides, in order to pro- 
 duce a great variety of colours, the effects 
 of which have been observed, but their 
 causes have not yet been explained. 
 
 OF MANGANESE. 
 
 Manganese is distinguished from all 
 other metals by the following properties. 
 It is of a brilliant whiteness approaching 
 to grey, which is quickly altered in the air ; 
 its texture is granulated, without being so 
 fine and close as that of cobalt ; its frac- 
 ture is rough and unequal : its specific 
 gravity is 6-850 ; it holds, together with 
 iron, the first rank in the order of hard- 
 ness ; it is one of the most brittle metals ; 
 at the same time it is one of the most diffi- 
 cult to be fused. Guyton places it im- 
 mediately after platina, and determines it 
 at the 160th degree of Wedgwood’s pyro- 
 meter. We know neither its dilatability 
 by caloric, nor its conducting property. It 
 is frequently susceptible of being attracted 
 by the load-stone, especially when it is in 
 the state of powder, on account of the iron 
 which it contains, and which is almost as 
 difficult to be separated from it as from 
 nickel; it has no perceptible smell nor 
 taste; in communication with other metals, 
 it exerts the galvanic action upon the 
 nervous and muscular systems of animals ; 
 its colour is extremely variable. 
 
 Only one ore of manganese is as yet well 
 known; namely, its native oxide, which 
 some modern mineralogists, amongst others 
 Mr. Kirwan, announced as being com- 
 bined with carbonic acid. This oxide is 
 frequently mixed with iron, barytes, silex, 
 lime, &c. ; it varies also by its state of 
 oxidation, or by the proportion of oxygen 
 which it contains. 
 
 The ores of manganese are not worked 
 in the large way, not merely on account of 
 the refractory nature of these ores, but 
 more especially because it is of no utility in 
 its metallic state. The places where the 
 native oxide of manganese is found are 
 merely worked, in order to furnish the 
 manufactories of glass, bleaching, &c. with 
 this oxide, which is employed in them. 
 
 OF COBALT. 
 
 The ores of cobalt have been used in 
 different parts of Europe since the be- 
 ginning of the sixteenth century, to tinge 
 glass of a blue colour. But the nature of 
 
 cobalt was altogether unknown till it was 
 examined by Brandt in 1733. This cele- 
 brated Swedish Chemist obtained from it a 
 new metal, to which he gave the name of 
 cobalt. Lehmann published a very full 
 account of every thing relating to this 
 metal in 1761. 
 
 Cobalt is of a grey colour, with a shade 
 of red, and by no means brilliant. Its 
 texture varies according to the heat em- 
 ployed in fusing it. Sometimes it is com- 
 posed of plates, sometimes of grains, and 
 sometimes of small fibres adhering to each 
 other. It has scarcely any taste or smell. 
 
 Its specific gravity, according to Barg- 
 man and the School of Mines at Paris, is 
 7*7. Mr. Hatchett found a specimen 7*645. 
 
 It is brittle, and easily reduced to pow- 
 der; but if we believe Leonhardi, it is 
 somewhat malleable when red hot. Its 
 tenacity is unknown. 
 
 When heated to the temperature of 130° 
 Wedgewood, it melts ; but no heat which 
 we can produce is sufficient to cause it to 
 evaporate. When cooled slowly in a cru- 
 cible, if the vessel be inclined the moment 
 the surface of the metal congeals, it may 
 be obtained crystallized in irregular prisms. 
 
 Like iron, it is attracted by the magnet ; 
 and, from the experiments of Wenzel, it 
 appears that it may be converted into a 
 magnet precisely similar in its properties 
 to the common magnetic needle. 
 
 Cobalt is not used in its metallic form ; 
 but it is much employed to make blue 
 glasses or enamels. In the manufactories 
 of porcelain, much care is taken to have 
 the oxides of cobalt very pure and atte- 
 nuated. The grey ore is chosen well crys- 
 tallized ; this is roasted, and treated with 
 the nitric or muriatic acid, or otherwise it 
 is burned with nitrate of potash ; the oxide 
 is carefully washed with much water ; by 
 which treatment the oxide is obtained in 
 violet coloured powder, very fine and very 
 homogeneous, which affords the purest 
 and most beautiful blue when treated with 
 a vitreous flux. The elegant blue of the 
 porcelain of Sevres is of this nature. 
 
 OF TELLURIUM. 
 
 In the year 1797, Mr. Klaproth, of Ber- 
 lin, discovered a brittle whitish metal 
 among the ores of gold, brought from the 
 mountains of Transylvania, to which he 
 gave the name of Tellurium . 
 
 Pure tellurium is of a tin-white colour, 
 verging to lead-grey, with a high metallic 
 lustre ; of a foliated fracture, and very 
 brittle, so as to be easily pulverized. Its 
 specific gravity is 6*115 ; it melts before 
 ignition, requiring a little higher heat than 
 lead, and less than antimony ; and, accord- 
 ing to Gmelin, is as volatile as arsenic. 
 When cooled without agitation, its surface 
 has a crystallized appearance. Before 
 
138 
 
 THE ARTISAN. 
 
 the blow-pipe on charcoal, it burns with a 
 vivid blue light, greenish on the edges, 
 and is dissipated in greyish white vapours 
 of a pungent smell, which condense into a 
 white oxide. This oxide, heated on char- 
 coal, is reduced with a kind of explosion, 
 and soon again volatilized. Heated in a 
 glass retort, it fuses into a straw-coloured 
 striated mass. It appears to contain about 
 16 per cent, of oxygen. 
 
 Nothing decisive can yet be said con- 
 cerning the uses of this metal, on account 
 of its scarcity, and its recent discovery. 
 But should it be found in other ores, as 
 well as in those of Transylvania, it may 
 become of great utility in the arts, as 
 appears from its extreme fusibility, and its 
 slight adhesion to oxygen. 
 
 OF ARSENIC. 
 
 From the earliest period in which man- 
 kind worked the metallic ores, they must 
 have ascertained the volatility, the odour, 
 and the noxious effects of arsenic. Never- 
 theless, it remained unknown as a metal, 
 and was not placed among the semi-metals, 
 or brittle metallic bodies, till the beginning 
 of the eighteenth century ; when Paracel- 
 sus announced, that it might be obtained 
 white in the metallic form. Schroder, in 
 1649, mentioned a metal extracted from 
 orpiment and arsenic; and Lemery, in 
 1675, described a process, which is at 
 present used with success in the mixture 
 of fixed alkali and soap with this oxide, 
 to obtain what is called the regulus. The 
 ancients were acquainted with its oxide, 
 its yellow and red sulphuret, under the 
 name of arsenic, sandarach, and orpiment. 
 Mineralogists were, for a long time, con- 
 tent to range it among sulphurous matters, 
 and considered it only as a mineralizer of 
 the metals. Brandt, in 1733, and Mac- 
 quer, in 1746, showed that it is a true 
 metal, possessing properties highly cha- 
 racteristic, and different from those of 
 every other metal. 
 
 Arsenic has a blueish white colour not 
 unlike that of steel, and a good deal of 
 brilliancy. It has no sensible smell while 
 cold ; but when heated, it emits a strong 
 odour of garlic, which is verycharacteristic. 
 
 Its specific gravity is 8*31. 
 
 It is perhaps the most brittle of all the 
 metals, falling to pieces under a very mo- 
 derate blow of a hammer, and admitting of 
 being easily reduced to a very fine powder 
 in a mortar. 
 
 Its fusing point is not known, because it 
 is the most volatile of the metals, sub- 
 liming without melting when exposed in 
 close vessels to a heat of 356 u . 
 
 Arsenic, in the metallic form, is but little 
 employed, except in chemical laboratories, 
 where various experiments, researches, 
 and demonstrations are carried on. 
 
 As it is sometimes employed for killing 
 flies, great caution should be used in ap- 
 plying it to this purpose; for this sub- 
 stance, which is sold under the name of 
 testaceous cobalt, or fly-powder, is very 
 dangerous to animals of every description. 
 
 In some manufactories it is alloyed with 
 various metals, in order to whiten and 
 harden them ; the white copper is fre- 
 quently an alloy of this kind. But though 
 such alloys may be of use in some cases, 
 they ought never to be employed for the 
 preparation of food, drinks, or medicines. 
 
 OF CHROMIUM. 
 
 The analysis of a mineral made by other 
 means, and with more care than hitherto 
 had been applied to its examination, pre- 
 sented in December, 1797, to Vauquelin, 
 the discovery of this new metal. It is of a 
 white colour, inclining to grey, very hard, 
 brittle, and extremely difficult of fusion. 
 The small quantity which Vauquelin 
 could procure, did not permit him to 
 ascertain many of its properties. v 
 
 It is but little altered by exposure to 
 heat, and probably would be affected 
 neither by the action of air nor of water. 
 Acids act upon it but slowly ; nitric acid 
 gradually converts it into an oxide by 
 communicating oxygen. 
 
 It is hardly to be supposed that a metal 
 so recently discovered can have yet been 
 applied to any use, However, Vauquelin 
 has already observed, that its oxide may 
 be used in the fabrication of glass and 
 enamel ; and it may even, perhaps, have 
 been already employed, without suspect- 
 ing it, in the mixtures of the products of 
 minerals ill understood or analyzed, of 
 which it may form a part. 
 
 OF MOLYBDENUM. 
 
 The name of molybdena, which was 
 formerly synonymous with that of plum- 
 bago, or black lead, or the natural com- 
 bination of iron and charcoal, or carburet 
 of iron, is at present given to a brittle and 
 acidifiable metal, of which the ore was 
 confounded with that coally substance. 
 Many considered them as one and the 
 same substance, and they were sold under 
 the same denomination, till Scheele, in 
 1778, published, in the volumes of the 
 Stockholm Academy, a memoir, in which 
 he showed that the substance called 
 molybdena is very different from the car- 
 buret of iron, and contains a combination 
 of sulphur, with a substance which he 
 took for a peculiar acid. 
 
 Hitherto molybdenum has only been ob- 
 tained in small agglutinated metallic 
 grains ; the greatest heat of our furnaces 
 not being sufficient to melt it into a button. 
 Hence we are but imperfectly acquainted 
 with its properties. 
 
THE ARTISAN. 
 
 139 
 
 The specimens procured by Hielm were 
 of a yellowish white colour, and internally 
 greenish white. 
 
 Its specific gravity he found as high as 
 7*400. From his experiments, compared 
 with those of Klaproth and Buckolz, on 
 uranium, it seems probable that molybde- 
 num is even more refractory than that 
 metal. 
 
 When exposed to heat in an open vessel, 
 it gradually combines with oxygen, and is 
 converted into a white oxide, which is vo- 
 latilized in small brilliant needle-form crys- 
 tals. This oxide, having the properties of 
 an acid, is known by the name of molybdic 
 acid. 
 
 OF TUNGSTEN. 
 
 The name Tungsten, which signifies 
 heavy stone, was given by the Swedes to 
 a mineral, which Scheele found to contain 
 a peculiar metal, as he supposed, in the 
 state of an acid, united with lime. The 
 same metallic substance was afterwards 
 found by Don d’Elhuyart united with iron 
 and manganese in wolfram. 
 
 Tungsten is of a greyish white colour, 
 or rather like that of iron, and has a good 
 deal of brilliancy. 
 
 It is one of the hardest of the metals ; 
 for Vauquelin and Hecht could scarcely 
 make any impression upon it with a file. 
 It seems also to be brittle. Its specific 
 gravity, according to the D’Elhuyarts, is 
 17*6; according to Allen and Aiken, 17 22. 
 It is therefore the heaviest of the metals 
 after gold and platinum. 
 
 It requires for fusion a temperature at 
 least equal to 170° Wedgewood. It seems 
 to have the property of crystallizing on 
 cooling, like all the other metals ; for the 
 imperfect button procured by Vauquelin 
 and Hecht contained a great number of 
 small crystals. 
 
 Nothing has yet been observed respect- 
 ing the uses of a metal so little known or 
 examined as tungsten. No trial has yet 
 been made with regard to its useful pro- 
 perties ; and it is to be feared, that its re- 
 duction and fusion being difficult, will 
 render it so intractable as not to be used 
 but with great difficulty. 
 
 OF COLUMB1UM. 
 
 This metal was discovered by Mr. 
 Hatchett, in a mineral belonging to the 
 cabinet of the British Museum, supposed 
 to be brought from Massachusetts, in 
 North America. 
 
 Its lustre was glassy, and in some parts 
 slightly metallic. It was moderately hard, 
 but very brittle. By trituration it yielded 
 a powder of a dark chocolate brown, not 
 attracted by the magnet. Its specific gra- 
 vity, at the temperature of 65°, was 5-918. 
 
 OF SELENIUM. 
 
 In 1819 M. Berzelius extracted a new 
 elementary body from the pyrites Fahlun, 
 which, from its chemical properties, he 
 places between sulphur and tellurium, 
 though it has more properties in common 
 with the former than with the latter sub- 
 stance. It was obtained in exceedingly 
 small quantity from a large portion of 
 pyrites. 
 
 When it is fused it becomes solid, its 
 surface assumes a metallic brilliancy of a 
 deep brown colour. Its fracture is con- 
 choidal, vitreous, of the colour of lead, 
 and perfectly metallic. 
 
 OF OSMIUM. 
 
 This singular metal was discovered by 
 Mr. Tennant, about the year 1804, in the 
 ore of platina, combined with another me- 
 tallic substance, which received the name 
 of Iridium. 
 
 Osmium has a dark-grey or blue colour, 
 and the metallic lustre. When heated in 
 the open air, it evaporates with the usual 
 smell ; but in close vessels, when the ox- 
 idizement is prevented, it does not appear 
 in the least volatile. 
 
 When subjected to a strong white heat 
 in a charcoal crucible, it does not melt nor 
 undergo any apparent alteration. 
 
 It is not acted upon by any acid, not 
 even the nitro-muriatic, after exposure to 
 heat; but when heated with potash it 
 combines with that alkali, and forms with 
 it an orange-yellow solution. 
 
 OF RHODIUM. 
 
 This metal is of a white colour. Its specific 
 gravity seems somewhat to exceed 11. No 
 degree of heat hitherto applied is capable 
 of fusing it. It is, therefore, uncertain 
 whether it be malleable ; but as it forms 
 malleable alloys with the other metals, it 
 is probable that it would not be destitute 
 of malleability, if it could be fused into a 
 button. 
 
 OF IRIDIUM. 
 
 This metal was discovery by Mr. Smith- 
 son Tennant in 1803, in the ore of crude 
 platina. 
 
 The iridium which was thus obtained 
 was while, and could not be melted by 
 any heat Mr. Tenant could employ. Vau- 
 quelin considers it as brittle, and as even 
 occasioning the brittleness of platinum; 
 but as it has not been obtained in a metal- 
 lic button, and as it forms malleable alloys 
 with all metals tried, that property does 
 not seem to be sufficiently decided. 
 
 It resists the action of all acids, even 
 the nitro-muriatic acid. 
 
140 
 
 THE ARTISAN. 
 
 OF URANIUM. 
 
 This metal was discovered by Klaproth 
 in a mineral which contains uranium com- 
 bined with sulphur. 
 
 By treating the ores of the metal with 
 the nitric or nitro-muriatic acid, the oxide 
 will be dissolved, and may be precipitated 
 by the addition of a caustic alkali. It is 
 insoluble in water, and of a yellow colour; 
 but a strong heat renders it of a brownish 
 grey. 
 
 OF TITANIUM. 
 
 Titanium is obtained from a mineral 
 found in Hungary, called red schorl, or 
 titanite : and also in a substance from the 
 valley of Menachan, in Cornwall, termed 
 menachanite. It was in the latter sub- 
 stance that it was originally discovered by 
 Mr. Gregor, of Cornwall ; and its charac- 
 ters have since been more fully investigated 
 by Klaproth, Vauquelin, Hecht, Lovitz, 
 and Lampadius. 
 
 Its colour is that of copper, but deeper. 
 It has considerable lustre. It is brittle, 
 but in thin plates has considerable elas- 
 ticity. It is highly infusible. 
 
 When exposed to the air, it tarnishes, 
 and is easily oxidized by heat, assuming a 
 blue colour. It detonates when thrown 
 into red hot nitre. 
 
 OF CERIUM. 
 
 Cerium was discovered by Messrs. 
 Berzilius and Hisenger, of Stockholm, in 
 a mineral from Bastreas, in Sweden, to 
 which they gave the name of Cerit, and 
 which had been for some time before sup- 
 posed to be an ore of tungsten. This dis- 
 covery has since been confirmed by the ex- 
 periments of Vauquelin. 
 
 OF WODANIUM. 
 
 This is a new metal, recently discpvered 
 by Lampadius in the mineral called 
 Woodan pyrites. This metal has a bronze- 
 yellow colour, similar to that of cobalt 
 glance; and its specific gravity is 11*470. 
 It is malleable ; its fracture is hackly ; it 
 has the hardness of fluor spar; and is 
 strongly attracted by the magnet. 
 
 It is not tarnished by exposure to the 
 atmosphere at the common temperature; 
 but when heated, it is converted into a 
 black oxide. 
 
 ALKALINE AND EARTHY METALS. 
 
 The remaining substances contained in 
 the table of metals, at page 361, vol. i, are 
 the bases of the two fixed alkalies (Potash 
 and Soda,) and of the eleven substances at 
 present considered as earths. 
 
 The two first, Potassium and Sodium, as 
 well as Barium, and a few of the others, 
 were obtained by Sir H. Davy, by decom- 
 
 posing the Alkalies and Earths by gal- 
 vanic electricity; whilst the others are 
 merely considered as the metallic bases of 
 the respective earths whose names they 
 bear. 
 
 We are sorry that our limits will not 
 permit us to give a more detailed account 
 of these bodies. 
 
 ASTRONOMY. 
 
 OF THE QUANTITY OF MATTER IN THE SUN 
 AND PLANETS, AND THE FORCE OF GRA- 
 VITY AT THEIR SURFACES. 
 
 On first view, it almost appears impos- 
 sible to determine the respective masses of 
 the sun and planets, and to measure the 
 height from which bodies fall in a given 
 time, by the action of gravity at their sur- 
 faces. But the connection of facts with 
 each other, often leads to results which 
 appear inaccessible, when the principle on 
 which they depend is unknown. 
 
 It was, therefore, perfectly natural even 
 for astronomers to consider it impossible 
 to determine the intensity of gravity at the 
 surface of the planets, while the principle 
 of universal gravitation remained un- 
 known;* and it is just as natural for those 
 who are unacquainted with mathematics 
 and astronomy to consider the same thing 
 impossible, even although they have heard 
 of such a principle as universal gravita- 
 tion. We shall, therefore, state what has 
 been the result of the calculation of some 
 of the first-rate astronomers of the present 
 day on this curious and interesting subject. 
 
 From the fact that action is always 
 accompanied by re-action, astronomers 
 conclude, that gravitation among terres- 
 trial bodies is the mutual tendency of the 
 particles of matter to one another. And, 
 from analogy, they think it perfectly rea- 
 sonable to suppose, that this is true in all 
 cases; and that the force of gravitation 
 towards different bodies, the distance 
 being the same, is proportional to the quan- 
 tities of matter , or the masses of the bodies. 
 
 This supposition is the foundation of all 
 the calculations respecting the masses of 
 the planets ; and from it formulas have 
 been deduced, for calculating the relative 
 quantity of matter in such of the primary 
 planets as have satellites revolving round 
 them ; but the quantify of matter in those 
 that have no satellites, can only be guessed 
 at by the effect they produce in disturbing 
 the motions of the other planets .f 
 
 * It was this discovery which rendered it practica- 
 ble to measure the intensity of gravity at the sur- 
 faces of the planets. 
 
 •f The quantities of matter in any two primary 
 planets are direcly as the cubes of the mean distan- 
 ces at which their satellites revolve, and inversely 
 as the squares of their periodic times. 
 
THE ARTISAN, 
 
 141 
 
 The quantity of matter in the moon, 
 however, may be determined by compar- 
 ing its influence with that of the sun in 
 producing the tides, and the precession of 
 the equinoxes. By these means it has 
 been ascertained, that the mass of the moon 
 is about ^jth part of that of the earth. 
 And La Place, in his Mecanique Celeste , 
 has determined the quantity of matter in 
 each of the primary planets, from the 
 most exact data, to be as follows ~ 
 
 Quantity of matter in the Sun . 1 
 
 Mercury 
 
 
 
 2025810 
 
 Venus 
 The Earth 
 
 
 
 1 
 
 553157 
 
 32963(5 
 
 Mars . 
 
 
 
 T333o92 
 
 Jupiter 
 
 
 
 ToBT-09 
 
 Saturn 
 
 
 
 5339-3 
 
 Uranus* 
 
 
 
 T9303 
 
 The masses of the planets being known, 
 and their bulks being also known, their 
 densities are easily determined, for these 
 are proportional to the masses divided by 
 the bulks. 
 
 La Place, taking the mean density of 
 the sun as unity , finds the density of such 
 planets as have satellites to be as follows : 
 The Earth, 3*9395 ; Jupiter, 0*8601 ; Sa- 
 turn, 0*4951 ; Uranus, 1*1376. 
 
 Knowing the masses of the planets, and 
 their diameters, the force of gravity at 
 their surface may be determined ; for, sup- 
 posing them to be spherical, and to have 
 no rotation on their axis, the force with 
 which a body placed on their surface gra- 
 vitates to them, will be proportional to 
 their masses divided by the squares of 
 their diameters. From the masses of Ju- 
 piter and the Earth, La Place calculates 
 that a body which weighs one pound at 
 the earth’s equator, if carrried to Jupiter’s 
 equator would weigh 2f pounds, suppos- 
 ing these bodies to have no rotation, 
 and supposing the weights to be mea- 
 sured by the pressure exerted in the two 
 situations. If the same body were carried 
 to the surface of the sun, it would weigh 
 about 27§ pounds ; from which it follows, 
 that a heavy body would there descend 
 about 444 feet in the first second of time. 
 
 Although all the planets gravitate to the 
 sun, yet the centre of the sun is not the 
 centre of gravity of the whole solar system. 
 The centre of the sun is, however, never 
 distant from that point so much as his own 
 diameter, consequently the centre of gra- 
 vity of the whole system is always within 
 the body of the sun. But as this point and 
 the centre of the sun do not coincide ex- 
 
 * By adding these fractions together, it will be 
 found that the quantity of matter in all the planets 
 together is not ^tli part of the matter in the sun ! 
 
 actly, and as the gravitation of the planets 
 to the sun must be accompanied by the 
 gravitation of the sun to the planets, from 
 the quailty of action and re-action, it fol- 
 lows that the sun must have a motion in a 
 small orbit round the centre of gravity of 
 the whole system. The form of this orbit 
 is, however, very complicated, on account 
 of the disturbing forces of so many planets, 
 which are sometimes exerted toward one 
 side and sometimes toward another ; and 
 even unequally exerted on different sides 
 at the same time, according to the situation 
 of the planets in their orbits. 
 
 Thus we see the extraordinary and uni- 
 versal principle called gravitation, has not 
 only been the means of making us ac- 
 quainted with a great number of inequa- 
 lities in the motion of the heavenly bodies^ 
 which it would have been impossible to 
 have discovered by observation, but it has 
 furnished us with the means of subjecting 
 these motions to precise and certain rules. 
 
 The motion of the earth, which had ob- 
 tained the assent of astronomers, on ac- 
 count of the simplicity with which it ex- 
 plained the celestial phenomena, has re- 
 ceived a new confirmation, which has car- 
 ried it to the highest degree of evidence of 
 which physical science is susceptible. 
 Without the knowledge of this universal 
 principle, the ellipticity of the planetary 
 orbits ; the laws which the planets and 
 comets obey in their revolution round the 
 sun ; their secular and periodical inequa- 
 lities; the numberless inequalities of the 
 moon, and the satellites of Jupiter; the 
 precession of the equinoxes ; the nutation 
 of the earth’s axis; the motions of the 
 lunar axis ; and the ebbing and flowing 
 of the sea, would only be insulated facts,, 
 and unconnected phenomena. It is, there- 
 fore, a circumstance which can scarcely 
 be sufficiently admired, that all these phe- 
 nomena, which at first sight appear so un- 
 connected, should be explained by one 
 'principle — that of the mutual gravitation 
 of all bodies with forces directly as their 
 quantities of matter, and inversely as the 
 squares of their distances. 
 
 OF THE PRINCIPAL SYSTEMS OF ASTRO- 
 NOMY. 
 
 After the description which has been 
 given of the various phenomena of the 
 heavens, both as viewed with the naked 
 eye and the telescope, it may not be un- 
 necessary, nor unacceptable to the reader, 
 to give a short account of the principal 
 theories, or systems, which have been 
 formed at various periods to account for 
 some of these appearances, and particu- 
 
142 
 
 THE ARTISAN. 
 
 Jarly for the apparent motions of the celes- 
 tial bodies, 
 
 The explanation of the celestial motions 
 which naturally occurred to those who be- 
 gan the study of the heavens, was, that 
 the stars are so many luminous points 
 fixed in the surface of a sphere, having the 
 earth in its centre, and revolving on an 
 axis passing through that centre, in the 
 space of twenty-four hours. When it was 
 observed, that all the stars did not partake 
 of this diurnal motion in the same degree, 
 but that some were carried slowly towards 
 the east, and that their paths estimated in 
 that direction, after certain intervals of 
 time, returned into themselves, it was be- 
 lieved that they were fixed in the surfaces 
 of spheres, which revolved westward more 
 slowly than the sphere of the fixed stars. 
 The spheres were supposed transparent, 
 or made of some crystalline substance, and 
 from this arose the name of the crystal- 
 line spheres, by which they were distin- 
 guished. Though this system grew more 
 complicated, as the number and variety of 
 the apparent phenomena increased, yet it 
 was the system of Aristotle and Euodxus ; 
 and, with few exceptions, of all the phi- 
 losophers of antiquity.* 
 
 But when the business of observation 
 came to be regularly pursued, little was 
 said either of the fixed stars, or of the 
 crystalline spheres ; astronomers being 
 chiefly bent on ascertaining the laws or 
 general facts connected with the motions 
 of the planets. 
 
 To do this, however, without the intro- 
 duction of hypotheses, at this period, was 
 scarcely possible. The simplest and most 
 natural hypothesis was, that the planets 
 moved eastward in circles, at a uniform 
 rate. But when it was found that, instead 
 of moving uniformly to the eastward, 
 every one of them was subject to great 
 irregularity, the motion eastward becoming 
 slower, at certain periods, and at length 
 vanishing altogether, so that the planet be- 
 came stationary, and afterwards acquiring 
 a motion in the contrary direction, and 
 proceeded for a time to the westward, it 
 was far from obvious that all these ap- 
 pearances could be reconciled with the 
 idea of a uniform circular motion. 
 
 The solution of this difficulty is attri- 
 buted to Apollonius Pergaeus, one of the 
 most celebrated mathematicians of anti- 
 quity. He conceived that each planet 
 
 * Although it is said that Pythagoras taught that 
 the earth was a planet, and that the sun was fixed in 
 the centre of the planetary system ; that the apparent 
 revolution of the heavens was produced by the diur- 
 nal revolution of the earth; and that the apparent 
 annual motion of the sun was occasioned by the 
 earth moving round him like the other planets; yet 
 this doctrine was never taught publicly, and in a 
 very short time it was completely forgotten. 
 
 moved in a small circle, and that the cen- 
 tre of this small circle moved in the cir- 
 cumference of a large circle, which had 
 the earth for its centre. The first of these 
 circles was called the epicycle , and the 
 second the deferent; and the motion in the 
 circumference of each was supposed uni- 
 form. Lastly, it was conceived that* the 
 motion of the centre of the epicycle in the 
 circumference of the deferent, and like- 
 wise the motion of the planet in that of the 
 epicycle, were in opposite directions ; the 
 first being towards the east, and the se- 
 cond towards the west. In this way, the 
 change from progressive to retrograde, as 
 well as the intermediate stationary points, 
 were readily explained. 
 
 But, notwithstanding the accomplish- 
 ment of this important object, no regular 
 system of astronomy appears to have been 
 framed or taught by any individual till the 
 appearance of the celebrated Ptolemy, who 
 has always been reckoned the prince of 
 ancient astronomers, not so much on ac- 
 count of being the founder of the system 
 which goes by his name, as for the number 
 of observations which he made, and the 
 extent of his astronomical writings. 
 
 As we have already given an account of 
 this, as well as the Tychonic and Coperni- 
 can systems, at page 46, vol. i, we shall 
 conclude this subject by giving a short 
 description of the Cartesian system. 
 
 CARTESIAN SYSTEM. 
 
 The founder of this system, Rhhnfc Des 
 Cartes flourished about the beginning of 
 the 17th century. He supposed that every 
 thing in the universe was formed from very 
 minu te bodies, called atoms , which had been 
 floating in open space. To each atom he 
 attributed a motion on its axis; and he 
 also maintained that there was a general 
 motion of the whole universe round like a 
 voxtex, or whirpool. In the centre of this 
 vortex was the sun, with all the planets cir- 
 culating round him at different distances; 
 those that were nearer the sun circulating 
 faster than those at a greater distance, as 
 the most distant parts of a vortex or whirl- 
 pool are known to do. Besides this general 
 vortex, each of the planets had a particu- 
 lar vortex of its own, by which its satel- 
 lites, if it had any, were whirled round, 
 and any other body that came within its 
 reach. 
 
 This is the celebrated system of vortices, 
 invented by Des Cartes. The fabric, it 
 must be confessed, is raised with great art 
 and ingenuity, and is evidently the pro- 
 duce of a lively fancy and a fertile imagi- 
 nation. But then, it can be considered 
 only as a philosophical romance, which 
 amuses without instructing us ; and serves 
 
THE ARTISAN. 
 
 143 
 
 principally to shew that the most shining 
 abilities are frequently misemployed. 
 
 In this hypothesis, Des Cartes supposes 
 extension to constitute the essence of mat- 
 ter, and wholly neglects solidity , as well 
 as the inertia by which it resists any 
 change in its state of motion or rest, 
 which principally distinguishes body from 
 space ; and, consequently, the doctrine of 
 an universal plenum, deduced from this 
 definition, is founded upon false principles. 
 
 That there is such a thing as a vacuum 
 in nature, or a space void of body, may be 
 demonstrated from various experiments. 
 By means of the air-pump, we can so far 
 exhaust the air from a glass receiver, that 
 a piece of gold and a feather, let fall to- 
 gether, from the top of the vessel, shall 
 both descend equally swift, and come to 
 the bottom at the same time : which evi- 
 dently shews, that, the air being taken 
 away, there remains no other matter suffi- 
 cient to cause any sensible resistance, or 
 that in the least impedes or obstructs their 
 passage. 
 
 It was said by many of the ancient phi- 
 losophers, that nature abhors a vacuum ; 
 and by means of this dogma, and others of 
 a like nature, they attempted to prove and 
 illustrate the doctrine of an universal ple- 
 num, like that of Des Cartes. But this is 
 an assertion, unsupported by facts, and too 
 idle a notion to require any formal refuta- 
 tion : and in nearly the same predicament 
 are most of the other arguments which 
 have been used in defence of this doctrine. 
 They are all sufficiently exposed, not only 
 by the Torricilian experiment, and the 
 nature of pumps in general, but likewise 
 from the most obvious phenomena of the 
 constant and free motion of bodies, whe- 
 ther celestial or terrestrial, which come 
 continually under our inspection. 
 
 On the system of Des Cartes, and all 
 others that depend on the same principle, 
 we may remark, that if the planets be 
 carried round the sun in vortices, the 
 quantity of matter in the sun cannot affect 
 the velocity of the vortex, or the bodies 
 immersed in it; consequently the velocity 
 might be the same though there were no 
 central body whatsoever. The quantity of 
 matter in the sun, therefore, cannot have 
 the least effect in retaining the planets in 
 their orbits. But the quantity of matter 
 in the sun does affect the planet, and is a 
 material element in its gravitation towards 
 the centre of its orbit. It is therefore im- 
 possible that the action of a vortex, can 
 have any effect whatever upon that gravi- 
 tation. This argument is perfectly con- 
 clusive and fatal to the sysem of vortices. 
 But we may observe that this system owed 
 its downfal to another argument, equally 
 if not still more powerful ; viz. that when- 
 ever you suppose the vortex so arranged 
 
 that it will explain one of those great facts 
 in the planetary motions, known by the 
 name of Kepler’s Laws, it becomes quite 
 inconsistent with the rest. 
 
 The vortices of Des Cartes have, there- 
 fore, ceased to afford any satisfaction even 
 to the most superficial reasoner, and are 
 now only known in the history of opinions ; 
 in which they will ever furnish a most in- 
 structive chapter. 
 
 SOLUTIONS OF QUESTIONS. 
 
 Quest. 65* (page 112) answered by 
 J. M. Edney, Broad-street , Bloomsbury. 
 
 Let 4 x and 5 a: be the sums subscribed 
 by each lady. Then by the quest. 4:r) 2 -j- 
 (5 a;) 2 zz 69-5.9fg ZZ 69’29; that is, 41a: 2 
 zz 69 29, or x 2 zz 1*69, and x zz 1*3. 
 Hence 4 a: zz 5 2 zz £5 4s. ; and 5 a; ~ 
 6*5 zz £6 10s. the sums required. 
 
 This question was also correctly an- 
 swered by Mr. J. Harding, Mr. J. Whit- 
 combe, and by the Proposer. 
 
 Queit. 66, answered by Mr. J. Whit- 
 combe, Private Teacher of Mathematics , 
 Lothbury. 
 
 Let ADC denote the given semicircle. 
 
 D 
 
 and let D B divide it into two equal quad- 
 rants. Bisect the quadrantal arch D C in 
 F, by the radius B F ; draw F H parallel 
 to D B, and draw F E parallel to A C, also 
 E I parallel to D B and F H, and the thing 
 is done ; for I E F H is the parallelogram, 
 whose area is a maximum. 
 
 Demon. As the quadrantal arch DC is 
 bisected in F by the radius or diagonal 
 line B F, it is evident the angles F B H, 
 OBF, HFB, and BFO are equal, con- 
 sequently the rectangle BOFH is a 
 square: then per Simpson’s Geometry, 
 Theo. V, on Maxima and Minima, the tri- 
 angles B F H and BFO are each of them 
 a maximum, because they are each Isoce- 
 les : consequently the rectangle BOFH 
 is also a maximum. It is also evident that 
 the rectangle BOFH is half the parallel- 
 ogram I EF H ; hence it is manifest that 
 this parallelogram is also a maximum. 
 
 * By mistake this question was numbered the 
 same as one at page 96. 
 
144 
 
 THE ARTISAN. 
 
 The Editor takes this opportunity of thanking his Mathematical Correspondents for 
 their respective Communications during the progress of the Work ; and is happy to 
 find that his labours and discrimination, in this department at least, have given satis- 
 faction to all. 
 
 He also thinks it proper to inform them, as the Work is now concluded, that the 
 Solutions to the firstwine Questions, with the exception of the 6th and7th, were supplied 
 by himself, as well as the 14th, 19th, 23d, 24th, 40th, 43d, 52d, 56th, 59th, and 62d. 
 
 THE END,