im 4 A COMPENDIUM NATURAL PHILOSOPHY ADAPTED TO THE USE Or THE GENERAL READER, AND OF SCHOOLS AND ACADEMIES. BY DENISON OLMSTED, A. M. PIOFMSOR Or MATHEMATICS AND NATURAL PHILOSOPHY IN YALE COLLEGE. NEW HAVEN: PUBLISHED AND SOLD BY HEZEKIAH HOWE & CO. Sold also by COLLINS & HANNAY, New York; CARTER, HENDEE & Co., Bo$- ton; TRUMAN, SMITH & Co., Cincinnati. 1833. ' Entered according to Act of Congress, in the year 1833, by DENISON OLMSTED, in the Clerk's office of the District Court of Connecticut. Printed by Hezekiah Howe & Co. ' ' PREFACE. IT is the object of this work, to present to the general reader, and to the more advanced pupils in our Schools and Academies, the most important PRACTICAL RESULTS of Natural Philosophy, (without the demonstrations,) in as condensed and intelligible a form as possible, and to exemplify them by a great variety of applications to the phe- nomena both of nature and art. Within a few years past, great efforts have been made, especially in England, to divest science, as far as possible, of every thing tech- nical, and to render its most important practical principles intelligible to every well informed reader. The profoundest truths, are often capable of being expressed in terms that are plain and easily under- stood, although the reasonings by which those truths were investiga- ted, and the proofs by which they are established, may involve re- fined and intricate mathematical processes. Leaving, therefore, the demonstrations to such as are professionally devoted to science, it has been proposed to take the results only for the use of the general reader, and to show their applications to the useful arts, and to the explanation of natural phenomena. By this means, not only will scientific knowledge be far more widely diffused, but the useful discoveries of science may thus be rendered available to artists, and others, who will reduce them to practice. It was with this view, that the scientific treatises in the Library of Useful Knowledge, were prepared and published, at the suggestion, and under the auspices, of the present enlightened Lord Chancellor of England. Some of those treatises are well adapted to the purpose in view ; others are ill-suited to the wants of the gen- eral reader, and they were evidently composed by men little con- versant with the tastes and attainments of those for whom they were professedly written. Individuals, also, of profound acquirements and of high standing in the scientific world, have embarked in the same enterprise. Among the most successful of these, is Dr. Lardner of the London University, whose writings on the several branches of Mechanics, and Leclures'on the Steam Engine, are among the best IV PREFACE. attempts at reducing scientific principles to the popular standard. Dr. Bigelow's "Elements of Technology," is a highly useful and respectable work of the same class; and a few others might be men- tioned which are deserving of a similar character. Many of the writers, however, who have published scientific works designed for general reading, or for schools, make their works easy of compre- hension, merely because they introduce into them nothing but the simplest and most superficial parts of the subjects of which they treat, and consequently give to the learner nothing but a smattering of sci- ence, too little either to enlighten his mind, or to qualify him to ap- propriate the resources of science to his practical benefit. During the years 1831 and 1832, the writer published a work on Natural Philosophy, in two volumes 8vo. designed as a text book for students in college. He has been frequently solicited to prepare a volume like the present, suited to the purposes of the general reader, and adapted to a portion of the students in our High Schools and Academies, who have not made the attainments in mathematics re- quisite for perusing the larger work. Such a work is the volume now offered to the public. It contains the most important principles of Natural Philosophy, with extensive practical applications, and re- quires no farther attainments in mathematics than a knowledge of common arithmetic. The writer, while he has studied plainness and perspicuity, has not deemed it either necessary or expedient, to expound the doctrines of Philosophy in a juvenile, not to say puerile, style, with the view of making it more intelligible or more attractive to young minds. Such a style he believes to be no more intelligible than the ordinary style of phflosophical writing ; and he would desire the youngest student of philosophy to receive the impression, that the study owes its at- tractions to its own inherent dignity and utility, to the elevation of its truths, and to their great practical importance. The elevated course of study adopted in some of our schools, both male and female, requires a corresponding improvement in the books prepared for their use. In many of these seminaries, it is hoped that there will be pupils sufficiently advanced in mathematics, to read the more elaborate works on Natural Philosophy ; while a still larger proportion, perhaps, will find the present treatise sufficient- ly extensive for their use. PREFACE. The numerous Voluntary Associations formed in various parts of our country, for philosophical inquiry, will, it is believed, find the present work well adapted to promote their objects ; especially, on account of its numerous practical applications of the principles of science to the arts, and the purposes of life. Professional gentle- men, also, and others of liberal education, will find this small treatise favorable for reviewing subjects, which, in the couhe of their colle- giate education, they may have studied in a more difficult form. They may, moreover, meet with some things here, which the pro- gress of the science has brought to light, since the time when (hey were students in philosophy. To teachers who may use this book, the writer begs leave to re- commend a free use of the Analysis. This furnishes a clue to all the leading truths contained in the text ; and the learner can be con- sidered as having gained entire possession of the contents of the book, only when he is prepared to give a correct and full account of each of these heads. This will be done most effectually by frequently reiterating the Analysis during the perusal of the text, at the com- mencement or at the close of each lesson. By this means, each of the heads will afterwards call up, by association, the train of ideas of which they are the index ; and thus the leading truths and prac- tical applications of philosophy, will be indelibly engraven on the memory of the learner. These heads, moreover, will serve as common places, a depository, where he may advantageously ar- range all his subsequent acquisitions on the same points. With respect to the sources from which the materials of this vol- ume have been drawn, they are, for the most part, the same as those of the larger work, where they are indicated in the margin. Such references are omitted here for want of room. Some remarks will be found at the end of the book, on the sub- ject of philosophical apparatus, which may contain useful informa- tion for teachers. Yale College, Aug. 1, 1833. ANALYSIS.* PART I. MECHANICS. CHAPTER I. PRELIMINARY PRINCIPLES. Page. NATURAL PHILOSOPHY defined, Term Law, how used, . Natural Philosophy divided into four parts, MECHANICS defined, Body, particle, Statics and Dynamics, Hydrostatics and Pneumatics, Two essential properties of matter, 2 Extension defined, Impenetrability do. GRAVITY do. . .3 Force of gravity, how related to the quantity of matter, . . 3 Extent to which the law of gravity prevails, Attraction of Gravitation reciprocal, 8 Weight defined, . . 4 Gravity, how related to the distance, 4 Case of a body within a hollow sphere, 5 Force of attraction below the Earth's surface, ... 6 INERTIA defined, . 6 how related to the quantity . of matter, . 7 CHAPTER II. MOTION AND FORCE. Absolute motion, Relative do. Apparent do. Uniform do. Accelerated do. Uniformly accelerated, . Space, how related to time and velo- city, Time, how related to space and velo- city, . ;;* Velocity, how related to time and space, .... Page, Examples, 9 Momentum defined, . . 10 how related to velocity and quantity of matter, . 10 Force defined, . . .11 how measured, Examples, . . . 11 CHAPTER III. THE LAWS OF MOTION. FIRST LAW, . 12 f Expresses the doctrine of inertia in four particulars, . . 12 Proofs of the tendency of bodies to continue in rest or in motion, . 13 Illustrations of the tendency to rest, 13 Do. do. to motion, 14 Tendency, by inertia, to uniform motion, . . .15 Proved by At wood's Machine, . 16 Atwood's Machine described, . 16 Tendency of bodies to move in right lines, . . . . . 17 Why natural motions are usually curved, . . .17 Centrifugal force defined, . 17 Illustrations of it, . . 17 Whirling Tables described, . 18 Centrifugal force, how related to the specific gravity of a body, . 18 Do. to the velocity, . . 18 Spheroidal figure of the planets, 19 In what part of the earth does cen- trifugal force act most, . 20 How it affects the weight of bodies, 20 SECOND LAW. 2Ty Proofs that motion is proportioned to the/orce, . 21 Proofs that motion is in the direction of the force, . . .21 Proofs that the smallest force can move the greatest body, . 22 ^-^ THIRD LAW, . 22 \ * This copious table of contents is designed to answer the purpose of questions. In pre] for examination, the learner is requested to be ready to give a full account of each of these repeating definitions especially with the greatest correctness and precision. V111 ANALYSIS. Page. Illustrations, . . .28 Collision of two equal bodies moving in the same direction, . 24 Ditto moving in opposite directions, 24 Elastic and Non-elastic bodies de- fined, . . . .25 Examples of each, . . 25 Velocity lost or gained by the collis- ion of perfectly elastic bodies, 25 Case of two equal balls A and B, when A. overtakes B, . .25 Do. when A and B meet from oppo- site directions, . . .25 Do. when A strikes upon B at rest, 25 This law applicable to cases of press- ure and mutual attraction, . 26 Sum of all the motions in the world estimated in one and the same line, 26 Illustrations of this principle, . 26 A great momentum obtained in two ways, . . . .26 The body which gives the blow, re- ceives an equal shock, . 27 Cases where action and reaction de- stroy each other, . . 28 Proofs of the Laws of Motion, . 28 CHAPTER IV., VARIABLE MOTION. Variable Motion defined, . 29 Falling bodies, why they fall towards the center of the earth, . 29 Spaces described by falling bodies, how related to the times, . 30 How far does a body fall from rest in ont second, . . .30 Impetuosity of falling bodies, . 31 Motion of a body moving with the last acquired velocity, . 31 Spaces, how related to the acquired velocities, . . .31 Case of a body projected perpendicu- larly upwards, . . 32 Case of a body projected downwards, 32 Laws of falling bodies, how proved by experiment, . . 33 Curvilinear motion of projectiles, 34 Revolution of the moon round the earth, . . . .35 Gravity detected in small masses, 35 CHAPTER V. COMPOSITION AND RESOLUTION OF MOTION. Simple and compound motion, 36 Motion of a body acted on by two forces in different directions, 36 When the two forces acting sepa- Page. rately would make a body describe the two sides of a triangle, . 37 Illustrations of this principle, . 37 When the forces would make the body describe all the sides of a polygon except the last side, . 38 When the forces would make the body describe all the sides of a polygon, . . .39 Resolution of a given force, . 39 Sailing of a ship, . . 40 Case of a body acted on by three forces corresponding to the three sides of a triangle, . . 40 Principle illustrated by a kite, . 41 When does a body describe a curve, 41 CHAPTER VI. CENTER OF GRAVITY. Center of Gravity defined, . 42 Utility of its doctrines, . . 42 Center of gravity of regular plane figures, , .43 To find it by experiment, . 43 A body resting on its center of gravity, 44 To find the distance of the center of gravity of a number of bodies from a given point, . . .45 Supposition of all the matter of a body concentrated in the center of gravity, . . 45 Motion of the center of gravity of a system of bodies, . . 46 Ratio of the weights of two bodies balanced on their center of gravity, 46 When will bodies standing on a hori- zontal plane remain stable or fall, 46 Position of the line which joins the point of suspension and the cen- ter of gravity when a body is at rest, .... 47 A body revolving vertically around its center of gravity at rest only in two points, . . 47 Illustrations of bodies stable and un- stable, . . . .40 Motions of animals, how related to the center of gravity, . . 49 Hope and Wire dancing, . 49 Stability af vegetables, . . 50 Center of gravity not changed by the mutual action of bodies, . 50 Problems on the center of gravity, 50 CHAPTER VII. PROJECTILES AND GUNNERY. Projectile defined, . . 51 Random do. . . . 51 ANALYSIS. IX Page. Random, when greatest, . 51 o'f a body thrown horizontally, 51 Curve described by projectiles, . 52 Theory of projectiles inapplicable to practice, . . .52 Experiments of Robins, . . 63 Velocity of a musket ball, . 54 of a cannon ball, . 54 Ratio of the weight of powder to that of the ball, . .54 Carronadef, . . .55 TVindage, . . .55 Rifles, principle on which they act, 55 Ricochet firing, ... 56 CHAPTER VIII. MACHINERY. THE LEVER. Tools, machines arid engines, . 56 Maphines, their use among the an- cients, . . . .56 Mechanical Powers, the elements of machinery, . . . ' 57 LEVER defined, . . .57 Fulcrum, Power, Weight, defined, 57 Axioms, . . . .57 Levers of three kinds, . . 58 Compound Lever defined, . 59 When do the power and weight bal- ance each other, . . 59 Examples, . . .60 Balance, what kind of lever is it ? 61 Description, . . .61 Construction of a perfect balance, 62 Sensibility of certain balances, . 63 Bent Lever Balance, . . 63 Steelyards, construction and principle, 64 Spring steelyards, . . 64 Compound steelyards described, 65 How to find the weight of a body too heavy for the steelyards, . 65 Proportion of a load shared between two bearer?, . . .65 Examples of levers, single and double, . . .66 Bones of animals, their mechanical construction, . .67 CHAPTER IX. MACHINERY CONTINUED. WHEEL WORK. WHEEL AND AXLE described, 68 Law of equilibrium, . . 69 Different modes of applying the power, . . . .69 Compound Wheel and Axle, law of equilibrium, . . 69 Principle of the/Msee of a watch, 70 Examples, . . . '.* . 70 Page. Communication of motion by wheel work, .... 71 Different modes, . . 71 Regulation of velocity by wheel work, . . . .73 Illustrated by clock-work, . 75 Wheel carriages, the advantages of wheels, . . .76 Height of the center of the wheel, 77 Position of the line of draught, 77 Most advantageous mode of coupling horses, . . .77 CHAPTER X. MACHINERY CONTINUED. PULLEY, INCLINED PLANE, SCREW, AND WEDGE. PULLEY defined, . . 78 Fixed pulley, its advantage, . 78 Fire escapes, . . '. 78 Movable pulley, law of equilibrium, 79 Examples, . . .80 INCLINED PLANE, law of equilib- rium, . . . .80 How it modifies motion, . . 80 Illustrations, . . .81 Railways, construction and principle, 82 Use in locks, . . .82 Law of gravity in the inclined plane, 82 Velocity acquired in descending the plane, . . . .83 SCREW, its analogy with the inclined plane, . . . .84 Law of equilibrium, . . 85 Use and application of the screw, 85 Hunter's screw, construction and principle, . . .86 Micrometer screw, . . 87 Example of a remarkable combina- tion of the mechanical powers, 88 WEDGE, its analogy with the inclin- ed plane, . 88 Law of equilibrium, . . 89 Use and application of the wedge, 89 Its relation to friction, . . 89 Comparative velocities of the power and weight in all machines, . 90 Illustrated in each of the mechanic- al powers, . . .90 CHAPTER XI. MACHINERY CONCLUDED. Boast of Archimedes, . . .92 No momentum gained by machinery, 92 Its real advantage, \nfour particulars, 93 Regulation of machinery, its impor- tance, . . 95 B ANALYSIS. Page. Regulators, large machines them- selves, . . . . . 95 Do. Pendulum, . . .96 Do. Fly wheel, . . .96 Fly used to accumulate motion, 97 Whether it increases the force of a machine. . . .97 Rectilinear motion, how produced, 98 Gearing, spur gearing, spiral gearing, 98 Revel gearing, . . , 98 Universal joint, . . .99 Ratchet wheel, . 99 Eccentric wheel, . . 99 Crank, . .100 CHAPTER XII. PENDULUM STRENGTH OF MATERI- ALS FRICTION. Three important applications of the pendulum, . . . 100 Pendulum defined, . . 100 Center of suspension, center of oscil- lation, . . .101 Vibrations performed in equal times, 101 Times as the square roots of the length, . . . 101 Length of a pendulum vibrating sec- onds, . . . .102 Do. vibrating once an hour, . 102 Times of vibration, how related to the distance from the center of the earth, . . .102 Page, Use of the pendulum to measure the figure of the earth, . . 103 Ditto, as a standard of linear meas- ure, . . . .103 STRENGTH OF MATERIALS, prac- tical importance of the subject, 103> Strength of a beam, to what propor- tioned, . . .103 A triangular beam stronger when resting on its broad base, . 104 Strength of a bar in the direction of its length, . . . 104 Lateral strength of a beam, how re- lated to its length, . .104 Tendency to fracture, in a horizon- tal beam, to what proportioned, 105 Tendency of large structures to fall by their own weight, . 106 Comparative strength of hollow and solid cylinders, . 106 FRICTION, its origin, . . 107 Experiments, how made, . 109 Effect of extent of surface, . 109 of pressure, . . 109 of remaining in contact, 109 Friction between surfaces of the same and different kinds, . 110 Friction at first starting a load, 110 Friction at different velocities, . 110 Comparative friction of sliding and rolling bodies, . . Ill Friction wheels described, . Ill Methods of diminishing friction, 112 Friction, its use in machinery, . 112 PART II. IfYDROSTATICS, CHAPTER I. FLUIDS AT REST. Page. Fluid denned, . . . 114 Hydrostatics defined, . . 115 Equal pressure of fluids in all di- rections, . . . 115 Effects of a Now upon any part of a fluid 115 Hydrostatic Press, construction and principle, . . .116 Explanation of its great power, 117 Surface of ^fluid at rest, . 117 Levelling, . . . 118 Relation of pressure to the depth, 118 Pressure of a column of water 8, 64 and 96 feet deep, . .119 Do. 1 and 5 miles deep, . 119 Illustrations of this pressure, . 120 Page- Compression of water at the depth of 1000 fathoms, . .120 Pressure of a fluid against a surface in a perpendicular direction, 121 Level of a fluid in opposite arms of a tube, . . . . 121 Water rises as high as its source, 122 Aqueducts of the Romans, . 122 Pressure of a column of fluid upon a horizontal base, . . 122 Hydrostatic Paradox, SPECIFIC GRAVITY defined, 124 Standard for liquids, do. for gases, 124 Loss of weight in water, . 124 To find the specific gravity Ditto when the body is lighter than water, . 125 To find the specific gravity of K- quids, . . 125 125 ANALYSIS. XI Page. Heights of two fluids in equilibrium in opposite arms of a tube, . 126 How much water does a floating body displace, . 126 Specific gravities of various bodies, 127 Estimation of a ships' weight by the quantity of water displaced, . 128 Swimming, . . .128 Force with which a body will as- cend or descend in a fluid, . 128 The Camel described, . . 129 Stones raised by ice, . . 129 Structure of life boats, . . 129 Estimation of the magnitudes of ir- regular bodies, . . ISO CHAPTER II. FLUIDS IN MOTION. Hydraulics defined, . . 130 Velocity of fluids in different parts of a pipe of unequal bore, . 130 Rivers, false doctrine applied to # thern, . . . .131 Cause of the increased velocity dur- ing a freshet, . . . 131 Cause of the increased momentum, 181 Slow motion of rivers examples, 131 Velocity of a spouting fluid compar- ed with that of a falling body, 132 Quantities of water from a spout, Page, how related to the depth, . 132 Velocity of the fluid uniformly re- tarded as the vessel empties itslf, 133 Clepsydra, its construction and prin- ciple, .... A vessel delivers double the quanti- ty when kept constantly full, Curve of a spouting fluid, Random, when greatest, Friction of fluids., Effect of a pipe attached to the ori- fice, .... 133 133 134 134 134 135 CHAPTER III. CAPILLARY ATTRACTION RESIST- ANCE OF FLUIDS WAVES. CAPILLARY ATTRACTION defined, 136 Size of the tubes, . . 136 Height of the liquid, how related to the diameter of the bore, . 136 Phenomena explained by capillary attraction, . . .137 RESISTANCE OF FLUIDS how re- lated to the velocity, . . 138 Illustrations of this principle, . 138 WAVES, their nature, . . 139 how produced, . 140 Depth to which the agitation extends, 140 Jlccumulation of waves, . 141 Questions in Hydrostatics, . 141 PART III. PNEUMATICS. CHAPTER I. MECHANICAL PTOPERTIES OF AIR. Page. 143 143 143 144 144 144 144 145 145 145 Pneumatics defined, Vapors and gases distinguished, Air material, . . : . Air a fluid, . . . Air an elastic fluid, Illustrations of these propositions, AIR PUMP described, . Valve defined, . Piston and Cylinder, Mode of producing a Vacuum, . Principle of the air pump explained, 146 Pressure of the air illustrated, . 147 Elasticity do. i" ' . 147 Relations of air to sound and com- bustion, . . .148 CONDENSER described, . 148 Air-Gun, , . . 149 Page- Diving Bell, . . 149 Barometer described, . . 150 Torricellian Vacuum, . . 150 Pressure of the atmosphere on a square inch, . . . 151 Pressure in a square foot, . 151 Graduation of the barometer, . 151 Indications of weather, . . 152 Mean Pressure of the atmosphere, 152 Range of the barometer ia the equa- torial and polar regions compa- red, . . . .152 Use of the barometer to measure heights, . . .152 Relation between the pressure and space, . . .153 Relation between the density and pressure, . .153 Relation between the elasticity and density, . . .153 Xll ANALYSIS. CHAPTER II. THE ATMOSPHERE. Page. Weight of the entire atmosphere, 154 how ascertained, . 154 Law of decrease in density on as- cending from the earth, . 155 Rarity at the height of 7 miles, 155 do. 49 and 100 miles, 155 Increase of density on descending into the earth, ' .155 Density at the depth of 34 and 48 miles, .... 155 Effect of heat and cold on the baro- meter, . . .156 Term of Perpetual Congelation, 156 Comparative heights in different cli- mates, . . . 157 Cold of the upper regions of the at- mosphere, . . . 157 Air, how put in motion, . . 157 Ventilation of Mines, . .158 How smoke ascends in a chimney, 159 Draught, how increased or diminish- ed, . . . 159 Jlmount of air that should traverse a fire, . . . .160 Winds, their general cause, . 160 Land and Sea breezes explained, 161 Trade Winds described and explain- ed, . . . 161 METEOROLOGY, . . 162 Capacity of air for moisture, how increased and diminished, . 162 Dew, the cause explained, . 163 its unequal deposition, . 163 Fogs, how produced, . . 163 Clouds, their analogy to fogs, . 164 Rain, how produced, . . 164 Effect of constant and variable winds respectively, . . . 164 Hail, how produced, . . 165 Hail storms, climates where they oc- cur, . .165 CHAPTER III. MECHANICAL AGENCIES OF AIR AND STF-AM. Syphon described, . . 166 its principle, . . 166 Suction Pump described, . 167 its principle, . 167 Height to which it will raise water, 168 No force gjned by it, . . 168 Forcing Pump described, . 168 Page. Forcing Pump, its principle, . 169 Fire Engine described, . 169 STEAM ENGINE, , . . 169 Property of steam on which its me- chanical agencies depend, . 170 Elasticity ot steam, its relations to temperature and density, . 170 Great elasticity of steam when heated, . . 171 Steam Engine described in all its parts, , . Economy of steam, . . 173 Improvements of Watt, . 173 Description from the plate, . 174 Steam engines which act expan- sively, . . . 176 Self-regulating powers of the steam engine, . . .177 CHAPTER IV. ACOUSTICS. Acoustics defined, . . 177 Cause of sound, . . 178 Vibrations of a string performed in equal times, . . . 178 Vibrating body in wind instruments, 179 Pitch depends on four circumstances, 179 Bell, its change of figure in vibrating, 180 Propagation of sound, . . 180 Air, the usual medium, . . 180 its agency explained, . 181 Conducting power of solid bodies, 182 Manner in which sound passes from one medium into another, . 182 Velocity of sound per second, . 183 Estimation of distances by sound, 183 Conducting power of liquids, . 184 Stethoscope, its construction, . 185 Reflexion of sound, . . 185 Echo, how formed, . . 185 Effect of the furniture of a room on sound, . . . 186 Rolling of thunder explained, . 187 Speaking Trumpet explained, 187 Musical sounds, how produced, 188 Musical intervals, . . 189 Why musical sounds have ratios to each other, . .189 Melody and harmony defined, . 189 Chords, how produced, . 190 Use of discords in music, . 190 Theory of stringed instruments ex- plained, . . 191 Do. wind instruments, . . 191 Do. mixed, as the organ, . 191 ANALYSIS. Xlll PART IV. ELECTRICITY. CHAPTER I. GENERAL PRINCIPLES. Page. Electricity defined, . . 192 How manifested, . . 192 When a body is said to be excited, 192 Do. electrified, 192 Conductors and non-conductors de- fined, . 192 Electroscopes and Electrometers do. 192 Pendulum Electrometer described, 192 Gold Leaf do. . . 193 Electricity, how produced, . 193 Properties when excited from glass and amber respectively, . 194 When bodies attract, when repel, 195 Two electricities produced simulta- neously, . V. 196 Comparative conducting power of bodies, . ; 196 Insulation, how effected, . 197 Sphere of influence and sphere of communication, . 198 Induction defined, . . 198 CHAPTER II. ELECTRICAL APPARATUS. Object of electrical machines, . 199 Cylinder Machine described, . 199 -flmalgam, how composed, . 200 Plate Machine described, . 201 Quadrant Electrometer, . 202 How to construct a cheap apparatus, 202 Cement, how composed, . 202 Experiments with the electrical ma- chine, . . 203 Force of electrical attraction and re- pulsion at different distances, 205 Electricity confined to the surface, 205 Leyden Jar described, . . 205 Discharging Rod, . ... 206 Shock imparted by the Jar, . 206 History of the Leyden Jar, . 206 Experiments with the Jar, . 207 How charged, . . . 207 State of the opposite sides, . 208 Outside must be uninsulated, . 208 Second Jar charged from the first, 208 To charge a Jar negatively, . 208 Two Jars charged oppositely, must have their outsides connected, 209 Electrical spider, .. . 209 Page. Charge of a Jar, how divided, . 209 Office of the coatings of a Jar, 210 Charge of a Jar long retained, . 210 Effects of the Leyden Jar explained, 210 CHAPTER III. ELECTRICAL LIGHT BATTERY ME- CHANICAL AND CHEMICAL AGEN- CIES OF ELECTRICITY. Electrical Light, when it appears, 211 How produced, . . . 212 How the spark passes in a vacuum, 212 Do. in condensed air, . . 213 Do. through various media, . 214 Illuminated figures, how produced, 214 Origin of electric light, . . 214 Battery described, . . 216 Great battery of Haarlem described, 216 Its effects, . 217 Sound of an explosion, how produ- ced, . . . .217 Rending of bodies by electricity, 217 Expansion of fluids by do. . 218 Chemical effects enumerated, . 218 Motions instantaneous, . . 219 Selects the best conductors, . 219 Preference of a shorter route, . 220 Influence of points, . . 220 CHAPTER IV. EFFECTS OF ELECTRICITY UPON ANI- MALS LAWS OF ELECTRICAL PHE- NOMENA. The electric shock, how communi- cated, . . .220 Effects in proportion to the charge, 221 The shock, how given to a number of persons, . . . 221 Effects of taking the shock on the insulating stool, . . 221 Shock, how given to any part of the system, . . . 222 Application of electricity to medicine, 223 Medicated tubes, . * . 223 Medicinal properties of this agent, 223 ! Cause of electrical phenomena, 22o j Probability of the existence of a pe- culiar electric fluid, . . 224 ! Properties of a fluid exhibited by electricity, . . . 225 XIV ANALYSIS. Page. The two hypotheses of electricity compared, . . 226 Arguments in favor of the doctrine of one fluid, . . .226 Do. of two fluids, . . 228 CHAPTER V. ATMOSPHERICAL ELECTRICITY THUNDER STORMS LIGHT- NING RODS. How the electrical state of the at- mosphere is ascertained, . 229 Mode of drawing electricity from the clouds, . . . 229 Experiments made in France, . 229 Analogies between electricity and lightning, . . . 230 First experiments of Franklin, 231 Source of atmospherical electricity, 232 Thunder Storms, leading facts res- pecting, . . . 233 cause of, . 234 Lightning Rods, how constructed, 234 their efficacy, 235 CHAPTER VI. PRECAUTIONS FOR SAFETY DURING THUNDER STORMS ANIMAL ELEC- TRICITY CONCLUDING REMARKS. Page. Liability of solitary buildings to be struck, . . .236 Liability of ships and barns, . 236 Silk dresses, how far they afford pro- tection, . . . 236 Feather beds, do. . . 236 Danger of taking shelter under a tree, . . . .237 Tall trees, their influence in protect- ing houses, . . . 237 Chimnies, their liability to be struck, 237 Electricity of the Torpedo and Gym- notus, . . .238 The Torpedo described, . 238 The Gymnotus do. . . 238 The Silurus electricus, . Electricity of furred animals, . 240 Electrical light from pointed objects, 240 Agencies of electricity in natural phenomena, . . > :i 241 PART V. MAGNETISM. GENERAL PRINCIPLES. Page, Magnetism denned, Magnets, loadstone, . . 242 Jtttractive power, when discovered, 242 Directive do. . - . 242 Poles of a magnet, axis, . 243 Needle how prepared for experi- ments, . Four leading properties, . 243 CHAPTER I. MAGNETIC ATTRACTION. Mutual attraction between iron and the magnetic pole, . . 244 Other metals that are attracted by the magnet, . . 244 Action of similar and dissimilar poles, . .244 Magnetic Induction explained, . 245 Effects of induction upon the nearer and the remoter end of a piece of iron, . .245 The power of the magnet increased by action, . . 246 Effect of a strong magnet upon the poles of a weaker magnet, . 246 Page. Effect when the north pole of a mag- net is placed on the center of an iron bar, . . 246 Do. when placed on the center of an iron disk, . . . 246 Magnetism exists only between the opposite poles of magnets, . 247 Relations of soft iron and hardened steel to magnetism, . . 247 How the process of magnetising is promoted, . 248 How the virtues of a magnet are im- paired, . . .248 Case of a steel bar magnetized by in- duction when separated into parts, 248 Effects compared with those of elec- tricity, . . 248 Force of magnetic attraction at differ- ent distances, . . 249 Magnetic power confined to the sur- face, . 249 CHAPTER II. DIRECTIVE PROPERTIES OF THE MAGNET. Effect on a needle when suspended near the pole of a magnet, 249 ANALYSIS. Page. Action of a magnetic bar on iron fi- lings, . . . .250 Declination or variation of the nee- dle, .... 250 Course of the line of no variation, 251 Actual variation of the needle at sev- eral places, . . . 251 Diurnal variation, . . 251 Dip of the needle, . . 252 Magnetic intensity defined, . 252 How measured, . . . 252 Earth itself a magnet, . . 253 Page. Magnetism of the violet rays, . 254 Electricity and Magnetism, their analogies, . . . 254 Several methods of making artificial * magnets, . . . 255 Horse shoe magnets, their construc- tion and advantage, . . 256 Kater's rule for making magnets, 257 Compass described, . . 258 Mariner's do. . . . 259 How it maintains its horizontal po- sition, . . .259 PART VI. OPTICS. PRELIMINARY OBSERVATIONS AND DEFINITIONS. Page. Optics defined, . ".* 261 Luminous bodies of two kinds, 261 Kays of light proceed in right lines, 262 Velocity of light, . . ' . 263 How estimated, . . 263 Intensity of light at different distan- ces, . .: 264 CHAPTER I. REFLEXION OF LIGHT. Reflexion defined, . : ;.- 264 Mirrors and speculums, j. 264 Angles of incidence and reflexion defined, .. . . 265 Their relations to each other, . 265 Reflexion from plane mirrors, incli- nation of the reflected rays, . 266 Image, distance behind the mirror, and magnitude, . . 266 Velocity of the image compared with that of the mirror when revolving, 267 Reflexion of an object between two parallel mirrors, '.'.."'*" * ' 268 Do. between two inclined mirrors, 268 How to judge of the qualities of a mirror, . ;*.;. . 269 Proportion of reflected rays from wa- ter, glass, &c. . 269 Reflexion from concave mirrors, 270 General office of concave mirrors, 270 Several cases according to the posi- tion of the radiant, . . 270 Experiments with a candle placed before a concave mirror, . 271 Use of concave mirrors by showmen, 272 Do. as burning instruments, . 273 Reflexion from convex surfaces general office of a convex mirror, , 273 Page. Several cases, . . . 274 Images formed by convex mirrors, 274 CHAPTER II. REFRACTION OF LIGHT BY LENSES AND PRISMS. Light passing from a rarer into a denser medium, . . 275 Do. from a denser into a rarer me- dium, .... 275 Illustrations of these principles, 275 Comparative refracting powers of different media, . . 276 Various lenses defined, . . 276 Office of a convex lens, . . 277 Do. concave lens, . 277 Images, how formed with the con- vex* lens when the radiant is pla- ced at different distances, 277 Radiant must be farther from the lens than the focus of parallel rays, 278 Spherical aberration explained, . 279 Prism described, . 280 Course of a ray of light through a prism. 281 CHAPTER III. SOLAR SPECTRUM COLORS. Different refrangibility of the rays of light, . . 281 Method of producing the solar spec- trum, . . 282 Simple rays no longer change color by refraction, . . 283 Composition of solar light, . 284 Prismatic rays united to form white light, *. 14 . . 284 XVI ANALYSIS. Page. Colors produced by the mixture of others, . 285 Rainbow described, . . 286 Position of the spectator with respect to the sun and the bow, . 288 Cause of the inner bow, . 289 Do, outer bow, . 289 How the line from the sun to the eye of the spectator, passes with respect to the bow, . 290 Height of the bow when the sun is on the horizon, . . 291 How high is the sun when the top of the bow just comes to the hori- zon? ... 291 Peculiar bows seen on high moun- tains, ... 291 Colors of bodies, their general cause, 291 CHAPTER IV. VISION. Circular image of the sun shining into a dark room through an orifice of any shape, . . 292 Camera obscura, how formed, 293 Picture formed by a lens in the win- dow shutter, . . 294 The Eye, its parts, . . 295 Contrivance in the crystalline lens for preventing spherical aberration, 296 Protrusion of the cornea, its advan- tages, ... 297 Extent of horizontal vision, . 297 How the distinct vision of objects at different distances is effected, 297 Perfection of the eye, . 298 Peculiar structure of the eyes of dif- ferent animals, . . 298 Use of convex spectacles, . 300 Do. concave, do., . 300 How distances and magnitudes are estimated, . . 300 CHAPTER V. MICROSCOPES. Microscope defined, . . 303 Simple Microscope, how it aids the eye, ... 303 Why it increases the distinctness and size, . . 304 Effect of shortening the focal distance upon the Magnifying power, 305 Page. Do. upon the field of view, . 305 Diamond and Sapphire Microscopes, their great excellencies, . 306 Fluid Microscopes, . . 307 Perspective Glass described, 308 Magic Lantern do. . 311 Solar Microscope do. . 312 Discoveries of the Solar Microscope in the vegetable and animal king- doms, . . . 314 Circulation of the blood, cristalliza- tion of salts, . . 314 How opake objects are represented, 314 Compound Microscope described, 314 Its Magnifying power, how estima- ted, ... 315 Shape of the tube, . . 315 Field glass, . . 316 Portable Camera Obscura, described,316 CHAPTER VI. TELESCOPES. Telescope defined, . . 317 Its lending principle enunciated, 317 Astronomical Telescope described, 318 Its analogy to the compound micro- scope, . 319 Difficulties in the construction of the Telescope, . . 320 Spherical aberration, how corrected, 320 Chromatic aberration, do. . 323 Dispersion defined, . . 323 Dispersive power of different bodies, 324 How the Telescope is rendered achromatic, . . 324 Perfection of the Achromatic Tele- scope, . . . 325 Use of a large aperture, . 326 Want of field, how obviated, 327 Imperfections of glass facts, 327 How far the difficulties have been overcome, . . . 328 Barlow's fluid object glasses, 328 Their advantages, . . 329 Day Telescope, described, . 329 Mode of adjusting the eye tube, 330 Reflecting Telescope described, 331 Advantages and disadvantages of the reflecting Telescope, . 332 HerscheFs great Telescope describ- ed, . . . . 332 FART I. MECHANICS. CHAPTER 1. PRELIMINARY PRINCIPLES. 1. NATURAL PHILOSOPHY is the science which treats of the Laws of the, material world. The term Law, as here used, signifies the mode in which the pow- ers of nature act. Laws are general truths, comprehending a great number of subordinate truths. Natural Philosophy, is divided into Mechanics, Electricity, Mag- netism, and Optics. 2. MECHANICS is that branch of Natural Philosophy, which treats of the equilibrium and motion of bodies.* This definition re- fers to Mechanics as a science; the principles of the science applied to the purposes of life, as in the construction of machinery, consti- tute Practical Mechanics. Body, is any collection of matter existing in a separate form. The word particle is much used in writings on physical subjects. In Natural Philosophy, we mean by particles, the smallest parts into which a body may be supposed to be divided by mechanical means, without any reference to the different elements of which such parti- cles may be composed. Inquiries of the latter kind belong to chem- istry ; and, in general, we recognize no distinctions among the diffe- rent kinds of matter which constitute various bodies, and classes of bo- dies, (except what relates to the states of solid and fluid,) leaving to chemistry all inquiries respecting the composition of bodies, and the changes of nature which bodies undergo by their action on each other. * That is, of bodies in a state of rest or motion, and of the forces that keep them in these states respectively. 1 3 MECHANICS. 3. Force is any cause which moves or tends to move a body, or which changes or tends to change its motion. Thus the elastic pow- er of steam in propelling a boat, the action of the wind upon a sail, of a weight upon a clock, and of an animal in dragging a carriage, are severally examples of forces in actual operation. That part of Mechanics which relates to the action of forces pro- ducing equilibrium or rest in bodies, is called Statics ; that which re- lates to the action of forces producing motion, is called Dynamics. 4. The laws of equilibrium and motion undergo certain modifica- tions in consequence of the peculiar properties of fluids. Hence, that branch of Mechanics which treats of the equilibrium and mo- tion of fluids in the form of water, is called Hydrostatics ; and that which treats of the equilibrium and motion of fluids in the form of air, is called Pneumatics. 5. The two essential properties of matter, both of which are in- separable from it, are extension and impenetrability. Extension, in the three dimensions of length, breadth, and thickness, belongs to matter under all circumstances ; and impenetrability, or the property of excluding all other matter from the space which it occupies, ap- pertains alike to the largest body and to the smallest particle, and to bodies under* every form, solid, fluid, and aeriform. In Geome- try, we conceive figures to possess extension only without solidity ; or to occupy space without excluding other bodies from it; but in Mechanics, we take objects as they occur in nature, viz. not only extended but impenetrable. Thus, in the demonstrations of geome- try, a sphere is represented as existing in the midst of a cylinder, both bodies being supposed, for the sake of comparing their relations with one another, to occupy the same space ; but when we seem to penetrate matter, as in driving a nail into wood, the nail does not penetrate the wood, it displaces it ; and the same is the case when a body is introduced into water or air. 6. Beside the two essential properties of matter, extension and impenetrability, there are various other properties which are not considered as essential to the very existence of matter, since bodies might be conceived to exist without them, although some of them are in fact always present. Of these, two are intimately connect- PRELIMINARY PRINCIPLES. O ed with the phenomena and laws of motion : they are Gravity and Inertia. GRAVITY is that property, by which all terrestrial bodies tend towards the center of the earth. It is in this sense that gravity is understood as a force in Mechanics. But in order to give the learn- er correct views of this important subject, we subjoin a few other particulars respecting it. 7. Gravity is a property of matter, universally; and the force of gravity in any body, is proportioned to its QUANTITY OF MATTER. 4 Gravity extends to all bodies in the universe, from the smallest to the greatest ; but the consideration of the subject, in this extent, be- longs to astronomy. We at present contemplate gravity only as it affects terrestrial bodies. By it all bodies are drawn towards the center of the earth, not because there is any peculiar property or power in the center, but because, the earth being a sphere, the ag- gregate effect of the attractions exerted .by all its parts upon any body exterior to it, is such as to direct the body towards the center. This property discovers itself, not only in the motion of falling bod- ies, but in the pressure exerted by one portion of matter upon anoth- er which sustains it ; and bodies descending freely under its influ- ence, whatever be their figure, dimensions, or texture, are all equal- ly accelerated, in a direction perpendicular to the horizon. The apparent inequality of the action of gravity upon different species of matter near the surface of the earth, arises entirely from the resist- ance which they meet with in their passage through the air. When this resistance is removed, (as it may be done by means of an instru- ment called the Air Pump, to be described hereafter,) no such ine- quality is perceived ; but a guinea, a feather, and the smallest par- ticle of matter, if let fall together, from the same height, will reach the plane exactly at the same instant. 8. The attraction of gravitation is RECIPROCAL, or every body at- tracts every other precisely as much as it is attracted by it. The sun has about a million times as much matter as the earth, yet the earth attracts the sun just as much as the sun does the earth. Nor is this doctrine inconsistent with that asserted in article 7, name- MECHANICS. ]y, that the force of gravity in a body is proportioned to the quanti- ty of matter ; for although the sun by containing a million times as much matter as the earth, exerts a force a million times as great as it would do were it of the same weight with the earth, yet it also, on the same account, is capable of receiving from the earth a million times as much; and what the sum gains by its greater power of im- parting, the earth gains by the sun's greater power of receiving. The weight of a body is the force it exerts in consequence of its gravity, and is measured by its mechanical effects, such as bending a spring, or turning a balance ; or it is measured by the force which it takes to hold a body back, so as to keep it from falling. The force thus exerted by a given mass of matter, (as a cubic foot of water,) being taken as the standard, called 1000, and accurately counter- poised in a balance, by some substance easily susceptible of division, as a mass of lead, for example, multiples or aliquot parts of this standard weight afford the means of estimating the weights of all other bodies. Hence, weights are nothing more than measures of the force of gravity in different bodies ; but since the force of gravi- ty is proportioned to the quantity of matter, (Art. 7.) weights are also measures of the comparative quantities of matter in different bodies. 9. Gravity at different distances from the earthy varies inversely as the SQUARE OF THE DISTANCE from its center. The meaning of this proposition is, first, that as the distance from the center of the earth increases, the force of gravity diminishes ; and secondly, that the degree of diminution, is not simply proportion- al to the increase of distance, so as to be one half at double the dis- tance, and one third at three times the distance, but it is proportion- ed to the square of the distance, so that at twice the distance it is only one fourth as great, at three times the distance, only one ninth, and at a hundred times the distance, only one ten thousandth part as great. ,-The weight of a body, therefore, will vary at different heights above the earth's surface. Thus at the height of 4000 miles, (which is about twice as far from the center of the earth as bodies on the surface are,) a body would weigh only half as much as at the earth ; and the moon, being about 60 times as far from the center PRELIMINARY PRINCIPLES. O of the earth, as the distance from that center to the surface, the at- traction of the earth upon the moon is the square of sixty, that is, 3600 times less than upon bodies near the earth ; and, consequently, very heavy bodies would become very light, if carried to such a dis- tance from the earth. For example, a cart load weighing a ton, would if lifted to such a height as the moon, weigh less than ten ounces ; and a man of the largest size, whose weight was four hun- dred pounds, would under such circumstances, weigh less thafti two ounces. But the heights at which experiments are commonly made upon the weights of bodies, are so small in comparison with the ra- dius of the earth, that the loss of weight, at different elevations, is hardly perceptible. At the height of half a mile, the loss could not amount to more than T ^ ^th part of the weight at the general level of the earth, so that a ton of lead would lose only about nine oun- ces, by being weighed on the top of a mountain half a mile high ; but at such an elevation as the top of Chimborazo, (which is nearly four miles high,) the diminution of weight would be material, being, in a ton, about four pounds and nine ounces. For, since the weights are inversely as the square of the distances from the center of the earth, 4004 3 t 4000 3 : :2240lbs. : 22351bs. 7 oz. That is, a ton of lead would weigh on the top of Chimborazo 2235 pounds and 7 ounces, and of course would lose 4 pounds and 9 ounces. Hence, standard weights are adjusted at the level of the sea. 10. A body situated within a hollow sphere, would remain at rest in any part of the void. Were the earth a hollow shell, with a crust more or less thick, a ball introduced into any part of the empty space, would remain per- fectly at rest, and not fall either way. Were the ball placed in the center, it is easy to see that this would be the case, since it would be attracted equally on all sides ; but were it placed out of the center, and much nearer to one side than to the other, it would still remain at rest ; for while the nearer portions of the crust would attract it more than the remoter portions, there would be so much more matter on the side of the latter, as to counterbalance the advantage which the former derived from its greater proximity. MECHANICS. Thus in Fig. 1. if the space be- tween the two concentric circles repre- sents the supposed crust of the earth, and a body were situated in the void at P, it would be attracted as much more on the left of the line C D, on account of its being nearer to the mat- ter on that side, as it would be on the right of the same line in consequence of the greater quantity of matter in that direction. It would therefore remain at rest between equal forces. If therefore, a man were let down by a rope through a hole which penetrated the crust, the force required to support him, (in other words, his weight] would grow continually less and less until he reached the void, when it would be nothing. 1 1 . The force of gravity below the earth's surface is, at different distances from the center, directly proportioned to those distances. Since the force of gravity, acting on bodies exterior to the earth, increases rapidly as they approach the earth, some have erroneously supposed that if a body could be let down through a pit towards the center of the earth, its weight would be greatly augmented ; but, so far is this from the fact, that were a body thus to descend into the earth, its weight would be continually diminished until it reached the center where it would be nothing. This will be plain, if it be con- sidered, that weight is nothing .more than the measure of the force of attraction (Art. 9.) ; that a body when placed at the center of the earth would be attracted equally in all directions ; and that, at any point above the center, there would be matter exterior to it which, by its attraction, would draw it back, and counteract its tendency to descend, and of course detract so much from its weight. 12. INERTIA is a property of matter by which it resists any change of stafyj whether of rest or motion. The inertia of a body at rest, is the resistance to be overcome to bring it to a given velocity ; or, in common language, " to start it ;" and the inertia of a body in motion, is the resistance it makes to MOTION AND FORCE. ' being stopped, after the moving force is withdrawn. Thus the iner- tia of a steam boat, while getting under weigh, requires a great ex- penditure of force to bring the boat to its final velocity ; but its in- ertia carries it still forward after the engine is stopped. Since every particle is endued with this property, the inertia of a body is propor- tional to its quantity of matter, and of course to its weight. CHAPTER II. OF MOTION AND FORCE. 13. Motion and rest are accidental states of bodies, nor is a body naturally prone to one state, more than to the other. If it is found at rest, it is because it is kept at rest by opposite and equal forces ; and if it is found in motion, it is because it has been put in motion by some force extrinsic to itself. The resistances to motion which ex- ist near the surface of the earth, particularly gravity, create a seem- ing tendency to a state of rest ; but in reality rest is no more the nat- ural state of bodies than motion is. 14. Motion is distinguished into absolute and relative. Absolute motion, is a change of place with respect to any fix- ed point : relative motion, is a change of place in bodies with res- pect to each other. When a man walks towards the stern of a ship, he is in motion with respect to the ship, but may be at rest with respect to the shore. When a balloon, carried along by the wind, attains the same velocity as the wind, it is relatively at rest, and appears to the aeronaut to be in a perfect calm, though it may be actually moving sixty miles an hour. Since the earth, in its annual revolution round the sun, is moving eastward at the rate of 90,000 feet per second, were a cannon ball, at a certain time of day, fired eastward at the rate of 2000 feet per second, the only effect would be to add 2000 feet to the velocity which the ball had before in common with the earth ; and were it fired westward, the effect would be merely to stop 2000 out of 90,000 parts of its previous motion, while the cannon - would proceed onwards leaving it behind. Did not the atmosphere partake of the diurnal motion of the earth, but were it to remain at rest with respect to this motion, the progress of any place to the east- MECHANICS. % ward, would cause a relative motion of the air, or a wind westward, which would blow with a violence far surpassing that of the most ter- rible hurricanes. 15. .Apparent motion, as distinguished from relative, is that in which the moving body is quiescent, and the motion is owing to a real motion in the spectator. Thus the backward motion of the trees to one riding rapidly, the receding of the shore to one who is sailing from it with a fair wind, and the diurnal motion of the heav- enly bodies from east to west, in consequence of the revolution of the spectator in an opposite direction : these are severally examples of apparent motion. It is often a very difficult problem to deduce the real from the apparent motion. While a planet, as Venus, is re- volving about the sun in an orbit nearly circular, its motions, as seen from the earth, are extremely irregular. The planet moves for a few weeks or months eastward, then becomes stationary, and finally returns westward again. To make all these apparent irregularities consistent with the real motions, has been a perplexing problem in as- tronomy. We can sometimes decide that a given motion is real, be- cause we observe a cause in operation which is competent to produce it. The impulse of the wind, or the direction of the current, will satisfactorily account for a ship's receding from a given object, while no cause appears why the object should recede from the ship. The revojution of the earth on its axis, is competent to explain the appar- ent revolution of the heavens, while we can find no cause for their actual revolution. The effects also of a given motion, enable us to decide whether it is real or apparent. Thus, a constant tendency to move in a straight line, is characteristic of real motion. 16. There are three particulars which are concerned in all the phenomena of motion ; namely, the space over which a body moves, the time of its motion, and the velocity with which it moves. If the motion of a body be such, that it describes equal spaces in equal successive parts of time; then it is said to move with uniform ve- locity.^ Thus when a ball rolls just as far the second second as the first, and the third as the second, its velocity is uniform. When the spaces described in equal successive parts of fime continually increase, it is said to move with an accelerated velocity ; and with a retarded velocity, when those spaces continually decrease. If its MOTION AND FORCE. motion be so regulated, that it receives equal increments of velocity in equal successive parts of time, then it is said to be uniformly accelerated; and uniformly retarded, if the body suffers equal decre- ments of velocity in those equal portions of time. The leading principles of Uniform Motion, are comprehended in the three following propositions, which are to be treasured up in the memory. 17. I. The SPACE equals the product of the time multiplied into the velocity.* Thus, a body moving at the rate of 40 feet per second for 10 seconds, would evidently pass over a space equal to ten times 40, that is 400 feet. 18. II. The TIME equals the space divided by the velocity. If, for example, a body has passed over 400 feet at the rate of 10 feet per second, then 10 : 1": :400 : 4 T Y=40 seconds. 19. HI. The VELOCITY equals the space divided by the time. Thus, if a body has passed over 400 feet in 10 seconds, it must have proceeded at the rate of 40 feet per second ; for, 10" : 400 ::i" : 4 T v>=40. Hence, in uniform motions, if any two of the three particulars, space, time and velocity, be given, the other may be found. This may be illustrated by a few examples. Examples. 20. Ex. 1. If a body moves uniformly 9 seconds with a velocity of 17 feet per second, through what space will it pass ? According to Proposition I. the space is equal to the product of the time and velocity; therefore 9x17=153 feet. Ex. 2. The space described by a body is 540 feet ; the velocity with which it moves is 6 feet per second ; what will be the time of its motion ? * The young learner is apt to be puzzled with such abstract ex- pressions as time multiplied into velocity ; but it may be observed, that by velocity is meant nothing more than the space passed over in one second ; which may evidently be so multiplied as to equal another space. 2 10 MECHANICS. By Prop. II. the time equals the space divided by the velocity ; therefore 5 | 90" Ans. Ex. 3. A body describes 560 feet in 9 seconds : what is its velocity ? By Prop. III. the velocity equals the space divided by the time ; hence, 5 62f feet per second, Ans. Questions on Uniform Motions. 21. Ex. 1. A bird of passage was observed to fly with a uniform velocity of 15 feet per second : over what Space would she pass in 24 hours? Ans. 245 T 5 T miles. 2. A lame man set out to travel round the world. He could walk but one mile an hour for eight hours out of the twenty four. Pro- vided he could go forward, without impediment, on the circumfer- ence of a great circle of the globe, which is 25,000 miles round, what Time would he require to complete the journey ? Ans. 8 years and 205 days. 3. A wind blows uniformly from the equator to the pole (say 6000 miles) in ten days : what is its Velocity per hour ? Ans. 25 miles. Momentum and Force. 22. The MOMENTUM of a body is its quantity of motion, and is proportioned to the product of its quantity of matter and velocity. If two balls, equal in weight, be rolled with the same velocity, it is evident that they will together have twice as much motion as either of them alone. Also, ten balls, in like circumstances, would have ten times as much motion as one ball. Nor would it make any difference, as to the amount of motion, whether they moved sepa- rately, or were united in one mass. With a given velocity, therefore, the momentum is proportioned to the quantity of matter. But the same balls, moving with twice or thrioe as great velocity -as before, would have twice or thrice as much motion : that is, the whole amount of motion, or the momentum, is found by multiplying the . quantity of matter by the velocity. Thus a single ball mdy have as much momentum as one hundred similar balls, if it moves a hundred times as fast as they do ; or, in general, a small mass of matter may have the same momentum with a large mass, if its velocity be as much greater as its weight is less. MOTION AND FORCE. 11 23. FORCE is any cause which moves or tends to move a body, or which changes or tends to change its motion. (See Art. 3.) The -measure of a force, is the change of motion which it produ- ces ; and the momentum of a body is determined by the force re- quired to stop it. Momentum is estimated in pounds weight, a weight just sufficient to balance it being supposed to act against it by means of a cord passing over a pulley. Thus a cannon ball may be said to move with a momentum of 1,000 pounds, because, were a scale loaded with this weight and attached to one end of a cord, while the other end was attached to the ball, (the cord passing over a pulley,) the ball and the weight would exactly balance one anoth- er, and the ball would be said to move with a momentum of 1000 pounds. The weight, moreover, would be a /orce, acting against the ball, tending to move it in the opposite direction. Examples. 24. Ex. 1. A weighs 50 pounds and moves af the rate of 60 feet in a second : B weighs 300 pounds and moves at the rate of 10 feet per second : How are their momenta? Ans. equal; for 50x60= 300x10. Ex. 2. A weighs 7 Ibs. and is moving with a velocity of 9 feet in a second ; B weighs 5 Ibs. and moves with a velocity of 1 1 feet in a second : What are their comparative momenta ? Momentum of A : momentum of B:: 7x9 : 5x11; that is, 63 : 55 Ans. Ex. 3. Suppose the battering ram of Vespasian, weighed 10,000 pounds, and was propelled with a velocity of 20 feet per second, and that this force was found sufficient to demolish the walls of Jerusa- lem. With what velocity must a 32 pound ball move to do the same execution ? The ball, in order to do the same execution as the battering ram, must have the same force, that is the same momentum. Now the mo- mentum ofthe battering ram is 10,000x20=200,000; and this di- vided by 32 gives 6,250 for the number of feet per second the ball must move in order to have a momentum of 200,000 pounds. Ex. 4. Suppose a grain of light, moving at the rate of 195,000 miles per second, should impinge directly against a mass of ice, float- ing at the rate of one foot per second : what weight of ice would the light stop? Ans. 147085.7042 Ibs; or more than 65 tons. 12 MECHANICS. Ex. 5. The earth being 8000 miles in diameter, if a ball of the same density with the earth, T ^th of a mile in diameter, were placed at the distance of ^th of a mile above the earth ; what space would the earth move through to meet it? Ans. j o^o-o-lo o^o o tn mcn - nearly.* CHAPTER III. OF THE LAWS OF MOTION. 25. THERE are three fundamental principles of motion, of most extensive application in Mechanics, which are called the Laws of Mo- tion. They are very rejnarkable examples of a happy generalization ; but their very comprehensiveness renders them difficult to be under- stood by the young learner; nor can they be thoroughly mastered, in all their relations, until after considerable proficiency is made in the science of Mechanics. We shall endeavor to make them as plain as possible by a variety of illustrations. 26. FIRST LAW. Jl body continues always in a state of rest, or of uniform motion in a right line, till by some external force, it is made to change its state. This law contains the doctrine of Inertia, expressed in four particu- lars. First, that unless put in motion by some external force, a body always remains at rest ; secondly, that when once in motion, it con- tinues always in motion unless stopped by some force ; thirdly, that the motion arising from inertia, is always uniform ; and, fourthly, that this motion is in right lines. 27. That a body at rest will continue at rest, is a consequence immediately arising from the inertia of matter. (Art. 12.) That a * In order to solve this question, the learner must bear in mind, ihat the two bodies would approach each other with equal momenta (Art. 8.) ; but that the space over which the earth would pass, would be as much less than that of the smaller body, as its quantity of mat- ter was greater ; and that the quantities of matter in spheres, are pro- portioned to the cubes of their diameters. LAWS OF MOTION. 13 body in motion will continue to proceed uniformly along the right line in which it began to move, until it is acted upon by some external force, is inferred from the fact, that any deviation from uniform^ rec- tilinear motion, in a moving body, is observed to be owing to some external force; and that such deviation is diminished as such exter- nal force is withdrawn : hence, were it entirely withdrawn, the mo- tion of the body would become altogether uniform, rectilinear, and perpetual. We may see approximations to such a state, in a ball rolled successively on 'the earth, on a floor, and on smooth ice. Although, on account of the numerous impediments to motion which exist at the surface of the earth, bodies are unable to maintain for any considerable time, the motion they have acquired, yet we see the first law of motion, so far as it respects the tendency of bodies to persevere in motion, fully confirmed in the continued and unalter- ed revolution of the heavenly bodies. These are impelled by no renewed forces, but revolve from age to age in an undeviating course, simply because they meet with no impediments. 28. We may see various exemplifications of this law, in the oc- currences that daily present themselves to our observation. And first, with respect to bodies at rest. Their tendency to remain at rest is seen, when a horse starts suddenly forward, and his rider is thrown backward. In consequence of the inertia of matter, before a body can be brought to the required velocity, this velocity must be impressed on every particle of matter it contains. Hence the more numerous its particles, the greater is the resistance from iner- tia ; that is the resistance is proportioned to the quantity of matter. A vast weight may be moved on a horizontal rail way by a compara- tively small force, provided it can be got into motion, with the re- quired velocity. In transporting large quantities (eighty tons for in- stance,) of coal, the weight is distributed into a number of different cars, connected together by a loose chain, in order that the inertia of the several parts may be overcome successively. 29. In consequence of the inertia of matter, the motion applied to a body, does not instantly pervade the mass. In order to this, motion must be applied gradually, especially if the body is large ; 14 MECHANICS. for, if it is applied suddenly, it is frequently all expended on a part of the mass, the cohesion is overcome, and the body is broken. This explanation may be applied to several familiar facts. When a team starts suddenly forward with a heavy load, the effort is either wholly ineffectual, or some part of the harness or tackling gives way. If we draw a heavy weight by a slender string, a slow and steady pull will move the weight, when a sudden twitch would break the string without starting the mass. The same principle applies to bodies al- ready in motion. Thus, when a horse in a carriage starts suddenly forward, he may break loose as well when the carriage was previously in motion as when it was at rest. The inertia of a body is in fact the same whether the body is in motion or at rest, opposing the same resistance to its moving with increased velocity, as to its beginning to move from a state of rest. 30. Several singular phenomena result from the same cause, showing that time is necessary in order that motion communicated by impulse, may pervade the entire mass. A pistol ball, fired through a pane of glass, frequently makes a smooth well defined hole, and does not fracture the other parts of the glass. Here, the moment- um of the ball is communicated to the particles of glass immediately before it. Had the impulse been gradual, the same motion would have diffused itself over the whole pane, and every part would have felt the shock. A ball fired through a board delicately suspended, causes no vibration in the board. A cannon ball, having very great velocity, passes through a ship's side, and leaves but a little mark, while one with less speed, splinters and breaks the wood to a con- siderable distance around. A near shot thus often injures a ship less than one from a greater distance. A soft substance, as clay or tal- low, may be fired through a plank before the motion has had time to diffuse itself through the contiguous parts. The whole momentum being concentrated upon the part immediately before the body, the cohesion of that part is destroyed. 31. Secondly, let us consider the effects of Inertia as it respects bodies in motion. All bodies in contact with each other acquire a common motion ; as, for example, a horse and his rider, a ferry boat and its passengers, a ship and every thing within it, the earth and all LAWS OF MOTION. 15 things on its surface. Whenever either of these bodies stops sud- denly, the movable bodies connected with it, are thrown forward* Were the revolution of the earth on its axis to be suddenly arrested, the most dreadful consequences would ensue ; every thing movable on its surface, as waters, rocks, cities, and animals, not receiving, instantaneously, this backward impulse, would fly off eastward, in promiscuous ruin. Were the diurnal motion of earth, however, very gradually diminished, until it finally ceased, so that time should be affocded to communicate the loss of motion by slow degrees to the bodies on its surface, no such effects would take place. If a pas- senger leaps from a carriage in rapid motion, he will fall in the di- rection in which the carriage is moving at the moment his feet meet the ground ; because his body, on quitting the vehicle, retains, by its inertia, the motion which it had in common with it. When he reaches the ground, this motion is destroyed by the resistance of the ground to the feet, but is retained in the upper and heavier part of the body, so that the same effect is produced as though the feet had been tripped. Coursing owes all its interest to the instinctive con- sciousness of the nature of inertia, which seems to govern the meas- ures of the hare. The greyhound is a comparatively heavy body moving at the same or greater speed in pursuit. The hare doub- les, that is, suddenly changes the direction of her course, and turns back at an oblique angle with the direction in which she had been running. The greyhound, unable to resist the tendency of its body to persevere in the rapid motion it had acquired, is urged forwards many yards before it is able to check its speed and return to the pursuit. Meanwhile the .hare is gaining ground in the other direc- tion, so that the animals are at a very considerable distance asunder when the pursuit is recommenced. In this way a hare, thlough much less fleet than a greyhound, will often escape it. 32. Thirdly, bodies in consequence of their inertia, have a ten- dency to move over equal spaces in equal times, that is, to move uniformly. In a ball rolled on ice, in a pendulum continuing to vi- brate after the moving force is withdrawn, and in numerous cases similar to these, we observe both in nature and art this tendency to uniform motion ; but in all these cases, the motion is not abso- lutely uniform, but is more or less retarded by the resistances en- 16 MECHANICS. countered. A much nearer approximation to the truth is obtained by means of an apparatus called Jltwooffs Machine, (Fig. 2.) Its con- struction, omitting some parts not essential to the principle, is as follows. The triangular base and upright pillars (which are usually of mahogany) constitute the frame, which is sur- mounted by a horizontal table or plate of wood A B, perforated with several holes. C is a vertical wheel, which by a contrivance called friction wheels, (not represented in the figure,) is made to revolve with the least possible resist- ance from friction. D and E are two weights exactly equal, and connected by a slender string passing over the wheel C. FG is a perpen- dicular scale graduated into inches from top to bottom, extending from to 60 or 70, accord- ing to the height of the machine. H is a mov- able ring which slides up and down on the scale, and K is a brass plate sliding in the same manner. There are also sometimes connect- ed with the machine, a pendulum, and such parts of a clock as are necessary for beating seconds, in order that the time of each exper- iment may be accurately noted. 33. A great variety of the principles of tion, may be established by means of this apparatus, but we are at present concerned only with the method of showing that a body when once put in motion continues, by its inertia, to move uniform- 'ty, after the moving force is withdrawn. It is obvious that the weights D and E balance each other, and consequently that the power of gravity is entirely removed from D, so that it is at liberty to obey the full and exclusive influence of any force that may be applied'-to it. If therefore, an impulse be given, by the finger, for example, to D when at the top of the scale, it ought in conformity to the law under consideration to move uniformly along down the scale, passing over the same number of inches in each successive second. Such appears to be the fact ; but in order to give a still LAWS OF MOTION. 17 greater precision to the experiment, a small brass bar is laid on D, which communicates motion to it, accelerating its progress until it comes to the brass ring H, where the bar lodges and the weight proceeds on with the velocity acquired. This velocity is found to be uniform ; that is, the weight D after it leaves the ring passes ac- curately over the same number of inches on the scale in each suc- cessive second. 34. Fourthly, moving bodies have a constant tendency to move in right lines. In nature, there occur, indeed, but few examples of rectilinear motion, but almost every moving body describes a curve. Thus, the heavenly bodies move in ellipses or ovals ; bodies thrown into the air describe a curve called a parabola ; or if their direction is so altered by a resisting medium that their path is no longer a par- abola, it is still changed to some other curve ; and a ship sailing across the ocean, describes a curvilinear path on the surface of the earth. The waving of trees and plants, the courses of rivers, the spouting of fluids, the motions of winds and waves, are likewise more or less curvilinear. Bodies falling towards the earth by grav- ity, present almost the only examples we observe in nature of a mo- tion purely rectilinear ; and this is so only in appearance. But not- withstanding the deviation from a right line, observable in actual mo- tions, yet we find that there is always some extraneous cause in op- eration which accounts for such deviations. 35. In consequence of this tendency of moving bodies to proceed in right lines, when a body revolves in a curve, around some center of motion, it constantly tends to fly off in a straight line which is a tangent* to its orbit. The force which thus carries a body off from the center of motion, is called the centrifugal force. A stone from a sling, water escaping from the circumference of a revolving wheel, and water receding from the center of a tumbler or pail when the vessel is whirled, are familiar instances of the tendency of bodies when revolving in circles to fly off in straight lines. If a pail, con- taining a little water, be hung up by the ears, by a cord suspended * A tangent is a straight line which touches the circumference of a circle. 3 18 MECHANICS. from the ceiling of a room, on turning the pail and F| g- 3 - . . . iimimiiiiiiiiimmiiimiiiii twisting up the cord, and then suffering it to untwist so as to give a rapid revolution to the pail, the water will rise on the sides of the vessel, and, if the motion be sufficiently rapid, it will be thrown out of the ves- sel in lines which are tangents to the surface of the vessel. If a glass vessel of suitable size and shape* be substituted for the pail, the experiment is observ- ed to better advantage. Such a vessel is represented in the annexed figure. 36. The action of the centrifugal force may be stud- ied still more advantageously by means of the appara- tus called the Whirling Tables. These consist of two small circular tables, to which (by means of a crank) is communicated a horizontal revolution around their centers. Bodies laid on the Ta- bles in different ways, are made to participate in their rotary mo- tions, and thus the laws of the centrifugal force may be observed. By means of this apparatus, the following propositions are established. 37. (1.) The centrifugal force of bodies revolving in a given cir- cle, is proportioned to their densities or specific gravities. If quicksil- ver, water, and cork, be whirled together in a tub or vessel, these bodies arrange themselves in the inverse order of their specific gravities, so that the cork will be at the least, and the quicksilver at the greatest distance from the center of the vessel. f 38. (2.) When bodies revolve in the same circle with different velocities, the centrifugal forces are proportioned to the squares of the velocities. By doubling the velocity of a revolving body its centrifugal force is quadrupled ; and ten times a former velocity, gives one hundred times the former centrifugal force. Millstones, revol- ving horizontally, communicate their circular motion to the corn that is introduced between them, near the center. The corn, by the * A large bell glass receiver belonging to the air pump, answers well for this purpose. t This experiment may be conveniently performed in the suspen- ded vessel Fig. 3. LAWS OF MOTION. 19 centrifugal force which it gradually acquires, recedes from the center and passes out at the circumference. If too great a velocity be given to millstones, they sometimes burst with violence. A horse in swift motion, on suddenly turning a corner, throws his rider ; and a car- riage turning swiftly is overset on the same principle. In feats of horsemanship, when the equestrian rides rapidly round a small ring, he inclines his body inwards in different degrees according to the velocity with which he is moving, and thus counteracts his tendency to fall outwards by the centrifugal force. 39. (3.) Hence, when spherical bodies revolve on their axis, the equatorial parts being farther from their center of motion, and conse- quently moving faster than the other parts, have a proportionally greater centrifugal force. If the revolving body is soft so as to yield, it is ele- vated in the equatorial and depressed in the polar parts. Thus a mass of clay revolving on a potter's wheel, swells out in the central parts and becomes flattened at the two ends. The earth itself, by its figure, which is an oblate spheroid,* indicates the operation of this principle ; and the planet Saturn, which has a far more rapid revo- lution on its axis, indicates the same modification of its figure in a still higher degree, being strikingly elevated at the equator and de- pressed at the poles. Let the circle in Fig. 4. represent a section of the earth, A B being the axis on which it revolves. This rotation causes the matter, which composes the mass of the earth, to re- volve in circles round the different points of the axis as centers, at the various dis- tances at which the component parts of the mass are placed. As they all revolve with the same angular velocity, they will be affected by the centrifugal forces, which will be greater or less in propor- tion as their distances from the center are greater or less. Con- * A spheroid differs from a globe or sphere, in being flattened in one direction and lengthened in the other. The spheroid is oblate when its figure is flattened like an orange, and prolate when elongated like a lemon. 20 MECHANICS. sequently, the parts of the earth which are situated about the equator, Q, will be more strongly affected by centrifugal forces than those about the poles A, B : the effect of the difference has been, that the component matter about the equator has actually been driven farther from the center than that about the poles, so that the figure of the earth has swelled out at the sides, and appears proportionally depressed at the top and bottom, resembling an orange in shape. 40. The centrifugal force of the earth's rotation also affects de- tached bodies on its surface. If such bodies were not held upon the surface by the earth's attraction, they would be immediately flung off by the whirling motion in which they participate. The centri- fugal force, however, really diminishes the effect of the earth's attrac- tion on those bodies, or what is the same diminishes their weights. If the earth were not revolving on its axis, the weight of bodies in all places equally distant from the center would be the same ; but this is not so when the bodies, as they do, move round with the earth. They acquire from the centrifugal force a tendency to fly off from the axis ; which increases with their distance from that axis, (Art. 39.) and is therefore greater the nearer they are to the equator, and less as they approach the pole. But there is another reason why thp centrifu- gal force is more efficient, in the opposition which it occasions to gravi- ty, near the equator than near the poles. This force does not act from the center of the earth, but its direction is in a line perpendicular to the earth's axis. Thus in Fig. 4, the centrifugal forces act, not in the lines C F, C F, but in the lines O F, O F, &c. This force is there- fore not directly opposed to gravity, except on the equator itself. On leaving the equator and proceeding towards the poles, it is less and less opposed to gravity. If the diurnal motion of the earth around its axis, were about seventeen times faster than it is, the centrifugal force would, at the equator, be equal to the power of gravity, and all bodies there would entirely lose their weight ; and if the earth re- volved, still quicker than this, they would all fly off. *V 41. The consideration of centrifugal force proves, that if a body be observed to move in a curvilinear path, some efficient cause must exist which prevents it from flying off, and which compels it to revolve round the center. Thus the bodies of the solar system are constantly LAWS OF MOTION. 21 impelled or drawn towards the sun by a force which we denominate gravity. If this force did not act constantly, they would resume their motion in the right line in which they were originally projected, when they were first launched into space, and would continue moving in it forever. 42. SECOND LAW. Motion, or change of motion, is propor- tional to the force impressed, and is produced in the right line in which that force acts. First, motion is proportional to the force impressed. This is very satisfactorily shown by means of Atwood's Machine. (Fig. 2.) When the box D is loaded with bars of different weights, (the bars being left on the ring, H, as in Art. 32.) the box descends along the scale, in consequence of the motion given it by the bar, with ve- locities exactly proportional to the weights of the bars respectively. 43. Secondly, motion is in the direction of the force impressed. Notwithstanding the diversity of motions to which eyery terrestrial body is constantly subject, the effect of any force to produce motion, is the same, when the spectator has the same motion with the body, as though that body were absolutely at rest. In other words, all mo- tions are compounded so as not to disturb each other ; each remain- ing, relatively, the same as if there were no others. Since, for exam- ple, by the diurnal motion of the earth, places towards the equator move faster than those towards the poles, if the foregoing principle were not true, the same forces would produce different quantities of motion in different latitudes ; and a body struck in a direction north or south, would not move in that direction, but would deviate to the east or west. ,A pendulum, also, would vibrate differently accordingly as it moved in a north and south, or in an east and west direction, whereas not the slightest difference of time can now be detected. If we are in a ship, moving equably, any force which we can exert will produce the same motion relative to the vessel, whether it be or be not in the direction of the vessel's motion. If we stand on the deck, supposed to be level, and roll a body along it, the same effort will pro- duce the same velocity along the deck whether the motion be from head to stern, or from stern to head, or across the vessel. Also a body dropped from the top of the mast will not be left behind by the motion of the ship, but will fall along the mast as it would if the mast 22 MECHANICS. were at rest, and will reach the foot of it at the same time. If a body be thrown perpendicularly upwards, it will rise directly over the hand and fall perpendicularly upon it again ; and if it be thrown in any other direction, the path and motion relative to the person who throws it will be the same as if he were at rest. 44. Since, according to the second law of motion, the change of motion is proportional to the force impressed, it follows that the smallest force is capable of moving the largest bodies. Agreeably to this doctrine, a blow with a hammer upon the earth ought to move it, and that it would do so may be inferred from the following reasons. (1.) We can conceive the earth to be divided into parts so small, that the blow would produce upon one of them even a sensible mo- tion. Then it would produce on two of the parts half as much ve- locity ; and upon all the parts together a velocity as much less than upon one, as their number was greater than unity. This velocity might be appreciable in numbers, although too small to be observed by the senses. (2.) Very heavy weights may be actually put in motion by small forces. Leslie asserts that a ship of any burden may in calm weather and smooth water, be gradually pulled along, even by the exertions of a boy. (3.) The repetition of very small blows, finally produces sen- sible effects upon large bodies. The wearing away of stone by the dropping of water, the abrasion of marble images by the kisses of pilgrims, and especially, the demolition of the strongest fortresses by repeated blows of the battering ram, are examples of the power- ful effects produced by small impulses, each of which must have contributed its share, since the addition of any number of nothings is nothing still. 45. THIRD LAW. When bodies act upon each other, action and reaction are equal and in opposite directions. If I strike one hand upon the other at rest, I perceive no differ- ence in 'the sensations experienced by each. The resistance to the hand which gives the blow is equal to the impulse given. A boat- man presses against the bank with his oar, and receives motion in the opposite direction, which being communicated through him to the LAWS OF MOTION. 23 boat, makes it recede from the shore. He strikes the water, the reaction of which, at every impulse carries the boat forward in the opposite direction. An infirm old man presses the ground with his staff, and thus by lightening the pressure on his lower limbs, makes his arms perform a part of the labor of walking. A bird beats the air with his wings, and by giving a blow whose reaction is more than sufficient to balance the weight of his body, rises with the difference. When the wings are small and slender, as those of the humming bird, and disproportioned to the weight of the body, the defect is compen- sated by more frequent blows, giving nimble motions suited to their short but swift excursions, while the long wings of the eagle are equally fitted, by their less rapid, but more effectual blows, for their distant journeys through the skies. Hence, propelling and rowing a boat, flying, and swimming, are processes analogous to each other, depending on the principle of reaction. 46. If a man stands in a boat and pulls upon a rope which is fas- tened to a post ori the shore, the force of the man is expended on the post in one direction, and the post, by its reaction, draws the man in the opposite direction, namely, towards the shore. Call, the man A, and let another man B, take the place of the post. If B pulls with a force just equal to that of A, he will do nothing more than what the post did before, and therefore the two men together will bring the boat ashore no sooner than A would have done alone in the former case. If A pulls with more force than B, he pulls B towards him and the reaction, or the force which carries the boat ashore, is the same as before, namely the force of B. If B were to pull with more force than A, he would pull A out of the boat, were not A at- tached firmly to the boat, in which case the velocity of the boat would be augmented. By attentively considering this and all analogous ca- ses, we shall perceive that whenever two bodies act against each other, they give and receive equal momenta, and the momenta being in opposite directions, it follows, that bodies do not alter the quantity of motion they have, estimated in a given direction, by their mutual action on each other. 47. These familiar illustrations may serve to give a general notion of the doctrine of action and reaction, as contained in the third law of mo- 24 MECHANICS, Fig. 5. tion ; but this law is susceptible of more precise experimental proof by means of the following apparatus, (Fig. 5.) Two equal bodies, whose quantities of matter, or weights are respectively represented by A and B, are suspended contiguous to each other by strings of equal length. A is pulled from its per- pendicular position, and let fall upon B at rest. This space through which each body passes in a given time, as indicated by the graduated arc 5 Y, is a mea- sure of its velocity, and, in all ca- ses velocity multiplied into the weight, is a measure of the momentum. (Art. 22.) From experi- ments with this apparatus, the following truths are established : (1.) That, when A is equal to B, the two bodies move together after im- pact with half the velocity of A before impact ; and since the quan- tity of matter in both is double that of A, the two bodies moving with half the velocity of one of them, have the same momentum, that is, the same after impact as before, and consequently as much motion as A imparted to B by its action, just so much B took from A by its reac- tion. (2.) That, when A is greater than B, it still holds true that the momentum of the mass composed of both bodies united, is the same after impact as before : consequently B extinguishes in A just as much motion as it receives from it. (3.) That when the two bodies move in opposite directions, the quantity of motion after impact is equal to the difference of their momenta before impact. Thus if A and B are equal, and they meet with equal velocities, each receiv- ing what it gives in an opposite direction, both are brought to a state of rest. If B has half the velocity of A then it will extinguish an equal amount in A, and will return in company with A with the same velocity as before. 48. In order to understand the doctrine of the collision of bodies, it is necessary to advert to the distinction between elastic and non- elastic bodies. Elastic bodies are such as when compressed, restore themselves to their former state. If they restore themselves with a LAWS OF MOTION. 25 force which is equal to the compressing force, then they are said to be perfectly elastic. Sponge is a substance of the kind which pos- sesses greater or less degrees of elasticity. Glass, ivory, marble, and steel, are among the most elastic substances of any with which we are acquainted. Two masses of lead, or earth, when struck to- gether, scarcely rebound at all, and are therefore non-elastic. AJr, when compressed, restores itself with a force equal to that which compresses it, and is therefore perfectly elastic ; but most of the other elastic substances above mentioned, possess this property in an imperfect degree only. 1 In the experiments mentioned in article 47, the impinging bodies are supposed to be non-elastic. 49. In the collision of perfectly elastic bodies, the velocity lost by the one and gained by the other, is i?wicE that which it would have been, had they been perfectly non-elastic. Let us take the case of two equal bodies, as two ivory balls, sup- posing each to be perfectly elastic, and calling one A and the other B. First, let A overtake B moving in the same direction ; then B will move off with the original velocity of A, and A will move with that of B ; that is, the two will interchange their velocities. Sec- ondly, let the two bodies meet from opposite directions ; each will return with the original velocity of the other. Thirdly, let A strike upon B at rest ; then A will stop, and B will proceed with the mo- tion A had before. Again, let^us take the case of a row of equal elastic bodies as A BODE X o ooooo o will communicate its motion to B and stop ; and- thus each of the bodies will successively transmit its motion to the next body and be brought to rest, while the last body, X, will move off with the original velocity of A. 50. It is a general law in the material world, that no body loses motion in any direction, without communicating an equal quantity to other bodies in that same direction ; and conversely, that no body ac- 4 26 MECHANICS. quires motion in any direction, without diminishing the motion of other bodies by an equal quantity in that same direction. This law of motion applies not only to the impact of bodies, but to every case in which one body acts upon another. It holds good, not only when bodies come into actual contact, but when they act upon one another at any distance whatever. A body A, for in- stance, is sustained by another body B, and both bodies remain at rest ; if the pressure exerted by the two bodies were not equal, it is evident that some motion would ensue ; which is contrary to the sup- position. If motion does ensue, then the case becomes in a great measure, analogous to that of impact; and the effects produced, es- timated in a similar manner, are found to observe the same law. The mutual attractions of bodies are also subject to this law. Thus if two equal magnets, 'connected with two equal and similar pieces of cork, be made to float upon the surface of water ; as soon as they come within the sphere of attraction, they are observed to move to- wards each other in a right line, with equal velocities, and conse- quently with equal momenta ; and as the resistance which each body meets with from the fluid, is evidently the same, we infer that their actions upon each other are equal. 51. Hence it follows, that the sum of the motions of all the bodies in the world, estimated in one and the same line of direction, and always the same way, is eternally and invariably the same. Whatever motion, therefore, one body receives towards another, whether it is drawn towards it by attraction, or by a rope, or by any other method, precisely the same quantity of motion it imparts to the other body in the opposite direction. If a man in a boat pulls at a rope attached to another boat of equal weight, the boats will move towards each other with equal velocities ; but a man in a boat pull- ing a rope attached to a large ship seems only to move the boat, but he really moves the ship a little, although its velocity is as much less than that of the boat as its weight is greater. A pound of lead and the earth-jittract each other with equal force, and the two bodies ap- proach each other with equal momenta. (See Art. 8.) 52. Since momentum is proportioned to the joint product of the velocity and quantity of matter, a great momentum may be obtain- LAWS OF MOTION. 27 ed, either by giving a slow motion to a great mass, or a swift motion to a small body. A striking illustration of this is afforded by ex- ample 4. p. 11, where on the supposition that a grain of light moving with its usual velocity, were to impinge directly against. a mass of ice floating at its ordinary slow rate, the grain of light would be compe- tent to stop about sixty five tons of ice. Islands of ice move with such vast momentum, that they instantly demolish the largest ship of war if it comes in their way. 53. If a body in motion strikes a body at rest, the striking body must sustain as great a shock from the cgllision as if it had been at rest, and struck by the other body with the same force. For the loss of force which it sustains in one direction, is an effect of the same kind as if, being at rest, it had received as much force in the opposite direction. If a man walking rapidly, or running, encount- ers another standing still, he suffers as much from the collision as the man against whom he strikes. When two bodies moving in op- posite directions meet, each body sustains as great a shock as if, be- ing at rest, it had been struck by the other body with the united for- ces of both. For this reason, two persons walking in opposite di- rections, receive from their encounter a more violent shock than might be expected. If they be of nearly equal weight, and one be walking at the rate of three nd the other of four miles an hour, each sustains the same shock as if he had been at rest, and struck by the other running at the rate of seven miles, an hour. This principle accounts for the destructive effects arising from ships running foul of each other at sea. If two ships of 500 tons burden encounter each other, sailing at ten knots an hour, each sustains the shock which, being at rest, it would receive from a vessel of 1000 tons bur- den sailing ten knots an hour. It is a mistake to suppose, that when a large and a small body encounter each other, the smaller body re- ceives a greater shock than the larger. The shock which they sus- tain is the same ; but the larger body is better able to bear it. When the fist of a pugilist strikes the body of his antagonist, it sustains as great a shock as it gives ; but the part being more fitted to receive the blow, the injury and pain are inflicted on his opponent. This is not the case, however, when fist meets fist. Then the parts in collision are equally sensitive and vulnerable, and the effect is aggra- 28 MECHANICS. vated by both having approached each other with great force. The effect of the blow is the same as though one fist, being held at rest, were struck with the combined force of both. 54. The question may be asked, why are the effects so much more injurious to fall from an eminence upon a naked rock, than up- on a bed of down ? In both instances our fall is arrested, and we sustain a contrary and equal reaction ; yet in the one case we might suffer hardly any injury, while in the other, we should be bruised to death. The reason of the difference is this : when we fall on a bed of down, the resistance is Applied gradually ; when we fall on a rock it is applied instantaneously. We do not strike the bed with the same force that we do the rock ; we move along with the bed, and of course do not lose our motion at once, and we receive in the op- posite direction merely what we lose. A violent blow, if equally diffused over the human body, may be sustained without injury. Thus, if an anvil be laid on the breast, a man may receive on it a heavy blow with a great hammer with impunity. 55. There are many instances where action and reaction mutual- ly destroy each other, and no motion results. Thus, when a child stands in a boat and pulls by a rope attached to the stern, he labors in vain to make the boat advance. Dr. Arnott tells us of a man who attached a large bellows to the hinder part of his boat, with the view of manufacturing a breeze for himself, being ignorant that the reaction would carry the boat backward, as much as the impulse of the artificial wind carried it forward. A force which begins and ends with a machine has no power to move it. 56. The three Laws of motion, which, on account of their ex- tensive application to the phenomena of motion, we have endeavored to render familiar to the learner by a variety of illustrations, are to be regarded as the fundamental principles of mechanics. Their truth rests on three different kinds of evidence : 1 . They are conformable to all experience and observation. 2. They are c6nfirmed by various accurate experiments. 3. The conclusions deduced from them have always proved true in fact, without exception. VARIABLE MOTION. 29 CHAPTER IV. OF VARIABLE MOTION. 57. When a moving body is subjected to the energy of a force which acts on it without interruption, but in a different manner at each instant, the motion is called in general variable motion. We have instances of variable motion in the action of gun powder on a ball while it is passing through the barrel of a gun, and in the action of the wind on the sails of a ship. In each of these cases, the ve- locity of the moving body is constantly augmented, yet the degree of augmentation is diminishing until it finally ceases. When a moving body receives each successive instant the same in- crease of velocity, it is said to be uniformly accelerated. If a small wheel were revolving without resistance, and, at the end of every second, I should apply a given impulse, the wheel would be uniform- ly accelerated ; for, by its own inertia, it would retain all its previous motion, and, by the second law of motion, the repetition of the same force, at equal intervals, would increase its velocity at a uniform rate. If the intervals at which this force was repeated were indefinitely diminished, the same kind of effect would take place; and the same would evidently be the case, were the force to operate without ces- sation. Such a force is that of gravity, the consideration of which will be pursued in the following sections. Falling Bodies. 58. In consequence of gravity, all bodies near the earth fall to- wards its center. We are not to infer from this fact, that there is any peculiar force, (like that of a large magnet for example,) residing at the center, but merely that the effect of the earth, taken as a whole, is the same as though its matter were condensed into the center. Thus in Fig. 7, if we con- sider how a body at A would be attracted' to- wards the earth, recollecting that every parti- cle of matter in the earth exerts its share in the effect, we shall perceive that while the matter on one side would attract it to the right of the line A B, the matter on the other side would attract it to the left of the same line ; conse- quently, both together would carry it directly 30 MECHANIC. forward in the line A B towards the center ; and the same would be true were the body A placed in any other point exterior to the earth. The leading truths respecting falling bodies will be stated in the form of propositions, which the learner is requested to commit accu- rately to memory. The illustrations subjoined to each will, it is be- lieved, render perfectly intelligible whatever may not be fully under- stood from the proposition as enunciated. 59. I. The spaces described by bodies falling from a state of rest under the influence of gravity, are proportioned to the SQUARES OF THE TIMES, during which they are falling. Thus, if a body be let fall from the top of a tower, or from the brow of a precipice, it will fall in two seconds not merely twice as far as in one second, but four times as far ; in three seconds nine times as far ; in ten seconds one hundred times as far ; and so on, the spaces being proportioned, not simply to the times 1, 2, 3, and 10, but to their squares, 1, 4, 9, and 100. It is found by actual experiment that the space through which a body falls in one second from a state of rest, is 16^ feet. Hence, it is easy to estimate the space corresponding to any other time ; for the space belonging to two seconds must be 4X16^, or 64J feet; to three seconds, 9 X 16-^, or 144 feet ; and to ten seconds, 100 X 16^, or 160SJ feet. To find the number of feet therefore, through which a body falls, the time being known, we have the following RULE. Multiply the square of the number of seconds by 16^. Ex. A body has been falling 7 seconds : through what space has it fallen? Ans. 788 r V feet. 60. A body descending by gravity is in the same situation as a ball rolled on smooth ice, which should receive a new impulse every mo- ment. Retaining all its previous motion and receiving more contin- ually, its speed would shortly become very great ; and were these new accessions of velocity without intermission and uniform (as is actually the case with gravity) the velocity acquired would be propor- tioned^to the time the ball had been moving ; so that at the end of two seconds it would be twice as great as at the end of one second ; at the end of ten seconds ten times as great ; and so on. 61. It appears from the foregoing principle, that the progress of a falling body is rapidly accelerated. In nature, however, the resis- VARIABLE MOTION. 31 tance of the air prevents a body which falls through it, from acquir- . ing so great a velocity as it would otherwise do ; still we see indica- tions of the principle of acceleration, in the impetuosity with which bodies fall from any considerable height above the earth. Mete- oric stones falling from the sky, sometimes bury themselves deep in the ground. Aeronauts that have fallen from balloons have been dashed in pieces. It is, however, a rare occurrence to see a body falling from any great height perpendicularly ; most instances of ac- celerated motion which come under our observation are bodies falling down inclined planes, where the same law of acceleration prevails. A fragment of rock descending from the side of a mountain, has its speed augmented as it goes, until its momentum becomes irresistible, and large trees are prostrated before it. 62. II. If a body after it has fallen from rest, through any space, should then cease to receive any farther impulse from gravity, but should proceed on uniformly with the last acquired velocity, it would describe TWICE the space in the same time as that during which it has fallen to acquire that velocity. Thus, at the end of one second having fallen 16 T \ feet, it would have acquired a velocity which, in the next second, would carry it 32-J feet; at the end of four seconds, its space being (4 a Xl6-f?) 257J, it would, without any farther impulse descend during the next four seconds 514| feet. 63. III. The spaces described by falling bodies are also proportioned to the squares of the velocities which they acquire in falling over those spaces. Ex. 1. Through what space must a body fall to acquire a velocity of 60 feet per second ? In falling from rest 16 T ^ feet a body ac- quires a velocity of 32 feet ; therefore, the square of the velocity acquired, that is, the square of 32|, will bear the same ratio to its space, namely 16^ feet, that the square of 60 bears to the space required ; that is, (32i) 2 : 16 T ' T : : (60) 2 : 55-96 feet, Ans.* * Since (32i) 2 =(2X16 T V) 2 =2 2 Xl6 T VX16 T V, by dividing the two first terms by 16^ we have Z 2 X[6^ : 1, that is, 641 : 1 ; hence to find the space from the velocity, we derive the following RULE. Di- vide the square of the velocity by 64. 32 MECHANICS. Ex. 2. From what height must a body fall to acquire a velocity of 50 feet, per second? Ans. 38.86 feet. 64. As in the descent of a body, the force of gravity generates equal increments in equal times, so in its ascent, equal portions of ve- locity will be destroyed in equal times; that is, as a body is uniform- ly accelerated as it falls, so it is uniformly retarded as it rises. Hence, IV. If a body be projected perpendicularly upwards, with the ve- locity which it has acquired in fatting from any height, it ivill rise to the height from which it fell, before it begins to descend again. It will also occupy the same time in rising as in falling. Ex. 1. To what height will a body rise, when projected perpen- dicularly upwards with a velocity of 120 feet per second ? As it will rise to the same height as that from which it must have fallen to acquire this velocity, we have only to find this space. Ac- (120) 2 cording to proposition III, gTT~ = 223.8 Ans. Ex. 2. How high will a body rise when thrown perpendicularly upwards with a velocity of 100 feet, per second? Ans. 155.4 feet. 65. The law of descent of falling bodies, as enunciated in proposi- tion I., (Art. 59.) goes on the supposition that the body begins its descent from a state of rest, and that it afterwards receives no im- pulse from any force beside gravity ; but we may have occasion to estimate the motion of a falling body which receives, either at first or during ks descent, an impulse from some extraneous force. In this case we must add the amount of the impulse to the ordinary force of gravity, as expressed in the following proposition. V. The space described in any given time by a body projected downwards with a given velocity, is equal to the space which would be described with that velocity continued uniformly for that time, to- gether with the SPACE through which a body would fall from rest by the action of gravity for the same time. Ex. 1. A body is projected downwards with a velocity of 30 feet in a second : how far will it fall in 4 seconds ? VARIABLE MOTION. 33 First, by a uniform motion of 30 feet for four seconds, the body would describe - - 120 feet. Secondly, by gravity it would, in the same time describe 257 J Hence, the entire space is 377J feet. Ex. 2. A body after falling 3 seconds passes by a window in a tower, from which a person standing in the tower, gives it a blow downwards, which increases its velocity 20 feet per second, after which it falls during 2 seconds more and then reaches the ground : what is the height from which it fell ? First, the descent by gravity for 5 seconds, is - 402^ feet. Secondly, the uniform motion of 20 feet for 2 seconds, is, 40 Whole space 442 T V Ex. 3. Suppose a body to be projected downwards with a velo- city of 17 feet per second : how far will it fall in 5 seconds? Ans. 487 T 'a feet. 66. The laws of falling bodies are susceptible of very accurate experimental proof by means of Atwood's Machine (Art. 32). Be- fore the invention of this apparatus, there were two difficulties in the way of such a verification, namely, the little time occupied in de- scending through such perpendicular heights as the experimenter can command, and the resistance of the air, whicji, when the velo- city becomes great, acts as a powerfully retarding force. We can rarely command a perpendicular eminence of more than 400 feet, and yet the time of passing over this space is only about five sec- onds, a period too short to enable us to mark distinctly the respect- ive rates at which the successive intervals are described. Atwood's Machine affords the means of obviating both these difficulties, and of verifying the laws of falling bodies with great accuracy. The ob- ject of the machine, so far as it respects experiments on falling bod- ies, is to render the descent of bodies so gradual, that the relations between the times and spaces can be accurately observed. By re- currence to the figure, and to the description given in art. 32, we shall readily see how this object is accomplished. The weights D and E are each equal to 31 J oz. and of course the quantity of matter in both is 63 ounces. Now, since one of these weights rises as the other de- scends, the force of gravity retards the one as much as it accelerates 5 34 MECHANICS. the other, and they are in effect the same as though they were en- tirely destitute of gravity. If a small weight, as one ounce, were let fall freely from the top of the machine, it would fall through this small space almost in an instant, and we should be uanble to mark the rate at which it passed over the successive portions of the scale FG; but if it be laid on the weight D, it must carry D along with it ; that is, it must make D descend and E ascend, and therefore the motion belonging to one ounce, will be distributed through 64 ounces, and the velocity retarded in the same ratio. Consequently, the weight D will descend only ^th part as fast as a body falling freely ; and as a body falling freely descends about 16 feet, or 192 inches in one second, the weight D will descend y/ = 3 inches in the same time. The comparative progress of this weight, and of a body fall- ing freely for several successive seconds, will be seen in the follow- ing table. Time, in seconds, 1 2 64 3 A | 402 T ', 6 Body falling freely, in feet, 16 T ', 144J 257J 579 Do. in Atwood's Machine, in inch's, 2 12 27 48 75 108 67. Hence it appears, that in 6 seconds, while a body would fall freely through 579 feet, it would in the same time descend only 9 feet in Atwood's Machine. But the latter is a uniformly accelera- ted velocity, and subject to the same laws as the former and it may therefore be employed to investigate the laws of falling bodies. The results correspond remarkably with theory, so that when the instru- ment is" well constructed and managed skilfully, the descending weight clicks upon the stage or brass plate K, at the very instant required. 68. It is not alone by the direct fall of bodies that the gravitation of the earth is manifested. The cur- vilinear motion of bodies projected in directions different from the perpen- dicular, is a combination of the effects of the unijbrm velocity which has been given to the body by the impulse which it has received, and the accelerated or retarded velocity which it receives from the earth's attraction. Suppose a body placed at any point P (Fig. 8.) VARIABLE MOTION. 35 above the surface of the earth, and let P A be the direction of the earth's center. If the body were allowed to move without receiving any impulse, it would descend to the earth in the direction P A, with an accelerated motion. But suppose that at the moment of its departure from P, it receives an impulse in the direction PB ; then it would fall towards the earth, between the actions of the two forces, in the curve line P D. The greater ihe velocity of projection in the direction P B, the greater sweep the curve will take. Thus it will suc- cessively take the forms P D, P E, P F, &c. until, when the velocity of projection is increased to a certain amount, the body would sweep quite clear of the earth, and revolve around it, as the moon does around the earth. Thus a cannon ball shot horizontally from the top of a lofty mountain, would go three or four miles. If there were no atmos- phere to resist its motion, the same original velocity would carcy it thirty or forty miles before it fell ; and if it could be dispatched with about ten times the velocity of a cannon shot, the centrifugal force would exactly balance the force of gravity, and the ball would go quite round the earth. 69. Hence it is obvious, that the phenomenon of the revolution of the moon round the earth, is nothing more than the combined ef- fects of the earth's attraction, and the impulse which it received when launched into space by the hand of its Creator ; and were any of the heavenly bodies to explode, we may conceive that the frag- ments would proceed in a rectilinear direction, until approaching, severally, within the sphere of influence of some large body, whose attraction would combine with their projectile force,- they would forever afterwards continue to revolve around that body, as the sat- ellites revolve around the primary planets. 70. The attraction of gravitation is manifested by comparatively small masses of matter. The effect of a high mountain is percep- tible upon a plumb line, causing it to deviate sensibly from a perpen- dicular, so that the same star in the zenith would change its appa- rent place when viewed on opposite sides of the mountain. 36 MECHANICS: CHAPTER V. OF COMPOSITION AND RESOLUTION OF MOTION. 71. SIMPLE motion is that which arises from the action of a single force ; compound motion is that which is produced by several forces acting in different directions. Strictly speaking, we have no example of a simple motion, since in the absolute motion of all bo- dies, their own proper motion is combined with that of the earth in its diurnal and annual revolutions, and we know not with how many others. In an enlarged sense therefore all motions are compound. But in the foregoing distinctions we have reference only to relative mo- tions, as those which take place among bodies on the earth. 72. When a body is acted upon at the same time, by two or more forces, whose directions are not in the same straight line, it is evi- dent that it will deviate from the course in which it would have mo- ved by the single action of either of those forces, and will proceed in some intermediate direction. Let .us first consider the case of a body acted upon by two forces. If I place a small ball at one of the corners of a table, and give it a snap with my thumb and finger, in a direction parallel to one edge of the table, it will of course move along that edge ; or if I give the impulse with the thumb and finger of the other hand, in the direction of the edge which is at right angles to the former, the ball will move along this edge ; but if I give both these impulses at the same moment, the ball will move diagonally across the table from corner to corner. If the force applied to each be accurately proportioned to the length of the corresponding side of the table, (as it may be by means of springs fixed to the corner of the table,) the ball will reach the opposite corner in the same time, as it would have taken it to describe either side separately. This fact is gene- ralized jn the following fundamental proposition. 73. Tivo impulses, which, when communicated separately to a bo- dy would make it describe the adjacent sides of a parallelogram in ft given time, will, when they are communicated at the same instant, COMPOSITION AND RESOLUTION Olf MOTION. cause it to describe the diagonal in the same time ; and the motion in the diagonal will be uniform. Suppose a body pla- Fi g- 9 - cedatA (Fig. 9.) to be acted upon by two for- ces, one of which would cause it to move uni- formly over the line AB, and the other over the line AC in the same A time, then if both forces act at the same instant upon the body, it will by their joint action move uniformly over the diagonal AjfJ in the same time it would have taken to describe AB or AC by the forces acting separately. By the second law of motion, every force applied to a body produces the same change of motion as though it were the only force applied. Consequently the force applied in the direction of AC will carry a body just as far towards the line CD as though the force which acts in the direction of AB were not applied. In the same manner, by the other force it will be carried just as far towards BD as though there were no other force acting upon it. Hence, the body will be found both in the lines CD and DB, when acted upon by the two forces conjointly, in the same time, that it would reach those lines respectively if acted on by each force sepa- rately. Being therefore at the end of this time in both the lines, it must be at their intersection, that is, at the point D. 74. Since AB is equal to CD and parallel to it, the two forces may be considered as acting in the direction of the two sides AC and CD of the triangle ACD ; and hence when a body would describe the two sides of a triangle by two forces acting separately, it will in the same time, describe the third side by the two forces acting jointly. 75. We daily observe examples strikingly illustrative of the principle just explained. In crossing a river, the boatman heads up the stream, and so combines the direction of the boat with that of the currents, as to move directly across in a line which is the diagonal be- tween the two directions j or he describes the third side of a triangle by the action of two forces which would severally carry him over tlin 38 MECHANICS. other two sides. Rowing, swimming, and flying are severally in- ' stances of motion in the diagonal between two forces. In feats of horsemanship, when the rider leaps up from his saddle, we are sur- prised not to see the horse pass from under him ; but he retains the the motion he has in common with the horse, and does not in fact as- cend perpendicularly, but obliquely, rising in one diagonal and fall- ing in another. Two men in a boat under rapid sail, sitting on op- posite sides and tossing the ball from one to the other, catch the ball in the same manner as though they were at rest. While, indeed, the ball is crossing the boat, the opposite man advances; but the ball also participating in the same common motion of the boat, advances mean- while in the same manner, and in reaching the other side, actually moves diagonally, with respect to the surrounding space, though with respect to the boat its motion is directly across. A body let fall from the top of a mast, when the ship is under sail, falls along down the mast and strikes at its foot in the same manner as though the ship were at rest, partaking of the common motion of the ship, and therefore describing a diagonal between this forward direction and that of gravity. 76. If a body be impelled by any number offerees which, acting separately, would, in a given time, make it describe all the sides of a polygon, except the last side; ivhen all these forces act at the same instant, the body will be made to describe the remaining side in the same time. Fig. 10. Thus in Fig. 10, a body pla- ced at A, and acted on by two forces represented in quantity and direction by AB and BC, would describe the side AC. Therefore, AC may be taken as the equiva- lent of those two forces, Or as the representative of a force equal to them both, and producing pre- cisely ther same effects as they would do. For the same reason the two forces AC and CD would cause the body to to describe AD ; and AD, therefore, represents a force equivalent to the three forces AB, AC, CD, and may be substituted for them ; and, in like man- COMPOSITION AND RESOLUTION OF MOTION. 39 ner AE may be substituted for AD and DE. Therefore under the action of the several forces AB, BC, CD, and DE, the body would describe the last side AE. 77. If the number of forces were equal, in quantity and direction, to all the sides of the polygon, then the body would remain at rest under their joint action. For the forces acting in the direction of AE, would in this case be exactly balanced by those acting in the direction of EA. 78. A given motion may be D Fi S- 11< considered as caused by two, three, or any number of forces as will be evident from the fol- lowing figure. AB will repre- sent a motion resulting either from the combined action of forces represented in quantity and direction, by AD and DB, or from AC and CB, or from the sides of various other tri- angles of which AB may be considered as the third side. In the same manner, any one side of the polygon, (Fig. 10.) may be considered as the representative of a motion produced by forces corresponding to all the other sides of the figure. 79. JL given force may be resolved into an unlimited number of others, .acting in all possible directions. Thus (Fig. 11.) AD and DB, or AC and CBmay be substituted for AB, representing forces which are equivalent to that represented by AB ; and any force represented by one side of the polygon (Fig. 10.) may be resolved into forces corresponding to all the other sides, the united effect of which is only equal to that of this side. The sailing of a ship affords an instructive illustration of the princi- ples of the composition and resolution of motion. To one unacquaint- ed with these principles, it is apt to appear mysterious that a ship is able to sail with a wind partly ahead, and still more that two ships are able to sail in exactly opposite directions by the same wind. Let us see how this takes place. 40 MECHANICS* Fig. 12. Let AB (Fig. 12.) repre- sent the keel of a ship, and CD the sail ; and let the wind come in from the side, in the direction of HD. Let DE represent the whole force of the wind, and resolve it into two forces, viz. into EF per- pendicular, and FD parallel to the sail DC. Then it is manifest that EF alone re- presents the effective force of the wind upon the sail. But EF is not wholly employed in x urging the ship forward, since it is ob- lique to her course ; therefore, again resolve EF into FG parallel with the course and GE at right angles with it. The force re- presented by GE is lost by the lateral resistance of the water, or is counteracted by the helm, while FG is employed in propelling the ship on her way. By inspecting Fig. 12. it will readily be seen that another ship may sail in the opposite direction by the same wind ; only the sail is raised on the left side when the ship is heading one way, and on the right side when it is heading the other way. When the wind strikes the sail at right angles, only one resolution is necessary ; for if FE represents the whole force of the wind, FG will represent the force which propels the ship forward, while GE will represent the part which is lost by the lateral resistance of the water. 80. Since, resolving the force of the wind after the foregoing manner, the effective part of the force, viz. FG, will not wholly dis- appear until the wind is directly ahead, it might seem possible to sail much nearer the wind than is found to be actually practicable. But though on account of the peculiar shape of vessels, the forward re- sistance is much less than the lateral, yet it is something, and there- fore retires more or less of the force that acts parallel to the keel to overcome it. 81. /2 body acted upon at the same time by three forces represented in quantity and direction by the three sides of a triangle taken in or- der, (or by lines parallel to these) will remain at rest. COMPOSITION AND RESOLUTION OF MOTION. 41 Since AD (Fig. 9.) represents a force which is equivalent to those corresponding to the two sides AC, CD, if upon a body placed at A, two such forces were to act while a third force corresponding to the side DA were to act upon it in the direction DA, the body being acted upon by two opposite and equal forces would remain at rest.* 82. A kite at rest in the air is commonly mentioned as an exam- ple of this, the three forces being, the direction of the wind, the weight of the kite, and the action of the string. Let AB be a kite, held by the string AS. Let DF represent the force of the wind blowing horizontally, and resolve it into two forces, viz. DC perpen- dicular and CF parallel to the kite. Then DC will be the only ef- fective part of the wind, since that part which acts parallel to the kite, can have no influence on its motions. Again, resolve CD into two forces, namely, CE perpendicular and DE parallel to the hori- zon. Then CE will represent the upward force of the wind, and DE its force in a horizontal direction. Now when the string AS makes such an angle with the kite that its downward force AG, added to the weight of the kite, shall equal CE, and its horizontal force HG shall equal DE, the kite will be at rest. 83. When two motions which are not in the same straight line are combined, one of which is uniform and the other accelerated, the moving body describes a curve. * The three forces are properly represented by AC and AB acting against DA; but CD is parallel amjl equal to AB, and may therefore be substituted for it. MECHANICS. Fig. 14. Thus, (Fig. 14.) when a body is N thrown obliquely upwards in the direc- tion of PN, the force of gravity will draw it continually away from that line* towards the earth ; and as gravity is a force which increases the motion of a falling body every instant, the body will Q at first recede slowly from the line PN, but more and more rapidly as it advan- ces, describing a curve whose deviation from the line of projection continually increases, as POQ. Now, the spaces X 4V PM and PN, representing the uniform motion in the line of projec- tion are to one another as the squares of the spaces MO and NQ which represent the descent towards the earth. But a curve de- scribed between two forces bearing this relation to each other, is known to be .the curve called a parabola, being one of the curves which result from the sections of a cone. The parabola, therefore, is the curve ^belonging to all bodies projected from the earth into the atmosphere, as is seen when a stone is thrown upwards, or a fluid spouts obliquely. Forces differently proportioned to each other, describe different curves, as circles, ellipses, &c. Thus, the planets revolve around the sun in ellipses, between the force of projection and that of attraction towards the central luminary. CHAPTER VL OF THE CENTER OF GRAVITY. 84. The center of gravity of a body is that point, about ivhich, if supported, all the parts of a body (acted upon only by the force of gravity) would balance each other in any position. Thus, a staff poised across the finger, rests only when the finger is under the cen- ter of gravity. The principles which have been discovered respecting the com- position and resolution of forces, and respecting the center of gravity, have alike contributed greatly to simplify the doctrines -of Mechanics. It is characteristic of a great and penetrating mind, to- CENTER OF GRAVITY. 43 devise means of divesting intricate subjects of their complexity and thus to bring easily within the grasp of the mind, subjects otherwise too much involved to be within its comprehension. By the rule of simple multiplication, we easily multiply any number by one thousand : indeed, it is nothing more than to annex three cyphers to the number itself; but how tedious would be this process, were the rule of multipli- cation undiscovered, and we were unacquainted with any other method of arriving at the result, except to add the given number to itself one thousand times. In like manner by means of the rules for the com- position of motion, we are enabled to reduce a thousand different motions to one ; and by the doctrine of the center of gravity we are taught how we may make a force, situated at one single point, equiv- alent to an infinite number of forces, situated in as many different points ; and, instead of pursuing the endless diversities of motion to which the different parts of a complicated system of bodies may be subject, we are taught how to follow merely the motions of a sin- gle individual point. 85. In regular plane figures, such as squares, parallelograms, cir- cles, fyc. the center of gravity is the same with the center of the figure. In the following figures, the lines AB and CD, (Fig. 15.) bisect each Fig. 15. B AM D D other in the center $f the figure. Each line obviously has its center of gravity in the point of bisection, and that is the point where the quantities of matter on all sides are equal, and therefore exactly bal- ance one another. The same is true of such regular solid figures as a cube, a sphere, a cylinder, &c. 86. To find the center of gravity by experiment, several different methods present themselves. We will first suppose the body to be in the shape of a piece of board, of uniform thickness. Suspend it by one corner, and from the same corner let fall a plumb line, and 44 MECHANICS. mark its line of direction on the surface of the board. Suspend the board from any other point, and mark the line of direction of the plumb line as before, and the point where these lines intersect each other, must obviously be the center of gravity, since that center is in both of the lines. 87. But when the body is not of uniform thickness, but is any irregular solid, suspend the body by a thread, and let a small hole be bored through it, in the exact direction of the thread, so that if the thread were continued below the point where it is attached to the body, it would pass through this hole. The body being successively suspended by several different points in its surface, let as many small holes be bored through it in the same manner. If the body be then cut through, so as to discover the directions which the sev- eral holes have taken, they will be all found to cross each other at one point within the body. Or the same fact may be discovered thus : a wire which nearly fills the holes being passed through any one of them, it will be found to intercept the passage of a similar wire through any other. 88. A convenient method of finding the center of gravity of a body is, to balance it in different positions across a thin edge, as the edge of a knife or a prism. The same thing may be effected, when the shape of the body will admit of it, by laying it on the edge of a table, and letting so much of it project over the edge, that the slight- est disturbance will cause it to fall. The center of gravity is the point in which the several lines marked on the body, where the edge cuts it, intersect one another. From some or all of the foregoing trials, the center of gravity of bodies may be ^nearly ascertained ; but in order to find it with absolute exactness, we are frequently obliged to resort to intricate mathematical processes. By whatever method the center of gravity of a body has been ascertained, we shall find that when that is supported, the body will remain at rest in every position. Thus a globe will stand se- curely on a*very small perpendicular support, since that support will necessarily be under the center of gravity; a lever, as the beam of a balance, poised on its center of gravity, will be at rest in every po- sition it takes while turning round the fulcrum, and however irregu- CENTER OF GRAVITY. 45 lar the body may be, it will, when balanced on its center of gravity, obstinately maintain its position. 89. We may find the distance of the common center of gravity of any number of bodies from a given point, upon the following principles. First, suppose the bodies have their centers of gravity in the same right line, as in figure 16, then the distance of the common center of Fig. 16. A B C D O G gravity of all the bodies from the point O, will be found by multiply- ing each body into its distance from that point, and dividing by the sum of the bodies. Indeed, it is not essential that the matter in question should even reside in one and the same mass, for this prin- ciple holds good for any number of separate bodies. 90. In figure 16, A, B, C, D, are bodies of different weights con- nected together by a wire which is balanced on the center of gravity G. Now we may find the distance of G from any point O in the same line, by multiplying A into AO, B into BO, C into CO, and D into DO, and dividing the sum of these products by the sum of the bodies A, B, C and D. Secondly, suppose that the bodies are not in the same right line, but are situated like a^number of balls of different weights hanging at different distances from the ceiling of a room. Thus, we may find the distance of their common center of gravity from the perpendicular wall of the room, by multiplying each body into its distance from the wall, and dividing the sum of the pro- ducts by the sum of the bodies. 91. When a body is supported by a prop placed under its center of gravity, the pressure will be the same, whether this whole quantity of matter be uniformly diffused through the space occupied by the body, or whether it be all concentrated in that center of gravity. In consequence of this law of the center of gravity, the reason- ings on mechanical subjects are often greatly simplified. Thus, in- 46 MECHANICS. stead of estimating the pressure and other mechanical effects of a large body like the earth by considering the united effects of all its separate parts, we rnay often arrive at a far more simple conclusion by considering all the matter of the earth as residing in the center of gravity, and reasoning respecting it accordingly. When bodies that compose a system are in motion, their common center of gravity will move in the same manner as if a body equal to the sum of the bodies were placed in that point, and the same motions were commu- nicated to it as are communicated to the bodies separately. 92. Two weights or pressures acting at the extremities of an in- flexible rod void of gravity, will be in equilibrium about a given point, when their distances from that point are to each other inversely as those weights or pressures. Thus, (Fig. 17.) if a weight ^J Fig. 17. of one pound, and another of ten pounds, be connected by a wire, and balanced by laying the wire across a thin edge, it will be found that the smaller weight is ten times as far from the support, or fulcrum, as the larger weight is, 93. Whatever be the form or dimensions of a body upon a plane parallel to the horizon, it will remain at rest, if the line drawn from its center of gravity perpendicular to the horizon falls within its base. For let ABCD Fi S- 18 - (Fig. 18.) repre- A D A D sent the section of a body, passing through its center of gravity G, and draw GF perpen- dicular'fo HO the H BF C F B C plane upon which it stands ; then, since the tendency of the body to descend is the same as if its whole weight were concentrated in G, it will rest CENTER OP GRAVITY. 47 or fall according as G is supported or not ; i. e. according as F falls within or without the base BC ; moreover, the stability of the body will depend upon the distance at which the point F falls with- in the base. i ; 94. If a body be suspended from any point, it will not rest till the line which joins the center of gravity and point of suspension is per- pendicular to the horizon. For let ABCD (Fig. 19.) represent Fi S- 19 - the section of a body as before, G its center of gravity, S the point of suspen- sion ; join SG, and draw SOW perpen- dicular to the horizon ; produce SG to N, and draw GR parallel to SW ; then, since the weight of the body may be considered as collected in G, its tenden- cy to motion will be along the line GR. Let GR therefore represent this tenden- cy, which resolve into GN in the direc- tion SG, and RN perpendicular to it ; the part GN is counteracted by the reac- tion from the point of suspension S, and NR is employed in producing motion in the direction of the circular arc GO ; G therefore (and consequently the body) will not remain at rest till NR vanishes, i. e. till the angle NGR (=OSG) vanishes, or SG coincides with SO. 95. When a body is suspended from a center of motion, and re- volves around it, it will be at rest only when the center of gravity is either directly below, or directly above the center of motion. For it is only in these two cases, that the center of gravity will he in the line which is drawn through the center of motion perpendicular to the horizon. The stationary point above the center of motion is very unstable, since the slightest disturbing force, throws the body out of the line of direction, when, by the force of gravity, it imme- diately descends to the lowest point it can reach, and vibrates about that point until it finally settles itself with the center of gravity im- mediately under the point of suspension ; and whenever it is thrown 48 MECHANICS. out of this position, the same vibrations are renewed until it resumes it. When, therefore the center of gravity is at the lowest point it is capable of reaching, the equilibrium is stable, since the body ob- stinately maintains that position. On this principle, gates which have their center of gravity raised as they are opened, shut spon- taneously. 96. The stability of a body not only requires that the center of gravity should be low, but that the line of direction (or, the line which is drawn through the center of gravity perpendicular to the horizon) should fall within the base. The farther it falls from the extremity of the base, the more stable is the position. Hence the stability of a pyramid when standing on its broad base, and its insta- bility when inverted. For the same reason, all broad vessels, as steam boats, are difficult to upset, while vehicles with narrow bases are easily overturned. When a load is so situated as to raise the center of gravity, it increases the liability to upset, because it in- creases the facility with which the line of direction is thrown without the base. Thus carts loaded with hay, or bales of cotton, are very liable to be overturned. The same is true of stages carrying pas- sengers or baggage on the top. On the other hand, a large ship well supplied with ballast is capsized with 'great difficulty, since the the center of gravity of all parts of the ship is so low, as to render it difficult to throw the line of direction without the base. Yet if the center of gravity is very low, a ship will rock excessively in a rough sea, since the upper parts near the deck, move over a great- er space in proportion as their distance from the center of gravity is greater. 97. There are many remarkable structures which lean or incline a little ; but so long as the line of direction falls within the base, and the parts of the mass have sufficient tenacity among themselves to hold together, the structure will stand. The famous tower of Pisa, was built ^intentionally inclining, to frighten and surprise : with a height of one hundred and thirty feet, it overhangs its base sixteen feet. This circumstance greatly enhances the emotion of the spectator from its summit. Many ancient spires and other tall structures, are found to have lost something of their perpendicularity. CENTER OF GRAVITY. 49 98. Rocking stones are rocks which are sometimes found so ex- actly poised upon their center of gravity, that a very small force is sufficient to put them in motion. The rocking of a balloon when it begins to ascend, affords an illustration of the tendency of bodies to vibrate around the center of gravity. 99. The motions of animals are regulated in conformity with the doctrines of the center of gravity. A body is seen tottering in pro- portion as it has great altitude and a narrow base ; but it is a pecu- liarity in man to be able to support his figure with great firmness, on a very narrow base, and under constant changes of attitude. The faculty is acquired slowly, because of the difficulty. The great fa- cility with which the young of quadrupeds walk, is ascribed in part to their broad supporting base. Many of our most common motions and attitudes, depend for their ease and gracefulness, upon a prop- er adjustment of the center of gravity. The erect posture of a man carrying a load upon his head leaning to one side when a heavy weight is carried in the opposite hand leaning forward when a weight is on the back or backward when the weight is in the arms ; these are severally examples in point. When a man rises from his chair, he brings one foot back, and leans the body forward, in order to bring the center of gravity over the base ; and without adjusting it in this manner, it is hardly possible to rise. A man standing with his heels close to a perpendicular wall, cannot bend forward suffi- ciently to pick up any object that lies on the ground near him, with- out himself falling forward. 100. The art of rope or wire dancing, depends in a great degree upon a skilful adjustment of the center of gravity. The rope dan- cer frequently carries in his hand a stick loaded with lead, which' he so manages as to counterbalance the inclinations of his body which would throw the line of direction out of the base. Upon a similar principle the equestrian balances himself on one foot on a galloping horse. 101. The vegetable creation is subject also to these general laws of nature. Trees by the weight and height of their tops would seem* peculiarly liable to fall ; but their roots afford a corresponding breadtfo 50 MECHANICS. of base, while their perpendicular trunks, and the symmetrical dispo- sition of the branches, conspire to increase their stability. 102. The position of the center of gravity of any number of sep- arate 'bodies, is never altered by the mutual action of those bodies on each other. If, for example, two bodies, by mutual attraction, approach each other, the center of gravity remains at rest, until finally the bodies meet in this point. If, by their mutual action, they contribute to make each other revolve in orbits, it is around their common center of gravity. Thus the earth and moon revolve around a common center of gravity, which remains fixed : the same is true of the sun and all the bodies that compose the solar system. Were the centrifugal force to be suspended, and the bodies abandoned to the mutual action of each other, they would all meet in their 'common center of gravity. This naturally results from the principle that the momenta on opposite sides of the center of gravity are equal, and that bodies by their mutual action produce equal momenta in each other. 103. The doctrines of the center of gravity, suggest the readiest method of solving a great number of practical problems. We an- nex a single example. Suppose three persons were carrying a stick of timber, (A by him- self supporting one end, and B and C by a handspike lifting together towards the other end,) and it were required to determine at what distance from the end of the stick the handspike must be placed, in order that three persons might bear equally. A stick of timber being a body of regular shape and uniform density, has its center of ' gravity coincident with the center of magnitude. We may therefore proceed on the supposition that the entire weight is collected in the center. Now in order that B and C may together lift twice as much as A, they must be twice as near the center. But the distance of A from the center is half the length of the stick ; therefore the distance of the reqnired point from the center is one fourth the length of the stick, and consequently it is one fourth the same length from the end of the stick. To test this case by experiment, we might rest one end of the stick upon a support, and ascertain, by a pair of steelyards, the weight at a distance from the other end equal to J the length of the sti ck. It would be found equal to | the weight of the whole stick, PROJECTILES AND GUNNERY. 51 CHAPTER VII. OF PROJECTILES AND GUNNERY. 104. A projectile, is any body thrown into the atmosphere. A ball fired from a cannon, a stone thrown by the hand, and an arrow shot from a bow, are severally examples of projectiles. According to article 83, projectiles rise and fall in the curve of a parabola under the combined forces of projection, which tends to carry them uni- formly forward, and of gravity, which brings them with accelerated velocity towards the earth. 105. The random of a projectile is the horizontal distance between the point from which it is thrown, and that where it falls to the earth. For example, when I throw a stone obliquely into the air, it rises and falls in a curve, (the parabola) and the distance from the place where I stand to the place where it falls, measured on the surface of the earth, is its random. The random is greatest when the angle of elevation is 45 degrees, and is the same at elevations equally distant above and below 45 degrees. It is the same, for instance, at 60 and at 30 degrees. A projectile rises to the greatest height when thrown perpendicu- larly upwards, and it remains, in this case, longest in the air ; or the time of flight is greatest when a body is projected directly upwards. 106. When a body is thrown horizontally from any elevation, with a velocity equal to that which it would have acquired by falling from that elevation to the earth, its random is twice as great as that height. Thus, if I throw a ball from a chamber window, with a velocity which it would have acquired in falling from the window to the ground, it will fall at a distance from the foot of the building equal ' to twice the height of the window. 107. The foregoing principles hold good only when projectiles move without resistance. But this is far from being the fact, since the resistance of the air, especially to bodies moving swiftly through it, is very great ; and hence the discordance between theory and experiment is such, that the mathematical principles of projectiles are found to be wholly inapplicable to practice. 52 MECHANICS. It is ascertained, in general, that projectiles moving slowly, des- cribe curves which are nearly parabolas ; while such as move swiftly deviate very far from this curve. The parabolic figure described in the case of projectiles which move slowly, may be observed in tracing the path of a small stone thrown into the air, and more espe- cially in the curves described by jets of water spouting upwards, as in fountains. But when the jet is more rapid, and spouts at a high angle, as forty five degrees for example, we can plainly see that the curve deviates greatly from a parabola. The remote branch of the curve is seen to be much less sloping than the rising branch ; and in very great jets, which are to be seen in some great water works, the falling branch is almost perpendicular at its remote extremity ; and the highest point of the curve is far from being in the middle between the spout and the place where the water falls. The unequal division of the curve by its highest point, may also be observed in the flight 4 of an arrow or a bomb shell. 108. The following facts also shew the discordance between the parabolic theory of gunnery and experience. A cannon ball, fired in such a direction and with such a velocity, that its random or hori- zontal range, ought to be twenty four miles, comes to the ground short of one mile. The times of rising and falling, if that theory held good, ought to be equal ; but the time of rising is greater than that of falling at great elevations, and at small elevations, less than that of falling. According to the theory, the greatest random, is at an angle of elevation of forty five degrees, but in practice it is found to be much below this. The greatest random of an arrow, is when the elevation is about thirty six or thirty eight degrees. Indeed the angle for the greatest horizontal range, may be at all degrees from 45 to 30 ; the slowest motions and the largest shot being almost at 45, but gradually more and more below that degree as the shot is smaller and the velocity is greater, till at length with the most rapid motions, and the smallest shot, the angle is little above 30. The following 'Experiments were made in France by Borda, with a twenty four pounder, with the same charge of powder in each experiment. PROJECTILES AND GUNNERY. 53 Elevation. Range. 15 1950 30 - - 2235 45 2108 60 1700 75 - 950 Whence it appears that at the elevations of 15 and 75, the ran- doms instead of being the same (being equally distant from 45,) were as the numbers 1950 and 950. 109. All this discordance between theory and practice is owing to the resistance of the air, which, when the projectile moves with great velocity, becomes enormous. Nor will it be difficult, on a lit- tle reflection, to comprehend the reason why this resistance should be so great. The force with which a projectile strikes the air at rest, is the same as that with which the air moving with equal velocity would strike the body at rest. This, in the case of a can- non ball, would greatly exceed the most violent hurricane. Again, as a ball moves through the air, it displaces, that is, gives mo- tion to, great quantities of air ; yet whatever motion it imparts to other bodies is extinguished in itself. The loss of motion, there- fore, increases very fast with the velocity. It is said to be in gen- eral as the square of the velocity : so that a body moving through the air with ten limes the velocity of another body, would encounter one hundred times as much resistance. In very swift motions, the resistance was ascertained by Robins to be even much greater than in the ratio of the square of the velocity. 110. The researches of Mr. Robins were made chiefly by the aid of an instrument of his own invention, called the Ballistic Pen- dulum. It consists of little more than a large block of wood, like a log, suspended after the manner of a pendulum. Now if a bullet be tired into the block, as the bullet will be stopped, and as it imparts to the block whatever motion it loses, consequently the momentum of the block after the stroke, is precisely that of the ball before the stroke. Hence the weight of the block -and that of the ball being known, and the velocity imparted to the block being easily determined by observation, it is easy to find the velocity of the ball ; for the weight of the ball is to the weight of the block, as the velocity of the block is to the velocity of the ball. MECHANICS. 111. This simple apparatus is sufficient for ascertaining a great number of particulars relative to the art of gunnery. If the ball is fired nearly in contact with the block, we find with what velocity it leaves the gun; if at different distances from the block, we find how much the velocity is retarded by passing through the air, for those distances respectively. If, at a given distance, we vary the charge of powder, we find the respective changes which the velocity undergoes, and hence learn the ratio that ought to be observed be- tween the powder and the ball, in order to produce the maximum effect. The effects resulting from variations in the length, shape and bore of the gun, are also ascertained with equal facility. 112. The following are some of the practical results ascertained by the experiments of Mr. Robins, Count Rumford, and Dr. Hut- ton. A musket ball, discharged with a common charge of powder, issues from the muzzle of the piece with a velocity between 1600 and 1700 feet in a second. The utmost velocity that can be given Co a cannon ball is 2000 feet per second, and this it has only at the moment of leaving the gun. In order to increase the velocity from 1600 to 2000 it requires half as much more powder, which involves a hazardous strain upon the gun, and the velocity will be reduced to 1300 before the ball has proceeded 500 yards. 113. From the foregoing considerations it is inferred that great charges of powder are absolutely useless in the service of artillery, especially when the distance of the object is considerable, and that a velocity exceeding 1100 should not be aimed at. The maximum service charge is f the weight of the ball. In close naval engage- ments, great velocities are injurious, for the ball may then pass through both sides of the vessel without lodging, and the number of splinters produced by a ball in rapid motion, is much less than is caused by one moving more slowly. By reducing the charge we may also re- duce the size and strength of the gun ; and hence guns are made of smaller dimensions now than formerly, in order to do the same exe- cution. The velocity with which a charge of powder expands itself at first, is estimated by Hutton as high as 5000 feet per second. As it expands, this velocity is of course constantly diminishing, but will exceed that of the ball while the latter is passing through the barrel PROJECTILES AND GUNNERY. 55 of the gun, and will act as a constantly accelerating force. Long guns, therefore, give to balls a greater velocity than short ones ; but the gain secured in this way after a moderate length is so small, (there being also some disadvantages peculiar to long guns,) that cannon have of late years been much shortened. In the naval ser- vice, carronades have been introduced. These are a short kind of gun, with small bore, requiring for a charge of powder, only one twelfth the weight of the ball. Their weight and thickness are pro- portionally reduced, yet in close action they produce effects superior to those of long guns. 114. It has been found that no difference is caused in the velocity, or range, by varying the weight of the gun, nor by the use of wads, nor by different degrees of ramming, nor by firing the charge of powder in several places at the same time ; but that a very great difference in the velocity arises from a small degree in the windage, or the difference between the diameter of the ball and that of the gun. Indeed, with the usual established windage only, viz. about aV of the calibre, no less than between J and J of the powder escapes and Is lost, and as the balls are often smaller than the regulated size, it fre- quently happens that half the powder is lost by unnecessary windage. To this cause also, namely, too great windage, Dr. Hutton ascribes a great part of the sideways deviation of a ball ; since when, in pass- ing through the barrel of the gun, it is knocked from side to side, ft will finally take the last direction which it happened to have at the muzzle of the gun. Another cause of this deviation from the line of direction, arises from a want of perfect sphericity in the ball, by which means the two sides do not meet with equal resistance. Ri- fles owe their superiority over common guns, chiefly to their obvia- ting this deviation. They have a spiral groove cut in their bore, making about a turn and a half in the whole length of the barrel. The ball, which is made to fit close to avoid too great windage, has a corresponding motion impressed on it, which it retains after it 'leaves the gun, continuing to revolve around the line of direction. What- ever inequalities, may exist in the ball, their effects are neutralized, by their being first on one side and then on the other of this line. 115. When a ball is projected from a piece of ordnance, at a small angle of elevation, and falls upon water, or on a plane of hard MECHANICS. earth, its flight will not cease, but it will rise again and .describe a second curve, similar to the first but less ; and it will continue to rebound, until the whole of its projectile velocity is destroyed. This species of firing is called Ricochet. It is applied with great advantage from sea coast batteries upon shipping, and in the attack of fortresses. The pieces are fired with small charges of powder and elevated only from 3 to 6 degrees. The word signifies duck and drake, or rebounding ; because the ball or shot thus discharged, goes bounding and rolling along, killing or destroying every thing in its way, like the bounding of a flat stone along the surface of water when thrown almost horizontally. CHAPTER VIII. OF MACHINERY. THE LEVER. 116. THE organs employed in communicating motion, are tools, machines, and engines. Tools are the simplest instruments of art ; these when complicated in their structure, become machines; and machines when they act with great power,. take the name of engines. Among the ancients, machines were confined chiefly to the purposes of architecture and war ; and they were moved almost exclusively by the strength of animals. Thus, in building one of the great Pyramids of Egypt, vast masses of stones were raised to a great height, amounting together to 10,400,000 tons. In this labor were employed 100,000 men for twenty years. The advantage which man has gained by pressing into his service the great powers of na- ture, instead of depending on his own feeble arm, is evinced by the fact, that by the aid of the steam engine, one man can now accom- plish as much labor as 27,000 Egyptians, working at the rate at which they built the pyramids. In war also, while the use of gun- powder was unknown, engines of great power were invented for throwing stones and javelins, and for demolishing fortifications. Such were the'jCatapulta, the Ballista, and the Battering Ram, of the Romans. Yet it is remarkable, that during many ages, while such powerful auxiliaries were employed in architecture and in war, the ancients should have made so little use as they did of machinery in the ordinary processes of the arts. The practice of grinding corn by MACHINERY. 57 hand, which was chiefly performed by women, was prevalent at Rome until the time of Augustus, when we find the first mention of water mills. The elements of machinery are found in what are called the Me- chanical Powers. They are six in number, viz. the Lever, the Wheel and Axle, the Pulley, the Inclined Plane, the Screw, and the Wedge. THE LEVER. 117. 1. The LEVER is an inflexible bar or rod, some point oj which being supported, the rod itself is movable freely about that point, as a center of motion. 2. This center of motion is called the FULCRUM OR PROP. 3. Wtien two forces act on one another by means of any machine, that which gives motion is called the POWER ; that which receives it the WEIGHT. 4. A lever is straight when its arms (or the parts on each side of the fulcrum) are in one continued straight line ; bent, when the two arms are straight, but make any angle with each other at the center of mo- tion ; and crooked, when one or both arms deviate from a straight line. 118. In treating of the Mechanical Powers, the first inquiry is, what are the conditions of an equilibrium; that is, when do the pow- er and weight exactly balance each other ? This point being ascer- tained, any addition to the power, puts the weight in motion. The investigation first proceeds on the supposition that the action of the mechanical powers is not impeded by their own weight, or by fric- tion and resistance, a suitable allowance being afterwards made for the various impediments. 119. The following principles are regarded as self-evident. Axiom 1 . If two weights balance each other upon the opposite arms of a straight lever, the pressure upon the fulcrum is equal to the sum of the weights, whatever be the length of the lever. Ax. 2. If a weight be supported on a lever which rests on twoful- crums, the pressure upon the fulcrum is equal to the whole weight. Ax. 3. Equal forces acting perpendicularly at the extremities of equal arms of a lever, exert the same effort to turn the lever round. 120. Two weights will balance each other upon the arms of a lever when they are to each other inversely as their respective distances from the fulcrum. 8 58 MECHANICS. 1 1 Thus in Fig. 20, if A Fig. 20. c W is as much heavier than P as AC is greater than BC, the two weights j^ ^ W will exactly balance one another. Here the product of P jnto AC, is equal to the product of W into BC, and in all cases where the product of the weight into its distance from the fulcrum, is equal to the product of the power into its distance ; the weight and the power will be in equilibrium. This is true even where there are several weights on. each side as in figure 21. If the products of A and B into their respective distan- Fig. 21. D G ces from G, be equal to the similar products of C and D, the weights on the opposite sides will balance on another. 121. Levers are divided into three different orders, accord- ing to the position of the pow- er and weight with respect to the fulcrum. 1. In a lever of the first kind the fulcrum is between the power and the weight, as in Fig. 20. 2. In a lever of the second kind, the weight is applied be- tween the power and the ful- crum, as in Fig. 22. 3. In a*lever of the third kind the power is applied be- tween the weight and the ful- crum, as in Fig. 23. Fig. 22. C B r T A Fig> 2 3. MACHINERY. 59 The same law of equilibrium (Art. 120.) holds good in the three kinds of levers ; and where the power is at a greater distance from the fulcrum than the weight, as in the first and second kinds, it is proportionally less than the weight, and where it is nearer the fulcrum than the weight, as in the third kind, it is proportionally greater than the weight, or acts under what is called a mechanical disadvantage. 122. When levers are not straight, but more or less crooked, a sim- ilar principle of equilibrium holds good, the distance of the weight or power from the fulcrum being estimated by the length of a perpendicu- lar drawn from the fulcrum to the line of direction in which the power acts. Thus in figure 24, ABC is a crooked lever, in which the power Fig. 24. and weight act in the directions of the lines BS and AS. Now the distances from the fulcrum being measured by the perpendiculars CM and CN, the general law of equilibrium holds, viz. that the pow- er is to the weight, as the distance of the weight from the fulcrum is to the distance of the power from the fulcrum. 123. A compound lever consists of several simple levers combin- ed together. In a compound lever, the power arid the weight balance each other, when the product of the power multiplied into all the arms on the side next to it, is equal to the product of the weight into all the arms next to the weight. 60 MECHANICS. Fig. 25. Q A oj G E w Thus, in figure 25, the product of P X AC XBF xDG=W X GE X FD X CB. Suppose, for example, the longer arms of the lever are severally twice the length of the shorter, and that the weight to be raised equals 400 pounds ; what power must we apply ? 1 X 1 X 1 X400 =2X2X2X50. Hence, 50 Ibs. applied at P would bal- ance 400 Ibs. at W. 124. Examples. 1. Upon the extremities of a straight lever, are hung two weights, A and B, the former weighing 15 and the latter 60 pounds; how much farther is A from the fulcrifm than B ? By figure 20, AC : CB: :60 : 15; but 60 : 15: :4 : 1 ; therefore, the smaller weight is four times as far from the fulcrum as the larger. 2. One end of a lever is 44 feet, ,and the other 5 feet; what power must I apply to the longer end to balance a weight at the shorter end of 500 Ibs. ? 5x500 44 : 5::500 : 44 =56 Ibs. 13 T ' T oz. Ans. 3. In a compound lever, (Fig. 25.) the lengths of the longer arms are 5, 10, 16 feet, respectively, and of the shorter 1, 2, 3 feet; what power, applied to the longer side, will be required to balance a weight of 100 pounds? 5X10X16 : Ix2x3::100 : f Ib. Ans. 4. Wishing to lift from its bed a rock weighing 1000 Ibs., I take a handspike 6 feet long, and applying the shorter end to the rock, rest it on a fulcrum at the distance of Ij feet from the rock; how much force must I exert at the end of the longer arm to raise the rock? Ans. 333 J Ibs.* * This force would just balance the weight ; any additional force would raise it. MACHINERY. 61 5. A lever of the second order is 20 feet long : at what distance from the fulcrum must a weight of 112 Ibs. be placed, so that it may be supported by a power able to sustain 50 Ibs. acting at the ex- tremity of the lever? Ans. 8 feet and 11} inches. 6. In a compound lever, the three shorter arms are, respectively, 1, 2, 4 feet; the three longer arms 9, 11, 12; the power applied at the end of the longer arm is 3 pounds : what weight will it raise ? Ans. 445J Ibs. 125. The principle of the lever, has a most extensive application in the arts, and the forms under which it occurs are very various. We may contemplate it as having equal or unequal arms. The balance affords the most common example of a lever with equal arms. The necessity of arriving at the weight of bodies with the greatest degree of accuracy in pecuniary transactions, and more especially in delicate scientific researches, as those of chemical anal- ysis, has induced men of science, and^artists, to bestow great and united attention upon the construction of this instrument, until they have brought it to an astonishing degree of perfection. Fig. 26. 126. The princi- pal parts of the bal- ance are the beam GH (Fig. 26.) the points of suspen- sions G and H, and the fulcrum F. In order to construct a perfect balance, the most important par- ticulars to be at- tended to, are the length of the arms, that is, of the beam; the situation of the center of gravity of the whole instrument, with respect to the fulcrum or center of motion ; and the position of the point of suspension. 62 MECHANICS. (1.) The sensibility of the balance is increased by increasing the lengths of the arms; but unless the arms, when long, are at the same time of considerable weight, they will not have the requisite strength, but will be liable to bend ; and an increase of weight, adds to the amount of friction on the center of motion. It is not common there- fore to make the arms of a very delicate balance more than nine inches in length ; and, for the purpose of uniting lightness with strength, the beam is composed of two hollow cones placed base to base, as in Fig. 26. (2.) The center of gravity of the instrument, must be a little be- low the center of motion. For if the beam is balanced on its cen- ter of gravity, it will remain at rest in every position, whereas it must be at rest, only when in a horizontal position. If the center of grav- ity is above the center of motion, the position is too unstable, and on the least disturbance of the equilibrium, the beam will be liable to upset. Finally if the center of gravity is too far below the cen- ter of motion, the equilibrium will be too stable. Hence, in very delicate balances, the center of motion is placed a little above the center of gravity. (3.) The points of suspension must be in the same right line with the center of motion. For since when weights are added to the scales, the effect is the same as though they were concentrated in the points of suspension ; and were those points above the center of motion, the center of gravity would be liable to be shifted above the center of motion, when the beam would upset ; and if the same points were below the center of motion, unless the weights added were large, the center of gravity would be too low, and the equi- librium too stable. 127. In order to prevent friction as much as possible, the fulcrum is made of hardened steel, and shaped into a triangular prism, or knife edge, smoothly rounded, and turning on a plane of agate or steel, or some othervery hard and polished substance. It is.^nly by a nice attention to all these particulars that artists have been able to give to the balance so great a sensibility. Some balances have been made to turn with the 1000th part of a grain. By loading MACHINERY. 63 the beam the sensibility of the instrument is diminished ; (Art. 124.) it is customary, therefore, to estimate its power by finding what part of the weight with which it is loaded it takes to turn it. Thus, if when loaded with 7000 grains, it will turn with 1 grain, its power is T ^ 7 . A balance constructed by Ramsden, a celebrated English artist, for the Royal Society, turned with the ten millionth part of the weight. Delicate balances are usually covered with a glass case to prevent agitation from the air, and to secure them from injury. Figure 26. represents an instrument of this kind made for the Royal Institution of Great Britain. 128. The bent lever balance is represented in figure 27. The weight C acts as though it were concentra- ted in the point D, and the weight in the scale acts at K ; hence an equilibrium will take place, when the article weighed has to C the same ratio as DB has to BK. Now every increase of weight added to the scales causes C to rise on the arc F G, and D to recede from B. Hence the different posi- tions of C, according as different weights are added to the scale, may be easily de- termined, and the corresponding numbers marked on the scale F G. 129. It is essential to an accurate balance, that the two arms should be precisely equal in length. The false balance, which is sometimes used with a design to defraud, has its arms unequal. The dealer turns such an instrument to his account both in buying and selling. In buying, he puts his weights on the longer side, for then it takes more than an equivalent to balance them ; and, in selling, he puts his weights on the shorter side, because less than an equivalent will produce an equilibrium. The fraud may be detected by ma- king the weights and the merchandize change places. The true weight may be determined from such a balance, by putting the arti- cle whose weight is to be determined, into one scale, and counter- poising it with sand, shot, or any convenient substance, in the other scale, and then, removing the article, and finding the exact weight 64 MECHANICS. of the counterpoise. It is evident that the weight of the merchan- dize will be the same as that of the weights employed to balance its counterpoise. 130. The steelyard is a lever having unequal arms, in which the same body is made to indicate different weights, by placing it at dif- ferent distances from the fulcrum. A pair of steelyards has usual- ly two graduated sides for determining smaller or greater weights. It will be seen that on the greater side, the weight is placed nearer the fulcrum. Consequently, the weight indicated by the counter- poise, when at a given distance from the fulcrum, will be proportion- ally greater. This instrument is very convenient because it requires but one weight. The pressure on the fulcrum, excepting that of the apparatus itself, is only that of the article weighed, whereas in the balance, the fulcrum sustains a double weight. But the balance is susceptible of more sensibility than the steelyard, because the sub- divisions of its weights can be effected with a greater degree of pre- cisionlhan the subdivision of the arm of a steelyard. 131. The spring steelyard is a very convenient instru- ment for weighing in cases where the subdivisions of weights are large. It depends on the elasticity of a spiral steel spring, to compress or extend which requires a force pro- portioned to the degree of compression or extension. The manner of applying it will be easily understood from the representation in figure 28. After continued use, espe- cially when loaded with heavy weights, the elasticity of the spring is liable to be impaired, and the accuracy of the instrument diminished. When made, however, in the best manner, spring steelyards retain their accuracy for a long time. 132. The steelyards or balance used for estimating very heavy weighty as loaded carts, depends upon the principle of the com- pound lever. The several levers are usually placed beneath a plat- form, which rests on pivots connected with the shorter arms, while the counterpoise is connected with the extremity of the longer arms. MACHINERY. 65 In figure 29, is repre- Fi S- 29 sented a weighing ma- chine employed in Eng- land, for estimating loads that are transported on turnpike roads. It con- sists of a platform rest- ing on four levers of the second kind, the weight being between the ful- C crum and the power. The fulcrums are A, B, C, D, and the plat- form, and consequently the weight rests on the points a, b, c, d. Suppose AF to be ten times the length of Aa, then 10 pounds at F, would balance 100 pounds at , and if the arm EG is ten times the length of EF, then ten pounds at G will balance 100 pounds at F. Let us then apply 10 Ibs. at G; this pressing upon F with the force of 100 Ibs., will press upon a with the force of 1000 pounds. This would be the case were only one lever employed in the place of the four : the fulcrums a, b, c, dj divide this pressure equally among themselves. 133. When a weight is supported by a lever which rests on two props the pressure upon both fulcrums is equal to the whole weight. This principle is sometimes applied in ascertaining the weight of a body too heavy for the steelyards. The body is suspended immov- ably near the center of a pole, and the steelyards are applied to each end of the pole separately, the other end meanwhile resting on its fulcrum. The two weights being added together, make the entire weight of the body. If the body is suspended exactly in the center of the pole, it will be sufficient to obtain the weight of one end and double it. The weight of the lever should, in both cases, be sub- tracted from the entire weight. 134. Since when a weight 'is sustained between two props, the part sustained by each prop is inversely as the distance of the weight from it, it follows that a load borne on a pole, between two bearers, is distributed in this ratio. As the effort of the bearers, and the di- rection of the weight are always parallel, it makes no difference 9 66 MECHANICS. whether the pole is parallel to the horizon or inclined to it. Wheth- er the bearers ascend or descend, or move on a level plane, the weight will be shared between them in the same constant ratio. 135. Handspikes and croivbars are familiar examples of levers of the first kind. A hammer affords an example of the bent lever; and shears, pliers, nutcrackers, and all similar instruments, are double levers; that is, they consits of two levers united. A pair of shears with long handles, like those used by tinners, exhibit very strikingly the increase of power gained by bringing the weight or substance acted on riearer to the fulcrum. The jaws of animals ex- hibit a similar property. An oar, applied to a boat rowed by hand, a wheelbarrow, and a door shut by the hand applied to the edge re- mote from the hinges, severally furnish instances of levers of the se- ond kind, where the weight is between the fulcrum and the power. 136. The erane is a lever of the second kind which is much used when great weights are transported for a short distance, as heavy boxes of merchandize from a vessel to the wharf, or great masses of stone from the quarry to a car or boat. An example of the crane, on a small scale, is seen in the apparatus of a kitchen fire-place. 137. When one raises a ladder from the ground by one of the lower rounds, the ladder becomes a lever of the third kind, the pow- er being applied between the weight and the prop. Since in all the mechanical powers, the power and weight have equal momenta, and since, in the third kind of lever, the weight has more velocity than the power, the power is as much greater than the weight, as the velocity with which it moves is less. The difficulty experienced in raising a ladder from the ground by taking hold of the lowest round, or of shutting a door by applying the hand to the side next to the hinges, shews the mechanical disadvantage under which a lever of this kind acts. Yet it is very useful in cases where it is required to give great velocity to the body moved. Sheep shears, consist of two levers of this kind united. Here the whole force required is so small that to save it is of no consequence, while so soft and flexible a substance .as wool, requires the shears to be moved with consider- able velocity. A pair of tongs is composed in the same manner ; and therefore it is only a small weight that we can lift with them, es- pecially when the legs are long. MACHINERY. 67 138. One of the most remarkable applications of the third kind of lever, is in the bones of animals. These are levers, the joints are the fulcrums, and the muscles are the power. The muscles are endowed with a strong power of contraction, by which they are made to pull upon a tendon or cord, which is inserted in the bone near the fulcrum. Thus, the fore-arm moves on the joint near the elbow as a fulcrum, a little below which is inserted a tendon, connected with a muscle near the shoulder called the deltoid muscle. The arrangement may be well represented by attaching a small cord to one of the legs of a pair of tongs, near the joint. It will require a considerable force to lift the leg by pulling at the string, especially if the string be pulled in a direction nearly parallel with the leg, as it ought to be, since the tendon which lifts the fore-arm acts in such a direction with respect to the arm. The muscles therefore act, in moving thfft)ones, under a double mechanical disadvantage, their force being applied both obliquely and very near the fulcrum. The force which the deltoid muscles exert in raising a weight held in the palrn of the hand, is enormous, as will be comprehended from the following illustration. Let AB represent the fore-arm, moving on the D Fig. so. elbow-joint at A. and having the tendon inserted at C, which we will suppose to be one hundred times nearer to A than B is to A. * Con- sequently, a weight of 1 Ib. at B, would require a force at C, acting directly upwards, of 100 Ibs. But the force of the tendon does not act directly upwards in the direction of CD, but very obliquely, as in the direction of CE, of which the part E A only can contribute to sup- port the weight. Suppose this part to equal y^th of the whole force CE, and it follows that the muscular force exerted to raise a weight of 1 Ib. in the palm of the hand, would, were it to act without any mechanical disadvantage, be sufficient to raise a weight of 1000 Ibs. Yet Dr. Young informs us, that a few years ago there was a person at Oxford, who could hold his arm extended for half a minute, with half a hundred weight hanging to his little finger. 139. But by giving to the muscle the position it has, the greatest possible compactness of structure is obtained, while by making it act Oo MECHANICS. so near the fulcrum, wHat is lost in force, is gained in velocity ; and while the power acts through a small space, the hands are moved quickly through a great distance. In consequence of the dominion which man can gain over the stronger animals, and especially over the great powers of Nature, he has little occasion to exert great strength with his naked hands : the celerity of their movements, is to him a far more important endowment. CHAPTER IX. MACHINERY CONTINUED. OF WHEEL WORK. 140. When a lever is applied to raise a weight, or to overcome a resistance, the space through which it acts at one time is small, and the work must be accomplished by a succession of short and inter- mitting efforts. The common lever is, therefore, used only in cases where weights are required to be raised through small spaces. When a continuous motion is to be produced, as in raising ore from a mine, or in weighing the anchor of a vessel, some contrivance must be adopt- ed to remove the intermitting action of the lever, and render it con- tinual. The wheel and axle, in its various forms, fully answers this purpose. It may be considered as a revolving lever. Thus in Fig. 31, DE, is an axle resting upon two supports, Land Fig. 31. N T ~ S JVI IT MACHINERY. 69 M ; NAO, SVU are wheels connected with the axle ; W is the weight which may be balanced either by a weight, hung to the cir- cumference of the wheel as w, or by a power applied in the manner of P. The latter mode renders obvious the analogy between the lever and the wheel and axle, since PK, one of the spokes of the wheel, evidently corresponds to a lever of the first kind. In the wheel and axle, the law of equilibrium is as follows : The power is to the weight as the diameter of the axle is to the diam- eter of the wheel. If the diameter of the wheel is ten times that of the axle, a power of one pound will balance a weight of ten. 141. In numerous forms of the wheel and axle, the weight is ap- plied by a rope coiled upon the axle ; but the manner in which the power is applied is very various,- and not often by means of a rope. The circumference of a wheel sometimes carries projecting pins, to which the hand is applied to turn the machine, as in Fig. 31. An instance of this occurs in the wheel used in the steerage of a vessel. In the common windlass the power is ap- plied by means of a winch which corres- ponds to the radius of a wheel. The axis is sometimes placed in a vertical po- sition, and turned by levers moved hori- zontally. The capstan of a ship (Fig. 32.) is an example of this. Levers an- swering to the radii of a wheel are inser- ted in holes mortised in the axis, and turned by several men work- ing together. In some cases, as in the treadmill, the wheel is turn- ed by the weight of animals walking on the circumference with a motion like that of ascending a steep hill. 142. In the COMPOUND WHEEL AND AXLE, the power is to the weight as the product of the diameters of all the smaller wheels is to the product of the diameters of all the larger ivheels. 70 MECHANICS. Thus in Fig. 33, the pow- Fig. 33, er being applied to the winch PQ acts upon the small wheel A, which acts upon the large wheel B, this upon C, and so on. Now if the diameters of the three smaller wheels in- cluding that of the axle, be severally one fourth those of the larger wheels, (of which the diameter of the wheel de- scribed by the winch PQ, that is, twice PQ, must be consid- ered as one) then the pow- er will be to the weight as IXlXl : 4x4x4, that is, as 1 to 64 ; and a force of ten pounds applied at P will balance a weight of 640 pounds applied at W. 143. It is sometimes desirable to make a variable power produce a constant force. This may be done by making its velocity increase as its intensity diminishes. We have an example of this in the re- ciprocal action between the main spring and fusee of a watch. (Fig. 34.) The main spring is coiled up in the box A, and is connected with the fusee B by a chain. When the watch is first wound up, the spring acts with its greatest intensity, but then as the wheel B turns, it uncoils with the least velocity ; but on account of the varying diameters of the wheels of the fusee, the velocity is continally increased as the intensity of the spring is diminished. In a similar manner a varying weight may be moved by a constant power. 144. Examples. Ex>l. The diameter of a wheel is 4j feet, and that of its axis 1| : what power will be required to balance a weight of 100 Ibs. ? 4J : ij : : 100 : yj =2 Ibs. 123- oz. Ans. Fig. 34. MACHINERY. 71 Ex. 2. What must be the diameter of a wheel by which a weight of 100 Ibs. suspended by a rope going round an axle whose diameter is 1 foot, is balanced by a power of 12 Ibs.? 12 Ibs. : 100 Ibs. ::i : " T y=8ifeet, Ans - Ex. 3. A power of 3 Ibs. acts upon a wheel whose diameter is 6 feet; what weight will balance it upon an axle of 5 inches diameter? Ans. 431 Ibs. Ex. 4. A power of 5 Ibs. balances a weight of 150 Ibs. by means of a wheel 10 feet in diameter : what is the diameter of the axle? Ans. 4 inches. Ex. 5. Four wheels, A, B, C, D, whose diameters are 5, 4, 3, 2 feet respectively, are put in motion by a power of 10 Ibs. applied at the circumference of the wheel A ; the wheels act upon each other by means, of three smaller wheels, the diameter of each of which is 8 inches ; the last wheel D, turns an axle whose diameter is 6 in- ches ; what weight may be sustained by a rope going over the axle ? Ans. 8100 Ibs. Communication of Motion by Wheel Work. 145. Motion may be transmitted by means of wheel work in seve- ral different methods, the principal of which are, the friction of the circumference of one wheel, upon that of another the friction of a band and the action of teeth. One wheel is sometimes made to turn another, by the mere fric- tion of the two circumferences. If the surfaces of both were per- fectly smooth so that all friction were removed, it is obvious that either would slide over the surface of the other, without communica- ting motion to it. But, on the other hand, if there were any asper- ities, however small upon their surfaces, they would become mutu- ally inserted among each other, and neither the wheel nor axle could move without causing the asperities on its edge to encounter those which project from the surface of the other ; and thus both wheel and axle would move at the same time. Hence if the surfa- ces of the wheel and axle are by any means made rough, and press- ed together with sufficient force, the motion of either will turn the other, provided the load or resistance be not greater than the force necessary to break off these small projections which produce friction. 72 MECHANICS. 146. In some cases where great power is not required, motion is communicated in this way through a train of wheel work, by render- ing the surfaces of the wheel and axle rough, either by facing them with buff leather, or with wood cut across the grain. The commu- nication of motion between wheels and axles by friction has the ad- vantage of great smoothness and evenness, and of proceeding with little noise ; but this method can be used only in cases where the resistance is not very considerable, and therefore it is seldom adopted in works on a large scale. Dr. Gregory mentions an instance of a saw mill at Southampton, where the wheels act upon each other, by the contact of the end grain of the wood. The machinery makes very little noise and wears well, having been used not less than twenty years. 147. Wheel work is extensively moved by the friction of aband. When a round cord is used, any degree of friction may be produced, by letting the cord run in a sharp groove at the edge of the wheel. When a strap or flat band is used, its friction may be increased by increasing its width. The surface at the circumference of a wheel which carries a flat band, should not be exactly cylindrical, but a little convex, in which case if the band inclines to slip off at either side, it returns again by the tightening of its inner edge, as may be seen in a turner's lathe. When wheels are connected in the shortest manner by a band, they move in the same direction ; if the band be crossed, they will move in opposite directions. (Fig. 35.) Wheels are sometimes turned by chains in- stead of straps or- bands, and are then called rag wheels. The chains lay hold upon pins, or en- ter into notches, in the circumfe- rence of the wheels so as to cause Tl them to turn simultaneously. They are used when it is necessary that the velocities should be uniform, and where great resistance is to be overcome, as in locomotive steam engines, chain water wheels; &c. MACHINERY. Fig. 36. 148. But the most common mode of moving wheel work, is by means of teeth cut in the circumference of the wheels. The wheels of necessity turn in opposite directions. The connexion of one toothed wheel with another is called gearing. In the formation of teeth, very minute attention must be given to their figure, in order that motion may be communicated from one wheel to another, with- out rubbing or jarring. If the teeth are ill matched as in figure 36, when the tooth A, comes into contact with JB, it acts obliquely upon it, and as it moves, the corner of B slides upon the plane surface of A in such a manner as to produce much fric- tion, and to grind away the side of A, and the end of B. As they approach the position CD, they sustain a jolt the moment their surfaces come into full contact ; and after passing the position CD, the same scraping and grinding effect is produced in the opposite direction, until by the revolution of the wheels the teeth become disengaged. To avoid these evils, the surfaces of the teeth are frequently curved so as to roll on each other with as little friction, and with as uniform force and velocity as pos- sible. (Fig. 37.) Much pains and skill have been bestowed on this subject by mathemati- cians, with the view of ascertaining the kinds of curves which fulfil these purposes best. Regulation of Velocity by Wheel Work. 149. Wheel work serves the purpose, not only of forming a convenient communication of motion between the power and the weight, but also of regulating its velocity.- Thus, when the connexion is formed by means of a band, as in figure 35, the veloci- ty of the wheel B, that carries the weight or sustains the pressure may be altered at pleasure, by altering the ratio between the diameters' of the two wheels. If the diameters are equal, the wheels will revolve with equal velocity; if A remains the same, while the diameter of B is increased or diminished, the velocity of B will be increased or di- minished in the same ratio; or if B remains the same, while the di- ameter of A is changed, the velocity of B will be changed in the 10 74 MECHANICS. same manner. We see familiar examples of the application of this principle in the common spinning wheel, and the turner's lathe. In the spinning wheel, a band passes round a large wheel and a small one called a spool, having the spindle for its axis; and in consequence of the great disparity in the size of the wheels, a grefit velocity is given to the spindle by a comparatively slow revolution of the wheel. In a turner's apparatus, machinery for spinning cotton, and the like, a large hollow cylinder or drum, is fixed horizontally, which is kept revolving by the moving power, and from which, motion is convey- ed by bands to lathes, spindles, &ic., to which any required veloci- ty is given, by altering the diameter of the small wheel that is con- nected with them and turns them. Sometimes a change of veloci- ty is effected by making the drum of a conical shape, and then the velocity imparted to the lathe or the spindle, will be greater or less, according as the band proceeds from the larger or smaller part of the drum. 150. A more exact method of regulating the velocity of motion, is by means of wheels and pinions. An example of this kind is seen in Fig. 38. where A, B, C, are three wheels, and #, &, c, are the corresponding pinions. As the leaves of the pinions succes- sively pass between the teeth of the wheel, they must be equal and similar to them ; and since magnitudes have the same ratio to each other as their like parts, it follows that the number of teeth in a wheel, and of leaves in the pinion that acts upon it, express the ratio of the circum- ference or radius of the wheel to that of the pinion. Hence, in an equilibrium, the power multiplied by the product of the numbers ex- pressing the amount of teeth in all the wheels respectively, is equal to the ^eight multiplied by the product of the several numbers deno- ting the leaves in each of the pinions. 151. It is farther evident that the velocity of a wheel and that of the pinion connected with its circumference, will be inversely as the MACHINERY. 75 number of teeth in each. Thus in Fig. 38. if the pinion a has 10 teeth, and the wheel B has 100, a will move ten times as fast as B. For the same reason b will move ten times as fast as C, so that, in this arrangement, the power moves with 100 times the velocity of the weight. By varying the ratio between the number of teeth in the pinion, arid the number of teeth in the wheel with which it is con- nected, we may vary the velocity of any wheel at pleasure. 152. A familiar instance of this is afforded in the mechanism of a common clock. A pendulum by falling gains a quantity of mo- tion sufficient to carry it on the other side to the same height as that from which it fell ; and were it not for the resistance of the air and the impediments, a pendulum when once set in motion would con- tinue to vibrate by its own inertia, and would thus afford, without the aid of any machinery, an exact measure of time. But, in order to continue its vibrations, some small force must be applied to it to compensate for the loss of motion from friction and resistance. This force is supplied to the pendulums of clocks by the weight, and an analogous force is supplied to the balance wheel of watches and chronometers by springs. In Fig. 39. let A B be a wheel having 30 teeth, and let N, M, be a pendulum, connected with the wheel by the pallets I, K ; and to the axis a, let a weight be hung. It is evident that this weight, were there nothing to arrest' it, would descend by the force of gravity with accelerated velocity. It endeavors thus to descend, and hence exerts the required force on the pallets of the pendu- lum. For, every time the pendulum performs a double vibration*, (returning to the same point from which it set out) a tooth of the wheel escapes,* and the wheel runs down until the next tooth strikes upon the pallet, and thus gives it the impulse which is necessary to keep up the vibrations. 153. It would seem therefore that, for beating seconds, only a sin- gle wheel is necessary ; nor would any more be absolutely indispen- Fig. 39. K * Hence this wheel is called the scapement. 76 MECHANICS. sable ; but in this case the weight would descend so fast, as soon to reach the floor, and the clock would require to be wound up again every few minutes. Hence a series of wheels are interposed be- tween the pendulum and the weight, by which the descent of the latter is retarded upon the principle explained in Art. 151. and the descent of the weight is slower in proportion as the series is more extensive. In cheap clocks, as some of those made with wooden wheels, the series is short, or the number of wheels employed for re- tarding the descent of the weight is small, and such clocks require frequent winding up ; but in clocks of finer workmanship, a greater number of wheels is interposed, and such clocks require to be wound up less frequently. Many go eight days, and some are made to go a whole year without winding. Wheel Carriages. 154. In wheel carriages, wheels are not used as mechanical pow- ers ; for, since they move with the same velocity as the power which propels them, there is no mechanical advantage gained by them. When we shut a door by taking hold of the edge most remote from the hinges, the door becomes a lever of the second kind, and we act under a mechanical advantage. When we shut the door by ap- plying the hand near the hinge, the door becomes a lever of the third kind, and we act under a mechanical disadvantage. There is, however, a point between the inner and outer edge, where the force would act without either advantage or disadvantage. In like man- ner, a carriage wheel is turned on the ground as.on a hinge by a force applied at its center of gravity ; and, in passing over an obsta- cle, it rolls over it as a door turns on its hinges. The necessity of a certain amount of resistance or friction in the plane on which the wheel revolves is obvious, because otherwise there could be no ful- crum or hinge on which it could turn. Thus wheels moving on smooth ice, slide instead of turning ; and when the power is applied to the circumference, if the friction is not sufficient to act as a ful- crum, the wheel turns without advancing, as a wheel turning in the air. Large wheels appear in theory to be much more advantageous than small ones. A large wheel will better surmount stones and other obstacles, since in turning over, the ascent is more gradual and easy. In passing over holes, it sinks less, and occasions less jolting and less expenditure of power. The wear of small wheels exceeds MACHINERY. 77 that of large ones ; for if we suppose a wheel to be three feet in di- ameter, it will turn round twice, while a wheel of six feet in diame- ter turns ronnd once. Of course its tire will come twice as often in contact with the ground, and its spokes will twice as often have to support the weight of the load. So that by calculation, it should last but half the length of time. On these accounts it would be advantageous to augment the diameter of wheels to a great extent were it not for certain practical limits which it is found useful not to exceed. One of them is found in the nature of the materials which we are obliged to use, and which if employed to make wheels of great size at the same time preserving the requisite strength, would render them cumbersome and too heavy for use. Again, a wheel should seldom be of such dimensions, that its center is higher than the breast of the horse or other animal by which it is drawn ; because when this is the case, the horse draws obliquely downwards as well as forward, and expends a part of his strength against the ground. 155. The line of draught should not be horizontal but inclined upwards towards the breast of the horse, in an angle not less than 15 degrees with the horizon. This brings the strain nearly at right angles with the collar, whereas a horizontal draught lifts the collar upwards, by which the force is wasted and the animal is choked. 156. The effect of suspending a carriage on springs, is to equal- ize the motion by causing every change to be more gradually com- municated to it, and to obviate shocks. Springs are not only useful for the convenience of passengers, but they also diminish the labor of draught ; for whenever a wheel strikes a stone, it rises against the pressure of the spring, in many cases without materially disturbing the load, whereas without the spring, the load, or a part of it, must rise with every jolt of the wheel, and will resist the change of place with a degree of inertia proportionate to the weight, and the sudden- ness of the percussion. Hence springs are highly useful in baggage wagons and other vehicles used for heavy transportation. A pair of horses draw more advantageously abreast than when one is harnessed before the other. In the latter case, the forward horse, being attached to the ends of the shafts, draws in a line nearly hori- zontal ; consequently he does not act with his whole force upon the load, and moreover expends a part of his force in a vertical pressure on the back of the other horse. 78 MECHANICS, CHAPTER X. i MACHINERY CONTINUED. THE PULLEY, INCLINED PLANE, SCREW AND WEDGE. THE PULLEY. 1 57. A PULLEY is a small grooved wheel movable about a pivot, the pivot itself being at the same time either fixed or movable. The fixed pulley is represented in Fig. 40. By it no mechanical advantage is gained, but its use consists in furnishing a convenient mode of changing the direction of the power. Thus, it is far more convenient to raise a bucket from a well by drawing downwards, as is the case where the rope passes over a fixed pulley above the head, than by drawing upwards, leaning over the well. By means of the pulley, great facilities are afforded for managing the rigging of a ship. The sails at mast head can be easily raised, while the hands stand upon the deck, whereas, without the aid of ropes and pulleys, the same force removed to the mast head would operate under very great disadvantages. Similar facilities are afforded by this kind of apparatus for raising heavy weights, as boxes of mer- chandize, or heavy blocks of stone in building. Fire escapes sometimes consist merely of a pulley fixed near the window of the apartment, around which a rope may be easily placed, having a basket attached to the end. The man seats himself in the basket, grasping, at the same moment, the rope on the other side of the pulley, and thus he lets himself gradually down. 15& The movable pulley is attended with a mechanical advantage, so that by its aid, a comparatively small power may be made to raise great weights. Fig. 41, represents a movable pulley E in con- nexion with a fixed one A. The weight MACHINERY. 79 Fig. 42. _ '- ..... W bears equally upon the two parts of the rope, and consequently that which acts against the power P sustains only half the weight. An equilibrium will therefore be produced when the power is equal to half the weight. In Fig. 42, blocks of pulleys are represented, , in which the weight is distributed over a greater number of parts of the rope ; each part there- fore sustains a proportionally smaller portion of the load, and yet one of these parts is all that acts immediate- ly against the power. Hence the power will be as much less than the weight as the number of parts of the rope is greater than unity, Thus, where there are six parts, three on each side, a power of one pound will balance a weight of six pounds. This principle is generalized in the following proposition. In the pulley an equilibrium is pro- duced, when the power is to the iveight as one to the number of ropes. 159. The ascent of the weight is in all cases retarded in pro- portion as the efficacy of a given power is increased. Moreover, in using any system of movable pulleys, the whole weight of the pulleys themselves, together with the resistance occasioned by the rigidity and friction of the rope, acts against the power, and so far lessens the weight which it is capable of raising. In the more complex sys- tem of puljeys, it is estimated, that at least two thirds of the pow- er is expended on the machinery itself. On account therefore of slowness of the motion which the weight receives, and the loss of power from the resistance of the ropes and blocks, such systems of pulleys are seldom employed. It is only in raising vast weights, such as large ships, or great masses of stone from a quarry, that they are ever used. For managing the rigging of a ship, the com- 80 MECHANICS. bination usually employed consists of not more than two or three movable pulleys. From its portable form, however, its cheapness, and the facility with which it can be applied, especially in changing or modifying the direction of motion, the pulley is one of the most convenient and useful of the mechanical powers. 160. Examples. Ex. 1. I wish to raise a block of stone weighing two tons, or 4480 Ibs. but can command a power only equal to 746| Ibs. : What num- ber of pulleys shall I require ? 746| ; 4480 : : 1 : 6 ropes, or 3 mov- able pulleys, Ans. Since the number of ropes (or parts of the rope,) must be 6, and since each movable pulley has two ropes, as in Fig. 42, therefore the number of movable pulleys must be three ; or the block must be analogous to one of those represented in Fig. 42. In this and other similar estimates no allowance is made for the weight of the pulleys and other parts of the machinery which are raised along with the weight. The amount of these must be added to the weight in order to ascertain the power required. Ex. 2. By a system of pulleys containing 6 movable pulleys, the same string going round the whole as in Fig. 42, what power will be necessary to sustain a weight of 112 Ibs. ? Ans. 9J. Fig. 43 THE INCLINED PLANE. 161. Let Fig. 43, represent an Incli- ned Plane whose length is AC, height AB, and base BC ; and let W be a weight drawn up this plane by a power applied at P and acting parallel to the plane. Then an equilibrium is produced, when the power is to the weight, as the height of the plane to its length. 162, The inclined plane becomes a mechanical power in conse- quence of its supporting a part of the weight, and of course leaving only a part to be supported by the power. Thus the power has to encounter only a portion of the force of gravity at a time, a por- tion which is greater or less, according as the plane is more or less MACHINERY. 81 elevated. When a plane is perfectly horizontal, it sustains the entire pressure of a body that rests on it ; that is, the pressure on the plane is equal to the whole force of gravity acting on the body. As one end of the plane is elevated, this force is resolved into two, one of which is parallel and the other perpendicular to the plane. In pro- portion as the plane is more elevated, the part of the force which acts parallel with the plane is increased, until, when the plane becomes perpendicular to the horizon, it no longer sustains any portion of the weight, and the latter descends with the whole force of gravity. 163. The simplest example we have of the application of the In- clined Plane, is that of a plank raised at the hinder end of a cart for the purpose of rolling in heavy articles, as barrels or hogsheads. The force required to roll the body on the plank, setting aside friction, is as much less than that required to lift it perpendicularly, as the height of the plane above the ground is less than its length. Every one knows how much the facility of moving heavy loads is increased by such means, and how the force required to move them is dimin- ished, by increasing the length of the plane while the height remains the same. Long inclined planes, constructed of plank, are frequent- ly employed in building, especially where high walls are built of large masses of stone, the materials being trundled up the plane on wheel barrows, or transported on heavy rollers, ft is even supposed that in building the pyramids of Egypt, the huge masses of- stone were elevated on an inclined plane. Roads also, except when they are perfectly level, afford examples of this mechanical power. When a horse is drawing a heavy load on a perfectly horizontal plane, what is it that occasions such an expenditure of force ? It is not the weight of the load, except so far as that increases the friction ; for gravity, acting in a direction perpendicular to the horizon, can oppose no re- sistance in the direction in which the load is moving. The answer is, that the force of the horse is expended chiefly in overcoming friction, and the resistance of the air. But when a horse is drawing a load up a hill, he has not only these impediments to encounter, but has also to overcome more or less of the force of gravity; that is, he lifts such a part of the load as bears to the whole load the same ra- tio, that the perpendicular height of the hill bears to its length. If the rise is one foot in twenty, he lifts on twentieth of the load, and 11 82 MECHANICS. therefore encounters so much resistance in addition to the resistan- ces which he had to overcome on the horizontal plane. If the ascent were one foot in four, and the load were a ton, the additional force required above what would he necessary on level ground, would be 560 pounds* 164. Railways afford another striking exemplification of the prin- ciples of the Inclined Plane. By means of them the irregular sur- face of a country, however hilly and uneven, is reduced to horizon- tal levels and inclined planes. These are sometimes inclined at so low an angle, that the tendency of the cars down the plane, is only just sufficient to balance their friction, and they would remain at rest of themselves in any part of the plane, while a small force would move them either way. In other places the Inclined Planes are very steep for a short distance ; and the cars ascending upon them are sometimes drawn up by means of a power (a steam engine for exam- ple,) stationed on the summit, and sometimes cars descending on one side, are made to draw up others on the other side, the two being connected by a chain or rope which passes round a pulley on the summit. It is said that on a well constructed horizontal railway a single horse will draw a load weighing ten tons. 165. The Inclined Blane has been very advantageously substitu- ted for Locks on Canals. The method, in general, is to construct around the Falls a railway in the form of an inclined plane ; and then the boat being floated into a large cistern of water, the whole is placed on the inclined plane, (the lower end of the cistern being supported so as to keep the surface of the water level,) and is rolled up or down the plane, either by making descending draw up ascend- ing loads, or by drawing up the ascending cistern with its boat by means of machinery. In the latter case, the water fall itself acting on a wheel, may be made to afford the requisite power. 166. The motion of bodies descending down inclined planes, is subject* to the same law of gravity as bodies falling freely ; that is, it is uniformly accelerated. Consequently, here, as in the case of bo- dies falling without impediment, the spaces described are proportioned to the squares of the times, and to the squares of the velocities acqui- red. (Arts. 59 and 63.) MACHINERY. 83 167. The velocity acquired in fatting down an inclined plane is the same as that acquired in fatting through the perpendicular height of the plane. When a plane is but slightly elevated, as in rail-roads, the accele- ration, though constant, is comparatively slow;but after rolling freely through such a distance as several miles, the motion may become exceedingly rapid. A very remarkable example of the acceleration of bodies descending down inclined planes, occurs at the Slide of Alpnach in Switzerland. On Mount Pilatus, near Lake Lu- zerne, is a valuable growth of fir trees, which, on account of the in- accessible nature of the mountain, had remained for ages uninjured, until within a few years, a German engineer contrived to construct a trough in the form of an inclined plane, by which these trees are made to .descend by their own weight, through a space of eight or nine miles from the side of the mountain to the margin of the lake. Although the average declivity is no more than about one foot in sev- enteen, and the route often circuitous and sometimes horizontal, yet so great is the acceleration, that a tree descends -the whole distance in the short space of six minutes. To a spectator standing by the side of the trough, at first is heard on the approach of a tree, a roar- ing noise, becoming louder and louder ; the tree comes in sight at the distance of half a mile, and in an instant afterwards shoots past with the noise of thunder and the rapidity of lightning. WJien a tree happens to " bolt" from the trough, it cuts the standing trees quite off. 168. It takes as much longer for a body to descend down an in- clined plane, than to fall through its perpendicular height as the length of the plane exceeds its height. A Thus, in Fig. 44, a body in .descending successively down the planes AC, AD, AE, would acquire in each case the same velocity, being the same as it would ac- quire by falling down AB ; but the times of describing these several lines would be proportioned to their respective lengths. 84 MECHANICS. THE SCREW. 169. When a road, instead of ascending a hill directly, winds round it to the summit, so as to lengthen the inclined plane, and thus aid the moving force, the Inclined Plane becomes a Screw. In the same manner a flight of stairs, winding around the sides of a cylindri- cal tower, either within or without, affords an instance of an inclined plane so modified as to become a screw. These examples show the strong analogy which subsists between these two mechanical powers ; or rather, they show that the screw is a mere modification of the Inclined Plane. This correspondence between the Inclined Plane and the Screw is exhibited in the annexed figure. The Fi S- 45 - distance between two con- tiguous threads of a screw, corresponds to the height C of an inclined plane, and the circumference of the cylinder corresponds to the base of the same plane ; hence the forces necessary to produce an equilibrium in the screw, are the same as in the inclined plane. Thus, let the inclined plane ABC be wrapped round a cylin- der, the circumference of whose base is equal to the line AB; then the point A being placed on A 7 , the point B will come round to A', and the point C will fall on C 7 , and the line AC will trace out the thread of the screw on the surface of the cylinder as far as C 7 , and may be continued in the same manner. It will be re- marked that the power here acts parallel to the base of the incli- ned piaffe. Thus in figure 46, the power is applied to the han- dle B, which revolves parallel to the base of screw, or the base of the inclined plane of which the screw is formed Fig. 46. MACHINERY. 85 170. In the screw, an equilibrium is produced when the power is to*the weight, as the distance between two contiguous threads is to the circumference of the base. By inspecting figure 45, it will be seen that "the distance be- tween two contiguous threads," is the height CB of the inclined plane ABC, while " the circumference of the base" is the base AB of the same plane. The law of equilibrium of the screw is there- fore the same as in the inclined plane when the power act's in a di- rection parallel with the base ; in this case the power being to the weight as the height of the plane to the base. 171. The power however is not always applied directly to the circumference of the screw, but frequently at the end of a lever in- serted into the screw as in figure 46, and as in the common cider press. Hence a more general law of equilibrium is as follows : In the screw, an equilibrium is produced when the power is to the weight, as the distance between two contiguous threads is to the cir- cumference of the circle described in one revolution of the power. 172. The Screw is generally employed where severe pressure is to be exerted through small spaces, and is therefore the agent in most presses. Being subject to great loss from friction, (upon which however, its chief utility depends, as will be shown hereafter,) it usu- ally exerts but a small power of itself, but derives its principle effi- cacy from the lever, or from wheelwork, with which it is very easily combined. Thus, in figure 46, were the power applied directly to the screw, the mechanical advantage gained wpuld hardly more than compensate for the loss by friction ; but by means of the lever (which may be lengthened or shortened at pleasure) the power is greatly in- creased. The endless screw is represented in figure 48. It is used in connexion with toothed wheels. By means of the endless screw, combined with the wheel and axle, a very powerful force may be exerted ; and as the mechanical power of the screw depends upon the relative magnitude of the circumference through which the pow- er revolves, and the distance between the threads, it is evident that, to increase the efficacy of the machine, we must either increase the length of the lever by which the power acts, or diminish the distance 86 MECHANICS. between the threads. Although,' in theory, there is no limit to the increase of the mechanical efficacy by these means, yet practical fn- convenience arises from the great space over which a very long lev- er traverses. If, on the other hand, the power of the machine is increased by diminishing the distance between the threads, and of course their size, the thread will become too slender to bear a great resistance. The cases in which it is necessary to increase the pow- er of the machine, being those in which the greatest resistances are to be overcome, the object will evidently be defeated, if the means chosen to increase that power, deprives the machine of the strength which is necessary to sustain the force to which it is to be sub- mitted. 173. These inconveniences are remedied by Hunter's Screiv, which, while it gives to the machine . all the requisite strength and compactness, allows it to have an almost unlimited degree of me- chanical efficacy. This screw is composed of a smaller and a larger thread, the former turning upwards while the latter turns downwards with a little greater velocity, and consequently the screw, on the whole, advances with the difference between the larger and the small- er threads ; and since this difference .may be small to any extent, so the efficacy of the power may be increased indefinitely. It will be seen, however, that the motion of such a Fig 47 screw is exceedingly slow. Thus, in fig- ^^ ure 47, A descends, while B, playing in a concave screw in A, ascends ; but the dis- tance between the threads of A being great- er than the distance between those of B, the screw, on the whole, advances with the dif- ference. Suppose that A has 20 threads in an inch and B 21 ; then during one rev- olution, A will descend through the 20th, while B ascends through the 21st part of an inch. The compound screw, therefore, will advance through a space -oqual to the difference ; that is, through a space equal to ^V ,_i T =_.i-th of an inch. This small space is therefore, in effect, the distance between two contiguous threads ; and the power of the ma- chine is, as usual, expressed by the number of times their distance * MACHINERY. 87 is contained in the circumference described in one revolution of the power. For example, let the circumference of the circle be one foot; then 12-~ io=5040= the weight or resistance, the power being 1 ; or, in other words, the efficacy of the power is increased five thousand and forty times. 174. It is obvious, however, from principles already explained, that the power will in this case move over 5040 times as great a space as the weight. It is on this principle that the Screw affords the means of measuring very minute spaces, and hence is derived the Micrometer Screw. The very slow motion which may be imparted to the end of a screw, while the power moves over a space vastly greater, renders it peculiarly adapted to this purpose. For example, suppose a screw to be so cut as to have 50 threads in an inch : then each revolution of the screw will advance its point through the 50th part of an inch, and if that point acted against a thread or wire, it would move it over a graduated space only that distance in a whole revolution of the screw. Now suppose the head of the screw to be a circle an inch in diameter, and of course something more than three inches in circumference. This circumference may easily be divided into a hundred equal parts, distinctly visible ; and if a fixed index be applied to it, the hundredth part of a revolution of the screw maybe observed, by noting the passage of one division of the head under the index. But the hundredth part of a revolution carries the point of the screw only through the ( T i 7 of I 1 - = ) J ^-th part of an inch. Such an apparatus is frequently attached to the limbs of graduated instruments, for the purposes of astronomical and other observations ; by which means, a potion of the graduated are no greater than the 100th part of a second, can be estimated. In like manner, any other small space may be measured by the aid of the Micrometer Screw. Thus, any aliquot part of a pound, or an ounce, in the steelyards, may be found by adapting the screw to the counterpoise so as to move it slowly over the space between two notches, and at the same time point out, by an index on its head, the exact portion of the space over which it passes. I 4ft 175. Several of the mechanical powers are frequently combined in the same machine. The manner in which this is done is exem- plified in the figure annexed to the following problem. 88 MECHANICS. Fig. 48. A shipwright wishing to' haul a ship upon the stocks, employed a machine, combining the lever, the screw, the wheel and axle, the pulley, and the inclined plane, as represented in the annexed dia- gram. The handle of the winch BCs=18 inches. The distance of the threads on CD=1 inch. The diameter -of the wheel ED =4 feet. The diameter of the axle EF=lfoot. G is a fixed, and H a movable pulley, the number of strings =4. Height of the plane equals half its length. Allowing a man to turn on the handle B with a power equal to 100 Ibs., how much force could he exert on the ship? By Art. 171. 100 Ibs. exerted at B would become, atD, 11309.76 And since the diameter of the wheel is four times that of the axle, X 4 Again, this is rendered fourfold by the four strings of the pulley, f Finally, this is doubled by the plane, 45239.04 180956.16 2 361812.32 Hence, the force exerted on the ship would amount to more than 361812 Ibs., or more than 161 J tons. THE WEDGE. *> 176. If instead of moving a load on an inclined plane, the plane itself is moved beneath the load, it then becomes a Wedge. Thus, if a perpendicular beam have one end resting upon an inclined plane, (the beam being so secured as to be capable of moving only up and MACHINERY. 89 down,) and the plane be drawn under it, the beam will be elevated; and the power required to effect this will be to that required to raise the beam when applied directly to it, as the height of the plane to its length : or, considering the plane as a half wedge, the propor- tion will be, as half the back of the wedge to its length. 111. In the arts and manufactures, wedges are used where an enormous force is to be exerted through a very small space. Thus it is resorted to for splitting masses of timber or stone. Ships are raised in docks by wedges driven under their keels. The wedge is the principal agent in the oil mill. The seeds from which the oil is to be extracted are introduced into hair bags, and placed between planes of hard wood. Wedges inserted between the bags are driv- en by allowing heavy beams to fall on them. The pressure thus excited is so intense, that the seeds in the bags are formed into a mass nearly as solid as wood. Instances have occurred in which the wedge has been used to restore a tottering edifice to its perpen- dicular position. All cutting and piercing instruments, such as knives, razors, scissors, chisels, nails, pins, needles, awls, &c. are wedges. The angle of the wedge, in these cases, is more or less acute, accord- ing to the purpose to which it is applied. In determining this, two things are to be considered the mechanical power, which is increas- ed by diminishing the angle of the wedge ; and the strength of the tool, which is always diminished by the same cause. There is, therefore, a practical limit to the increase of the power, and that degree of sharpness only is to be given to the tool, which is consist- ent with the strength requisite for th6 purpose to which it is to be applied. In tools intended for cutting wood, the angle is generally about 30; for iron it is from 50 to 60; and for brass, from 80 to 90. Tools which act by pressure may be made more acute than those which are driven by a blow; and, in general, the softer and more yielding the substance to be divided is, and the less the power required to act upon it, the more acute the wedge may be constructed. 178. In many cases, the utility of the wedge depends on that which is entirely omitted in the theory, viz. the friction which arises between its surface and the substance which it divides. This is the case when 12 90 MECHANICS. pins, bolts, or nails, are used for binding the parts of structures to- gether ; in which case, were it not for the friction, they would recoil from their places and fail to produce the desired effect. Even when the wedge is used as a mechanical engine, the presence of friction is absolutely indispensable to its practical utility. The power generally acts by successive blows, and is therefore subject to constant inter- mission, and but for the friction, the wedge would recoil between the intervals of the blows with as much force as it had been driven for- ward, and the object of the labor would be continually frustrated. 179. The following principle is of great importance in relation to all the mechanical powers, and deserving of particular attention. In each of the mechanical powers, and in every machine, the power and weight balance each other, when the power moves as much faster than the weight as its quantity of matter is less. We can, therefore, make a small power raise a very great weight, by so connecting it with the weight, as to make it move over a very great space while the weight moves over a very small space. By reviewing the several mechanical powers, we shall recognize the operation of this principle in each of them. 180. In levers of the first and second kind, (Figs. 20, 22.) the power being applied at the extremity of the longer arm and farther from the fulcrum than the power, moves over a proportionally great- er space as the lever turns on its fulcrum ; but in the lever of the third kind, (Fig. 23.) the power being applied nearer the fulcrum than the weight, moves with less velocity than the weight, and con- sequently acts under a mechanical disadvantage, and requires to be proportionally greater than the weight. 181. In the wheel and axle, (Fig. 31.) as both the wheel and its axle revolve in the same time, it is obvious that the power applied at the circumference of the wheel must move as much faster than the weight, g the circumference of the wheel is greater than that of the axle. , 182. In the pulley, when the rope merely passes over a fixed pulley, (as in Fig. 40.) the power and weight move over the same MACHINERY. 91 space, and no mechanical force is either gained or lost ; but in the movable pulleys represented in figure 24, the strings that raise the weight are equally shortened, and the power is lengthened by an amount equal to that by which the several pahs are shortened ; consequently, the power moves as much faster than the weight as the number of ropes is greater than unity. When the number of mova- ble pulleys is great, the great space over which the power must move in order to raise the weight over a comparatively small space, presents a practical inconvenience. 183. In the inclined plane, the greater the length of the plane in proportion to its height, the slower will be the perpendicular ascent of the weight. For example, if the length of the plane be twice its height, the power must move over twice the space, as it would if it rose perpendicularly, and hence the mechanical advantage gained is in the same ratio, that is, the power required is so much less than the weight. 184. In the screw, while the power performs one complete revo- lution, the weight is elevated only the distance between two contigu- ous threads. Hence, when the power is applied at the end of a long lever, and the distance between two contiguous threads is small, the forward motion of the screw is very slow, while the power traverses a great space. 185. In a combination of the mechanical powers, such as that represented in Fig. 48, we see the same principle very strikingly exhibited. Here the power moves 3619 times as fast as the weight, and the mechanical advantage gained is in the same ratio. 186. Finally, in the wedge, the power of overcoming resistances is proportioned to the acuteness of the wedge ; and the distance to which the parts are separated, that is, the space over which the weight moves, when compared with the space through which the power, (namely, the wedge itself in the direction of the power,) moves, is constantly diminished as the acuteness of the wedge is in- creased. 92 MECHANICS. CHAPTER XI. MACHINERY CONCLUDED. 187. Archimedes is said to have boasted to King Hiero, that " if he would give him a place to fix his machine, (tfoo tf7w,) he would move the world." Yet there can be no machine by the aid of which Archimedes could move the world, in any other way, than by moving, himself, over as much more space than that over which he moved the earth, as his weight was less than that of the whole earth. If Archimedes had received the place he desired, and had also em- ployed what was equally indispensable, a machine which operated free of all resistance, he must have moved with the velocity of a cannon ball, to have shifted the earth only the twenty seven millionth part of an inch in a million of years. 188. From the foregoing principles it will be inferred, that no mo- mentum, or effective force is gained by any of the mechanical pow- ers, or by any machine. If a man with his naked hands, can lift to a given height, as one foot, only 150 pounds in one second, it is im- possible for him to perform any more labor than this by any mechan- ical contrivances. On the contrary, when the structure of the ma- chine is complicated, there is a loss of force, by employing the ma- chine instead of the naked hands, proportioned to the resistance of the parts of the machine itself. It is to be remarked, however, that this doctrine proceeds on the supposition that the useful effect produ- ced is estimated from the joint product of the force, velocity and time. A convenient method of estimating different forces is to draw a heavy weight out of a well, by a rope passing horizontally over a fixed pulley, near the top of the well. Suppose that a man can draw up a rock weighing 100 Ibs. through the space of 50 feet in one minute. He would, of course, be able to draw up ten such masses in ten minutes, weighing in all 1000 pounds. Now by passing the rope over five pulleys, (allowing nothing for the friction of the pull- eys,) he might with the same force lift the whole 1000 pounds at once, but it would rise ten times as slowly as the 100 pounds did before, and consequently would be ten minutes in reaching the top. There- fore, in a given time, it appears that the man would raise the same weight through a given space, with or without the aid of machinery. MACHINERY. 93 In the former case, the 100 Ibs. might have been raised during the ten minutes through the space of 500 instead of 50 feet; but 100X500X10=1000X50X10; so that the labor performed would have been the same in both cases. Let us suppose that P is a pow- er amounting to an ounce, and that W is a weight amounting to 50 ounces, and that P elevates W by means of a machine. In virtue of the property already stated, it follows, that while P moves through 50 feet, W will be moved through 1 foot; but in moving P through 50 feet, fifty distinct efforts are made, by each of which, if applied directly, 1 ounce would be moved through 1 foot. 189. What then, it may be asked, are the advantages gained by Machinery 1 ? The advantages are still very great, for the following reasons. (1.) By the aid of machinery we can frequently apply our force to much better purpose. Thus in lifting a weight out of a well, or in raising ore out of a mine, it is obvious with how much more effect a man can work at the arm of a windlass than he could draw directly upon the rope stooping over the well. So in raising a rock from its bed by means of a handspike or crowbar, we can easily see bow much more effectually we can bring our force to bear upon it than we could do by our naked hands. (2.) By the aid of machinery, a man may be able to perform works to which his naked strength would be wholly incompetent. Thus, as in the preceding exanmple, one might be able to lift a rock from its bed with a handspike upon which he could make no im- pression with his naked hands ; or, by means of pulleys, he might raise a box of merchandize from the hold of a ship, which he could not start at all with riis unassisted force. In each of these cases, if the weight could be divided into small parcels, and if the force could be as advantageously applied without machinery as with it, the labor would be performed as easily in a given time in one way as in the other. But it might not be possible or at least convenient thus to divide it. Or if, instead of dividing it into a number of parcels, the same number of men could act directly upon a weight at once, the amount of labor which they would all exert in raising the weight without machinery, would be the same as that which the single man before supposed would exert with his machinery. But it might not 94 MECHANICS. be convenient to assemble so many hands at a time ; or perhaps such a number could not work advantageously together. A farmer has many occasions for lifting or removing great weights when his labor- ers are not more in number than two or three in all. These must therefore perform the labor of 50 times as many men by being 50 times as long about it. Thus, in the example given on page 88, of a combination of the mechanical powers employed to haul a ship on the stocks, where a single man turning on a winch, with the force of 100 Ibs. exerts a force on the ship amounting to 161 J tons, the ship would move as much slower than the hand as 100 Ibs. is less than 161 J tons; and consequently a great length of time would be re- quired for an individual to perform this labor, even supposing no resistance were encountered from the machinery itself. (3.) Machinery frequently enables a man to exert his whole force in circumstances where, without such aid, he could employ but a part of it. Thus, in winding silk or thread, to turn a single reel might not require one fiftieth part of the force which the laborer was capa- ble of exerting. Suitable machinery would enable him to turn fifty spools at once. (4.) But the most striking advantage of Machinery is not found in the facilities which it lends to the personal strength of man : It lies in this, that it affords the means of calling in to his assistance the superior powers of the horse and the ox, of water, of wind, and es- pecially of steam. Here we find the excellence of mechanical con- trivances fully exhibited ; and no where else has the inventive genius of man displayed itself to so great advantage. But here, as in all other cases, the various combinations of mechanical powers produce no force : k they only apply it. They form the communication be- tween the moving power and the body moved ; and while the power itself may be incapable of acting except in one direction, we are able, by means of cranks, levers and toothed wheels, to direct and modify that force to suit our convenience or necessities. Every one may see examples of this in the construction of the most common saw mill or, flour mill, turned by water. In a mill for grinding wheat, the stones are required to move horizontally, while the action of the water fall is perpendicular. We there'fore receive the whole force on the circumference of a wheel, and transmit it through several in- termediate wheels to the revolving stone, where the grinding is per- MACHINERY. formed. So in a saw mill, the water first communicates a rotary motion to the wheel, and this motion is converted by means of a crank into what is called a reciprocating motion, as that of the saw in its ascent and descent. By means of wheel work the velocity o-f the moving body is increased or diminished at pleasure. 190. In short, machines enable us to form a convenient communi- cation between the power and the weight ; to give to the weight any required direction or velocity ; to apply force to the best advantage ; to vary the circumstances of velocity and time as the amount of our force may require ; and to bring to our aid the great moving powers that exist in nature. Our next object, therefore, will be to see by what particular methods, these several purposes are accomplished. Regulation of Machinery, and Contrivances for Modifying Motion. 191. It is highly important to the successful operation of any ma- chine, that its motion should be regular and uniform. Jolts and ir- regular movements waste the power, wear upon the machine, and perform the work unevenly. The sources of irregularity are vari- ous, but they are chiefly the three following, viz. variations in the power, variations in the weight or resistance, and changes of veloci- ty in parts of the machine itself. Thus in the steam engine, the fire may burn with more or less intensity and produce corresponding quan- tities of the moving power ; the load to be carried (as that of a steam boat,) may be much greater at one time than at another, and be sub- ject to sudden changes ; and the motion of the piston, which carries the machinery, ceases altogether at the highest and lowest points, and would move a machine by hitches or separate impulses, were there no contrivance connected with it for keeping up a uniform mo- tion. 192. The kinds of apparatus employed to obviate these difficul- ties, and to secure uniform movements to machines, are, in general called REGULATORS. Large machines or engines themselves, in con- sequence of their inertia, acquire and maintain, to a considerable ex- tent, uniformity of motion. A flour mill carried by water, when it has acquired^ certain rate of going, will not suddenly change that rate by any alteration in the force of the stream ; and a ship sailing 96 MECHANICS. 49. between the opposite forces, arising from the impulse of the wind and the resistance of the water will move steadily along, notwithstand- ing the breeze that carries it snay fluctuate continually. We can see this principle sometimes operating on a smaller scale. A grindstone turned by a winch moves steadily, although the force applied at one part of the revolution is much greater than at another. Large grind- stones exhibit the advantage of this principle much more than small ones. But in many instances, this natural tendency towards uniform motion is not sufficient, and artificial contrivances are introduced ex- pressly for this purpose. As examples of Regulators we may espe- cially notice two, the Pendulum, and the Fly Wheel. 193. The Pendulum, by its equal vibrations, communicates to del- icate machinery a motion extremely regular, and hence its applica- tion to the measurement of time. The Fly Wheel, affords the most common and effectual method of equalizing motion, especially in heavy kinds of machinery. It consists of a heavy wheel (Fig. 49,) affording as much weight as possible under as small a sur- face, in order that the inertia may be great while the resistance from the air is small. It is therefore usually a heavy hoop of iron with thick bars of the same metal. The Fly is balanced on its axis, and so connected with the machinery as to turn rapidly around with it, and receiving a constant impulse from the moving power, it becomes a magazine or repository of motion. Consequently, by its inertia, it is ready to supply any deficiency of power that may arise from the sudden dim- inution of the moving force or to check any sudden impulse which may result from an accidental excess of that force. Suppose, for example, the handle of a pump to be connected with a water wheel, and to be carried by it. Here the power, namely the water fall, is constant, while the weight is subject to continual alternations, amount- ing to a heavy load as the piston is ascending, but opposing scarcely any resistance while the piston is descending. The motion, there- fore, would vary between nothing and a highly accelerated velocity, and the machinery would be subject to constant strains and jolts. A MACHINERY. 97 Fly prevents these alternations and renders the ascent and descent of the piston nearly uniform. In pile engines or stamping mills, a team of horses is sometimes employed to raise a heavy weight, which when at a certain elevation, is suddenly disengaged and falls with great force. As the disengagement is instantaneous, the horses would instantly tumble down were not their motion checked by some contrivance which should prevent the machinery from receiving any sudden increase of velocity. This purpose is completely answered by the Fly. 194. Beside the use of the Fly Wheel in regulating the action of Machinery, it is employed for the purpose of accumulating suc- cessive exertions of a power so as to produce a much more forcible effect by their aggregation, than could possibly be done by their sepa- rate actions. If a small force be repeatedly applied in giving rota- tion to a Fly Wheel, and be continued until the wheel has acquired a very considerable velocity, such a quantity of force will be at length accumulated in its circumference, as to overcome resistance and pro- duce effects utterly disproportionate to the immediate action of the original force. Thus it would be very easy in a few seconds, by the mere action of a man's arm, to impart to the circumference of a Fly Wheel, a force which would give an impulse to a musket ball equal to that which it receives from a full charge of powder. 195. The same principle explains the force with which a stone may be projected from a sling. The thong is swung several times around by the arm until a considerable portion of force is accumu- lated, and then it is projected with all the collected force. If a heavy leaden ball be attached to the end of a strong piece of cane or whalebone, it may easily be driven through a board : by taking the end of the rod remote from the ball in the hand, and striking the board a smart blow with the end bearing the ball, s'-xh a velocity may easily be given to the ball as will drive it through the board. 196. The astonishing effects of a Fly Wheel, as an accumulator of force, have led some into the error of supposing that such an appa- ratus increases the actual force of a machine. So far from this, since a Fly cannot act without friction and resistance from the air, a por- tion of the actual moving force must unavoidably be lost by the use 13 98 MECHANICS. of this appendage. In cases, however, where a Fly is properly ad- justed and applied, this loss of power is inconsiderable, compared with the advantageous distribution of what remains. As an accu- mulator of force, a Fly can never have more force than has been applied to put it in motion. In this respect it is analogous to an elas- tic spring. la bending a spring, a gradual expenditure of power is necessary. On the recoil, this power is exerted in a much shorter time than that consumed in its production, but its total amount is not altered* In this way the Fly Wheel is used. Thus, in mills for rolling metal, the water wheel or other moving power, is allowed for some time, to act upon the Fly alone, no load being placed upon the machine. A force is thus gained which is sufficient to roll a large piece of metal, to which, without such means, the mill would be quite inadequate. In the same manner, a force may be gained by the arm of a man acting on a Fly for a few seconds, sufficient to impress an image on a piece of metal by an instantaneous stroke. 197. We have already explained the mode in which motion is communicated, and its velocity regulated, by wheel work. We pro- ceed now to consider a few examples of the more special contrivan- ces by which motion is modified to suit particular purposes, recom- mending it to the student of mechanics to make himself acquainted with other contrivances of the same nature, by the actual inspection of machinery as opportunity may offer. 198. The motion required for a particular purpose may be recti- linear as that of a carriage or bucket drawn out of a well, or rotary as in ordinary wheel work, or reciprocating as in a saw mill, or a pendulum. The simplest mode of producing rectilinear motion is by means of a rope or chain, instances of which are familiar to every one. The simplest mode of changing the direction is by means of pulleys ; but toothed wheels are also extensively employed for the same purpose. The connexion of one toothed wheel with another is called gearing. When both wheels with their teeth are in the direction of the same plane, it is called spur gearing (figs. 36. 7. and 8.) ; if the teeth, in- stead of being cut on the circumference in a direction parallel to the axis, are cut obliquely, so that if continued they would pass round MACHINERY. the axis like a screw, it is called spiral gearing (Fig. 50.) ; and when wheels are not situated in the same or parallel planes, but form an angle with each other, the wheels themselves are sometimes shaped like frustums of cones, having their teeth cut obliquely, and converg- ing toward the point where the apex of the cone would be situated, and it is thi called bevel gearing, (Fig. 51.) Fig. 50. Fig. 51. Fig. 52. Fig. 53. 199. The universal joint consists of two shafts or arms, each ter- minating in a semicircle, and connected together by means of a cross upon which each semicircle is hinged. (Fig. 52.) When one shaft is turned, either to the right or left, the other shaft turns in the same direction. The ratchet wheel (Fig. 53.) is used to prevent motion in one di- rection while it permits it in the opposite. The teeth are cut with their faces inclining as in the figure, and a catch is so placed as to stop the wheel in one direction, while it slides over the teeth without obstruction in the opposite direction. 200. The. eccentric wheel (Fig. 54.) revolves about an axis which is more or less removed from the cen- ter, and, consequently, the different portions of the circumference move with different degrees of velo- city. Hence, if this wheel is made to act upon a shaft or pinion, as in the figure, it will carry it with a corresponding movement. In orreries, such wheels are employed for indicating the variable velocities of the heavenly bodies, as they revolve about their cen- ters of motion. Fig. 54. 100 MECHANICS. 201. RECIPROCATING MOTION is produced in various ways. The most common method is by means of the crank. In figure 55, a shaft AB is urged backwards or forwards, (either vertically or horizontally,) by means of the crank ab, moving on a wheel H, which may be turned by water or any other power acting at H. By consider* ing the different positions of the crank during the revolu- tion of the wheel, it will be readily seen that the shaft will move up and down like the saw in a saw mill, or backwards and forwards, a use to which it is applied in polishing plane surfaces, as marble. The motion produced by cranks is easy and gradual, being most rapid in the middle of the stroke, and gradu- ally retarded towards the extremes ; so that shocks and jolts in the moving machinery are diminished, or wholly prevented by their use. . The steam engine, as seen in steam boats, furnishes to the student of Mechanics a valuable opportunity of observing various contrivances for producing, regulating, and modifying motion. Lev- ers and wheels of various kinds and variously connected ; fly wheels and cranks ; circular and reciprocating motions ; and numerous oth- er particulars which appertain to the " elements of machinery," are there seen to the greatest advantage, CHAPTER XII. OF THE PENPULUM, OF STRENGTH OF MATERIALS, AND OF FRICTION. The Pendulum, 203. The practical application of the Pendulum to three most im- portant objects, namely, the measurement of time, the estimation of the figure of the earth, and as a standard of weights and measures, renders it deserving of the attention of students of Natural Philosophy. 204. JL Pendulum is a body suspended by a right line from any point, and moving freely about that point as a center. The point PENDULUM, 101 about which the pendulum revolves, is called the center of suspen- sion. The vibration of a pendulum, is its motion from a state of rest at the highest point on one side, to the highest point on the other side. The center of oscillation of a pendulum, is such a point that, were all the matter of the pendulum col- lected in it, the quantity of motion (or mo- mentum) would be equal to the sum of the momenta of all the parts taken separately. Thus, the parts of the pendulum about 6, (Fig. 56.) move faster than those about a, and consequently have more momentum ; but there is a point about which the momenta balance each other, and therefore, in the investigations relating to the pendulum, all the parts of which it consists may be considered as concentrated in that point. The center of oscillation is below the center of gravity; for since the parts more remote from the center of suspension have more ve- locity than the parts that are nearer to it, the quantity of matter be- low the center of oscillation must be less than the quantity of matter above it. 205. The doctrine of the Pendulum is mainly comprised in the following propositions. A pendulum of given length, performs its vibrations in equal times, whether it vibrates in longer or in shorter arcs. Upon this property of the pendulum, depends its application to the measurement of time, as explained in Art. 152. 206. The times of vibration of pendulums of different lengths, are proportioned to the square roots of their lengths. Thus, a pendulum, in order to vibrate half seconds, is only one fourth as long as one that vibrates seconds, for 1 (the time of the longer) : J (time of the shorter) : : VI : 1/|. 102 MECHANICS. What must be the length of a pendulum to vibrate quarter seconds? Ans. It must be y 1 ^ the length of the seconds pendulum, the square root of yV being J of 1 ; and since the length of a pendulum beat- ing seconds is about 39 inches, that of a pendulum beating quarter seconds, is ff =2.44 nearly. Ex. 3. What would be the length of a pendulum that should vi- brate once an hour, the length of the seconds pendulum being 39 T '- - inches ? Ans. 7997.7 miles, equal to the diameter of the earth, nearly. 207. The times of vibration of the same pendulum on different parts of the earth's surface, are proportioned, to the distances of these points from the center of the earth. Hence, the pendulum affords the means of measuring the heights of mountains, and even of ascertaining the figure of the earth itself. For, since the times of vibration are as the respective distances from the center of the earth, and since the longer the time occupied in one vibration, the smaller the number of vibrations in an hour, con- sequently, the number of vibrations in an hour at the level of the sea would be to the number on the top of a mountain, as the dis- tance of this last point from the center of the earth, to the distance of the general level from the center. For example, a pendulum which vibrated seconds at the level of the sea, was found to vibrate only 3590 times on the top of a high mountain ; what was the height of the mountain ? 3590 : 3600: :3956* : 3,969, or nearly 4 miles. Ex. 2. A pendulum which vibrated seconds at the general level of the sea, was found to vibrate but 3597 times in an hour, on the top of a neighboring mountain : required the height of the mountain? Ans. 3 r \ miles. 208. Again, the pendulum affords us the means of ascertaining the figure of the earth ; for by counting the number of vibrations perforn^ed at various places on the earth's surface, (at the level of the sea,) we determine the respective distances of those points from * The diameter of the earth is 7912 miles. STRENGTH OF MATERIALS. 103 the center of the earth. Now, if these distances" should be all equal to each other, then the earth would be found to be a perfect sphere ; but it is found, by actual experiment, that the number of vibrations increases as we advance from the equator towards the poles, indica- ting that the polar diameter is less than the equatorial. Example. If a pendulum which beats seconds at the equator, should be found to vibrate 3613 times in an hour at the pole, how much less is the polar than the equatorial diameter ? 3613 : 3600: : 4000 : 39S5 T V This result being subtracted from 4000, (the equatorial radius,) leaves 14,\ miles, which, being doubled, gives 28 fV miles, as the difference between the polar and equatorial diameters. 209. The fact that at any given place, a pendulum which vibrates seconds, or which makes 3600 vibrations in an hour, is necessarily of the same length at all times, has led several nations to adopt this as the standard of linear measure. The square of this will serve as a standard for superficial, and its cube as a standard for solid measures. Strength of Materials. 210. The importance to the architect and the engineer of ascer- taining the form and position of the materials which he employs, in order to secure the greatest degree of strength and stability at the least expense, has led mathematicians and writers on mechanics, to devote much attention to this subject. How is the strength of a beam affected by giving to it different shapes and different positions; how must a given quantity of matter be disposed of in order that it may have the greatest possible degree of strength ; and upon what principles depends the stability of columns, roofs, and arches : these, and many similar inquiries, have been objects of profound investi- gation. 211. The power of a regular beam, like a stick of timber, to resist fracture when supported horizontally at the two ends is proportioned to the depth of the center of gravity below the upper surface. Hence an oblong beam is much stronger with its narrow than with its broad 104 MECHANICS. side upwards, as will be seen by inspecting Fig. 57 ; for the center of gravity being here the center of the stick, its depth EG is greater when the narrow side is uppermost than Eg, the depth when the beam rests on its broadside. Thus, if a joist be 10 inches broad and 2J thick, it will bear four times more weight when B laid on its edge, than when laid flat-wise. Hence the modern mode of flooring with very thin, but deep pieces of timber. A triangular beam is twice as strong when resting on its broad base, as when resting on its edge. For the center of gravity being | the distance from the vertex to the base, its depth is twice as great when the beam rests on its base as when it rests on its edge. These principles apply not only to beams, but to bars, and similar struc- tures of every sort of matter. 212. The strength of any bar in the direction of its length is pro- portional to the area of its transverse section. If a number of cords were hanging -side by side from the same hook in the ceiling they would be competent to sustain a weight as much greater than a single cord would sustain as their number was greater than unity. Fifty cords all bearing equally, would obviously bear fifty times as great a weight without breaking as a single cord would do. Nor would their power be altered by being placed close- ly in contact with each other so as to constitute one and the same cord. If, in the place of one of these strings, we suppose rows or particles of any kind of matter, the strength of the whole would be in propor- tion to their number, and this would be measured by the area of a cross section. Hence, the various shapes of bars make no difference in their absolute strength, since this depends only on the area of the section, and must obviously be the same when the area is the same, whatever be the figure. A rope, therefore, or a wire, to which a weight is appended, is as likely to break in one place as in another;, but when the weight of the rope becomes considerable, and the force is applied perpendicularly, the increase of weight as its length increa- ses, renders it more liable to break in the upper than in the lower parts. 213. The lateral strength of a beam is inversely as its length- STRENGTH OF MATERIALS. 105 Hence a beam twice as long as another equal to it in all other re- spects, has only half the strength. Long beams are weak from their own weight ; and the length may be so increased, that they will break from this cause alone. 214. The tendency to fracture on any part of a horizontal learn supported at both ends, is proportional to the product of the distan- ces of that part from the supported ends. In a common stick of timber, therefore, resting horizontally like the joist of a floor, the liability to break is greatest in the middle, and decreases both ways to the ends ; for the product of the two halves is the greatest that can result "from any two parts, and the more un- equal the parts are, the less is the product. Hence a beam, in order to be equally strong throughout must be made tapering, being largest in the center, and growing less and less towards the ends. Exact calculation shows, that the true figure of such a beam is that whose section is an ellipse. The timbers which compose the horizontal part of the frame of a house, being usually rectangular parallelopipeds of uniform dimen- sions thoughout, it is manifest that a considerable portion of the ma- terial is wasted : but in such cases the attempt to save the material, would be attended with paramount disadvantages. When, however, the material is expensive, or where lightness is important, as in many kinds of machinery, the foregoing principle may be applied with great advantage. A useful application of it is seen in the shape giv- en to the iron bars of railways, as is represented in the following figure. Fig. 58. 215. On the foregoing principles Dr. Gregory makes the follow- ing remarks, most of which were originally suggested by Galileo, to whom we are indebted for the earliest investigation of these proposi- tions. From the preceding deduction (says Gregory) it follows, that greater beams and bars must be in greater danger of breaking than less similar ones ; and that, though a less beam may be firm 14 106 MECHANICS. and secure, yet a greater similar one may be made so long as neces- sarily to break by its own weight. Hence Galileo justly concludes, that what appears very firm, and succeeds well, in models, may be very weak and unstable, or even fall to peices by its weight, when it comes to be executed in large dimensions, according to the model. From the same principles he argues that there are necessarily limits in the works of nature and art, which they cannot surpass in magni- tude ; that immensely great ships, palaces, temples, &tc., cannot be erected, since their yards, beams, bolts, and other parts of their frame, would fall asunder by their own weight. Were trees of a very enormous magnitude, their branches would, in like manner, fall off. Large animals have not strength in proportion to their size ; and if there were any land animals much larger than those we kjiow, they could hardly move, and would be perpetually subjected to the most dangerous accidents. As to marine animals, indeed, the case is different, as the specific gravity of the water sustains those ani- mals in a great measure ; and in fact these are known to be some- times vastly larger than the greatest land animals.* It is (says Galileo) impossible for Nature to give bones to men, horses, or other animals, so formed as to subsist, and proportionally to perform their offices, when such animals should be enlarged to immense heights, unless she uses matter much firmer and more resisting than she com- monly does ; or should make bones of a thickness out of all propor- tion ; whence the appearance and figure of the Animal must be mon- strous. Hence we naturally join the idea of greater strength and force with the grosser proportions, and that of agility with the more delicate ones. The same admirable philosopher, likewise remarks, in connexion with this subject, that a greater column is in much more danger of being broken by a fall than a similar small one ; that a man is in greater danger from accidents than a child ; that an in- sect can sustain a weight many times greater than itself, whereas, a much larger animal, as a horse, could scarcely carry another horse of his own size. 216. 5%e lateral , strengths of two cylinders, of the same matter y and of equal weight and length, one of which is hollow and the oth- er solid, are to each other as- the diameters of their sections. * Whales in the Northern Regions, are sometimes found sixty feet long, and weighing seventy tons.' FRICTION. 107 The strongest form, therefore, in which a given quantity of mat- ter can be disposed, is that of a hollow cylinder. From this propo- sition Galileo justly concludes, that Nature in a thousand operations greatly augments the strength of substances without increasing their weight; as is manifested in the bones of animals, and the feathers of birds, as well as in most tubes or hollow trunks, which, though light, greatly resist any effort to bend them. Thus (says he) if a wheat straw, which supports an ear which is heavier than the whole stalk, were made of the same quantity of matter, but solid, it would bend or break with far greater ease than it now does. And with the same reason, art has observed, and experience confirmed the fact, that a hollow cane, or tube of wood or metal, is much stronger or firmer, than if, while it continues of the same weight and length, it were sol- id ; as it would then, of consequence, be not so thick. For the same reason, lances, when they are required to be both light and strong, are made hollow. Friction. 217. The term Friction, in its usual acceptation, being generally understood, we have already employed it in the foregoing pages, but we proceed now to inquire more particularly respecting its nature, the laws of its action, and its effects upon machines. In investigating the mathematical principles of Mechanics, we first proceed on the supposition that the forces in question act with- out any impediments ; that the surfaces which move in contact are perfectly polished and suffer no friction ; that axes and pivots are mathematical lines and points ; that ropes are perfectly flexible ; and, in short, that the power is transmitted through the machine to the working point without sustaining the least loss or diminution. Great simplicity is attained by first bringing the subject to this ideal standard of perfection, and afterwards making suitable allowances for all those causes which operate in any given case to prevent the perfect action of a machine. 218. Surfaces meet with a certain degree of resistance in moving on each other, in consequence of the mutual cohesion of the parts, a principle which has the greater influence in any given case, in pro- portion as the surfaces are smooth. But a much greater resistance 108 MECHANICS. arises from the asperities which the surfaces of all bodies have, though in very different degrees, according to their different degrees of smoothness. An extreme case is that of two brushes moving on each other, the hairs of which become interlaced, (especially when the brushes are pressed together,) and oppose a great resistance. Even bodies apparently very smooth, as polished metals, exhibit un- der the microscope numerous inequalities. Under the solar micro- scope, the finest needle exhibits a surface as rough as the coarest iron tools do when viewed by the naked eye. To these inequalities of surface, is principally ascribed the friction of bodies, when closely in contact ; the prominent parts interlock with one another, or meet, and must be broken down before the surfaces can move. Hence, friction is diminished by processes which level these inequalities, either by polishing the surface, or by smearing it with some lubri- cating substance which fills up the cavities. 219. Forces of this nature, which' act by the resistance they oc- casion to motion are called passive forces. They produce very dif- ferent effects in machines when in a state of equilibrium, and in a state of motion. In the one case they assist the power ; in the other case they oppose it. Thus, a weight placed on an inclined plane, will require a less power to support it in consequence of the friction of the plane; and a weight suspended by a rope passing over a pulley will require a less weight to balance it, on account of the friction of the axle. But the same passive forces operate in just the contrary way when a machine is to be put in motion ; for then a power must be applied, which is sufficient not only to overcome the weight itself but also the amount of all the resistances. For example, in order to draw a load up an inclined plane, we have to overcome not only the force of gravity by which the load endeavors to descend down the plane, but also the amount of the friction and all the other resistances which impede its motion, although the load would be kept from de- scending, that is, in a state of equilibrium by a less force in conse- quence of these resistances. The principle is most strikingly ob- served in the wedge, where the difficulty of making the wedge ad- vance, is greatly increased by friction, but the same cause operates to prevent it from recoiling. FRICTION. 109 220. The forms under which this sort of resistance presents itself, are chiefly of two kinds, namely, that of bodies sliding, and of bodies rolling on each other. To the former of these let us first attend. Experiments on the friction of sliding bodies may be made, either by placing them on a table, and observing the weights which they respectively require to drag them along the table, or by placing them on an inclined plane, and observing at what angle the plane must be elevated in order that the body may begin to slide. In the former case, the table is prepared by attaching a vertical pulley to one edge, over which a string is passed, one end being connected to the body in question, and the other end to a pan, like that of a balance, for containing weights. From this simple arrangement, a great variety of particulars may be ascertained respecting the friction of sliding surfaces. A body shaped like a brick, wiih a broader and a narrower side, may be tried on each of its sides separately, and thus it may be seen whether, in a given weight, the extent of surface of contact makes any difference ; the body may be loaded with differ- ent weights, and hence may be learned the influence of pressure upon friction ; the body may be tried as soon as it is laid on the ta- ble, and after remaining on it for*a longer or shorter time, in order to learn whether this circumstance alters the friction ; different kinds of bodies may be tried, and the influence of different materials as- certained ; and finally by dragging the body off the table with differ- ent degrees of velocity, the relation of friction to velocity may be investigated. 221. From experiments like the foregoing, endlessly varied, the following conclusions have been established : (1.) In a given body extent of surface makes no difference in re- gard to friction ; a brick laid on its edge meets with the same resist- ance from this cause as when laid on its side. (2.) Friction is proportioned to the pressure. If the pressure of the brick be doubled or trebled by laying weights upon it, the amount of friction will be increased in the same ratio. (3.) Friction is increased by bodies remaining for some time in contact with each other. In some cases it does not reach its maxi- mum under four or five days. This principle therefore affects slow motions much more than such as are rapid. In the mutual contact 110 MECHANICS. of metals, the friction attains its maximum almost instantaneously. But when metal rubs against wood, or one piece of wood against another, the friction is always increased by resting. (4.) The friction is less between surfaces of different kinds of matter, than between those of the same kind. Copper slides on cop- per, or brass on brass with greater difficulty than copper on brass ; and it is a general rule never to let two substances of the same hard- ness move upon each other. To this rule, cast steel is said to form the only exception ; in other cases pivots revolve with less resistance -on either harder or softer substances than upon those of the same material with themselves. When between the surfaces of wood neatly planed the friction would be equal to one half the pressure, and when between two metallic surfaces it would be equal to one fourth, between the wood and metal it would amount to only one fifth the pressure. (5.) Friction is much greater at the first moving of a load, than after it is brought freely into motion. In many instances, it is re- duced, when a body has attained its final velocity, to less than one half of what it was at first. With regard to different degrees of ve- locity in moving bodies, it is a general principle, that the friction is the same for all velocities; that a carriage, for example, in travel- ling from one place to another, would encounter the same resistance from friction, whether it performed the journey in one hour or in ten. The amount of friction, however, is augmented in very slow motions, and greatly diminished in those that are very swift. In this instance, the increase in the one case and the diminution in the other appears to have some relation to the principle, that the friction of bodies is in- creased by their remaining in contact. From some observations of Professor Playfair made at the slide of Alpnach, where large fir trees are carried with great velocity down an inclined plane eight miles in length, it would appear that, in the case of very great velocities, fric- tion is not, according to the common doctrine, either proportioned to the pressure or independent of the velocity ; but that the ratio to the pressure is greatly diminished, and the actual resistance is far less tharT at common velocities. Thus, none but large trees could descend the plane at all ; and when a tree broke into two pieces, the larger part would proceed while the smaller would stop ; and the trees acquired in their descent a rapidity of motion, incompatible FRICTION. Ill with the supposition that " friction acts as a uniformly retarding force," which has been considered as an established principle. The foregoing considerations are in favor of rapid travelling, wheth- er on common roads or on railways, since the amount of the resis- tances is so much less than in slow movements j and accordingly it is said that the great speed given to stage coaches in England, amount- ing in some instances to ten or twelve miles per hour, has not been attended with the degree of exhaustion to the teams that would have been anticipated. 222. The laws of friction in rolling bodies are ascertained by comparing the forces necessary to roll a cylinder upon a table under various circumstances ; and by similar experiments, are found the modes in which friction takes place in bodies revolving on an axis* The comparative loss of power which takes place in these three ca- ses is as follows : Friction of the sliding body equal to J the pressure or 25 per cent, do. revolving do. 15' do' rolling do. 5 In the case of hollow cylinders revolving on an axis, the leverage? of the wheel aids in overcoming friction. Let fig. 59, represent a section of the wheel and axle. Let C be the center of the axle, and let BE be the hollow cylinder in the nave of the wheel' in which the axle is inserted. If B be the part on which the axle presses, and the wheel turn in the direction N DM, the fric- tion will act at B in the direction BF, and with the leverage BC. The power acts against this at D in the direction DA, and with the leverage DC. It is therefore evident, that as DC is greater than BC, in the same proportion does the pow- er act with mechanical advantage over the friction. On this principle an important advantage is sometimes gained in machines by transfer- ring the friction from one point to another, as from the circumference to the axis of a pulley. 223. Friction Wheels, a contrivance by which friction is dimin- ished in the greatest degree possible, owe their efficacy in part to the operation of the same principle. Here the axis of a wheel, instead of revolving in a hollow cylinder, or instead of rubbing against a fixed MECHANICS. surface, rests at each of its extremities, on the circumference of two wheels placed close by the side of each other, with their circumfer- ences intersecting. The axis rests at the point of intersection, and as it revolves, the wheels revolve with it with the same velocity and thus all friction between them and the axis is prevented, and what remains in the machine in consequence of the weight of the wheels themselves is transferred to their axles, and therefore is diminished^ in the ratio of the diameter of one of the wheels to that of its axis. This combination may be repeated by several pairs of friction wheels. Eight wheels would contract the friction to the thousandth part. 224. Other more common methods of diminishing friction are, by rendering the surfaces smooth, by using rollers, and by lubrica- ting the parts in contact. The amount rof friction in the several me- chanical powers is very different. In the lever it is very small, es- pecially when the turning edge is of hardened steel and shaped like a knife or prism, and turns upon a hard and smooth basis. The Wheel and Axle acting upon the same principle as the lever, occa- sions but little friction. The stiffness of the cordage, however, and the friction of the gudgeons of the axis have an effect in most cases equal to about 8 or 10 per cent, of the entire resistance. The Pulley is attended with great loss from this source. It is rarely less than 20 per cent and often exceeds 60. The Inclined Plane in- volves but little friction when bodies simply roll on it ; but when heavy bodies rest on axes, as in wheel carriages, the resistance from friction takes place jn the same manner as upon plane surfaces. The transportation on inclined planes, as railways, is usually by means of wheels, since the resistance to sliding movements is too great to per- mit the use of them. The Screw is attended with a great deal of friction. Those with sharp threads have more than those with square threads and the endless screw has most of all. In both the Screw and the Wedge, the friction evidently exceeds the resistance ; other- wise they would not retain their position. 225. Friction is not, therefore, in all cases to be considered as unfavorable to the operation of machinery. It is, in many instances, a highly useful force. Many structures, as those of Brick and stone, owe no small part of their stability to the roughness of the materials FRICTION. , 113 of which they are composed ; without this resistance, the screw and the wedge would lose their efficacy, and the wheels could not advance, nor could animals walk on the ground ; and nails would lose their power of binding separate parts together. The art of polishing sur- faces depends on the same cause, and the edges of most cutting in- struments are saws, the teeth of which are more or less fine, and act on a similar principle. Even in certain rotary motions, friction becomes a moving force and urges a body in particular directions contrary to the force of gravity. 15 "-. 1J4 PART II. HYDROSTATICS. CHAPTER I. OF FLUIDS AT REST. 226. THE principles of Mechanics demonstrated and explained in the foregoing pages, are universal in their application, extending alike to all bodies, whether solid or fluid. But in addition to those properties which fluids have in common with solids, and which bring them under the general laws of Mechanics, they have also proper- ties peculiar to themselves, which give rise to a distinct class of me- chanical principles, not applicable to solid bodies. These are em- braced under the heads of HYDROSTATICS and PNEUMATICS, the former division comprising the doctrine of liquids, and the latter that pf aeriform bodies or gases. 227. A FLUID is a body whose particles move easily among them- selves , and yield to the least force impressed ; and which, when thai force is removed, recovers its previous state. Since water, wind, and steam, are the only fluids that are usually employed as mechanical agents, the doctrines of Hydrostatics and Pneumatics, have regard chiefly to them ; but the principles estab- lished respecting these, are applicable also to all analogous bodies. It has been usual to denominate liquids and gases respectively elastic and non-elastic fluids, on the supposition that water and other liquids are nearly or quite incompressible. An experiment perform- ed by the Florentine academicians, as long ago as 1650, seemed to prove that water is wholly incompressible. They filled a hollow ball of gold with water, and subjected it to a strong pressure. The water, nof yielding to the compression, oozed through the pores of the gold. Considering the great density and compactness of this metal, the experiment was for a long time held as proving decisively that water is wholly incompressible. Although this experiment shows FLUIDS AT RfcST. 115 that water is compressed with great difficulty, yet later experiments have proved, that it is still capable of compression. The most decn sive evidence of this point has heen recently afforded by the expert ments of Mr. Perkins. It had been previously ascertained that by a pressure equivalent to that of the atmosphere, or about fifteen pounds to the square inch, water is compressed about one part in twenty two thousand, Mr. Perkins by methods to be described hereafter, ap- plied successive degrees of pressure up to that of two thousand at- mospheres, and found the contraction of volume to increase nearly in the ratio of the compressing force. 228. HYDROSTATICS is that branch of N'atural Philosophy which treats of the mechanical properties and agencies of LIQUIDS* 229. Fluids at rest press equally in all directions* A point in a mass of flu-id, taken at any depth, exerts and sustains the same pressure in all directions, upwards, downwards, or lat- erally. This is the most remarkable property of fluids, and is what particularly distinguishes them from solids, which press only down- wards, or in the direction of gravity. This property naturally results from the freedom of motion that subsists between the particles of fluids ; for if, when a fluid is at rest, the pressure on any given por- tion were not equal in all directions, that portion would move in the direction in which the resistance was least. But by the supposition it does not move : therefore it is kept at rest by equal and contrary forces acting on all sides. But the most satisfactory evidence of this truth is obtained from experiment. On opening an orifice in the side of a vessel of water, and estimating the force with which the water issues, it is found to be qual to the weight of the incumbent fluid ; and the upward pressure of water at a certain depth is found to sustain the heaviest bodies when exposed to its action alone, the column above the bodies, and of course the downward pressure, be- ing removed, 230. A given pressure or blow impressed on any portion of a mass of water confined in a vessel, is distributed equally through all part? of the mass. 116 HYDROSTATICS. A given pressure, as that made by a plug forced inwards upon a square inch of the surface of a fluid confined in a vessel, is suddenly communicated to every square inch of the vessel's surface, however large, and to every inch of the surface of any body immersed in it. Thus, if I attempt to force a cork into a vessel full of water, the pressure will be felt not merely by the portion of the water directly in the range of the cork, but by all parts of the mass alike ; and the liability of the bottle to break, supposing it to be of uniform strength throughout, will be as great in one place as another, and a bottle will break at the point where it happens to be weakest, however that point may be situated relatively to the place where the cork is applied ; and the effect will be the same whether the stopper be inserted at the top, the bottom, or the side of the vessel. 231. It is this principle which operates with such astonishing effect in the Hydrostatic Press, by means of which a single man can exert a force equal at least to 25000 Ibs. and adequate to crush the hard- est substances, or cut in two the largest bars of iron. Its construc- tion is as follows. Fig. 60 represents a press made of the strongest timbers, the foundation of which is commonly laid in solid masonry. AB is a small cylinder in which moves the piston of a forcing pump, and CD is a large cylinder in which also moves a piston, having the upper end of its rod pressing against a movable plank E, be- tween which and the large beam above is placed the substance to be subjected to pressure, as for example a pile of new bound books. By the action of the pump hancfle, water is raised into ihe'smalltyl- inder, and, on depressing the piston, it is forced through a valve at B into the larger cylinder and raises the piston D, which expends its whole force on the bodies confined at E. Now since, whatever force is applied to any one portion of the fluid, extends alike to every part, therefore the force which is exerted by the pump upon the smaller column, is transmitted unimpaired to every inch of the larger column, and tends to raise the movable plank E with a force as much greater, in the aggregate, than that impressed upon FLUIDS AT REST. 117 the surface of the smaller, as this surface is smaller than that of the larger column ; or (which is the same thing) as the number of square inches in the end of the piston B is less than that of the piston D. The power of such a machine is enormously great ; for, supposing the hand to be applied at the end of the handle, with a force of only ten pounds, and that this handle or lever is so constructed as to mul- tiply that force but five times, the force with which the smaller pis- ton will descend will be equal to 50 Ibs. ; and let us suppose that the head of the larger piston contains the smaller 50 times, then the force exerted to raise the press board, will equal 2500 Ibs. A man can indeed easily exert ten times the force supposed, ^and can therefore exert a force upon the substance under pressure, equal to 25000 Ibs. 232. The rationale of the principle of the Hydrostatic Press, will be best understood by recurring to the doctrine of Virtual Velocities. It will be. recollected that opposite forces are in equilibrium when their momenta are equal ; that a small power may be made to" bal- ance a great weight, by making it move, in a given time, over a 'space as much greater than the larger does, as its weight is smaller ; and that it may be made to overcome that resistance or weight, and give motion to it, if its velocity is greater than that of the latter in a still higher ratio. Now to apply these principles to the case before us, it is evident that any quantity of water forced out of the smaller into the larger cylinder, must rise in the latter as much slower as the area of the horizontal section is larger. If, for example, the capacity of the larger cylinder were ten times that of the smaller, then a quan- tity of water one inch in height, transferred from the smaller to the greater cylinder, would occupy only the height of one tenth of an inch, and consequently the depression of the small piston one inch would raise the large one only the tenth of an inch. This case, therefore, resolves itself into that general principle, according to which a vast force is exerted through a short distance, by moving a small force through a distance much greater. 233. The surface of a fluid at rest is horizontal. The evidence of the truth of this proposition is threefold. First, this result is a natural consequence of the mobility of fluids, since, if 118 HYDROSTATICS. any portion is raised above the rest, having nothing to support it, and being acted on by gravity, it must descend in the same manner as a body placed on a perfectly smooth inclined plane. Secondly, when- ever a body is free to move, its center of gravity will descend as low as possible. When, therefore, any portion of a fluid is raised above the general level, the center of gravity of the mass is raised, and it must return before the fluid can be at rest. Thirdly, experience shows that the proposition is true, since fluids, when free to move, always settle themselves with their surfaces parallel to tbe horizon. It must be understood, however, that the surface of large bodies of water is not, strictly speaking, a horizontal level, but is a portion of the convex surface of the earth ; for since the center of gravity of every portion of the fluid will descend as low as possible, the whole will dispose itself around the center of attraction so as to form a por- tion of the earth's surface. For small distances the curvature is so slight that it may be neglected, not amounting to one second of a de- gree for 100 feet; and for the distance of a mile, the deviation from a straight line, drawn in the direction of a tangent, is not more than 8 inches. 234. A practical application of this principle is made in the art of levelling. A level is sometimes made by merely cutting a groove or channel in a flat piece of board and filling it with water. When the board is brought into such a situation that the water in the groove re- mains stationary, the position is horizontal. But the spirit level is the instrument more commonly employed for this purpose. This consists of a small cylindrical tube of glass, from two to six inches long, filled with spirits of wine or ether, except a small space which is occupied by a movable bubble of air. When such a tube is placed horizontally, the bubble of air will remain stationary in the center of the- tube, at a fixed mark ; but whenever the tube is inclined, in the least degree, the bubble will ascend towards the elevated end. Spirit levels are much used for adjusting astronomical, surveying, and other delicate instruments. 235. The pressure upon any particle of a fluid of uniform densi- ty, is proportioned to its depth below the surface. FLUIDS AT REST. 119 Thus in Fig. 61, the pressure exerted by the fluid at different depths as x and y is found to be exactly proportioned to their depth below the surface, so that if y be twice as deep as a?, a body at y would sustain twice as much pressure as at x. But since the inclined column AC etc, is of the same perpendicular height as the erect column ABCD, both exert the same pressure on the base AC. (i) A C 236. According to Art. 229, the lateral is equal to the downward pressure ; and consequently on this principle may easily be estimated the amount of pressure on the sides of any column of water, or on the banks of rivers, canals, &c. At the depth of 8 feet, the press- ure on a square foot is equal to the weight of a column of water, whose base is 1 foot and depth 8 feet, and consequently its solid con- tents 8 cubic feet; and since 1 cubic foot of water weighs 1000 ounces or 62jlbs. therefore the weight of the column = 8x62j= 500 Ibs. Hence the pressure on a square foot, at different depths, will be as in the following table. Depth in feet 8 . Pressure on a square foot. ./>. ., 500 Ibs. Depth in feet. Pressure on a square foot, 56 .... 3500 Ibs. 16 . .. ; . . 1000 64 .... 4000 24 . : ;-;. . . 1500 72 .... 4500 32 . . . . 2000 80 .... 5000 40 . . . . 2500 38 .... 5500 48 . .. ' . . 3000 96 .... 6000 1 mile or 5280 feet, 5 " . . . 330,000 Ibs. 1.650.000 Hence it appears that at the moderate depth of 64 feet, the pressure of a column of water on the bottom or sides of the containing pipe, becomes 4000 Ibs. to the square foot ; and the pressure on the bot- tom of the sea, where it is one mile in depth, is 330,000 Ibs. to the square foot, and where it is five miles deep, that pressure is no less than 1,650,000 Ibs.* From these considerations we may readily * Allowance must always be made for the saltness of the sea, salt water being heavier than fresh. 120 HYDROSTATICS. apprehend the cause of the great difficulty experienced in confining a high column of water; and hence also may be inferred the immense pressure that is exerted on the bottom of the sea. 237. Indications of this vast pressure in deep waters, are mani- fested by several interesting facts. It has long been known to mari- ners, that if a common square bottle be let down into the sea, its sides are crushed inwards before it has reached the depth of ten fathoms. If a stronger bottle, (a common junk bottle, for example,) be filled with water, corked close, and let down to a certain depth, either the cork will be forced inwards, or if that is secured in its place, the salt water will make its Way into the bottle in spite of it, either by com- pressing the cork or by forcing in water through it. It was by sink- ing an apparatus to the depth of 500 fathoms, that Mr. Perkins first proved the compressibility of water, as mentioned in Art. 227. The apparatus consisted of a hollow brass cylinder, resembling a small cannon, and furnished with a stopper so contrived as to indicate, when the apparatus was drawn up, how far it had been driven in while at the lowest depth. The same experiments were afterwards repeated on shore, a pressure being applied to the plug, by means of the hydrostatic press, equivalent to 2000 atmospheres. Tire-increase of pressure in proportion to the depth of the fluid, renders it necessary to make the sides of pipes or masonry, in which fluids are to be contained, stronger the deeper they go. The same remark applies to dams, flood-gates, and banks. 238. 'At the depth of 1000 fathoms, the compression of water is one twentieth of its bulk, and its specific gravity is increased in the same ratio ; so that bodies which sink near the surface of the sea, may float at a certain depth before they reach the bottom. On the other hand, a porous body, that is light enough to float near the sur- face, will have so much water forced into its pores, when it is sunk to a great depth, as never to rise. This is the case with ships that are wrecked in deep water ; the parts of the wreck do not rise to the surface, as they do in shallow water. 239. When a portion, as a square foot, of the lateral surface of a column of water, is taken, all parts of it are not equally distant from the surface of the fluid ; and, in this case, the average depth, or FLUIDS AT REST. 121 (which is the same thing) the depth of the center of gravity, is to be understood according to the following proposition, which applies to every sort of surface, however inclined to the horizon. The pressure of a fluid against any surface, in a direction per- pendicular to it, varies as the area of the surface multiplied into the depth of its center of gravity below the surf ace of the fluid. Hence, the pressure on the side of a cubical vessel, filled with fluid, is one half the pressure against the bottom ; and the whole pressure against the sides and bottom, is equal to three times the weight of the fluid in the vessel. 240. Fluids rise to the same level in the opposite arms of a re- curved tube. Let ABC, (Fig. 62.) be a recurved tube : if Fig. 62. water be poured into one arm of the tube, it will rise to the same height in the other arm. For, by Art. 235, the pressure upon the lowest part at B, in opposite directions, is proportioned to its depth below the surface of the fluid/ Therefore, these A depths must be equal, that is, the heights of the two columns must be equal, in order that the fluid at B may be at rest ; and unless this part is at rest, the other parts of the column cannot be at rest. Moreover, since the equilibrium depends on nothing else than the heights of the respective columns, therefore, the opposite columns may differ to any degree in quantity, shape, or inclination to the ho- rizon. Thus, if vessels and tubes very diverse in shape and capaci- ty, as in Fig. 63, be connected with a common reservoir, and water Fig. 63. 122 HYDROSTATICS. be poured into any one of them, it will rise to the same level in them all. The reason of this fact will be farther understood from the ap- plication of the principle of Virtual Velocities, (Art. 179.) ; for it will be seen that the velocity of the columns, when in motion, will be as much greater in the smaller than in the larger columns, as the quantity of matter is less ; and hence the opposite momenta will be constantly equal. 241. Hence, water conveyed in aqueducts or running in natural channels, will rise just as high as its source. Between the place where the water of an aqueduct is delivered and the spring, the ground may rise into hills and descend into valleys, and the pipes which convey the water may follow all the undulations of the coun- try, and the water will run freely, provided no pipe is laid higher than the level of the spring. Waters running in natural channels in the earth are governed by the same law. 242. The acqueducts constructed by the ancient Romans, were among the most costly ornaments of their arts. Several of them were from thirty to one hundred miles in length, and consisted of vast covered canals, built of stone. They were carried over valleys and level tracts of country upon arcades, which were sometimes of stu- pendous height and solidity. From the fact that the ancients built acqueducts with so much labor, raising them to a great height in cross- ing valleys, instead of availing themselves of the principle under con- sideration, some have supposed that they were unacquainted with this principle. It appears nevertheless that they were acquainted with it and even understood the use of pipes in conveying water; but prob- ably the expense of pipes, and the difficulty of making them strong enough to resist the pressure when laid at a considerable depth below the source, prevented their general use. 243. The pressure upon the horizontal base of any vessel contain- ing a fluid is equal to the weight of a column of the fluid, found by multiplying'lhe area of the base into the perpendicular height of the column, whatever be the shape of the vessel. This follows from Art. 239, since, here the distance of the center of gravity from the surface of the fluid, is the same as the perpen- FLUIDS AT REST, 123 Fig. 64. dicular height of the column. With a given base and height, there- fore, the pressure is the same whether the vessel is larger or smaller above, whether its figure is regular or irregular, whether it rises to the given height in a broad open funnel, or is carried up in a slender tube. Hence, any quantity of water, however small, may be made to balance any quantity, however great. This is called the hydro- static paradox. The experiment is usually performed by means of a water bellows, as is represented in Fig. 64. When the pipe AD is filled with water the pressure upon the sur- face of the bellows, and consequently the force with which it raises the weights laid on it, will be equal to the weight of a cylinder of water, whose base is the surface of the bellows and height that of the column AD. Therefore, by making the tube small and the bellows large, the power of a given quantity of water, how- ever small, may be increased indefinitely. The pressure of the column of water in this case corresponds to the force applied by the piston in the Hydrostatic Press, (Art. 231.) .and the explanation according to the principle of vir- tual velocities, is the same in both cases. 244. The principle of the Hydrostatic Paradox, is sometimes ex- emplified in pouring liquids into casks, throngh long tubes inserted in the bung holes. As soon as the cask is full, and the water rises in the pipe to a certain height, the cask bursts with violence. The same cause is supposed sometimes to produce great effects in nature, such as splitting rocks, heaving up mountains, and other effects re- sembling earthquakes. For, suppose that in the interior of a moun- tain there were an empty space ten yards square, and only an inch deep, in which water had lodged so as to fill it entirely; and suppose that a crevice in the earth should extend from this spot 200 feet above, which should also become filled with water by rain or other- wise : the force exerted would be adequate to shake the mountain, and perhaps rend it asunder. 245. Although the weight of a given quantity of water will not be altered by varying the shape of the vessel, yet the pressure which it 124 HYDROSTATICS. exerts on the bottom of the vessel will be greater in proportion as the altitude of the mass is greater, and of course greater in a narrow vessel than in a wide one. If it be asked why the weight is not in- creased as the downward pressure is increased, the answer is that the pressure in that direction is exactly counterbalanced by an equal pressure in the opposite direction. Specific Gravity. 246. The Specific Gravity of a body, is its weight compared with the weight of another body of the same bulk, taken as a standard. Water is the standard for all solids and liquids, and common air for the gases. Therefore, the specific gravity of a solid or a liquid body is the ratio of its weight to the weight of an equal volume of water ; and the specific gravity of an aeriform body, is the ratio of its weight to the weight of an equal volume of air. But a ratio is ex- pressed by a vulgar fraction, whose numerator is the antecedent and whose denominator is the consequent. If, therefore, the weight of a body is made the numerator, and the weight of an equal volume of water .the denominator, the value of the fraction, that is, the quotient, will express the specific gravity of the body. Hence, the weight of a body being given, and being made the numerator, every process for finding the specific gravity consists in finding for the denominator the weight of an equal bulk of water or air. The principles upon which the methods of doing this depend, are now to be explained. 247. A body immersed in a fluid, loses as much weight as is equal to the weight of an equal volume of the fluid. Let EF (Fig. 65.) be a solid body im- mersed in a vessel of water or any fluid, and suppose it divided into an indefinite number of perpendicular columns, reach- ing to the surface of the fluid, as mon. Now the upward pressure at n is as its depth, and the downward pressure at o as its depth ; therefore the upward pressure exceeds the downward, by the weight of a column of water equal to n o. The same is true SPECIFIC GRAVITY. 125 of all the columns, however numerous they may be, that can be drawn parallel to n o; but these columns, taken collectively, make up a body of water equal in bulk to the solid. Hence, the solid is pressed upwards more than downwards, by the weight of a quantity of water of the same magnitude, and consequently loses so much of its weight. Hence, the specific gravity of any solid body that will sink in water, is found by the following RULE. Divide the weight of the body by its loss of weight in water. 248. When the body whose specific gravity is required is lighter than water, as a cork, for example, the object is still to find the weight of an equal bulk of water, since that will constitute the denominator, or divisor, as before. To ascertain this, suspend any heavy body, as a mass of lead or glass, in water and find its weight. Attach to it the lighter body. Now the cork will not only lose all its own weight but will diminish the weight of the heavy body; and the weight of an equal bulk of water will be indicated by the whole of what the cork loses, namely, its own weight added to the loss occasipned to the other body. Whence we have the following RULE. To find the specific gravity of a body lighter than wa- ter. Divide its weight by the sum of its weight added to the loss of iveight which it occasions in a heavy body previously balanced in water. 249. A solid which is soluble in water, as a lump of salt, is pro- tected from solution by smearing it with oil or a thin coat of bees wax ; and solids that are very porous and would absorb water, and thus increase their specific gravities, as certain kinds of wood, are first covered with varnish. The specific gravity of solid substances, .which are too minutely divided to be weighed in water separately, as grains of sand or shot, may be found by weighing them in a small bucket previously balanced in water. 250. The specific gravity of liquids may be ascertained by seve- ral different methods. RULE I. Weigh equal volumes of the liquid and of water, and divide the former result by the latter. 126 HYDROSTATICS. Fig. 66. RULE II. Ascertain the loss of weight of any solid body, first in the liquid and then in water, and divide the former result by the latter. Both these rules obviously depend upon the same principles as those explained in Art. 246, the weight of the liquid being immedi- ately compared with that of an equal bulk of water; but there is another method, founded on the following proposition. 251. Two columns of fluids of different specific gravities, pressing freely on each other at their bases, balance one another when their heights are inversely as their specific gravities. Let AB (Fig. 66.) be a recurved tube, and let the height of the column of the fluid B be as much great- er than that of A, as the fluid B is lighter than the fluid A ; the two columns will then be in equilibrio. If the tube be of uniform bore throughout, then the proposition is manifestly true, because the quantities of matter pressing on each other in opposite directions will be equal, and will have equal momenta ; but from the peculiar nature of fluids, (Art. 235.) the opposite pressures will be the same, when the heights of the columns are the same, whatever may be the shape or capacity of the tube. If we introduce mercury into one arm of the tube and water into the other, the graduated scale will indicate that the water stands 13 times as high as the mercury. Therefore, the specific gravity of mercury is 13J. Proof spirit will stand at .923; sweet oil at .915; and their specific gravities are the same, water being 1 . 252, If a body floats on a fluid, it displaces as mucJi of the fluid as is equal to its own weight. If into a vessel full of water a floating body, as a piece of wood, be introduced, the quantity of water displaced will be found to be exactly^qual in weight to the body. Or if the vessel of water be accurately balanced in a scale, and then removed and the piece of wood introduced, the vessel on restoring it to the scale, will -still re- main in equilibrium, the wood exactly compensating for the water it displaced. SPECIFIC GRAVITY. 127 253. An accurate knowledge of the specific gravities of bodies, is of great use for many purposes of science and the arts, and they have therefore been determined with the greatest possible precision. The heaviest of all known substances is platina, whose specific gravi- ty, in its state of greatest condensation, is 22, water being 1 ; and the lightest of all ponderable bodies is hydrogen gas, whose specific gravity is .073, common air being 1 . By calculation, it will be found that platina is about 247,000 times as heavy as hydrogen, and hence a wide range is allowed to the various bodies which lie between these extremes. The metals, as a class, are the heaviest bodies ; next to these come the metallic ores ; then the precious gems ; and finally, minerals in general, animal, liquid and vegetable substances, in order, according to the following table. Metals, (pure,) not including the bases of the alkalies and earths, from - 5 to 22 Gold 19.25 Steel - 7.84 Quicksilver - 13.58 Iron - 7.78 Lead - 11.35 Tin - - 7.29 Silver - - 10.47 Zinc . 7.00 Copper - - 8.90 Metallic Ores, lighter than the pure metals, but usually above 4.00 Precious Gems, as the ruby, sapphire and diamond, 3 4 Minerals, comprehending most stony bodies, 2 3 Liquids, from ether highly rectified to sulphuric acid highly concentrated, - - 5 2 Acids in general, heavier than water. Oils, do. lighter ; but the oils of cloves and cinnamon are heav- ier than water; the greater part lie between .9 and 1. - .9 1 Milk, - 1.032 Alcohol (perfectly pure,) - - .797 Do. of commerce, - .835 Proof Spirit, - . .923 Wines ; the specific gravity of the lighter wines, as Champagne and Burgundy, is a little less, and of the heavier wines, as Malaga, a little greater, than that of water. Woods, cork being the lightest and lignum vitas the heaviest, J to 1 J. 254. If we balance, in a pair of scales, a tumbler filled with water to a certain mark near the top, and then, turning out all the water 128 HYDROSTATICS. except a small quantity, introduce any solid body, (as a tumbler a little less than the first,) so as to raise the water on the sides to the same mark as before, the equilibrium will be restored. Here, the space occupied by the solid immersed, is the same with that before occupied by the water. On the same principle, a ship is floated in a dock with a very small quantity of water, and still rides as freely as on the ocean. By the ascent of the water on the sides, the up- ward pressure on the bottom is increased, on the same principle as in the Hydrostatic Paradox, (Art. 243.) Though, in this case, we cannot say that a quantity of water is displaced equal in weight to the solid, (since the whole of the water originally in the vessel may not have been nearly sufficient to fill the space occupied by the ship,) yet the effect is the same, in regard to the pressure on the water be- low the ship, and of course on the upward pressure, (Art. 229.) as though the space occupied by the ship below the level of the fluid on its sides, were filled with water. On this principle, the weight of a loaded boat in the lock of a canal is easily estimated. Boats are sometimes made of iron instead of wood, their thickness being so much less, that the entire weight of the boat, is not greater than when made of wood. 255. The human body, when the lungs are filled with air, is lighter than water, and but for the difficulty of keeping the lungs constantly inflated, it would naturally float. With a moderate de- gree of skill, therefore, swimming becomes a very easy process, es- pecially in salt water. When, however, a man plunges, as divers sometimes do, to a great depth, the air in the lungs becomes com- pressed, and the body does not rise except by muscular effort. The bodies of drowned persons rise and float after a few days, in conse- quence of the inflation occasioned by putrefaction. Quadrupeds swim much more easily than man, because the motion of the limbs necessary to sustain themselves, nearly coincide with their natural motions in walking, while the body maintains nearly its usual posture. 256. Ma body is held beneath the surface of a fluid, the force with which it will ascend, if it is lighter than the fluid, or with wKich it will descend, if it is heavier, is equal to the difference between its own weight and the weight of an equal quantity of the fluid. SPECIFIC GRAVITY. On the foregoing principle, is founded the construction of a ma- chine called the Camel, for raising sunken vessels, or for lifting ships over sand banks. Empty hogsheads or boxes sunk by means of weights which are afterwards detached, being fixed to a sunken ship, may give it so much buoyancy as to cause it to float. Suppose, for example, a hundred empty hogsheads were thus attached, what up- ward force would they exert ? The number of gallons in a hogshead, 63, multiplied by 231, the number of inches in a gallon, gives 14553 inches ; which, divided by 1728, gives 8.4 cubic feet in a hogshead. But a cubic foot of water weighs 62J pounds. Therefore, 62.5 X 8.4=525 lbs.=weight of a hogshead of water. Now 100 cubic inches of air weighs 30 J grains ; therefore, 100 : 30J: 114553 : 4438.66=grains of air in a hogshead; or (since 437.5 grs. equal an ounce) the number of ounces of air in a hogshead is 10,14. Hence 525 Ibs.- 10,14 oz. = 534 Ibs. 6 oz. nearly, for the upward force of an empty hogshead sunk in water ; consequently, the buoyancy of 100 hhds. is 52437.5 pounds, or al- most 23J tons. A similar effect is exhibited in rivers, where the ice is formed upon the stones at their bottom. Ice is specifically lighter than wa- ter, and therefore when it accumulates to a certain degree around the stones, the upward pressure upon the stones exceeds their press- ure downwards, and they are brought to the surface, having been sometimes torn up with great force. Huge masses of stones appear in many cases to have been floated by the ice adhering to them, and carried to a great distance from the place .of their formation. 257. Rocks and stones being only a little more than twice as heavy as water, of course nearly half their weight is sustained while they are immersed in water ; and hence the increased weight which is felt when a large stone is lifted from the bed of a river, as soon as it reaches the surface. Large masses of rocks are transported with 1 far greater facility by torrents, on account of their diminished weight. On the same principle, the limbs feel very heavy on leaving a bath. Life boats have a large quantity of cork mixed in their structure ; or of air-tight vessels of thin copper or tin plate, so that, even when 17 130 HYDROSTATICS. the boats are filled with water, a considerable part still floats above the surface. 258. The magnitudes of bodies may frequently be most conven- iently and accurately estimated from the doctrine of specific gravities. Suppose we wish to ascertain the exact number of solid inches con- tained in a stone of rude and irregular shape, we should find great difficulty in applying to it any linear measurements ; but if we ascer- tain its loss of weight in water, we then have the weight of an equal bulk of water, and since 1000 ounces contain 1728 cubic inches, we may easily find how many cubic inches correspond to the weight of water of equal magnitude with the body in question. For exam- ple, when we want to find the number of solid inches in a chain, the irregularity of its shape prevents our applying to it any linear measure ; but if we weigh it in water, and subtract this weight from its weight in air, the difference gives us the weight of a,n equal bulk of water, which we can easily convert into solid inches. Suppose the chain loses 2.34 ounces by being weighed in water, then 1000 oz. : 1728 in. :: 2.34 oz. I 4.04 inches. That is, the chain contains a little more than four solid inches. CHAPTER II. OF LIQUIDS OR NON-ELASTIC FLUIDS IN MOTION. 259. That branch of Natural Philosophy which treat of fluids in motion, is usually denominated Hydraulics. It embraces the phe- nomena exhibited by water issuing from orifices in reservoirs pro- jected obliquely or perpendicularly flowing in pipes, canals, and rivers oscillating in waves or opposing a resistance to the progress of solid bodies. 260. If a fluid runs through any lube, pipe, or canal, and keeps it constantly full, its velocity in any part of its course, will be in- versely a&4he area of the section at that part. Thus, in a pipe of unequal bore, in different parts it is obvious that the same quantity of water must, in a given time, flow through the smaller parts of the tube as through the larger : it must therefore low proportionally faster. PHENOMENA OF RIVERS. 131 261. This proposition supposes the fluid to move free of all resist- ance, and hence it can never hold accurately true in practice. In every canal or river, the velocity of the surface is always greater than that of any other part, being less retarded by the friction of the bottom and sides ; and in a tube, the particles near the axis always move most rapidly. It is of consequence to avoid all unnecessary expansions, as well as contractions, in pipes or canals, since there is always a useless expense of force in restoring the velocity which is lost in the wider parts. 262. The phenomena of RIVERS have sometimes been explained on the supposition that rivers are bodies falling freely down inclined planes. But the conclusions deduced from this doctrine, are so at variance with experience, as to be of no value. Were every part of the bed of a river uniform, like a tube, the channel or por- tion which moves with the greatest velocity, would be in the center of the surface ; but inequalities in the sides and bottom usually throw it out of the center and incline it to one side or the other. The in- creased velocity of a stream during a freshet, while the stream is con- fined within its banks, exhibits something of the acceleration which belongs to bodies falling freely down an inclined plane. It presents the case of a river flowing upon the top of another river, and conse- quently meeting with much less resistance than when it runs upon the rough uneven surface of the earth itself. The augmented force of a stream in a freshet, arises from the simultaneous increase of the quantity of water and the velocity. In consequence of the friction of the banks and beds of rivers, and the numerous obstacles they meet with in their winding course, their progress is very slow, where- as, were it not for these impediments, it would become immensely great, and its effects would be exceedingly disastrous. A very slight declivity is sufficient for giving the running motion to water. Three inches per mile, in a smooth, straight channel, gives a velocity of about three miles per hour. The Ganges, which gathers the waters of the Himalaya Mountains, the loftiest in the world, at the distance of eighteen hundred miles from its mouth, is only eight hundred feet above the level of the sea, that is, about twice the height of Sjt. Paul's church in London ; and to fall these eight hundred feet, in its long course, the water requires more than a month. The great river 132 HYDROSTATICS. Magdalena in South America, running for a thousand miles between two ridges of the Andes, falls only five hundred feet in all that dis- tance. 263. The velocity with which a fluid issues from a small orifice in the bottom or side of a vessel, kept constantly full, is equal to that which a heavy body would acquire, by falling from the level of the surface to the level of the orifice. In the construction of water works, it is customary to conduct the stream, or such a part of it as is required, into a cubical cistern, and to let it issue from the side of this, near to the bottom, and thus fall upon the main wheel. Instead of admitting the water to the wheel in this manner, it has sometimes been supposed that an advan- tage might be gained by letting the water fall down a height equal to that of the top of the cistern, perpendicularly upon the wheel, on the supposition that we might thus avail ourselves of the force acquired by the water in falling. But according to the preceding proposition, the force would be the same whether the water issued from the cis- tern and thus applied itself to the wheel, or whether it fell upon the wheel from a height equal to that of the surface of the water in the reservoir above the orifice. This is true in theory; but in practice it would be found more advantageous to take the water out of the cistern, since the force of water falling through the air is considera- bly diminished by the resistance of the air. 264. The quantities of water which issue from orifices of the same dimensions, in the side of a cistern or column, are proportional to the square roots of their depths below the surface of the fluid. According to the last proposition, the velocities are equal to those acquired by bodies falling freely through the depths of the orifices ; but the velocities acquired by falling bodies are as the square roots of the spaces ; that is, the velocities are proportional to the square roots of the depths ; and since the quantities must evidently vary as the velocities, therefore, the quantities discharged by orifices of the same size at different depths are as the square roots of their depths. Accordingly, an orifice sixteen inches from the surface will dis- charge twice as much in a given time as one four inches deep ; and LAWS OF SPOUTING FLUIDS. 133 in order to draw off from a given cistern four times as much water as before, we must place the orifice or gate sixteen times as deep. A gate opened in a reservoir at the depth of 64 inches, will discharge only four times as much as it would at the depth of 4 inches. 265. If a cylindrical or prismatic vessel, of which the horizontal section is every where the same, is filled with fluid, and empties itself by an orifice, the velocity with which the surface descends, and also the velocity with which the water issues, is uniformly retarded. The velocity with which the surface descends is proportional to that with which the fluid issues from the orifice, and therefore is as the square root of the depth. But the velocities of bodies projected perpendicularly upwards are in the same ratio to their spaces, and therefore a body projected perpendicularly upwards is in the same relative circumstances as the descending surface of the fluid ; and as the projected body is uniformly retarded, the same is true of the descending surface. On this principle is constructed the Clepsydra, or water-clock. Since the descent of the surface is uniformly retarded, the spaces which it describes in equal times, reckoning from the bottom, are as the odd numbers 1, 3, 5, 7, &c.; and if a cylindrical vessel of water be furnished with an oriffce at the bottom which will exactly discharge the whole column in twelve hours, and the sides of the vessel be di- vided into spaces corresponding to the foregoing numbers, the suc- cessive heights of the column become measures of time. 206. If we accurately mark the time in which a cylindrical or pris- matic vessel, whose horizontal section is every where the same, dis- charges itself to the level of a given orifice, and then draw off for the same time, keeping the vessel constantly full, we shall obtain double the quantity of fluid in the latter case as in the former. When the vessel is kept constantly full, the velocity at the orifice (and of course the quantity discharged) continues uniformly the same as at first; and since the circumstances of this case are exactly analo- gous .to those of a body projected perpendicularly upwards ; and since, if a body thus projected were to continue to ascend with the first velocity, it would pass over a space twice as great in the same 134 HYDROSTATICS. time as when uniformly retarded ; therefore, the truth of the propo- sition is manifest. 267. A fluid spouting from the side of a vessel, describes the curve of a parabola. The fluid is precisely in the same circumstances as a projectile ac- ted on by the force of projection (viz. the pressure of the incum- bent fluid) and by the force of gravity. Therefore, according to Art. 83. it describes the curve of a parabola. As in the case of other projectiles, the proposition holds good, whatever may be the angle of elevation of the jet. 268. When a fluid spouts from the side of a perpendicular col- umn its random or horizontal distance will be the greatest when it spouts from the center, and it will be equal at equal distances from the center above and below. The lower parts of the column being subjected to the strongest pressure, namely, that of the incumbent column, we might suppose that the lower the orifice, the greater would be the random ; but we must recollect, that such a spout would reach the plane sooner than those at a higher elevation. 269. The term FRICTION is applied to the obstruction occasioned to the passage of fluids in the same manner as it is to solids ; and it exists to such an extent as to become an object of considerable in- convenience in practice. It can be obviated only by making the conveying pipe of much larger dimensions than would otherwise be necessary, so as to allow the free passage of a sufficient quantity of fluid through the center of the pipe, while a ring or hollow cylinder of water is to be considered to be at rest all around it. Other circumstan- ces beside friction likewise tend to diminish the quantity of fluid which would otherwise pass through pipes, such as the existence of sharp or right angled turns in them, permitting eddies or currents to be formed, or not providing for the eddies or currents that form natural- ly* by suiting the shape of the pipe to them. It follows, therefore, that whenever a bend or turn is necessary in a water pipe, it should be made in as gradual a curve or sweep as possible ; that the pipe should not only be sufficiently capacious to afford the necessary sup CAPILLARY ATTRACTION. 135 ply, but should be of an uniform bore throughout, and free from all projections or irregularities against which water can strike, and form eddies or reverberations, since these will impede the progress of the fluid as effectually as the most solid obstacles. 270. An unexpected facility is gained in the discharge of a fluid from the bottom or side of a vessel, by applying a pipe to the orifice. On account of the friction known to occur in the passage of a fluid through a tube, it might be supposed that a simple orifice made in the vessel might fce more favorable to the discharge of the fluid than an opening- prolonged by a tube ; but it has been found by experiment, that a vessel of tin, with a smooth hole formed in its bottom, did not discharge water as rapidly as another containing the same weight of water, and an orifice of the same dimensions, to which a short pipe was applied. By varying the length of the pipe, it is found that when its length is twice its diameter, it produces the most rapid discharge, delivering, in this case, 82 quarts of water in 100 seconds, while the simple hole delivered but 62 quarts in the same time. If, however, the pipe projects into the vessel, the quantity discharged is diminished instead of being increased by the pipe. CHAPTER III. OF CAPILLARY ATTRACTION, OF THE RESISTANCE OF FLUIDS, AND OF WAVES. Capillary Attraction. 271. The definition of a fluid, proceeds on the supposition that fluids are destitute of cohesion, and that their particles move among themselves without the slightest impediment. All liquids, however, have in fact more or less cohesion or mutual attraction among their particles. This is apparent in their forming drops, and in the viscidi ty of certain liquids, as oil and tar, which on account of this property are sometimes denominated semi-fluids. It is owing to this property that water so readily forms itself into drops, and that its surface, when viewed in a small cup or wine glass, appears convex. Both of these properties are still more observable in quicksilver, which, when poured on a table, forms numerous globules of a perfectly spherical 136 HYDROSTATICS. figure ; and the convex figure of the surface, as seen in a wine glass is very striking. When we dip a glass tube into water, it comes out covered with drops of the fluid, which are held by the attraction of the glass for water ; but the tube when dipped into quicksilver comes out dry, because the cohesion between the particles of quicksilver for one another is greater than the mutual attraction that "exists be- tween the metal and the glass. Hence, a solid body when immer- sed in a fluid, is sometimes wet by it and sometimes not, according as the attraction between the solid and the fluid is greater or less than that which exists between the particles of the fluid forone another. 272. CAPILLARY ATTRACTION is the attraction which causes the ascent of fluids in small tubes. The tubes must be less than one tenth of an inch in diameter, and tubes whose bores are no larger than a hair, (capillus,) present the phenomenon the more strikingly. But though the rise of water above its natural level is most manifest in small tubes, it appears, in a de- gree, in all vessels whatsoever, by a ring of water formed around the sides, with a concavity upwards. 273. When small tubes, open at both ends, are immersed perpen- dicularly in any liquid, the liquid rises in them to a height which is inversely as the diameter of the bore. Though tubes of glass are usually employed in experiments on this subject, yet the tubes made of any other material, exhibit the same property. Nor does the thick- ness of the solid part of the tube, or its quantity of matter, make the least difference, the effect depending solely on the attraction of the surface, and consequently extending only to a very small distance. Fluids rise in a similar manner between the plates of glass, metal, Sic. placed perpendicularly in the fluids and near to one another. If the plates are parallel, the height to which a fluid will rise is in- versely as the distance between the plates ; and -the whole ascent is just half that which takes place in a tube of the same diameter. If the plates be placed edge to edge, so as to form an angle, and they be inynersed in water, with the Jine of their intersection vertical the water will ascend between them in a curve having its vertex at the angle of intersection. CAPILLARY ATTRACTION. 13* 274. Various Phenomena in nature and art are explained upon the principles of capillary attraction. Capillary action is not confined to tubes, but is exerted among all substances which are perforated by pores, or subdivided by fissures or interstices. On this power de- pend chiefly the functions of the excretory vascular system in plants and animals, and hence also the ascent of humidity thiough the shiv- ered fragments of rocks, unglazed pottery, gravel, earth, and sand. Thus if the pores of the human skin (which are known to be exceed- ingly small) are estimated at the TTJ \ 7 part of an inch in diameter, they will support the fluids that circulate through them to the height of 120 inches, or ten feet, or higher than is required for the animal system. The ascent of the sap in trees has usually been ascribed to capillary attraction, their circulating vessels being a congeries of small tubes ; but physiologists^ now maintain that this action is de- pendent not on the mechanical structure, but upon something which they denominate the living principle of vegetables. 275. According to Professor Leslie, if a soil of gravel contains pores 100th part of an inch in diameter, water will ascend in it by capillary action more than four inches ; and supposing the particles of coarse sand to have interstices of 500th part of an inch, the water would rise through a bed of sixteen inches ; and if the pores were diminished to the 10,000th part of an inch, water would rise twenty five and a half feet. Hence, in agriculture, are derived the advan- tages of deep and perfect tillage ; since the more effectually a soil is pulverized, the better fitted it is to raise and retain water near the surface. Several familiar examples of capillary attraction may be added. A piece of sponge, or a lump of sugar, touching water by its lowest corner, soon becomes moistened throughout. The wick of a lamp lifts the oil to supply the flame, to the height of several inches. A capillary glass tube bent in the form of a syphon, and having its shorter end inserted into a vessel of water, will fill itself and deliver over the water in drops. A lock of thread or of candle wick, in- serted in a vessel of water in a similar manner, with one end hanging over the vessel, will exhibit the same result. An immense weight or mass may be raised through a small space, first by stretching a* dry rope between it and a support and then wetting the rope, 18 138 HYDROSTATICS. Resistance of Fluids. 276. The resistance which a- plane surface meets with while it moves in a fluid, in a direction perpendicular to its plane, is pro- portioned to the square of its velocity. Hence, a boat in the water encounters but little resistance when moving slowly, but the resistance increases rapidly as the speed is augmented. Doubling the velocity increases the resistance fourfold ; tripling the velocity renders the resistance nine times what it was before. This proposition is found to hold good in practice, where the velocity is very small, as in the motions of boats or vessels in water; but when the velocity becomes very great, as that of a can- non ball, the resistance increases in a much higher ratio than as the square of the velocity. Since action a^id reaction are equal, it makes BO difference, in the foregoing proposition, whether we consider the plane in motion and the fluid at rest, or the fluid in motion and striking against the plane at rest. On account of the rapidity with which the resistance increases as the velocity is augmented, when a vessel or a steam-boat is moving in water, it is only a comparatively moderate velocity that can possi- bly be given to it. A vessel driven by a wind which moves 60 miles an hour, is not carried forward faster than at the rate of 12 or 14 miles per hour. Steam-boats are sometimes urged forward at the rate of 16 miles an hour; but to gain the additional speed over and above 12 miles, requires a great expenditure of force. If a steam engine of 20 horse power give a motion of 4 miles an hour, it would require one of 180 horse power to increase the speed to 12 miles an hour. But, it must be observed that the resistance decreases as fast when the velocity is diminished, as it increases when the velocity is augmented ; and consequently, that canals may have the advantage over railways, when heavy articles are to be transported by very slow motions, although railways, encountering only the resistance of the air instead of water, have greatly the advantage when the motion is swift. It follpws from the foregoing doctrine that a body descending free- ly through the air by gravity for a great distance, does not continue to be accelerated throughout the whole distance, but is finally brought, by the resistance of the air, to a uniform motion. WAVES. 139 277. The motion of fluids in pipes and otherwise, is modified so much by the impediments arising from friction against the sides of the pipe or channel, from resistance of the air, and from more or less cohesion in the fluid itself, that the foregoing principles dedu- ced from theory require great allowances to be made when applied to practice. The nature of these impediments, however, is so well understood that the theoretical principles of hydraulics, may be re- duced to practice without , an error exceeding one fifth or ev v en one tenth of the whole. 278. Undulation of Fluids and the formation of Waves. When the surface of water is pressed upon unequally, in parts contiguous to one another, the columns most pressed are shortened, and sink beneath the natural level of the surface, while those that are least pressed 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 con- tinue so, until the columns that were at first most depressed have become most elevated, and those that were most elevated have be- come most depressed. The alternate elevations and depressions of the surface of a body of water, produced by a force acting unequal- ly on the surface, are called waves. The water in the formation of waves has a vibratory or reciprocating motion, both in a horizontal and in 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 is not necessary to undu- lation. 279. Sir Isaac Newton first observed the analogy between the motions of waves and the vibrations of a column of water in a re- curved tube, and upon this analogy he founded his theory of waves. Let AFGB (Fig. 67.) be a bent lube, of equal bore throughout, having its sides parallel and perpendicular to the horizon. Suppose it to be filled with water or any fluid to the height MM 7 . . By any pressure applied at M', let the column be depressed to N' and raised to E in the oppositee arm. The pressure being re- moved, the longer column EF will preponder- ate, and seek to regain its original level, but 140 HYDROSTATICS. the ascending column will not stop at M', but on account of its iner- tia will ascend to E', that is, to the same height as that from which it descended on the other side. It will now descend again, and these reciprocal motions will continue until destroyed by the natural im- pediments to motion. On account of these, each successive vibra- tion is shorter than the preceding, but all of them, like those of a pendulum, are performed in equal times ; for the moving force is ob- viously proportioned to the column EM, that is, to the space through which the whole column vibrates ; and when the forces are as the spaces, the times are equal. 280. Now when the surface of water is smooth and at rest, if any force (as the action of the wind or the fall of a stone) depress that surface in any particular place, the contiguous water will necessarily rise al] around that place. The water which has thus been elevated, descends soon after in consequence of its gravity ; and by the time it has reached the original level, it will have acquired velocity suffi- cient to carry it lower than that level ; therefore, it now acts as an- other original moving force, in consequence of which, the water will be raised on both sides of it. And for the same reason, the descent of those elevated parts will produce other elevations contiguous to them, and so on. Thus the alternate rising and falling of the water in ridges, will expand all around the original place of motion ; but as they recede from that place, so the ridges, as well as the adjoin- ing hollows, grow smaller and smaller until they vanish. This dim- inution of size is produced by three causes, namely, by the want of perfect freedom of motion amongst the particles of water, by the re- sistance of the air, and by the remoter ridges being larger in diame- ter than those which are nearer. 281. From a variety of experiments and observations, it appears that the utmost force of the wind cannot penetrate a great way into the water ; and that even in violent storms the water of the sea is slightly agitated at the depth of twenty feet below the usual level, and probably not moved at all at the depth of thirty feet. Therefore, the actuaj displacing of the water by the wind cannot be supposed to reach nearly so low ; and hence it would seem that the greatest waves rould not be so very high as they are often represented by navigators. JFJut it must be observed, that in storms waves increase to an enor- QUESTIONS. 141 mous size from the accumulation of waves upon waves ; for, as the wind is continually blowing, its action will raise a wave upon another wave, and a third wave upon a second, in the same manner as it raises a wave upon the flat surface of the water. In fact, at sea, a variety of waves of different sizes are frequently seen one upon the other, especially while the wind is actually blowing. When it blows fresh, the tops of the waves, being lighter and thinner than the other parts, are impelled forward, broken, and turned into a white foam, particles of which, called spray, are carried to a great distance. Whilst the depth of the water is sufficient to allow the oscillation to 'proceed un- disturbed, the waves 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 to the surface, or by the shelving of the^fire^ oscillation is prevented or much retarded, the waves in the deep ter are not balanced by those in the shallower, and therefore acquire a progressive motion in this last direction, and form breakers. Hence it is that waves always break against the shore, whatever be the di- rection of the wind. 282. Questions in Hydrostatics. 1. In a Hydrostatic Press, (Fig. 60.) the height of the small col- umn AB on which the power acts is 2 feet above the bottom of the larger piston CD ; the diameter of the cylinder AB is one inch, and of the cylinder CD 1 foot. By means of a screw turned by a lever, a man can exert a force on A equal to 500 Ibs. What amount of pressure can he apply with the aid of this press, combining his own strength with the pressure of the column of water AB ? Ans. 72098.17 Ibs. 2. A Junk Bottle, whose lateral surface contained 50 square inch- es, was let down into the sea 500 fathoms, (3000 feet :) What press*- ure would the sides of the bottle sustain, no allowance being made for the increased specific gravity of the sea water ? Ans. 65104.166 Ibs. 3. A Greenland Whale sometimes has a surface of 3600 square feet : What pressure would he bear at the depth of 800 fathoms r Ans. 1080,000,000 Ibs. or more than 482142 tons. 4. A mineral weighs 960 grains in air, and 739 grains in water ; What is its specific gravity ? Ans. 4.343. 142 HYDROSTATICS. 5. What are the respective weights of two equal cubical masses of gold and cork, each measuring 2 feet^on its linear edge ? Ans. The gold weighs 9625 Ibs. =4.278 tons; the cork weighs 120 Ibs. 6. On one of the peaks of the Alps, is a single mass of granite rock of nearly a globular shape, which is estimated by measure to contain 5049 cubic feet. The whole mass is so nicely balanced on its center of gravity, that a single man may give it a rocking motion. By trial made upon a small fragment, its specific gravity was found to be 2.6 : What is its weight? Ans. 366.277 tons. 7. Wishing to ascertain the exact number of cubic inches in a very irregular fragment of stone, I ascertained its loss of weight in water $0 be 5.346 ounces: Required its dimensions ? Ans. 9.238 cubic inches. 143 PART III. PNEUMATICS. CHAPTER I. OF THE MECHANICAL PROPERTIES OF AIR. 283. PNEUMATICS is that branch of Mechanics, which treats of the equilibrium and motion of elastic fluids. Those laws of equilibrium which are founded on the peculiar na- ture of fluids, arising from the mobility of their particles, are equally applicable to Hydrostatics and Pneumatics. But certain additional properties result from the elasticity of vapors and gases, which may be conveniently considered under the latter head. 284. Vapors are elastic fluids which are produced from liquid* or solid bodies, by the agency of heat, and which readily become liquid or solid again on the application of cold. Thus steam is raised from boiling water, and is again easily condensed by cold into the liquid state. Gases are permanently elastic fluids. They are never met with in nature, either in the liquid or solid state, and it is only by means of extraordinary degrees of cold or pressure, that they caff be made to give up their elasticity and become liquids. Atmospheric air is a body of this class ; and since air and steam are, with slight exceptions, the only elastic fluids employed as mechanical agents? it is to these, chiefly, that our attention- will be devoted. 285. The properties of air may be- exhibited under the form of a few simple propositions. (1.) Jlir is material. The two essential properties of matter are extension and impene- trability. That air has extension, needs no proof. That it is im- penetrable, or has the property of excluding all other matter from the space which it occupies, is proved by experiment. Thus, if we depress in water a tall jar, or a tumbler, we shall find that the water rises only through a certain part of the vessel, to whatever depth we immerse it; and if, to a hollow cylinder, made smooth and closed at the bottom, we fit closely a stopper or solid cylinder, called 144 PNEUMATICS. a piston, moving freely in it, on applying the piston, 110 force wil enable us to bring it into contact with the bottom of the cylinder, unless we permit the air within it to escape. Two other properties exhibited by air, likewise indicate that it is material : these are iner- tia and weight. The inertia of air is manifested by the resistance it opposes to bodies moving in it ; as, for example, an open umbrella moved through the air, in a direction parallel with the staff; and the weight of the air is shown by the fact that a vessel, as a bottle', from which the air has been withdrawn (by methods to be described here- after) weighs less than before. A vessel of the capacity of a wine quart, weighs about eighteen grains less after the air is exhausted, than before. One hundred cubic inches of air weighs thirty grains and a half. (2.) Air is a fluid. This property is manifested not only by the great mobility of its parts, but also by the, distinguishing property of fluids, viz. that any portion of air at rest, presses and is pressed equally in all directions; and that a pressure or blow applied to any part, is propagated through the whole mass, and affects every part alike. (3.) Mr is an ELASTIC fluid. Thus, when an inflated bladder is compressed, it immediately re- stores itself to its former situation. Indeed, since air, when com- pressed, restores itself, or tends to restore itself, with the same force as that with which it is compressed, it is a perfectly elastic body. 286. Before we proceed further, it is necessary for the learner to be made acquainted with the apparatus, by which the mechanical prop- erties of air are illus- trated. The Mr Pump. The Air Pump (Fig. 68.) is an in- strument used for the Fig. 68. tfECHAJUCAL PROPERTIES Of AIR. purpose of exhausting the air from any given space. Though of several different forms, yet the most common construction is that represented in Fig. 68. The chief parts are the plate A, the bar- rels EE, and the pipe or canal C, leading from the plate to the barrels. The glass vessels which are set upon the plate, are called in general receivers. A guage is sometimes employed (as repre- sented by D in the figure) to indicate the degree of exhaustion ; but the nature of this appendage will be better understood hereafter. Such is the construction of the air pump in general ; but the impor- tance of this apparatus entitles it to a more minute description. In order, then, fully to understand the principle of the air pump, and other kinds of apparatus designed for producing a vacuum, we must understand the construction of valves, and of the cylinder and piston, 287. A VALVE is a contrivance which permits a fluid to pass in one direction, but prevents its passing in the opposite direction. The clapper seen on the under side of a pair of bellows, is a familiar ex- ample of a valve. The valve employed in the air pump, usually consists merely of a strip of oiled silk, tied over a small orifice. The air by pressing outwards from the orifice raises the silk, opens the valve, and makes its escape ; while by pressing inwards upon the orifice, it keeps the strip of silk close to the orifice, and is therefore prevented from passing in that direction. The piston and cylinder are exemplified in a common syringe. It consists of a hollow cylinder,- or barrel, to which is fitted a short solid cylinder called the piston, which is moved up and down the barrel by means of a projecting handle called the piston-rod, and is fitted so closely to the barrel as to be air tight. Suppose now that the cylinder is in a perpendicular position, closed below but open above, and that the piston rests ort the bottom. On drawing up the piston, the air above it is lifted out f and the space below it is a vacuum. If a small orifice be made in the bottom of the barrel, then as the piston is drawn upwards, the air will flow in and no vacuum will be formed ; and as the piston is de- pressed again, the air is forced back. But by attaching a valve to the orifice, we may admit or exclude the external air at pleasure. If the strip of silk be tied on the outside, then, on drawing up the pis- ton, the air will not follow, but the piston will go up heavily, since if tifts up the entire weight of the column of air that rests upon it, (there 19 146 PNEUMATICS. being nothing below it to act as a counterpoise,) and if the hand be withdrawn from the piston rod, the piston will descend spontaneous- ly. Again, if the valve be placed on the inside, then the external air will follow the piston as it rises, and no vacuum will be formed. If now the piston be depressed, the air cannot be expelled, (since the valve closes on the orifice in that direction,) and the piston cannot be forced down to the bottom of the barrel, unless a valve is placed in the piston itself, opening outwards ; in this case, the air of the barrel may be expelled by depressing the piston. 288. We have been thus minute in the description of the con- struction of valves, and of the cylinder and piston, because when these things are clearly understood, the learner will easily compre- hend the principle of the air pump, of the common house pump, of the steam engine, and of every other species of pneumatic apparatus. Let us now return to the air pump. In the barrels, two pistons play up and down, each of which is fur- nished with a valve opening upwards into the open space, through which the piston rods move. Another valve is placed at the bottom of each barrel, opening into the barrel. The piston rods are indented bars, to which a toothed wheel (concealed in Fig. 6.8, but seen in Fig. 69,) is adapted, which, being turned backwards and forwards Fig. 69. MECHANICAL PROPERTIES OF AIR. 147 by means of the winch G, (Fig. 68.)* alternately raises and depresses the two pistons, as is represented in figure 69. Suppose now the receiver to be placed on the plate of the pump, one of the pistons being at the top, and the other at the bottom of the barrel. We turn the winch, the piston rises, and the air of the receiver opens the valve at the bottom of the barrel, and diffuses itself equally through the barrel and the receiver. We turn the winch in the opposite di- rection, the piston descends, compresses the air in the barrel before it, which, as it cannot go back into the receiver, opens the valve in the piston itself, and escapes into the vacant space in which the arm of the piston moves. This process is repeated every time the piston rises and falls; and it is the same in both barrels, two being employed for no other reason than to accelerate the process of exhaustion. 289. By means of this instrument, we may obtain very striking illustrations of the mechanical properties of air. (1.) The pressure of the air acts with great force on all bodies at the surface of the earth, amounting, as we shall show hereafter, to nearly 15 pounds upon every square inch, or more than 2000 pounds upon a square foot. Upon so large a surface, therefore, as that of the human body, the pressure amounts to no less than 13 or 14 tons; but being so uniformly distributed within and without, and on all sides, it is, when the air is at rest, scarcely perceptible. In consequence of this pressure the air insinuates itself into all fluids, and fills the pores of all solids except the most dense, as gold or platina. The pressure of the air diminishes the tendency of fluids to pass into the state of vapor, and of course raises their boiling point. Warm water, at a temperature much below the boiling point, will be set a boiling under the receiver of an air pump, or in a vacuum formed in any other way. Indeed, if it were not for atmospheric pressure, water )vould require only the moderate heat of 72 instead of 212 degrees of heat to make it boil ; and the more volatile fluids, as alcohol and ether, would hardly be found in nature, in the liquid state. (2.) The elasticity of the air is such, that the smallest portion of it may be expanded beyond any known limits, by removing the exter- nal pressure. By this means, a bubble may be made to fill a very large space. On the other hand, air has been condensed by press- ure, until its density has been greater than than of water, still retain- J48 PNEUMATICS. Fig. 70. ing the elastic invisible state, In consequence of its elasticity, air is set in motion by the least disturbance of its equilibrium, whether by condensation or rarefaction, thus giving rise to the phenomena of winds. (3.) Air is essential to the support of combustion, and to the respiration of animals ; and finally, it is the principal medium of sound. It may be farther shown, that the weight of bodies is dimin- ished by the bouyancy of air, (acting on the same principle as water, and that light bodies are sustained in it, in consequence of its greater specific gravity, while, in a vacuum, bodies of various densities, as a guinea and a feather, fall towards the earth with equal velocities. The Condenser. 290. The condensation of air is usually effected by means of the Condensing Syringe. This instrument is a cylinder and piston, the cylinder having a valve opening outwards, while the piston is without a valve. The principle of its op- eration will be readily understood from the figure. Near the top of the cylinder is a small hole in the side, which is immediately below the piston, when this is drawn up to the top of the cylinder. On forcing down the piston, the air is driven before it, and expelled through the valve at the bottom. By connecting a bottle or other close vessel with the bottom, the air expelled may be driven into that, its return being prevented by the same valve. The piston being drawn up again above the opening in the cylinder, another similar portion of air may be forced into the condensing bottle ; and thus the pro- cess may be continued indefinitely. 291. The Condensing Fountain is a bottle, usually of copper, partly filled with water, upon the surface of which the air is condens- ed by means of the condensing syringe. The fluid being thus brought under a strong pressure, it tends to issue with great force whenever a pipe, that is inserted in the bottle, and extends below the surface of the water, is opened. The celebrated spouting springs of Iceland, called the Geysers, in which water accompanied by large MECHANICAL PROPERTIES OF AIR. 149 masses of rock, is thrown to the height of 200 feet, ante from pneu- matic pressure acting upon the surface of water in the interior of the earth, the aeriform substance, whatever it may be, being produced by means of volcanic action. 292. The Mr-Gun is an instrument in which condensed air is sub- stituted as the moving force instead of gun-powder. By means of a condensing syringe, air is strongly condensed in a metallic ball fur- nished with a valve at the mouth, where it is screwed on the gun be- low the lock. As the lock is sprung, it falls upon a plug, and forces it upon the valve, which suddenly opens, and the air rushes into the barrel of the gun, and by its sudden expansion, propels a ball much in the same manner as gun-powder would do in its place. 293. The Diving Bell is an apparatus employed for exploring the depths of the sea. It was formerly made in the shape of a bell, but is now more commonly made square at the top and bottom, the bot- tom being a little larger than the top, and the sides slightly diverging from above. The material is sometimes cast iron, the whole ma- chine being cast in one piece, and made very thick, so that there is no danger either from leakage or fracture. Sometimes the diving bell is made of planks of two thicknesses, with sheet lead between them. In the top of the machine are placed several strong glass lenses for the admission of light, such as are used in the decks of vessels to illuminate the apartments below. 294. The diving bell depends for its efficacy on that quality of air, which is common to all material substances, impenetrability; that is, the exclusion of all other bodies from the space it occupies. The principle may be illustrated by depressing a tumbler or jar in water, with the mouth downwards: it will be seen (Art. 285.) that the water will ascend so far as to occupy only a pact of the capacity of the ves- sel, the upper part being occupied by air. As the diving bell de- scends in the water, the air inclosed in it is subject to its pressure, (which increases with the depth,) and by virtue of its elasticity, it will become condensed in proportion to this pressure. Thus at the depth of about thirty four feet, the hydrostatic pressure will be equal to that of the atmosphere, and consequently, the air being under a pressure equivalent to that of two atmospheres, it will be condensed into one 150 PNEUMATICS. half its original volume. As the depth is increased, the space occu- pied by the air in the bell will be proportionally diminished. Seats are furnished for the workmen, and shelves for tools and various other conveniences. Although at the depth of thirty four feet, the water would occupy one half the capacity of the vessel, and more or less at different depths, yet by means of a forcing pump or condensing syringe communicating between the atmosphere above and the ma- chine, through a pipe, air may be thrown in so as to exclude the water entirely. . By the same means fresh air may be conveyed to the workmen, the portion of air rendered impure by respiration being at the same time suffered to escape by opening a stop-cock in the top of the machine. The Barometer. 295. Let us take a glass tube, about three feet in length, F g- 71 olosed at one end and open at the other. We fill the tube with quicksilver, and invert it in a vessel of the same fluid. The column of quicksilver falls to a certain height, about twenty nine or thirty inches, where, after vibrating a few times, it remains at rest. The space in the tube above the quicksilver being void of air or any other substance, it is of course a vacuum, and is usually denominated the Torri- cellian vacuum, from Torricelli, an Italian philosopher, who first discovered this method of producing a vacuum. Va- rious precautions are necessary, in order to preserve this space free from air or any aeriform substance ; when these precautions are taken, this vacuum is the most complete of any that we can command. 296. The column of quicksilver is sustained by the pres- sure of the atmosphere, on the open mouth of the tube which is immersed in the same fluid ;* and it must have the same weight with a column of the atmosphere of the same base, otherwise it would not be in equilibrium with it. We hence arrive at an accurate knowledge of the actual * As young learners sometimes find a dificulty in conceiving clear- Jy how the pressure of the air act? in this case, we subjoin a remark THE BAROMETER. 151 weight and pressure of the air, since it is equal to the weight of a column of quicksilver of the same base, thirty inches in length. The weight of such a cylinder of quicksilver is easily ascertained, and it results, that the pressure of the air on every square inch of surface is, as stated in Art. 289, about 15 Ibs. or more than 2000 Ibs. upon a square foot. Since different fluids balance each other in opposite columns pressing base to base, when their heights are inversely as their specific gravities, a column of water in the place of the mercu- ry would stand at the height of about 34 feet. For quicksilver be- ing 13.57 times heavier than water, the latter column must be 13.57 times higher than the other; that is, 30x13.57=407.1 inches =33.84 feet. 297. By observing from day to day the height of the column of quicksilver prepared as above, we shall find that it varies through a space of two or three inches, showing that the atmosphere does not always exert the same pressure, but that a given column of the air is sometimes lighter and sometimes heavier. This instrument, there- fore, enables us to ascertain the relative weight of the air at any giv- en time, and hence its name barometer.* For the purpose of indi- cating these variations with minuteness and precision, a graduated scale is attached to the barometer, divided into inches and tenths of an inch, and usually extending from twenty seven to thirty one in- ches, a space which is more than sufficient to comprehend all the natural variations in the weight of the atmosphere. 298. Since the variations of the barometer correspond to the va- riations in the weight of the air at the same place, and since these variations are connected with changes of weather, this instrument thus becomes a weatherglass, and enables us, in certain cases* to fore- see changes of weather. The most uniform indications of the ba- or two. It must be recollected, that any impulse or pressure exerf- ed on the surface of the fluid in the vessel, extends alike to every part of it; and since fluids act upwards as well as downwards, it is plain that the pressure acts in sustaining the column of mercury in the same manner as though it were applied directly to the mouth of the tube. * From <> weight, and /j^lpov measure. 152 PNEUMATICS. rometer are, that its rise denotes fair, and its fall denotes foul weather whatever may be its absolute height. Also a sudden and extraordi- nary descent of the mercury attends, and frequently precedes a vio- lent wind. 299. The mean pressure of the atmosphere, as indicated by the barometer, is nearly the same, at the level of the sea in all parts of the earth corresponding very nearly to 30 inches of mercury. This fact has been verified by numberless observations, made with the ba- rometer in both hemispheres, from the equatorial to the polar regions. The following results for several places, in different latitudes, correct- ed for temperature, elevation above the level of the sea, and the in- fluence of the earth's rotation on its axis, are nearly uniform. Latitude. Bar. Pressure. Calcutta, - - - 22 35' - 29.776 London, 51 31 - 29.827 Edinburgh, - 55 56 - 29.835 Melville Island, 74 30 - 29.884 But, though the mean pressure of the atmosphere is nearly the same, at the level of the sea, over the whole globe, the extent of the variations to which it is liable, is exceedingly different in different parallels of latitude. At the equatorial regions, the range of the ba- rometer is much more limited than within the polar circles ; and in the frigid zones,, it is more limited than in the temperate. Within the tropics the fluctuations of the barometer do not much exceed J of an inch, while beyond this space, they reach to 3 inches. The most extensive variations take place between the latitudes of 30 and 60, being the zone in which the annual changes of temperature and hu- midity possess the widest range. 300. Shortly after the invention of the barometer, it was observed that the mercury descends, when the instrument is carried to a more elevated situation. The descent is found to be about T \ of an inch for 87 feet. From this observation, we may deduce the specific gravity of air compared with mercury or water ; for y 1 ^ of an inch of mercury has, it appears, the same weight as 87 feet, or 1044 inches, of air/ Consequently, 1 inch of mercury weighs as much as 10440 / 10440 \ inches of air; that is, mercury is 10440 times, and water is i 13 57 == ) 769 times, heavier than air. ATMOSPHERE. 153 301. As the air pump enables us to investigate the mechanical properties of any portion of air, so the barometer enables us to study the properties and relations of the entire body of the air, that is, the atmosphere. By means of these two instruments, the following facts are well established. ( 1 . ) The space occupied by any given portion of otr, (as 1 00 grains for example,) is inversely as the pressure. A weight of two atmos- pheres diminishes the bulk to one half; of three atmospheres, to one third ; and of one hundred atmospheres, to one hundreth part of its former bulk. (2.) As the density is likewise inversely as the space occupied, therefore, the density is as the pressure. (3.) Since air when compressed, endeavors to restore itself, with a force which is equal to that which compresses it, (being when at rest in equilibrium with that force,) therefore, the elasticity is as the , density and inversely as the space occupied. In this proposition, the temperature is supposed to remain uniform. But, the bulk and den- sity of a portion of air remaining the same, the elasticity is as the temperature. Hence the elasticity of air maybe increased either by compressing it, or by heating it in a confined state ; and its elas- ticity may be diminished either by lessening the pressure, or by cool- ing it. The elasticity of springs is known to be frequently impaired by continual action. This is not the case with air. Air has been left for several years very much compressed in suitable vessels, in which there was nothing that could have a chemical action upon it ; and afterwards, on removing the unusual pressure, and restoring the same temperature, the air has been found to recover its original bulk which shows that the continuance of the pressure had not diminished the elasticity of it in the least perceptible degree. CHAPTER II. OF THE ATMOSPHERE. 302. The knowledge now acquired of the properties of elastic' fluids, will qualify the learner to enter advantageously upon the study of the entire body of the air, which constitutes the atmosphere, 20 154 PNEUMATICS. Let us therefore now proceed to consider its weight, its extent and density, its relations to heat and moisture, giving rise to the various phenomena of Meteorology, and its relations to sound, whence arises the science of Acoustics. 303. The WEIGHT of the entire atmosphere may be easily esti- mated by means of the barometer ; for taking the. medium height of the mercury at thirty inches, the weight of the atmosphere is equal to that of a sea of quicksilver, covering the whole earth to the depth of two and a half'feet. This would add five feet to the diameter of the globe, and the contents of the whole mass of quicksilver, in cubic feet, would be equal to the difference between the solid con- tents of the globe, and those of a sphere of a diameter five feet great- er. Having the number of cubic feet of quicksilver, 'we have only to multiply that number by the weight of one foot, and we obtain, for the weight of the whole atmosphere, 11,624914,803603,492864 Ibs., or more than eleven trillions of pounds, or five thousand billions of tons. 304. Were the atmosphere of equal density throughout, it would be easy to determine its height, since opposite columns of different fluids are in equilibrium, when their heights are inversely as their specific gravities, (Art. 251.) Therefore, as the specific gravity of air is to that of quicksilver, so is the height of the column of quick- silver to the corresponding height of the column of air that balances it. That is, 1 : 10440: :2.5 : 26100 feet=5 miles nearly. But the atmosphere is very far from being throughout of uniform density. Several causes conspire to produce this result. 1. The different quantities of superincumbent air at different altitudes; 2. The decreasing attraction of the earth in proportion as the square of the distance from its center increases ; 3. The influence of heat and cold; 4. The admixtures of vapors and other fluids ; 5. The attrac- tion of the moon and other celestial bodies. That the lower strata of the atmosphere are far more dense than the upper, will be obvious from this consideration, that the portions which rest on the surface of the ear,th, sustain the weight of the whole body of the atmosphere, which, as appears from Ail. 303, is immensely great. But the den- sity of air is as the compressing force. (Art. 301.) As we ascend from the earth, the weight sustained is constantly diminished, and the density lessened, according to the following law. ATMOSPHERE. 155 305. The densities of the air decrease in a geometrical, as the distances from the earth increase in an arithmetical ratio. 306. By observations on the barometer at different altitudes, aid- ed by calculation, it is ascertained, that at the height of seven miles above the earth, the air is only one fourth as dense as it is at the surface. Hence if we take an arithmetical series, increasing by seven, to denote different heights, and a geometrical series whose constant multiplier is one fourth, to denote the corresponding densi- ties, we may easily ascertain the density of the air at any proposed elevation. Arithmetical series, 7 14 21 28 35 42 49 Geometrical series, { T V T ' T }g- ' T oVe TFFTI From this table it appears, that at the height of twenty one miles, the air is sixty four times as rare as at the surface of the earth ; at the height of forty nine miles, sixteen thousand three hundred and eighty four times as rare ; and if we pursue the calculation, we shall find that its rarity at the moderate distance of only one hundred miles, is one thousand millions of times greater than at the earth, and of course would oppose no sensible resistance to bodies revolving in it. De Luc ascended in a balloon to such a height that his barometer fell to twelve inches. Supposing the barometer at the surface to have stood, at that time, at thirty inches, it follows that he must have left three fifths of the whole atmosphere below him ; for six inches being one fifth of thirty, twelve inches must be two fifths, and consequently three fifths of the whole must be below. His elevation was upwards of twenty thousand feet. If there were an opening into the interior of the earth, which would permit the air to descend, its density would increase in the same manner as it diminishes in the opposite direction. At the depth of about thirty four miles, it would be as dense as water ; at the depth of forty eight miles, it would be as dense as quicksilver ; and at the depth of about fifty miles, as dense as gold. 307. The foregoing law, however, does not afford exact data for estimating the density of the air at any given elevation, since the den- sity is affected by the several other circumstances mentioned in arti- cle 304, which are not here taken into the account. Since the force of attraction diminishes as the square of the distance from the center of the earth increases, this diminution will occasion a corresponding 156 PNEUMATICS. decrease of density. However, as the force of attraction will be very nearly the same at such elevations as the highest mountains, as at the general level of the earth, no allowance is made on this account for barometric measurements, except in cases when extreme accu- racy is required. Changes of temperature produce a much greater effect, since heat expands and cold contracts the air ; and therefore, in estimating altitudes, the state of the thermometer is always to be taken into account, in connexion with the height of barometer. Heat and cold also affect the height of the mercury in the barometer, independently of the pressure of the atmosphere without, and there- fore it becomes necessary to reduce the observations to a fixed {standard of temperature. 308. As we ascend from the earth, the temperature of the air constantly diminishes until we arrive at a region of frost, the lower limit*of which is called the term of perpetual congelation. The heights of the term of congelation for every parallel of latitude from the equator to the north pole, have been computed, partly from ob- servation, and partly from the known mean temperature of each par- allel, and the decrement of heat as we ascend in the atmosphere ; and the result is expressed in the following table : Latitude. Mean height of the term Differences for every of congelation in feet. 5 deg. of latitude. ' 15577 5 15455 - 122 10 . 15067 388 15 14498 569 20 13719 ^ 779 25 - 13030 - - 689 30 11592 1438 35 10664 928 40 9016 1648 45 7658 1358 50 6260 1398 55 4912 1348 6p 3684 1238 65* 2516 1168 70 1557 959 75 748 809 80 - - 120 628 ATMOSPHERE. 157 From this table it appears, that the height of the region of per- petual frost at the equator is almost three miles ; at the parallel of 35, about two miles ; and at the latitude of 54, about one mile; while at the latitude of 80, this region approaches very near to the earth, and at the pole it probably comes nearly or quite down to the earth. It is farther to be remarked, that the different heights decrease very slowly as we recede from the equator, until we reach the limits of the torrid zone, when they decrease much more rapidly the maximum being at the parallel of 40. The average difference for every five degrees of latitude from 30 to 60, is 1334, while from the equator to 30, the average is only 509, and from 60 to 80, it is only 891. Important meteorological phenomena depend on this fact. 309. As a portion of air rarefied by heat at the earth's surface ascends, the diminishing pressure which it sustains as it rises, has a tendency to enlarge its volume. But on the other hand, an enlarge- ment of volume, increases its capacity for heat, and lowers its temper- ature, which tends to condense it. At a moderate elevation above the earth, these causes operate to keep the air at rest and thus the heat of the earth is incapable of raising the temperature of the air, except within a moderate distance, beyond which the region of frost pervails, and the cold continues to increase, until it probably reaches at a comparatively moderate distance from the earth, an intensity al- most inconceivable. Relations of Mr to Heat. 310. Air is set in motion by every cause which disturbs its equili- brium. It is more sensible than the most delicate balance, and'moves with the slightest inequalities of pressure. Air is put in motion by 'the least change of temperature. Heat rarefies it, and renders it specifically lighter than the neighboring por- tions, and it ascends, while colder and denser portions flow in to re- store the equilibrium. On the other hand, if air be condensed by cold, it descends, or flows off, until it meets with air of the same density, where it rests. These effects naturally result from the per- fect fluidity and elasticity of this substance. 158 PNEUMATICS. Fig. 72. 311. An illustration of this principle is seen in the manner in which air circulates in the shaft or pit of a deep mine. Such a circulation is kept up briskly, even amounting sometimes to a strong wind, when two shafts or pits of unequal heights are made to communi- cate with each other by means of a horizontal gallery, called a drift. The earth remains nearly at the same temperature summer and winter, while the external air is hotter in summer and colder in win- ter, than that within the mine. Now were the air within the earth and without, of the same density then the air of the two shafts and of the drift would remain in equilibrio, the longer shaft A, being counterbalanced by the shorter shaft B, extending so as to embrace C, a portion of the ex- ternal air, to the same height as the column A. But suppose it summer ; then the air in A, becoming condensed by the influence of the colder earth, *s rendered specifically heavier, and . overpowers in the columns B and C, the latter consisting of air more rarefi- ed than that within the earth. Hence the air will flow down the longer, and out of the shorter shaft ; and by bring- ing all parts of the mine into the cir- culation the whole interior will be ventilated. Again, suppose it win- ter ; then the air in the longer shaft being warmer and more rarefied than the compound column BC, the latter preponderates, and the air flows in the opposite direction ; namely, down the shorter and out at the longer shaft. In spring and autumn, when the temperature of the atmosphere and the mine are nearly equal, the miners complain much of the suffocating state of the air. . 312. The contemplation of the motions of the atmosphere on a large scale, as they exist in nature, leads to the subject of Winds ; but we. may see the same principles exemplified in chimnies and fire- places. A chimney may be regarded as a perpendicular tube, con- taining a column of air. Since the density of the air is less above than below, and consequently the resistance less at the top than at Hor. drift. ATMOSPHERE. 159 the bottom of the chimney, the tendency of any current of air through the tube is upward, flowing in the direction in which the resistance is least. When the air of the chimney is rarefied by heat from the fire-place, the cold air from below makes its passage upwards into the partial void, and thus supplies air to the fire to support its com- bustion, and carries up along with it the smoke and vapors which proceed from the fire. The smoke, it will be remarked, is carried up, mechanically, by the ascending current of hot air; for smoke is itself heavier than air, and sinks or descends when not thus support- ed.* The draught of the chimney, or the strength and velocity of the ascending current, is influenced by several circumstances. (1.) Long chimnies have a stronger draught than short ones, be- cause they present a longer column of rarefied air ; but they may be so long as to cool the air too much before it has reached the top, in which case the smoke falls by its greater specific gravity. Long horizontal pipes, connected with fire-places or stoves, are apt to smoke, for a similar reason. (2.) A narrow throat, opening into a large pipe or funnel, makes a strong draught, because the velocity of the ascending current is thus increased, it being in different parts of the chimney inversely as the area of the section. The throat of the chimney, however, must be wide enough to admit freely all the mixed products of the ascending current, including the rarefied air, smoke, watery vapor, and so on; and, consequently, a wider throat is required for green wood than for dry, and least of all for anthra- cite coal, where the amount of volatile substances expelled from the fuel is comparatively small. (3.) A fire-place with a low front or breast, has a strong draught, because, in this case, no air can enter the chimney, except such as has felt the influence of the fire, and is thus fitted to keep the chimney warm ; whereas, if the throat of the fire-place is high, much of the air that flows into it is cold and cools the chimney, and of course diminishes the degree of rarefac- tion in it. Moreover, when the throat is near the fire, it becomes * This fact is illustrated by an experiment, suggested by Dr. Frank- lin, viz. by blowing the smoke of a tobacco pipe through water in a tumbler. The smoke r being cooled by this process, rests upon the surface of the water. 160 PNEUMATICS. more intensely heated, and thus the degree of rarefaction of the cur- rent of air that passes through it is augmented and its velocity in- cr.eased. In the structure of fire-places and stoves, it is an impor- tant principle, that as little air as possible should get into the flue of the chimney, except what passes through the fire ; and it is another important principle, in regard to the economy of fuel, that no more air should traverse the fire than what is necessary to support the combustion. All the air that passes through the fire, over and above what undergoes decomposition, cools it, and carries a portion of the heat up chimney. It is obvious that the air of an apartment must be denser than that at the top of the chimney, otherwise the current will flow downwards, as is sometimes the case when the room is very close, and the throat of the fire-place so large as to require a great quantity of air to fill the rarefied space, in which case, the air of the room is speedily exhausted. Hence, the advantage, in close apart- ments, of small fire-places, or stoves which require but a small sup- ply of air. 313. But a much more extensive operation of the same principles is exhibited to us by nature, in the phenomena of WINDS. Rarefac- tion by heat and condensation by cold are the chief causes of winds. Their distinct existence and modes of operation, can frequently be discovered ; and, in cases where we can discover neither, we are au- thorized to infer the presence of such a cause, since it is so constant- ly connected with the same effects in very numerous examples that daily pass before our eyes, while we are unacquainted with any other adequate causes of the same phenomena. The motion of the air, however, producing a wind, may be merely relative, arising from the motion of the spectator. Thus a steam boat, moving at the rate of sixteen miles an hour in a perfect calm, would appear to one on board to be facing a wind, moving at the same rate in the opposite direc- tion ; or if, in the diurnal revolution of the earth on its axis, any point of the earth's surface should move faster than the portion of the atmosphere above it, a relative wind in the opposite direction would ,be the result. The direction of the wind may be modified by various causes, the actual direction being the resultant of two or more currents which meet from different directions, or of several dif- ferent forces. ATMOSPHERE, 161 314. Land and sea breezes afford a striking exemplification of the principle in question. These winds prevail in most maritime coun- tries, but more especially in the islands of the torrid zone, blowing off from the land at night, and towards the land in the day time. If we place a hot stone in a room, (says Dr. Robison,) and hold near to it a candle just extinguished, we shall see the srtioke move towards the stone, and then ascend up from it. Now, suppose an island re- ceiving the first rays of the sun in a perfectly calm morning ; the ground will become warm, and will rarefy the contiguous air. If the island be mountainous, this effect will be more remarkable ; because the inclined sides of the hills will receive the heat more directly. The midland air will therefore be most warmed ; the heated air will rise, and that in the middle will rise fastest ; and thus a current of air upwards will begin, which must be supplied by air coming in on all sides, to be heated and to rise in its turn ; and thus the morning sea breeze is produced, and continues all day. This current will frequently be reversed during the night, by the air cooling and gli- ding down the sides of the hills, and we shall then have the land breeze. 315. The trade winds afford an example of the operation of the same causes on a still greater scale. These winds prevail in the tor- rid zone and a little beyond it, extending to nearly 30 on both sides of the equator. When not affected by local causes, they blow con^ stantly at the same place, in one and the same direction, throughout the year. Their general direction is from north-east to south-west on the north side of the equator, and from south-east to north-west on the south side of the equator. They owe their origin to the com- bined agency of two causes, namely, the movement of the air on ei- ther side 01 the equator, northward or southward towards the place of greatest rarefaction, and the westerly tendency arising from the effect of the earth's diurnal rotation on its axis, since they do not instan- taneously acquire the greater velocity which the equatorial regions have, in consequence of the earth's revolution oti its axis. The dura- tion of the trade winds is variously modified in different parts of the world, but always in such a manner, that they blow towards the point of greatest rarefaction, and receive a relative motion from the effect of the earth's diurnal rotation. 21 162 PNEUMATICS. Relations of Mr to Moisture. 316. The foregoing atmospheric phenomena arise chiefly from the relations of air to Heat; we are next to trace a few of the lead- ing phenomena, which result from the relations of air to Moisture. By the action of the sun's heat upon the surface of the earth, whether land or water, immense quantities of vapor are raised into the atmosphere, supplying materials for all the water that is deposited again in the various forms of dew, fog, rain, snow, and hail. Our limits will now allow us to enter largely into Meteorology, under which head the various phenomena of the atmosphere are included, but we shall be able barely to glance at the subject. 317. The leading principle upon which the precipitaton of moist- ure from the atmosphere, under any form, depends, is the follow- ing : The capacity* of air for moisture is increased by heat and dimin- ished by cold. In other words, air by being heated is rendered capable of taking up and holding a greater quantity of water in the invisible state, and by being cooled, its power of thus holding water is lessened. Again, the capacity of air for moisture increases faster than the temperature; so that the addition of ten degrees of heat to air already at the temperature of 70, will increase the capacity for water much more than the same addition would do when made to air at the tem- perature of 40. On the other hand, the cooling of hot air dimin- ishes its capacity for moisture much faster than the cooling of air already cold. * The term capacity being frequently employed in the physical sci- ences, it is important for the student to obtain clear and correct views of its meaning. The power of a sponge to hold water, to stow it away in the interior, so as to render it invisible, is the capacity of the sponge for water. This capacity is capable of increase or diminution. Take a piece of dry sponge,, and soak it in water; as its volume en- larges, its capacity for water increases remove it from the water, and squeeze it gently ; a part of the water runs out suffer it to expand and it appears nearly dry; squeeze it again, and it becomes wet. Hence we say its capacity is increased by an enlargement of volume, and diminished by compression. ATMOSPHERE. 163 318. DEW is formed when the air comes in contact with a sur- face in a certain degree colder than itself. This is the simplest de- position of moisture from the atmosphere. Thus dew is formed copiously on a cup of cold water during summer, particularly be- fore a thunder shower ; because then the air is hot, and saturated with moisture, a portion of which it deposits as soon as it is cooled, its capacity for moisture being thus diminished. It is ascertained by actual observation that on those nights when copious dews occur, the ground becomes twelve or fourteen degrees colder than the air a few feet above it. Consequently whenever the air, by circulating over the surface of the ground, comes in contact with this colder surface, it deposits a portion of moisture upon it. The quantity actually de- posited will of course be greater as the difference of temperatures between the air and the ground is greater, and the air is more nearly saturated with moisture. Dew is found to be deposited on different substances unequally, more on vegetables than on drysand; very little on bright metallic surfaces ; and none at all on large bodies of water, as the ocean. In all cases, however, these surfaces are observed to maintain a corre- sponding difference in the temperature they acquire, some growing much colder than others equally exposed, while the surface of the ocean remains at the same temperature as the air incumbent on it. The air therefore sustains no reduction of capacity by circulating upon it, and no dew is deposited. 319. FOGS are produced by watery vapor coming in contact with air colder than itself. The vapor may be such as is just rising from the ground, or such as before existed in a body of common air that meets and mixes with the colder air. Thus, in a cold morning, smoke proceeds from va- rious moist substances, as from the breath of animals, from a hole in the ice of a river, from wells, and from many other sources. In each case, the vapor meets with cold air, which having so small a capacity for moisture, is unable to hold it in solution, and it is deposited in the form of fog. A striking example of fogs is seen over rivers, partic- ularly in a summer morning, marking out their courses for a great distance. Here, since the temperature of the water changes but lit- tle during the night, while the neighboring land, and of course the air 164 PNEUMATICS. over the land, has become cold, the vapor which rises from the river during the night, and meets with cold air, is condensed into a fog. The fogs formed over shoals and sand banks, as the banks of New- foundland, are deposited, from the warm and humid air of the ocean, which is cooled by mixing with the cold air over the banks. Fogs are phenomena of cold climates, and are not so common in hot countries ; the air in such situations having too great a capacity for moisture, to permit it to condense into a fog near the surface of the earth. 320. CLOUDS are dependent on the same principle as fogs, consist- ing of vapor condensed by the cold of the upper regions. They are formed over water, or moist places, by vapor rising so high, as to reach a degree of cold sufficient to condense it ; or they result from the mixture of warmer with colder air, proceeding always from the warmer portion. 321. RAIN is produced by the sudden cooling of air, charged with large quantities of watery vapor. Suppose two bodies of air, a hotter and a colder portion, both sat- urated with moisture, to meet ; the compound would assume a tem- perature which was the mean between the two ; but the quantity of heat which the colder portion of air would gain, would not increase its capacity so much as that of the warmer body would be diminish- ed, by the loss of the same portion of heat. (Art. 317.) Hence the capacity of the mixture would be less^han the average capacities of the separate portions, and consequently water would be deposited. If the separate portions of air are not completely saturated with mois- ture, still the capacity of the mixture may be so much less than that of the constituents, as to render it unable to hold all the water they contained ; and in this case, more or less water would be deposited. 322. This view of the general cause of rain, (which is commonly called Button's Theory of Rain, from Dr. Hutton, of Edinburg, who first pjaoposed it,) is capable of being confirmed by an extensive in- duction of facts, by which it would appear, that variable winds, fa- vorable to the mixture of air of different temperatures, are accompa- nied by rain, while constant winds are accompanied by dry weather. MECHANICAL AGENCIES OF AIR. 165 323. HAIL is produced by the mixture of exceedingly cold air, with a body of hot and humid air. The cold wind is supposed to be derived from an elevation considerably above the term of perpet- ual congelation, and to be suddenly transferred to a body of hot and humid air, from which it preciptates the hail. Or it may be suppos- ed to result from a hot wind blowing from the torrid regions into the limits of perpetual frost, and thus having its watery vapor suddenly congealed. Or it may be the product of the meeting of a very cold with a very hot wind. All that the theory requires, in order that hail should be precipitated, is, that very hot and very cold bodies of air should be mixed in any way whatsoever. Accordingly, hail is found to be most frequent and violent in those regions where hot and cold bodies of air are most easily mixed. Such mixtures are rarely formed in the torrid zone, since there the portion of cold air would be wanting; and a similar difficulty exists in the frigid zone, for there the hot air is wanting ; but in the temperate climate, the heated air of the south, and the intensely cold winds of the north, may be much more easily brought together ; and, accordingly, in the temperate zones it is, that hail storms chiefly occur. Even in these climates they are most frequently found in places, where such mixtures are most easily formed, as in the south of France, lying, as it does, be- tween the Pyrenees and the Alps, which are covered with perpetu- al snows, while the intervening country is ^subject to become highly heated by the summer's sun, or is even visited, especially at a certain elevation, by occasional blasts of the hot winds that cross the Medi- terranean. CHAPTER III. OF THE MECHANICAL AGENCIES OF AIR AND STEAM. 324. In consequence of our power of forming a vacuum, either by the exhaustion of air or by the condensation of steam, and of di- recting the force with which these elastic substances rush into a void or press towards it, air and steam become important agents or prime movers, in various kinds of machinery. Many of the most useful machines involve in their construction the principles of both hydrau- lics and pneumatics, and therefore we have reserved an account of such machines to the present section. 166 PNEUMATICS. The Syphon. 325. If a tube having two arms, a longer and a shorter, be filled with water, and the mouth of the shorter arm be immersed in wa- ter, the fluid will run out through dl the longer arm until the whole contents of the vessel are discharged. Such a tube is called a syphon. It may be filled with the fluid, either by suction or by pouring water into it, keeping the two orifices closed until the shorter arm is immer- sed, Or, when the syphon is large, each orifice is plugged, and water is poured in through an opening in the top of the bend. The opening being closed, the shorter leg is placed in the cistern, and the plugs removed, the fluid is discharged as usual. The principle of the syphon is as follows. The atmosphere presses equally on the mouths of both arms of the tube ; but this pressure on each orifice is diminished by the weight of the column of water in the leg nearest to it; consequently, more of the atmospheric pressure is overcome by the longer than by the shorter column, and therefore the effective pressure, (or what remains,) is less at the mouth of the longer than at that of the shorter column, and the fluid runs in that direction in which the resistance is least. All this will be obvious by inspecting the figure. Were the shorter column thirty four feet in height, it would coun- terbalance the entire pressure of the atmosphere on the surface of the fluid, and consequently, there would be no force remaining to drive the water forward through the tube. The syphon, therefore, can never raise water to a greater height than thirty four feet, nor quicksilver high- er than about thirty inches. It is obvious, also, that the place of deliv- ery, that is, the mouth of the longer arm, must be at a lower level than the surface of the water in the reservoir ; so that this instru- ment cannot be used for elevating, but only for decanting fluids, or transferring them from one vessel to another. Its chief use is by grocers, in transferring liquors from one cask to another. It is some- times, employed in carrying water over a hill, or from a well to a level below the surface of the well. MECHANICAL AGENCIES OF AIR. 1C7 Fig. 74. B II The Common Suction Pump. 326. This pump consists of two hollow cylinders, placed one under the other, and communicating by a valve which opens upwards. The lower cylinder (which has its lower orifice under water) is called the suction tube. In the upper cylinder, a piston moves up and down from the bottom to a spout in the side near the top. This cylinder we call the exhausting tube. Suppose, at the commencement of the opera- tion, the piston is at the bottom of the exhausting tube in close contact with the valve. On raising it, the air in the suction tube having nothing to resist its upward pressure, lifts the valve and expands, so as to fill the void space which would otherwise be left in the lower part of the exhausting tube. By this means, the air in the suction tube is rarefied, and no longer being a counterpoise to the pressure of the atmosphere on the surface of the well, the latter predominates and forces the water up the tube until enough has been raised ex- actly to counterbalance the excess of the elasticity of the external air above that of the tube. As the piston descends, the air below it is prevented from returning into the suc- tion pipe by the valve which closes on its mouth, but escapes through a valve in the piston itself opening upwards in the same manner as in the barrels of the air pump. The piston being raised again, the col- umn of water ascends still higher, until it makes its way through the valve into the exhausting pipe. Then as the piston descends, the water opens its valve, and gets above the piston, and is lifted to the level of the spout, where it is discharged. The principle of the suction pump may therefore be thus enuncia- ted : The water is raised into the exhausting pipe by the pressure of the atmosphere^ and thence lifted to the level of the spout by means of the piston. Since a column of water thirty four feet in height, in the suction tube, would counterbalance the entire pressure of the atmosphere on the surface of the well, no force would remain to urge the column 168 PNEUMATICS. any higher, and therefore the valve at the top of the suction tube, must be less than thirty four feet above the well. 327. It is evident that the same force is expended in raising water by means of the pressure of the atmosphere, as when the force is applied directly. We lift upon the atmosphere, instead of lifting di- rectly upon the column of water. This method of raising water from a well, is frequently more convenient than by a simple bucket, but the expenditure of force is the same in both cases. The Forcing Pump. . 328. A cylinder ABC (Fig. 75.) is placed with its lower end C in the reservoir. It has a fixed valve at V, opening upwards, and a solid piston without a valve, playing air tight in the upper barrel AB. It is connected with another barrel DE by a valve V opening upwards and outwards. The tube DE is carried to whatever height it may be necessary to elevate the water. Let us suppose that the solid piston P is in con- tact with the valve V, and that the water in the lower barrel is at the same level C with the wa- ter in the reservoir. Upon raising the piston, the air in BC will be rarefied, and the water will ascend in BC exactly as in the suction-pump. Upon again depressing the piston, the air in PV will be depressed, and it will force open the valve V, and escape through it. The process, there- fore, until water is raised through V into the upper barrel, is precisely the same as for the suction pump, the valve V' taking the place of the piston-valve in that machine. Now, let us suppose that water has been elevated through V, and that the space PV is filled with it. Upon depressing the piston, this water, not be- ing permitted to return through V, is forced through V, and ascends in the tube DE. By continuing the process, water will accumulate in the tube DE, until it acquires the necessary elevation, and is dis- charged. Or, to enunciate the principle of this machine in general terms STEAM ENGINE. 169 Fig. 76. In the forcing pump, the piston has no valve, but the water being elevated into the exhausting tube, as in the suction pump, it is then forced, by the descent of the piston, into the ascending pipe through a valve placed in the side and at the bottom of the exhausting tube. 329. In forcing-pumps, since the power is applied by separate im- pulses, the water would issue in jets, were not some contrivance adopt- ed to equalize its flow from the tube. This purpose is effected by means of an air vessel, in which a portion of condensed air is made the medium of communication. The force imparted by successive blows of the piston is first received by this confined body of air, and this, by its elasticity, reacts on the surface of the water in the air vessel, and forces it out by the conducting pipe or hose. An example of this is afforded in the Fire Engine. The fire engine consists of two forcing pumps, which throw the water into an air vessel, from which it is thrown out of the conducting hose by the elastic pressure of condensed air. Thus, (Fig. 76.) AB, AB are two forcing-pumps, whose pistons P P are wrought by a beam whose fulcrum is at F; VV are valves which open upwards from a suction-tube T, which communicates with a reservoir ; tt are force-pipes, which communicate by valves V' V, opening into an air vessel M. A tube L is inserted in the top of this vessel, terminating in a leathern tube or hose, through which the water is forced by the pressure of the air confined in M, which, in consequence of its elas- ticity, acts nearly uniformly on the surface of the water, and forces it through the hose in a continual stream. The Steam Engine. 330. It belongs to Chemistry to investigate the properties of steam and to Natural Philosophy to apply it as a mechanical agent. The Steam Engine is the fruit of the highest efforts of both these sciences, and the most valuable present ever made by philosophy to the arts. 22 170 PNEUMATICS. As it is impossible clearly to understand the principles and construc- tion of this engine, without a knowledge of the properties of steam, on which they depend, we subjoin an account of a few of its lead- ing properties, referring to chemical authors for a more detailed view of this subject. 331. The great and peculiar property of steam, on which its me- chanical agencies depend, is its power of creating at one moment a high degree of elastic force, and losing it instantaneously the next moment. This force, acting on the bottom of the piston which moves in the main cylinder, raises it, and fills the space below it with steam. The steam is suddenly condensed, and hence no obstacle is opposed to the descent of the piston, but it is readily forced down again by steam acting from above. This alternate motion of the piston, the rod of which is connected with the working beam, is all that is required in order to communicate motion to all parts of the engine. 332. The elastic force of steam depends on its temperature and den- sity conjointly; and the temperature necessary to its production de- pends upon the pressure incumbent upon the water during its forma- tion. The reason why water boils at the temperature of 212 is, that at that temperature, the vapor acquires just elasticity sufficient to over- come the atmospheric pressure. Hence, steam produced at the tem- perature of boiling water, has a force equal to the pressure of the atmosphere. When formed at a lower temperature its elasticity di- minishes in a geometrical ratio, and increases in the same ratio when it is formed at a higher temperature. Water boils, or is converted into vapor, at a temperature less than 212, on high mountains, or under the receiver of an air pump, or in other situations where the pressure of the atmosphere is diminished ; and in a vacuum the boil- ing point of water is as low as 72. 333. Heat rapidly augments the elasticity of steam by increasing its density. If we introduce a few grains of water into a flask, and place it over the fire, the water will soon be converted into steam, which will expel the air of the vessel and fill its whole capacity. If we now close the orifice of the flask and continue the heat, the steam will increase in elastic force in the same manner as air would do un- der similar circumstances, which is at a comparatively moderate rate. STEAM ENGINE. 171 so that it might be heated 'red hot without exerting any very violent force. If, however, the vessel is partly filled with water, and the heat is continued as before, then the elastic force is rapidly augment- ed, and becomes at length so great as to burst almost any vessel that can be provided ; for every new portion of vapor that is raised from the surface of the water, adds to the density of that which was be- fore in the vessel, and proportionally increases its elasticity. In the experiments of Mr. Perkins, a confined portion of steam not in con- tact with water was heated to the temperature of 1400, and still its pressure did not exceed that of five atmospheres ; but, by injecting more water, althoagh the temperature was lessened, the elastic force was gradually increased to one hundred atmospheres. i 334. The space into ivhich a given quantity of water is expanded in becoming steam, depends upon the temperature, and of course upon the degree of pressure, at which it is formed. Water conver- ted into steam at the temperature of 212, expands nearly one thou- sand and seven hundred times; but at the temperature of 419, it expands but thirty seven times. According to Dr. Thomson, at a temperature not much higher than 500, steam would not much ex- ceed double the bulk of the water from which it is generated. The expansive force of such steam would be truly formidable. It would, when it issued into the atmosphere, suddenly expand six hundred and fifty times. We do not know at what temperature water would be- come vapor without any increase of volume, but we can estimate that it would then support a column of mercury three thousand two hun- dred and forty three feet (or more than half a mile) high, and would exert a pressure of nearly twenty thousand pounds on every square inch. 335. The difficulty of understanding the construction and princi- ples of the steam engine, (as is the case also with many other ma- chines where the parts are numerous,) is greatly enhanced, by the variety of accidental trappings or appendages that are employed about the machine, to perform subordinate offices. As these render the comprehension of the leading principles difficult, when the explana- tion is attempted from the engine itself, so these inferior parts are often so multiplied in diagrams as greatly to obscure the representa- PNEUMATICS. lion. We shall begin our explanation with a diagram which pre- sents the naked principles divested of all unnecessary appendages. The chief parts of the engine are the boiler A, the cylinder C, the condenser L, and the air-pump M. B is the steam-pipe, branching into two arms communicating respectively with the top and bottom of the cylinder ; and K is the eduction-pipe, formed of the two branches which proceed from the top and bottom of the cylinder, and commu- nicate between the cylinder and the condenser. N is a cistern or well of cold water in which the condenser is immersed. Each branch of pipe has its own valve, as F, G, P, Q, which may be open- ed or closed as the occasion requires. 336. Suppose, first, that all the valves are open, while steam is issu- ing freely from the boiler. It is easy to see that the steam would cir- culate freely through all parts of the machine, expelling the air, which would escape through the valve in the piston of the air-pump, and thus the interior spaces would be all filled with steam. This process is called blowing through : it is heard when a steam-boat is about set- ting off. Next the valves F and Q are closed, G and P remaining open. The steam now pressing on the cylinder forces it down, and the instant when it begins to descend, the stop cock O is opened, ad- mitting cold waier which meets the steam as it rushes from the cyl- inder and effectually condenses it, leaving no force below the piston * From Jones's Conversations on Chemistry, a work which contains a very luminous view of the elementary principles of the steam engine. STEAM ENGINE. 173 to oppose its descent. Lastly G and P being closed, F and Q are opened, the steam flows in below the piston and rushes from above it into the cpndenser, by which means the piston is forced up again with the same power as that with which it descended. Meanwhile the air-pump is playing, and removing the water and air from the condenser, and pouring the water into a reservoir, whence it is con- veyed to the boiler to renew the same circuit. 337. Among the different forces which may be employed to move machinery, such as animal strength, water, wind, and steam, the last is the most manageable of all, and therefore, for almost every pur- pose, the most convenient of all powers that are under the control of man. But whether, in a given case, we shall employ steam power, or one of the other forces, as water power for example, may depend on the comparative economy of the two forces. A water fall, near at hand, may furnish us with the required power, cheaper than we can produce it artificially from steam. In the earlier forms of con- struction adopted in the Steam Engine, so much of the steam was wasted by injudicious management, as greatly to diminish the useful- ness of this Engine, and to render it in most cases a less eligible force for carrying machinery than animal strength or water. The modern improvements in the Steam Engine have consisted, mainly, in preventing this waste of steam, and of course in economizing the amount of fuel required to produce the power. Previous to the year 1763, when Watt began his improvements on the steam engine, not less than three fourths of the steam produced in the boiler was wasted. 338. The greatest improvement introduced by Mr. Watt, consist- ed in performing the condensation in a separate vessel, (L, Fig. 77.) whereas the previous method was to admit a jet of cold water into the cylinder (CC) itself, which cooled the whole apparatus; and when steam was admitted again from the boiler, a great quantity of it was consumed in heating the cooled surface up to the boiling point, which must be done before the steam could have sufficient elasticity to move the machinery. Various subordinate contrivances were also employed, with the view of promoting convenience or economy, the principal of which will be understood from the description of the 174 PNEUMATICS. annexed plate, which represents the steam engine in its most im- proved state. 339. A. The BOILER, containing a large quantity of water which is constantly renewed as fast as portions are converted into steam* B. The STEAM PIPE, conveying the steam to the cylinder, having a steam-cock b to admit or exclude the steam at pleasure. C. The CYLINDER, surrounded by the jacket c c, a space kept constantly supplied with hot steam, in order to keep the cylinder from being cooled by the external air. D. The EDUCTION PIPE, communicating between the cyl- inder and the condenser. E. The CONDENSER, with a valve e, called the Injection cock, admitting a jet of cold water, which meets the steam the instant the latter enters the condenser. F. The AIR PUMP, which is a common suction pump, but is called the air pump because it removes from the condenser not only the water, but also the air and steam that escapes condensation. G. G. The COLD WATER CISTERN, which surrounds the con- denser and supplies it with cold water, being filled by H. The COLD WATER PUMP. I. The HOT WELL, containing water from the condenser. K. The HOT WATER PUMP, which conveys back the water of condensation from the hot well to the boiler. L. L. LEVERS, which open and shut the valves in the channel between the steam pipe, cylinder, eduction pipe, and condenser ; which levers are raised or depressed by projections attached to the piston rod of the con- denser. M. M. Apparatus for PARALLEL MOTION. By this contrivance the pis-ton rod is made to move in a right line, although the end of the working beam moves in the arc of a circle. N. N. The WORKING BEAM. STEAM ENGINE. 175 O. O. The GOVERNOR. This consists of two heavy balls, suspended from a perpendicular shaft in. such a man- ner as to be capable of falling close to the side of the shaft when at rest, but when made to revolve, they recede from it by the centrifugal force. Now, by connecting the governor with the fly wheel, it is made to participate of the common motion of the engine, and the balls will remain at a constant distance from the perpendicular shaft, so long as the motion of the engine is uniform ; but whenever the engine moves faster than usual, the balls will recede farther from the shaft, and by raising a valve connected with the boiler, will let off such a portion of the force as to reduce the speed to the rate required. P. The CRANK. This, when the end of the working beam, to which it is attached, descends, turns the fly wheel half round, and when it rises, completes the revolu- tion of the wheel. Q. Q. The FLY WHEEL. The motion of the piston, being communicated first to the Working Beam, and thence to the crank, is finally received by the Fly Wheel, which, by its inertia, as explained in Art. 193. ren- ders the force uniform. The main shaft or axis to which the fly wheel is attached, receiving 'thus a uni- form rotation, motion may be transferred from it to every part of the machinery. 340. The kind of valve chiefly employed in the steam engine is that called the puppet valve* It resembles the stopper of a decan- ter, but is more obtuse. All these various appendages of the ma- chine, are carried by the engine itself; the air pump is worked by having its piston rod attached to one arm of the working beam, and the valves are opened at the instant required by means of levers, to which also motion is communicated from the same source. * Several examples are seen in the plate, on the right of the cylin- der, above arid below. 176 PNEUMATICS. 341. Soon after the invention of these engines, Watt found that, in some instances, inconvenience arose from the too rapid motion of the steam piston at the end of its stroke, owing to its being meved with an accelerated motion.* This was owing to the uniform action of the steam pressure upon it. For on first putting it in motion, at the top of the cylinder, the motion was comparatively slow 1 , but from the con- tinuance of the same pressure, the velocity with which the piston de- scended was continually increasing, until it reached the bottom of the cylinder, when it acquired its greatest velocity. To prevent this, and to render the descent as nearly uniform as possible, it was pro- posed to cut off the steam before the descent was completed, so that the remainder might be effected merely by the expansion of the steam which was admitted to the cylinder, f To accomplish this he contrived, by means of a pin on the rod of the air-pump, to close the upper steam-valve when the steam-piston had completed one third of its entire descent, and to keep it closed during the remainder of that descent, and until the piston again reached the top of the cylin- der. By this arrangement, the steam pressed the piston with its full force through one third of the descent, and thus put it in motion ; during the other two thirds of the way, the steam thus admitted acted merely by its expansive force, which became less in exactly the same proportion as the space, given to it by the descent of the piston, in- creased. Thus, during the last two thirds of the descent, the piston is urged by a gradually decreasing force, which in practice is found just sufficient to keep up in the piston a uniform velocity. Another advantage gained by this contrivance independently of the uniformity of motion was, that two thirds of the fuel was saved ; for instead of consuming a cylinder full of steam each descent of the piston, only one third of a cylinder was necessary. 342. As an example of a self-regulating machine, the Steam En- gine surpasses all other forms of machinery. On this subject Dr. * For since the steam continues to act upon the piston during its descentv-its velocity would be constantly increased, like that of a ball in the barrel of a gun. t Steam engines constructed on this principle are said to act ex- pansively. VV '.\TT\S ACOUSTICS. 177 Arnott has the following remarks. " The Steam Engine, (says he,) in its present improved state, appears to be a thing almost endowed with intelligence. It regulates, with perfect accuracy and uniformity* the number of its strokes in a given time, and, moreover, counts or records them, to tell how much work it has done, as a clock records the beats of its pendulum. It regulates the supply of water to the boiler, the briskness of the fire, and the quantity of steam admitted to work ; opens and shuts its valves with absolute precision ; oils its joints 5 takes out any air which may accidentally enter into parts where a perfect vacuum is required ; and when any thing goes wrong which it cannot of itself rectify, it warns its attendants- by ringing a bell. Yet with all these talents and qualities, and even when pos- sessing the power of 600 horses, it is obedient to the hand of a child. Its aliment is coal, wood, charcoal, or other combustible ; but it con- sumes none while idle. It never tires, and wants no sleep ; it is not subject to any malady when originally well made, and only refuses to work when worn out with age. It is equally active in all climates, and will do work of any kind. It is a water pumper, a miner, a sailor, a cotton spinner, a weaver, a blacksmith, a miller > and a small engine in the character of a steam poney, may be seen dragging after it on a rail road a hundred tons of merchandize, or a regiment of soldiers, with greater speed than that of our fleetest coaches. It is the king of machines, and a permanent relization of the Genii of eastern fable, whose supernatural powers were occasionally at the command of man." CHAPTER V. OF ACOUSTICS, 343. ACOUSTICS w the science which treats of the nature and laws of SOUND. In comparing substances which have different properties in respect to sound^ as lead and glass, we shall find them distinguished from each other by the degree of vibration which they are capable of re- ceiving, and by the length of time during which they can preserve a vibratory motion ; those substances which are most capable of vi- 23 1*78 PNEUMATICS. bration being most sonorous, and those which can longest maintain a stale of vibration, also persevering longest in emitting sound. Bodies, though of the same substance, differ in these respects according as their form varies ; those forms which are most favorable to the pro- duction and continuance of a vibratory motion, being also most favor- able to the production and permanence of sound. Thus, a hollow globe of brass is far less sonorous than the hemispheres which are made by dividing it into two equal parts, since the structure of a globe is such that the parts mutually support each other, like a con- tinued arch, while the form of the hemispheres, which approaches that of a bell, is peculiarly liable to a tremulous vibratory motion. Indeed, when a body sounds powerfully, as a large bell, or the lowest string of a harpsichord, we can -perceive that it actually vibrates ; and even in cases where the vibration is imperceptible to the naked eye, we may detect it by the microscope, or by some other artifice. Thus, if we put some water into a glass tumbler or basin and make it sound, by applying the moistened finger, the water will be agitated. If we hold the hand over the pipe of an organ, we shall feel a trem- ulous motion in the air passing through it. Such experiments may be extended to all solid bodies by placing upon them pieces of paper or strewing them with fine sand. Hence, Vibrations, in the sounding body, are the immediate cause of sound. 344. The pitch of musical strings, is found by experience to de- pend on three circumstances 5 the length of the string, its weight, or quantity of matter, and its tension. The tone becomes more acute as we increase the tension, or diminish either the length or the weight. The operation of these several circumstances may be seen in a common violin. The pitch of any one of the strings is raised or lowered by turning the screw so as to increase or lessen its tension ; or, the tension remaining the same, higher or lower notes are pro- duced by the same string, by applying the fingers in such a manner as to shorten or lengthen the string which is vibrating ; or, both the tension and the Jength of the strhig remaining the same, the pitch is altered by making the string larger or smaller and thus increasing w diminishing its weight. 345. The vibrations of a string, fixed at both ends, are performed in equal times, whether the length of the vibrations be greater, or smaller. ACOUSTICS. 179 Upon this uniformity in the times of vibration depends the uni- formity of tone ; for if we employ a string of unequal thickness, and consequently one whose vibrations are performed in different times, the sound is confused and variable, and any other mode by which we destroy the isochronism, produces a similar effect. The same law has been found to extend to all other cases of musical sounds ; and, therefore, we may conclude, that isochronism in the vibrations of sonorous bodies, is essential to their producing musical sounds. 346. In wind instruments, a column of confined air itself is the vibrating body ; and here the vibrations are longitudinal instead oi lateral, as is the case with strings. That it is really the air whicli is the sounding body in a flute, organ pipe, or other wind instru- ment, appears from the fact, that the materials, thickness, or other peculiarities of the pipe, are of no consequence. A pipe of paper and one of lead, glass, or wood, provided the dimensions are the same, produce, under similar circumstances, exactly the same tone as to pitch. If the qualities of the tones produced by different pipes differ, this is to be attributed to the friction of the air within them, setting, in feeble vibration, their own proper materials. The class of bodies vibrating longitudinally, is not only more diversified in its powers than the other classes of sounding bodies, but also more ex- tensive in the range of substances which it comprehends. 347. The different pitch of bodies vibrating longitudinally, and free at both extremities, depends on four circumstances, viz. their elasticity, the temporary rate at which their elasticity is increased by condensation, their length, and their specific gravity, the tone of a body being more acute, according as the elasticity, and the rate of its increase by condensation, are greater, or the length and specific gravity less. The length of the sonorous body is almost exclusively the only one of these circumstances which we have completely in our power ; and with regard to ordinary wind instruments, and all musical instruments where common air is the vibrating body, the length is the circumstance of most importance, since the elasticity, rate of condensation, and specific gravity are then nearly constant quantities. The change of specific gravity, however, to which the 180 PNEUMATICS. air is subject in consequence of changes of temperature, materially affects the pitch of wind instruments. The frequency of vibration of a column of air is found to be increased about g\, by an elevation of 30 Fahrenheit. Thus, the tone of an organ has been found to be higher in summer than in winter ; and flutes and other wind in- struments become gradually more acute as the included air is heated by the breath. 348. If a bett be struck by a clapper on the inside, the bell is made to vibrate. The base of the bell is a circle ; but it has been found that, by striking any part of the circle on the inside, that part flies out, so that the diameter which passes through this part of the base, will be longer than the other diameters. The base is chang- ed by the blow into the figure of an ellipse, whose longer axis pass- es through the part against which the clapper is thrown. The elas- ticity of the bell restores the figure of the base, and again elongates the bell in a direction opposite to the former ; and the two elliptical figures thus alternate with each other, growing smalller and smaller, like the vibrations of a pendulum when ihe moving force is with- drawn, until the sound dies away. We may be convinced by our senses, that the parts of the bell are in a vibratory motion while it sounds. If we lay the hand gently upon it, we shall feel this tremu- lous motion, and even be able to stop it ; or if small pieces of paper be put upon the bell, its vibrations will set them in motion. We may conceive the bell to be formed of an infinitude of rings, placed one above another from the base to the highest point. The rings situated nearer to the base, having a greater circumference, tend to perform their vibrations more slowly, while the rings nearer to the summit, whose circumferences are smaller, tend to produce vibrations oftener. These sounds will so coalesce as to produce a mixed sound, intermediate between those of the higher and lower rings, Propagation of Sound. 349. AIR is, in general, the medium of sound. A bell struck under the receiver of an air pump, gives a feebler and feebler sound as the exhaustion proceeds, until, when the rarefaction is carried to 9 certain extent, it emits no sound at all. Hence, on the summit of ACOUSTICS. 181 high mountains, where the air is naturally rare, sound ought to be weaker than at the general level of the earth ; and such is found to be the fact. Saussure relates that upon the top of Mount Blanc, the firing of a pistol made a report no louder than that of a child's toy- gun. A fact mentioned by travellers in Alpine countries, is explained on this principle. They see distinctly a huntsman on a neighboring eminence, and observe the flashes of his gun, but can scarcely hear the report, even when comparatively near them. 350. The agency of air as the medium of sounds may be briefly expressed thus : Air receives from sounding bodies vibrations, which it communi- cates to the organs of hearing. In an open space, and in a serene atmosphere, sound is propoga- ted from the sounding body in all directions. Sounds, even the most powerful, when thus transmitted freely through the air, diminish ra- pidly in force, as they depart from their sources, and within moderate distances wholly die away. What law this dimunition follows, is not yet ascertained ; and is, indeed, in the present state of Acoustics, incapable of determination. Some writers have supposed that sound follows the common law of emanations radiating from a center, and, consequently, that its intensity at different distances from its source varies inversely as the square of the distance ; but we can estimate the force of sounds by the ear alone ; an instrument of comparison whose decisions on this point vary with the bodily state of the observ- er, and whose scale expresses no definite relation but that of equal- ity. Though sound has in general, at its origin, a tendency to dif- fuse itself in all directions, it is sometimes more propogated in one direction than in others. A cannon seems much louder to those who stand immediately before it, than to those who are placed behind it. The same fact is illustrated by the speaking trumpet ; the person to- wards whom the instrument is directed, hears distinctly the words spoken through it, while those who are situated a little to one side, hardly perceive any sound. 351. Sound is in a great measure intercepted by the intervention of any solid obstacle between the hearer and the sonorous body, 182 PNEUMATICS. Thus, if while a bell is sounding, houses intervene between us and the bell, we hear it sound but faintly compared with what we hear after we have turned the corner of the building. From this fact sound would seem to be propagated in straight lines. If, however, we peak through a tube, the voice will be wholly confined by the tube, and will follow its windings however tortuous ; hence we infer that sound is propagated not in right lines like radiant substances as heat and light, but in undulations, after the manner of waves, such as follow when a stone is thrown into still water. 352. Though air is the most common medium of sound, yet it is not the only medium. Various other bodies both solid and fluid, are excellent conductors of sound ; and the fainter sound of the bell when buildings intervene, as in the case supposed, arises from the fact that sound passes with difficulty from one medium into another. If a log of wood is scratched with a pin at one extremity, a person who applies his ear to the other extremity will hear the sound dis- tinctly, and when a long pole of wood is applied at one end to the teeth, the ticking of a watch may be heard at the other end, at a much greater distance, than when there is no medium of communica- tion but the air. The motion of a troop of cavalry is heard at a great distance by applying the ear close to the ground, and it is well known that dogs by this method first discover the approach of a stranger. v 353. The VELOCITY of sound is progressive. Thus when a gun is fired at a distance from us, we perceive the flash some time before we hear the report. Thunder follows the lightning at a perceptible interval, although they are known to be cotemporaneous events. If a gun be fired at a certain known distance, and we observe the in- terval between the flash and the report, we may obtain the rate at which sound passes, that is the velocity of sound. Many years since Dr. Derham made a number of accurate and diversified experi- ments on this subject, and fixed the velocity of sound at 1142 feet per seepnd. The mean of a great number of experiments give the average velocity of 1 130 feet per second ; but the velocity as deter- mined by Derham, namely, 1142 feet per second, is that which has been generally admitted as the standard. Since, however, the trans- ACOUSTICS, 183 mission of sound depends on the elasticity of the medium, (Art. 347.) causes which affect the elasticity, likewise affect the velocity of sound, Thus, the velocity is a little greater in warm than in cold air, and consequently is somewhat influenced by climate. 354. Sound moves with a uniform velocity ; that is, it passes over equal spaces in equal times. This important fact was first ascertain- ed by Derham, who found that it held good whether the sound were strong or feeble, whether it proceeded from a hammer or a cannon : iu short, that neither the strength nor the origin of the sound made any difference. M. Biot caused several airs to be played on a 'flute at the end of an iron pipe 3120 feet long, and the notes were dis- tinctly heard by him at the other end, without the slightest derange- ment in the order or quality of the sounds. The velocity of sound, however, when transmitted through the air, is slightly influenced by the strength and direction of 'the wind. Dr. Derham found that when the wind is blowing in the direction of the sound, its velocity must be added to the standard velocity of sound, and must be sub- tracted from it when opposed to it. A transverse wind does not affect the velocity of sound in the slightest degree. 355. From a knowledge of the velocity of sound, the distance of a sounding body may be estimated. Thus if the interval between seeing a flash of lightning, and hearing the thunder be six seconds the distance of the cloud is 6 X 1 142 = 6852 feet, or IfV miles. The air is a better conductor of sound when humid than when dry. Thus a bell is heard better just before a rain ; and this fact lends some countenance to an opinion of the ancients, that sound is heard better by night than by day. Humboldt was particularly struck with this fact, when he heard the noise of the great cataracts of Orinoco, which he describes as three times greater in the night than in the day. The distance to which sound may be heard, will of course vary with its force and various other circumstances which are incapable of being reduced to an exact law. Volcanoes, in South America, have some- times been heard at the distance of three hundred miles ; and naval engagements have been heard at the distance of two hundred miles. The unassisted human voice has been heard from Old to New Gib- raltar, a distance of ten or twelve miles, the watchword All's Well given at the former place being heard at the latter. Sounds are 184 PNEUMATICS. heard to a much greater distance over water than over land, and far- ther on smooth than on rough surfaces. 356. Liquors are good conductors of sound. Indeed, sound is conveyed with far greater velocity in water than in air, and this too in consequence of its greater elasticity; for, since water has been found by Perkins and others, capable of compression and of restoring itself when the compressing force is removed, it is to be accounted not only elastic, but as exceeding triform bodies in elasticity in proportion as the force required to compress it is greater. Dr. Franklin, hav- ing plunged his head below water, caused a person to strike two stones together beneath the surface, and heard the sound distinctly at the distance of more than half a mile. By similar experiments, it has been ascertained, that, though water is a much better conductor of sound than air, yet the sound is greatly enfeebled by passing out of one medium into the other. 357. Solid substances convey sound with various degrees of facili- ty, but in general much better than air, and as well or even better than fluids. By placing the ear against a long dry brick wall, and caus- ing a person at a considerable distance to strike it once with a ham- mer, the sound will be heard twice, because the wall will convey it with greater rapidity than the air, though each will bring it to the ear. The rate at which cast iron conducts sound, was ascertained by M. Biot in the following manner. He availed himself of the laying of a series of iron pipes to convey water to Paris. The pipes were about eight feet in length, and were connected together with small leaden rings. A bell being suspended within the cavity, at one end of the train of pipes, on striking the clapper at the same instant against the side of the bell, and against the inside of the pipe, two distinct sounds successively were heard by an observer stationed at the other extremity. With a train of iron pipes two thousand five hundred and fifty feet, or nearly half a mile in length, the interval be- tween the two sounds was found from a mean of two hundred trials, to be 1.79 seconds. But the transmission of sound through the in- ternar'eolumn of air, 'would have taken 2.2 seconds ; which shows that the sound occupied only .41 of a second in passing through the metal. From more direct trials, it was concluded that the exact in- terval of time, during which the sound performed its passage through ACOUSTICS. 185 the substance of the train of pipes, amounted to only the .26 of a second, showing that iron conducts sound about ten times as rapidly as air does. If a string be tied to a common fire shovel, and the two ends of the string be wound around the fore fingers of each hand, and the fingers be placed in the ears, on striking the bottom of the shovel against an andiron or other solid body, very deep and heavy tones will be heard, and the vibrations of the metal will be clearly perceived. The great power of solid bodies to conduct sound is exemplified in earthquakes, which are heard almost simultaneously in very dis- tant parts of the earth. Musical boxes sound much louder when placed on a table or some solid support, than when the air affords the only conducting medium. It is easy to ascertain whether a kettle boils, by putting one end of a stick or poker on the lid, and the other end to ' the ear : the bubbling of the water, when it boils, appears louder than the rattling of a carriage in the streets. A slight blow given to the poker, of which the end is held to the ear, produces a sound which is even painfully loud. 358. A physician of Paris introduced into medical practice an in- strument, depending on the power of solid bodies to conduct sound, called the Stethoscope, the object of which is to render audible the action of the heart and the neighboring organs. It consists of a wooden cylinder, one end of which is applied firmly to the breast, while the other end is brought to the ear. By this means, the pro- cesses that are going on in the organs of respiration, and in the large blood vessels about the heart, may be distinctly heard ; and it is said that the stethoscope, when skillfully used, " becomes the means of ascertaining some diseases in the chest, almost as effectually as if there were convenient windows for visual inspection." Reflexion of Sound. 3&9. Sounds are reflected by hard bodies, producing the well known phenomenon called an ECHO. If a straight line be drawn from the sounding body to the reflecting surface representing the course of the sound before reflexion, and another straight line be drawn from the reflecting surface, in the direction of the sound after reflexion, these two lines will make equal angles with that surface ; 24 186 PNEUMATICS. that is, when sound is reflected, the angle of reflexion is equal to the angle of incidence. The surfaces of various bodies, solids as well as fluids, have been found capable of reflecting sounds, viz. the sides of hills, houses, rocks, banks of earth, the large trunks of trees, the surface of water, especially at the bottom of a well and sometimes even the clouds. It is therefore evident that in an extensive plain, or at sea, where there is no elevated body capable of reflecting sounds, no echo can be heard. It is hence easy to see why the poets, who convert Echo into an animated being, place her habitation near mountains, rocks, and woods. An echo is heard when a person stands in a position to hear both the original and the reflected sound ; and the interval will be greater or less according to the distance of the reflecting surface from the sounding body and from the hearer, and hence the interval may be made a measure of the distance. If the sound of the voice returns to the speaker in two seconds, the distance of the reflecting surface is one thousand one hundred and forty two feet, and in that proportion for other intervals. Thus the breadth of a river may be ascertained when there is an echoing rock on the farther shore. A perpendicular mountain's side, or lofty cliffs, such as fre- quently skirt the sea coast, sometimes returning an echo of the dis- charge of artillery, or of a clap of thunder, to the distance of many miles. The number of syllables that can be pronounced in half the interval, will be repeated distinctly ; but a greater number would be blended with the commencement of the echo. 3GO. The furniture of a room, especially the softer kind, such as curtains or carpets, impair the qualities of sound by presenting surfaces unfavorable to vibrations. A crowded audience has a simi- lar effect, and increases the difficulty of speaking. Halls for music or declamation, should be constructed with plain bare walls. Alcoves, recesses, and vaulted ceilings, produce reverberations which often greatly impair the distinctness of elocution. Indeed, the qualities of a room, in regard to sound, are modified by so many circumstances, that the science of acoustics is worthy of more attention from the architect than it has generally received. Plane and smooth surfaces reflect sound without dispersing it, convex surfaces disperse it, and concave surfaces Collect it. The concentration of sound by concave surfaces, produces many curious effects both in nature and art. REFLEXION OF SOUND. 187 There are remarkable situations where the sound from a cascade is concentrated by the surface of a neighboring cave, so completely, that a person accidentally bringing his ear into the focus, is astound- ed by a deafening noise. Sound issuing from the center of a circle, is, by reflexion, returned to the center again, producing a very pow- erful echo. Such effects are observed in the central parts of a cir- cular hall. An elliptical apartment conveys sound very perfectly from one focus to the other. A whisper uttered by a person in one focus of such a chamber, will be audible to a person in the other focus, though not heard by persons between. 361. The rolling of thunder has been attributed to echoes among the clouds ; and that such is the case has been ascertained by direct observation on the sound of cannon. Under a perfectly clear sky, the explosion of guns is heard single and sharp, while, when the sky is overcast, or when a large cloud comes over head, thp reports are accompanied by a continued roll, like thunder, and occasionally a double report arises from a single shot. The continued sound of distant thunder, which is sometimes prolonged for many seconds, is not always owing to reverberation, but frequently arises simply from the different distances of the same flash. Although the progress of a flash of lightning through the air were absolutely instantaneous, still, if its path were in a line that would carry it farther from the ear in one place than in another, there would be a corresponding difference in the times at which the sound generated in different por- tions of the path would reach the ear. Herschel observes, that if (as is almost always the case) the flash be zigzag, and composed of broken rectilinear and curvilinear portions, some concave, some con- vex to the ear ; and especially, if the principal trunk separates into many branches, each breaking its own way through the air, and each becoming a separate source ef thunder, all the varieties of that awful sound are easily accounted for. 362. The Speaking Trumpet has been supposed by most writers on sound, to owe its peculiar properties, to its multiplying sound by nu- merous reflexions. Hence is suggested the form of a parabolic conoid, or a tube, the section of which is a parabola, the place of the mouth being at the focus of the parabola. The vibrations emanating from the 188 ACOUSTICS. mouth would then be reflected into straight lines parallel with the axis of the trumpet, and would thus go forward in a collected body to a distant point. And, since such a form is also favorable for col- lecting distinct sounds into one point, the same figure is proposed as most suitable for the Ear Trumpet. But the sound of these in- struments may be regarded as merely the longitudinal vibration of a body of air, to which momentum is given in the direction of the axis, not by reflexion from the sides, but by the direct impulse of the mouth. The ancients were acquainted with the speaking trum- pet. Alexander the Great is said to have had a horn, by means of which he could give orders to his whole army at once. 363. When separate sounds are repeated with a certain degree of frequency, the ear loses the power of distinguishing the intervals, and they appear united in one continued sound. By this means also sounds harsji and dissonant in themselves, form a soft and agreeable tone. Any sound whatever, repeated not less than thirty or forty times in a second, excites in the hearer the sensation of a musical note. Nothing is more unlike a musical sound than that of a quill drawn slowly across the teeth of a coarse comb ; but when the quill is applied to the teeth of a wheel whirling at such a rate that 720 teeth pass under the quill in a second, a very soft, clear note is heard. In like manner the vibrations of a long harp-string, while it is very slack, are separately visible, and the pulses produced by it in the air are separately audible ; but as it is gradually tightened, its vibrations quicken, and the eye soon sees, when it is moving, only a broad shadowy plane; the distinct sounds which the ear lately per- ceived, run together, owing to the shortness of the intervals, and are heard as one uniform continued tone, which constitutes the note or sound proper to the string. Nature presents us with numerous examples of a musical sound produced by the rapid succession of an individual sound, not at all musical in itself. The hum of winged insects, produced by the fre- quent motion of their wings, the murmur of a forest occasioned by (he agination of the .leaves and boughs, and the sublime roar of the ocean constituted of the separate sounds produced by innumerable waves, are familiar examples of the operation of this principle, PHILOSOPHICAL PRINCIPLES OF MUSIC. 189 364. Musical intervals, or sounds differing from each other in pitch by a certain interval, are found by^experience to be peculiarly agreeable to the human ear, a fact for which we can assign no reason except that such is the constitution of the mind. Birds may some- times exhibit a fine voice ; but their singing is not musical, having nothing to do with musical intervals. Musical sounds have certain ratios to one another, and are thus brought into the province of Mathematics, because the number of vibrations which produce one musical note, has a constant ratio to the number which produces another musical note. Thus, if we di- minish the length of a musical string one half, we double the num- ber of its vibrations in a given time, and it gives a sound eight notes higher in the scale than that given by the whole string. Therefore, these sounds are represented by the numbers 2 and 1, and are said to be in the ratio of 2 to 1. The upper note is said to be the octave of the lower ; and from its great resemblance to the fundamental note, or that afforded by the whole string, it is considered as'the commencement of a repetition of the same series ; so that all audi- ble sounds are considered as repetitions of a series contained within the interval of an octave. 365. A succession of single musical sounds, constitutes melody ; the combination of such sounds, at proper intervals, forms chords ; and a succession of chords constitutes harmony. Two notes pro- duced by an equal number of vibrations in a given time, and of course giving the same sound, are said to be in unison. The relation be- tween a note and its octave is, next after that of the unison, the most perfect in nature ; and when the two notes are sounded at the same time, they almost entirely unite. Chords are characterized by fre- quent coincidences of vibration, while in the discords such coinci- dences are more rare. Thus injunison, the vibrations are perfectly isochronous ; in the octave the two coincide at the end of every vi- bration of the longer string, the shorter meanwhile performing just two vibrations ; and in the fifth, they coincide at the end of every two vibrations of the longer string, the shorter vibrating three limes in the same period. But in the second, the longer and shorter vi- brations can coincide only after eight of the longer and nine of the shorter, and in the seventh, only after eight of the longer and fifteen 190 ACOUSTICS. of the shorter. Hence the concord is more perfect as the common period is shorter. Musical intervals therefore are divided into chords and discords. The octave, the major fifth, the major and minor thirds, the major and minor sixths, are concords, and are pleasing in themselves. The seconds, the sevenths, the minor fifth and major fourths, are discords. The chord consisting of the fundamental note with its third and fifth, and called the harmonic triad, forms the most perfect. harmony, and contains the constituent parts of the most simple and natural melo- dies. 366. Discords, however, are employed in musical compositions; but their use is limited by special rules. Of the occasion and man- ner of introducing them, the following extract from Burney's History of Music, will give the learner a general idea. " While harmony was refining and receiving new combinations, it was found, like other sweet and luscious things to want qualification to keep off languor and satiety, when some bold musician had the courage and address to render it piquant and interesting, by means of discords, in order to stimulate attention ; and thus by giving the ear a momentary un- easiness, and keeping it in suspense, its delight became the more ex- quisite, when the discordant difficulty was solved. Discord in mu- sical composition, however, does not consist in the excess or defect of intervals, which, when false, produce jargon, not music; but in the warrantable and artful use of such combinations as, though too disa- greeable for the ear to dwell upon, or to firnish a musical period, yet so necessary are they to modern counterpoint, and modern ears, that harmony without their relief, would satiate, and lose many of its beautiful effects." 367. The theory of Musical Instruments will be readily under- stood from the principles already explained. It will be seen thai they all owe their power of producing musical sounds to their sus- ceptibility of vibrations ; that the force or loudness of the sounds they afford depends on the length of the vibrations, and the gravcness or acuteness of the sound, in other words the pitch, on their slow- ness or frequency ; an/1 that their chords depend, in general, upon frequency of coincidence in the vibrations that afford the several PHILOSOPHICAL PRINCIPLES OF MUSIC. sounds of the concord. The nature of stringed instruments may be learned from the violin. Here the strings are of the same length, but differ in weight and tension ; those designed to afford the lower notes being heavier and less strained, and those for the higher notes being lighter and more tense. The lengths, moreover, are altered by applying the fingers. The several strings are usually so adjusted to each other, that is, so tuned, that any two contiguous strings make a t fifth. Hence the fourth or highest stop on one string brings it into unison with the string above ; and the third stop on any string forms an octave with the open string next below. On account of this power of altering the effective lengths of the strings at pleasure, of devel- oping the harmonic sounds by a skilful application of the fingers, and of varying constantly the degrees of fullness or force in each sound by a dexterous use of the bow, the violin becomes, in the hands of an accomplished performer, an instrument of great power and com- pass, while it is capable of greater variety than any other musical instrument. The flute affords 'an example of wind instruments. Here the vibrating body is a column of air to which different lengths are given by means of the stops which are opened and closed by the fingers. The rapidity of the vibrations, and consequently the pitch,, is also changed a whole octave by the management of the breath* 3C8; In mixed wind instruments, the vibrations or alternations of solid bodies are made to cooperate with the vibrations of a given por- tion of air. Thus, in the trumpet, and in horns of various kinds, the force of inflation, and perhaps the degree of tension of the lips, de- termines the nnmber of parts into which the tube is divided, and the harmonic which is produced. The hautboy and clarionette have mouth-pieces of different forms, made of reeds or canes ; and the reed-pipes of an organ, of various constructions, are furnished with an elastic plate of metal, which vibrates in unison with the column of air which they contain. An organ generally consists of a number of different series of pipes, so arranged, that, by means of registers, the air proceeding from the bellows may be admitted to supply each series, or excluded from it at pleasure ; and a valve is opened when the proper key is touched, which causes all the pipes belonging to the note, in those series of which the registers are open, to sound at once. 192 PART IV. ELECTRICITY. CHAPTER 1, OF THE GENERAL PRINCIPLES OF THE SCIENCE. 369. The term ELECTRICITY is used to denote both the unknown cause of electrical phenomena, and the science which treats of elec- trical phenomena and their causes. The most general effect by which the presence of electricity is manifested is attraction. Thus, when a glass tube is rubbed with a dry silk or woollen cloth, it acquires the property of attracting light bodies, as cotton, feathers, &ic. When, by any process, a body is made to give signs of electricity, it is said to be excited. When a body receives the electric fluid from an excited body, it is said to be electrified. Since there is found to be a greater difference in bodies in regard to the power of transmitting electricity, all bodies are divi- ded into two classes CONDUCTORS and NON-CONDUCTORS. Conduc- tors are bodies through which the electric fluid passes readily ; non- conductors are bodies through which the electric fluid either does not pass at all, or but very slowly. The latter bodies are also de- nominated electrics, because it is by the friction of bodies, of this class that electricity is usually excited. An electrified body is said to be insulated^ when its connexion with other bodies is formed by means of non-conductors, so that its electricity is prevented from escaping. Instruments employed to detect the presence of electri- city are denominated electroscopes; such as are employed to estimate its comparative quantity, are called electrometers. This distinction, however, is neglected by some writers, and, to avoid the unneces- sary multiplication of terms, it will be neglected in the present trea- tise, instruments of either kind being called electrometers. 370. The Pendulum Electrometer is formed by suspending some light conducting substance by some non-conducting substance. Thus, a small ball of the pith of elder hung by a silk thread, constitutes a GENERAL PRINCIPLES. Fig. 78, very convenient instrument for detecting the presence and examining the kind of electricity. Figure 78, represents a pen- dulum electrometer, consisting of a glass rod fixed in a stand, and bent at the top so as to form a hook. From this hook hangs a thread of raw silk, to the bot- tom of which is attached a small pith ball, made smooth and round, and weighing only a small part of a grain. The attenuated thread of silk y unwound from the ball of the silk worm, forms a very delicate insulator; but for ordinary purposes, a common thread of silk may be untwisted, and a single filament taken for the suspending thread. For the purposes of the learner, it may even be sufficient to suspend a ball of cork, or a lock of cotton, or a feather by a thread of silk. The Gold Leaf Electrometer, represented in Fig. 79, consists of two strips of gold leaf suspend- ed from the metallic cover of a small glass cylinder. By this arrangement, the pieces of gold leaf are insu- lated, they are protected from agitation by the air, and Electricity is easily conveyed to them by bringing an electrified body into contact with the cover. The approach of an electrified body causes the leaves to separate, or when previously separated, to collapse according to principles to be explained presently. By the aid of the foregoing instruments, or even by means of the pendulum electrometer alone, we may ascertain the following LEADING FACTS, which are so many fundamental truths, in the sci- ence of Electricity. 371. PROP. I. Electricity is produced by the Friction of all bodies. Fig. 79, Although friction is the most common and by far the most exten- sive means of exciting bodies, yet it is not the only means. Elec- tricity is manifested during the changes of state in bodies, such as liquefaction and congelation, evaporation and condensation. Some bodies even are excited by mere pressure ; others by the contact or separation of different surfaces. Most chemical combinations and 25 194 ELECTRICITY. decompositions are also attended by the evolution of Electricity which manifests its presence to delicate electrometers. If we rub a piece of amber, sealing wax, or any other resinous sub- stance on dry wollen cloth, or fur, or silk, and bring it towards an elec- trometer, it will give signs of electricity. A glass tube may be exci- ted in a similar manner. Moreover if we bring the excited tube near the face, it imparts a sensation resembling that produced by a cobweb. If the tube is strongly excited, it will afford a spark to the knuckle, accompanied by a snapping noise. A sheet of white paper, first dried by the fire, and then laid on a table and rubbed with India rubber, will become so highly excited as to adhere to the wall of the room, or any other surface to which it is applied. Indeed fric- tion is so constantly attended by Electricity, that in favorable weath- er the fluid is abundantly indicated on brushing our clothes, which thus are made to attract the light downy particles that are floating in the air. 372. Our proposition asserts that Electricity is produced by the friction of all bodies, whereas if we hold in the hand a metallic sub- stance, a plate of brass or iron, for example, and subject it to friction, we shall not discover the least sign of electrical excitement. In such cases, however, the Electricity is prevented from accumulating in consequence of the substance being a good conductor, and thus con- veying the fluid to the hand, which is another good conductor, by which means it is lost as fast as it is excited. But if we insulate a metallic body, or any other conducting substance, then on being rubbed, it gives signs of , Electricity, like electrics. 373. PROP. II. The Electricity which is excited from GLASS and a numerous class of bodies, exhibits different properties from that which is excited from AMBER, or sealing wax, and a class of bodies equally numerous with the other. The kind of fluid excited from glass and analogous bodies is called vitreous, and that from amber and analogous bodies, resinous Elec- tricity. .-/The term positive is also used instead of vitreous, and negp- twe instead of resinous. In order to understand the applications of the preceding terms vitreous and resinous, positive and negative, it is necessary to know GENERAL PRINCIPLES. 195 something of the two hypotheses upon which these terms are respec- tively founded. The first hypothesis is that proposed by Du Fay. It ascribes all electrical phenomena to the agency of two fluids spe- cifically different from each other, and pervading all bodies. In un- electrified bodies, these two fluids exist in combination, and exactly neutralize each other. By the separation of the two fluids it is that bodies are electrified, and it is by the re-union of the two fluids, that the Electricity is discharged, or bodies cease to be excited. The second hypothesis was proposed by Dr. Franklin. It ascribes all electrical phenomena to the agency of one fluid, which, as in the other case is supposed to pervade all bodies, being naturally in a state of equilibrium. It is only when this equilibrium is destroyed that bodies become electrified, and it is by the restoration of the equi- librium that the Electricity is discharged, or bodies cease to be ex- cited. But a body is electrified when it has either more or less of the fluid tha'n its natural share ; in the former case it is positive- ly, in the latter case negatively, electrified ; positive Electricity there- fore, implies a redundancy, and negative Electricity, a deficiency of the fluid. 374. PROP. III. Bodies electrified in different ways attract, and in the same way repel each other. Thus, if an insulated pith ball, (Art. 370.) or a lock of cotton, be electrified by touching it with an excited glass tube, it will immedi- ately recede from the tube, and from all other bodies which afford the vitreous Electricity, while it will be attracted by excited sealing wax, and by all other bodies which afford the resinous Electricity. If a lock of fine, long hair be held at one end, and brushed with a dry brush, the separate hairs will become electrified, and will repel each other. In like manner, two insulated pith balls, or any other light bodies will repel each other when they are electrified the same *way, and attract each other when they are electrified different ways. Hence it is easy to determine, whether the Electricity afforded by a given body is vitreous or resinous; for, having electrified the elec- trometer by excited glass, then all those bodies which, when exci- ted, attract the ball, afford the resinous, while all those which repel the ball afford the vitreous Electricity, 196 ELECTRICITY. 375. PROP. IV. The two kinds of Electricity are produced simul- taneously ; the one kind in the body rubbed, the other in the rubber. For example, if we rub a glass tube with a silk or woollen cloth, the glass becomes positive, and the cloth negative. The foregoing Jaw holds true universally ; but the kind of Electricity which each substance acquires, depends upon the substance against which it is rubbed. If we rub dry woollen cloth against smooth glass, it ac- quires the resinous, and the glass, the vitreous Electricity ; but if we rub the same cloth against rough glass, it becomes positively, while the glass becomes negatively, electrified. The following table contains a number of electric substances, arranged in such a way that when they are rubbed against each other, any substance in the list be- fore another becomes positively, and any substance below it, nega- tively, electrified. 1. Fur of a Cat, 6. Paper, 2. Smooth Glass, 7. Silk, 3. Woollen Cloth, 8. Lac, , 4. Feathers, 9. Rough Glass, 5. Wool, 10. Sulphur. The fur of a cat, when rubbed against any of the bodies in the table, always affords the vitreous, and the sulphur always the resinous elec- tricity. Feathers become negative when rubbed against the fur of a cat, smooth glass, or woollen cloth; but positive when rubbed against wool, paper, silk, lac, rough glass, or sulphur. 376. PROP. V. Electricity passes through some bodies with the. greatest facility ; through others with the greatest apparent difficul- ty > or scarcely at all ; and others have a conducting power interme- diate between the two. Metals and charcoal, water and all liquids (oils excepted) are good conductors. Melted wax and tallow are good conductors ; but these bodies while solid conduct very badly. Glass, resins, gums, sealing wax, silk, sulphur, precious stones, oxides, air, and all gases, are non- conducfeo,rs, or at least very bad conductors. Atmospheric air is a non-conductor of the highest class, when perfectly dry ; but it be- comes a conductor, either when moist or when rarefied. The elec- tric fluid easily pervades the vacuum of an air pump, or of the Torn- GENERAL PRINCIPLES. 197 cellian tube ; but these are imperfect vacuums ; it is said that Elec- tricity cannot pass through a perfect vacuum. The conducting pow- ers of most bodies are influenced by changes of temperature, and also by changes of form. Water, in its natural state, is a good con- ductor 5 but its conducting power is increased by heat and diminish- ed by cold. The same body frequently exhibits great changes in conducting power by changes of state, or chemical constitution. Thus, green wood is a conductor, dry baked wood a non-conductor ; charcoal a conductor, ashes a non-conductor. It is particularly important to remember that Metals, Water and all moist substances, Animal sub- stances, as the human body, and the Earth itself, are conductors ; while the Air, when dry, and all Resinous and Vitreous substances are non-conductors. These bodies are those which are chiefly con- cerned in making experiments with electrical apparatus. 377. PROP*. VI. Insulation is effected in various degrees of per- fection, according to the state of the atmosphere, and the nature of the substances employed as insulators. If the air were a conductor, it is not easy to see how the electric fluid could be confined so as to be accumulated. It is, moreover, only when the air is dry that it is capable of insulating well ; hence, in damp, foggy and rainy weather, electrical apparatus will not work well, unless the air is dried artificially by operating in a close room highly heated by a stove. Lac, drawn into fine threads, is the most perfect insulator. Compared with silk thread, such a filament is ten times more effectual in preventing the loss of the fluid. Fine silk thread, however, when perfectly dry, is among the best insulators, and where great delicacy is required, a single filament of silk as it comes from the ball of the silk worm is employed. Its conducting power is somewhat influenced by its color, black being the worst, and a gold yellow the best color for insulating. Glass is much used as an insulator, especially when great strength is required, as in sup- ports to various kinds of electrical apparatus. Glass, however, is liable to acquire moisture on its surface, in consequence of which its properties as an insulator are materially impaired. This inconven- ience is obviated by giving it a thick coat of varnish. Fine hair is a good and convenient substance in some cases of insulation. 198 ELECTRICITY. In some cases, conducting or uninsulating threads are required. Then fine silver wires, or linen threads first steeped in a solution of salt and dried, are used. 378. The sphere of communication is the space within \vhich a spark may pass from an electrified body, in any direction from it. It is sometimes called the striking distance. The sphere of influence is the space within which the power of attraction of an electrified body extends in every way, beyond the sphere of communication. A glass tube strongly excited will exert an influence upon the gold leaf electrometer at the distance of ten or even twenty feet, although a spark could not pass from the tube to the cap of the electrometer at a greater distance than a few inches. 379. The electricity which a body manifests by being brought near to an excited body, without receiving a spark from it, is said to be acquired by Induction. When an insulated conductor, unelectrified, is brought into the neighborhood of an insulated charged conductor, its Electricity un- dergoes a new arrangement. The end of it next to the excited conductor, assumes a state of electricity opposite to that of the ex- cited conductor ; while the farther extremity assumes the same kind of electricity. Suppose the excited conductor is electrified positive- ly. The end of the insulated conductor next to it, becomes negative, and the remoter end positive ; and intermediate between these two points, there occurs a place where neither positive nor negative elec- tricity can be perceived. This place is called the neutral point. The reason why unelectrified bodies are attracted by excited elec- trics is, that they are put into the opposite state by induction, and then attracted upon the general principle laid down in Prop. III. When they come into the sphere of communication of the excited body, they immediately acquire the same kind of electricity, and are repelled. If they come into contact with uninsulated bodies they lose the electricity they have acquired, are again put into the opposite state byjnduction, again attracted and again repelled. This process will go on until the electricity of the insulated conductor is all con- veyed away. ELECTRICAL APPARATUS. 199 The foregoing general principles may be verified with very sim- ple apparatus such as pith balls, a glass tube, and a stick of seal- ing wax. But the same facts may be exhibited in a much more striking and impressive manner by the electrical machine and its ap- pendages, and our attention will therefore be now turned to the con- sideration of the subject of electrical apparatus. CHAPTER II. OF ELECTRICAL APPARATUS. 380. The object of the electrical machine is to accumulate elec- tricity. It is made of several different forms, but two of these forms are predominant, which it will be sufficient for our present purpose to describe ; of these one is called the Cylinder, the other, the Plate machine. The CYLINDER MACHINE is represented in figure 80. Fig. 80. The principal parts belonging to it, are the cylinder, the frame, the rubber, and the prime conductor. The cylinder (A) is of glass, from eight to twelve incbes in diameter, and from twelve to twenty four inches long. It should be perfectly cylindrical, otherwise it will not press the cushion or rubber evenly when turned. It must be as smooth as possible, for rough glass becomes a partial conductor. 200 ELECTRICITY. The cylinder should be so mounted on the frame as to revolve without waddling, for such a motion would prevent its being in uniform contact with the rubber. The Frame (B B) is made of wood, which must be close grained, well seasoned, and baked in an oven, and finally coated with varnish, the object of all this preparation being to dimin- ish its conducting powers, and thus preveBt its wasting the electricity of the cylinder. The Rubber (C,) consists of a leathern cushion, stuffed with hair like the padding of a saddle. This is covered with a black silk cloth, having a flap which extends from the cushion over the top of the cylinder to the distance of an inch from the points con- nected with the prime conductor, to be mentioned presently. The rubber is coated with an amalgam* made of mercury, zinc, and tin, which preparation has been found, by experience, to produce a high degree of electrical excitement, when subjected to the friction of glass. The rubber is insulated by placing it on a solid glass pillar, and it is made to fit closely to the cylinder by means of a spring worked by a screw. The Prime Conductor D, is usually a hollow brass cylinder with hemispherical ends. It is mounted on a solid glass pillar, with a broad and heavy foot made of wood to keep it steady. The cylin- der is perforated with small holes, for the reception of wires (c) with brass knobs. It is important to the construction of an electrical machine, that the work should be smooth and free from points and sharp edges* * The amalgam recommended by Singer, one of the ablest practi- cal electricians, is composed of zinc two ounces, of tin one ounce, and of mercury six ounces. The zinc and tin may be melted together in a ladle or crucible, and poured into a mortar, previously heated to prevent the sudden congelation of the melted metals. As soon as they are introduced, they mast be rapidly stirred with the pestle, du- ring which process the mercury may be added, and the stirring con- tinued until the amalgam is cold, when it will be in the form of paste or fine powder. A little lard is added, to give the amalgam the prop- er consistence ; but if, when applied, it be warmed a little, but a small proportion of lard need be used. In hot weather, less quicksilver is to be employed. ELECTRICAL APPARATUS. 201 since these have a tendency to dissipate the fluid, as will be more fully understood hereafter. For a similar reason the machine should be kept free from dust, the particles of which act like points, and dissi- pate the electricity. 381. The PLATE MA- CHINE (Fig. 81.) con- sists of a circular plate of glass from eight- een to twenty four inch- es or more in diameter, turning vertically on an axis that passes through its center. The frame is composed of materi- als similar to those which compose the frame of the cylindri- cal machine. This ma- chine is furnished with two pairs of rubbers, attached to the top and bottom of the plate. The prime conductor consists of a brass cylinder, proceeding from the center in a line with the axis, and having two branches which serve to increase its surface, and at the same time to connect it with the opposite sides of the plate, so as to receive the Electricity as it is evolved from each cushion. It is not agreed which of these two machines affords the greatest quantity of Electricity from the same surface ; but the cylinder is less expensive than the plate, and less liable to break, and is more convenient for common use. 382. The principles of the electrical machine, will be readily comprehended from what has gone before. It differs from the glass tube, only in affording a more convenient and effectual mode of pro- ducing friction. By the friction of the glass cylinder or plate against the rubber, electricity is evolved, which is immediately transferred to- the prime conductor, and may be taken from the latter by the knuek- 26 202 ELECTRICITY. le, or any other conducting substance. If the glass and rubber both remain insulated, the quantity of Electricity which they are capable of affording, will soon be exhausted. Hence, a chain or wire is hung to the rubber and suffered to fall upon the table or the floor, which, communicating as it does with the walls of the building, and finally with the earth, supplies an inexhaustible quantity of the fluid to the rubber. In cases where very great quantities of electricity are required, a metallic communication may be formed immediately be- tween the rubber and the ground.* 383. In order to indicate the degree of excitement in the prime conductor, the Quadrant Electrometer is attached to it, as is repre- sented at E in Fig. 80. This electrometer is formed of a semicir- cle, usually of ivory, divided into degrees and minutes, from to 180, ( the graduation beginning at the bottom of the arc. The in- dex consists of a straw, moving on the center of the disk, and carry- ing, at the other extremity, a small pith ball. The perpendicular support is a pillar of brass, or some conducting substance. When this instrument is in a perpendicular position and not electrified, the * As electrical machines are expensive, and not always easily pro- cured by the private learner, it may be useful to suggest a mode of fitting up a cheap apparatus. A large tincture bottle may be procured of the apothecary, for the cylinder. A cover of wood may be ce- mented to each end, to the center of which, next to the bottom, is screwed a projecting knob for one end of the axis, while the part of the axis to which the handle is attached, is screwed into the center of the cover of wood next to the nozzle. Thus prepared, it may be mounted on such a frame of hard dry wood as every joiner or cabinet maker can construct. A tinner can make the prime conductor, and several other appendages to be described hereafter. Junk bottles or long vials servo well as insulators. Ingenious students of electricity, frequently amuse themselves with making machines of this description, some of which have answered nearly every purpose of the most ex- pensive Jkinds of apparatus. A cement, for electrical purposes, maybe made by melting together five ounces of resin, one ounce of beeswax, one ounce of Spanish brown, and a tea spoonful of plaster of Paris, or brick dust. t Sometimes the division is carried only to 90, which is all that is necessary. ELECTRICAL APPARATUS. 203 index hangs by the side of the pillar, perpendicularly to the horizon ; but when the prime conductor is electrified, it imparts the same kind of electricity to the index, repels it, and causes it to rise on the scale towards an angle of 90, or to a position at right angles with the pillar. 384. When an electrical machine is skillfully fitted up, and works well, on turning it, circles of light surround the cylinder or plate, and brushes or pencils of light emanate copiously from the cushion and other parts of the machine. The circles of light consist of electric sparks, which discharge themselves between the excited surface, and the rubber, their passage being so rapid as to appear like a continued line, like that of a small stick ignited at the end and whirled in the air. The brushes of light arise from the facility with which the fluid escapes from points or thin edges. The experiments which were previously performed on electrical attractions and repulsions, (Arts. 369 376.) may now be repeated in a much more striking manner, and various other experiments add- ed, which can be shown only when electricity is accumulated. 385. We proceed to enumerate a few of the effects of electricity as they are exhibited by the electrical machine, confining ourselves, for the present to those experiments, which relate to attraction and repulsion, and the passage of the spark, reserving such as relate to light and heat to future sections. The following effects may be ob- served with a machine of moderate powers, the rationale of which the learner will readily supply from the propositions given in Art. 378. (1.) When the machine is turned, a downy feather, or a lock of cotton held in the hand by a conducting thread,* will be strongly at- tracted towards the excited surface. (2.) A skein of thread, or lock of fine hair, looped and suspend- ed by the loop from llie prime conductor, will exhibit strong repul- sions between the threads or hairs. (3.) The quadrant electrometer being attached to the prime con- ductor, the conducting powers of different substances may be readily tried. Thus, an iron rod held in the hand, and applied to the prime * The conducting power of linen or cotton threads is improved by moistening them with the breath. 204 ELECTRICITY. conductor, will cause the index of the electrometer to fall instantly ; and the same effect will follow the application of any metallic rod. A wooden rod of the same dimensions, will cause the index to de- scend more slowly ; and a glass rod will hardly move it at all. These experiments show that iron is ajperfect, and wood an imperfect con- ductor,' and glass a non-conductor. In the same manner the con- ducting powers of a stick of sealing wax, a roll of silk, or cloth, and of various other bodies, may be illustrated. (4.) If a pith ball or feather or any other light body held by a silk thread, be, presented to the prime conductor, it will 6rst be at- tracted and then repelled, and it cannot again be brought into con- tact with the electrified conductor, until its electricity is discharged by communicating with the finger or some unelectrified conductor. (5.) By placing light bodies between an electrified conductor and an uninsulated body, they may be made to move with great rapidity backwards and forwards, from one surface to the other, being alter- nately attracted and repelled by the electrified surface. By this means are performed electrical dances, the ringing of bells, and a variety of interesting and amusing experiments. (6.) If the rubber be insulated while the machine is turned, the rubber and the glass cylinder, or plate will be found to be in differ- ent electrical states ; an insulated body attracted by the one will be repelled by the other. Bodies are electrified positively by connecting them with the glass, by means of the prime conductor, and negatively by connecting them with the rubber, the latter being insulated, and the prime conductor uninsulated. (7.) An electrified body frequently exhibits a tendency to separate into minute parts, these parts being endued with the power of mutual repulsion. Thus, a lock of cotton, when electrified, is separated into its minutest fibres. Melted sealing wa^ when attached by a wire to the prime conductor, is divided into filaments so small as to resemble red wool. Water dropping from a capillary syphon tube, on being electrified, is made to run out in a great number of exceed- ingly fine 'streams. Water spouting from an air fountain (Art. 291.) is, divided into a number of rays, presenting the appearance of a brush.* (8.) A portion of electrified air, in consequence of the mutual re- pulsion between its particles, expands, and when at liberty to escape, LEYDEN JAR. 205 becomes rarefied. Thus, a current of air may be set in motion from an electrified point, or small ball, or be made to issue from the neck of a bottle. Such are some of the leading experiments which may be perform- ed with the common electrical machines, in addition to those which are connected with light and heat, to be more particularly described hereafter. 386. The force of electrical attraction or repulsion^ at different distances from an electrified body, varies inversely as the square of the distance. \ Hence electrified bodies exhibit strong attractions and repulsions only when very near to each other, and the force decreases rapidly with the distance, being diminished four times by doubling the dis- tance, and nine times by trebling it. It is worthy of remark that the foregoing law is the same as that of gravitation. Electricity resides only at or near the surfaces of bodies. A hol- low metallic globe, for example, takes the same charge as a solid globe of the same dimensions. Bodies of different figures, however, have the electricity distributed over their surfaces in different man- ners. Thus, in a conductor of an elongated figure, the electricity is accumulated towards the two ends, and more or less withdrawn from the central parts. The Leyden Jar. 387. This instrument, which is a very important and interesting article of electrical apparatus, consists of a glass jar, coated on both sides with tin foil, except a space on the upper end, within two or three inches of the top, which is either left bare, or is covered with a coating of varnish, or a thin layer of sealing wax. To the mouth of the jar is fitted a cover of hard baked wood, through the cen- ter of which passes a perpendicular wire, terminating above in a knob, and below in a fine chain, that rests upon the bottom of the jar. On presenting the knob of the jar near to the prime conductor of an electrical machine, while the latter is in operation, a series of sparks passes between the conductor and the Jar, which will gradually grow more 206 ELECTRICITY. and more feeble, until they will cease altogether. The Jar is then said to be charged. If now we take the Discharging Rod, (which is a crooked wire, armed at each end with knobs, and insulated by a glass handle, as in Fig. 83,) and apply one of the knobs to the outer coating of the Jar, and bring the other to the knob of the Jar, a flash of intense brightness, accompanied by a loud report, immediately ensues. On applying the dis- charging rod a second time, a feeble spark passes, being the residuary charge, after which all signs of electricity disappear, and the Jar is said to be discharged. 388. If, instead of the discharging rod, we apply one hand to the outside of the charged Jar, and bring a knuckle of the other hand to the knob of the Jar, a sudden and surprising shock is felt, con- vulsing the arms, and, when sufficiently powerful, passing through the breast. 389. The Leyden Jar derives its name from the place of its dis- covery. In the year 1746, while some philosophers of Leyden were performing electrical experiments, one of them happened to hold in one hand a tumbler partly filled with water, to a wire con- nected with the prime conductor of an electrical machine. When the water was supposed to be sufficiently electrified, he attempted, with the other hand, to detach the wire from the machine ; but as soon as he touched it, he received the electric shock. It was by imitating this arrangement, that the Leyden Jar was constructed ; for here was a glass cylinder, having good conductors on both sides, viz. the hand on the outside, and the water on the inside, which were prevented from communicating with each other by the non-conduct- ing powers of the glass. A metallic coating, as tin foil or sheet lead, was substituted for the two conductors, and a jar for the glass cylin- der, and thus the electrical jar was constructed. 390,- Those who first received the electric shock from the Leyden Jar, gave the most extravagant accounts of its effects. M. Musch- enbroeck, a philosopher of Leyden, of much eminence, said that " he felt himself struck in his arms, shoulders and breast, so that he lost his breath ; and it was two days before he recovered from the LEYDEN JAR. 207 effects of the blow and the terror ; adding, that he would not take a second shock for the kingdom of France." M. Winkler, of Leipsic, testified, that " the first time he tried the Leyden experiment, he found great convulsions by it in his body; and that it put his blood into great agitation, so that he was afraid of an ardent fever, and was obliged to use refrigerating medicines. He also felt a heaviness in his head, as if a stone lay upon it, and twice it gave him a bleeding at the nose. n 391. In an age less enlightened than the present, and less familiar with the wonders of philosophy and chemistry, the striking and truly surprising effects of Electricity, as exhibited by the Leyden Jar, would naturally excite great admiration and astonishment. Accordingly, showmen travelled with this apparatus through the principal cities of Europe, and probably no object of philosophical curiosity ever drew together greater crowds of spectators. It was this astonishing experi- ment, (says Dr. Priestley,) that gave eclat to Electricity. From this time, it became the subject of general conversation. Every body was eager to see, and, notwithstanding the terrible account that was re- ported of it, to feel the experiment; and in the same year in which it was discovered, numbers of persons, in almost every country in Europe, got a livelihood by going about and showing it. All the electricians of Europe, also, were immediately employed in repeat- ing this great experiment, and in attending to the circumstances of it. With similar assiduity and unequalled success, Dr. Franklin be- took himself to experiments on the Leyden Jar. He effectually in- vestigated all its properties, by very diversified and ingenious experi- ments, and gave the first rational explanation of the cause of its phe- nomena. The following experiments may be easily repeated. 392. (1.) The Jar is charged by bringing the knob near the prime conductor, while the, machine is in operation. One mode of charg- ing the Jar has been already mentioned in Art. 387. It may, now- ever, either be held in the hand, or placed on the table, or on any conducting support : the only circumstance to be attended to is, that the outside shall be uninsulated. A Jar, while charging, will some- times discharge itself spontaneously. This effect will be more likely to happen, if the uncoated interval is very clean and dry, and may be prevented altogether, by previously breathing on the uncoated part. 208 ELECTRICITY. (2.) The opposite sides of a charged Jar, are in different electrical states, the one positive and the other negative. Thus, if a pith ball, suspended by a silk thread, be applied to the knobj it will first be at- tracted to it. and then repelled ; but it will now be attracted by the outside coating, until it becomes electrified in the same way, and then repelled, and so on. (3.) In order to receive the charge, the outside of the Jar must be uninsulated. If we attach a string to the knob of the Jar, and sus- pend it, in the air, to the prime conductor, and put the machine in operation, no charge will be communicated to the Jar. The same result will follow, if the Jar stands on an insulating stand,* or is in- sulated by any other method. An insulated Jar, however, may be charged by connecting its knob with the positive conductor, and its outer coating with the rubber. (4.) A second Jar may be charged, by communication with the outside of the first, while the latter is receiving its charge. The charge communicated to the second Jar, is of the same kind as that of the first, and nearly of the same degree of intensity, provided the capacity of the two Jars be the same. Moreover, if a third, a fourth, or any number of Jars, of the same size, be connected, in a similar manner, with each other ; namely, having the knob of each in com- munication with the outside coating of the next preceding, then all the Jars will be charged with the same kind of electricity, but the degree of intensity will decline a little in the successive Jars. If the charge be derived, through the prime conductor, from the cylin- der or plate, as is usually the case, it will be the positive or vitreous electricity. (5.) JL Jar may be charged negatively, by receiving the electricity of the rubber, the rubber being insulated, and the prime conductor uninsulated. For this purpose, the chain usually attached to the rubber may be transferred to the prime conductor. * An insulating stand, is any flat support, insulated by a pillar of glass. *'*The pillar is usually a solid cylinder of glass, from six to twelve inches long, varnished so as to protect it from moisture. A junk bottle, surmounted by a circular piece of wood, dry and varnish ed, makes a very good insulating support. LEYDEN JAR. 209 (6.) When two Jars are charged^ the one positively and the other negatively, on forming a communication between the insides of both, by connecting the two knobs, no discharge will take place, unless the outsides be in conducting communication. Thus, if two Jars be charged, the one from the prime conductor and the other from the rubber,* and placed at the distance of a few inches from each oth- er, on insulated supports, on connecting the two knobs by the dis- charging rod, no discharge will follow ; but, let a wire be laid across the supports, touching the outside of each Jar ; then, on applying the discharging rod to the two knobs, an explosion will immediately > ^ By means of two Jars differently charged, and placed as above, with their outsides in conducting communication, the experiment .,/ may be exhibited, which is called the Electrical Spider. It consists of a small piece of cork, so fashioned as to represent the body of a spider, and blackened with ink, having a number of black linen threads drawn through it to represent the legs. This is suspended by a silk thread, half way between the knobs of the two Jars, and vibrates for a long time from one knob to the other, until both Jars are discharged. The rationale will be obvious on a little reflection. (7.) The charge of any Jar may be divided into definite parts; that is, the half, the fourth, or any aliquot part of the charge may be ta- ken. This may be done by connecting the inner and outer coating of the charged jar, with the inner and outer coating of an unelectrified jar, of the same size and thickness. The respective charges will be measured by the quadrant electrometer, (Fig. 80.) (8.) The electricity is accumulated on the surface of the glass, and the coatings serve merely as conductors of the charge. This is proved by the fact, that when the coatings are movable, so that they can be taken off from the jar after it is charged, neither of them exhibits the least sign of electricity ; while if another pair of cqatings is substitu- ted, which have not been electrified, on forming the communication between the inside and outside, the usual discharge takes place, * And both may be thus charged at the same time, by connecting one with the insulated rubber, and the other with the Insulated prime conductor, the Jars themselves being uninsulated. 27 210 ELECTRICITY. showing that the whole of the charge was retained on the glass sur- faces of the jar. (9.) The charge of a Leyden Jar may be retained for a long time. If the surfaces are well separated from each other, the charge re- mains for many days or even weeks. The charge is usually dissipa- ted by the motion of particles of dust, or other conducting substan- ces in the atmosphere, from one of the coatings to the other, or by the uncoated interval becoming 'moist, and losing its insulating power; consequently a jar will retain its charge longer in dry than in damp weather. Covering the uncoated part of the jar with melted seal- ing wax or varnish, prevents the deposition of moisture upon it, and consequently tends also materially to prevent the dissipation of its charge. 393. For the purpose of making the theory of the Leyden Jar familiar, we may now recur to the experiments mentioned in Art. 392, and attempt the explanation of them. In the structure of the Jar, we recognise the operation of the prin- ciple of induction. Here, an unelectrified body (the outer surface) is brought very near to an electrified body, (the inner surface,) without the possibility of communicating with each other, on account of the non-conducting properties of the glass. The nearer the two surfaces can be brought to each other, the more powerful is the ef- fect of induction, that effect being inversely as the square of the dis- tance. Accordingly, the thinner the jar, the more powerful is the charge it will receive; but the danger of breaking prevents our em- ploying such as are very thin. To trace the process of charging a jar a little more minutely, let us suppose the jar connected with the prime conductor of an elec- trical machine, from which a spark is communicated to the inner coating. This, according to the principles of induction, expels a similar quantity of the same fluid from the opposite unelectrified sur- face, ana 1 renders that negative, in the same degree as the inside is positive. Being negative, it increases the attraction of the inner sur- face fo the opposite species of fluid, and another spark is received, which again expels an additional quantity of the same species of fluid from the outside, and thus the two surfaces continue to act upon each other reciprocally, though- with constantly diminishing power, until the ar is charged. ELECTRICAL LIGHT. 211 The reason also is plain, why the outside of the jar must be un- insulated ; since it is only in such case, that the foregoing process of induction can take place ; and we readily see why a series of jars may be charged, from the portion of electricity which is expelled from the outside of the first jar. 394. When a jar is charged negatively from the rubber, just the opposite process in all respects takes place, the outside becoming posi- tive by induction, and reacting upon the inside. The case men- tioned in Art. 392, (6.) where two jars differently charged, cannot be discharged except their outer surfaces be in conducting commu- nication, will be readily understood ; for it is impossible for the equi- librium to be restored by the union of the electricities on the inside, while the outside remains electrified. If we could suppose this to take place for a moment, and the electricity within to be restored to its natural state, it wduld again be immediately decomposed by the inductive influence of the electrified coating without. 395. The phenomena of the Leyden Jar, may be equally well explained, by substituting the terms vitreous and resinous, instead of positive and negative, on the supposition of two fluids, since the prin- ciples of induction apply equally well to both hypotheses. Thus, it is as easy to suppose that the resinous electricity is induced upon the outside by the attraction of the vitreous electricity within, as it is to suppose that the outside becomes negative by the loss of a portion of its natural share ; and the necessity of the outer surface being unfn- sulated, is as apparent in the one case as* in the other. * CHAPTER III. OF ELECTRICAL LIGHT, OF THE BATTERY, AND OF THE MECHAN- ICAL AND CHEMICAL AGENCIES OF ELECTRICITY. Electrical Light. 396. Electrical light appears whenever the fluid is discharged, in considerable quantity, through a resisting medium. Accordingly, no light is perceived when electricity flows freely through good conductors ; but if such conductors suffer any interrup- 212 ELECTRICITY. tion, as by the intervention of a space of air, or even of an imperfect conductor, then the attendant light becomes manifest. We shall best learn the properties of the electrical spark, by attending to a variety of experiments in which it is exhibited.* A glass tube rubbed with black silk, which has been smeared with a little electrical amalgam, will yield copious sparks and flashes of light. The tube should be warm, dry, and smooth, and of a size not jess than two feet in length, and three fourths of an inch in diameter. The electrical machine, when in vigorous action, affords bril- liant circles and streams of light. In order to render the light af- forded by turning the machine abundant, several practical expedients are necessary. All parts of the machine must be dry and warm, (but not hot.) It is useful to rub very freely the glass plate or cylinder, with an old silk handkerchief. Black spots or lines that collect on the glass, especially when the amalgam is new, are to be carefully rubbed off, and should dust or down collect on the amalgam of the rubber, this must be removed. The action of the cylinder will be increased by the following process : smear the bottom of the cylinder with a thin coat of tallow ; then turn the machine until the tallow is all taken up by the rubber and flap. The pores of the flap will then become rilled with tallow, it will apply itself more closely to the cyl- inder, and the supply of electricity will become more copious. A convenient method of recruiting the action of the machine, is to coat a circular disk of paste board or leather with amalgam, and to apply it to the glass plate or cylinder while the machme % is turning. If the chain be removed from the rubber to the prime conductor, so that the former shall be insulated and the latter uninsulated, on bringing the ends of the fingers near the rubber, a stream of diluted Jight will pass between the fingers and the rubber. 397. The electric spark passes, with increased facility, through rarefied air ; and the distance to which it will pass between two con- ductors, is augmented as the rarefaction is made more complete. Instead of the distance of five or six inches, which is the limit of the sparfc from the prime conductor of an ordinary machine in the * In experiments on electrical light, the room is supposed to br* dark. They appear to best advantage in the night. ELECTRICAL LIGHT. 213 open air, the spark will pass through the space of eighteen inches or more, in an exhausted receiver. If a pointed wire, terminating in a knob above, be introduced into the top of a tall receiver, and the re- ceiver be placed on the plate of the air pump, on connecting the knob of the wire with the prime conductor, and turning the machine, a brush of light only will appear at the extremity of the wire ; but, on exhausting the air, this brush will enlarge, varying its appearance and becoming more diffused as the air becomes more rarefied, until at length the whole receiver is pervaded by a beautiful bluish light, changing its color with the intensity of the transmitted electricity, and producing an effect which with an air pump of considerable power, is pleasing in the highest degree. When a charged jar is placed under the receiver of an air pump, as the exhaustion proceeds, a luminous current flows over the edge of the jar from the positive to the negative side, until the equilibrium is restored. Electric light exhibits a very beautiful appearance, as it passes or flows, through the Torricellian Vacuum.* The color is of a very delicate bluish or purple tinge, and the light per- vades the entire space. But the most pleasing exhibtions of this kind, are made by forming an artificial atmosphere of vapor in the Torricellian tube. Ether or alcohol, passes into the state of vapor when the pressure of the atmosphere is removed ; and accordingly, on introducing a drop of one of these fluids into the Torricellian va- cuum, it immediately evaporates and fills the void. If, now, a strong spark be passed from the prime conductor through this vapor, the spark will exhibit various colors : in ether, it is an emerald green, or mingled red and green ; in alcohol it is red or blue ; but the colors vary somewhat with the distances at which they are seen. 398. In condensed air, on the contrary, the spai'k passes with greater difficulty than ordinary. In such case, also, its whiteness, and brilliancy are augmented, and its. course is zigzag. These ap- pearances are even exhibited by passing the spark through confined air, of only the ordinary density. The colors of the spark, are pleasingly varied by passing it, in a condensed form, as in the Ley- * This is the vacuum produced by means of quicksilver in an in- verted glass tube, as the barometer, Art. 295. 214 ELECTRICITY. den Jar, through media of different kinds. The experiment is per- formed by making the given body form a part of the circuit of com- munication, between the inside and outside of the Leyden Jar. A ball of ivory in this situation exhibits a beautiful crimson ; an egg. a similar color- but somewhat lighter ; a lump of sugar, gives a very white light, which remains for some time after the spark has passed ; and fluor spar exhibits an emerald green light, or, in some cases, a purple light, which also continues to glow in the dark for some seconds. The great intensity of the light is shown by the strong illumination which the sparks in the jar communicate to bodies slightly transparent. Thus an egg has its transparency greatly increased ; and if the thumb be placed over the space which separates the two conducting wires that communicate with the two sides of the jar re- spectively, the illumination is so powerful, that the blood vessels and interior organization of the organ may be distinctly seen. 399. Metallic conductors, if of sufficient size, transmit electricity without any luminous appearance, provided they are perfectly con- tinuous 5 but if they are separated in the slightest degree, a spark will occur at every separation. On this principle, various devices are formed by pasting a narrow band of tin foil on glass, in the re- quired form, and cutting it across with a pen knife, where we wish sparks to appear. If an interrupted conductor of this kind be pasted round a glass tube in a spiral direction, and one end of the tube be held in the hand, and the other be presented to an electrified conductor, a brilliant line of light surrounds the tube, which has been called the spiral tube, or diamond necklace. By enclosing the spiral tube, in a larger cylinder of colored glass, the sapphire, topaz, eme- rald and other gems may be imitated. Words, flowers, and other complicated forms, are also exhibited nearly in the same manner, by a proper disposition of an interrupted line of metal, on a flat piece of glass. 400. The light of the electric spark, is not a Constituent part of electricity, but arises from the sudden compression of the air, or other mediumFthrough which it passes. It is well known, that air is capable of affording a spark by sudden compression. There is a kind of match constructed on this princi- ELECTRICAL LIGHT. 215 Fig. 84. pie, in which a small portion of air contained in a close cylinder, be- ing suddenly compressed by forcing down a piston, yields a spark sufficient to light a quantity of tinder at the bottom of the cylinder. Now it is found by actual experiment, that electricity has the power of condensing air. This fact is shown by means of a small instrument called Kinnersley's Air Thermometer. It consists of a glass tube, closed air tight at the two ends by brass caps, through each of which passes a movable wire, terminated within by a small ball. Through the low- er cap is inserted a small glass tube open at both ex- tremities, and turned upwards parallel to the cylin- der. Into this tube is introduced a quantity of water sufficient to cover the bottom of the cylinder, and of course to rise a little way into the tube. The two balls being set at some distance from each other, and a spark from the Leyden Jar being passed between them, the air within is suddenly rarefied, and the wa- ter ascends in the tube, and again descends, when the explosion is over. This sudden rarefaction of a portion of air before the electric spark, must cause a sudden and powerful compression in the portions of air immediately adjacent. The im- mense velocity of the spark must greatly increase the resistance, and of course the force of compression. This appears to be an ad- equate cause for the production of the light that accompanies the electric discharge, and hence we conclude, that light is not inherent in the fluid itself. The greater density and brilliancy of the spark in condensed air, and its feebleness and difFuseness in a rarefied me- dium, are facts which accord well with the supposed origin ; and the zigzag form of the spark when long, or when passing through con- densed air is well explained ,by the same theory. For the electric fluid in its passage through the air, condenses the air before it, and thus meet with a resistance which turns it off laterally; in this direc- tion it is again condensed, and has its course again changed; and so on, until it reaches the conductor towards which it is aiming. The zigzag form of lightning is accounted for on this principle. Electrical light is found by optical experiments, to have precisely the same nature with the light of the sun, being like this resolved into various colors by the prism, and possessing other properties, to be described under the head of Optics, which identify it with solar light. 216 ELECTRICITY. Battery. 401. Jin electric battery consists of a number of Ley den Jars so combined) that the whole may be either charged or discharged at once. Very large jars cannot be obtained ; it is rare to find one more than two feet high, by one and a half in diameter. Yet some of the mechanical effects of electricity, to be described hereafter, re- quire a much greater accumulation of the fluid than can be obtained from any single jar. t The battery is constructed as follows. Large jars, twelve or fourteen inches high, by five or six inches in diameter are coated like ordinary Leyden Jars. Twelve of these constitute a battery sufficiently powerful for most purposes, but the power of the battery may be carried to an indefinite extent by increasing the num- ber of jars. When the number is twelve, they are placed four in a row in a box, the bottom of which is coated with tin-foil, by means of which the outsides of the jars are all in conducting communica- tion. Each jar is separated from the rest by a slight partition of wood. To connect the insides of the jars, their knobs are joined by large brass wires. It is obvious, therefore, that the battery 'is equivalent to a single jar of enormous size, comprehending the same number of square feet. The object of the battery is to accumulate a great quantity of the electric fluid, which is in proportion to the extent of surface ; the in- tensity, or elastic force, as indicated by the quadrant electrometer, is no greater in the battery when charged, than in a single charged jar. The battery, like the common jar, is charged by bringing the inside into communication with the prime conductor of an active and powerful electrical machine : it is discharged, as usual, by forming a connexion between the inside and outside, commonly by means of the discharging rod. 402. The largest machine and battery hitherto constructed, were made for the Teylerian m'useum, at Haarlem. It consists of two cir- cular plates of glass each five feet five inches in diameter. The prime'eonductor consists of several pieces, and is supported by three glass pillars, nearly five feet in length. The force of two men is re- quired to work the machine ; and when it is required to be put in ac- tion for any length of time, four are necessary. EFFECTS OF ELECTRICITY. 217 At its first construction nine batteries were applied to it, each hav- ing fifteen jars, every one of which contained a square foot of coat- ed glass ; so that the grand battery, formed by the combination of all these, contained one hundred and thirty five feet. As examples of the great power of the Teylerian machine, we may mention the following ; it charged a Leyden jar by turning the handle half round, a charge which the jar would receive, and lose by discharging it- self spontaneously, eighty times in a minute. A single spark from the conductor melted a considerable length of. gold leaf. A spark, or zigzag stream of fire would dart from the prime conductor to a neighboring conductor to the distance of ten feet. A wire three eighths of an inch in diameter, was found to be insufficient to trans- mit the whole charge of the prime conductor, but the wire would give small sparks to a conductor brought near to it. The sphere of influ- ence (Art. 379.) extended to the distance of forty feet, so as sensibly to affect the pith ball electrometer. The spider web sensation (or that peculiar sensation resembling that of the spider's web) which is experienced by holding an excited glass tube to the face, was felt by bystanders to the distance of eight feet from the machine. Mechanical Effects of Electricity. 403. The sound produced by an electric discharge, is ascribed to the sudden collapse of the air, which has been displaced by the passage of the electric fluid. Hence the sound is greater in proportion to the quantity and inten- sity of the charge. A battery, when fully charged, gives a loud ex- plosion. 404. Imperfectly conducting substances, through which a powerful electric charge is passed, are torn asunder with more or less violence. A large Leyden Jar is sufficient for exhibiting some of these me- chanical effects : others require the power of the Battery. When the charge is passed through a thick card, or the cover of a book, a hole is torn through it, which presents the rough appearance of a bur on each side. By means of the Battery, a quire of strong paper may be perforated in the same manner ; and such is the velocity with 28 218 ELECTRICITY. which the fluid moves, that if the paper be freely suspended, not the least motion is communicated to it. (See Art. 29,) Pieces of hard wood, of loaf sugar, of stones, and many other brittle non-con- ductors, are broken or even torn asunder with violence, by a power-. ful charge from the battery. If two wires be introduced into a soft piece of pipe clay, and a strong charge be passed through them, the clay will be curiously expanded in the interval between the wires. The expansion of fluids by electricity is very remarkable, and productive of some singular results. When the charge is strong, no glass vessel can resist the sudden impulse. JBeccaria inserted a drop of water between two wires, in the center of a solid glass ball of two inches diameter ; on passing a shock through the drop of water, the ball was dispersed with great violence. In like manner, by the sud- den expansion of a small body of confined air, strongly electrified, explosions maybe produced, and bodies that resist its expansion are projected with violence. Even good conductors, when minutely di- vided, are expanded by electricity. Thus, mercury, confined in a capillary glass tube, will be expanded with a force sufficient to splin- ter the tube. Chemical Effects of Electricity. 405. By means of Electricity, more or less accumulated, a. variety of chemical effects may be produced; such as the combustion of inflam- mable bodies, the oxidation, fusion, and even combustion of metals, the separation of compounds into their elements, or the union of ele- ments into compounds. Ether and alcohol may be inflamed by passing the electric spark through them ; nor is the effect diminished by communicating the spark by means of a piece of ice or any othefr cold medium. The finger may be conveniently employed to inflame these substances. Phosphorus, resin, and other solid combustible bodies, may be set on fire by the same means ; gunpowder and the fulminating powders may be exploded ; and a candle may be lighted. Gold leaf and fine iron wire^may be burned, by a charge from the battery.* Wires of lead, tin, zinc, iron, copper, platina, silver and gold, when subjected to the charge of a very large battery, burn with explosion and are converted into oxides. MOTIONS OF THE ELECTRIC FLUID. 219 The same agent, moreover, is capable of reviving these oxides ; that is, restoring them to the state of pure metals. By a similar contrariety of properties, water is decomposed into its gaseous ele- ments, and the same elements are reunited to form water ; and the constituent gases of atmospheric air are, by passing a great number of electric charges through a confined portion of air, converted into nitric acid. Motions of the Electric Fluid. 406. The velocity of the electric fluid is apparently instantaneous. A circuit of four miles has been formed, by means of wire, between the inside and outside of a Leyden Jar, and no perceptible interval was occupied during the discharge. Analogy, however, would lead us to believe that Electricity, like light, is progressive in its motions, but that it moves with a velocity too great to be measured, except for intervals of immense extent.* 407. The electric fluid, in its route, selects the best conductors. The Leyden Jar may be discharged with a wire held in the hand, without the insulating handle used in the Discharging Rod ; since metallic wire is a better conductor than the hand, and the fluid will take its route through that in preference to the hand. But if a wood- en discharger be substituted for the wire, the shock will be felt, since animal substances are better conductors than wood. It is necessary to remark, however, that when the charge is very intense or the quantity great, as in the Battery, then some portion of the fluid will escape from the discharging wire and pass through the hand. In such' cases, therefore, it is prudent to make use of the Discharging Rod. * * The velocity of light appears to be instantaneous, for such dis- tances as four miles ; but when such intervals are taken as the diame- ter of the earth's orbit, light is found to have a progressive velocity of 192,500 miles per second^ If, therefore, electricity actually moves with a progressive velocity like that of light, still the time occupied in traversing the space of four miles would be inappreciable, since it would equal only about j oT 7 part of a second. 220 ELECTRICITY. Lightning, in striking a building, usually takes a course which indi- cates the preference of the fluid for the best conductors. 408. The electric fluid will sometimes take a shorter route through a worse conductor, in preference to a longer route through a better conductor. The spark will pass through a short space of air, instead of following a small wire thirty or forty feet. The preference of the shorter route is sometimes indicated in taking the electric shock. "While one person is receiving the shock from the Leyden Jar, an- other may grasp his arm without feeling the least effect from the charge. 409. The course of the charge is frequently determined by the influence of points^ either in dissipating or in receiving the fluid. Sharp points connected with the best conductors, greatly favor the dispersion of the fluid during its passage, and sharp pointed con- ductors draw the charge towards them, from a great distance around. The finest needle, held in the hand towards the knob of one of the jars of a charged battery, will silently discharge it, in a few seconds; and if we apply one hand to the outside of a Leyden Jar, and with the other bring a fine needle to the knob of the Jar, only a compara- tively feeble shock will be felt, the charge being rapidly dissipated while the needle is approaching the knob. CHAPTER IV. OF THE EFFECTS OF ELECTRICITY UPON ANIMALS, AND OF THE LAWS OF ELECTRICAL PHENOMENA. . 410. We have already several times incidentally adverted to the shock communicated to the animal system, when it is brought into the electric circuit, so that the charge passes through it. We now propose to consider this interesting part of the subject more particu- larly. The Electric Shock is received, whenever the animal system is made a part of the conducting communication) between the inside and outside of a charged Leyden Jar. A convenient method of ad- ministering the shock, is to place the charged jar on a table, resting EFFECTS ON ANIMALS. 221 immediately on a metallic plate,* as a plate of tin, lead, or copper; then grasping a metallic rod in each hand, touch one of them to the plate and the other to the knob of the Jar, and a sudden convulsion of the limbs or the breast will be experienced, more or less violent according to the strength of the charge. The effect is greatly height- ened by feelings of dread or apprehension, and it may be resisted to a considerable degree by voluntary effort. A slight charge affects only the fingers or the wrists ; a stronger charge convulses the large muscles above the arm-pits ; a still greater charge passes through the breast and becomes in some degree painful. Electricians, how- ever, have frequently adventured upon charges sufficiently powerful to convulse the whole frame. 411. The shock may be communicated to any number of persons at once. This is usually effected by their joining hands, while the first in the series holds one of the metallic rods, with which he touches the plate or outside of the jar, and the last in the series holds the other rod, with which he touches the knob of the Jar, at which instant the whole number receive the shock at the same mo- ment, and that however extensive the circle of persons may be. The charge of a large battery is sufficient to destroy human life, especially if it be received through the head. By standing on the Insulating Stool, which is a stool with glass feet, a person becomes an insulated conductor, and may be electrified like any other insulated conductor. A communication being made with the machine, the fluid pervades the system, but excites hardly any sensation except a prickling of the hair, which at the same time rises and stands erect ; for the hairs, being similarly electrified, mutually repel each other. 412. While in'this situation, the human system exhibits the same phenomena as the prime conductor when charged ; that is, it attracts light bodies, gives a spark to conductors brought near it, and commu- nicates a slight shock to another person who receives the spark from it. Indeed, the same shock is felt by both parties. * It is safer to employ such a plate than to bring the conducting rod immediately into contact with the outside coating of the Jar; for, in such case, persons unaccustomed to receive the shock, are apt to over- turn the Jar and break it. 222 ELECTRICITY. By means of the insulating steol, the most delicate shocks may be given ; for the charge may be drawn off from any part, by imperfect conductors. Thus, a pointed piece of wood will draw off the charge from the eye, in a manner so gentle, as to secure that tender organ against any possibility of injury. By a variety of conductors, of dif- ferent powers, and by points and balls, the sensations may be accom- modated, with much delicacy, to the state of the patient, or to the nature of the affected part. 413. The shock may be communicated directly to any individual part of the system, without affecting the other parts, by making that part form a portion of the electric circuit, between the inside and outside of a Leyden Jar. Thus, let it be required to electrify an arm. Two directors, (consisting of wires terminating in brass knobs, and insulated by glass handles,) are connected by chains with the knob, and the outside coating of a charged Jar ; then on applying one of the directors to the hand, and the other to the naked shoulder, the arm is convulsed. In cases where the patient requires only a moderate shock, the charge is regulated by a contrivance attached to the Jar called Lane's Discharging Electro- Fig. 85 meter, represented in Fig. 85. S is a stick of solid glass ; B, R, two brass knobs, connected by a wire, which slides back and forth in such a way that it may be set at any required dis- tance from the knob of the Jar. If the ball B be set in contact with the knob, then on touch- ing the ball and the outer coating of the Jar; the entire charge of the Jar is received ; but by removing the ball B from the knob, the half, fourth, or any aliquot part of the charge, may be taken at first, and afterwards the remainder may be taken by sliding the wire nearer to the Jar. 414. Soon after the discovery of the Leyden Jar, commenced the application of Electricity to Medicine; and Medical Electricity, became ^henceforth a distinct branch of the science. The first cure said to have been effected by this agent, was upon a paralytic. Electricity shortly became very celebrated for the cure of this dis- order, and patients flocked in great numbers to the practitioners of CAUSE OF ELECTRICAL PHENOMENA. 223 this branch of the profession. As usual, the effects of this new remedy were greatly exaggerated, and it was widely extolled, not only for the cure of palsy, but of all other diseases. It was even pretended that the virtues of the most valuable medicines might be transferred into the system through the medium of electricity, pre- serving their specific properties in the same manner as when taken by way of the stomach. Preparations of this kind were called Medicated Tubes. Pavati, an Italian, and Winkler, a German, were especially celebrated for this species of practice. The mode was to enclose the medicines in a glass tube, then to excite the tube, and with it to electrify the patient. In this way, it was said, the healing virtues of the medicines were communicated to the system in a manner at once efficacious and agreeable. 415. Pretensions so extravagant could not long be sustained, and the natural consequence was that the use of electricity in medicine soon fell into great neglect, and has remained in this situation to the present time. There are, however, certain properties inherent in this agent, which deserve the attention of the enlightened physician, and inspire the hope that, in judicious hands, it may still be auxiliary to the healing art. First, the great activity of this agent, particular- ly the facility and energy with which it can be made to act upon the nervous system, indicate that it has naturally important relations to medicine. The power of being applied, locally, to any part of the system, renders it a convenient application in cases where other local remedies cannot be administered. Secondly, the acknowledged property of electricity to promote the circulation of fluids through capillary tubes, Art. 385. (7.) suggests the probability of its being efficacious in promoting the circulation of the fluids of the animal sys- tem, and in increasing the quantity of insensible perspiration. Thirdly, in the history of medical electricity are recorded well attested cures, effected by means of electricity, of such diseases, as palsy, rheumatism, gout, indolent tumors, deafness, and A variety of other disorders. Cause of Electrical Phenomena. 416. For the sake of convenience, and for the purpose of avoid- ing repetition and circumlocution, we have made occasional use of the phrase electric fluid. It may be proper now to inquire whether 224 . ELECTRICITY. there are any just grounds for supposing such a fluid or fluids to be present in electrical phenomena. There are two modes by which the existence of such a fluid may be rendered probable : the first is, by showing that such a supposi- tion is conformable to the analogy of nature ; the second is, by prov- ing that the agent of electrical phenomena exhibits the properties of a fluid. 417. First, there are some reasons derived from analogy for believ- ing in the existence of an electric fluid. (1.) The reasons in favor of supposing the light and heat are caused by the agency of peculiar fluids, (arguments, however, that we cannot discuss here,) which have induced a general belief, are for the most part equally applicable to electricity. (2.) In the present state of our knowledge, the most subtile of all fluids, indeed the most attenuated form of matter, is hy- drogen gas, of which one hundred cubic inches weigh only two and a quarter grains, which is nearly fourteen times lighter than common air. But at no distant period, means had not been devised by mankind for proving the materiality of common air, nor even of identifying the existence of the other gases which now bear so conspicuous a part in experimental philosophy. But as knowledge and experimental researches have advanced, a series of fluids still more subtile than air, have come to light, until we have reached a body nearly fourteen times lighter than air, at which, at present, the series stops. Is it probable, however, that nature stops in her processes of attenuation precisely at the point where, for want of more delicate instruments, or more refined and powerful organs of sensation, our methods of investigation, and powers of discrimination, come to their limit ? An examination of the general analogies of nature, will lead us to think otherwise. The subordination which exists among the different classes of bodies that compose the other departments of nature, is endless, or at least indefinite. In the animal creation, for example, beginning with the mammoth or the elephant, we descend through numerous tribes to the insect which is barely visible in the sunbeam. Before Jjuman ingenuity had devised means of aiding the powers of vision, the naturalist might have fixed this as the limit of the animal creation. But the invention of the microscope has carried the range of human vision immeasurably farther; and at each successive im- CAUSE OF ELECTRICAL PHENOMENA. provement in that instrument, new tribes of insects or animalcules have been revealed to the eye, still more and more attenuated. A similar subordination might be found in the vegetable kingdom, and in the organic structure of both animals and vegetables. To apply this analogy to the case before us, we begin the series of inorganic bodies with platinum, and descend through classes of bodies constantly diminishing in density, until we come to ether, the lightest of liquids, and on the confines of those bodies which are invisible to the eye, and manifested only by the effects which they produce. By modern discoveries the series has been extended to hydrogen, a body 247000 times lighter than platinum. Here for the present we pause, standing in the same relation with respect to any fluids that may lie beyond, that the ancients stood with respect to common air, and all the other aeriform fluids. Considerations of this nature lead us to believe that there are> in nature, fluids more subtile than hydrogen ; and, such being the fact, we can hardly resist the belief, that Heat, Light and Electricity, are bodies of this class, bodies which make themselves known to us by the most palpable and energetic effects, although their own constitu- tion is too subtile and refined for our organs to recognise, or our in- struments to identify them as material. 418. Secondly, in addition to the foregoing presumptions, in favor of the supposition that electricity is a peculiar fluid, it exhibits in itself the properties of a fluid. The rapidity of its motions, the power of being accumulated, as in the Leyden Jar, its unequal distribution over the surfaces of bodies, its power of being confined to the surfaces of bodies by the pressure of the atmosphere, its attractions and re- pulsions, are severally properties which we can hardly ascribe to any thing else than an elastic fluid of the greatest tenuity. But granting the presence of an elastic fluid in electrical phe- nomena, it remains to be determined whether, according to the hy- pothesis of Franklin, these phenomena are to be ascribed to the agency of a single fluid, or whether, according to that of Du Fay, they imply the existence of two distinct fluids. The numerous facts with which the learner has been made acquainted in the preceding pages, will fit him to appreciate the evidence offered in favor of or against these hypotheses respectively. 29 226 ELECTRICITY. 419. The principles of each hypothesis have been already ex- plained, (see Art. 373.) and they have been rendered familiar by repeated application. It will be recollected, that they concur in supposing that all bodies are endued with a certain portion of elec- tricity, called their natural share, in which the fluid, whether sin- gle or compound, is in a state of perfect equilibrium ; and that, in the process of excitation, this equilibrium is destroyed. But here the two views begin to diverge : the one supposes that this equi- librium is destroyed in consequence of the separation of two fluids, which, like an acid and an alkali combining to form a neutral salt, exactly neutralize each other by mutual saturation, but which, when separated, exhibit their individual properties; the other, that the equi- librium is destroyed, like that of a portion of atmospheric air. by great- er or less exhaustion on the one side, or condensation on the other. In the former case, moreover, the equilibrium is restored by the re- union of the two constituent fluids ; in the latter, by the movement of the redundant portion to supply the deficient, as air rushes into the exhausted receiver of an air pump. It is a remarkable fact, that nearly every electrical phenomenon, maybe perfectly explained in accordance with either hypothesis; nor is it agreed, that an experimentum crucis* has yet been found. 420. One of the latest advocates of the hypothesis of a single fluid is Mr. Singer, an able practical electrician, and the most dis- tinguished defender of the doctrine of two fluids is M. Biot. In support of the former doctrine, are offered such arguments as the following. (1.) Its greater simplicity. It is supposed to be more conformable to the Newtonian rule of philosophizing, " to ascribe no more causes than are just sufficient to account for the phenome- na." The known frugality of nature, in all her operations, might lead us to suppose, that she would not employ two agents to effect a given purpose, when a single agent would be competent to its pro- duction. This argument, however, cannot be applied, either where * The "experimentum crncis," is a phrase introduced by Lord Ba- con, implying a fact which can be explained on one of two opposite hypothesis, and not on the other. The figure is derived from a cross set up where two roads meet, to tell the traveller which road to take. CAUSE OF ELECTRICAL PHENOMENA. 227 one cause is not sufficient to account for the phenomena, or where there is direct proof of the existence of more agents than one. (2.) The appearance of a current, circulating from the positive to the negative surface, analogous to the passage of air of greater density into a rarefied space. This point is much insisted on by Singer, and numerous examples are brought forward, where the pro- gress of such a current is manifest to the senses. Thus, the flame of a candle, brought into the circuit between the inside and outside of a Leyden Jar, is, on the discharge of the Jar, bent towards the negative side ; a pith ball, under similar circumstances, moves in the same direction ; when a charged Jar is placed under the receiver of an air pump, and the air is exhausted, a luminous cloud flows from the positive to the negative side, in whichever way the Jar is electri- fied. None of these arguments, however, are found to be conclu- sive, for the mechanical effects, which are here ascribed to an elas- tic fluid, that is, the electric fluid, flowing towards the negative side, can all be accounted for, either upon the principles of attraction and repulsion, common to both hypotheses, or from the mechanical im- pulse of a current of air, which is known to be repelled from a point positively electrified. The electric spark passing instantaneously, or at least with a velocity entirely inappreciable, it is impossible to de- termine its direction. The fact that bodies negatively electrified repel each other, (Art. 374.) is a strong argument against the truth of the hypothesis under consideration. It is not difficult to conceive that a self repellent fluid should communicate the same property to two pith balls in which it ' resided ; but that the mere deficiency oCthe fluid should produce the same effect is incredible. This fact drove ^Epinus, (a celebrated German electrician, who brought this hypothesis to the test of Math- ematical demonstration,) to the necessity of supposing that unehctri- fied matter is self repellent, a supposition which is not only desti- tute of proof, but which is inconsistent with the general laws of nature, from which it appears that attraction and not repulsion exists mutu- ally between all kinds of bodies. In the distribution of electricity upon surfaces differing in shape and dimensions, the fluid is found to arrange itself in strict accordance with hydrostatic principles, and that too in bodies negatively as well as positively electrified. Now that the privation, or mere absence of a fluid, should exhibit such properties of a present fluid, is inconceivable. 228 ELECTRICITY. 421. In favor of the doctrine of two fluids the following arguments are urged. (1.) Two opposite currents are supposed to be some- times indicated. Thus, (Art. 405.) a card perforated by a strong electric discharge, exhibits burs or protrusions on both sides. The appearance of the electric spark, passing between two knobs, is sup- posed by some writers to indicate the meeting of two fluids from opposite parts. When the spark is short, the whole distance between the two knobs through which it passes, is illuminated. But when the spark is long, those portions of it which are nearest to the knobs, are much brighter than the central portions. Near the knobs the color is white, but towards the center of the spark it is purplish. Indeed, if the spark is very long, the middle part of it is not illuminated at all, or only very slightly. Now this imperfectly illuminated part, is obviously the spot where the two electricities unite, and it is in con- sequence of this union, that the light is so imperfect. (2.) The two electricities are characterized by specific differences. The light afforded by the vitreous surface is different from that of the resinous ; when the two opposite portions of the spark meet, as above, the place of meeting is only half the distance from the negative that it is from the positive side ; the bur protruded from the card is larger in the direction of the vitreous than in that of the resinous fluid ; and the two severally produce certain chemical effects in bodies which are peculiar to each. (3.) But the most conclusive argument in favor of two fluids, is the perfect manner in which this supposition accounts for the distribution of electricity on bodies of different dimensions. On the hypothesis that electrical phenomena are owing to the agencies of two fluids, both perfectly incompressible, the particles of ivhich possess perfect mobility, and mutually repel each other, while they attract those of the opposite fluid, with forces varying in the inverse ratio of the squares of the distances,- on this hypothesis, M. Poisson, a celebrated mathematician of France, applied the exhaustless re- sources of the calculus, to determine the various conditions which electricity would asswme in distributing itself over spheres, spheroids, and bodies of various figures. The results at which he arrived were such as accord in a very remarkable degree with experiment, and leave littkfdoubt that the hypothesis on which they were built must be true. Nor is any supposition involved in the hypothesis itself in- consistent with established facts. (4.) Finally, authority is, at the ATMOSPHERICAL ELECTRICITY. 229 present day, almost wholly on the side of the doctrine of two fluids, an opinion which has constantly gained new adherents with every new discovery in the science of electricity, particularly in the depart- ment of Galvanism. CHAPTER V. OF ATMOSPHERICAL ELECTRICITY. THUNDER STORMS. LIGHT- NING RODS. 422. Having learned the laws of electricity from a great variety of experiments, the student is now prepared to look upon the works of nature, and to study the phenomena which the same agent produces there on a most extensive scale. The atmosphere is always more or less electrified. This fact is ascertained by several different forms of apparatus. For the lower regions, it is sufficient to elevate a metallic rod a few feet in length, pointed at the top, and insulated at the bottom. With the lower ex- tremity is connected an electrometer, which indicates the presence and intensity of the electricity. For experiments on the electricity of the upper regions, a kite is employed, not unlike a boy's kite, with the string of which is intertwined a fine metallic wire. The lower end of the string is insulated by fastening it to a support of glass, or by a cord of silk. 423. The most powerful apparatus ever employed for atmospher- ical electricity, was constructed in France by M. de Romas. He procured a kite seven feet long and three feet wide, and elevated it to the height of five hundred and fifty feet. A cloud coming over, the most striking and powerful electrical phenomena presented them- selves. Light straws that happened to be on the ground near the string of the kite, began to erect themselves, and to perform a dance between the apparatus and the ground, after the manner of dancing images, as exhibited in ordinary electrical experiments. Art. 386. (5.) At length streams of fire began to dart to the ground, some of which were an inch in diameter, and ten feet long, exhibiting the most ter- rific appearance. The foregoing facts evince the abundance of electricity in the at- mosphere at particular period5 ; but experiments of a less forrnida- 230 ELECTRICITY. ble kind have been instituted, to ascertain the electrical changes of the air. For this purpose, Mr. Canton, an English philosopher, con- structed an ingenious apparatus which warned him of the presence of any unusual quantity of electricity, by causing it to ring a bell connected with the lower extremity of the apparatus. 424. Obvious as is the connection between the phenomena of com- mon electrical apparatus, and those exhibted in the heavens during a thunder storm, yet the identity of lightning with the electric spark, was not dreamed of by the earlier electricians. To Dr. Franklin, is universally conceded the merit of having established this fact, first by reasoning on just principles of analogy, and afterwards by actual- ly bringing down the lightning from the skies. The resemblance between the appearances of lightning and electricity, were thus enu- merated. (1.) The zigzag form of lightning corresponds exactly in appear- ance with a powerful electric spark, that passes through a considera- ble interval of air. (2.) Lightning most frequently strikes such bodies as are high and prominent, as the summits of hills, the masts of ships, high trees, towers, spires, &c. So the electric fluid, when striking from one body to another, always passes through the most prominent parts. (3.) Lightning is observed to strike most frequently into those sub- stances that are good conductors of electricity, such as metals, water, and moist substances ; and to avoid those that are non-conductors. (4.) Lightning inflames combustible bodies ; the same is effected by electricity. (5.) Metals are melted by a powerful charge of electricity : this phenomenon is one of the most common effects of a stroke of light- ning. (6.) The same may be observed of the fracture of brittle bodies. (7.) Lightning has been known to strike people blind : Dr. Frank- lin found, that the same effect is produced on animals, by a strong electric charge. (8.) Lightning destroys animal life : Dr. Franklin killed turkies of abotit ten pounds weight, by a powerful electric shock. (9.) The magnetic needle is affected in the same way by light- ning and by electricity,. and iron may be rendered magnetic by both ATMOSPHERICAL ELECTRICITY. 231 causes. The phenomena therefore are strictly analogous, and differ only in degree ; but if an electrified gun barrel will give a spark, and produce a loud report at two inches distance, what effect may not be expected from 10,000 acres of electrified cloud ? But (said Frank- lin,) to ascertain the accuracy of these ideas, let us have recourse to experiment. Pointed bodies receive and transmit electricity with facility; let therefore a pointed metal rod be elevated into the atmos- phere, and insulated ; if lightning is caused by the electricity of the clouds, such an insulated rod will be electrified whenever a cloud passes over it ; this electricity may be then compared with that ob- tained in our experiments. 425. Such were the suggestions of this admirable philosopher; they soon excited the attention of the electricians of Europe, and having attracted the notice of the King of France, the approbation he ex- pressed excited in several members of the French Academy, a de- sire to perform the experiment proposed by Franklin, and several in- sulated metallic rods were erected for that purpose. On the 10th of May, 1752, one of these, a bar of iron forty feet high, situated in a garden at Marly, became electrified during the passage of a stormy cloud over it; and during a quarter of an hour, it afforded sparks, by which jars were charged, and other electrical experiments per- formed. During the passage of the cloud, a loud clap of thunder was heard, so that the identity of these phenomena was thus com- pletely proved. Similar experiments were made by several electri- cians in England. *426. Doctor Franklin had not heard of these experiments, and was waiting for the erection of a spire at Philadelphia to admit an op- portunity of sufficient elevation for his insulated rod, when it occur- red to him that a kite would obtain more ready access to the re- gions of thunder than any elevated building. He accordingly ad- justed a silk handkerchief to two light strips of cedar, placed cross- wise ; and having thus formed a kite, with a tail and loop, at the ap- proach of the first storm, he repaired to a field accompanied by his son. Having launched his kite with a pointed wire fixed to it, he waited its elevation to a proper height, and then fastened a key to the end of the hempen cord, and attached this by means of a silk 232 ELECTRICITY. lace (which served to insulate the whole apparatus) to a post. The first signs of electricity which he perceived, was the separation of the loose fibres of the hempen cord : a dense cloud passed over the ap- paratus, and some rain falling, the string of the kite became wet ; the electricity was then collected by it more copiously, and a knuckle being presented to the key, a stream of acute and brilliant sparks was obtained. With these sparks, spirits were fired, jars charged, and the usual electrical experiments performed. Thus was the iden- tity of lightning and electricity, which had been indicated by so many analogies, now established by the most decisive experiments. 427. It is a matter of much importance to the science of Meteo- rology, (Art. 316.) to ascertain from what source atmospherical electricity originates. Among the known sources of this agent none seems so probable, as the evaporation and condensation of watery vapor. We have the authority of two of the most able and accurate philosophers, Lavoisier and La Place, for stating that bodies' in pass- ing from the solid or liquid state to that of vapor, and, conversely, in returning from the aeriform condition to the liquid or solid state, give unequivocal signs of either positive or negative electricity* Combustion is also attended with the evolution of electricity, and even the friction of opposite currents of wind, or of a high wind against opposing objects, probably generates more or less of the same agent. The production of electricity during evaporation and con- densation may be rendered evident by delicate instruments ; as may that evolved during the friction of air. If the stem of a tobacco pipa be heated red hot, and a drop of water be introduced by way of the bowl, the jet of steam falling on a delicate electrometer, will indi- cate the presence of electricity. It is obvious that a cause which produces only very feeble signs of electricity, in so small a quantity of vapor as that which arises from a single drop of water, may still be sufficient to occasion a vast accu- mulation of the same agent, in such a quantity of vapor as that which is daily ascending into the atmosphere. For it has been calculated, that *oiore than two thousand millions of hogsheads of water are evap- orated from the Mediterranean alone in one summer's day. THUNDER STORMS. 233 Thunder Storms. 428. The following are the leading facts respecting the electricity of the atmosphere in relation to this subject, and these are facts which have been established by numerous observers, of the most accurate and diligent class. Beccaria, an Italian electrician, continued his ob- servations on the electricity of the atmosphere for fifteen years with the greatest assiduity ; and Cavallo, Read, Saussure, and others, prosecuted the same inquiries with similar zeal. (1.) Thunder clouds are, of all atmospheric bodies, the most high- ly charged with electricity. But all single, detached, or insulated clouds, are electrified in greater or less degrees, and sometimes posi- tively and sometimes negatively. When, however, the sky is com- pletely overcast with a uniform stratum of clouds, the electricity is much feebler, than in the single detached masses before mentioned. And, since fogs are only clouds near the surface of the earth, they are subject to the same conditions ; a driving fog of limited extent, is often highly electrified. (2.) The electricity of the atmosphere is strongest when hot weath- er succeeds a series of rainy days, or when wet weather succeeds a series of dry days ; and during any single day, the air is most elec- trical when the dew falls before sunset, or when it begins to exhale before sunrise. (3.) In clear steady weather, the electricity generally remains pos- itive ; but in falling or stormy weather, it is constantly changing from positive to negative, or from negative to positive. Such are the circumstances of atmospheric electricity in general ; next, let us attend to the peculiar phenomena of thunder storms, chiefly as they are exhibited in our own climate. (1.) In thunder storms there is usually a singular and powerful combination of all the elements, of darkness, rain, thunder and light- ning, and sometimes hail. (2.) They occur chiefly in the hottest season of the year, and after mid-day ; and are more frequent and violent in warm, than in cold coutries. (3.) In this State (Connecticut,) thunder storms usually come from the west, either directly, or from the north-west or south-west ; but occasionally from the east. 30 234 ELECTRICITY. (4.) Violent thunder and lightning are frequently seen in volcanoes and water spouts. (5.) Thunder storms sometimes descend almost to the surface of the sea, and fall upon the sides of mountains ; in which case, they are extremely violent. (6.) We occasionally observe the following circumstances succeed each other in regular order : first, a vivid flash of lightning, then a loud peal of thunder, and, after a short interval, a sudden fall of rain, which sometimes stops as suddenly as it began. 429. There are in thunder storms evidently two distinct classes of phenomena to be accounted for. The first class consists of the com- mon elements of a storm, clouds, wind, and rain ; the second, of thunder and lightning. The following proposition embraces, in our view, the true explanation of both these classes of phenomena : The storm itself, including every thing except the electrical appear- ances, is produced in the same manner as other storms of wind and rain ; and the electricity, and of course the thunder and lightning, is owing to the rapid condensation of watery vapor. We do not, therefore, consider electricity as the cause, but as the consequence of the storm ; or as a concomitant of the clouds, wind, and rain. Lightning Rods. 430. Dr. Franklin had no sooner satisfied himself of the identity of electricity and lightning, than, with his usual sagacity, he conceiv- ed the idea of applying the knowledge acquired of the properties of the electric fluid, so as to provide against the dangers of thunder storms. The conducting power of metals, and the influence of pointed bodies, to collect and transmit the fluid, naturally suggested the structure of the Lightning Rod. The experiment was tried and has proved completely successful ; and probably no single application of scientific knowledge ever secured more celebrity to its author. tf 431. Lightning rods are at present usually constructed of wrought iron about three fourths of an inch in diameter. The parts may be made separate, but, when the rod is in its place, they should be LIGHTNING RODS. 235 screwed together so as to fit closely, and to make a continuous sur- face, since the fluid experiences much resistance in passing through links and other interrupted joints. At the bottom the rod should ter- minate in two or three branches, going off in a direction from the building. The depth to which it enters the earth should not be less than five feet ; but the necessary depth will depend somewhat on the nature of the soil : wet soils require a less, and dry soils a greater depth. In dry sand it must not be less than ten feet ; and in such situations, it would be better still to connect, by a convenient conduc- ting communication, the lower end of the rod with a well or spring of water. It is useful to fill up the space around the part of the rod that enters the ground, with coarsely powdered charcoaal, which at once furnishes a good conductor, and preserves the metal from corrosion. The rod should ascend above the ridge of the building to a height determined by the following principle : that it will protect a space in every direction from it, whose radius is equal to twice its height. It is best, when practicable, to attach it to the chimney ; which needs peculiar protection, both on account of its prominence, and because the products of combustion, smoke, watery vapor, &LC. are conduc- tors of electricity. For a similar reason a kitchen chimney, being that in which the fire is kept during the^ season of thunder storms, requires to be especially protected. The rod is terminated above in three forks, each of which ends in a sharp point. As these points are liable to have their conducting power impaired by rust, they are protected from corrosion by being covered with gold leaf; or they may be made of solid silver or platina. Black paint being made of charcoal, it forms a better coating for the rod than paints made of other colors, the bases of which are worse conductors. The rod may be attached to the building by wooden stays. Iron stays are sometimes employed, and in most cases they would be safe, since electricity pursues the most direct route ; but in case of an extraordi- nary charge, there is danger that it will divide itself, a part passing into the building through the bolt, especially if this terminates in a point. Buildings furnished with lightning rods have occasionally been struck with lightning ; but on examination it has generally, if not al- ways, been found that the structure of the rod was defective ; or that too much space was allotted for it to protect. When the fore- going rules are observed the most entire confidence may be reposed in this method of securing safety in thunder storms. 236 ELECTRICITY. CHAPTER VI. PRECAUTIONS FOR SAFETY DURING THUNDER STORMS ANIMAL ELECTRICITY CONCLUDING REMARKS. 432. The great number of pointed objects that rise above the gen- eral level, in a large city, have the effect to dissipate the electricity of a thunder cloud, and to prevent its charge from being concentrated on any single object. Hence damage done by lightning is less fre- quent in a populous town, than in solitary buildings. For similar reasons, a great number of ships, lying at the docks, disarm the light- ning of its power, and thus avert the injury to which the form of their masts would otherwise expose them. A solitary ship on the ocean unprotected by conductors, would appear to be peculiarly in danger from lightning ; but while the greater number of ships that traverse the ocean are wholly unprotected, accidents of this kind are comparatively rare. The reason probably is, that water being a bet- ter conductor than wood, the course of the discharge towards the water is not easily diverted, and will not take the mast in its way un- less the latter lies almost directly in its course. Barns are peculiarly liable to be struck with lightning, and to be set on fire ; and as this occurs at a season when they are usually filled with hay and grain, the damage is more serious, for the quantity of combustible matter they contain is such as to render the fire unmanageable. 433. Silk dresses are sometimes worn with the view of protec- tion by means of the insulation they afford. They cannot, however, be deemed very effectual unless they completely envelop the person ; for if the head and the extremities of the limbs be exposed, they will furnish so many avenues to the fluid as to render the insulation of the other parts of the system of htlle avail. The same remark applies to the supposed security that is obtained by sleeping on a feather bed. Were the person situated within the bed, so as to be entirely enveloped by the feathers, they would afford some protec- tion ; but if the person be extended on the surface of the bed, in the usual posture, with the head and feet nearly in contact with the bedsted, he would rather lose than gain by the non-conducting prop- erties of the bed ; since, being a better conductor than the bed, the charge would pass through him in preference to that. The horizon- SAFETY DURING THUNDER STORMS. 237 tal posture, however, is safer than the erect ; and if any advantage on the whole is gained by lying in bed during a thunder storm, it probably arises from this source. The same principle suggests a reason why men or animals are so frequently struck with lightning when they take shelter under a tree during a thunder storm. The fluid first strikes the tree, in consequence of its being an elevated and pointed object, but it deserts the tree on reaching the level .of the man or animal, because the latter is a better conductor than the tree. Tall trees situated near a dwelling house, furnish a partial protec- tion to the building, being both better conductors than the materials of the house, and having the advantage of superior elevation. 434. The protection of chimneys is of particular importance, for to these a discharge is frequently determined. When a fire is burn- ing in the chimney, the vapor, smoke, and hot air, which ascend from it furnish a conducting medium for the fluid ; but even when no fire is burning, the soot that lines the interior of a chimney, is a good con- ductor, and facilitates the passage of the discharge. It is quite essential, during a thunder storm, to avoid every con- siderable mass of water, and even the streamlets that have resulted from a recent shower ; for these are all excellent conductors, and the height of a human being, when connected with them, is very likely to determine the course of an electric discharge. The partial con- ductors, through which the lightning directs its course, when it enters a building, are usually the appendages of the walls and partitions ; the most secure situation is therefore the middle of the room, and this situation may be rendered still more secure by standing on a glass legged stool, a hair mattress, or even a thick woollen rug. The part of every building least liable to receive injury, is the middle story, as the lightning does not always pass from the clouds to the earth, but is occasionally discharged from the earth to the clouds. Hence it is absurd to take refuge in a cellar, or in the lowest story of a house ; and many instances are on record in which the basement story has been the only part of the building that has sustained severe injury. Whatever situation be chosen, any approach to the fire place should be particularly avoided. An open door or window is an un- safe situation, because the lightning is apt to traverse the large tim- 238 ELECTRICITY. bers that compose the frame of the house, and would be determined towards the animal system on account of its being a better conductor. In a carriage the passenger is safer in the central part than next to the walls ; but a carriage may be effectually protected by attaching to its upper surface metallic strips connected with the wheel tire. The fillets of silver plating which are frequently bound round the carriage, may be brought into the conducting circuit. Animal Electricity. 435. Of the natural agencies of electricity, one of the most re- markable, is that exhibited by certain species of fish, especially the Torpedo and the Gymnotus. This peculiar property of the Torpe- do was known to the ancient naturalists, and is accurately described by Aristotle and by Pliny. Aristotle says that this fish causes or pro- duces a torpor upon those fishes it is about to seize, and having by that means got them into its mouth, it feeds upon them. Pliny says that this fish, if touched by a rod or spear, even at a distance, para- lyzes the strongest muscles. 436. The fact, however, that this extrordinary power depended upon electricity, was not known until about the year 1773, when it was ascertained by Mr. Walsh, that the Torpedo was capable of giv- ing shocks to the animal system, analogous to those of the Leyden Jar. Though this property is regarded as establishing the identity of the power with the electric fluid, yet this power, as developed in the Torpedo, has never been made to afford a spark, nor to produce the least effect upon the most delicate electrometer. As late as the year 1828, experiments were made upon the Torpedo, by Sir Humphry Davy, and the conclusions to which he arrived, were that the electri- city resides in this animal in a form suited exclusively to the purpose of communicating shocks to the animal system, while it has little or nothing else in common with the properties of electricity, as develop- ed in various artificial arrangements. The Torpedo is a flat fish, seldom twenty inches in length, but one fouE^J on the British coast was four and a half feet long. The elec- tricity of the Torpedo has the same relation as common electricity to bodies in respect to their conducting power, being readily transmitted through metals, water, and other conductors, and not being transmit- ted through glass, and other non-conductors. ANIMAL ELECTRICITY. 239 437. The electric organs of the Torpedo are two in number, and placed one on each side of the cranium and gills. The length of each organ is somewhat less than one third part of the length of the whole animal. Each organ consists of perpendicular columns reaching from the under to the upper surface of the body, and varying in length according to the various thickness of the flesh in different parts. The number of these columns are not constant, being not only different in different Torpedos, but likewise in different ages of the animal, new ones seeming to be produced as the animal grows. In a very large Torpedo, one electric organ has been found to consist of one thousand one hundred and eighty two columns. The diameter of a column is about one fifth of an inch. Each column is divided by hori- zontal partitions, consisting of transparent membrane, placed over each other at very small distances, and forming numerous inter- stices, which appear to contain a fluid. The number of partitions contained in a column one inch in length, has been found in some in- stances not less than one hundred and fifty. By this arrangement, the amount of electrified surface is exceedingly great ; equivalent, in one instance, to one thousand and sixty four feet of coated glass. Hence, the effects of the electricity of the Torpedo are such as cor- respond to those which, in artificial arrangements, are produced by diffusing a given quantity of fluid over a great surface, by which its intensity is much diminished. 438. The Gymnotus, or Surinam eel, is found in the rivers of South America. It ordinary length is from three to four feet ; but they are said to be sometimes twenty feet long, and to give a shock that is instantly fatal. The electrical organs of the Gymnotus, con- stitute more than one third part of the whole animal ; they consist of two pairs, of different sizes and placed on different sides. The shock communicated to fishes instantly paralyzes them, so that they become the prey of the Gymnotus. By irritating the animal with one hand while the other is held at some distance in the water, a shock is received, as severe as that of the Leyden Jar. Unlike the Torpedo, the Gymnotus gives a small but perceptible spark, affording additional proof of the identity of the power with that of electricity. 240 ELECTRICITY. JVL Humboldt, in his travels in South America, describes a sin- gular method of catching the Gymnotus, by driving wild horses into a lake which abounds with them. The fish are weaned or exhaust- ed by their efforts against the horses, and then taken ; but such is the violence of the charge which they give, that some of the horses are drowned before they can recover from the paralyzing shocks of the eels. The Silurus electricus, is a fish found in some of the rivers of Africa. Its electrical powers are inferior to those of the Torpedo and Gymnotus, but they are still sufficient to give a distinct shock to the human system. 439. Certain furred animals, particularly the cat, become sponta- neously electrified. This is more especially observable on cold windy nights, when the state of the air is favorable to insulation. At such times a cat's back will frequently afford electrical sparks. Ancient historians mention a number of very remarkable occurrences, of good or evil omen, which are due to the electricity of the atmosphere. Herodotus informs us that the Thracians disarmed the sky of its thunder, by throwing their arms into the air ; and that the Hyperbo- reans produced the same effect, by launching among the clouds darts armed with points of iron. Caesar in his Commentaries, says that in the African war, after a tremendous storm which threw the whole of the Roman army into great disorder, the points of the darts of a great number of the soldiers shone with a spontaneous light. In the month of February (says he) about the second watch of the night, there sud- denly arose a great cloud, followed by a dreadful storm of hail, and in the same night the points of the darts of the fifth legion appeared on fire. During a dry snow storm, when electricity is evolved in great quan- tities, and, on account of the dry state of the air, is partially insula- ted on conducting bodies, similar appearances are exhibited. Thus the ears of horses and various pointed bodies emit faint streams of light. These phenomena are sometimes exhibited in a most striking manner in a storm at sea, when the masts of a ship, yard arms, and every other pointed object are tipped with lightning. CONCLUDING REMARKS. Concluding Remarks. 440. From the energy which electricity displays in our experi- ments, and much more in thunder storms, there can be no question that it holds an important rank among the ultimate causes of natural phenomena. Its actual agencies, however, are liable to be misinter- preted, and that they have been so in fact, is too manifest from the history of the science. After the splendid experiments with the Leyden Jar, and more especially, after the indentity of electricity with lightning had been proved, electricians fancied that they had dis- covered the clue which would conduct them safely through the laby- rinth of nature. Every thing not before satisfactorily accounted for, was now ascribed to electricity. They saw in it not only the cause of thunder storm, but of storms in general ; of rain, snow, and hail ; of whirlwinds and water spouts ; of meteors and the aurora borealis ; and finally, of tides and comets and the motions of the heavenly bodies. Later electricians have found in the same agent the main spring of animal and vegetable life, and the grand catholicon which cures all diseases. Recent attempts have been made to establish the very identity of galvanic electricity and the nervous influence, by which the most important functions of animal life are controlled. Among the most important of the agencies of electricity in the economy of nature, is that which, according to the views of Sir Humphry Davy, it sustains in relation to the chemical agencies of bodies. Chemical and electrical attraction, he supposes, are one and the same thing, or at least dependent on the same cause, the at- traction between the elements of a compound arising solely from their being naturally in opposite electrical states. But the discus- sion of this hypothesis belongs more appropriately to Galvanism, at branch of our subject which on account of its peculiarities, especial- ly in the mode of excitation, has been constituted a separate depart- nientof science. 242 PART V.- GENERAL PRINCIPLES. 44 J. MAGNETISM is the science which treats of the properties and effects of the magnet. The same term is also used to denote the unknown cause of magnetic phenomena ; as when we speak of mag- netism as excited, imparted, and so on. Magnets are bodies, either natural or artificial, which have the property of attracting iron, and the power, when freely suspended, of taking a direction towards the poles of the earth. The natural magnet is sometimes called the loadstone.* It is an oxide of iron of a peculiar character, found occasionally in beds of iron ore. Though commonly met with in irregular masses only a few inches in diameter, yet it is sometimes found of a much larger size. One recently brought from Moscow to London, weighed one hun- dred and twenty five pounds, and supported more than two hundred pounds of iron. 442. The attractive powers of the loadstone have been known from a high antiquity, and are mentioned by Homer, Pythagoras, and Aristotle. But the directive powers were not known in Europe, un- til the thirteenth century, when they were discovered by a Neapolitan named Flavio; though some writers have endeavored to trace the his- tory of the compass needle to a remoter period, and some have stren- uously maintained that the Chinese were in possession of it many centuries before it was known to Europeans. Magnetism is the most recent of all the physical sciences, and not- withstanding the numerous discoveries achieved in it within a few years, and the remarkable precision with which its laws have been ascertained, yet it is still to be regarded as a science quite in its in- fancy, although it is rapidly progressive. V * SaiJ to be derived from Icedan, a Saxon word which signifies to guide. GENERAL PRINCIPLES. 243 443. If a magnet be rolled in iron filings, it will attract them to itself. This effect takes place especially at two opposite points, where a much greater quantity of the filings will be collected than in any other parts of the body. The two opposite points in a mag- net,- where its attractive powers ap- Fig. 86. pear chiefly to reside, are called its poles. The straight line which joins the poles, is called the axis. If a large sewing needle or small bar of steel be rubbed on the loadstone, one extremity on one pole, and the other extremity on the other, the needle or bar will itself become a magnet, capable of exhibiting all the properties of the loadstone. Without staying at present to describe more minutely the process of making artificial magnets, we will suppose ourselves provided with several magnetic needles and bars, and we may proceed with them to study the leading facts of the science of magnetism. By attaching a fine thread to the middle of a needle, and suspending it so as to move freely in a hori- zontal plane ; or by resting it on a point, as is represented in figure 87, we shall have ~ a simple and convenient apparatus for nu- merous experiments. The needle thus sus- pended will place itself in a direction near- ly, though not exactly, north and south. If the needle is drawn out of the positiqn it assumes when at rest it will vibrate on either side of that position until it finally settles in the same line as before, one pole always returning towards the north, and the other towards the south. Hence the two poles are denominated re- spectively north and south poles. In magnets prepared for experi- ments, these poles are marked either by the letter N and S, or by a line drawn across the magnet near one end, which denotes that the adjacent pole is the north pole. 444. By means of the foregoing apparatus we may ascertain that the magnet has the following general properties, viz. First, powers of attraction and repulsion. , Secondly, the power of communicating magnetism to iron or steel by induction. Thirdly, polarity or the power of taking a direction towards the poles of the earth. 244 MAGNETISM, Fourthly, the power of inclining itself towards a point below the horizon, usually denominated the dip of the needle. The farther developement of these properties will constitute the subjects of the following chapters. CHAPTER I. OF MAGNETIC ATTRACTION. 445. When either pole of a magnet is brought near to a piece of iron, a mutual attraction takes place between them. Thus, when the ends of a magnetic bar or needle are dipped into a mass of iron filings, these adhere in a cluster to either pole. A bar of soft iron, or a piece of iron wire, resting on a cork, and floating on the surface of water or quicksilver, may be led in any direction by bringing near to it one of the poles of a magnet. This action is moreover reciprocal, that is, the iron attracts the magnet with the same force that the magnet attracts the iron. If the two bodies be placed on separate corks and floated, they will approach each other with equal momenta ; or if the iron be held fast, the magnet will move towards it. 446. Two other metals beside iron, namely, nickel and cobalt, are susceptible of magnetic attraction. These metals, however, ex- ist in nature only in comparatively small quantities, and therefore by magnetic bodies, are usually intended such as are ferruginous. Even iron, in some of its combinations with other bodies, loses its magnetic properties ; only a few of the numerous ores of iron are attracted by the magnet. But soft metallic iron, and some of the ores of the same metal, affect the needle even when existing in exceedingly small quantities, so that the magnet becomes a very delicate test of the pres- ence of iron. Compass needles are sometimes said to be disturbed by the minute particles of steel left in the dial plate by the graver ; and the proportion of iron in some minerals may be exactly estima- ted by the power they exert upon the needle. *' 447. In the action of magnets on each other, poles of the same name repel, those of different names attract each other. MAGNETIC ATTRACTION. 245 Thus the north pole of one magnet will repel the north pole of the other, and attract its south pole. The south pole of one will repel the south pole of the other and attracts its north pole. These effects it will be perceived, are analogous to those produced by the two spe- cies of electricity ; and they equally imply two species of magnetism or two magnetic fluids (as it is convenient to call them) namely, the northern, and the southern, or as they are now denominated the bo- real and the austral fluids. 448. By bringing a magnet near to iron or steel, the latter is ren- dered magnetic by Induction. Thus, let the north pole of a Fi S- 88 > magnetic bar A, (Fig. 88.) be brought near to one end of an un- magnetized bar of soft iron B : the iron will immediately become it- self a magnet, capable of attracting iron filings, having polarity when suspended and possessing the power of communicating the same properties to other pieces of iron. It is, however, only while the iron remains in the vicinity of the magnet, that it is endued with these pro- perties ; for let the magnet be withdrawn and it loses at once all the foregoing powers. This, it will be remarked is asserted of soft iron ; for steel and hardened iron are differently affected by induced mag- netism. On examining the kind of magnetism induced upon the two ends of the iron bar B, (Fig. 88.) which we may easily do by bringing near it the poles of the needle, (Fig. 87.) we shall find that the near- er end has south, and the remoter end north polarity. This effect also is analogous to that produced by electrical induction. A corres- ponding effect would have taken place, had the south instead of the north pole of the magnet been presented to the bar of iron ; in which case the nearer end would have exhibited northern, and the re- mote end southern polarity. Or, to express this important proposi- tion in general terms, Each pole of a magnet induces the opposite kind of polarity in that end of the iron which is nearest to it, and the same kind in that end which is most remote. 2445 MAGNETISM. 449. The power of a magnet is increased, by the exertion of its in- ductive power upon a piece of iron in its neighborhood. The end of the piece of iron contiguous to the pole of the mag- net, is no sooner endued with the opposite polarity, than it re-acts upon the magnet and increases its intensity, and a series of actions and re-actions take place between the two bodies, similar to what oc- curs in electrical induction. On this account the powers of a mag- net are increased by action, and impaired or even lost by long disuse. By adding, from time to time, small pieces of iron to the weight ta- ken up by a magnet, its powers may be augmented greatly beyond their original amount. Hence, the force of attraction of the dissim- ilar poles of two magnets, is greater than the force of repulsion of the similar poles ; because, when the poles are unlike, each contri- butes to enhance the power of the other, but when they are alike, the influence which they reciprocally exert, tends to make them un- like, and of course to impair their repulsive energies. Hence, also a strong magnet has the power of reversing the poles of a weak one. Suppose the north pole of the weaker body to be brought into contact with the north pole of the stronger ; the latter will expel north polarity, or the boreal fluid, and attract the austral, a change which in certain cases will be permanent. If the north pole of a magnetic bar be placed upon the middle of an iron bar, the two ends of the latter will each have north polarity while the part of the bar immediately in contact with the magnet re- ceives south polarity ; and if the same north pole be placed on the center of a circular piece of iron, all parts of the circumference will be endued with north polarity while the plate will have a south pole in the center. By cutting the plate into the form of a star, each ex- tremity of the radii becomes a weak north pole when the north pole of a magnet is placed in the center of the star. If an iron bar is placed between the dissimilar poles of two magnetic bars, both of the magnets will conspire to increase the intensity of each pole of the bar and the magnetism imparted to the bar will be considerably stronger than, from either magnet alone; but if the same bar be placed between the two similar poles, the opposite polarity will be imparted to each end, while the same polarity is given to the center of the bar. Thus if the bar be placed between the north poles of two magnets, each MAGNETIC ATTRACTION. 247 end of the bar will become a south pole and the center a north pole. When one end of a magnetic bar is applied to the ends of two or more wires or sewing needles, the latter arrange themselves in radii diverging from the magnetic pole. This effect is in consequence of their remoter ends becoming endued with similar polarity, and repel- ling each other. A like effect is observable among the filaments of iron filings, that form a tuft on the end of a magnetic bar. 450. The foregoing experiments are sufficient to show that when a piece of iron is attracted by the magnet, it is first itself converted into a magnet by the inductive influence of the magnetising body. Each of the iron filings which compose the tuft at the pole of a mag- netic bar or needle, is itself a magnet and in consequence of being such, induces the same property in the next particle of iron, and that in the next, and so on to the last. Hence magnetic attraction does not exist, strictly speaking, between a magnet and iron, but only be- tween the opposite poles of magnets ; for the iron must first become a magnet before it is capable of magnetic influence. 451. Soft iron readily acquires magnetism and as readily loses it ; hardened steel acquires it more slowly, but retains it permanently. In the preceding examples, the magnetism acquired by a bar of iron, by the process of induction, is retained only so long as the mag- netising body acts upon it. Soon after the two bodies are separated the bar loses all magnetic properties. When a bar of steel is placed very near a strong magnet, the ac- tion of the magnet commences immediately upon the end of the bar nearest to it, the north pole for example communicating south polarity to the contiguous extremity of the bar. According to our previous experience, we should expect to find the remote end of the bar a north pole ; but such is not the immediate result ; a sensible time is required before the north polarity is fully imparted to the remote ex- tremity. Indeed if the bar be a long one, it sometimes happens that the northern polarity never reaches the farthest end, but stops short of it at some intermediate point. This north pole is succeeded by a second south pole, that by another north pole, and thus several alternations between the two poles occur before reaching the end of the bar. 243 MAGNETISM. 452. The process of magnetizing a steel bar or needle is accelera- ted by any cause which excites a tremulous or vibratory motion among the particles of the steel. Striking on the bar with a ham- mer promotes the process in a remarkable degree, especially if it oc- casions a ringing sound, which indicates that the particles are thrown into a vibratory motion. The passage of an electric discharge through a steel bar under the influence of a magnet, produces permanent magnetism. Heat also greatly facilitates the introduction of the magnetic fluid into steel. The greatest possible degree of magnet- ism that can be imparted to a steel bar is communicated by first heating the steel to redness, and while it is under the influence of a strong magnet, quenching it suddenly with cold water. A magnet, however, loses its virtues by the same means as, du- ring the process of induction, were used to promote their acquisition* Accordingly any mechanical concussion, or rough usage impairs or destroys the powers of a magnet. By falling on a hard floor, or by being struck with a hammer it is greatly injured. Heat produces a similar effect. A boiling heat weakens and a red heat totally de- stroys the power of a needle. On the other hand, cold augments the powers of the magnet ; indeed they improve with every reduction of temperature hitherto applied to them. 453. If a steel bar, rendered magnetic by induction, be divided into any two parts, each part will be a complete magnet, having two opposite poles. We here meet with a remarkable distinction between magnetic and electric induction. When a body electrified by induction, is di- vided into two equal parts, -the individual electricities alone remain in each part respectively ; but in the case of magnetic induction, al- though no appearance of polarity be exhibited except at the two ends, yet wherever a fracture is made, the two ends separated by the fracture immediately exhibit opposite polarities, each being of an op- posite name to that of the original pole at the other end of the frag- ment. If each of the two fragments be again divided into any num- ber of*parts, each of these parts is a magnet perfect in itself, having two opposite poles. In magnetism therefore, there is never as in electricity, any trans- fer of properties, but only the excitation of such as were already in- MAGNETIC ATTRACTION. 249 herent in the body acted upon. Magnetism never passes out of one body into another ; nor can we ever obtain a piece of iron or steel that contains exclusively either northern or southern polarity. 454. The force of attraction, or of repulsion, exerted upon each other by the poles of two magnets, placed at different distances, varies inversely as the square of the distance. This law was ascertained by means of a very delicate appara- tus, in a manner similar to that adopted in investigating the law of electrical attraction. The same law, therefore, which governs the attraction of gravitation, likewise controls electrical and magnetic at- tractions. It is the most extensive law of the physical world. Nor is this action at a distance prevented, or even impaired, by the inter- position of other bodies not themselves magnetic. 455. The magnetic power of iron resides wholly on its SURFACE, and is independent of the mass. Thus, a hollow globe of iron of a given surface, will have the same effect on the needle as though it were solid throughout. In this fact we again meet with a striking analogy between magnetism and elec- tricity, the same property having before been shown to belong to the electric fluid. This is one of the most recent discoveries in magnet- ism, and was made by Professor Barlow of the Military Academy at Woolwich, (Eng.) to whose ingenious and assiduous labors are due many of the latest and most important investigations in this science. CHAPTER II. OF THE DIRECTIVE PROPERTIES OF THE MAGNET. 456. If a small needle be placed near one of the poles of a* magnet with its center in the axis of the magnet, it will take a direction in a line with that axis. Thus, let S N be a large mag- Fig. 89. netic bar and sn a small needle g placed near the north pole of the magnet with its center in the axis : it will be seen that the action of the 250 MAGNETISM. pole of the magnet is such as to bring the needle into a line with the magnet. The action of the bar upon the needle, tending to give it this direction, is equal to the sum of its actions upon both poles; while the attraction of the bar upon the whole needle, being only that by which the attraction for s, on account of its nearness, exceeds the repulsion of n, must be less than the directive force. 457. If the needle be placed at right angles to the bar with one of its poles directed towards the center of the bar, it will take a direction parallel to the bar. By supposing B (Fig. 89.) to be placed as indicated in the above proposition, it will be seen, that the actions of both poles of the magnet would conspire in relation to each pole of the needle, and that these forces can be in equilibrium only when the needle is parallel with the bar. The needle in this situation has a tendency to move towards the magnet, because the attractions being exerted on the nearer and the repulsions on the remoter poles, the sum of the attractions ex- ceeds that of the repulsions. 458. Iron filings or other ferruginous bodies, which are free to obey the action of a magnetic bar, naturally arrange themselves, in curve lines, from one pole of the magnet to the other. Thus, if we place a sheet of white paper on a magnetic bar, , ;,. A-V-VV ^o-.\\\ \ , laid on the table, and sprinkle iron filings on the paper, the filings will arrange themselves in curves around the poles of the magnet. 459. The magnetic needle when freely suspended seldom points di- rectly to the pole of the earth, but its deviation from that pole is call- ed the DECLINATION, or the VARIATION of the needle. A vertical circle drawn through the line in which the needle natu- rally places itself, is called the magnetic meridian. A plane passing at right angles to the magnetic meridian, through the center of the needle, is called its magnetic equator. A line drawn on the surface DIRECTIVE PROPERTIES OF THE MAGNET. 251 of the earth passing through the places where the needle points di- rectly to the north pole, and where of course the geographical and magnetic meridians coincide, is called the line of no variation. The line of no variation encompasses the globe, but its course is subject to numerous irregularities. The position of the north mag- netic pole, where it may be supposed to commence, is not exactly as- certained, but it lies in the northeastern part of Hudson's Bay. Pro- ceeding southwards it crosses the United States, passing a little to the eastward of Barbadoes, and touching the northeastern extremity of South America. Thence it extends across the Southern Atlantic to- wards the south pole, where navigators have not been able to trace it. The declination of the needle is not constant, but is subject to a small annual change, which carries it to a certain limit on one side of the pole of the earth, when it becomes stationary for a time ; and then returns to the pole and proceeds to a certain limit on the other side of it, occupying a period of many years during each vibration. In the United States, the variation of the needle, is given for dif- ferent places as follows : At Salem, Massachusetts, 1810, 6 22' 35''.Bowditch. New Haven, Connecticut, 1820, 4 25 25 . Fisher. Albany, New York, 1825, 600 .-De Witt. The annual variation is 2' 49", by which quantity the needle ap- proaches the pole. The variation of the needle however is not the same at the same time in all parts of the earth, but every place has its particular decli- nation. For instance, if we sail from the Straits of Gibraltar to the West Indies, in proportion as we recede from Europe and approach America, the compass will point nearer and nearer due north; and when we reach a certain part of the Gulf of Mexico it will point ex- actly north. But if we sail from Great Britain to the southern coast of Greenland, we shall find the needle deviate farther and farther form the north, as we approach Greenland, where the deviation will not be less than 45 or 50. In some parts of Baffin's Bay the needle points nearly due west. 460. Beside the annual variation, the magnetic needle is subject to daily changes called the DIURNAL VARIATION. 252 MAGNETISM. The deviation of the horizontal needle from its mean position is easterly during the forenoon, and arrives at its maximum about eight o'clock. Thence it returns rapidly to its mean position, which it reaches between nine and ten o'clock, and then its variation becomes westerly; at first increasing rapidly, so as to reach its maximum at about one o'clock in the afternoon, and then slowly receding during the rest of the day, and arriving at its mean position about ten o'clock at night. 461. Jl needle first balanced horizontally on its center of gravity and then magnetised, no longer retains its level, but its north pole spontaneously takes a direction to a point below the horizon called the DIP OF THE NEEDLE. The Dipping Needle, is represented Fie. 91. in Fig. 91. When used it is to be pla- ced in the magnetic meridian, and to ren- der the stand which supports it, perfectly level, by means of the adjusting screws attached. The dip of the needle is very different in different parts of the globe, being in genera] least in the equatorial and great- " ft w est in the polar regions. At certain places on the globe the needle has no dip, that is, becomes perfectly horizontal,' and a line uniting all such places is called the magnetic equator of the earth. Again, in the Polar Regions, the dipping needle sometimes becomes nearly perpendicular to the horizon. In the middle latitudes, .the dip is greater or less but does not correspond exactly to the latitudes. 462. The force exerted by the magnetism of the earth varies in dif- ferent places : its comparative estimate for any given place, is called the MAGNETIC INTENSITY /or that place. As in the case of the pendulum in its relation to the force of grav- ity, the magnetic intensity may be measured by the number of oscil- lations, ^which a needle drawn a given number of degrees from its point of rest, performs in a certain time, as a minute for example, the force being as the square of the number of oscillations. In gen- eral it is well ascertained that the magnetic intensity is least in the DIRECTIVE PROPERTIES OF THE MAGNET. 253 equatorial regions and increases, as we advance towards the poles. It is probably at its maximum at the magnetic poles. By ascertain- ing from actual observation, a number of different places on the sur- face of the earth where the magnetic intensities are equal, and con- necting them by a line, it appears that they arrange themselves in a curve around the magnetic pole. These lines are called isodynamic curves. Extensive journeys, have been undertaken by Humboldt, Sabine, Hansteen and others, to ascertain the point on the surface of the earth where the magnetic intensities are equal, for the purposes of describing these curves. The earlier results indicated the posi- tion of the magnetic pole to be in the northeastern part of Hudson's Bay, lat. 60 N. Ion. 80 W. ;* but the directions of these curves presented such anomalies as to suggest the idea of a second magnet- ic pole in the opposite hemisphere. With a view of ascertaining this point, Professor Hansteen of Christiana several years since, under- took a journey into Siberia, at the expense of the King of Sweden, and has fully confirmed the fact, that there exists a second magnetic pole to the north of Siberia, around which the isodynamic curves ar- range themselves in regular order. From experiments made in deep mines and in the upper regions of the atmosphere by aeronauts, it appears that in both these situations, the magnetic intensity is the same as at the corresponding places on the surface of the earth. 463. The effects produced by the earth on a magnetic needle, cor- respond to those produced on it by a powerful m agnet, and hence the earth itself may be considered as such a magnet. The magnetism of the earth has been supposed by some to result, from a great magnet lying in the central parts of the earth ; by others, to be nothing more than the resultant of all the smaller mag- netic forces scattered through various parts of the terrestial sphere ; and by others to be excited on the surface of the earth by the action of the solar rays. The supposition of a great magnet in the interior of the earth, to which all the phenomena of terrestrial magnetism are to be ascribed * Capt. Parry fixes the place of the magnetic pole in 102 W. lon- and 73 N. lat. *? f * 254 MAGNETISM. is the earliest hypothesis, and is adequate to explain most of the facts of the science. But such a supposition is inconsistent with the re- cent discovery of two north poles implying the existence of four magnetic poles of the earth. The opinion of Biot, that terrestrial magnetism is only the aggregate or resultant, of all the individual magnetic forces residing in different parts of the earth, appears to be no improbable supposition, and accords well with the general doctrine of the composition of forces. 464. In the year 1813, Dr. Morichini, of Rome, announced that the violet rays of the solar spectrum have the property of rendering iron magnetic. In 1825, these experiments were repeated and ex- tended by Mrs. Sommerville, and resulted in proving that the magne- tizing power is not confined to the violet rays, but extends to the in- digo, blue, and green rays. The probable conclusion is, that a class of rays emanate from the sun which have the property of producing magnetism, and are distinct from those which afford light and heat, and produce chemical changes. Hence in the solar beam there are at least four distinct kinds of rays, denominated, respectively, colorific, calorific, chemical, and magnetising rays. 465. Electricity and magnetism are, in some of their properties, remarkably alike, but in others strikingly dissimilar. Several of these analogies have been already incidentally mention- ed ; but it will be useful to the student to consider them in connec- tion. Electricity and magnetism agree in the following particulars : (1.) Each consist of two species, the vitreous and resinous electri- cities, and the austral and boreal magnetisms. (2.) In both cases, those of the same name repel, and those of opposite names attract ea*ch other. (3.) The laws of induction in both are very analogous. (4.) The force, in each, varies inversely as the square of the dis- tance. (5.) The power, in both cases, resides at the surface of bod- ies, and is independent of their mass. But electricity and magnetism are as remarkably unlike in the fol- lowing, particulars. (1.) Electricity is capable of being excited in all bodies and of being imparted to all : magnetism resides almost exclusively in iron in its different forms, and, with a few exceptions, cannot be excited in any other than ferruginous bodies. (2.) Elec- DIRECTIVE PROPERTIES OP THE MAGNET. 255 tricity may be transferred from one body to another : magnetism is incapable of such transference ; magnets communicate their proper- ties merely by induction, a process in which no portion of the fluid is withdrawn from the magnetizing body. (3.) When a body of elon- gated figure is electrified by induction, on being divided near the middle, the two parts possess respectively the kind of electricity only which each had before the separation ; but when a bar of steel or a needle magnetized by induction, is broken into any number of parts, each part has both polarities and becomes a perfect magnet. (4.) The directive properties and the various consequences that result from it, the declination, annual and diurnal variations, the dip, and the differ- ent intensities in different parts of the earth, are all peculiar to the magnet and do not appertain to electrified bodies. Method of making Artificial Magnets. 466. If the learner has made himself acquainted with the princi- ples expounded in the preceding propostions, he will be qualified to proceed, with interest and intelligence, to an explanation of the lead- ing methods practised in the manufacture of artificial magnets. These methods also, by involving a practical application of those principles, will serve to impress them on the memory and to render the knowl- edge of them familiar. It will be recollected that magnets are made from other magnets ; that this is done not by any transference of a portion of the power of the magnetizing body, but by the development of the powers nat- urally residing in the body to be magnetized ; that this development is effected wholly on the principle of induction ; that the original magnet gains instead of losing by its action on other bodies ; that this power may be induced on iron by the agency of an artificial magnet, or of the loadstone, or of the earth which is itself a weak magnet, and acts upon the same principles as any other magnet. It must also be kept clearly in mind, that soft iron or steel readily ac- quires and as readily loses the magnetism induced upon it, and that hardened iron or steel receives it slowly and with much difficulty but retains it permanently. As the earth itself may be supposed to have been the original source of magnetism in all other bodies in which it is found, there are methods of magnetizing from the earth without the aid of either a loadstone or an artificial magnet. : '** 256 MAGNETISM. 467. Jl needle may be magnetized by simply suffering it to remain in contact with the pole of a strong magnet ; or better between the opposite poles of two magnets. The effect produced by two magnets is much more than double that of one magnet, as may be inferred from article 448. But if the needle be of considerable length, several intermediate sets of poles are sometimes developed, as will be seen by applying iron filings. It adds much to the power of the two magnetic bars between which the needle is placed, if to the extremity of the bar most re- mote from the needle, a mass of soft iron is placed. The iron in this case, acts and reacts by induction ; and hence whenever magnets are not in use, they require to be connected with iron to prevent the loss of their powers. Pieces of soft iron thus connected with mag- nets for the purpose of augmenting their power by induction, .are call- ed armatures. Thus A is the armature of the horse shoe magnet represented in figure 93. 468. But it must be recollected that the two species of magnet- ism are not, like those of electricity, separated to a distance from each other, so that one kind may be wholly collected at one end of the bar and the other kind at the other end ; but that the two are separated only at a minute distance remaining in the immediate vi- cinity of each other throughout the whole length of the bar. Hence, in order to give the magnetizing pole its full effect, it becomes neces- sary to apply it successively to every part of the bar from one end to the other. A more effectual method of magnetizing a needle is the following : Place two magnetizing bars A, B, par- allel to each other, with their dissimi- lar poles adjacent; unite the poles at one end by a piece of soft iron R, and apply the poles at the other end to the needle, as is represented in fig. 92. Upon this principle, that is, the increased energy with which the two poles act together, is formed what is called the horse shoe magnet, which derives its name from its peculiar figure, (fig. 93.) Bars of Fig. 93. this form are converted into magnets upon the same principles as straight A bars, the magnetizing bar, being made THE COMPASS. 257 to follow the curvature always in the same direction. A very effi- cacious mode of making horse shoe magnets is thus described by Professor Barlow. Two horse shoe bars may be united at their ends, in such a manner that the poles which are to be of opposite names shall be in contact. They are then to be rubbed with anoth- er strong horse shoe magnet, placing the latter so that its north pole is next to the south pole of one of the new magnets, and conse- quently its south pole next to the north pole of the same ; carrying the movable magnet round and round always in the same direction. This is esteemed one of the most eligible modes of making powerful magnets. The horse shoe magnet is itself very convenient for imparting mag- netism to other bodies. Place the poles near the center of the nee- dle ; move them along its surface backwards and forwards, taking care to pass over each half of it an equal number of times ; repeat the same operation on the other side ; and the needle will become speedily and effectually magnetized. 469. The best mode of making magnetic needles in general, is expressed in the following rule, given, as the result of very exten- sive and accurate experiments by Capt. Kater. Place the needle in the magnetic meridian ; join the opposite poles of a pair of bar magnets, (the magnets being in the same line) and lay the magnets so joined, flat upon the needle, with their poles upon its center ; then having elevated the distant extremities of the mag- nets, so that they may form an angle of about two or three degrees with the needle, draw them from the center of the needle to the ex- tremities, carefully preserving the same inclination; and having join- ed the poles of the magnets at a distance from the needle, repeat the operation ten or twelve times on each surface. The Compass. 470. The Compass, (the importance of which to mankind, has attached to the subject of magnetism its principal value,) is of many different forms, but the chief varieties are the Land compass, the Mariner's compass, the Azimuth compass, and the Variation- com- 33 258 MAGNETISM. pass. The needle, in all these varieties, is usually a thin flat plate of steel, tapering at the extremities ; but, a more eligible form has been proposed by Capt. Kater, consisting of four narrow strips of Fl 8- 94< steel, united in the form of a hol- low rhombus, (Fig. 94.) It is found advantageous to concen- trate the powers of the needle as much as possible in the two extremities, and to avoid all inequalities, arising from intermediate poles, or from a difference of strength in different parts. The needle is secured at the point of suspension, and furnished with a conical cap of brass which rests on a perpen- dicular pin ; and still farther to diminish friction, the point which rests on the extremity of the pin, is made of agate, one of the hard- est mineral substances. Since, if the needle is magnetized after having been balanced on its center of gravity, it would no longer remain horizontal, the equipoise is restored by attaching a small weight to the elevated side. 471. The compass, in its simplest form, consists of a needle like the foregoing enclosed in a suitable box covered with glass. This is all that is essential when it is required merely to know the direction of the meridian, or the north and south points. But, for most purpo- ses, the compass is furnished with a graduated circular card, divided into degrees and minutes ; and in the mariner's compass the card is also divided into thirty two equal parts called rhumbs. The card thus divided is fastened to the needle itself, and turns with it. i 472. Thin, slender needles have the greatest directive powers, and are most sensible, since they undergo less friction than those which are heavier, but due regard to strength requires them to be made of a certain degree of thickness ; an increase of length is attended with an increase of directive power ; but when the thickness remains the same, the weight, and consequently the friction, increases in the very same ^catio ; no advantage, therefore, as to directive power, can be obtained by any increase of length. Moreover, needles which ex- ceed a very moderate length, are liable to have several sets of poles, a circumstance which is attended with a great diminution of directive THE COMPASS. 259 force. On this account, short needles, made exceedingly hard, are generally preferable. 473. The great importance of the mariner's compass, has made its construction an object of much attention, and the best artists have tried their skill upon it. The compass is suspended in its box in such a manner as to remain in a horizontal position notwithstanding all the motions of the ship. This is effected by means of gimbals. This contrivance consists of a hoop, usually of brass, (Fig. 95.) fastened Fig. 95. horizontally to the box by two pivots placed opposite to each other, and constituting the axis on which the hoop turns up and down. At an equal distance from the pivots on each side, that is, at the distance of 90 from each pivot, two other pivots are attached to the ring at right angles to the former, on which the inner box that contains the card is hung. Of course when it turns on these pivots, its motion is at right angles with that of the hoop. Therefore, all the motions of which the compass box is capable, are performed around two axes which intersect each other at right angles ; consequently, the point of intersection, being in both axes, will not move at all. But the needle and the attached card rest upon this point, and are con- 260 MAGNETISM. nected with the compass box in no other point. Hence they remain constantly horizontal in every position of the box. The Azimuth compass* differs from the common mariner's com- pass only in having sights attached, by which the bearing of any ob- ject with the meridian may be ascertained. The Surveyor's corn- is a variety of the azimuth compass. * Azimuth, as applied to a star or any celestial object, is an arc of the horizon intercepted between the meridian and a vertical circle passing through the object. 261 PART VI. OPTICS. PRELIMINARY DEFINITIONS AND OBSERVATIONS. 474. OPTICS is that branch of Natural Philosophy which treats of Light and Vision. More particularly, it is the object of this science to investigate the nature of the agent on which the phenomena of vision depend ; to treat of the motions of light, in respect to its direction, its velocity, and its reflexion from the surfaces of bodies, to trace its change of direction, and the various other modifications it undergoes by passing through different transparent media ; to explain the phenomena of nature which depend upon the properties of light, embracing the doc- trine of color; to trace the relation between light and the structure of the eye, comprehending the subject of vision; and finally, to de- scribe the various instruments to which a knowledge of the principles of Optics has given birth, disclosing many new and wonderful prop- erties of light, and extending the range of human vision, on the one hand, to myriads of objects too minute, and on the other, to number- less worlds too remote, to be seen by the unassisted eye. 475. Luminous bodies are naturally of two kinds, such as shine by their own light, as a lamp or the sun, and such as shine by bor- rowed light, as the moon, and most of the visible objects in nature. A ray is a line of light ; or it is the line which may be conceived to be described by a particle of light. In a more general sense, the term is applied to denote the smallest portion of light which can be separately subjected to experiment. A beam is a collection of par- allel rays. A pencil is a collection of converging or diverging rays. A medium is any space through which light passes. When a space is a perfect void, so as to offer no obstruction to the passage of light, it is said to be a free medium ; when the space intercepts a portion only of the light, it constitutes a transparent medium. Transparency, however, may exist in different degrees. When the medium itself is 262 OPTICS. invisible, as portions of air, it is said to be perfectly transparent ; when the medium is visible, but objects are seen distinctly through it, as in the clearest specimens of glass and crystals, it is said to be, simply, transparent; when objects are indistinctly seen through it, it is semi-transparent ; and when a mere glimmering of light passes through, without representing the figure of objects, it is translucent. Bodies that transmit no light are said to be opake. 476. Rays of light, while they continue in the same uniform me- dium, proceed in straight lines. For objects cannot be seen through bent tubes ; the shadows of bodies are terminated by straight lines; and all the conclusions drawn from this supposition, are found by experience to be true. If two bodies with plane surfaces, as two disks of metal, be held between the eye and some luminous point, as a star, on bringing the two planes gradually towards each other, the star may be seen through the in- tervening space until the planes come completely into contact ; but if one of the surfaces is convex and the other concave, the light is intercepted before the surfaces have met. In consequence of the rectilinear motion of light, it forms angles, triangles, cylinders, cones, &c., and thus its affections fall within the province of geometry, the principles of which are applied with great effect to the development of the properties and laws of light, after a few fundamental properties are established by experiment. From every point in a luminous ob- ject, an inconceivable number of rays of light emanate in every di- rection when not prevented by obstacles that intercept it. Thus, from every point in the flame of a candle, as seen by night, light diffuses itself, pervading an immense sphere, and filling every part of the space so perfectly, that not the minutest point can be found des- titute of some portion of its rays. Any luminous body of this kind is called a radiant. The pencil of light which proceeds from a ra- diant, is a cone, the sections of which made by any plane corres- pond to the figures called conic sections. If any portion of the pencil be intercepted by a rectilateral figure, that portion constitutes a pyramid of which the figure is the base and the luminous point it- self is the vertex. 477. Light has a progressive motion of about one hundred and ninety two thousand Jive hundred miles per second. PRELIMINARY DEFINITIONS AND OBSERVATIONS. 363 The estimation of the velocity of light, (which may be classed among the greatest achievements of the human mind,) has been ef- fected in two different ways. The first method is by means of the eclipses of Jupiter's satellites. To render this mode intelligible to those who have not studied astronomy, it may be premised, that the planet Jupiter is attended by four moons which revolve about their primary as our moon revolves about the earth. These small bodies are observed, by the telescope, to undergo frequent eclipses by falling into the shadow which the planet casts in a direction opposite to the sun. The exact moment when the satellite passes into the shadow, or comes out of it, as seen by a spectator on the earth, is calculated by astronomers. But sometimes the earth and Jupiter are on the same side, and sometimes on opposite sides of the sun ; consequent- ly, the earth is, in the former case, the whole diameter of its orbit, or about one hundred and ninety millions of miles nearer to Jupiter than in the latter. Now it is found by observation, that an eclipse of one of the satellites is seen about sixteen minutes and a half sooner when the earth is nearest to Jupiter, than when it is most remote from it, and consequently, the light must occupy this time in passing through the diameter of the earth's orbit, and must therefore travel at the rate of about one hundred and ninety two thousand miles per second.* Another method of estimating the velocity of light, wholly independent of the preceding, is derived from what is called the aberration of the fixed stars. The full explanation of this method must be refer- red to astronomy ; but it may be understood, in general, that the apparent place of a fixed star is altered from the effect of the mo- tion of its light combined with the motion of the earth in its orbit. It will be remarked, that the place of a luminous object is determin- ed by the direction in which its light meets the eye. But in the case of light coming from the stars, the direction is altered in con- sequence of the motion of the earth in its orbit, being intermediate between the actual directions of the earth and the light of the star ; and the velocity of the earth in its orbit being known, that of light may be computed from the proportional part of the effect produced by it in causing the aberration. The velocity of light, as deduced 190000000 264 OPTICS. from this method, comes^out very nearly the same as by the other. Hence it is inferred that the velocity of light is uniform. 478. The intensity of light, at different distances from the radi- ant, varies inversely as the square of the distance. Thus if we carry a given surface, as a leaf of paper, to different distances from a candle, at the distance of six feet the surface will receive only J as much light as at the distance of three feet ; at 12 feet, or four times as far as at first, the light will be only T V as in- tense. Although the intensity of light decreases rapidly as we re- cede from the radiant, yet the Irightness of the object suffers little diminution by increase of distance.- A candle appears nearly as bright at the distance of a mile as when close to the eye. 479. Light, when it impinges on smooth surfaces, is reflected back into the same medium, and when it passes out of one medium into another, it is bent out of its former course, or refracted. The laws of reflexion and refraction constitute, severally, important depart- ments of the science of Optics, and to these our attention will now be directed. CHAPTER I. OF THE REFLEXION OF LIGHT. 480. Light is said to be reflected when, on impinging upon any surface, it is turned back into the same medium. Instruments employed as reflectors are divided into mirrors and speculums. The name mirror is applied to reflectors made of glass and coated with quicksilver, as common looking glasses : the word speculum is applied to a metallic reflector, such as those made of silver, steel, tin, or a peculiar alloy called speculum metaJ. As the light which falls on glass mirrors, is intercepted by the glass before it is reflected from the quicksilvered surface, a speculum, or a re- flector of polished metal, is that supposed to be employed in optic- al experiments, unless the contrary is specified. Such a surface, REFLEXION OF LIGHT. 265 indeed, is to be understood where the word mirror is used without distinction. The surface of the mirror or speculum may be either plane, con- cave, or convex, and the reflector is denominated accordingly. A ray of light before reflexion is called the incident ray. The angle made by an incident ray, at the surface of the reflector, with a perpendicular to that surface, is called the angle of incidence : the angle made by the reflected ray with the same perpendicular is call- ed the angle of reflexion. Thus, in Fig. 96, if MN represents the re- flecting surface, DC a perpendicular to it at the point C, AC the inci- dent, and BC the reflected ray ; then ACD will be the angle of incidence, and BCD the angle of reflexion. -^ ^ N l 481. Experiments on light are usually conducted in a room which can be made dark with close shutters, one of which is perforated with a circular hole, a few inches in diameter, for admitting a beam of light. This opening is rendered smaller to any required degree by covering it with a piece of board or metallic sheet, having a smaller aperture. And, as the sun may not shine directly into the shutter at the time required, a mirror is sometimes attached to the outside of the shutter, so-contrived that, by means of adjusting screws, it may be made to turn the rays of the sun into the opening, and to give them a horizontal or any other required direction. The course of the rays is rendered palpable to the eye, by the illuminated particles of dust that are floating in the air. 482. The angles of incidence and reflexion are in the same plane, and are equal to each other. Let a ray of light AC (Fig. 96.) admitted into a dark chamber as above, be incident upon a horizontal speculum MN at the point C, to which the line CD is perpendicular, and let CB be the reflected ray. Then if the plane surface of a board or a metallic plate, be made to coincide with the incident ray and the perpendicular, it will be found to coincide also with the reflected ray, showing that the three rays are in the same plane. Again, if, from the point C, with 34 266 OPTICS. the radius CA, a circle be described, on measuring the arcs subten- ded by the angles of incidence and reflexion, they will be found to be exactly equal to each other. The angles of incidence and reflex- ion are also equal when the reflexion takes place from a concave or convex surface ; for the reflexion being from a point, the curve and tangent plane at that point coincide, and have both the same perpen- dicular, namely the radius of the curve. Reflexion of Light from Plane Mirrors. 483. When rays of light are reflected from a plane surface, the reflected rays have the same inclination to one another as their cor- responding incident rays. When parallel rays as AB, CD, (Fig. 97.) fall upon a plane mir- ror, as RS, the reflected rays BG, DH, are also parallel. Fig. 97. Moreover when the rays diverge before reflexion (Fig. 98.) as RA, RB, they will diverge just as much after reflexion, pro- ceeding in the lines AD, BC, which will appear to come from F, a point just as far behind the mirror as R is before it ; or if DA and BC be considered as two converging rays, they will converge in the same degree after reflexion in the lines AR, BR, and will meet in R, a point just as far before the mirror, as the point P, towards which they tended, is behind it. 484. When an object is placed before a plane mirror, the image of it appears at the same distance behind it, of the same magnitude, and equally inclined to it. REFLEXION OF LIGHT. 267 A Let MN, (Fig. 99.) be a plane mir- ror, and AB an object before it, the eye being situated at /H. Now from every point in the object innumerable rays of light are constantly emanating which stri- king on all parts of the mirror, are re- flected off again in various directions. All that is essential to vision is that a sufficient number of these should be con- veyed to the eye. To avoid the confu- sion that arises from the representation of a great number of lines, we will consider those rays only which flow from the extreme parts of the object; the rays proceeding from the intermediate points will of course lie between these. From the point A, then, we may conceive of a vast number of rays of light as proceeding to all parts of the mirror, from which they are reflec- ted again in various directions ; but those only which fall upon the small part of the mirror FG, namely AF, AG, are conveyed to the eye. These therefore are the rays which serve to make the point A visible ; and since they come to the eye as though they diverged from a point a as far behind the mirror as A is before it, the point A will appear as though it were at a. For the same reason the point B will be rendered visible by the rays/H, gH 9 which appear to diverge from b a point as far behind the mirror as B is before it. All the other points in the line AB will take their respective places in the line ah, which will therefore form an exact image or picture of the object, affecting the eye in the same manner as the object would do in its place. It i important to remember, that how many reflexions soever light may undergo in passing from the object to the eye, the image will be determined as to position, magnitude, fyc. by the man- ner in which the rays finally reach the eye after the last reflexion. 485. When a plane mirror (as a common dressing glass) is turned on an axis, the image revolves twice as fast as the mirror. By turn- ing a mirror through 45, the image is carried through 90, so that a mirror set at an angle of 45 with the horizon represents horizon- tal objects in a perpendicular position, and perpendicular objects on a horizontal level. 268 OPTICS. 486. When an object is placed between two PARALLEL plane reflect- ors, a row of images is formed in each mirror, appearing in a straight line behind each other to an indejinite extent. Let there be two plane reflectors, parallel to each other ; and let an object, a candle for example, be placed between them. An im- age of the candle will be formed in each mirror, as far behind it as the object is before it. Again each of these images becomes in its turn a new object to the opposite mirror, and forms a corresponding im- age as far behind that mirror as it is itself before it, and thus the im- ages are repeated in a right line until the light becomes too feeble to be visible. Thus let AB, CD, (Fig. 100.) be two plane mirrors, and E an object between them : two images will be formed of E at E' and E' ; two more of E' and E 7 at E" E" ; and thus a succes- Fig. 100. A C B D sion of images will arise to an indefinite extent ; but since a certain part of the light is lost at every reflexion, each succeeding image is fainter than the preceding. The Endless Gallery is formed on this principle. It consists of a box in the opposite sides of which are placed two parallel reflectors, and between them a number of im- ages are placed, which are repeated in an endless succession. 487. If an object be placed between two plane reflectors INCLINED to each other, the images formed will lie in the circumference of a circle, The common dressing glasses which are mounted on mahogany frames, and turn on pivots fixed in the two ends, are convenient for performing this experiment. Two such mirrors may be placed side by side and a candle set between them. When the mirrors face each other, that is, are parallel, an indefinite number of images of REFLEXION OF LIGHT. 269 the candle may be seen in each mirror ; but on turning the mir- rors so as to bring their parallel edges at the bottom near each other while the upper edges are turned outwards, a circular row of images will be observed, the circle continually enlarging as the mirrors are brought nearer to parallelism, and contracting more and more as the inclination of the mirrors is increased. 488. The degree of perfection in the polish and figure of a plane speculum, may easily be known by observing whether the images seen in all positions, especially in very oblique ones, and from all parts of the speculum, appear exactly equal and similar to the ob- jects ; that is, whether the images (more particularly of the most dis- tant objects) in the room, appear naturally, without having any part of them distorted ; when this is the case, the speculum may be pro- nounced to be a perfect one. The straight edges of the rails of wainscot are the best objects for this experiment. A mirror must be exceedingly bad that will distort the face of a person looking into it, because the rays being returned almost directly back to the eye, small aberrations will not be rendered sensible ; but let two persons look at each other's image as obliquely as they can, and they will soon perceive whether or not the figure of the speculum is defective. -In all speculums, the better they are polished, other circumstances being the same, the brighter will be the images; that is the more light an eye will receive from a given object, which will enable us to ex- amine the goodness of speculums, as to their polish, whenever we have an opportunity of comparing several of the same sort, and in the same light together. We may also observe that cateris paribus, the darker the color of the speculum is, the better is the polish ; for the glass itself can be no otherwise seen than by the reflexions of those particles which have irregular positions with respect to the rest of the surface. But different glasses though equally well polished, will not always appear equally dark ; generally, however, the above rule may be observed. 489. It is found by experiment, that when a pencil of light is in- cident perpendicularly upon water, only 18 rays out of 1000 are re- flected while the greater part of the remaining rays are transmitted. As the angle of inclination is increased, the proportion of rays re- 270 OPTICS. fleeted is also rapidly increased, till at an angle of 75 the reflexion is 211 rays; at 85, 501 ; and at 89, 692. In glass 25 out of 1000 are reflected at a perpendicular incidence ; and the glass always re- flects more light than water, till we reach very great angles of inci- dence such as S7J, when it reflects only 584 rays, while water re- flects 614. Reflexion of Light from Concave Mirrors. 490. The office of concave reflectors, in general, is to collect rays of light. Hence, when applied to parallel rays, it makes them con- verge to a focus ; when applied to rays already converging, it makes them converge more ; to diverging rays, it makes them diverge less, or overcomes their divergency so completely as to make them par- allel, or eveji converging. By keeping steadily in mind the proposition, that the angle which the incident ray makes with a perpendicular to the reflecting surface is equal to that which the re- flected ray makes with the same perpendicular on the other side, the various modes in which light is reflected from a concave surface will be readily understood from the annexed figure. Let c c c represent a con- cave mirror, whose center is C, and radius of curvature Cc; (which radius it must be remembered is always perpendicular to the curve ;) then the various cases will be as follqws : Parallel rays, /c,/c, will pass to the other side of the REFLEXION OF LIGHT. 271 / perpendicular and meet in F,* which is half way from the mirror to its center C. Rays diverging from a point more remote than the center -, Ac, Ac, making a less angle with the perpendiculars than the parallel rays make, will also make a less angle on the other side of the perpen- diculars, meeting in a, between the focus and the center. Rays diverging from the center, Cc, Cc, will be reflected back to the center again. If we now pass to the other side of the center, we see that rays which diverge from a point between the center and the focus, as from 0, converge to a point on the other side of the center, as A. Rays diverging from the focus, go out parallel, as c/, cf. Rays that come to the mirror converging, as dc, dc, meet in a point between the focus and the mirror, as at D, and when diverging from this point they return in the lines cd, cd, appearing to proceed from a point behind the mirror, as A x , which is called the virtual focus. 491. The following experiments, which may be easily repeated, will serve to render familiar the different modes in which images are formed by concave mirrors. See Fig. 101. We will suppose a lighted candle to be placed very near to a con- cave mirror : it will form no image before it because the rays go out still diverging, but we see an enlarged image of the candle behind the mirror. As the radiant is withdrawn from the mirror towards the principal focus, the image will rapidly recede on the other side, and grow larger and larger until the radiant reaches the focus, when the image will suddenly disappear. On removing the radiant a little far- ther, the image will be found at a great distance before the mirror and very much enlarged. As the radiant approaches the center, the im- age approaches it rapidly on the other side of it, constantly diminish- es in size until they both meet and coincide in the center. Removing the radiant still farther, the image appears again between the center and the focus, diminished in size, and slowly approaching the focus as the radiant recedes but never reaches it, unless when the radiant may be considered as at an infinite distance, as in the case of the heavenly bodies. * F is called the focus of parallel rays. 272 OPTICS* i One who looks into a concave mirror sees his own face varied in the following manner. When he holds the reflector near to his face, he sees his image distinct, because the rays come to the eye diverging (which is their natural state with respect to near objects,) and enlarged, because, as the rays diverge less than before, the image is thrown back to a greater distance behind the mirror than the object is before it, and the magnitude is proportioned to that distance. As he withdraws the eye, the image grows larger and larger until the eye reaches the fo- cus. From the focus to the center, no distinct image is seen, be- cause the rays come to the eye converging, a condition incompatible with distinct vision. At the center the eye sees only its own image, since the image is reflected back to the object and coincides with it. Beyond the center, his face will be seen on the other side of the cen- ter before the mirror (though habit may lead him to refer it to a point behind it ;) and it will be diminished, being nearer to the mirror than the object is, and inverted, because an inverted image is formed when the rays are brought to a focus, and this becomes the object which is seen by the eye.* 492. Concave mirrors, in consequence of the property they have of forming images in the air, were in a less enlightened age than the present, frequently employed by showmen for exhibiting surprising appearances. The mirror was usually concealed behind a wall, and the object, which might be a skull, a dagger, Sic. was placed between it and the wall and strongly illuminated. The rays proceeding from the object fell upon the mirror and were reflected by it through an opening through the wall, and brought to a focus so as to form an im- age in the same room with the spectator. If a fine transparent cloud of blue smoke is raised, by means of a chafing dish, around the fo- cus of a large concave mirror, the image of any highly illuminated object will be depicted in the middle of it with great beauty. A dish of fruit thus represented invites the spectator to taste, but the instant he reaches out his hand a drawn dagger presents itself. * These phenomena may be all observed with an ordinary concave shaving glass. REFLEXION OF LIGHT FROM CONVEX SURFACES. 273 493. Concave mirrors have been used as light house reflectors, and as burning instruments. When used in light houses, they are form- ed of copper plated with silver, and they are hammered into a par- abolic form, and then polished with (he hand. A lamp placed in the focus of the parabola, will have its divergent light thrown, after re- flexion, into something like a parallel beam, which will retain its in- tensity to a great distance. When concave mirrors are used for burning, they are generally- made spherical, and regularly ground and polished upon a tool, like the specula used in telescopes. The most celebrated of these were made by M. Villele, of Lyons, who, executed five large ones. One of the best of them, which consisted of copper and tin, was very nearly four feet in diameter, and its focal length thirty ei^ht inches. It melted the metals, as silver and copper, and even some of the more infusible earths. Burning mirrors, however, have sometimes been constructed on a much larger scale by combining a great number of plane mirrors. It is supposed that it was a mirror of this kind which Archimedes em- ployed in setting fire to the Roman fleet under Marcellus. Athana- sius Kircher, who first proved the efficacy of a union of plane mir- rors, went with his pupil Scheiner to Syracuse, to examine the posi- tion of the hostile fleet ; and they were both satisfied that the ships of Marcellus could not have been more than thirty paces distant from Archimedes. Buffon, the celebrated naturalist, constructed a burning apparatus upon this principle, which may be easily explained. He combined one hundred and sixty eight pieces of mirror six inches by eight, so that he could, by a little mechanism connected with each, cause them to reflect the light of the sun upon one spot. Those pieces of glass were selected which gave the smallest image of the sun at two hundred and fifty feet. With one hundred and fifty four mirrors, he was able to fire combustibles at the distance of two hundred and fifty feet. Reflexion of Light from Convex Surfaces. 494. The office of a convex reflector is, in general, to separate rays of light. Hence, when applied to parallel rays, it makes them diverge^ to diverging rays it makes them diverge more, and to con- 35 274 OPTICS. Fig. 102. verging rays, it makes them converge less, even so much less, sometimes, as to become parallel or diverging. Thus (Fig. 102.) the parallel rays AM, AN, falling upon the convex mir- ror MN are reflected to the other side of the perpendiculars, CE, CE, into the diverging lines MB, NB, which appear to come from F behind the mirror, which point is called the vir- tual focus. In like manner the di- verging rays AM, AN, (Fig. 103.) are rendered more diverging than before, , a nd appear to come from a point F nearer the mirror than the focus of parallel rays. 495. When an object is placed before a convex mirror, the image of it appears nearer to the surface of the mirror than the object, and of a less size. Thus (Fig. 104.) AB is seen by the F] g- 104 - eye at ab, and the rays from every point in AB being rendered more divergent by reflexion they will appear to come from a nearer object ; and since the extreme points a and b, are nearer to each other than AB, the image will be smaller than the object. Convex mirrors exhibit their peculiar properties in the diminished representa- tion which they give of the furniture of a room ; and as objects sometimes appear more interesting and beau- tiful in miniature, hence the application of such mirrors for parlor glasses. REFRACTION OF LIGHT. 275 CHAPTER II. OF THE REFRACTION OF LIGHT, AND OF LENSES AND PRISMS. 496. When light passes out of one medium into another it is turn- ed out of its course, or refracted, according to the following law : Light, in passing out of a rarer, into a denser medium, is refrac- ted towards a perpendicular to that medium ; and in passing out of a denser into a rarer medium, it is refracted from the perpendiculaf. Thus if ab (Fig. 105.) be the surface of a vessel of water, a ray of light AB, passing out of air (a rarer) into water (a denser medium) will not pass in the di- rection of BC, but will be turned towards the perpendicular EB, and pass through the water in the line BD ; passing out of water into air, it will be turned away from the perpendicular BF, and pass through the air in the direction of BA. D E 497. We see an example of the foregoing principle in the bent appearance of an oar in the water, the light of the part immersed (by which it is visible) being turned from the perpendicular, and causing it to appear higher than its true place ; for objects appear in the di- rection in which the rays of light emanating from them finally come to the eye. In the same manner, the bottom of a river appears elevated, and diminishes the apparent depth of the stream. Per- sons have sometimes been drowned in consequence of venturing into water, that appeared, from the apparent elevation of the bottom, much shallower than it was. The following ancient experiment illus- trates the same principle. If a small piece of silver be placed in the bottom of a bowl, and the eye be withdrawn until the piece of silver disappears, on filling up the bowl with water, the silver comes ' into view. 498. Transparent bodies differ much among themselves in refract- ing potver. That is, some bodies have the power of changing the 276 OPTICS. Fig. 106. direction of light much more than others. Thus when a ray of light AN, (Fig. 106.) passes into water it will be turned into the line ND ; if the medium he sulphur, which is denser than water, the direction of the light will be changed more, being refracted farther towards the perpendicular into the line NF ; and if the medium be dia- mond the change will be greater still, the refraction being in the line NH. Among different bodies, certain salts of silver and lead, the dia- mond, phosphorus, and sulphur, rank highest in refracting power ; next come the precious gems, and flint glass, containing a large pro- portion of the oxide of lead, which has a refracting power conside- rably higher than crown glass, containing less metallic oxide ; to which succeed the aromatic oils. Among transparent solids, fluor spar is distinguished for its low refracting powers; but tabasheer, a substance formed from the concreted juice of the Indian bamboo, is more particularly remarkable for this property. 499. LENSES, on account of their extensive use in the construction of optical instruments, require very particular attention in the study of Optics. They are of several varieties, as is shown in the follow- ing figure. A double convex lens (A) is a solid formed by two segments of a sphere ap- plied base to base.* A plano-convex lens (B) is a lens having one of its sides convex and the other plane, being simply a segment of a sphere. Fig. 107. F E B A * Though this is the most common form of the double convex lens, yet it is not essential that the two segments should be portions of the same spheres they may be segments of different spheres in which ea*e the curvatures will be unequal on the two sides ef the lens. REFRACTION OF LIGHT. 277 A double concave lens (C) is a solid bounded by two concave spherical surfaces, which may be either equally or unequally concave. A plano-concave lens (D) is a lens one of whose surfaces is plane and the other concave. A meniscus (E) is a lens, one of whose surfaces is convex and the other concave, but the concavity being less than the convexity, it takes the form of a crescent, and has the effect of a convex lens whose convexity is equal to the difference between the sphericities of the two sides. A concavo-convex lens (F) is a lens one of whose surfaces is con- vex and the other concave, the concavity exceeding the convexity, and the lens being therefore equivalent to a concave lens whose sphericity is equal to the difference between the sphericities of the two sides. A line (MN) passing through the center of a lens perpendicular to its opposite surfaces, is called the axis. 500. The office of a convex lens is to COLLECT rays of light. Hence, when applied to parallel rays, it makes them converge ; to diverging rays, it makes them diverge less ; and to converging rays, it makes them converge more. Moreover, with regard to diverging rays, the degree of divergence may be reduced so much as to ren- der the rays parallel, or even to make them converge, which will depend both on the position of the radiant and on the power of the lens. On the contrary, the office of a concave lens is to SEPARATE rays of light. Hence, when it is applied to parallel rays, it makes them diverge; to rays already diverging, it makes them diverge more; and to converging rays, it makes them converge less, become par- allel, or even diverging^ 501. With these general priciples in view, we may now advanta- geously investigate the manner in which IMAGES are formed by means of lenses. 1. If we place a radiant, as a candle, nearer to a lens than its principal focus, then, since the rays go out diverging, no image will be formed on the other side of the lens. 2. If we place the radiant in the focus, the rays will go out par- allel, but will still not be collected into a distinct image. 278 . OPTICS. 3. If the radiant is removed farther from the lens than its princi- pal focus, then the rays will be collected on the other side of the lens so as to form a distinct representation of the object. As this last case is particularly important, since it exhibits the man- ner in which images are formed by means of convex lenses, let us examine it with more attention. 502. Rays of light diverging from the several points of any ob- ject, which is farther from a convex lens than its principal focus, will be made to converge on the other side of the lens, to points corres- ponding to those from which they diverged, and will form an image. Let MN (Fig. 108.) be a Fig> 108 . luminous object placed before a double convex lens L L. Now every point in the radi- ant sends forth innumerable . rays in every direction, part of which fall upon the lens LL. Each pencil may be considered as a cone of rays, having for its axis the straight line which passes through the center of the lens, which line suffers no change of direction, while those rays of the pencil which strike upon the extreme parts of the lens; form the exterior rays of the cone : all the others are of course included be- tween these. It will be sufficient to follow the course of the central and the two extreme rays. Let ML, MC, ML represent such a pencil. The two extreme rays will be collected by the lens and made to meet in the axis or central ray in some point on the other side, as at m. For the same reason, every other point in the object will have its corresponding point in the image, and all these points of the image taken together, form a true representation of the object. By inspecting the figure, it will be seen that the axes of all the pencils cross each other in the center of the lens ; that the image corres- ponding to the top of the object is carried to the bottom of the image, while tfcat corresponding to the bottom of the object is at the top of the image, and, consequently, that th image is inverted with respect to the object. It will be farther seen, that although the individual rays which make up a single pencil are made, on passing through REFRACTION OF LIGHT. 279 the lens, to converge, yet the axes of all the pencils go out diverg- ing from each other, which carries them farther and farther asunder, the farther they proceed before they come to a focus. Hence, the farther the image is formed behind the lens, the greater will be its diameter. The diameter of the image will not be altered by changing the area of the lens : for that diameter will be determined in all cases by the distance between the axes of the two pencils which come from the extremities of the object and cross each other in the center of the lens. The size of the image, however, will be affected by changing the convexity of the lens, while the object remains the same and at the same place. 503. Rays proceeding from any radiant point which are refracted by the different parts of the same lens, do not meet accurately in one focus, but their points of meeting are spread over a certain space, whose diameter is called the SPHERICAL ABERRATION of the lens. Let LL be a piano-con- * ^ Fig> 109 ' vex lens, on which are in- cident the parallel rays RL, ^ RL at the extremities, and R'L 7 , R'L' near the axis; the axis will proceed on "R L without any change of direction, and the rays which are very near to the axis, being also nearly perpendicular to the refracting surface, sustain only a slight change of direction, sufficient, however, to col- lect them into a focus at some distance from the lens in the point F. But the rays RL, RL, meeting the refracting surface more oblique- ly, are more turned out of their course, and are therefore collected into a focus in some point nearer to the lens than F, as at /. The intermediate rays refracted by the lens will have their foci between F and /. Continue the lines L/*and L/, till they meet at G and H, a plane passing through F. The distance /F is called the longitu- dinal spherical aberration, and GH the lateral spherical aberration. It is obvious that such a lens oannot form a distinct picture of any object in its focus F. If it is exposed to the sun, the central parts of the lens L'wzL', whose focus is at F, will form a pretty bright im- age of the sun at F; but as the rays of the sun which pass through 280 OPTICS. the outer part LL of the lens have their foci at points between /and F, the rays will, after arriving at these points, pass on to the plane GH, and occupy a circle whose diameter is GH ; hence the image of the sun in the focus F will be a bright disk, surrounded and rendered indistinct by a broad halo of light growing fainter and fainter from F to G and H. In like manner, every object seen through such a lens, and every image formed by it, will be rendered confused and indis- tinct by spherical aberration. If we cover up all the exterior portions of the lens, so as to per- mit only those portions of the rays which lie near the axis to pass through the lens, then the rays all meet at or very near to the point F, and a much more distinct image is formed ; but so much of the light is excluded by this process, that the brightness of the image is considerably diminished. The dimensions of the image are the same in both cases. 504. The Prism is an important instrument in Optics, especially as it affords the means of decomposing light, and enters into the con- struction of several optical instruments. The triangular prism is the only one employed in experiments, and of this nothing more is essential than barely the inclination of two plane transparent surfaces to one another. The optical prism, however, is usually understood to be a piece of solid glass, having two sides constituted of equal parallelograms, and a third side called the base. The line of inter- section of the two sides is called the edge, and the angle contained by the sides, the refracting angle of the prism. A straight line passing lengthwise of the prism, through its center of gravity and parallel to the edge, is called the axis. A section made by a plane perpendicular to the axis, is an isosceles triangle. Frequently, the three angles of the prism are made equal to one another, each be- ing 60.* * A very convenient prism for common experiments may be con- structed as follows. Select two plates of window glass of the best quality, or better, two pieces of looking glass, from which the silver- ing has been removed. The plates may be five or six inches long, and one and a half or two inches broad. They are to be united at their edges at an angle of about 60, and furnished with a tin case, THE SOLAR SPECTRUM. 281 Figure 110 represents a sec- Fig. no. lion of a prism ABC, of which AB is the base, and ACB the refracting angle. DE is a beam of the sun's light falling obliquely on the first surface AC, where one portion is reflected but an- other portion transmitted. The latter portion, instead of passing directly forward and forming an image of the sun at H, is turned upward towards the perpendicular pp', meeting the opposite surface CB in F, where it is again turned upward from the perpendicular p'p in the direction FG, carrying the image of the sun from H to G. CHAPTER III. OF THE SOLAR SPECTRUM, OF THE RAINBOW, AND OF COLORS IN NATURAL OBJECTS. 505. In tracing the course of rays of light through a refracting medium, we have thus far supposed them to be homogeneous, and to be all affected in the same manner. But in nature the fact is oth- erwise ; that is, The sun's light consists of rays which differ in refrangibilily and in color. The glass prism, in consequence of the strong refraction of light which it produces, (see Art. 504.) is well fitted for experiments of which shall afford the base and the two ends, and a covering for the edge. One of the ends has an orifice with a stopper, for the conven- ience of filling with a fluid, which may be pure water, or better, a saturated solution of the sugar of lead filtered perfectly clear. Pro- jections may be attached to the two ends to serve as handles or as an axis on which the prism may rest on supports. Instead of the tin case, we may employ a block of hard wood, first formed into a tri- angular prism, and then dug out so as to admit the plates. 36 282 OPTICS. this kind. We procure, therefore, a triangular prism of good flint glass, and having darkened a room, admit a sun beam obliquely through a small round hole in the window shutter. Across this beam, near the shutter, we place the prism, with its edge parallel to the horizon, so as to receive the beam upon one of its sides. The rays, on passing through the prism, will be refracted and thrown up- wards, as will be rendered evident by conceiving perpendiculars drawn to the surface of the prism at the points of incidence and emergence. If now we receive the refracted rays upon a screen, at some distance, they will form an elongated image, exhibiting the colors of the rainbow, namely, red, orange, yellow, green, blue, in- digo, violet, together composing the prismatic spectrum. (See Fig. in.) Fig. 111. ' S, a sun-beam. F, a hole in the window shutter. ABC, the prism, having its refracting angle ACB downwards. Y, a white spot, being an image of the sun formed on the floor be- fore the prism is introduced. MN, the screen containing the spectrum.* A pleasing way of exhibiting the separate colors of the spectrum, is to throw the prismatic beam on a distant wall or screen, so as to * The opposite white wall of plaster or stucco, may serve the pur- pose of a screen ; or the screen may be made of a large sheet of white paper ; but a convenient screen for the lecture room is made by past- ing a large sheet of drawing paper to a frame and attaching it to a movable stand. THE SOLAR SPECTRUM. 283 form a long spectrum, and into this beam, at some convenient dis- tance from the prism, to introduce a concave lens of a size sufficient to cover each of the different colored pencils successively. The lens will cause the rays of the same color to diverge, and to form a circular image on the screen, which will distinguish them very stri- kingly from the contiguous portions of the spectrum. 506. If rays of the same color in the prismatic beam be insulated from the rest and made to pass through a second prism, they are re- fracted as usual, (the amount of refraction being different for the different colored rays,) but they undergo no farther change of color. To perform this experiment, we provide a board, perforated with a small round hole, and mounted on a stand. This screen is placed across the prismatic beam, a little way from the prism, in such a manner as to permit rays of the same color only to pass through the aperture, while the other portions of the beam are intercepted. The homogeneous light thus insulated is made to pass through a second prism, and its image is thrown on the wall. The experiment will be more perfect, if the homogeneous pencil be made to pass through a second screen similar to the first, so as to let only the central rays fall upon the second prism. This second refraction produces no change of color. It will be found, however, that, while all other things remain the same, the several images formed of homogeneous rays, will occupy different positions on the wall, the red being lowest and the violet highest, and the intermediate colors arranged between them in the order of their refrangibilities. (See Fig. 112.) Fig. 112. In addition to the parts of the figure enumerated in Fig. Ill, DE represents the first screen, which permits only one sort of rays to pass by a small aperture at G, and de represents a second screen, which permits only the central rays of this pencil to pass by a small hole 284 OPTICS. atg; a be is the second prism, and M is the image of homogeneous light on the wall. 507. The light of the sun reflected from the first surface of bodies, and also the white flames of all combustibles, whether direct or re- flected, differ in color and refrangibility, like the direct light of the sun. The truth stated in this proposition was established by Newton, by experiments with the prism, similar to those detailed in connexion with the preceding propositions. 508. The sun's light is compounded of all the prismatic colors, mixed in due proportion. If we collect, by means of a convex lens, the different colored pencils in the prismatic beam, just after they have emerged from the prism, (see Fig. 111.) the image formed by the lens will be perfect- ly white. A concave mirror may be used instead of the lens, the image being thrown on a screen. Or the rays after they have pass- ed the prism may be received on a second prism of the same kind, placed near the first, but with its refracting angle in the opposite di- rection. In this case the second prisrn restores the light to its usual whiteness. That all the different colors of the spectrum are essential to the composition of white light, may be rendered evident by intercepting a portion of any one of the colors of the spectrum before they have been re-united as in the foregoing experiments. Thus if we intro- duce a thread or a wire into any part of the prismatic beam between the prisrn and the lens, the image formed by the lens will be no long- er white but discolored. If, instead of the wire, an instrument sha- ped like a comb with coarse broad teeth, be introduced into the beam, the discoloration of the image is more diversified, the col- ors of the image being those compounded of the prismatic colors, which are not intercepted by the comb. If the teeth of the comb be passed slowly over the beam, a succession of different colors ap- pears, such as red, yellow, green, blue and purple; but if the motion of the comb be rapid, all these different hues become blended into one by the momentary continuance of each in the eye, and the sen- sation is that of white light. THE RAINBOW. 285 509. For a similar reason, if the colors of the spectrum are paint- ed on a top, in due intensity and proportion, and the top be set to spin- ning, the sensation will be that of white light. Or the colors of the spectrum may be first laid on a sheet of paper, and this may be pasted on a cylinder of wood, which may be made to revolve on the whirling tables : the result will be the same. Newton tried various experiments with different colored powders, grinding together such as corresponded as nearly as possible to the colors of the spectrum. By this means he was able to produce, from the mixture of seven different colored powders, a greyish white, but could never reach a perfectly clear white, owing to the difficulty of finding powders whose colors corresponded exactly to those of the spectrum. 510. Several of the colors of the spectrum may be. produced by the mixture of other colors ; as green by the union of yellow and blue, orange by red and yellow, fyc. Experiments were devised by Newton for thus combining the colors of two contiguous spectrurns, transferring for example, the blue of one to the yellow of the other, and forming green by their union. On causing this compound green, however, to pass through the prism it is resolved into its original col- ors, yellow and blue, whereas, the green of the spectrum is not thus resolved by the prism. Hence Newton infers that the green of the spectrum is not a compound but a simple original color, and so of all the rest. 511. The knowledge of the composition of light, and of the prop- erties of the solar spectrum, naturally lead to an inquiry into the subject of colors, as exhibited in the phenomena of nature. The bright tints of the rainbow, the splendid hues sometimes exhibited by thin plates, as soap bubbles, and finally the diversified colors of ob- jects in all the kingdoms of nature, remained to be accounted for. Some of these we proceed to explain, but others are of a nature too intricate for the present work. The Rainbow* 512. The rainbow, one of the most striking and magnificent of the * The theory of the Rainbow is necessarily somewhat intricate, and possibly may prove too difficult for the young learner, though we shall endeavor to make it as plain as possible. 286 OPTICS. phenomena of nature, was long ago supposed to be owing to some modification which the light of the sun undergoes in passing into drops of rain, but the complete developement of the causes on which it depends, was reserved for the genius of Newton, and naturally followed in the train of those discoveries which he made upon the prismatic spectrum. The rainbow, when exhibited in its more perfect forms, consists of two arches, usually seen in the east during a shower of rain, while the sun is shining in the west. These arches are denominated the outer and the inner bow, of which the inner bow is the brighter, but the outer bow is of larger dimensions every way. The succession of colors in the one is directly opposite to that of the other. 513. Drops of rain, though small, are large in comparison with the minuteness of rays of light, and are to be regarded as spheres of wa- ter, exerting the powers of refraction and reflexion in the same man- ner as large globes of water would do. It was, in fact, by investiga- ting the manner in which globular glass vessels filled with water mod- ify the solar rays, that the first hints were obtained respecting the cause of the rainbow. In the year 1611, Antonio de Dominis made a considerable advance towards the theory of the rainbow, by suspen- ding a glass globe in the sun's light, when he found that while he stood with his back to the sun, the colors of the rainbow were reflect- ed to his eye in succession by the globe, as it was moved higher or lower. Let us therefore, in the first place, follow the course of a ray of light through a globule of water. Let SI (Fig. 113.) be a small beam of light from the sun, falling upon the surface of a globule of water at I. Agreeably to what is known of the laws of light in passing out of one transparent medium into another, a portion of the rays would be reflected at I, and another portion would pass into the drop and be refracted to the farther surface at Fi g- I 13 - F. The same effect would recur here, and\s also at I", and at \" ; and were the eye situa- V ted in either of the lines PR', I"R", or I'"R"', \ it wdilld perceive the prismatic colors, because JL^ \ some of the rays which composed the beam of light that reached -the eye, would be refracted more than others and thus the different colors THE RAINBOW. 287 would be made to appear. Or if a screen were so placed as to re- ceive these transmitted rays, a faint spectrum would be formed upon it. Such a progress of a beam of light admitted through the win- dow shutter, and made to fall on a globular vessel of water, may be actually rendered visible by experiment. 514. It may be remarked that but a comparatively small part of the solar rays that shine upon a drop of water, are required in order to produce the mild light of the rainbow, aided as its light is by the dark ground or cloud on which it is usually projected ; yet where the number of rays that enter the eye is diminished beyond a certain limit, the light becomes too feeble for distinct vision. It will also be observed, that a considerable portion of light is lost at each success- ive reflexion that takes place within the drop, so that a certain beam of light, conveyed to the eye after two reflexions, will be much more feeble than the same beam after one reflexion. Indeed, so much of the sun's light is dissipated at the first point of reflexion from the in- terior surface, added to what is transmitted at the same point, and of course never reaches the eye of the spectator, that, were it not for a great accumulation which the sun's rays undergo at a particular point in this drop, whence the light is reflected and conveyed to the eye, the phenomena of the rainbow would not occur. The manner in which this accumulation is effected, is now to be explained. Fig. 114. 515. Let fzpq (Fig. 114.) be the section of a drop of rain, fp a diameter, a &, e d, &c. parallel rays of the sun's light, falling upon the drop, Now yfj a ray coin- ciding with the diam- eter, would suffer no refraction; and a 6, a ray near to yf, would suffer only a very small inclination to- wards the radius, so as to meet the remoter surface of the drop very 288 OPTICS. near to p; but the rays which lie farther from yf, being inclined to- wards the radius in a greater angle, would be more and more re- fracted as they were farther removed from the diameter. The con- sequence would be, that after passing a certain limit, the rays that lay above that limit' would cross those which lay below it and meet the further surface somewhere between the diameter and the ray which passed through the said limit; that is, all the rays falling on the quad- rant/2, would meet the circumference within the arc kp. But when a quantity is approaching its limit, or is beginning to deviate from it, its variations are nearly insensible. Thus, when the sun is at the tropics, being the limits to which he departs from the equator, he appears for some lime to remain at the same point. In the same manner, a great number of the rays which lie contiguous to e d, on both sides of it, will meet in very nearly the same point on the con- cave surface of the drop at Jem. Consequently, a greater number of rays will be reflected from that point than from any other in the arc. Moreover, proceeding from a single point, they will emerge parallel, and therefore more of them will enter an eye favorably situated, than if they passed out diverging. On both these accounts, it appears, that there is a particular point in a drop of rain, where the rays of the sun's light seem to accumulate, and are therefore pe- culiarly fitted to make an impression on the organ of vision. It is found by calculation that the angle which the incident and emergent rays, in such cases, make with each other, is, for the red rays 42 2', and for the violet rays 40 17'. These are the angles when the rays emerge after two refractions and one reflexion : in the case of two refractions and two reflexions, the angles are, for the red rays 50 59', and for the violet 54 9'. 516. Let us next consider what must be the position of the spec- tator in order that his eye may receive the emergent rays which make the foregoing angle with the incident rays, and which of course are those which cause the phenomena of the rainbow. The spectator must stand with his back to the sun, and a line drawn from the sun towards the bow, so as to pass through his eye, will make the same angle with the emergent rays that they make with the incident rays. Thus, let AB be the incident and GI the emer- gent ray, and let the angle which these two rays make with each other THE RAINBOW 289 Fig. 115. be AKI; and let IT be a ray passing from the sun towards the bow through the eye of the spectator ; then, (since the rays of the sun may be regarded as parallel,) AB and IT are parallel, and the al- ternate angles AKI and KIT, equal. But AKI is the angle made by the incident and emergent rays, and KIT the angle made by the emergent ray, and a line drawn from the sun towards the bow through the eye of the spectator. 517. When the sun shines upon the drops of rain as 'they are fall- ing, the rays which come from those drops to the eye of the spectator after ONE REFLEXION AND TWO REFRACTIONS, produce the inner- most or primary rainbow ; and those rays which come to the eye after TWO REFLEXIONS AND TWO REFRACTIONS, produce the outer" most or superior rainbow. Let SOC* be a straight line passing from the center of the sun through the eye of the spectator at O towards the bow, and let SR, SV be incident rays which after one reflection and two re- fractions are conveyed to the eye at Q, making (Art. 516.) with SOC angles equal to those formed by the incident Fig. 116. * It will be observed that the line SOC is at right angles to the plane of the surface, that is, to the plane of the bows. 37 290 OPTICS. and emergent rays. If OV makes with SOC an angle of 40 IT, and be conceived to revolve around OC, describing the surface of a cone, all the drops of rain on this surface will be precisely in the situation necessary in order that the violet rays, after two refractions and one reflexion, may emerge parallel and arrive at the eye in O, and this will not take place in the same manner on any other part of the cloud ; so that by means of this species of rays, the spectator will see on the cloud a violet colored arc, of which OC will be the axis, and C the center. He will besides, see also an infinity of oth- er concentric arcs exterior to the violet, each one of which will be made up of a single species of rays ; and according as these rays are less refrangible, their areas will be of greater diameter, so that the largest, composed of the extreme red will subtend an angle ROC of 42 2'. Therefore, the whole width of the colored bow will be 42' 40 17', or 1 45', the red being on the outside and the violet within. The contrary order of colors will result from two reflexions and two refractions. Let SV, SR/, be the incident rays, which after two reflexions and two refractions are converged to the eye at O, making (Art. 516.) with SOC angles equal to those formed by the incident and emergent rays, namely, 50 59' and 54 9', and the lines RO 7 and VO', as before, be conceived to revolve around SOC; they will severally meet with all the drops, which having twice re- fracted and twice reflected the extreme red and violet rays, can transmit them to the eye parallel to each other. Between these two arcs, there will be others exhibiting all the intermediate prismatic colors; and the whole together will form a second bow, whose breadth will be 54 9' 50 59', or 3 10'. 518. The rays, therefore, which come from all the drops which make an angle of 42 2' with a line passing from the sun through the eye (which may be called the axis of vision) appear red ; and it is obvious that a collection of rays drawn all around this axis from the eye to drops thus situated would form a cone, of which the drops themselves would constitute the base, and of course would form a circle, 'fhe same is true of all the other colors which emerge from drops at angles which are different for different colors but constant for the same color. Hence, the line which passes from the sun COLORS OF BODIES. 291 through the eye of the spectator, passes also to the center of the bow, or is the axis of the cone of which the bow itself is the base. If the sun is on the horizon, this axis becomes a horizontal line ; con- sequently, the center of the arch rests on the opposite horizon, and the bow is a semi-circle, of which the highest point -has an altitude above the horizon of 42 2'. If the sun is at this altitude of 42 2' above the horizon, then the center of the bow will have the same depression below the opposite horizon, and the circumference, at its highest point will just reach that horizon. When the sun is between these two points, the elevation of the bow will be the difference be- tween the altitude of the sun and the foregoing angle. 519. When the spectator is on an eminence, as a high mountain, he may see more than half the bow, when the sun is near setting ; for the axis will in that case pass to a point above the opposite hori- zon. Travellers who have ascended very high mountains, have oc- casionally observed their shadows projected on the clouds below, with their heads encircled with rainbows. In this case, the axis pass- es to a point above the opposite horizon equal to or greater than the semi-diameter of the bow, so that the whole of 'the circumference comes into view ; and the eye of the spectator being in the axis, the entire bow is projected around that as a center, upon the sur- face of the clouds. Colors of Bodies. 520. According to the Newtonian theory, the color of a body de- pends on the kind of light which it reflects. A great number of bodies are fitted to reflect at once several kinds of rays, and conse- quently appear under mixed colors. It may even happen that of two bodies which should be green, for example, one may reflect the pure prismatic green, and the other the green which arises from the mix- ture of yellow and blue. This quality of selection as it were in bodies, which varies to infinity, occasions the different kinds of rays to unite in every possible manner and every possible proportion ; and hence the inexhaustible variety of shades which nature as in sport has diffused over the surfaces of different bodies. When a body absorbs nearly all the light that reaches it, that body appears black : it transmits to the eye so few reflected rays, that it 292 OPTICS. is scarcely perceptible in itself, and its presence and form make no impression on us, unless as it interrupts, in a manner, the brightness of the surrounding space. CHAPTER IV. OF VISION. 521. As" a preparation for studying the optical structure of the eye, and the laws of vision, it will be useful first to learn in what way images of external objects are formed in a dark room, by light admitted through a hole in the window shutter. 522. Jl beam of light from the sun, entering into a dark room through a small orifice and striking upon an opposite wall or screen, forms a circular image on the wall, whatever be the shape of the orifice. We will suppose the orifice to be comparatively large, as an inch in diameter, and of a triangular or of an irregular shape ; the image formed on the wall will still be circular. For, suppose the orifice to be reduced to a very small circular hole, as a pin hole, (which may easily be done by placing over the orifice a metallic plate, as a sheet of lead, pierced by a pin,) then the rays of the sun passing through this small opening would of course be circular. But the large irreg- ular orifice may be considered as made up of such smaller apertures, or the metallic plate may be conceived to be pierced with an indefi- nite number of pin holes, and the entire image formed upon the wall may be conceived to be made up of an assemblage* of all these images of the sun blended with each other, and therefore as bounded by innumerable curve lines composed of the individual circles. Fi s- 117 - If the screen be brought near to the ori- fice, however, the image will be of the same figure as- the orifice; for the rays after they have passed the orifice, must have diverged considerably before the sections that form the image shall afford circles so large, that their blended circumferences shall compose a circular figure. (See Fig. 117.) VISION. 293 If the plane which receives the image, be not parallel to the orifice, then the image will be elliptical, being the section of a cone oblique to its axis. Circular images of the sun are sometimes projected on the ground, through the small openings among the leaves of trees. During an eclipse of the sun, these images copy the figure of the eclipse. If there be various orifices near to each other, three, for example, through which a beam of the sun shines into a dark room, we shall observe at first, at a certain distance, three distinct luminous circles. At a greater distance, these three circles begin to be blended, and finally, on enlarging sufficiently, they unite to form a single circle. 523. lf t instead of a beam of solar light, we admit into a dark room, through an opening in the shutter, the light reflected from va- rious objects without, an inverted picture of these objects will be formed on the opposite wall. A room fitted for exhibiting such a picture is called a Camera Obscura. From what has been before explained, it will be readily under- stood, that from every point in the object, innumerable rays of light proceed and fall upon the window shutter. Of these, however, none can enter the aperture except such as are very near to each other, all others diverging too far to enter a small opening. It is essential to the distinctness of the picture that rays which proceed from every point in the object, should be collected into corresponding points in the image, and should exist there free from any mixture of rays from any other point ; and it is essential to the brightness of the picture, that as many rays as possible should be conveyed from each point in the object to its corresponding point in the image. To render the picture distinct, therefore, the opening in the window shutter must be small, else the pencils of rays from different points will overlap each other, and confuse the picture ; but as the orifice is diminished the brightness of the picture is impaired, since, in this case> a smaller number of rays is conveyed from the object to the image. These modifications of the picture according to the size of the aperture, may be easily exhibited by beginning with a circular aper- ture two or three inches in diameter, and reducing its size gradually 294 OPTICS. by covering it with a piece of board, or a metallic plate, perforated with' holes of different sizes.* 524. If, instead of passing through the naked orifice, the rays be received on a convex lens, an inch and a half or two inches in diam- eter fixed in the window shutter, a very bright and distinct picture of the external landscape will be formed on a screen, placed at the focal distance of the lens. The image is brighter and more distinct than when formed with- out the aid of the lens, first, because the diameter of the lens may be so great as to receive and transmit a much larger portion of the rays which proceed from each point of the object, than would be com- patible with distinctness, if so large a naked aperture were employ- ed ; secondly, because the rays of each pencil are brought more ac- curately to a separate focus; and, thirdly, because, the picture being formed nearer to the window shutter, it is smaller, and of course the light, being spread over less space, is more intense. A convex lens fixed in a ball, is used for this purpose, which is so attached to the opening in the shutter as to be capable of being turn- ed towards different parts of the landscape, like the eye-ball in its socket. Such a lens with its accompanying parts, is called a Sciop- tic ball. In a bright sunny day, where the sun is on the side of the house opposite to the shutter, and of course illuminating the sides of objects which face the window, we may form either with or without the aid of the scioptic ball, a very striking and beautiful picture of external * A small room, ten feet square, for example, having a window opening towards an unobstructed landscape, may easily be converted into a camera obscura. The perforation in the shutter, must be made equidistant from the sides of the room: and from the aperture as a center, with a radius equal to the distance of the opposite wall, de- scribe an arc of a circle, upon which as a base a new concave wall is to be constructed, finished with stucco. The other walls and ceiling are to be Colored a dead black, while the concave wall, for receiving the image, is made as white as possible. On admitting the light through an aperture half an inch in diameter, a beautiful and distinct picture will be formed on the opposite wall. VISION. 295 objects, exhibiting each in its relative situation, of a size and bright- ness corresponding to its distance, with all the colors and the most delicate motions of the landscape. The name camera obscura, which appropriately belongs to such a chamber, is also extended to certain boxes in which similar pictures are formed, with peculiar devices for rendering the image erect instead of inverted. The structure of these portable camera obscuras, may be described more particularly among other optical instruments. The eye is a camera obscura, and the analogy existing between its principal parts, and the contrivances employed to form a picture of external objects as in the preceding experiments, will appear very striking on comparison. 525. The EYE consists of three prin- Fig. us. cipal chambers, rilled with media of per- fect transparency. The first of these media, A, occupying the anterior cham- ber, is called the Aqueous Humor, and consists chiefly of pure water. The cell in which the aqueous humor is contain- ed, is bounded, on its anterior side, by a strong, horny, and delicately transparent coat, aa, and is called the cornea. The posterior surface of the chamber A of the aqueous humor is limited by the Iris cc, which is a kind of circular opake screen, con- sisting of muscular fibres, by whose contraction or expansion, an aperture in its center called the pupil is diminished or dilated ac- cording to the intensity of the light. In very strong lights, the open- ing of the pupil is greatly contracted, so as not to exceed twelve hundredths of an inch in the human eye, while in feebler illumina- tions it dilates to an opening not exceeding twenty five hundredths or double its former diameter. The use of this is evidently to mod- erate and equalize the illumination of the image on the retina, which might otherwise injure its sensibility. In animals, as the cat, which see well in the dark, the pupil is almost totally closed in the day time, and reduced to a very narrow line ; but in the human eye, the form of the aperture is always circular. The contraction of the pupil is involuntary, and takes place by the effect of the stimulus of the light itself; a beautiful piece of self-adjusting mechanism, the 296 OPTICS. play of which may be easily seen by bringing a candle near to the eye, while directed to its own image in a looking glass. Immediate- ly behind the opening of the Iris, lies the Crystalline Lens, B, en- closed in its capsule, which forms the posterior boundary of the chamber A. The figure of the crystalline lens is a solid of revolu- tion, having its anterior surface much less curved than the posterior. The consistence of the crystalline is that of a hard jelly, and it is pur- er and more transparent than the finest rock crystal. In the crystalline a very curious and remarkable contrivance is adopted, for overcoming or preventing the spherical aberration which (Art. 503.) belongs to lenses of this form, which refract the rays more towards their marginal than near their central parts, and hence do not bring all the rays belonging to one pencil to the same focus. Here the difficulty is obviated by giving to the central portions of the crystalline a proportionately greater density, thus increasing its refract- ive power so as exactly to correspond to that of the other portions of the lens. The posterior chamber C of the eye is filled with the Vitreous Humor. Its name is derived from its supposed resemblance to melted glass ; it is a clear, gelatinous fluid, very much resembling the white of an egg. Rays of light diverging from various objects without, on passing through the aqueous humor, (which is a concavo- convex lens) have their divergency much diminished, or even, in most cases are rendered converging^ and in this state are transmitted through the crystalline, which has precisely such a degree of refract- ive power as enables it to bring them to a focus at the distance of the retina, which, as a screen, is spread out to receive the image. The retina as its name imports, is a kind of white net-work, like gauze formed of inconceivably delicate nerves, all branching from one great nerve O, called the optic nerve, which enters the eye obliquely at the inner side of the orbit, next the nose. The retina lines the whole of the cavity C up to ii, where the capsule of the crystalline com- mences. Its nerves are in contact with, or immersed in, the pigmen- tum nigrum, a very black velvety matter, which covers the choroid membranfy mm, and whose office is to absorb and stifle all the light which enters the eye' as soon as it has done its office of exciting the retina ; thus preventing internal reflexions, and consequent confusion of vision. The whole of these humors and membranes are contain- VISION, 297 ed in a' thick tough coat, called the sderotica, which unites with the cornea and forms what is called the white of the eye. 526. Such in general, is the structure by which parallel rays, and those coming from very distant objects are brought to a focus on the retina. But there are special contrivances, suited to particular pur- poses, which are no less evincive of design and skill than the gener- al organization of the eye. Some of the most remarkable of these we proceed to mention. The cornea, by protruding, collects the rays of light that come to the eye laterally, and guides them into the eye, thus enlarging the range of vision. It answers to an appendage to the microscope, which will hereafter be described under the name of field glass. The motion of the eye-ball, by means of which the pupil may be turned in different directions, conduces to the same purpose. Hence, notwithstanding the minuteness of the aperture which admits the light (and it must be small, otherwise the image will not be distinct) the eye may take in at once, without moving the head, a horizontal range of 110 and a vertical range of 120, name- ly, 50 above, and 70 below a horizontal line. 527. As the radiant approaches the lens, the image recedes from it on the other side; (see Fig. 108;) and in our experiments on the formation of images we are obliged either to change the place of the screen every time the distance of the radiant is altered, or to substitute a new lens, which will either throw back the image as much as the increased distance of the radiant brings it forward, or which brings the image as much nearer as the altered place of the radiant tends to carry it off. How then is the distinctness of the im- age maintained in the eye, notwithstanding the immense variety in the distances of objects ? We can conceive of but two ways in which this can be accomplished : either by lengthening or shortening the diameter of the eye in the direction of its axis, so as to alter the dis- tance of the retina from the cornea and crystalline, or by altering the curvature of the refracting lenses themselves, increasing their convexity for near objects, and lessening it for objects that are more remote. Perhaps both causes may operate, but the effect is believed to be produced chiefly by the latter cause, namely, change of figure in the refracting lenses. On this subject, Sir J. Herschel remarks, 38 298 OPTICS. that it is the boast of science to have been able to trace so far the re- fined contrivances of this most admirable organ ; not its shame to find something still concealed from its scrutiny ; for, however anatomists may differ on points of structure, or physiologists dispute on modes of action, there is that in what we do understand of the formation of the eye so similar, and yet so infinitely superior, to a product of hu- man ingenuity, such thought, such care, such refinement, such' ad- vantage taken of the properties of natural agents used as mere in- struments, for accomplishing a given end, as force upon us a convic- tion of deliberate choice and premeditated design, more strongly, perhaps, than any single contrivance to be found, whether in art or nature, and render its study an object of the deepest interest. 528. Writers on comparative anatomy express the highest admi- ration of the adaptation of the eyes of different animals to the media in which they respectively live, and to the peculiar wants or habits of each. Thus the crystalline lens of the fish is formed with peculiar reference to the refracting properties of water. In the human eye, this lens has a refractive power only a little greater than that of water ; but since the light passes out of a much rarer medium, (air,) such a density is sufficient to bring the rays to a focus ; but were the density of the crystalline lens in the eye of the fish no greater than in the human eye, receiving the light from a medium (water) almost as dense as itself, it would be unable to give that change of direction to the rays which would be essential to distinct vision. But provision is made for this exigency by giving to the crystalline lens a much greater density, and of course a higher refracting power, which ena- bles it completely to fulfil its purpose. Animals which have occasion to see in the dark, as the owl and the cat, have the power of opening or closing the pupil to a much greater extent than man. By this means, they are enabled in the dark to collect a far greater number of rays of light. But as such an expansion of the pupil would, in broad day light, endanger the safety of eyes of such peculiar delicacy, the iris closes over the aperture and diminishes it with every increase in the intensity of the light, a change which is involuntary on the part of the animal. In animals, as birds, which pounce upon their prey, the pupil of the eye is elongated perpendicnlarly, while in those that ruminate, as the VISION. 299 ox, it is elongated horizontally ; being in each case, exactly adapted to the circumstances of the animal. 529. The images of external objects are of course formed invert- ed on the retina, and may be seen there by dissecting off the posterior coats of the eye of a newly killed animal, as an ox, and exposing the retina and choroid membrane from behind, like the image on a transparent screen, seen from behind. The appearance is particu- larly striking and beautiful when the eye is fixed like the scioptic ball, in the window shutter of a dark room. It is this image, and this only, which is felt by the nerves of the retina, on which the rays of light act as a stimulus ; and the impressions therein produced are thence conveyed along the optic nerve to the sensorium, in a man- ner which we must rank at present among the profounder mysteries of physiology, but which appear to differ in no respect from that in which the impressions of the other senses are transmitted. Thus, a paralysis of the optic nerve produces, while it lasts, total blindness, though the eye remains open, and the lenses retain their transparen- cy ; and some very curious cases of half blindness have been suc- cessfully referred to an affection of one of the nerves without the other. On the other hand, while the nerves retain their sensibility, the degree of perfection of vision is exactly commensurate to that of the image formed on the retina. In cases of cataract, when the crystalline lens loses its transparency, the light is prevented from reaching the retina, or from reaching it in a proper state of regular concentration ; being stopped, confused and scattered, by the opake or semi-opake portions it encounters in its passage. The image, in consequence, is either altogether obliterated, or rendered dim and indistinct. If the opake lens be extracted, the full perception of light returns ; but one principal instrument for producing the conver- gence of the rays being removed, the image, instead of being form- ed OTi the retina, is formed considerably behind it, and the rays being received on it in a state of convergence, before they are brought to a focus, produce no regular picture, and therefore no distinct vision. But if we give to the rays before they enter the eye, a certain degree of divergence, as the application of a convex lens, so as to render the lenses of the eye capable of finally effecting the exact conver- gence of the rays upon^the retina, distinct vision is the immediate r- 300 OPTICS. suit. This is the reason why'persons who have undergone the ope- ration for the cataract, (which consists either in totally removing, or in putting out of the way, the opake crystalline,) wear spectacles unu- sually convex. Such glasses perform the office of an artificial crystal- line. An imperfection of vision similar to that produced by the re- moval of the crystalline, is the ordinary effect of old age, and its remedy is the same. In aged persons, the cornea loses something of its convexity, or becomes flatter. The refracting power of the eye is by this means diminished, and a perfect image can no longer be formed on the retina, the point to which the converging rays tend being beyond the retina. The deficient power is supplied by a con- vex lens, in a pair of spectacles, which are so selected and adapted to the eye, as exactly to compensate for the want of refracting power in the eye itself, and thus the rays are brought to a focus at the reti- na, where alone a distinct image can be formed. 530. Short sighted persons have their eyes too convex, forming the image too soon, or before they reach the retina. Concave glass- es counteract this effect. Rare cases have occured where the cor- nea was so very prominent as to render it impossible to apply con- veniently a lens sufficiently concave to counteract its action. Such cases would be accompanied with immediate blindness, but for that happy boldness justifiable only by the certainty of our knowledge of the true nature and laws of vision, which in such a case has suggest- ed the opening of the eye and removal of the crystalline lens, though in a perfectly sound state. Other defects of eye sight, whose cause has been ascertained to depend on mal-conformation of the cornea, or some other part of the eye, have sometimes been remedied by adapting to them glasses of a peculiar construction, possessing optic- tal properties adapted to the particular defects they were required to remedy. 531. The estimation of the DISTANCES and MAGNITUDES of ob- jects is not dependent on optical principles alone, but the information afforded by the eye, is taken in connexion with various circumstances that influence the mind in judging of these particulars. In the first place we judge of the distance of an object by the in- clination of the optic axes, which is greater for nearer objects and VISION. 301 less for objects more remote. But beyond a certain distance, this method is very indeterminate, since great intervals among remote objects would scarcely affect the inclination of these axes. In the second place, we judge of distance by the apparent magnitude of known objects ; as when a ship of large size, or a high mountain, appears comparatively small, we refer it to a great distance. We are also frequently deceived in our estimate of distance when we are approaching large objects, as a great city, or a lofty mountain : we fancy they are nearer than they actually are. In the third place, we estimate the distance of objects by the degree of distinctness of the parts, or brightness of the colors. Thus a smoky mountain is refer- ed to a great distance ;* a mountain whose sides are precipitous and bare (especially where the rocks have a new and fresh appearance in consequence of having been quarried for use) appears nearer than the reality : vessels, or steam boats, seen through a mist in the night have sometimes run foul of each other, being supposed by the pilots to be much farther off, in consequence of the indistinctness of their appearance. In the fourth place, our estimate of distance is affec- ted by the number of intervening objects. Hence, distances upon uneven ground do not appear so great as upon a plain ; for the val- leys, rivers and other objects that lie low are many of them lost to the sight. On this principle, the breadth of a river appears less when viewed from one side than from the center ; a ship appears nearer than the truth to one unaccustomed to judge of distances on the water ; and the horizontal distance of the sky appears much great- er than the vertical distance, whence the aerial vault does not pre- sent the appearance of a hollow hemisphere, but of such a hemisphere much flattened in the zenith, and spread out at the horizon. 532. A similar variety of circumstances affects our estimate of the magnitudes of bodies seen at different distances. First, the vis- ual angle, that is, the angle subtended by the object at the eye, deter- mines the size of objects that are near ; but it is scarcely any guide to the dimensions of remote objects, since all such objects subtend * This appearance exhibits the true color of the atmosphere, be- coming visible in consequence of the extent of the stratum, and the dark ground which the mountain affords upon which to view it. 302 OPTICS. angles at the eye comparatively very small. Thus, on this principle a fly within a few inches of the eye would appear larger than a ship of war seen at some distance on the water. A giant nine feet in height, but thirty feet off, would appear no larger than a child three feet high seen at the distance of ten feet. But as this result is not con- formable to experience, it is evident that we must have means of judging of the magnitudes of objects, beside that derived from the visual angle. If the giant were to remove from the distance of ten feet from the eye to that of thirty feet, his image on the retina would be only one third as long as before ; but, on the other hand, the dis- tance is trebled, and the sort of combination that takes place in us of the two impressions, the one of magnitude the other of distance, is like the constant product of two quantities, of which one increases in the same ratio as the other diminishes ; whence the giant would ap- pear constantly of the same height, at whatever distance from us he was seen. 533. This corrected result, however, we can make only in cases when we are familiar with the actual size of the body. When not thus familiar, we rely too much on the visual angle, and are thus of- ten greatly deceived. A speck on the window being at the instant, supposed to be an object on a distant eminence, is magnified, in our estimation into a body of extraordinary size (as a line half an inch long into a may-pole) ; or distant objects supposed to be very near appear of an exceedingly diminutive size. Secondly, the effect of contrast is visible in our estimation of the magnitudes of bodies, a given ob- ject appearing much below its ordinary size, when seen by the side of those of very great magnitude. Men quarrying stone at the base of a high mountain, sometimes appear at a little distance like pig- mies, partly from the effect of contrast, but more perhaps from the impression which the mountain gives us of their being nearer than they actually are. Thirdly, objects seen at an angle considerably above or below us, as a man on the top of a spire, or a river in a deep valley seen from the top of a monntain, appears greatly dimin- ished. In these cases, since there are no intervening objects to aid us in estimating the distance, we estimate it too low, and hence (Art. 531.) the object appears less than the reality. Moreover, being seen obliquely, its apparent dimensions are diminished on this account, the MICROSCOPES. 303 apparent diameter being determined by the line into which the object is projected perpendicular to the axis of vision. Hence children judge much less accurately both of distances and of magnitudes than adults, and blind persons suddenly restored to sight have usually dis- played an utter inability to judge of these particulars. CHAPTER V. OF MICROSCOPES. 534. The Microscope, is an optical instrument, designed to aid the eye in the inspection of MINUTE objects.* Telescopes, on the other hand, assist the eye in the examination of distant bodies. These two instruments have probably more than any other, extended the boundaries of human thought, and no small part of the labor which has been bestowed upon the science of optics, has had for its ultimate object their improvement and perfection. With the hope of making the learner well acquainted with the principles of the microscope, we shall begin with those varieties of the instrument which are the most simple in their construction, and successively advance to others of a more complicated structure. 535. The simplest microscope is a double convex lens. This, it is well known, when applied to small objects, as the letters of a book, renders them larger and more distinct. Let us see in what manner these effects are produced. When an object is brought nearer and nearer to the eye, we finally reach a point within which vision begins to grow imperfect. That point is called the limit of distinct vision. Its distance from the eye varies a little in different persons, but aver- ages (for minute objects) at about five inches. If the object be brought nearer than this distance, the rays come to the eye too di- verging for the lenses of the eye to bring them to a focus soon enough, that is, so as to make the image fall exactly on the retina. More- over, the rays which proceed from the extreme parts of the object meet the eye too obliquely to be brought to the same focus with * fjuxpog, small, tfxotfg'w, to see. 304 OPTICS. those rays which meet it more directly, and hence contribute only to confuse the picture. We may verify these remarks by bringing grad- ually towards the eye a printed page with small letters. When the letters are within two or three inches of the eye, they are blended together, and nothing is seen distinctly. If we now make a pin hole through a piece of paper, (black paper is preferable,) and look at the same letters through this, we find them rendered far more distinct than before at nearer distances, and larger than ordinary. Their greater distinctness is owing to the exclusion of those oblique rays which, not being brought by the eye to an accurate focus with the central rays, only tend to confuse the picture formed by the latter. As only the central rays of each pencil can enter so small an orifice, the picture is made up, as it were, of the axes of all the pencils. The increased magnitude of the letters is owing to their being seen nearer than ordinary, and thus under a greater angle, an increase of the visual angle having much influence in our estimate of the magni- tude of near objects, though it has but little influence in regard to remote objects. (Art. 532.) 536. A convex lens acts on much the same principles, only it is still more effectual It does not exclude the oblique rays, but it di- minishes their obliquity so much, as to enable the eye to bring them to a focus at the distance of the retina, and thus makes them con- tribute to the brightness of the picture. The object is magnified as before, because it is seen nearer, and consequently under a larger an- gle, which enables minute portions to be distinctly recognized by the eye, which were before invisible, because they did not occupy a suf- ficient space on the retina. The power of a lens to accomplish these purposes, will obviously depend on its refractive power; and this, (supposing the material of which the lens is made to remain the same,) will depend on its increased sphericity, and diminished focal distance. Lenses of the smallest focal distance, therefore, other things being equal, have the greatest' magnify ing power, and, there- fore, spherules or perfect spheres, have the highest magnifying pow- ers G{ all. When the radiant is situated in the focus of a lens, the rays go out parallel. (Art. 501.) When thus received by the eye, they are capable of being brought to a focus by it, and of forming a distinct image. Hence, by means of a lens, an object may be seen MICROSCOPES. 305 distinctly when it is exceedingly near to the eye, provided it be situ- ated in the focus of the lens. The magnifying power of a lens, therefore, depends on the ratio between its focal distance and the limit of distinct vision. The latter being five inches, a lens whose focal distance is one inch, by bringing the object five times nearer magnifies its linear dimensions in the same ratio, and its superficial dimensions in the ratio of the square. Thus, in the case supposed, an object would appear five times as long and broad, and have twenty five times as great a surface. Lenses have been made ca- pable of affording a distinct image of very minute objects, when their focal distances were only ^\ of an inch. In this case, the magnifying power would be as j\ : 5, which is as 1 to 300, or as 1 to 9000 in surface. 537. When, however, an object is so near to the eye, a very minute space covers the whole field of vision, and it is only the minutest ob- jects, or the smallest parts of a body, that are visible in such micro- scopes. The extent of parts seen by a microscope is called the field of view. A microscope of small focal distance has a propor- tionally small field of view. Moreover, since, when the object is so near to the lens, the rays of light strike the lens extremely diverging, only the central rays of each pencil can be brought accurately to a focus. The more oblique rays, therefore, must be excluded by cov- ering up all but the central portions of the lens, by which means the brightness of the image is diminished. The part of a lens through which the light is admitted, is called its aperture. The aperture of a lens of small focal distance and high magnifying powers, must of necessity be small, and one of the principal difficulties in the use of such microscopes, is the want of sufficient light. Hence, micro- scopes of different focal distances are required for different purposes. Where we wish to view a large object at once, we must use a lens which has a large field of view, and of course but comparatively small magnifying powers. Such are the glasses used by watchma- kers and other artists. Microscopes which magnify but little, but afford a large field of view, are called magnifiers, or magnifying glasses. Such are the large lenses employed for viewing pictures. But for inspecting the minute parts of a small insect, we require a much higher power ; and, the object being very small, a large field 39 306 OPTICS. of view is not necessary. The only difficulty to be obviated is the want of light ; and this evil is remedied, either by placing the object in the sun, or by condensing upon it a still stronger light, by means of apparatus specially adapted to that purpose, which will be de- scribed hereafter.* 538. Among the most distinguished achievements of philosophical artists, in our own limes, has been the formation of microscopes out of the hardest precious gems, especially the diamond and the sap- phire. The diamond seems to unite in itself almost every desirable quality for this purpose. It will be recollected that this substance is distinguished for its high refractive powers ; hence, a given refract- ing, and of course magnifying, power may be attained with a lens of less curvature, and consequently subject to less spherical aberration, than glass lenses of the same power. Indeed, it is estimated, that the indistinctness arising from spherical aberration, is in a diamond lens only ^th as great as in a glass lens of equivalent power. The sapphire has analogous properties, as also the garnet; and pure rock crystal (quartz) is much esteemed for refracting lenses; but some of the pellucid gems are unsuitable for this purpose on account of their possessing the property of giving double images. The comparative curvatures and thicknesses of three lenses of the same refracting power, made respectively of diamond, sapphire, and glass, are ex- hibited in the following diagrams. Fig. 119. Glass. Sapphire. Diamond. Since, however, a diamond lens admits of being made much thin- ner than a glass lens of the same power, the loss of light by absorp- tion is far less and the brightness of the image is proportionally aug- mented. * A convenient pocket microscope is sometimes sold in the shops, consisting of a slide of ivory or horn, two or three inches in length, in which are set three or four lenses of different powers, adapted to ' various purposes. MICROSCOPES. 307 539. Another distinguished and valuable property of the diamond is that it combines with a high refractive, a low dispersive power. By dispersive power it will be observed, is meant the power of separating the different colored rays, that is,, of decomposing com- mon light into its prismatic elements. Hence, diamond lenses are naturally nearly achromatic, or afford images which are des- titute of color. But while these favorable qualities were known to appertain to the diamond, which, taken in connexion with its great transparency and purity of structure, were observed to fit it admira- bly for microscopes of great magnifying powers, yet the extreme hardness of the substance, seemed to render the difficulty of grind- ing it into the requisite shape almost insuperable. This difficulty has, however, within a few years, been completely overcome by Mr. Pritchard, an eminent English artist, who has constructed a number of diamond and sapphire microscopes, whose performances have equalled the most sanguine expectations. 540. A drop of a transparent liquor may be easily converted into a magnifier, constituting a Fluid Microscope. The simplest kind of fluid microscope is formed by drilling a small hole in a plate of brass or lead, and applying to it a drop of water from the point of a pin. If the plate be hollowed out on both sides around the aperture, the water will spontaneously .assume the shape of a convex lens. Water, however, possessing only a comparatively low refracting power, is less adapted to this purpose than several other fluids, particularly certain transparent balsams and aromatic oils. Sulphuric acid and castor oil answer well, but turpentine varnish and Canada balsam are preferred, especially because as they dry they become indurated, and form permanent microscopes. Instead of the aperture in a me- tallic plate above described, a small plate of glass may be employed, V in which case it is only necessary to drop the varnish or balsam on the surface of the plate ; and it will assume the figure of a plano-convex lens. The power of the microscope may be varied by employing a larger or a smaller drop, or by suffering it to spread itself on the upper or on the under surface, since the curvature of the drop, and of course its focal distance, is modified by each of these circum- stances. 308 OPTICSc 541. The PERSPECTIVE GLASS, which is used for viewing pic- tures, affords another example of the application of the simple mi- croscope. It consists of a large double convex lens fixed in a frame in a vertical position, from the top of which, on the back side, pro- ceeds a plane mirror which is fixed at an angle of 45 with the hori- zon, and of course it makes the same angle with the lens. Pictures to be viewed are placed in an inverted position, (that is, with the top towards the spectator,) on a table at the foot of the instrument. The mirror, being set at an angle of 45 with the horizon, renders horizontal objects erect. (Art. 531.) Its office, therefore, is merely to give a proper direction to the rays of light from the picture as they .enter the lens, causing them, in fact, to come to the lens in the same manner, as they would do were the mirror removed and the picture set up in a vertical position, parallel to the lens, at a distance from the lens equal to the length of any ray, measured from the picture to the mirror and from the mirror to the lens. (Art. 530.) Again, in order that the image may be erect, it is necessary that the picture should be placed with its top towards the observer ; for since the image of every point in the picture is just as far behind the mirror as the point is before it, those parts of the picture which are designed to occupy the highest parts of the image must be farthest below the mirror. This will be understood from the following diagram. AA, a convex lens fixed vertically in a frame. BB, a plane mirror making with the horizon an angle of 45. C, an object placed horizontally upon the table, the upper part being towards the observer. The object will be reflected by the mirror into a perpendicular position, and its rays will, therefore, fall on the lens in the same manner as they would were it actually situated perpendicu- larly, and no mirror were employed. Consequently, if the distance of C from the lens be equal to die focal dis- tance of the lens, the rays will come MICROSCOPES. to the eye parallel, and a distinct and magnified image will be form- ed. If the distance be greater than the focus (as it may be ren- dered by depressing C to a lower level) then the rays will come to the eye converging, and the image will be more magnified but less distinct. If the distance of C be less than the focus, the image will be less magnified, but it will be distinct within certain limits. The reasons of these several modifications, will be evident by reflecting on principles already expounded. When the glass is of good quality, and the picture executed agree- ably to the rules of perspective, the various parts are exhibited in their natural positions, and at their relative distances, so as greatly to improve the view. The greater distinctness of the parts, and more natural distribution of light and shade than what attends the naked view, is owing not only to the increased magnitude and to the great- er quantity of the light emitted from the picture which is collected by the lens and conveyed to the eye, but also to the separation of this portion of light from that which proceeds from various other ob- jects. The lens both conveys more of the light of the picture to the eye than would otherwise reach it, and it conveys it unmingled with extraneous light. The importance of the latter circumstance is manifested even by looking at the picture through an open tube, or through the hand so curved as to form a tube. 542. The microscopes hitherto examined are such as are design- ed to be interposed between the -eye and the object to be viewed, the latter being placed in the focus of parallel rays of the lens, or a little nearer to the lens than that focus, so that the rays of the same pencil may come to the eye either parallel or with so small a degree of divergency, that the lenses of the eye shall be competent to make them converge and form an image on the retina. In this case, as the rays come to the eye in the same manner as rays from larger objects, at a greater distance, seen without the aid of a lens, the po- sition of the object is not changed, that is, it is seen erect. Single microscopes, however, are also employed to form a magnified image on a wall or screen, which is seen by the eye instead of the object itself. Two celebrated instruments, the Magic Lantern and the So- lar Microscope, magnify their objects in this manner, in the construc- tion of which the principles under review are happily exemplified, 310 OPTICS. 543. From what has been already learned respecting lenses, the following points will be readily comprehended, being for the most part a recapitulation of principles already explained and demonstrated. If, in a dark room, we place before a convex lens any luminous object, as a candle, we shall observe the following phenomena. (See Art. 501.) 1. If the radiant be placed nearer to the lens than its focus, since the rays will go out diverging, no image will be formed on the other side of the lens. 2. Even when the radiant is in the focus, so that the rays go out parallel, they never meet in a focus, and of course never form an image.* 3. But when the radiant is farther from the lens than its focus, the rays converge on the other side, those of each pencil, proceeding from the same point in the object, being accurately united in one point in the image, and occupying that point alone, without the inter- ference of rays from any other point. 4. The axes of the rays from the extreme parts of the object cross each other in the center of the lens. Hence, they form an image inverted with respect to the object; and, although the rays which make up any individual pencil are made to converge by the lens, yet the axes (which determine the magnitude of the picture) diverge from each other after crossing at the center of the lens, and hence the image is greater in proportion as it is formed at a greater distance from the lens. When the object is only a little farther off from the lens than its focus, the image is thrown to a great distance, and is proportionally magnified. As the object is separated farther from the lens (which may be effected either by withdrawing the object from the lens or the lens from the object) the image is formed at a less distance, and is of a diameter proportionally less. (See Art. 502.) Suppose now that we employ a magnifier of so small focal distance, that when the object is placed within one tenth of an inch of the lens, the image is formed on the other side upon a screen or wall at * If will be remarked, that when the single microscope is used as an eye glass, the eye itself brings the parallel rays to a focus and forms the image. MICROSCOPES. 311 the distance of twenty feet ; the object will be magnified in the ratio of T V to (20X12=)240; that is, the image will be 2,400 limes greater than the object in diameter, and 5,760,000 times greater in surface. It would seem, therefore, as if nothing more were neces- sary in order to form magnified images of objects, than a dark room, a convex lens, and a screen or wall for the reception of the picture. It must be remarked, however, that when the light which proceeds from the object is diffused over so great a space, its intensity must be greatly diminished, so as to be either incapable of affording a picture which shall be visible at all, or at least sufficiently bright for the pur- poses of distinct vision. This difficulty is remedied by illuminating the object ; and it is for this purpose, that most of the contrivances employed in the magic lantern and solar microscope are designed. 544. The MAGIC LANTERN consists of a large tin canister either cylindrical or cubical in its figure, having an opening near the bottom into which air may enter freely to supply the lamp, and a chimney proceeding from the top and bent over so as to prevent the light of the lamp from shining into the room. The lantern has a door in the side which shuts close, the object being throughout to prevent any light from escaping into the room except what attends the picture. The room itself is made as dark as possible ; or, what is better, the experiments are performed by night. In front of the lantern is fixed a large tube, at the open end of which is placed the magnifying lens. In the same tube, at a distance from the lens somewhat greater than the focal distance, the object is introduced, -which is usually some figure painted on glass in transparent colors, the other parts of the glass being blackened so that no light can pass through except that which falls on the object and illuminates it, by which means we shall have a luminous image projected on a black ground. For illu- minating the object, an argand lamp is placed near the center of the lantern, the light of which is concentrated upon the object in two ways ; first, by means of a thick lens, usually plano-convex, so situ- ated between the lamp and the object that the rays which diverge from the lamp shall be collected and condensed upon the object ; and, secondly, by means of a concave reflector situated behind the lamp, which serves a similar purpose. 312 OPTICS, A, the magnifying Fig. 121. lens. B, the object, in- troduced through an qpening in the tube. C, the condensing lens. D, the lamp. E, the concave mirror. F, the image thrown on a screen, or a white"wall, in a dark room. a, a thumb-piece, by which the magnifier may be made to approach or to recede from the object, and thus the image be thrown to a greater or less distance, according to the magnitude required. As the image is inverted with respect to the object, it is only necessary to introduce the object itself in an inverted position, and the image will be erect. The objects employed in the Magic Lantern are very various, con- sisting of figures of men and animals ; of caricatures ; of representa- tions of the passions ; of landscapes ; and of astronomical diagrams. When the last are employed, this apparatus becomes subservient to a useful purpose in teaching astronomy, and is frequently so employed by popular lecturers on that subject. 545. The SOLAR MICROSCOPE does not differ in principle from the Magic Lantern, only the object is illuminated by the concentra- ted light of the sun instead of that of a lamp. And since a power- ful illumination may thus be effected upon minute objects placed be- fore a'magnifier of great power, the solar microscope is usually em- ployed to form very enlarged images of the most minute substances, as the smallest insects, the most delicate parts of plants, and other attenuated objects of natural history. For magnifiers, several of different focal distances are employed, varying from an inch to the T it being understood that those of the short- est foc,us and greatest magnifying powers can be used only for the minutest objects, since, when bodies of a larger size are brought so near a small lens, their light strikes the lens too obliquely to be trans- mitted through it. The magnifying lens is fixed into the mouth of MICROSCOPES. a tube and the object placed near its focus, much in the same man- ner as in the magic lantern ; but instead of the body of the lantern (which contains the illuminating apparatus) a mirror, about three or four inches wide, and from twelve to eighteen inches long, is attach- ed to the other end of the tube. This mirror is thrust through an opening in the window shutter of a dark room, and the mouth of the tube to which it is fixed is secured firmly to the shutter, so that the mirror is on the outside, and the tube with its lenses is on the inside of the shutter. By means of adjusting screws, the mirror is turned in such a way as to direct the sun's rays into the tube, where they are received by one or more of the lenses, called condensers, which col- lect them and concentrate them upon the object, which thus becomes highly illuminated, and capable of affording an image sufficiently bright and distinct, though magnified many thousands or even millions of times. It will be observed that the magnitude of the image depends here, as in other cases of the simple microscope, upon the ratio be- tween the distances of the object and the image from the center of the magnifier. If, for example, the object be within the tenth of an inch of the lens, and the image be thirty feet, or three hundred and sixty inches from it, then the image will be 3GO X 10=3600 times as large as the object in diameter, and (3600) 2 = 12,960,000 times in sur- face. With a given lens, the size of the image depends wholly on the distance to which it is thrown ; that is, on the distance of the wall or screen where it is formed. 546. When the solar microscope is well constructed, it affords the most wonderful results, and greatly enlarges our conceptions of the delicacy, perfection, and subtility of the works of nature. In in- specting vegetables, the eye is delighted with the regularity and beauty which characterizes the texture and intricate structure of plants and flowers. The most delicate fibres of a leaf, the pores through which the vegetable fluids circulate, the downy covering of plants, and foliage, as of certain mosses, which is too minute to dis- close its figure to the naked eye, objects of this kind, when expand- ed under the solar microscope, astonish and delight us by the sym- metry of their structure. Their appropriate colors are not so well exhibited by this instrument, as by some other forms of the micro- scope to be described hereafter. In the animal kingdom, the solar 40 314 OPTICS. microscope extends the range of vision in a manner no less surprising and instructive. The minutest insects we are acquainted with, are exhibited to us as animals of the largest size, and often of monstrous shapes, from the multiplicity of their parts and apparent dispropor- tion ; and animalcules, or those members of the animal creation which are too minute to be seen at all by the naked eye, are sud- denly brought into life in countless numbers. The forms, the mo- tions, and the habits of these beings, are amorfg the most curious revelations of the solar microscope. The circulation of the blood may be seen in the fins of fishes and other transparent parts of ani- mals, presenting a very curious and interesting spectacle. The crys- tallization of salts, which may be exhibited while the crystals are forming and arranging themselves, (as many of them do with great precision and symmetry,) is among the finest representations of this instrument. Since the light is transmitted through the objects, it will of course be understood, that only such objects as are transparent can be em- ployed in the manner already described. In some varieties of the solar microscope, there are special contrivances for exhibiting opake objects by means of reflected light. 547. If we form an image of an object with the single microscope, (as is done in the magic lantern and solar microscope,) if that image is not too large, we may obviously apply to it a magnifier as we would to an original object of the same size. This is the principle of the Compound Microscope. The COMPOUND MICROSCOPE consists of at least two convex lenses, one of which, called the olyect-glass, is used to form an enlarged image of the object, and the other, called the eye-glass, is used to magnify the image still far- ther. Thus, let ab (Fig. 122.) be the object, being placed a little farther from the object glass, cd, than the principal focus, the rays of light ema- nating from it will be collected on the other side of the lens and form an image, gh, whose diameter is as much larger than that of the ob- ject as its distance from the lens is greater. (Art. 502.) Let ef be the eye-glass, which Fig. 122. MICROSCOPES. 315 must be placed at such a distance from the image, that the latter shall be in the focus of parallel rays ; then the rays proceeding from the image will go out parallel,* and come to the eye, situated behind the glass, in a state favorable for distinct vision. 548. The magnifying power of the Compound Microscope is es- timated as follows. First, the diameter of the image will be to that of the object as their respective distances from the lens. Secondly, the image is magnified by the eye-glass according to the principles of the single microscope, (Art. 536.) namely, from the ratio of its focal distance to the limit of distincrvision. Thus, suppose the image is formed at ten times the distance of the object ; it will of course be magnified ten times. Again, suppose the eye-glass has a focal dis- tance of one inch, the limit of distinct vision being five inches ; the image will be farther magnified five times; by both glasses, therefore, the object will be magnified fifty times. If the first ratio be that of one to one hundred, then the instrument will magnify the linear di- mensions five hundred times, and the surface two thousand five hun- dred times. From this double magnifying process, it might be sup- posed that, by means of the compound microscope, it would be easy to attain a much higher magnifying power than by the single microscope ; but this is not the fact ; for, in the first place, we cannot form an image of a size beyond certain moderate limits, without making it too large for the eye-glass to cover ; or, if an eye-glass of very large field of view be employed, its focal distance must be great, and consequently its magnifying power small. We are, therefore, unable to employ so high a magnifier for our object-glass as we may apply to the naked eye, and we can employ only a microscope of still inferior power for our eye-glass. 549. On account of the necessity of using a large eye-glass to view the magnified image, compound microscopes require to have the tube which contains the glasses, larger towards the eye-glass than towards the object-glass. Although the compound does not * It is to be remarked here and in all similar cases, that it is only the rays of each individual pencil that are parallel ; that is, those rays which come from the same point in the object. The rays of differ- ent pencils may cross each other variously, and the different pencils may converge or diverge among themselves ; still if the rays of each pencil be parallel to one another, the vision will be distinct. 316 OPTICS. possess higher magnifying powers than the simple microscope, yet it commands a much greater field of view. We view the image with the eye-glass in the same manner as we view the object with a sin- gle microscope ; but having already a magnified representation of the object, we have no occasion to apply to the eye so high a mag- nifier, and therefore we may employ one of greater focal distance which consequently takes in a greater field of view. The field of view is still farther improved in some compound microscopes by in- terposing a field-glass, which is a convex lens introduced between the object-glass and the place of the image, and near the latter (as a little below gh 9 Fig. 122,) the effect of which is to diminish the divergency of the pencils of rays, and thus to bring into the range of the eye-glass those pencils, which would otherwise diverge too much to fall within it. It has been before remarked that the cornea performs a similar office for the crystalline lens of the eye. (Art. 526.) 550. The PORTABLE CAMERA OBSCURA, which is used chiefly for delineating landscapes, consists of a wooden box, (answering to the dark chamber, Art. 523.) with which is connected a convex lens so exposed to the landscape as to receive the rays of light from the various objects in it, and form a picture of them on a screen placed within the box at the focal distance of the lens. Such is a general description of the instrument, of which there are several different forms. The following diagram represents a convenient form. ABCD, a box usually made of thin pie- ces of mahogany. a d, a plano-convex lens, this form being preferred because it has less aberration than a double convex. ED, a plane mirror, turning on a hinge at D, and capable of being raised or low- ered, so as to admit more or less of the landscape. b c, a piece of pasteboard, covered with a sheet pf fine white paper and bent a so as to form a concave screen, and placed at the focal distance of the lens. A casting of stucco, of the figure of a concave por- A tion of a sphere affords the most perfect picture. Fig. 123. TELESCOPES. 317 The rays of light from external objects, falling upon the mirror ED are conveyed to the lens in the same manner, as though they came directly from objects at the same distance behind the mirror. Passing through the lens, they are brought to a focus and form a picture of the landscape on the screen, which may be viewed by an opening in 'the side of the box at F, and may be copied by a hand introduced into the box by an opening below. Although the image is inverted with respect to the objects, yet as the spectator, in looking into the box, stands with his back to the landscape, the picture appears erect. CHAPTER VI. OF TELESCOPES. 551. The Telescope is an optical instrument, designed to aid the eye in viewing distant objects.* The construction of this noblest of instruments, in its different forms, involves the application of all the leading principles of the science of Optics. The study of the Telescope is therefore the study of the science, and a distinct enunciation of the principles in- volved in it, will serve as a recapitulation of the most useful princi- ples of Optics. The advantage which the student will derive from reviewing these points, as exemplified in their application, will justify us in bringing up distinctly to view various principles already unfol- ded. 552. The leading principle of the Telescope may be thus enun- ciated : By means of either a convex lens, or a concave mirror, an image of the object is formed, which is viewed and magnified with a micro- scope. The most general division of the instrument is into Refracting and Reflecting Telescopes ; of which the former produce their image by * ryjXs, at a distance, tfwjrsu, to see. 318 OPTICS. means of a convex lens, and the latter by means of a concave mir- ror. The instrument, according to the uses to which it is applied, receives the farther denominations of the Astronomical and the Ter- restrial Telescope ; and also Telescopes are named, after their seve- ral inventors, Galileo's, Newton's, Gregory's, Herschel's, &c. The Astronomical Telescope. 553. We begin with this variety because it is one of the most sim- ple, and because in connexion with it, we may conveniently study the theory of the instrument at large. The Astronomical Telescope, has essentially but two glasses : these are usually fixed in a tube of brass, one at one end, and the other at the other end. The glass at the end of the tube which is directed to the object is called the object glass, and that at the end to which the eye is applied, is called the eye glass. The object glass is a con- vex lens which forms an image of a distant object, as a star, in its fo- cus of parallel rays, and the eye-glass is a microscope with which we view the image, at a distance equal to its focus of parallel rays. Of course, the distance of the two glasses from each other is equal to the sum of thir focal distances. See the annexed figure. Fig. 124. MN, object glass. PQ, eye glass. A'D', AD, A"D", parallel rays from the top of the object. B'D', BD, B 'D", " " " center ditto. C'D', CD, C"D", " " " bottom ditto. 6a, inverted image formed in the focus of parallel rays. 6PF r . a pencil of rays, proceeding from the top of the image to the eye glass and rendered parallel. cKF, a similar pencil from the center. QF, ditto the bottom. F, point where the different pencils cross the axis. TELESCOPES. 319 554. In ibis instrument we observe a striking resemblance to the Compound Microscope. (Fig. 122.) In the microscope, however, since the object is nearer than the image, the image is greater than the object ; but in the telescope, since the object is removed to a great distance, the image is formed much nearer to the lens than the object, and is proportionally smaller. Hence, Compound Mi- croscopes have their tubes enlarged in diameter towards the eye glass, while telescopes have their tubes diminished in that direction. Since the vertical angles at D, subtended on the one side by the ob- ject, and on the other by the image, are equal, were the eye situa- ted at the center of the object glass, it would see the object and the image under the same visual angle, and consequently, both would ap- pear of the same magnitude. Moreover, were the eye placed at the same distance from the image on the other side of it, it would be ap- parently of the same size as before and therefore of the same appa- rent diameter as the object. But by means of a microscope, such as the eye glass in fact is, we may view it at a much nearer distance and of course magnify it to any extent, as was fully shown in ex- plaining the principles of the simple microscope. (Art. 536.) Hence the magnifying power of the telescope depends on the ratio between the focal distances of the object glass and the eye glass. If, as in the figure, *the common focus is ten times nearer the eye glass than to the object glass, the instrument will magnify ten times ; if one hundred times nearer, one hundred times ; and so in all other cases. Hence we may increase the magnifying power of the instrument, either by em- ploying an object glass of very small curvature, which throws its im- age to a great distance, or an eye glass of high curvature and small fo- cal distance. Suppose for example, the object glass has a focal dis- tance of forty feet, or four hundred and eighty inches, and the eye glass has a focal distance of one tenth of an inch, then the magnify- ing power of this instrument would be four thousand and eight hun- dred in diameter, and the square of this number in surface. 555. As the sphericity of the eye glass may be increased indefi- nitely, and its focal distance diminished to the same extent, it would seem possible to apply very high magnifying powers in very short telescopes. For example, suppose the focal distance of the object glass is twenty four inches ; by using a microscope of T V of an inch focus, we have a power of two hundred and forty. But it must be 320 OPTICS. kept in mind, that such microscopes command only an exceedingly small field of view, and would, therefore, not enable us to see any thing more than a minute portion of an object of any considerable size ; and not sufficient light would be transmitted through such an aperture to e answer the purpose of vision. Since the image is inverted with respect to the object, and is view- ed in this situation by the eye glass, objects seen through Astronom- ical Telescopes appear inverted. By the addition of several more lenses, they may be made to appear erect, as will be shown in the de- scription of the Day Glass, or Terrestrial Telescope ; but at every new refraction a certain portion of light is extinguished, a loss which it is important to avoid in instruments designed to be used at night; while, in regard to celestial objects, it is not essential whether they are seen erect or inverted. The place for the eye to view the image with the best advantage is at F, where the pencils of parallel rays meet. 556. The difficulties to be overcome in the construction of a per- fect Refracting Telescope, (some of which are very formidable,) are chiefly the following : 1. Spherical aberration; 2. Chromatic aber- ration ; 3. Want of sufficient light ; 4. Want of a field of view suffi- ciently ample ; 5. Imperfections of glass. Each of these particu- lars we will briefly consider. 557. Spherical aberration, it will be recollected, occasions indis- tinctness in images formed by lenses, in consequence of the different rays of the same pencil not being all brought to a focus at the same point, those which fall upon the extreme parts of the lens being more refracted and coming to a focus sooner than those which are nearer to the axis. (See Art. 503.) The amount of this error is found to depend on two circumstances, namely, the diameter of the lens, or what is technically called its aperture, and its focal distance, increas- ing rapidly as the aperture is increased, and diminishing as the focal distance is increased.. Small apertures and flat or thin lenses are, therefore, most free from spherical aberration. But if we use small apertures we cannot have a strong light, which is a circumstance of the greatest importance in astronomical observations, since it is of little consequence to enlarge the dimensions of an object if we have not light enough to render it visible. Indeed, many astronomical objects, as small stars, are rendered visible by the telescope, not in consequence of any apparent increase of size, but because this in- TELESCOPES. 321 strument collects and conveys to the eye a much larger beam of light from them than would otherwise enter it. While the diameter of the beam which falls upon the naked eye is only the fraction of an inch, that collected by the telescope may be several inches, or even several feet, according to the size of the instrument. Hence, the advantages of large apertures is obvious. Again, we cannot wholly remedy the error in question, though we may diminish it by using very flat lenses which have great focal distances ; but the ten- dency of this expedient is to render the instrument inconveniently long. Other expedients, therefore, become necessary for correcting spherical aberation in refracting telescopes. 558. In the eye glasses, which are liable to the same difficulty, where the lens has a great curvature, as is the case with such as have high magnifying powers, the aperture is necessarily reduced very much, by excluding all the light except what passes through the cen- tral parts of the lens. At least this is the case where glass lenses are used. 'But the microscopes made of diamond, sapphire, and other gems, have not only high refractive powers, but are less sub- ject to spherical aberration than similar lenses of glass. But although eye pieces, on account of their small size, may sometimes be made of the precious gems, yet this can rarely be the case on account of the great expense attending them. It is obvious also that they cannot be employed for the object lenses. The most successful method of diminishing spherical aberration in eye pieces of glass, is by a combination of plano-convex lenses, by means of which a given refracting power may be attained with far greater dis- tinctness than by a single lens of the same power. Thus, when two plano-convex lenses are placed as in Fig. 125, it is found that the image has four times the distinct- ness of a double convex lens of equivalent power.* Here F is a lens which would bring the G -C... parallel rays to a focus and form the image at the distance of G ; * The Scioptic Ball, used in the camera obscura, (Art. 524.) is form- ed of two such lenses. 41 322 OPTICS. but E is another similar lens, which, receiving them in a converging state, makes them converge more and come to a focus at H. The double convex lens D would do the same, but with much greater spherical aberration. It appears, indeed, that the spherical aberra- tion may be wholly removed by combining a meniscus with a double convex lens of certain curvatures. 559. In object glasses, which, on account of their smaller curva- tures, are not so subject to error from spherical aberration as eye glasses are, the most advantageous form is that of a double convex lens of unequal curvatures, the radii of the opposite surfaces being as one to six, -(Art. 504.) and the flat side being turned towards the parallel rays. In short it appears, that in order to avoid the errors arising from spherical aberration, in large lenses, they must be made as thin as convenience will permit ; that where it is practicable, they may be most advantageously formed of the precious gems, particularly the diamond ; that a plano-convex lens with its convex side towards the parallel rays has less aberration than a double convex lens of equiv- alent power ; that two plano-convex lenses may be so combined as to have only one fourth as much aberration as the double lens, and a meniscus may be so united to a double convex lens as wholly to prevent aberration ; and finally, that the aberration may be reduced to a very small error simply by employing a double convex lens whose curvatures on the opposite sides are as 1 to 6. Since lenses having the curvature of one of the conic sections are free from spherical aberration, Sir Isaac Newton ground an object glass into the figure of a paraboloid. This was free from the error in question, but involved another still more formidable, since it de- composed the light and gave an image tinged with the colors of the rainbow. On observing this, Sir Isaac pronounced the farther im- provement of the refracting telescope to be hopeless, and betook himself to exclusive efforts for improving the reflecting telescope. But the combined ingenuity of philosophers and artists, has nearly overcomeahis error also. 560. The next difficulty, therefore, to be considered is that which arises from the separation of the prismatic colors, in consequence of TELESCOPES. 323 . the different refrangibility of the different rays, an error which is called Chromatic Aberration. The general principles of Chromatic Aberration, will be readily comprehended by calling to mind, that distinct images are formed only when the rays of the same pencil which flow from any point in the object are collected into one and the same point in the image, unmixed with rays from any other point ; that the prismatic rays which compose white light have severally different degrees of re- frangibility, some being more turned out of their course than others, in passing through the same medium ; that, consequently, the differ- ent colored rays of the same pencil would meet in different points, each set of colored rays forming its own image, but all these images becoming blended with one another, and thus composing a confused, colored picture. To illustrate these prin- Fig. 126. ciples let LL be a lens of crown glass, and RL, RL. rays of white light incident upon it, parallel to its axis Rr. Let the extreme vio- let rays be refracted so as to meet the axis in v ; then the extreme red will meet the axis at some point more distant from the lens, as at r. Cv and Cr are the focal distances of the lens for the violet and the red rays respectively. The distance m is the chromatic aberration, and the circle whose diameter is ab } which passes through the focus of the mean refrangible rays at 0, is called the circle of least aberration. 561. It is clear from these observations, that the lens will form a violet image of the sun at v, a red image at r, and images of the other colors of the spectrum at intermediate points between r and v; so that if we place the eye behind these images, we shall see a con- fused image, possessing none of that sharpness and distinctness which it would have had if formed only by one kind of rays. The separation of white light into its prismatic colors, is called Dispersion ; and the comparative power of effecting this separation, possessed by different media, is called the Dispersive power. The dispersive power is measured by the ratio which, in any case, the 324 OPTICS. separation of the red arid violet rays bears to the mean refraction of the compound ray. Thus, if a ray of solar light on passing through a lens, is turned out of its original direction 27, and the red and violet rays are separated from each other 1, then the dis- persive power is said to be ^ T , which is usually expressed in the form of a decimal fraction, .037 =^ T . 562. Different bodies possess different dispersive powers. The dispersive powers of a few of the most important substances in relation to the subject before us, are exhibited in the following table. Dispersive Power. Dis. Power. Oil of Cassia, 0.139 Plate Glass, 0.032 Sulphuret of Carbon, 0.130 Sulphuric Acid, 0.031 Oil of Bitter Almonds, 0.079 Alcohol, 0.029 Flint Glass, 0.052 Rock Crystal, 0.026 Muriatic Acid, 0.043 Blue Sapphire, 0.026 Diamond, 0.038 Fluor Spar, 0.022 Crown Glass, (green,) 0.036 From this table it appears, that the transparent substances which have the highest dispersive power, are the oil of cassia and the sul- phuret of carbon,* both of which fluids have been made to perform an important service in the construction of achromatic telescopes ; that flint glass, as that used for decanters, has a much higher disper- sive power than crown glass, or that which is analogous to window glass ; that the diamond has a low dispersive power, but is exceeded in this respect by rock crystal, the sapphire, and fluor spar, which last bodies have the least dispersive power of any known substances. 563. With these facts in view, we may now inquire by what means the object glass of the telescope is rendered achromatic. If we place behind LL (Fig. 126.) a concave lens GG of the same glass, and having its surfaces ground to the same curvature, such a lens having properties directly opposite to those of the con- vex lens will neutralize its effects. Consequently, the rays which A limpid fluid prepared from sulphur and charcoal. TELESCOPES. 325 were separated into their prismatic colors by the convex lens will be reunited by the concave lens, and reproduce white light. But though such a combination of the two lenses will correct the color, yet it also destroys the power of the convex lens to form an image, on which its use solely depends. Could we find a concave lens which would correct all the color and yet not destroy this refracting power, the two lenses would evidently form the achromatic combination sought for. Now this is what is actually done : by making the concave lens of a substance which has a higher dispersive power than that of which the convex lens is made, the curvature of the concave lens will not need to be so great as that of the convex lens, and of course the two together, constituting the compound lens, will be equivalent in refract- ing power to a single lens, whose convexity is equal to the difference of their curvatures. The most common combination is that of flint glass with crown glass, the concave lens being made of flint glass, and the convex of crown. By the table in Art. 562, it will be seen that the dispersive power of flint glass is 52 while that of crown glass is 36, which numbers are nearly as 3 to 2, and these numbers, there- fore, may be employed for the sake of illustration. Since the power of the concave lens to reunite the prismatic rays is so much greater than that of the convex lens to separate them, we shall not require a refractive power to effect this equivalent to that of the convex lens; that is, a concave lens of less curvature and proportionally greater focal distance, will serve our purpose. Therefore, An achromatic lens is formed by the union of a convex and a con- cave lens, whose dispersive powers are respectively proportional to their focal distances. 564. A telescope furnished with an object glass thus formed, is called an Achromatic Telescope. The spherical aberration being corrected by the methods pointed out in Art. 557, and the chro- matic aberration being destroyed in the manner above described, the Refracting Telescope becomes an instrument of great perfection, and is reckoned among the greatest works of art. Until recently, it was rare to meet with Refracting Telescopes of an aperture of more than from three to five inches. For we have already seen that the errors of spherical and chromatic aberration increase rapid- ly as the size of the aperture is augmented. 326 OPTICS. 565. If it be asked, what is the use of a large aperture, since the magnifying power does not depend upon the diameter of the object glass, but upon the ratio between the focal distance of the object glass and the focal distance of the eye glass, (Art. 554.) we answer, that the use of a large aperture is to admit, condense, and finally convey to the eye, a larger beam of light, and thus to render many objects, as the smaller stars, or Jupiter's belts, visible, which other- wise would not be so, on account of the feebleness of the light which they transmit to us. Want of light is in fact one of the great- est difficulties that the telescope has to contend with ; for, in the first place, the object glasses of most telescopes are comparatively small, and are necessarily so on account of the difficulty of procuring suit- able glass for those of a larger size ; and in the second place, of the light admitted through the object glass, a great proportion is inter- cepted and wasted in various ways, many instruments being able to save only the central rays without rendering the image indistinct and colored. Thus, when very high magnifiers are applied, (which of course have very small focal distances,) the rays proceed from the focus and fall upon the microscope so obliquely, that only those which pass through the central parts of the lens can be saved, since such as fall upon the marginal parts of the lens are too much affect- ed by spherical and chromatic aberration, to form with the others a distinct and colorless image. 566. Want of field of view is another difficulty to be surmounted. When we use an object glass of short focus with a high magnifier, the microscope must have a focus proportionally short, and of course the field of view will be very limited and the light but feeble. This difficulty may be obviated by using an object glass of very great fo- cal distance. If, for example, the focal distance of the object glass were only 12 inches, in order to attain a magnifying power of 120, we must employ a microscope whose focal distance is only y^th of an inch. But if the focal distance of the object glass were 10 feet, or 120 inches, then our microscope might have a focal distance of 1 inch, jyhich would give a larger field and a stronger light. With the view of obviating several of the foregoing difficulties, the earlier astronomers who used the telescope, employed their object glasses lenses whose focal lengths were very great. Cassini, an Italian as- TELESCOPES. 327 tronomer, constructed telescopes eighty, one hundred, and one hun- dred and thirty six feet long ; and Huygens employed such as were nearly the same length. The latter astronomer dispensed with the tube, fixing his object glass, contained in a short tube, to the top of a high pole, and forming the image in the air near the level of the eye, which image he viewed with an eye glass, as usual. With tele- scopes of this description, several of the satellites of Saturn were discovered. 567. But one of the most formidable difficulties hitherto encoun- tered in the construction of large Refracting Telescopes, has arisen from the imperfections of glass. When Dollond (the Engljsh artist who first perfected the Achromatic Telescope,) engaged in the manu- facture of his instruments, he fortunately had possession of a consid- erable quantity of very fine glass ; but when that was used up, no more of equal quality could be obtained in England.* On the con- tinent, however, one or two celebrated artists have been more suc- cessful. The most distinguished manufacturer of optical glass was M. Guinand of Switzerland, who died in 1823. He greatly excelled all his predecessors or cotemporaries in fabricating large masses of perfectly homogeneous glass. But even he could produce disks of twelve or eighteen inches in diameter in no other way, than by se- lecting the purest specimens of smaller pieces, and joining them to- gether. In 1805, M. Fraunhofer of Bavaria, a celebrated manu- facturer of telescopes, invited Guinand to become his associate in the manufacture of optical glass; and from the united efforts of these most ingenious men, proceeded glass of unexampled transparency and purity. Fraunhofer has recently deceased, and the difficulty of procuring perfect glass is renewed. This induced the Royal Society of London to appoint a committee to institute new experiments on this subject. These have been prosecuted with the greatest ability, but have as yet produced no important results. " * The present Mr. Dollond, a successor of the inventor of Achro- matic Telescopes, " has not been able to obtain a disk of flint glass four inches and a half in diameter, fit for a telescope, within the last five years, or a similar disk of five inches diameter within the last ten years." Faraday, Phil. Trans. 1830, 328 OPTICS. 568. These circumstances we have thought worthy of being reci- ted in order to impress on the mind of the learner the formidable na- ture, as well as the great number, of the difficulties to be overcome in the construction of a large Achromatic Telescope. Yet they have in several instances, been completely surmounted. Fraunhofer ex- ecuted two telescopes with achromatic object glasses, the one nine inches and nine tenths, and the other twelve inches in diameter ; and at the period of his death he was proposing to undertake one eight- een inches in diameter. That of 9.9 inches aperture was made for the Russian government for the use of the observatory at Dorpat, where under the direction of M. Struve, a distinguished astronomer, it has ajready achieved several valuable discoveries in astronomy. The object glass has a focal length of twenty five feet. The con- cave part of the compound lens is formed of a dense flint glass made by Guinand, and has a greater dispersive power than any obtained before. It is perfectly free from veins, and nearly from every impu- rity. The instrument has four eye glasses varying in magnifying power from one hundred and seventy five to seven hundred.* 569. The great difficulty of procuring perfect glass for achro- matic telescopes has led opticians to attempt the construction of len- ses for this purpose out of some transparent fluid which might be in- closed -in thin glass. Such a medium seemed peculiarly suited to take the place of the concave lens in which the principal difficulty resides. Professor Barlow, of the Military Academy of Woolwich, has recently made several telescopes on this principle, the last of which had an aperture of 7.8 inches, and performed as well as the larger kind of achromatic telescopes constructed in the usual way. The fluid employed for this purpose was the sulphuret of carbon, a limpid fluid prepared from sulphur and charcoal. It is singularly adapted to optical purposes, having a refracting power about equal to that of the best flint glass, with a dispersive power more than double * It is said that as a general rule, Achromatic Telescopes]are priced in the i^io of the cube of the aperture. If a telescope with an ob- ject glass three inches in diameter, is valued at five hundred dollars, one. of twelve inches would cost sixty four times as much, that is, thir- ty two thousand dollars. TELESCOPES. 329 that of the same substance. It is, moreover, perfectly colorless, beautifully transparent, and although it is very volatile yet when close- ly sealed it possesses nearly the same optical properties under all re- quired temperatures. The advantages of using sulphuret of carbon should the experiments finally succeed as well as is expected, are the following : 1. It renders us independent of flint glass. 2. It enables us to increase the aperture of the telescope to a very considerable extent. 3. It gives us all the light, field and focal power of a telescope of one and a half times at least, probably twice the length of the tube. 4. The expense of large telescopes (which consists mainly in the cost of the object glass) is greatly diminished, the most expensive part being supplied with less than one ounce of sulphuret of carbon of the value of three shillings. The Terrestrial or Day Telescope. 570. As the Astronomical Telescope represents objects inverted, it requires to be so modified for terrestrial views, that objects may appear erect. This is effected by the addition of two more lenses of similar figure to that of the eye glass, and of the same focal length. The first of these additional glasses forms a second image of the ob- ject inverted with respect to the first image and therefore erect with respect to the object. This image is viewed by the second glass 33 by any simple microscope. Thus, AB, the object glass forms an in- M li verted image nm of the object MN. Instead of viewing this image by the eye placed at L, as in the common astronomical telescope, we suffer the pencil of parallel rays to cross each other at L and fall upon a second lens EF (similar in all respects to CD) which collects them into an image m'n' in its focus of parallel rays, which image is 42 330 OPTICS. viewed by the eye glass GH in the same manner as the object itself would be. As some portion of the light is reflected, and some absorbed and dissipated by passing through these additional lenses, they of course diminish the brightness of the view ; but in the day time there will usually be light enough for distinct vision after this loss is sustained y while it is more agreeable and convenient to have the objects present- ed to us in their natural positions than inverted. It will be remarked that the additional lenses do not magnify, the focal length of each being the same as that of the first eye glass. Were they rendered smaller for the purpose of magnifying, the field of view and the light would both be impaired. 571. We usually find in telescopes, particularly those designed for terrestrial objects, some contrivance, as a draw tube, by which the eye glass can be brought nearer to, or withdrawn from the object- glass. This is to accommodate the instrument to objects at different distances. When it is directed to very near objects, the image is thrown farther back, and therefore in order that it may be in the fo- cus of the eye glass, (which is essential to distinct vision) the latter must be drawn backward ; but where the object is remote, the image is formed nearer to the object glass, and then the eye-glass must be moved forward, till its focus of parallel rays, comes to the place of the image. For a similar reason, near sighted persons require the eye-glass to be brought nearer than usual to the object-glass; for then the image will be nearer to the eye-glass than its focus of parallel rays, and the rays will meet the eye diverging, a condition favorable to eyes naturally too convex. For a contrary reason, long sighted persons, who usually wear convex spectacles, may adjust the telescope to suit their eyes without spectacles, by removing the eye- glass farther back than usual. Most terrestrial telescopes contain a greater number of glasses than are represented in Fig. 127. Such a number are used for the purpose of correcting spherical and chromatic aberration, these er- rors being less in several flat and thin lenses than in a smaller num- ber of equivalent lenses of greater curvature. Astronomical telescopes are easily adapted to terrestrial observa- tions, by removing the eye glass and substituting a tube containing the additional glasses for rendering the view erect. TELESCOPES. Reflecting Telescopes. 331 572. Reflecting Telescopes differ in principle from those already- described only in forming their image by a concave reflector, instead of a convex object-glass. The most common form of the Reflect- ing Telescope, is the Gregorian, so called from the inventor, Dr. James Gregory, of Scotland. The general principles of this instru- ment may be explained as follows : In the Gregorian Telescope, the light (supposed to come in par- allel rays) is first received by a large concave speculum, by which it is brought to a focus and made to form an inverted image. On the opposite side of this image, and facing the large speculum, is placed a small concave speculum, of greater curvature, at such a distance from the image that the rays proceeding from it and falling on the speculum are made to converge to a focus situated a small distance behind the large speculum, passing through a circular aperture in the center of it. This second image is magnified by a microscope as in the Refracting Telescope. This description may now be ap- plied to the annexed figure. Fig. 128. A B ABCD, a large open tube of brass, iron, or mahogany to contain the reflectors. abed, a smaller tube to receive the second image and the eye glass. EE, large concave speculum, usually composed of a metallic com- pound called speculum metal. FF, small concave speculum. win, image formed by the large reflector. nm, image formed by the small reflector. G, eye glass. WY, a metallic rod having a screw connected with the small re- flector, by means of which this reflector is made to approach the first image or to recede from it. 332 OPTICS. Some of the pencils of rays necessary to form the respective ima- ges are omitted in the figure to prevent confusion. 573. From the foregoing construction it is evident, first, that the image viewed by the eye being in the same position with the object, the latter will appear erect; secondly, that since the mirrors may be formed of a parabolic figure,* all spherical aberration may be easi- ly prevented ; thirdly, that since light is not decomposed by reflex- ion, reflecting telescopes are not subject to chromatic aberration : and, hence, that it is not necessary to lengthen the tube as the ap- erture is increased, as is the case in refracting telescopes (Art. 566.) ; but since the light will depend, chiefly, on the size of the large reflector, a strong light may be obtained with a comparatively short tube. The achromatic telescope, however, with all the latest improvements, is deemed a more perfect and more convenient in- strument than the reflecting telescope ; and it is supposed that there will be no occasion hereafter to construct reflectors of such enor- mous dimensions as those of Dr. Herschel. Some account of his forty feet reflector may form a suitable close to this sketch of optical instruments. 574. Under the munificent patronage of George III, Sir William Herschel began, in 1785, to construct a telescope forty feet long, and in 1789, on the day when it was completed, he discovered with it the sixth satellite of Saturn. The great speculum was more than four feet in diameter, and weighed two thousand one hundred and eighteen pounds. Its focal length was forty feet. The tube which contained it was made of sheet iron. The light afforded by this instrument was astonishingly great. The largest fixed stars, as Sirius, shone in it with the splendor of the sun. The reason of this will be obvious when we reflect that it collected and conveyed to the eye, in the place of the Small beam that enters the naked organ, a beam of light from the star more than four feet in diameter. Hence it was suited to reveal to the eye numberless stars and clusters of stars, which preceding telescopes had failed t<5 exhibit, because they could not collect a sufficient quan- An elliptical figure has the same properly TELESCOPES. 333 tity of their light. To economize the light to the best advantage, the small mirror employed in the Gregorian telescope (see Fig. 128.) was dispensed with, since every successive reflexion dissipates a con- siderable portion of the light, and the image was thrown near to the open mouth of the tube, where it was viewed by the eye-glass direct- ly, the observer being seated so as to look into the mouth in front. In- order to prevent the head from obstructing too much of the light, the image was formed near one side of the tube. Its greatest mag- nifying power was six thousand four hundred and fifty ; but this was used only for the smallest stars. This great telescope was mounted out of doors in a frame of pro- portional size ; but by exposure to the weather, the frame has re- cently become so much decayed that it has been taken down and another telescope of twenty feet focus erected in its place, with which Sir J. Herschel is prosecuting, with great success, the researches of his father. APPENDIX. OF PHILOSOPHICAL APPARATUS AND EXPERIMENTS. THE utility of experiments for verifying the truths of philosophy, and for impressing them upon the memory of the learner, is univer- sally acknowledged. Experiments, indeed, constitute the true and legitimate kind of entertainment, by which the dryer and less attract- ive parts of this science are to be rendered acceptable and pleasing to the young learner. In most of our schools, however, few or no experiments are given in connexion with the study of Natural Philosophy, either from the want of suitable apparatus, or of leisure or inclination on the part of the instructor. Although accurate and expensive instruments are highly useful for the purpose of verifying the doctrines of philosophy, still, numerous and useful illustrations of philosophical principles may be exhibited by apparatus of an inferior kind, such as can be constructed under the direction of the experimenter himself, by ordinary mechanics. An ingenious artisan, furnished with suitable cuts or drawings, with a few directions from the teacher, will construct many plain articles of apparatus, that will answer the purpose nearly as well as more ex- pensive instruments. For instruments of the better sort, however, it will generally be found more advantageous to apply to professed instrument makers, a number of whom will be found in each of our large cities. The following list of articles, with such additions as every one may easily make for himself, will be sufficient for performing the experiments necessary to accompany the present work. 1. dltwootfs Machine, (Fig. 2, p. 16.) This is one of the most useful articles of apparatus, since it affords the means of verifying the fundamental principles of mechanics. (See pp. 16, 21, and 34.) It is, however, too expensive to be comprised in small collections of apparatus. 2. Whirling Tables. These afford an instructive exemplification of the principles of rotary motion, and of the doctrine of centrifugal force. 3. Center of Gravity Apparatus. Several articles, of the nature of toy*, are sold at the instrument maker's, which afford a pleasing illustration of the doctrine of the center of gravity. 4. Mechanical Powers. A set of these, in brass, connected to- gether in the same frame, is sold in the shops. They afford pleasing illustrations of the principle of the Lever, the Wheel and Axle, &c. PHILOSOPHICAL APPARATUS. 335 The principles of HYDROSTATICS and PNEUMATICS, are suscepti- ble of very striking and accurate verification by means of suitable- apparatus. 5. Bent Tube, (Fig. 62.) Or, the apparatus represented in Fig. 63, may be easily formed by inserting into a strong wooden box y made water-tight, glass tubes, or vessels of almost any shape, as a broken decanter, or glass receiver. 6. Hydrostatic Paradox, (Fig. 54.) This may be made by a saddler, or better by a professed bellows-maker. Two circular pie- ces of hard, close-grained wood, eighteen inches in diameter and two inches thick, are used for the top and bottom. To these is nailed a piece of the strongest leather, well soaked with oil, or satu- rated with melted tallow. The glass tube, instead of ascending; from the side, as represented in figure 64, may more conveniently be attached to a large screw inserted in the top board, near one side. This may be unscrewed for the purpose of introducing water. The glass tube may be about three feet long, and of quarter inch bore. Although very heavy weights may be raised by a small quantity, as half a gill, of water, yet they rise through so small a space as hardly to be perceptible, and the experiment is not sufficiently striking to interest the spectator. The motion, however, may be multiplied by connecting a lever arid multiplying wheels with the bellows, by which means a very small motion of the bellows will give a rapid revolution to a pointer, and thus render the verification of the doctrine entirely satisfactory. Such a multiplying apparatus has been connected with the bellows belonging to the apparatus of Yale College, that half a gill of water will communicate a rapid motion to a pointer, when the bellows is loaded with a weight equivalent to ten fifty-sixes, or five hundred and sixty pounds. 7. Specific Gravity Apparatus. A box of instruments under this name is sold in the shops ; but an accurate pair of scales and weights, a hook being attached to the bottom of one of the scales, is all thai is absolutely required, beyond such apparatus as every one may command. 8. Air Pump, (Fig. 68.) A double barrelled air-pump, of the kind represented in figure 68, with the various appendages that usu- ally accompany it, is a most important article of philosophical ap- paratus. The experiments performed with it, upon the pressure and elasticity of the air, are easy to the experimenter, and novel, entertaining, and instructive to the learner. The barrels are some- times made of glass instead of brass, which has the advantage of rendering the process of exhaustion visible to the learner. Such barrels are also preferable to those of brass, on account of their being less liable to corrode from the action of the oil employed to soften the valves and tighten the juncture of the piston. 9. Condensing Syringe, (Fig. 70.) Sometimes a copper bottle furnished with several spouts for projecting water in different shaped 336 PHILOSOPHICAL APPARATUS. jets, is sold with the condensing syringe. This apparatus is useful for illustrating the principles of spouting fountains, the fire engine, &c. 10. Barometer. The mountain barometer, which is adapted ei- ther for indicating changes of weather, or for taking heights, is the kind to be preferred. Jt would be conducive to the interests of sci- ence, for every literary institution to keep an accurate daily register of the states of the barometer and thermometer. 11. Syphon Tube. A common glass tube, bent over a dish of coals, will answer every purpose of a syphon. 12. Pump Models, (Figs. 74. 75.) 13. Model of the Steam Engine. This will be found highly in- structive and interesting to pupils. They are made of various forms, but are usually somewhat expensive. 14. Electrical Machines, (Figs. 80. 81.) The subject of elec- tricity, can scarcely be understood without experiments. A consid- erable number of these, however, can be performed with such a hum- ble apparatus as that described on page 202 ; but a well selected electrical apparatus is not very expensive, and is a great ornament to a collection. Nearly all the articles represented in the figures under the head of Electricity are required, together with several that are mentioned in the text. 15. Horse-shoe Magnet. A large magnet of this kind will be suf- ficient for verifying the most important laws of magnetism. 16. Jl concave and a convex Mirror. 17. Two Prisms. 18. Perspective Glass, (Fig. 120.) The lens belonging to this instrument, (the mirror being taken off,) will be found very conven- ient for experiments on refraction, being ready mounted on a stand. 19. Microscope. One or two single microscopes of different pow- ers, will be sufficient to illustrate the theory of the instrument. 20. Magic Lantern. This apparatus with transparent figures, is not expensive, and affords a pleasing exemplification of the magnify- ing power of lenses. 21. Solar Microscope. This is a very interesting piece of appa- ratus, and should accompany every collection where the expense can be afforded. 22. Achromatic Telescope. A telescope of two inches aperture will, if well constructed, be sufficient to afford good views of the moon and of Jupiter's satellites. The expense of the foregoing apparatus will of course vary with its quality. The entire collection, made in the best manner, would not cost more than one thousand dollars ; and when constructed in a style less finished and elegant, but still in such a way as to answer the purpose of illustration, the cost might be as low as five hundred dollars. Taking out Atwood's Machine, the model of the Steam Engine, and the Telescope, the remaining articles would not cost more than from one hundred and fifty to two hundred dollars. 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