7. "ft 
 
BY THE SAME AUTHOR, 
 
 &#t-bo0k an 
 
 FOR THE USE OF SCHOOLS AND COLLEGES, 
 
 WITH NEARLY 300 ILLUSTRATIONS. 12MO, SHEEP. PRICE 75 CENTS. 
 
 (Third Edition, revised.) 
 
TEXT-BOOK 
 
 NATUKAL PHILOSOPHY. 
 
 FOR THE USE OF 
 
 SCHOOLS AND COLLEGES. 
 
 CONTAINING THE MOST RECENT DISCOVERIES AND FACTS COM- 
 PILED FROM THE BEST AUTHORITIES. 
 
 JOHN 'WILLIAM DRAPER, M.D., 
 
 PROFESSOR OF CHEMISTRY IN THE UNIVERSITY OF NEW YORK, AND FORMERLY 
 
 PROFESSOR OF NATURAL PHILOSOPHY AND CHEMISTRY IN HAMP- 
 
 DEN SIDNEY COLLEGE, VIRGINIA. 
 
 nearly Jfour ^untoretr Xllustratfons* 
 
 NEW YORK: 
 HARPER & BROTHERS, PUBLISHERS, 
 
 82 CLIFF STREET. 
 
 1847. 
 
Entered, according to Act of Congress, in the year one thousand 
 eight hundred and forty-seven, by 
 
 HARPER & BROTHERS, 
 
 in the Clerk's Office of the District Court of the Southern District 
 of New York. 
 
X7 
 
 PREFACE. 
 
 THE success which has attended the publication of my 
 '* Text-Book on Chemistry," four large editions of it 
 having been called for in less than a year, has induced 
 me to publish, in a similar manner, the Lectures I for- 
 merly gave on Natural Philosophy when professor of that 
 science. 
 
 It will be perceived that I have made what may appear 
 an innovation in the arrangement of the subject ; and, 
 instead of commencing in the usual manner with Me- 
 chanics, the Laws of Motion, &c., I have taught the 
 physical properties of Air and Water first. This plan 
 was followed by many of the most eminent writers of 
 the last century ; and it is my opinion, after an extensive 
 experience in public teaching, that it is far better than 
 the method ordinarily pursued. 
 
 The main object of a teacher should be to communi- 
 cate a clear and general view of the great features of his 
 science, and to do this in an agreeable and short manner. 
 It is too often forgotten that the beginner knows nothing ; 
 and the first thing to be done is to awaken in him an 
 interest in the study, and to present to him a view of the 
 scientific relations of those natural objects with which he 
 is most familiar. When his curiosity is aroused, he will 
 readily go through things that are abstract and forbidding ; 
 
IV PREFACE. 
 
 which, had they been presented at first, would have dis- 
 couraged or perhaps disgusted him. 
 
 I am persuaded that the superficial knowledge of the 
 physical sciences which so extensively prevails is, in the 
 main, due to the course commonly pursued by teachers. 
 The theory of Forces and of Equilibrium, the laws and 
 phenomena of Motion, are not things likely to allure a 
 beginner ; but there is no one so dull as to fail being 
 interested with the wonderful effects of the weight, the 
 pressure, or thje elasticity of the air. It may be more 
 consistent with a rigorous course to present the sterner 
 features of science first ; but the object of instruction ib 
 more certainly attained by offering the agreeable. 
 
 But though this work is essentially a text-book upon my 
 Lectures, I have incorporated in it, from the most recent 
 authors, whatever improvements have of late been intro- 
 duced in the different branches of Natural Philosophy, 
 either as respects new methods of presenting facts or the 
 arrangement of new discoveries. In this sense, this work 
 is to be regarded as a compilation from the best authori- 
 ties adapted to the uses of schools and colleges. 
 
 Disclaiming, therefore, any pretensions to originality, 
 except where directly specified in the body of the work, 
 I ought more particularly to refer to the treatises of 
 Lame and Peschel as the authorities I have chiefly fol- 
 lowed in Natural Philosophy ; to Arago, Herschel, and 
 Dick in Astronomy. To the treatises of M. Peschel and 
 the astronomical works of Dr. Dick I am also indebted 
 for many very excellent illustrations. 
 
 Those subjects, such as Caloric, which belong partly 
 to Chemistry and partly to Natural Philosophy, and 
 which, therefore, have been introduced in my text-book 
 on the former subject, I have endeavored to present here 
 in a different way, that those who use both works may 
 have the advantage of seeing the same subject from dif- 
 
PREFACE. V 
 
 ferent points of view. The laws of Undulations, now 
 beginning to be recognized as an essential portion of this 
 department of science, I have introduced as an abstract 
 of what has been written on this subject by Peschel and 
 Eisenlohr. 
 
 It will, therefore, be seen that the plan of this work is 
 essentially the same as that of the Text-Book on Chem- 
 istry. It gives an abstract of the leading points of each 
 lecture three or four pages containing the matter gone 
 over in the class-room in the course of an hour. The 
 lengthened explanations and demonstrations which must 
 always be supplied by the teacher himself are, therefore, 
 except in the more difficult cases, here omitted. The 
 object marked out has been to present to the student a 
 clear view of the great facts of physical science, and 
 avoid perplexing his mind with a multiplicity of details. 
 
 There are two different methods in which Natural 
 Philosophy is now taught: 1st, as an experimental 
 science ; 2d, as a branch of mathematics. Each has its 
 own peculiar advantages, and the public teacher will 
 follow the one or the other according as it is his aim to 
 store the mind of his pupil with a knowledge of the great 
 facts of nature, or only to give it that drilling which arises 
 from geometrical pursuits. From an extensive compari- // 
 son of the advantages of these systems, I believe that 
 the proper course is to teach physical science experi- 
 mentally first a conviction not only arising from consid- 
 erations respecting the constitution of the human mind, 
 the amount of mathematical knowledge which students 
 commonly possess, but also from the history of these 
 sciences. Why is it that the most acute mathematicians 
 and metaphysicians the world has ever produced for two 
 thousand years made so little advance in knowledge, and ,/- 
 
 why have the last two centuries produced such a 
 derful revolution in human affairs 1 It is from the lesstm 
 
VI PREFACE. 
 
 first taught by Lord Bacon, that, so liable to fallacy are 
 the operations of the intellect, experiment must always 
 be the great engine of human discovery, and, therefore, 
 of human advancement. 
 
 To teachers of Natural Philosophy I offer this book as 
 a practical work, intended for the daily use of the class- 
 room, and, therefore, so divided and arranged as to en- 
 able the pupil to pass through the subjects treated of in 
 the time usually devoted to these purposes. A great 
 number of wood cuts have been introduced, with a view 
 of supplying, in some measure, the want of apparatus or 
 other means of illustration. The questions at the foot of 
 each page point out to the beginner the leading facts 
 before him. 
 
 JOHN WILLIAM DRAPER. 
 
 University, New York, 
 July 16, 1847. 
 
CONTENTS. 
 
 Lecture -'^ i Pg 
 
 I. Properties of Matter . . .* .-. -.,_*/. 1 
 
 II. Properties of Matter and Physical Forces . .' . 6 
 
 III. Natural Philosophy Pneumatics .../* . 11 
 
 IV. Weight and Pressure of the Air . - : >r. . 17 
 V. Pressure of the Air .. .. 22 
 
 VI. Pressure and Elasticity of the Air . . . . 26 
 
 VII. Properties of Air .... . . . . ; 31 
 
 VIII. Properties of Air (continued) " f ', ..'--'' . . 36 
 
 IX. Hydrostatics Properties of Liquids v \ * . . 41 
 
 X. The Pressures of Liquids . , ,\\ ... 45 
 
 XI. Specific Gravity . . , ' . . . .50 
 
 XII. Hydrostatic Pressure 55 
 
 XIII. Flowing Liquids and Hydraulic Machines . -." - '-'.4Q 
 
 XIV. Theory of Flotation : . ' . " i ' 6* 
 
 XV. Mechanics Motion and Rest . r ' '; ' -i""'-v - '*' . 69 
 
 XVI. Composition and Resolution of Forces ... 72 
 
 XVII. Inertia . . . -V^Vr^l^v ^i -i . 77 
 
 XVIII. Gravitation . . . i - ^^r . . 81 
 
 XIX,. Descent of Falling Bodies .. e :: ' k r.. PJ>* M ', - ; .. . 85 
 
 XX. Motion on Inclined Planes Projectiles . . . 90 
 
 XXI. Motion round a Center '--.*; *./;-..;. ... 94 
 
 XXII. Adhesion and Capillary Attraction . .- .^:- :; . 101 
 
 XXIII. Properties of Solids . . : . ^ fci -.- . . 107 
 
 XXIV. Center of Gravity - ./ ',. '^: .* ' .^ ! .^ no 
 XXV. The Pendulum "> ' *. * '--4 'v.;,. ...V. . 116 
 
 XXVI. Percussion 121 
 
 XXVII. The Mechanical Powers the Lever . . . .126 
 
 XXVIII. The Pulley the Wheel and Axle . . . . 131 
 
 XXIX. The Inclined Plane Wedge Screw . . . .137 
 
 XXX. Passive 'or Resisting Forces . . % . 141 
 
 XXXI. Undulatory Motions . '. . . . 147 
 
 XXXII. Undulatory Motions (continued) . .. '. . ' . 152 
 
 XXXIII. Acoustics Production of Sound ... . . . 157 
 
 XXXIV. Phenomena of Sound . . . .:-... . . 161 
 XXXV. Optics Properties of Light 168 
 
 XXXVI. Measures of the Intensity and Velocity of Light . 172 
 
 XXXVII. Reflexion of Light 178 
 
 XXXVIII. Refraction of Light . . . . . . 184 
 
Vlll CONTENTS. 
 
 Lecture Page. 
 
 XXXIX. Action of Lenses 190 
 
 XL. Colored Light 195 
 
 XLI. Colored Light (continued) 200 
 
 XLII. Undulatory Theory of Light 205 
 
 XLIII. Polarized Light 210 
 
 XLIV. Double Refraction 215 
 
 XLV. Natural Optical Phenomena 221 
 
 XLVI. The Organ of Vision 227 
 
 XLVIL Optical Instruments Microscopes ..... 232 
 
 XL VIII. Telescopes 238 
 
 XLIX. Thermotics the Properties of Heat . . . .244 
 
 L. Radiant Heat 249 
 
 LI. Conduction and Expansion ...... 253 
 
 LII. Capacity for Heat and Latent Heat . . . . 258 
 
 LIII. Evaporation and Boiling 262 
 
 LIV. The Steam Engine 267 
 
 LV. Hygrometry 272 
 
 LVI. Magnetism 278 
 
 LVIL Terrestrial Magnetism 283 
 
 LVIII. Electricity 288 
 
 LIX. Induction and Distribution of Electricity * 293 
 
 LX. The Voltaic Battery ....... 298 
 
 LX1. Electro-magnetism 304 
 
 LXII. Magneto-electricity Thermo-electricity . . . 309 
 
 LXIII. Astronomy 315 
 
 LXIV. Translation of the Earth round the Sun ... 321 
 
 LXV. The Solar System *. .328 
 
 LXVI. The Solar System (continued) 334 
 
 LXVIL The Secondary Planets 340 
 
 LXVIII. The Fixed Stars 346 
 
 LXIX. Causes of the Phenomena of the Solar System . .353 
 
 LXX. The Tides 358 
 
 LXXI. Figure and Motion of the Earth . 363 
 
 LXXII. Of Perturbations 369 
 
 LXXIII. The Measurement of Time . .373 
 
INTRODUCTION. 
 
 CONSTITUTION OP MATTER. 
 
 LECTURE I. 
 
 PROPERTIES OF MATTER. The Three Forms of Mat- 
 ter. Vapors. The distinctive, essential, and accessory 
 properties. Extension. Impenetrability. Unchangea- 
 bility. Illustrations of Extension. Methods of measur- 
 ing small spaces. The Spherometer. Illustration of 
 Impenetrability. The Diving-Bell. 
 
 ^MATERIAL substances present themselves to us under 
 three different conditions. Some have their parts so 
 strongly attached to each other that they resist the intru- 
 sion of external bodies, and can retain any shape that 
 may be given them. These constitute the group of SOL- 
 IDS. A second class yields readily to pressure or move- 
 ment, their particles easily sliding over one another ; and 
 from this extreme mobility they are unable of themselves 
 to assume determinate forms, but always copy the shape 
 of the receptacles or vessels in which they are placed 
 they are LIQUIDS. A third, yielding even more easily 
 than the foregoing, thin and aerial in their character, and 
 marked by the facility with which they may be compress- 
 ed into smaller or dilated into larger dimensions, give us 
 a group designated as GASES. Metals may be taken as 
 examples of the first ; water as the type of the second ; 
 and atmospheric air of the third of these states or condi- 
 tions, "which are called " the three FORMS of bodies." 
 
 In some instances the same substance can exhibit all 
 three of these forms. Thus, when liquid water is cooled 
 
 Under how many states do material substances occur? What are 
 solids? What are liquids ? What are gases? Give examples of each. 
 What is the technical designation given to these states ? Give an exam- 
 ple of a substance that can assume all three forms. 
 
 A 
 
2 DISTINCTIVE PROPERTIES. 
 
 to a certain degree, it takes on the solid condition, as ice 
 or snow ; and when its temperature is sufficiently raised, it 
 assumes the gaseous state, and is then known as steam. 
 Writers on Natural Philosophy have found it convenient, 
 for many reasons, to introduce the term Vapors, meaning 
 by that a gas placed under such circumstances that it is 
 ready to assume the liquid state. As the steam of water 
 conforms to this condition, it is therefore regarded as a 
 vapor. 
 
 Under whichever of these forms material substances are 
 presented, they exhibit certain properties: these are, first, 
 Distinctive ; second, Essential ; third, Accessory. 
 
 There is a certain bright white metal passing under the 
 name of Potassium, the distinctive character of which is, 
 Fig. I. that, when thrown on the surface of water, it 
 gives rise to a violent reaction, a beautiful 
 violet-colored flame being evolved. A piece 
 of lead, which, to external appearance, is 
 not unlike the potassium when brought in 
 contact with water, exhibits no such phe- 
 nomenon, but, as every one knows, remains quietly, neither 
 disturbing the water nor being acted upon by it. 
 
 Such distinctive qualities are the objects of a Chemist's 
 studies. It belongs to his science to show how some gases 
 are colored and others colorless; some supporters of com- 
 bustion, while others extinguish burning bodies ; how some 
 liquids can be decomposed by Voltaic batteries and some 
 by exposure to a red heat. The general doctrines of af- 
 finity, the modes in which bodies combine, and the char- 
 acters of the products to which they give rise all these 
 belong to Chemistry. 
 
 But beyond these distinctive qualities of bodies, there 
 are, as has been observed, certain other properties which 
 are uniformly met with in all bodies whatever, and hence 
 are spoken of as ESSENTIAL. TThey are, 
 
 Extension. 
 
 Impenetrability. 
 
 Unchangeability. 
 
 By EXTENSION we mean that all substances, whatever 
 
 Into what classes may the properties of bodies be divided ? Give an ex- 
 ample of distinctive properties. What is the object of the science of 
 Chemistry? What are the essential properties of bodies? What is 
 meant by extension ? What by impenetrability ? 
 
ESSENTIAL PROPERTIES. 
 
 their volume or figure may be, occupy a determinate por- 
 tion of space, We measure them by three dimensions 
 length, breadth, and thickness. 
 
 IMPENETRABILITY points out the fact that two bodies 
 cannot occupy the same space at the same time. If a nail 
 is driven into wood, it enters only by separating the woody 
 particles from each other; if it be dropped into water, it 
 does not penetrate, but displaces the watery particles : 
 and even in the case of aerial bodies, through which 
 masses can move with apparently little Fig. 2. 
 
 resistance, the same observation holds 
 good. Thus, if we take a wide-mouthed 
 bottle, a, Fig. 2, arid insert through its 
 cork a funnel, b, with a narrow neck, and 
 also a bent tube, c, which dips into a glass 
 of water, d, on pouring any liquid into 
 the funnel, so that it may fall drop by drop 
 into the bottle, we shall find, as this takes 
 place, that air passes out, bubble after bubble, through 
 the water in d. The air is, therefore, not penetrated by 
 the water, but displaced. 
 
 The same fact may also be proved by 
 taking a cupping-glass, a. Fig. 3, and im- 
 mersing it, mouth downward, in a glass of 
 water, b. If the aperture, c, of the cup- 
 ping-glass be left open the air will rush out 
 through it, and the water flow in below : 
 but if it be closed by the finger, as the air 
 can now no longer escape, the water is un- 
 able to enter and occupy its place. 
 
 Similar experiments establish the impenetrability of 
 liquids by solids. If in a glass of water, Fig. 4, Fig. 4. 
 a leaden bullet is immersed, it will be seen that 
 as the bullet is introduced the water rises to a 
 higher level, showing, therefore, that a liquid can 
 no more be penetrated by a solid than . as was seen 
 in the former experiment, can a gas by a liquid. 
 Two bodies cannot occupy the same space at the same 
 time. 
 
 The third essential property of matter is its UNCHANGE- 
 
 Give an illustration that air is not penetrable by water. Give an illus- 
 tration of the displacement of air by water. What is meant by unchange- 
 ability as a property of bodies ? < 
 
4 UNCHANGEABILITY OF MATTER. 
 
 ABILITY. This property may be looked upon as the foun- 
 dation of Chemistry ; and though there are many phenom- 
 ena which we constantly witness which seem to contradict 
 it, they form, when properly considered, striking illustra- 
 tions of the great truth that material substances can nei- 
 ther be created nor destroyed, and that the distinctive 
 qualities which appertain to them remain forever un- 
 changed. The disappearance of oil in the combustion of 
 lamps, the burning away of coal, the evaporation of wa- 
 ter, when minutely examined, far from proving the per- 
 ishability of matter, afford the most striking evidence of 
 its duration. Nor is a solitary fact known in the whole 
 range of Chemistry, Natural Philosophy, or Physiology, 
 which lends the remotest countenance to the opinion that, 
 either by the slow lapse of time or by any artificial pro- 
 cesses whatever, can matter be created, changed, or de- 
 stroyed. Even the bodies of men and animals, the struct- 
 ures of plants, and all other objects in the world of organ- 
 ization, which seem characterized by the facility with 
 which they undergo unceasing and eventually total change, 
 are no exception to the truth of this observation. The 
 bodies which we possess to-day are made up of particles 
 which have formed the bodies of other animals in former 
 times, and which will again discharge the same duty for 
 races that will hereafter come into existence. 
 
 As illustrations connected with the extension and im- 
 penetrability of matter, I may give the following in- 
 stances : 
 
 We are frequently required to measure the dimensions 
 of bodies ; that is, to determine their length, breadth, or 
 thickness. It is a much more difficult thing to do this ac- 
 curately than is commonly supposed. It requires an artist 
 of the highest skill to make a measure which is a foot or 
 a yard in length, or which shall contain precisely a pint or 
 a gallon. With a view of facilitating the measurement of 
 bodies, a great many contrivances have been invented, 
 such as verniers, spherometers, and screw machines of 
 different kinds. 
 
 The spherometer, which is a beautiful contrivance for 
 measuring the thickness of bodies, is constructed as foi- 
 
 ls there any reason to believe that new material particles can be ere 
 ated by artificial processes, or old ones destroyed ? 
 
THE SPHERO.METER. 
 
 Fig 5. 
 
 lows : It has three horizontal steel branches, a, &, c, Fig. 
 5, which form with each other 
 angles of 120 degrees. From the 
 extremities of these branches 
 there proceed three delicate steel 
 feet, d, e,f, and through the cen- 
 ter, where the branches unite, a 
 screw, g, the thread of which is 
 cut with great precision, and 
 which terminates in a pointed 
 foot, , passes. The head of this 
 screw carries a divided circle, m. 
 Now, suppose the instrument is 
 placed on a piece of flat glass, it 
 will be supported on its three 
 feet, which are all in the same plane ; but if in turning the 
 screw we depress its point, i, beneath the plane of its feet, 
 it can no longer stand with stability on the glass, but tot- 
 ters when it is touched, and emits a rattling sound. By 
 altering the screw, therefore, we can give it such a posi- 
 tion that both by the finger and the ear we discover that 
 its point is level with the points d, e,f. Now let the ob- 
 ject, the thickness of which is to be measured, be placed 
 on the glass, and the screw turned until the instrument 
 stands without tottering, it is obvious that its point must 
 have been lifted through a distance precisely equal to 
 the thickness of the object to be measured, and the 
 movement of the head of the screw read off upon the 
 scale, n, against which it works, indicates what that thick- 
 ness is. 
 
 This instrument, therefore, serves to show that in the 
 measurement of small spaces, the senses of touch and 
 hearing may often be resorted to with more effect than 
 the eye. The spherometer is here introduced in connec- 
 tion with these general considerations respecting the ex- 
 tension of matter, as affording the student an illustration 
 of the delicate methods we possess of determining the mi- 
 nutest dimensions of bodies. 
 
 As an illustration of the impenetrability of matter, the 
 machine which passes under the name of the diving-bell 
 
 Describe the spherometer. What is its use ? By what senses may we 
 often form a better estimate of small spaces than by the eye ? 
 
6 ACCESSORY PROPERTIES. 
 
 may be mentioned. It consists of a vessel, <z, a, Fig. 6, 
 Fig. 6. of any suitable shape, and heavy enough 
 
 to sink in water when plunged with its 
 mouth downward. Owing to the impen- 
 etrability of the air the water is excluded 
 from the interior, or only finds access to 
 such an extent as corresponds to the press- 
 ure of the depth to which it is sunk. 
 Light is admitted to the bell through thick 
 pieces of glass in its top, and a constant 
 stream of fresh air thrown into it from a 
 tube, b, and forcing-pump above, the at- 
 mosphere in the inside being suffered to escape through 
 a stop-cock as it becomes vitiated by the respiration of 
 the workmen. Diving-bells are extensively resorted to 
 in submarine architecture, and for the recovery of treas- 
 ure lost in the sea. 
 
 LECTURE II. 
 
 PROPERTIES OF MATTER. The Accessory Properties of 
 Matter. Compressibility. Expansibility. Elasticity. 
 Limit of Elasticity. Illustrations of Divisibility. 
 Porosity and interstitial spaces. Weight. 
 
 PHYSICAL FORCES. Attractive and Repulsive Forces. 
 Molecular Attraction. Gravitation . Cohesion. Con- 
 stitution of Matter. 
 
 HAVING disposed of the essential, we pass next to a con- 
 sideration of the accessory properties of matter. They are, 
 
 ' Compressibility. 
 Expansibility. 
 - Elasticity. 
 Divisibility. 
 Porosity. 
 Weight. 
 
 That substances of all the three forms are compressi- 
 ble is capable of easy proof. In the process of coining, 
 pieces of metal are exposed to powerful pressure between 
 the steel die's', sO that they become much denser than be- 
 
 Describe the diving-bell. On what principle does it act ? Why must 
 the air in its interior be renewed from time to time ? What are the acces- 
 soiy properties of matter? 
 
EXPANSIBILITY AND ELASTICITY. 7 
 
 fore. By inclosing water or any other liquid in a strong 
 vessel, and causing a piston, driven by a screw, to act 
 upon it, it may be reduced to a less space, and gaseous 
 substances, such as atmospheric air when inclosed in an 
 India-rubber bag, or even a bladder, may be compressed 
 by the hands. 
 
 Under the influence of heat all substances expand. 
 This may be proved for such solids Ff^. 7. 
 
 as metals by the apparatus represent- 1 j^^^^^^^^^jl 
 ed in Fig. 7. It consists of a stout I aT <*^l 
 
 board, a b t on which are fastened two ^ 
 brass uprights, c, d, with notches cut in them so as to re- 
 ceive the ends of a metallic bar, e. This bar is slightly 
 shorter than the whole distance between the notches, so 
 that when it is set in its place it can be moved backward 
 and forward, and emits a rattling sound. But if boiling 
 water be poured upon it, it expands and occupies the 
 whole distance, and can no longer be moved. The ex- 
 pansion of liquids is well shown in the case of common 
 thermometers, which contain either quicksilver or spirits 
 of wine those substances occupying a greater volume as 
 their temperature rises. The air thermometer proves the 
 same thing for gases. 
 
 By elasticity we mean that quality by which bodies, 
 when their form has been changed, endeavor to recover 
 their original shape. In this respect there are great dif- 
 ferences. Steel, ivory, India-rubber are highly elastic, 
 and lead, putty, clay less so. Perfectly elastic bodies re- 
 sist the action of disturbing causes without any ulterior 
 change: thus a quantity of atmospheric air, compressed 
 into a copper globe, recovers its original volume as soon 
 as the pressure is removed, though it may have been shut 
 up for years. By the limit of elasticity we mean the 
 smallest force which is required to produce a permanent 
 disturbance in the structure of an imperfectly elastic 
 body. No solid is perfectly elastic. An iron wire, drawn 
 a little aside, recovers its original straightness ; but if 
 more violently bent, it takes a permanent set, because its 
 limit of elasticity is overpassed. The elasticity of a given 
 
 Give proofs that solids, liquids, and gases are all compressible. How 
 can it be proved that solids, liquids, and gases are expansible ? What is 
 meant by elasticity ? Give examples of highly elastic and less elastic 
 bodies. What is meant by the limit of elasticity ? 
 
8 DIVISIBILITY. 
 
 substance can often be altered by mechanical processes, 
 such as by hammering, or by heating and cooling, as in 
 the process of tempering. 
 
 The divisibility of matter maybe proved in many ways. 
 By various mechanical processes metals may often be re- 
 duced to an extreme degree of tenuity : thus it is said 
 that gold-leaf may be beaten out until it is only ^oVo^ ^ 
 an inch thick. By chemical experiments a grain of cop- 
 per or of iron may be divided into many millions of parts. 
 For certain purposes artists have ruled parallel lines 
 upon glass, with a diamond point, so close to each other 
 that ten thousand are contained in a single inch. The 
 odors which are exhaled by strong- smelling perfumes, as 
 musk, will for years together infect the air of a large 
 room, and yet the loss of weight by the musk is imper- 
 ceptible. Again, there are animals whose bodies are so 
 minute that they can only be seen by the aid of the mi- 
 croscope. The siliceous shells of such infusorials occur 
 in many parts of the earth as fossils. Ehrenberg has 
 shown that Tripoli, a mineral used in the arts, is made 
 up of these a single cubic inch of it containing about 
 forty-one thousand millions that is, about fifty times as 
 many individuals as there are of human beings on the face 
 of the globe. 
 
 As substances of all kinds may be reduced to smaller 
 dimensions, either by pressure or the influence of cold, 
 and as it is impossible for two particles to occupy the 
 same place at the same time, or even for one of them par- 
 tially to encroach on the position occupied by the other, 
 it necessarily follows that there must be pores or inter- 
 stices even in the densest bodies. Thus quicksilver will 
 readily soak into the pores of gold, and gases ooze through 
 India-rubber. Writers on Natural Philosophy usually 
 restrict the term "pore" to spaces which are visible to 
 the eye, and designate those minute distances which sep- 
 arate the ultimate particles of bodies by the term " inter- 
 stices." 
 
 All bodies have weight or gravity. It is this which 
 
 How may the elasticity of a given substance be changed ? Give some 
 illustrations of the great divisibility of matter, derived from mechanical, 
 chemical, physiological, and geological facts. How may it be proved that 
 all bodies are porous? What is meant by a "pore," and what by "inter- 
 stices ?" 
 
FORCES OF ATTRACTION AND REPULSION. 9 
 
 causes them to fall, when unsupported, to the ground, or 
 when supported, to exert pressure upon the supporting 
 body. Nor is this property limited to terrestrial objects ; 
 for in the same way that an apple tends to fall to the earth, 
 so too does the moon; and all the planets gravitate to- 
 ward each other and toward the sun. It was the consid- 
 eration of this principle that led M. LEVERRIER to the dis- 
 covery of a new planet beyond Uranus this latter star 
 being evidently disturbed in its movements by the influ- 
 ences of a more distant body hitherto unknown. 
 
 OF PHYSICAL FORCES. All changes taking place in 
 the system of nature are due to the operation of forces. 
 The attractive force of the earth causes bodies to fall, and 
 a similar agency gives rise to the shrinking of substances 
 their parts coming closer together when they are exposed 
 to the action of cold. In like manner, when an ivory 
 ball is suffered to drop on a marble slab, its particles, 
 which have been driven closer to one another by the force 
 of the blow, instantly recover their original positions by 
 repelling one another ; that is to say, through the agency 
 of a repulsive force. Of the nature of forces we know- 
 nothing. Their existence only is inferred from the effects 
 they produce ; and according to the nature of those ef- 
 fects, we divide them into ATTRACTIVE and REPULSIVE 
 FORCES the former tending to bring bodies closer to- 
 gether, the latter to remove them farther apart. 
 
 It has been found convenient to divide attractive forces 
 into three groups, according as the range of their action 
 or the circumstances of their development differ. When 
 the attractive influence extends only to a limited space, it 
 is spoken of as molecular attraction ; but the attraction of 
 gravitation is felt throughout the regions of space. By 
 cohesion is meant an attractive influence called into ex- 
 istence when bodies are brought to touch one another. It 
 is to be understood that these are only conventional dis- 
 tinctions; and it is not improbable that all the phenomena 
 of attraction are due to the agency of one common cause. 
 
 Chemists have shown that, in all probability, material 
 substances are constituted upon one common type. They 
 
 What is meant by weight or gravity ? Is it limited to terrestrial ob- 
 jects ? What is meant by forces ? How many varieties of them are there ? 
 Into what three groups are attractive forces divided ? What is the dis- 
 tinction between them ? 
 
 # 
 
10 NATURE OF ATOMIC FORCES. 
 
 are made up of minute, indivisible particles, called atoms, 
 which are arranged at variable distances from each other. 
 These distances are determined by the relative preva- 
 lence of attractive and repulsive forces, resident in or 
 among the particles themselves ; and so too is the form 
 of the resulting mass. If the cohesive predominates over 
 the repulsive force, a solid body is the result ; if the two 
 are equal it is a liquid, and if the repulsive prevails it 
 is a gas. 
 
 There are many reasons which lead us to suppose that 
 the repulsive force, which thus tends to keep the particles 
 of matter asunder, is the agent otherwise known as heat. 
 Whenever the temperature of a body rises it enlarges in 
 volume, because its constituent particles move from each 
 other, and on the temperature falling the reverse effect 
 ensues. If, as many very eminent philosophers believe, 
 heat and light are in reality the same agent, it follows, by 
 a necessary consequence, as will be gathered from what 
 we shall hereafter have to say on optics, that the atoms of 
 bodies vibrate unceasingly, and that instead of there be- 
 ing that perfect quiescence among them which a superfi- 
 cial examination suggests, all material substances are the 
 seat of oscillatory movements, many millions of which are 
 executed in the space of a single second of time ; the 
 number increasing as the temperature rises, and dimin- 
 ishing as it falls. 
 
 What is the true constitution of material substances? What are the 
 forces residing among the particles of bodies ? What are the conditions 
 which determine the solid, liquid, and gaseous forms ? What is probably 
 the nature of the force of molecular repulsion? If light and heat are trie 
 same agent, what is the condition of the particles of bodies ? 
 
PNEUMATICS. 
 
 NATURAL PHILOSOPHY, 
 
 PROPERTIES OF THE AIR. 
 
 PNEUMATICS. 
 
 LECTURE III. 
 
 NATURAL PHILOSOPHY. Observations on this branch of 
 Science. 
 
 PNEUMATICS. General Relations of the Air. Its connec- 
 tion with Motion and Organization. Limited Extent. 
 Constitution. Compressibility. Causes which Limit 
 the Atmosphere. Its Variable Densities. Proportion- 
 ality of its Elastic Force and Pressure. 
 
 A VERY superficial knowledge of those parts of the 
 world to which man has access readily leads to their class- 
 ification under three separate heads the air, the sea, and 
 the solid earth. This was recognized in the infancy of 
 science, for the four elements of antiquity were the di- 
 visions which we have mentioned, and fire. 
 
 NATURAL PHILOSOPHY or PHYSICAL SCIENCE, which, in 
 its extended acceptation, means the study of all the phe- 
 nomena of the material world, may commence its inves- 
 tigations with any objects or any facts whatever. By pur- 
 suing these, in their consequences and connections, all the 
 discoveries which the human mind has made in this de- 
 partment of knowledge might successively be brought 
 forward. But when we are left to select at pleasure our 
 point of commencement, it is best to follow the most nat- 
 ural and obvious course. All the advances made in our 
 times by the most eminent philosophers, and our powers 
 of appreciating and understanding them, depend on clear- 
 ness of perception of the great fundamental facts of sci- 
 ence a perspicuity which can never arise from mere ab- 
 stract reasonings or from the unaided operations of the 
 
 What were the elements of the ancients ? What is Natural Philosophy ? 
 
12 RELATIONS OF THE ATMOSPHERE. 
 
 human intellect, but which is the natural consequence of 
 a familiarity with absolute facts. These serve us as our 
 points of departure, and in the more difficult regions of 
 science they are our points of reference often by their 
 resemblances, and even by their differences, making plain 
 what would otherwise be incomprehensible, and spread- 
 ing a light over what would otherwise be obscure. 
 
 In the three divisions of material objects, which are so 
 strikingly marked out for us by nature, we find traits that 
 are eminently characteristic. All our ideas of perma- 
 nence and duration hiave a convenient representation in 
 the solid crust of the earth, the mountains, and valleys, 
 and shores of which retain their position and features un- 
 altered for centuries together. But the air is the very type 
 and emblem of variety, and the direct or indirect source 
 of almost every motion we see. It scarce ever presents 
 to us, twice in succession, the same appearance ; for the 
 winds that are continually traversing it are, to a proverb, 
 inconstant, and the clouds that float in it exhibit every 
 possible color and shape. It is, in reality, the grand ori- 
 gin or seat of all kinds of terrestrial motions. Storms in 
 the sea are the consequences of storms in the air, and even 
 the flowing of rivers is the result of changes that have 
 transpired in the atmosphere. 
 
 But the interest connected with it is far from ending 
 here. The atmosphere is the birthplace of all those" 
 numberless tribes of creation which constitute the vege- 
 table and animal world. It is of materials obtained from 
 it that plants form their different structures, and, therefore, 
 from it that all animals indirectly derive their food. It is 
 the nourisher and supporter of life, and in those process- 
 es of decay which are continually taking place during 
 the existence of all animals, and which after death totally 
 resolve their bodies into other forms, the air receives the 
 products of those putrefactive changes, and stores them 
 up for future use. And it is one of the most splendid 
 discoveries of our times, that these very products which 
 arise from the destruction of animals are those which are 
 used to support the life and develop the parts of plants. 
 They pass, therefore, in a continual circle, now belong- 
 ing to the vegetable, and now to the animal world ; 
 
 What appears to be the leading characteristic of the atmosphere ? What 
 are its relations to the organic world ? 
 
EXTENT OF THE ATMOSPHERE. 13 
 
 they come from the air, and to it they again are re- 
 stored. 
 
 It is not, therefore, the beautiful blue color which the 
 air possesses, and which people commonly call the sky, 
 or the points of light which seem to be in it at night, or 
 the moving clouds which overshadow it and give it such 
 varied and fantastic appearances, or even those more im- 
 posing relations which bring it in connection with the 
 events of life and death, which alone invest it with a pe- 
 culiar claim on the attention of the student. Connected 
 as it is with the commonest every-day facts, it furnishes 
 us with some of our most appropriate illustrations those 
 simple facts of reference of which I have already spoken, 
 and to which we involuntarily turn when we come to in- 
 vestigate the more difficult natural phenomena. 
 
 Astronomical considerations show that the atmosphere 
 does not extend to an indefinite region, but surrounds the 
 earth on all sides to an altitude of about fifty miles. Com- 
 pared with the mass of the earth its volume is quite insig- 
 nificant ; for as it is nearly four thousand miles from the 
 surface to the center of the earth, the whole depth of the 
 atmosphere is only about one-eightieth part of that dis- 
 tance. Upon a twelve-inch globe, if we were to place a 
 representation of the atmosphere, it would have to be less 
 than the tenth of an inch thick. 
 
 Seen in small masses, atmospheric air is quite colorless 
 and perfectly transparent. Compared with water and 
 solid substances, it is very light. Its parts move among 
 one another with the utmost facility. Chemists have 
 proved that it is not, as the ancients supposed, an ele- 
 mentary body, but a mixture of many other substances. 
 It is enough at present for us to know that its leading 
 constituents are two gases, which exist in it in fixed quan- 
 tities they are oxygen and nitrogen but other essential 
 ingredients are present in a less proportion, such as car- 
 bonic acid gas, and the vapor of water. 
 
 Atmospheric air is taken by natural philosophers as 
 the type of all gaseous bodies, because it possesses 
 their general properties in the utmost perfection. In- 
 dividual gases have their special peculiarities some, for 
 
 What is the altitude of the atmosphere? What comparison does this 
 bear to the mass of the earth ? What are its general properties ? What 
 bodies constitute it ? Of what class is it the type ? 
 
14 COMPRESSIBILITY OF AIR. 
 
 example, are yellow, some green, some purple, and some 
 red. 
 
 The first striking property of atmospheric air which we 
 encounter, is the facility with which the volume of a given 
 quantity of it can be changed. It is highly compressible 
 and perfectly elastic. A quantity of it tied tightly up in 
 a bladder or India-rubber bag, is easily forced, by the 
 pressure of the hand, into a less space. The materiality 
 of the air, and its compressibility, are simultaneously il- 
 lustrated by the experiment of the diving-bell, described 
 under Fig. 6. A vessel forced with its mouth downward 
 under water, permits the water to enter a little way, be- 
 cause the included air goes into smaller dimensions 
 under the pressure ; but as soon as the vessel is again 
 brought to the surface of the water, the air within it ex- 
 pands to its original bulk. 
 
 Fig. 8. This ready compressibility and expansibility may 
 be shown in many other ways. Thus, if we take 
 a glass tube, Fig. 8, with a bulb c, at its upper 
 end, the lower end being open and dipping into a 
 i| vessel of water, d, and having previously partially 
 filled the tube with water to the height, a, it will be 
 found, on touching the bulb with snow, or by pour- 
 ing on it ether, or by cooling it in any manner, that 
 the included air collapses into a less bulk. It is 
 therefore compressible, and on warming the bulb 
 with the palm of the hand, the air is at once dilated. 
 
 It is this quality of easy expansibility and compressi- 
 bility which distinguishes all gaseous substances from sol- 
 ids and liquids. It is true the same property exists in 
 them, but then it is to a far less degree. On the hypoth- 
 esis that material bodies are formed of particles which do 
 not touch one another, but are maintained by attractive 
 and repulsive forces at determinate distances, it would 
 appear that, in a gas like atmospheric air, the repulsive 
 quality predominates over the attractive ; while in solids 
 the attractive force is the most powerful, arid in liquids 
 the two are counterbalanced. 
 
 Again, as respects relative weight, the gases, as a 
 tribe, are by far the lightest of bodies ; and, indeed, it is 
 
 How may it be proved to be compressible ? What does the diving-bell 
 prove ? Describe the experiment, Fig. 8. In gaseous bodies does the at- 
 tractive or repulsive force predominate ? 
 
ELASTICITY OF AIR. 
 
 15 
 
 among them that we find the lightest substance in nature 
 hydrogen gas. They are 1 , moreover, the only perfectly 
 elastic substances that we know. Thus, a quantity of at- 
 mospheric air compressed into a metal reservoir will re- 
 gain its original volume the moment it has the opportuni- 
 ty, no matter how great may be the space of time since 
 it was first shut up. 
 
 Under a relaxation of pressure this perfect elasticity 
 displays itself in producing the expansion of a fig. 9. 
 gas. If a bladder partially full of atmospheric 
 air be placed under an air-pump receiver, as the 
 pressure is removed it dilates to its full extent, 
 and might even be burst by the elastic force of 
 the air confined within. The force with which 
 this expansion takes place is very well display- 
 ed by putting the bladder in a frame, as shown in Fig. 
 10, and loading it with heavy weights ; as it Fig. 10. 
 expands by the spring of the air, it lifts up all 
 the weights. 
 
 If we were to imagine a given volume of 
 gas placed in an immense vacuum, or under 
 such circumstances that no extraneous agen- 
 cy could act upon it, it is very clear that its 
 expansion would be indefinitely great the 
 repulsive force of its own particles predom- 
 inating over their attraction, and there being nothing to 
 limit their retreat from one another. But when a gas- 
 eous mass surrounds a solid nucleus, the case is different 
 an expansion to a determinate and to a limited extent 
 is the result. And these are the circumstances under 
 which the earth and every planet surrounded by an elas- 
 tic atmosphere exists ; for in the same way that our globe 
 compels an unsupported body to fall to its surface, and 
 makes projectiles as bomb-shells and cannon-shot no 
 matter what may have been the velocity with which they 
 were urged return to the ground, so the same attractive 
 force restrains the indefinite expansion of the air, and 
 keeps the atmosphere, instead of diffusing away into empty 
 space, imprisoned all round. 
 
 Besides this cause gravitation to the earth a second 
 
 Are gases perfectly elastic ? What does experiment Fig. 9 prove ? What 
 would happen to a volume of gas placed in an indefinite vacuum ? What 
 limits the atmosphere to the earth ? 
 
16 VARIABLE DENSITY OP THE ATMOSPHERE. 
 
 one, for the limited extent of the atmosphere, may also 
 be assigned contraction 'sensing from cold. Observa- 
 tion has shown that, as we rise to greater altitudes in the 
 air, the cold continually increases ; and gases, in common 
 with all other forms of body, are condensed by cold. 
 The attempt at unlimited expansion which the atmos- 
 phere, by reason of its gaseous constitution exerts, is, 
 therefore, kept in bounds by two causes the attractive 
 force of the earth and cold and accordingly its altitude 
 does not exceed fifty miles. 
 
 From the circumstance that air is thus a compressible 
 body, we might predict one of the leading facts respect- 
 ing the constitution of the atmosphere it is of unequal 
 densities at different heights. Those portions of it which 
 are down below have to bear the weight of the whole su- 
 perincumbent mass ; but this weight necessarily becomes 
 less and less as we advance to regions which are higher 
 and higher; for in those places, as there is less air to press, 
 the pressure must be less. And all this is verified by ob- 
 servation. The portions which rest on the ground are of 
 the greatest density, and the density steadily diminishes 
 as we rise. Moreover, a little consideration will assure 
 us that there is a very simple relation between the press- 
 ure which the air exerts and its elastic force. Consider 
 the condition of things in the air immediately around us : 
 if its elastic force were less, the weight of the superincum- 
 bent mass would crush it in ; if greater, the pressure 
 could no longer restrain it, and it would expand. It fol- 
 lows, therefore, in the necessity of the case, that the elas- 
 tic force of any gas is neither greater nor less, but pre- 
 cisely equal to the pressure which is upon it. 
 
 What is the agency of cold in this respect ? Why is the atmosphere of 
 unequal density at different heights ? What relation is there between its 
 pressure and its elastic force ? 
 
THE AIR-PUMP. 
 
 17 
 
 Fig. 11. 
 
 LECTURE IV. 
 
 WEIGHT AND PRESSURE OF THE AIR. Description of the 
 Air-pump.- Its Action. Limited Exhaustion. Fun- 
 damental fact that Air has weight. Relative weight of 
 other Gases. Weight gives rise to Pressure. Experi- 
 ments illustrating the Pressure of the Air. 
 
 Ix the year 1560, Otto Guericke, a German, invented an 
 instrument which, from its use, passes under the name of 
 the air-pump, and exhibited a number of very striking 
 experiments before the Emperor Ferdinand III. This 
 incident forms an epoch in physical science. 
 
 Otto Guericke's instrument was imperfect in construc- 
 tion and difficult of management. The apparatus re- 
 quired to be kept under water. More convenient ma- 
 chines have, therefore, been devised. The following is a 
 description of one of the most simple : Upon a metallic 
 basis, //, Fig. 11, 
 are fastened two ex- 
 hausting syringes, a 
 
 a, which are worked 
 by means of ahandle, 
 
 b, the two screw col- 
 umns, d d, aided by 
 the cross-piece, e e, 
 tightly compressing 
 them into their pla- 
 ces. A jar, c, called 
 a receiver, the mouth 
 of which is carefully 
 ground true, is pla- 
 ced on the plate of 
 
 the pump, f f, which is formed of a piece of metal or 
 glass ground quite flat. This pump-plate is perforated in 
 its center, from which air-tight passages lead to the bot- 
 
 When and by whom was the air-pump invented ? Give a description of 
 its general external appearance. What is the receiver ? What is the 
 pump-plate ? What passages lead from the center of the plate ? What 
 is the use of the screw g ? 
 
18 
 
 STRUCTURE OF THE AIR-PUMP. 
 
 Fig. 12. 
 
 torn of each syringe, and when the handle, b, is moved 
 the syringes withdraw the air from the interior of the jar. 
 From the same central perforation there is a third pass- 
 age, which can be opened or closed by the screw at g, so 
 that when the experiments are over, by opening it the air 
 can be readmitted into the interior of the receiver. 
 
 So far as its exterior parts are concerned, this air-pump 
 consists of a pair of syringes worked by a handle, and 
 producing exhaustion of the interior of a jar, with a vent 
 which can be closed or opened for the readmission of air. 
 The syringes are constructed 
 exactly alike. The glass model 
 represented in Fig. 12 exhibits 
 their interior; each consists of a 
 cylinder, a a, the interior of which 
 is made perfectly true, so that a 
 piston or plunger, d, introduced at 
 the top may be pushed to the bot- 
 tom, and, indeed, work up and 
 v down without any leakage. There 
 \X\ is a hole made through the piston, 
 d, and over it a valve is laid. This 
 consists of a flexible piece of mem- 
 brane, as leather, silk, &c., which 
 being placed on the aperture opens 
 in one direction and closes in the 
 other. Such a valve is in the pis- 
 ton, and there is another one, c, resting on an aperture in 
 the bottom of the cylinder. 
 
 To understand the action of this instrument, let us sup- 
 pose a glass globe full of atmospheric air to be fastened 
 air-tight to the bottom of such a syringe, and the piston 
 then lifted to the top of the cylinder. As it moves with- 
 out leakage, it would evidently leave a vacuum below it 
 were it not that the air in the globe, exerting its elastic 
 force, pushes up the valve c, arid expands into the cylin- 
 der. In this way, therefore, by the upward movement of 
 the piston, a certain quantity of air comes out of the globe 
 and fills the cylinder. The piston is now depressed: the 
 moment it begins to descend, the valve c, which leads 
 
 What are the parts of each syringe ? How many valves has it ? Which 
 way do they open ? Describe what takes place during the upward motion 
 of the piston. What takes place during the downward motion ? 
 
STRUCTURE OF THE AIR-PUMP. 19 
 
 into the globe shuts ; and now as the piston comes down 
 it condenses the air below it, and as this air is condensed 
 it resists exerting its elastic force. The piston-valve, d, 
 under these circumstances, is pushed open, and the com- 
 pressed air gets away into the atmosphere. As soon as 
 the piston has reached the bottom of the cylinder all the 
 air has escaped, and the process is repeated precisely as 
 before. The action in the syringe is, therefore, to draw 
 out from the globe a certain quantity of air at each up- 
 ward movement, and expel this quantity into the air at 
 each downward movement. 
 
 For reasons connected with the great pressure of the 
 air, and also for expediting the process of exhaustion, two 
 syringes are commonly used. To their pistons are at- 
 tached rods which terminate in racks, b b ; between 
 these there is placed a toothed wheel, which is turned on 
 its axis by the handle, its teeth taking into the teeth of 
 the racks. When the handle is set in motion and the 
 wheel made to revolve, it raises one of the pistons, and at 
 the same time depresses the other. The ends of these 
 racks are seen in Fig. 12. The wheel is included in the 
 transverse wooden bar, e e, Fig. 11. 
 
 By the aid of this invaluable machine numerous striking 
 and important experiments may be made. The form de- 
 scribed here is one of the most simple, and by no means 
 the most perfect. For the higher purposes of science 
 more complicated instruments have been contrived, in 
 which, with the utmost perfection of workmanship, the 
 valves are made to open by the movements of the pump 
 itself, and do not require to be lifted by the elastic force 
 of the air. In such pumps a far higher degree of rare- 
 faction can be obtained. 
 
 No air-pump, no matter how perfect it may be. can 
 ever make a perfect vacuum, or withdraw all the air from 
 its receiver. The removal of the air depends on the ex- 
 pansion of what is left behind, and there must always be 
 that residue remaining which has forced out the portion 
 last removed by the action of the syringes. 
 
 The fundamental fact 'in the science of Pneumatics is, 
 that atmospheric air is a heavy body, and this may be 
 
 How are the pistons rftoved by the rack ? What contrivances are intro- 
 duced in the more perfect air-pumps ? Can any of these instruments 
 make a perfect vacuum ? What is the cause of this ? 
 
WEIGHT OF THE AIR. 
 
 proved in a very satisfactory manner by the aid of the 
 Fig. 13. pump. Let there be a glass 
 
 flask, a, Fig. 13, the mouth of 
 which is closed with a stop-cock, 
 through which the air can be re- 
 moved. If from this flask we ex- 
 haust all the air, and then equi- 
 poise it with weights at a balance 
 as soon as the stop-cock is open- 
 ed and the air allowed to rush in 
 the flash preponderates. By add- 
 ing weights in the opposite scale, 
 we can determine how much it 
 requires to bring the balance 
 back to equilibrio, and there- 
 fore what is the weight of a vol- 
 ume of air equal to the capacity 
 of the flask. 
 
 Upon the same principles we 
 can prove that all gases, as well 
 as atmospheric air, have weight. 
 It is only requisite to take the exhausted flask, and hav- 
 ing counterpoised it as before, 
 screw it on to the top of a jar, 
 c, Fig. 14, containing the gas 
 to be tried. On opening the 
 stop-cocks, e d, the gas flows 
 out of the jar and fills the flask, 
 which, being removed, may be 
 again counterpoised at the bal- 
 ance, and the weight of the gas 
 filling it determined. There are 
 very great differences among 
 gases in this respect. Thus, 
 if we take one hundred cubic 
 inches of the following they will severally weigh : 
 
 Hydrogen 2-1 grains. 
 
 Nitrogen 30'1 " 
 
 Atmospheric air 31-0 " 
 
 Carbonic acid 47-2 " 
 
 Vapor of Iodine 269-8 " 
 
 What is the fundamental fact in Pneumatics ? flow may the weight of 
 the air he proved ? How do other gases compare with it in this respect ? 
 Mention some of them. 
 
 Fig. 14. 
 
PRESSURE OF THE AIR. 21 
 
 From the fact that the air has weight, it necessarily 
 follows that it exerts pressure on all those portions that 
 are in the lower regions, having to sustain the weight 
 of the masses above. And not only does this hold good 
 as respects the aerial strata themselves, it also holds 
 for all objects immersed in the air. In most cases, the 
 resulting pressure is not detected, because it takes effect 
 equally in all directions, and pressures that are equal and 
 opposite mutually neutralize each other. 
 
 But when by the air-pump we remove the pressure 
 from one side of a body, and still allow it to be exerted 
 on the other, we see at once abundant Fi s- 
 
 evidence of the intensity of this force. 
 Thus, if we take a jar, Pig. 15, open at 
 both ends, and having placed it on the 
 pump-plate, lay the palm of the hand 
 on the mouth of it ; on exhausting the 
 air the hand is pressed in firm contact 
 with the jar, so that it cannot be lifted without the exer- 
 tion of a very considerable force. 
 
 In the same way, if we tie over a jar a piece of blad- 
 der, and allow it to dry, it assumes, of course, a perfectly 
 horizontal position ; but on exhausting the air within very 
 slightly, it becomes deeply depressed, and is 
 soon burst inward with a loud explosion. This 
 simple instance illustrates, in a very satisfacto- 
 ry way, the mode in which the pressure of the 
 air is thus rendered obvious ; for so long as 
 the jar was not exhausted, and had air in its 
 interior, the downward pressure of the atmosphere could 
 not force the bladder inward, nor disturb its position in 
 any manner : for any such disturbance to take place the 
 pressure must overcome the elastic force of the air with- 
 in, which resists it, pressing equally in the opposite way 
 But on the removal of the air from the interior, the press- 
 ure above is no longer antagonized, and it takes effect 
 at once by crushing the bladder. 
 
 Why does the air exert pressure ? What follows on removing the press- 
 ure from one side of a body ? Describe the experiment in Figs. 15 and 16. 
 Why is not the bladder crushed in until the air is exhausted ? 
 
PRESSURE OP THE AIR. 
 
 LECTURE V. 
 
 THE PRESSURE OF THE Am. The Magdeburg Hemis- 
 pheres. Water supported by Air. The Pneumatic 
 Trough. 
 
 THE BAROMETER. Description of this Instrument. Cause 
 of its Action. Different kinds of Barometers. Meas- 
 itrement of Accessible Heights. 
 
 MANY beautiful experiments establish the fact that the 
 atmosphere presses, not only in the downward direc- 
 tion, but also in every other way. Thus, if we take a pair 
 Fig. 17 of hollow brass hemispheres, a b, Fig. 17, which 
 fit together without leakage, by means of a flange, 
 and exhaust the air from their interior through a 
 stop-cock affixed to one of them, it will be found 
 that they cannot be pulled apart, except by the 
 exertion of a very great force. Now it does not 
 matter whether the handles of these hemispheres 
 are held in the position represented in the fig- 
 ure, or turned a quarter way round, or set at any an- 
 gle to the horizon they adhere with equal force togeth- 
 er; and the same power which is required to pull them 
 asunder in the vertical direction, must also be exerted in 
 all others. This, therefore, proves that the pressure of 
 the air takes effect equally in every direction, whether up- 
 ward, or downward, or laterally. 
 
 In Fig. 18 a very interesting experiment is rep- 
 resented. We take a jar, a, an inch or two wide 
 and two or three feet long, closed at one end and 
 open at the other, and having filled it entirely with 
 water, place over its mouth a slip of writing pa- 
 per, b. If now the jar be inverted in the position 
 represented in the figure, it will be seen that the 
 column of fluid is supported, the paper neither 
 dropping off nor the water flowing out. This 
 remarkable result illustrates the doctrine of the up- 
 ward pressure of the air. Nor does it even require that 
 
 Prove that the air presses equally every way. Describe the apparatus 
 in Fig. 18. Why does not the paper fall from the mouth of the jar T 
 
PRESSURE OF THE AIR. 
 
 23 
 
 Fig. 20. 
 
 a piece of paper should be used provided the glass has 
 
 the proper form. Thus, let there be a bottle, a, F*g- 19. 
 
 Fig. 19, in the bottom of which there is a large 
 
 aperture, b. If the bottle be filled with water, 
 
 and its mouth closed by the finger, the water will 
 
 not flow out, but remain suspended. And that 
 
 this result is due to the upward pressure of the 
 
 air is proved by moving the finger a little on 
 
 one side, so as to let the air exert its pressure on the top 
 
 as well as the bottom of the water, which immediately 
 
 flows out. 
 
 If we take ajar, a, Fig. 20, and having filled it full of 
 water, invert it as is represented, in a 
 reservoir or trough : for the reason ex- 
 plained in reference to Fig. 18, the 
 water will remain suspended in the 
 jar. Such an arrangement forms the 
 pneumatic trough of chemists. It en- 
 ables them to collect the various gas- 
 es without intermixture with atmos- 
 pheric air ; for if a pipe or tube 
 through which such a gas is coming be depressed beneath 
 the moiith of the jar a, so that the bubbles may rise into 
 the jar, they will displace the water, and be collected in 
 the upper part without any admixture. 
 
 If in this experiment we use mercury instead of water, 
 the same phenomenon ensues the mercury being support- 
 ed by the pressure of the air. Now it might be inquired, 
 as the atmosphere only extends to a certain altitude, and 
 therefore presses with a weight which, though great, must 
 necessarily be limited, whether that pressure could sus- 
 tain a column of mercury of an unlimited length ? If we 
 take a jar a yard in length, and fill it with mercury, and 
 invert it in a trough, it will be seen that the mercury is 
 not supported, but that it settles from the top and de- 
 scends until it reaches a point which is about thirty inches 
 above the level of the mercury in the trough. Of course, 
 as nothing has been admitted, there must be a vacant 
 
 Will the same take place without any paper? Prove that it is due to 
 the upward pressure of the air. What is the pneumatic trough? On 
 what principle does it depend ? Will the same take place if mercury is 
 used instead of water? What takes place when the jar is more than thirty 
 inches high ? 
 
24 THE BAROMETER. 
 
 space or vacuum between the top of the mercury and the 
 top of the jar. 
 
 Fig. 21. This experiment which, as we are soon to see, 
 is a very important one, is commonly made with 
 a tube, a b, Fig. 21, instead of a jar the tube 
 being more manageable and containing less mer- 
 cury. It should be at least thirty-two inches long, 
 and being filled with quicksilver, may be inverted 
 in a shallow dish containing the same metal, c. It 
 is convenient to place at one side of the tube a 
 scale, d, divided into inches, these inches being 
 counted from the level of the mercury in the dish, 
 c. Such an instrument is called a Barometer, or 
 measurer of the pressure of the air. 
 
 Let us briefly investigate the agencies which operate 
 in the case of this instrument. If, having closed the mouth 
 of the tube b with the finger, we lift it out of the dish c, 
 it will be found that we must exert a considerable degree 
 offeree in order to sustain the column of mercury, which 
 presses against the finger with its whole weight, and tends 
 to push it away. Consequently, the mercury is continu- 
 ally exerting a tendency to flow out, and therefore two 
 forces are in operation : on the one hand, the weight of 
 the mercury attempting to flow out of the tube into the 
 dish ; and on the other, the weight or pressure of the at- 
 mosphere attempting to push the mercury up in the tube. 
 Fig. 29. If the pressure of the air were greater, it would 
 push the mercury higher; if less, the mercury 
 would flow out to a corresponding extent. Thus, 
 the length of the mercurial column equilibrates 
 the pressure of the air, and we therefore say that 
 the atmospheric pressure is equal to so many 
 inches of mercury. 
 
 That the whole thing depends on the pressure 
 of the air may be beautifully proved by putting 
 the barometer under a tall air-pump receiver, as 
 represented in Fig. 22, and exhausting. As the 
 pressure of the air is reduced the mercurial col- 
 umn falls ; and if it were possible to make a per- 
 
 How is this experiment commonly made ? Describe a barometer. What 
 are the forces which operate in this instrument ? What does the mercu- 
 rial column equilibrate ? What is it equal to ? How may it be proved to 
 depend on the pressure of the air ? 
 
THE BAROMETER. 25 
 
 feet vacuum by such means, the mercury would sink in 
 the tube to its level in the dish. On readmitting the air 
 the mercury rises again, and when the original pressure 
 is regained it stands at the original level. 
 
 There are many different forms of barometers, Fig. 23. 
 such as the straight, the syphon, &c., but the prin- 
 ciple of all is the same. The scale must uni- 
 formly commence at the level of the mercury in 
 the reservoir. Now it is plain that this level 
 changes with the height of the column ; for if 
 the metal flows out of the tube it raises the level 
 in the reservoir, and vice versa. In every per- 
 fect barometer, means, therefore, should be had 
 to adjust the beginning of the scale to the level 
 for the time being. In some barometers, as in 
 that represented in Fig. 23, this is done by hav- 
 ing the mercury in a cistern with a movable bot- 
 tom, and by turning the screw V, the level can be 
 precisely adjusted to that of the ivory point, a. 
 
 A barometer kept in the same place under- 
 goes variations of altitude, some of which are reg- 
 ular and others irregular. The former, which 
 depend on diurnal tides in the atmosphere, anal- 
 ogous to tides in the sea, occur about the same 
 time of the day the greatest depression being 
 commonly about four in the morning and eve- 
 ning, and the greatest elevation about ten in the 
 morning and night. In summer, however, they 
 occur an hour or two earlier in the morning, and 
 as much later at night. The irregular changes depend 
 on meteorological causes, and are not reduced as yet to 
 any determinate laws. In amount they are much more 
 extensive than the former, extending from the twenty-sev- 
 enth to more than the thirtieth inch, while those are lim- 
 ited to about the tenth of an inch. 
 
 A very valuable application of the barometer is for the 
 determination of accessible heights. The principle upon 
 which this depends is simple the barometer necessarily 
 
 What would ensue if a perfect vacuum could be made ? What takes 
 place on readmitting the air? From what point should the scale of the 
 barometer commence? What are the regular barometric changes? What 
 is the extent of the irregular ones ? How is the barometer applied to the 
 measurement of heights ? 
 
 B 
 
26 MEASURE OF ATMOSPHERIC PRESSURE. 
 
 standing at a lower point as it is carried to a higher posi- 
 tion. In practice it is more complicated, and to obtain ex- 
 act results various methods have been given by Laplace, 
 Baily, Littrow, and others. 
 
 LECTURE VI. 
 
 THE PRESSURE OF THE AIR. Measure of the Force with 
 which the Air presses. Different Modes of Estimating 
 it. Experiments Illustrating this Force. 
 
 ELASTICITY OF THE AIR. Experimental Illustrations. 
 The Condenser. 
 
 HAVING, in the preceding lecture, explained the cause 
 and illustrated the pressure of the air, we proceed in the 
 next place to determine its actual amount. 
 
 JV * r - 24 - There are many ways in 
 
 gjjjjJH^ which this may be done. The 
 
 jjT following is simple : Take a 
 
 ,s~^&= . pair of Magdeburg hemis- 
 
 pheres, the area of the sec- 
 tion of which has been pre- 
 viously determined in square 
 inches; exhaust them as per- 
 fectly as possible at the pump; 
 and then, fastening the lower 
 handle, a, to a firm support, 
 hang the other, I, Fig. 24, to the hook of a steelyard, 
 and move the weight until the hemispheres are pulled 
 apart. It will be found that this commonly takes place 
 when the weight is sufficient to overcame a pressure of 
 fifteen pounds on every square inch. 
 
 This may serve as an elementary illustration, but there 
 are other methods much more exact. Thus, by the ba- 
 rometer itself we may determine the value of the pressure 
 with precision. If we had a barometer which was ex- 
 actly one square inch in section, and weighed the quanti- 
 ty of mercury it contained at any given time, it would 
 
 What may the Magdeburg hemisphere be made to prove? How may 
 = b ! P r r, ed by the barometer ? What is *e pressure of the air on 
 
PRESSURE OF THE AIR. 
 
 27 
 
 give us the value of the atmospheric pressure on one 
 square inch, because the weight of the mercury is equal 
 to the pressure of the air. And by calculation we can, in 
 like manner, obtain it from tubes of any diameter. 
 
 The phenomena of the barometer teach us that this 
 pressure is not always the same, but it undergoes varia- 
 tions. It is commonly estimated at fifteen pounds on the 
 square inch. 
 
 There are two other ways in which the value of the 
 pressure of the air is stated. It is equal to a column of 
 mercury thirty inches in length, or to a column of water 
 thirty-four feet in length. 
 
 We are now able to understand the reason of the great 
 effects to which the pressure of the air may give rise. In 
 most instances these effects are neutralized by counter- 
 vailing pressures. Thus, the body of a man of ordinary 
 size has a surface of about two thousand square inches, 
 the pressure upon which is equal to thirty thousand pounds. 
 But this amazing force is entirely neutralized, because, 
 as we have seen, the atmospheric pressure is equal in all 
 directions, upward, downward, and laterally. All the 
 cavities and the pores of the body are filled 
 with air, which presses with an equal force. 
 
 The following experiments may further 
 illustrate the general principle of atmospher- 
 ic pressure : 
 
 On a small, flat plate, a, Fig. 25, furnished 
 with a stop-cock, b, which terminates in a 
 narrow pipe, c, let there be placed a tall re- 
 ceiver from which the air is to be exhausted 
 by the pump. The stop-cock b being clo- 
 sed, and the instrument being removed from 
 the pump, b is to be opened, while the lower 
 portion of its tube dips into a bowl of water. 
 Under these circumstances the water is 
 pressed up in a jet through c, and forms a 
 fountain in vacuo. 
 
 On the top of a receiver, Fig. 26, let 
 there be cemented, air-tight, a cup of wood, 
 
 What is the length of an equivalent column of mercury ? What is it in 
 the case of water? What amount of pressure is there on the body of a 
 man ? By what is this counteracted ? Describe the fountain in vacuo. 
 How may mercury be pressed through the pores of wood ? 
 
28 
 
 ELASTICITY OF AIR. 
 
 Fig. 26. a, terminating in a cylindrical piece, b, the 
 pores of which run lengthwise. Beneath this 
 let there be placed a tall jar, c. Now, if the 
 wooden cup be filled with quicksilver, the jar 
 being previously placed on the pump, and ex- 
 haustion made, the metal will be pressed 
 through the pores of the wood and descend 
 in a silver shower. The jar, c, should be so 
 placed as to prevent any of the quicksilver 
 getting into the interior of the pump. 
 
 There are many substances which exist in 
 the liquid condition, merely because of the press- 
 ure of the air. Take a glass tube, A, Fig. 27, 
 closed at one end and open at the other, and 
 having filled it with water, invert it in a jar, B ; 
 introduce into it now a little sulphuric ether, 
 which will rise, because of its lightness, to the 
 top of the tube, at a. Place the apparatus be- 
 neath the receiver of the air-pump, arid exhaust. The 
 ether will now be seen to abandon the liquid and assume 
 the gaseous form, filling the entire tube and looking like 
 air. On allowing the pressure again to take effect, it again 
 relapses into the liquid form. 
 
 Fig. 28. The following experiments illustrate the elas- 
 ticity of the air : 
 
 Take a glass bulb, a, Fig. 28, which has, a 
 tube, b, projecting from it, the open extremity 
 of which dips beneath some water in a cup, c; 
 the tube and the bulb being likewise full of 
 water, except a small space which is occupied 
 by a bubble of air at a. Invert over the whole 
 ajar, d, and, placing the arrangement on the pump, ex- 
 haust. It will be found, as the exhaustion goes on, that 
 the bubble a steadily increases in size until it fills all 
 the bulb, and even the tube. On readmitting the press- 
 ure the bubble collapses to its original size. The air 
 is, therefore, dilatable and condensible that is, it is 
 elastic. 
 
 If a bottle, the sides of which are square and the mouth 
 hermetically closed, be placed beneath a receiver, and 
 
 Why does sulphuric ether retain the liquid state ? When the pressure 
 what becomes of the ether? What does experiment Fig. 28 
 
THE CONDENSER. 
 
 29 
 
 Fig. 29. 
 
 the pressure removed, tbe air imprisoned in 
 the interior exerting its elastic force, will vio- 
 lently burst the bottle to pieces.' It is, there- 
 fore, well to cover it with a wire cage, as rep- 
 resented in Fig. 29. 
 
 The elastic force of the air increases with its 
 density. Powerful effects, therefore, arise by 
 condensing air into a limited space. The con- 
 denser, which is an instrument for this pur- 
 pose, is represented in Fig. 30. It consists 
 of a tube, a b, in which there moves by a 
 handle, g, a piston^ In one side of the tube, 
 at c, there is an aperture, and at the lower 
 part, d, there is a valve, e, opening down- 
 ward. On pushing the piston down, the airbe- 
 iieathit is compressed, and, opening the valve 
 e, by its elastic force, accumulates in the re- 
 ceiver, R. When the piston is pulled up a ; 
 vacuum is made in the tube; but as soon as 
 it passes the aperture, c, the air rushes in. 
 Another downward movement drives this 
 through the valve into the receiver, and 
 the process may be continued until the elas- 
 tic force of the included air becomes very 
 great. 
 
 If the receiver be partly filled with water, 
 and there be placed in it a piece of wax, an egg, 
 or any yielding or brittle bodies, it will be found 
 impossible to alter their figure by condensing 
 the air to any extent whatever. And this arises 
 from the circumstance already explained that 
 the pressure generated is equal in all direc- 
 tions. 
 
 The Cartesian image is a grotesque figure, 
 made of glass, Fig. 31, hollow within and filled 
 with water to the height c d. The upper part, 
 a, is filled with air. The water is introduced through the 
 tail, 6, and the quantity of it is so adjusted that the figure 
 just floats in water. If, therefore, it be placed in a deep 
 
 Under what circumstances may flat bottles be broken ? What relation 
 is there between elastic force and density ? Describe the condenser. Why 
 are not brittle bodies broken in such an instrument ? What is the reason 
 of the motions of the Cartesian images ? 
 
 Fig. 31. 
 
30 MISCELLANEOUS EXPERIMENTS. 
 
 jar quite full of that liquid, and a cover of India-rubber 
 Fig. 32. or bladder tied on, as seen in Fig. 32, the fig- 
 ure floats up at the top ; but by pressing with 
 the finger on the cover, more water is forced into 
 its interior, through the tail, b, and it descends 
 to the bottom. On removing the finger the elastic 
 force of the air, a, drives out this excess of wa- 
 ter, and the image, becoming lighter, reascends. 
 If the tail be turned on one side, as represent- 
 ed, the efflux of the water taking effect in a lat- 
 eral direction, the figure spins round in its move- 
 ments and performs grotesque evolutions. 
 
 On precisely the same principle, if a small 
 k] a( jder, only partly full of air, be sunk by a 
 weight, Fig. 33, to the bottom of a deep glass 
 of water, on covering the whole with a re- 
 ceiver and exhausting, the elastic force of the 
 included air dilates the bladder, which rises 
 to the top, carrying with it the weight. 
 When the pressure is readmitted the blad- 
 der collapses and descends again to the bot- 
 tom of the jar. 
 There are numerous machines in which the elastic force 
 of air is brought into operation, such as the air-gun, 
 blowing machines, &c. Indeed, the various applications 
 of gunpowder itself depend on this principle that ma- 
 terial on ignition suddenly giving rise to the evolution of 
 an immense quantity of gas, which exerts a great elastic 
 force. 
 
 What is the cause of the ascent and descent of the little bladder, Fig. 
 33 ? On what do the air-gun and the action of gunpowder depend 1 
 
MARRIOTTE'S LAW 31 
 
 LECTURE VII. 
 
 PROPERTIES OF THE AIR. Marriotte's Law. Proof for 
 Compressions and Dilatations. Case in which it Fails. 
 Resistance of the Air to Motion. The Parachute. 
 The Air transmits Sound; supports Animal Life, Com- 
 bustion, and Ignition. Exists in the pores of some Bodies 
 and is dissolved in others. 
 
 ATMOSPHERIC air being thus a highly compressible and 
 expansible substance, we have next to inquire what is 
 the amount of its compressibility under different degrees 
 of force ] This has been determined experimentally by 
 different philosophers, the true law having first been dis- 
 covered by Boyle and Marriotte. 
 
 The density and elasticity of air are directly as the force 
 of compression. 
 
 The volume whicJi air occupies is inversely as the press- 
 ure upon it. 
 
 To illustrate, and at the same time to prove these laws, 
 we make use of a tube, a d c b, so' bent that it has Fitr- 34. 
 two parallel branches, a and b. It is closed at b, 
 and has a funnel-mouth at a. Sufficient mercury is 
 poured into the tube to close the bend and to insu- 
 late a volume of air in b d. Of course this air ex- 
 ists under a pressure of one atmosphere equal to a 
 column of mercury thirty inches long. Through the 
 funnel, a, mercury is now to be poured ; as it accu- 
 mulates it presses upon the air in d b, and re- 
 duces its volume to c. If, in this manner, a column 
 thirty inches long be introduced, it will be found that the 
 air in b d is reduced to half. There are, therefore, now 
 two atmospheres pressing on the included air the atmos- 
 phere itself being one, and the thirty inches of mercury 
 the other. Two atmospheres, therefore, reduce a given 
 quantity of air into half its volume. 
 
 In the same manner it could be proved, if the tube 
 
 What is Marriotte's laXv ? Describe Marriotte's instrument. What is 
 its use ? When the pressure on a gas is doubled, tripled, quadrupled, what 
 Aolume does it assume ? 
 
RESISTANCE OF AIR. 
 
 Fig. 35. 
 Id 
 
 were long enough, that the introduction of another thirty 
 inches of mercury, giving a pressure of three atmospheres, 
 would condense the air to one-third, that four would com- 
 press it to one-fourth, five to one-fifth, &c. 
 
 The truth of this law may be proved for rare- 
 factions as well as condensations. For this 
 purpose let there be taken a long tube, a b, 
 Fig. 35, open at the end, b, and closed at a, 
 with a screw ; a jar, A, filled with mercury to a 
 sufficient height, is also to be provided. Now 
 let the screw at a be opened and the tube. de- 
 pressed in the mercury until the metal, by 
 rising, leaves in the tube a few inches of air. 
 The screw is now to be closed and the tube lift- 
 ed. The included air at once dilates and a col- 
 umn of mercury is suspended. It will be found 
 that when the air has dilated to double its vol- 
 ume, the length of the mercurial column in the 
 tube will be fifteen inches that is, half the ba- 
 rometric length. 
 
 * By such experiments, it therefore appears that 
 Marriotte's- law holds both for condensations and rarefac- 
 tions. This law has been verified until the air has been 
 condensed twenty-seven times and rarefied one hundred 
 and twelve times. In the case of gases, which easily as- 
 sume the liquid form, it is, however departed from as that 
 point is approached. 
 
 Besides the properties already de- 
 scribed, atmospheric air possesses 
 others which require notice. Among 
 these may be mentioned its resist- 
 ance to motion. 
 
 This property may be exhibited 
 by means of the two wheels, a b, Fig. 
 36, which can be put in rapid rota- 
 tory motion by the rack, d, which 
 moves up and down through an air- 
 tight stuffing-box, e. The wheels 
 are so arranged that the vanes of a 
 move through the air edgewise, but 
 
 How may this be proved for rarefactions ? To what extent has this law 
 been verified ? How may the resistance of the air be proved ? In a vacu- 
 um is there any resistance ? 
 
 Fig. 36. 
 
RESISTANCE OP AIR. 
 
 33 
 
 Fig. 37. 
 
 those of b with their broad faces. On pushing down the 
 rack, d, and making the wheels rotate with equal rapid- 
 ity in the atmospheric air, one of them, a, will be found 
 to continue its motion much longer than the other, b: and 
 that this arises from the resistance which b experiences 
 from the air is proved by making them rotate in the 
 receiver from which the air has been exhausted, when b 
 will continue its motion as long as a, both ceasing to re- 
 volve simultaneously. 
 
 The water-hammer affords another instance of the same 
 principle. It consists of a tube a foot or more long and 
 half an inch in diameter. In it there is included a small 
 quantity of water, but no atmospheric air. When it is 
 turned upside down the water drops from end to end, and 
 emits a ringing, metallic sound. If there was any air in 
 the tube, it would resist or break the fall of the water. 
 A well-made mercurial thermometer exhibits the same 
 fact. If there is a perfect vacuum in its tube, on turning 
 the instrument upside down the metal drops like a hard, 
 solid body against the closed end. 
 
 The Parachute is a machine 
 by which aeronauts may de- 
 scend from a balloon to the 
 ground in safety. It bears a 
 general resemblance to an 
 umbrella, and consists of a 
 strong but light surface, a a, 
 Fig. 37, from which a car, 
 b, is suspended. When it 
 is detached from the bal- 
 loon, it descends at first with 
 an accelerated velocity, but 
 this is soon checked by the 
 resistance of the air, and the 
 
 | machine then falls at a rate 
 
 i nearly uniform, and very mod- 
 
 ; erate. 
 
 In virtue of its elasticity, atmospheric air is the common 
 
 I medium for the transmission of sounds. Under the receiv- 
 
 \ er of an air-pump let there be placed a bell, a, Fig. 38, the 
 hammer, b, of which can be moved on its pivot, c, by means 
 
 Describe the parachute and its mode of action. How may it be proved 
 that atmospheric air transmits sound ? 
 
34 
 
 AIR SUPPORTS LIFE. 
 
 of a lever, h, which is worked by a rod passing through 
 Fig. 38 the stuffing-box, e. The bell is placed 
 
 on a leather drum, g, and fastened 
 down to the pump-plate by means 
 of a board, d. While the air is yet 
 in the receiver, the sound is quite 
 audible, but on exhausting it becomes 
 fainter and fainter, and at last can no 
 longer be heard. On readmitting the 
 air the sound gradually increases, arid 
 at last acquires its original intensity. 
 The leather cushion,^, is necessary to 
 prevent the transmission of the sound 
 through the solid part of the pump. 
 The air also is absolutely necessary for the support of 
 Fig. 39. life. The higher warm-blooded animals 
 
 die when the air is only partially rare- 
 fied. A rabbit, or other small animal, 
 placed under an air-pump jar may re- 
 main there several minutes without being 
 much disturbed ; but if we commence 
 withdrawing the air the animal instantly 
 shows signs of distress, and if the exper- 
 iment is continued, soon dies. 
 
 So, too, if a jar containing some small 
 fishes be placed under an exhausted re- 
 ceiver, the animals either float on their 
 backs at the surface of the water, or 
 descend only by violent muscular exertions. Fishes 
 respire the air which is dissolved in water, and hence 
 it is somewhat remarkable that they continue to live 
 for a considerable length of time in an exhausted re- 
 ceiver. 
 
 The air is also necessary to all processes of combustion. 
 If a lighted candle be placed under a receiver, it will 
 burn for a length of time ; but if the air be withdrawn 
 by the pump, it presently dies out. The smoke also 
 descends to the bottom of the receiver, there being no 
 air to buoy it up. 
 
 Why is it necessary that the bell should rest on a cushion ? Prove that 
 air is necessary for the support of life. Do fishes die at once in an ex- 
 hausted receiver? Prove that the air is necessary to support combus- 
 tion. 
 
AIR EXISTS IN PORES. 
 
 35 
 
 If a gun-lock be placed- in an exhausted receiver, and 
 the flint be made to stiike, no sparks pig. 40. 
 
 whatever appear ; and, consequently, 
 if there were powder in the pan, it 
 could not be exploded. The produc- 
 tion of sparks by the flint and steel is 
 due to small portions of the latter which 
 are struck off by the percussion burn- 
 ing in the air, and when the air is re- 
 moved that combustion can, of course, 
 no longer take place. 
 
 By taking advantage of the expansi- 
 bility of the air, we are able to prove 
 Fig. 41. tnat it is included in the pores 
 of many bodies. Thus, if an 
 egg is dropped into a deep jar 
 of water, and this covered with 
 a receiver as soon as exhaustion is made, a multi- 
 tude of air bubbles continually ascend through the 
 water. Or if a glass of porter be placed beneath 
 such a receiver, its surface is covered 
 with a foam, the carbonic acid gas, 
 which is the cause of its agreeable 
 briskness, escaping away. And even com- 
 mon river or spring water treated in the same 
 manner exhibits the escape of a considerable 
 quantity of gas, which ascends through it in 
 small bubbles, and gives it a sparkling ap- 
 pearance. 
 
 Why does a gun-lock fail to give sparks in vacuo ? How may the pres- 
 ence of air in the pores of bodies be proved I Does water contain dis- 
 solved air ? 
 
36 LOSS OF WEIGHT IN AIR. 
 
 LECTURE VIII. 
 
 PROPERTIES OF THE AIR. Loss of Weight of Bodies in 
 the Air. Theory of Aerostation. The Montgolfier 
 Balloon. The Hydrogen Balloon. Mode of Controll- 
 ing Ascent and Descent. Artificial and Natural Cur- 
 rents in the Air. Velocity with which Air flows into a 
 Vacuum. Velocity of Efflux of different Gases. Prin- 
 ciples of Gaseous Diffusion. These Principles regulate 
 the Constitution of the Atmosphere. 
 
 ON principles which will be fully explained when we 
 come to speak of specific gravity, it appears that a solid 
 immersed in a fluid loses a portion of its weight. It 
 follows, of course, that a substance weighs less in the air 
 than it does in vacuo. 
 
 To one arm of a balance, a, Fig. 43, let there be. hung 
 Fig. 43. a light glass globe, c, coun- 
 
 terpoised in the air on the 
 other arm, b, by means of a 
 weight. If the apparatus be 
 placed beneath a receiver, 
 and the air exhausted, the 
 H globe c, descends, but on re- 
 admitting the air the equi- 
 librium is again restored. 
 This instrument was former- 
 ly used for determining the 
 density of the air. 
 A substance that has the same density as atmospheric 
 air, when it is immersed in that medium, loses all its 
 weight, and will remain suspended in it in any position 
 in which it may be placed. But if it be lighter, it is 
 pressed upward by the aerial particles, and rises upon 
 the same principle that a cork ascends from the bottom 
 of a bucket of water. And as the density of the air con- 
 
 What difference is there in the weight of a body in the air and in vacuo ? 
 What fact is illustrated by the instrument, Fig. 43 ? Under what circum- 
 stances does a substance in the air lose all its weight ? On what principle 
 do air balloons depend ? 
 
AIR BALLOON. 37 
 
 tinually diminishes as we go upward, it is evident that 
 such a body, ascending from one stratum to another, will 
 finally attain one having the same density as itself, and 
 there it will remain suspended. 
 
 On these principles aerostation depends. Air balloons 
 are machines which ascend through the atmosphere and 
 float at. a certain altitude. They are of two kinds: 1st, 
 Montgolfier or rarefied air balloons ; and, 2d, Hydrogen 
 gas balloons. 
 
 The Montgolfier balloon, which was invented by the 
 person whose name it bears, consists of a light bag of 
 paper or cotton, which may be of a 
 spherical or other shape ; in its lower 
 portion there is an aperture, with a 
 basket suspended beneath for the pur- 
 pose of containing burning material, as 
 straw or shavings. On a small scale, a 
 paper globe two or three feet in diam- 
 eter, with a piece of sponge soaked in 
 spirits of wine, answers very well. The 
 hot air arising from the burning matter 
 enters the aperture, distending the balloon, and makes it 
 specifically lighter than the air, through which, of course, 
 it will rise. 
 
 The hydrogen gas balloon consists, in like manner, of 
 a thin, impervious bag, filled either with hydrogen or com- 
 mon coal gas. The former, as usually made, is from ten 
 to thirteen times lighter than air ; the latter is somewhat 
 heavier. A balloon filled with either of these possesses, 
 therefore, a great ascentional power, an % d will rise to 
 considerable heights. Thus, Biot and Gay Lussac, in 
 1804, ascended in one of these machines to an elevation 
 of 23,000 feet. When the balloon first ascends, it ought 
 not to be full of gas, for as it reaches regions where the 
 pressure is diminished, the gas within it is dilated, and 
 though flaccid at first, it will become completely distended. 
 If it were full at the time it left the ground, there would 
 be risk of its bursting open as it arose. The gas balloon 
 requires a valve placed at its top, so that gas may be 
 
 How many kinds of them are there ? Describe the Montgolfier balloon. 
 Describe the hydrogen balloon. What is the relative weight of hydrogen 
 and air ? Why must not the machine be full when it leaves the ground ? 
 How is it made to ascend and descend ? 
 

 38 CURRENTS IN THE AIR. 
 
 discharged at pleasure, and the machine made to descend. 
 The aeronaut has control over its motions by taking up 
 with him a quantity of sand in bags, as ballast. If he 
 throws out sand the balloon rises, and if Tie opens the 
 valve and lets the gas escape, it descends. 
 
 The rarefaction which air undergoes by heat makes it, 
 of course, specifically lighter. Warm air, therefore, as- 
 cends, and cold air descends. When the door of a room 
 which is very warm is open, the hot air flows out at the 
 top, and the cold enters at the floor: these currents may 
 be easily traced by holding a candle near the bottom and 
 top of the doOr. In the former position the flame leans 
 inward, in the latter it is turned outward, following the 
 course of the draught. 
 
 The drawing of chimneys, and the actipn of furnaces 
 and stoves depends on similar principles : the column 
 of hot air contained in the flue ascending, and cold air 
 replacing it below. 
 
 Similar movements take place in the open atmosphere. 
 When the sun shines on the ground or the surface of the 
 sea, the air in contact becomes warm, and rises ; it is 
 replaced by colder portions, and a continuous current is 
 established. The direction of these currents is changed 
 by a variety of circumstances, as the diurnal rotation of 
 the earth and other causes less understood. On these 
 depend the various currents known as Breezes, Trade- 
 winds, Storms, Hurricanes. 
 
 The atmosphere does not rush into a void space instan- 
 taneously, but, under common circumstances of density 
 and pressure, jwith a velocity of about 1296 feet in one 
 second. Its resisting action on projectiles moving through 
 it with great velocities is intimately connected with this 
 fact. A cannon-ball, moving through it with a speed of 
 two or three thousand feet, leaves a total vacuum behind 
 it, and condenses the air correspondingly in front. It is, 
 therefore, subjected to a very po-werful pressure continu- 
 ally tending to retard it. The rush of the air flowing 
 into the vacuous spaces left by moving bodies is the cause 
 'of the loud explosions they make. 
 
 How does increase of heat affect the air? How may the currents in a 
 warm room be traced ? What is the principle on which furnaces and stoves 
 depend ? How do winds and currents in the air arise ? What is the rea- 
 son that a cannon-ball moving in the air has its velocity rapidly reduced ? 
 
DIFFUSION OF GASES. 39 
 
 When gases of different densities flow from apertures 
 of the same size, the velocities with which they issue are 
 different, and are inversely as the square roots of their 
 densities. The lighter a gas is the greater is its issuing 
 velocity ; and therefore hydrogen, which is the lightest 
 body, moves, under such circumstances, with the greatest 
 speed. 
 
 The experiment represented in Fig. 45 illustrates 
 these principles. Let there Fig. 45. 
 
 be a tube, a b, half an inch , 
 
 in diameter and six inches 
 long, the end, b, being open 
 and a closed with a plug 
 of plaster of Paris, which 
 is to be completely dried. 
 Counterpoise this tube on 
 the arm of a balance, and 
 fill it with hydrogen gas, 
 taking care to keep the 
 plug dry, letting the open end, b, of the tube dip just be- 
 neath the surface of some water contained in a jar, C. 
 In a very short time it will be discovered that the hydro- 
 gen is escaping through the plaster of Paris, and the tube, 
 filling with water, begins to descend; and after a few min- 
 utes much of the gas will have gone out, and its place be 
 occupied partly by atmospheric air, which comes in in the 
 opposite direction, and partly by the water which has risen 
 in the tube. 
 
 Even when gases are separated from each other by 
 barriers, which, strictly speaking, are not porous, the same 
 phenomenon takes place. Thus, if with the finger we 
 spread a film of soap-water over the mouth of a bottle, 
 , and then expose it under a jar to some other Fig.4f>. 
 gas, such as carbonic acid, this gas percolates rap- 
 idly through the film, and, accumulating in the bot- 
 tle, distends the film into a bubble, as represented 
 in Fig. 46. Meanwhile, a little atmospheric air es- 
 capes out of the bottle through the film in the op- 
 posite direction. 
 
 What is the law under which gases flow out of apertures? How may 
 it be proved that gases can percolate through porous bodies, such as plugs 
 of stucco? How may it be proved that they pass through films of 
 water ^ 
 
40 DIFFUSION OF GASES. 
 
 This propensity of gases to diffuse into each other is 
 clearly shown by filling a bottle, H, Fig. 47, 
 with a very light gas, as hydrogen ; and a second 
 one, C, with a heavy gas, as carbonic acid, and 
 putting the bottles mouth to mouth. Diffusion 
 takes place, the light gas descending and the 
 heavy one rising until both are equally com- 
 mixed. We see, therefore, that this property of 
 gases is intimately concerned in determining the 
 constitution of the atmosphere, which is made 
 up of different substances, some of which are light and 
 some heavy the heavy ones not sinking, nor the light ones 
 ascending, but both kept equally commixed by diffusion 
 into each other. 
 
 Do the same phenomena ensue when no boundaries or harriers inter- 
 vene ? What have these principles to tlo with the constitution of the at- 
 mosphere '! 
 
PROPERTIES OF LKJUID8. 41 
 
 PROPERTIES OF LIQUIDS. 
 
 HYDROSTATICS AND HYDRAULICS. 
 
 LECTURE IX. 
 
 PROPERTIES OP LIQUIDS. Extent and Depth of the Sea. 
 Its Influence on the Land. Production of Fresh Wa- 
 ters. Relation of Liqiiids and Gases. Physical Con- 
 dition of Liquids. Different Degrees of Liquidity. 
 Florentine Experiment on the Compression of Water. 
 Oersted's Experiments. Compressibility of other Li- 
 quids. 
 
 HAVING disposed of the mechanical properties of at- 
 mospheric air, which is the type of gaseous bodies, in the 
 next place we pass to the properties of water, which is the 
 representative of the class of Liquids. 
 
 About two thirds of the surface of the earth are covered 
 with a sheet of water, constituting the sea, the average 
 depth of which is commonly estimated at about two miles. 
 This, referred to omr usual standards of comparison, im- 
 presses us at once with an idea of the great amount of 
 water investing the globe ; and, accordingly, imaginative 
 writers continually refer to the ocean as an emblem of 
 immensity. 
 
 But, referred to its own proper standard of compari- 
 son the mass of the earth it is presented to us under a 
 very different aspect. The distance from the surface to 
 the center of the earth is nearly four thousand miles. 
 The depth of the ocean does not, therefore, exceed ?T Vir 
 part of this extent : and astronomers have justly stated, 
 that were we on an ordinary artificial globe to place a 
 
 What are the estimated dimensions of the sea ? How do these coin- 
 pare with the size of the earth itself? 
 
42 THE SEA. 
 
 representation of the ocean, it would scarcely exceed in 
 thickness the film of varnish already placed there by the 
 manufacturer. 
 
 In this respect the sea constitutes a mere aqueous film 
 on the face of the globe. Yet, insignificant as it is in 
 reality, it has been one of the chief causes engaged in 
 shaping the external surface, and also of modeling the 
 interior to a certain depth for geological investigations 
 have proved the former action of the ocean on regions now 
 far removed from its influence, in the interior of conti- 
 nents ; and also its mechanical agency in the formation 
 of the sedimentary or stratified rocks which are of enor- 
 mous superficial extents and often situated at great depths. 
 
 Besides the salt waters of the sea, there are collections 
 of fresh water, irregularly disposed, constituting the dif- 
 ferent lakes, rivers, &c. The direct sources of these 
 are springs, which break forth from the ground, the little 
 streams from which coalesce into larger ones. But the 
 true source of all our terrestrial waters is the sea itself. By 
 the shining of the sun upon it a portion is evaporated into 
 the air, and this, carried away by winds and condensed 
 again by cold, descends from the atmosphere as showers 
 of rain, which, being received upon the ground, perco- 
 lates until it is stopped by some less pervious stratum, 
 and flowing along this at last breaks out wherever there 
 is opportunity in the low grounds thus constituting a 
 spring. Such streamlets coalesce into rivers, which find 
 their way back again to the sea, the point from which 
 they originally came an eternal round, which is repeat- 
 ed for centuries in succession. * 
 
 From these more obvious phenomena of nature we dis- 
 cover a relationship between aerial and liquid bodies 
 the one passing without difficulty into the other form 
 and, indeed, many of the most important events around 
 us depending on that fact. Experiment also shows that, 
 in many instances, substances which under all common 
 circumstances exist in the gaseous condition, can be made 
 to assume the liquid. Thus, carbonic acid, which is one 
 of the constitutents of the atmosphere, can by pressure 
 be reduced to the liquid form, and can even be made to 
 
 What great phenomena have arisen from the action of the sea ? To what 
 source are rivers and springs due? How is it they are formed? What re 
 lation is there between gases and liquids ? 
 
DEGREES OF LldUIDITY. 43 
 
 assume that of a solid. The main agents by which such 
 transmutations are affected are cold and pressure. 
 
 The parts of liquids seem to have little cohesion. View- 
 ing the forms of matter as being determined by the rela- 
 tion of those attractive and repulsive forces which are 
 known to exist among particles, it is believed in that^ 
 now under consideration the liquid that these forces 
 are in equilibrio. For this reason, therefore, the parti- 
 cles of such bodies move freely among one another; and 
 liquids, of themselves, cannot assume any determinate 
 shape, but conform their figure to the vessels in which 
 they are placed. Portions of the same liquid added to 
 one another readily unite. 
 
 Among liquids we meet with what may be termed dif- 
 ferent degrees of liquidity. Thus the liquidity of molasses, 
 oil, and water, is of different degrees. It seems as though 
 there was a gradual passage from the solid to this state, 
 a passage often exhibited by some of the most limpid 
 substances. Thus alcohol, when submitted to an extreme 
 degree of cold, assumes that partial consistency which is 
 seen in melting beeswax, yet at common temperatures it 
 is one of the most mobile bodies known. So, too, that 
 compound of tin and lead which is used by plumbers as a 
 solder, though perfectly fluid at a certain heat, passes, in 
 the act of cooling, through various successive stages, and 
 at a particular point becomes plastic and may be molded 
 with a cloth. 
 
 If a quantity of atmospheric air is pressed upon by any 
 suitable contrivance, it shrinks at once in volume. We 
 rhave already proved this phenomenon and determined its 
 laws. If water is submitted to the same trial, the result 
 is very different it refuses to yield : for this reason, inas- 
 much as the same fact applies to the whole class, liquids 
 are spoken of as incompressible bodies. 
 
 It was at one time thought that the experiment of the 
 Florentine academicians, who filled a gold globe with 
 water, and on compressing it with a screw found the wa- 
 ter ooze through the pores of the gold, proved completely 
 the incompressibility of that liquid. But more recent ex- 
 Do the parts of liquids cohere ? What is the relation between their at- 
 tractive and repulsive forces ? Mention some of the distinctive qualities 
 ol liquids. Give examples of different degrees of liquidity. What exper- 
 iment has been supposed to prove that water is incompressible ? 
 
44 
 
 COMPRESSIBILITY OF LIQJJIDS. 
 
 periments have shown, beyond all doubt, that liquids are 
 compressible, though in a less degree than gases. Thus, 
 it is a common experiment to lower a glass bottle, filled 
 with water and carefully stopped with a cork, into the sea. 
 Fig. 48. On raising it again the cork is often found forced 
 in, and the water is uniformly brackish. But in 
 a more exact manner the fact can be proved, 
 and even the amount of compressibility meas- 
 ured, by QErsted's'machine. This consists of a 
 strong glass cylinder, a a, Fig. 48, filled with 
 water, upon which pressure can be exerted by 
 a piston driven by a screw, b. When the screw 
 is turned and pressure on the liquid exerted, it 
 contracts into less dimensions, but at the same 
 time the glass, a a, yielding, distends, and the 
 contraction of the water becomes complicated 
 with the expansion of the glass in which it is 
 placed. 
 
 To enable us to get 7 % id of this difficulty, the instru- 
 ?49. ment, Fig. 49, is immersed in the cylinder of 
 water, as seen at Fig. 48. This consists of a 
 glass reservoir, e, prolonged into a fine tube, e f t 
 with a scale, x, attached to it. The reservoir and 
 part of the tube are filled with water, and a little 
 column of quicksilver, x, is upon the top of the wa- 
 ter, serving to show its position. On one side there 
 is a gage, d, partially filled with air. It serves to 
 measure the pressure. 
 
 Now when the instrument, Fig. 49, is put in the 
 cylinder in the position indicated in Fig. 48, and 
 pressure made by the screw, b, it is clear that the 
 water in the reservoir will be compressed, and the 
 glass which contains it being pressed upon equally, 
 internally and externally, will yield but very little. Mak- 
 ing allowance, therefore, for the small amount of com- 
 pression which the glass thus equally pressed upon un- 
 dergoes, we may determine the compressibility of the 
 water as the force upon it varies. It thus appears that 
 water diminishes ^i^ P art of its volume for each at- 
 mosphere of pressure upon it. In the same way the com- 
 pressibility of alcohol has been determined to be TT o^. 
 
 Mention some that prove the contrary. Describe (Ersted's machine. 
 What is the amount of the compressibility of water ? 
 
HYDROSTATIC PRESSURE. 45 
 
 LECTURE X. 
 
 THE PRESSURES OP LIQUIDS. Divisions of Hydrodynam- 
 ics. Liquids seek their own Level. Equality of press- 
 ures. Case of different Liquids pressing against each 
 other. General Law of Hydrostatics. Hydrostatic Par- 
 adox. Law for Lateral Pressures. Instantaneous com- 
 munication of Pressure. Bramah's Hydraulic Press. 
 
 To the science which describes the mechanical proper- 
 ties of liquids the title of HYDRODYNAMICS is applied. It 
 is divided into two branches, Hydrostatics and Hydraul- 
 ics. The former considers the weight and pressure of 
 liquids, the latter their motions in canals, pipes, &c. 
 
 A liquid mass exposed without any confinement to the 
 action of gravity would spread itself into one continuous 
 superficies, for all its parts gravitate independently of one 
 another, each part pressing equally on all those around it, 
 and being pressed on equally by them. 
 
 A liquid confined in a receptacle or vessel of any kind 
 conforms itself to the solid walls by which it is surround- 
 ed, and its upper surface is perfectly plane, no part 
 being higher than another. This level of surface takes 
 place even when different vessels communicating with 
 each other are used. Thus, if into a glass of water we 
 dip a tube, the upper orifice of which is temporarily 
 closed by the finger, but little water will enter, owing to 
 the impenetrability of the air ; but, as soon as the finger 
 is removed, the liquid instantly rises, and finally settles at 
 the same level inside of the tube that it occupies in the 
 glass on the outside. 
 
 This result obviously depends on the equality of press- 
 ure just referred to, and it is perfectly independent of 
 the form or nature of the vessel. If we take a tube bent 
 
 Into what branches is Hydrodynamics divided ? Under the action of 
 gravity what form does a free liquid assume ? What is the effect when it 
 is inclosed in a vessel ? Give an illustration of the equality of pressure. 
 
46 
 
 PRESSURE OF DIFFERENT LIQUIDS. 
 
 fig. 50. 
 
 in the form of the letter U, and closing one of its branches 
 with the finger, pour water into the other, as soon as the 
 finger is removed the liquid rises in the empty branch, 
 and, after a few oscillatory movements, stands at the same 
 level in both. 
 
 If one of the branches of such a tube is much wider 
 than the other, the same result still ensues. 
 Thus, as in Fig. 50, we might have a reser- 
 c voir, A I, exposing an area of ten, or a huri- 
 > dred, or ten thousand times that of a tube 
 rising from it, B G C H, but in the latter a liquid 
 would rise no higher than in the former, both 
 being at precisely the same level, A D. We 
 perceive, therefore, from such an experiment, 
 , that the pressure of liquids does not depend 
 on their absolute weight, but on their vertical 
 altitude. The great mass of liquid contained 
 in A exerts no more pressure on C than would 
 a smaller mass contained in a tube of the same 
 dimensions as C itself. 
 
 j- A variation of this experiment will throw 
 much light upon the subject. Instead of using 
 one, let there be two liquids, of which the spe- 
 cific gravities are different. Put one in one of 
 the branches of the tube,aZc, Fig. 51, and the 
 i4 other in the other. Let the liquids be quicksil- 
 13 ver and water. It will be found, under these 
 circumstances, that the water does not press 
 the quicksilver up to its own level, but that, 
 for every thirteen and a half inches vertical 
 height that it has in one of the branches the 
 quicksilver has one inch in the other. Of 
 course, as they communicate through the hori- 
 zontal branch, Z>, the quicksilver must press 
 against the water as strongly as the water 
 presses against it; if it did not, movement would ensue. 
 And such experiments, therefore, prove that it is the prin- 
 ciple of equality of pressures which determines liquids to 
 seek their own level. 
 
 From this it therefore appears that a liquid in a vessel 
 
 Does this depend on the mass of a liquid ? Prove that it depends on its 
 height. What takes place when liquids of different densities are used ? 
 In what directions do liquids press ? 
 
 51. 
 
HYDROSTATIC PRESSURES. 
 
 47 
 
 Fig. 52. 
 
 not only exerts a pressure upon the bottom in the di- 
 rection in which gravity acts, but also laterally and up- 
 ward. 
 
 From what was proved by the experiment represented in 
 Fig. 50, it follows that these pressures are by no means ne- 
 cessarily as the mass, but in proportion to the vertical height. 
 If one hundred drops of water be arranged in a vertical line, 
 the lowest one will exert on the surface on which it rests 
 a pressure equal to the weight of the whole. And from 
 such considerations we deduce the general rule for esti- 
 mating the pressure a liquid exerts upon the base of a 
 vessel. " Multiply the height of the fluid by the area of 
 the base on which it rests, and the product gives a mass 
 which presses with the same weight." 
 
 Thus in a conical vessel, E C 
 D F,^. 52, the base,CD, sus- 
 tains a pressure measured by 
 the column A B C D. For all 
 the rest of the liquid on.ly 
 presses on ABCD laterally, 
 and resting on the sides EC 
 and F D, cannot contribute 
 any thing to the pressure on 
 the base, C D 
 
 But in a conical vessel, EC 
 D F, Fig. 53, the pressure on 
 A B is measured by A B C D, 
 as before ; but the other por- 
 tions of the liquid, not rest- 
 ing upon the sides, press 
 also upon the bottom, E F, 
 and the retult, therefore, is 
 the same as if the vessel 
 were filled throughout to the 
 height C A. 
 
 This law is nothing more than an expression of the fact 
 that the actual pressure of a liquid is dependent on its 
 vertical height and the area of its base. Its applications 
 give rise to some singular results. Thus, the Hydro- 
 static bellows consists of a pair of boards, A, Fig. 54, 
 
 Fig. 53. 
 
 Give the rule for finding the pressure of a liquid 01 
 sel containing it. Describe the hydrostatic bellows. 
 
 on the base of the ves- 
 
48 
 
 HYDROSTATIC PARADOX. 
 
 united together by leather, and from the 
 >e lower one there rises a tube, e B e, ending 
 in a funnel-shaped termination, e. If heavy 
 weights, bed, are put upon the upper 
 board, or a man stands upon it, by pour- 
 ing water down the tube the weight can 
 be raised. It is immaterial how slender 
 the tube, and, therefore, how small the 
 quantity of water it contains, the total 
 pressure resulting depends on the area of 
 the bellows-boards, multiplied by the ver- 
 tical height of the tube. 
 
 Theoretically, therefore, it appears that 
 a quantity of water, however small, can 
 be made to lift a weight however great a principle 
 sometimes spoken of as the HYDROSTATIC PARADOX, 
 
 But liquids exert a pressure against the sides as well as 
 upon the bases of the containing vessel the force of that 
 pressure depending on the height. The law for estima- 
 ting such pressure is, " The horizontal force exerted 
 against all the sides of a vessel is found by multiplying 
 the sum of the areas of all the sides into a height equal to 
 half that at which the liquid stands." 
 
 When bodies are sunk in a liquid, the liquid exerts a 
 pressure which depends conjointly on the surface of the 
 solid and the depth to which its center is sunk. Thus, if 
 into a deep vessel of water we plunge a bladder, to the 
 neck of which a tube is tied, the bladder and part of the 
 tube being filled with colored water, it will be seen, as the 
 bladder is sunk, that the colored water rises in the tube. 
 A pressure exerted against one portion of a liquid is 
 instantly communicated throughout the whol&mass, each 
 particle transmitting the same pressure to those around. 
 A striking illustration of this is seen when a Prince Ru- 
 pert's drop is broken in a glass of water, the glass being 
 instantly burst to pieces. 
 
 Bramah's press, or the Hydrostatic press, is an illus- 
 tration of the principle developed in this lecture that 
 every particle of a fluid transmits the pressure it receives, 
 in all directions, to those around. It consists of a small 
 
 What is meant by the hydrostatic paradox ? Give the rule for finding 
 lateral pressures. Prove that a liquid exerts a pressure on bodies plunged 
 in it. Give an illustration of the instantaneous communication of pressure. 
 
THE HYDRAULIC PRESS. 
 
 49 
 
 Fig. 55. 
 
 metallic forcing-pump, a, Fig. 55, in which a piston, s, is 
 worked by a lever, c b d. This little pump communicates 
 with a strong cyl- 
 indrical reser- 
 voir, A, in which 
 a water-tight pis- 
 ton, S, moves, 
 having a stout 
 flat head, P, be- 
 tween which and 
 a similar plate, 
 R, supported in 
 a frame, the sub- 
 stance to be com- 
 pressed, W, is 
 placed. The cyl- 
 inder, A, and the 
 forcing-pump, with the tube communicating between them, 
 are filled with water, the quantity of which can be in- 
 creased by working the lever, d. Now it is obvious that 
 any force, impressed upon the surface of the water in the 
 small tube, a, will, upon the principles just described, 
 be transmitted to that in A, and the piston, S, will be 
 pushed up with a force which is proportional to its area, 
 compared with that of the piston of the little cylinder, a. 
 If its area is one thousand times that of the little one, it 
 will rise with a force one thousand times as great as that 
 with which the little one descends the motive force ap- 
 plied at d, moreover, has the advantage of the leverage 
 in proportion as c d is greater than c b. On these princi- 
 ples it may be shown that a man can, without difficulty, 
 exert a compressing force of a million of pounds by the 
 aid of such a machine of comparatively small dimensions. 
 
 Describe the hydraulic press. 
 
 c 
 
 
50 SPECIFIC GRAVITY. 
 
 LECTURE XI. 
 
 SPECIFIC GRAVITY. Definition of the term. The Stand- 
 ards of Comparison. Method for Solids. Case when 
 the Body is Lighter than Water. Method for Liquids 
 by the Thousand-Grain Bottle. Effects of Temperature. 
 Standards of Temperature. Other Methods for Li- 
 quids. Method for Gases. Effects of Temperature and 
 Pressure. The Hydrometer or Areometer. 
 
 BY the specific gravity of bodies we mean the propor- 
 tion subsisting between absolute weights of the same vol- 
 ume. Thus, if we take the same volume of water and 
 copper, one cubic inch of each, for example, we shall find 
 that the copper weighs S'G times as much as the water: 
 and the same holds good for any other quantity, as ten 
 cubic inches or one cubic foot. When of the same vol- 
 ume the copper is always S'6 times the weight of the 
 water. 
 
 Specific gravity is, therefore, a relative affair. We must 
 have some substance with which others may be compared. 
 The standard , which has been selected for solids and 
 liquids is water; that for gases and vapors, atmospheric 
 air. 
 
 When we speak of the specific gravity of a substance 
 which is of the liquid or solid kind, we mean to express 
 its weight compared with the weight of an equal volume 
 of water. Thus, the specific gravity of mercury is 13-5; 
 that is to say, a given volume of it would weigh 13-5 times 
 as much as an equal volume of water. 
 
 Apparently the simplest way for the determination of 
 specific gravities of solids, would be to form samples of 
 a uniform volume; as, for instance, one cubic inch. 
 Their absolute weight, as determined by the balance, 
 would be their specific gravities. 
 
 But in practice so many difficulties would be encoun- 
 tered in such a process that its results would be quite in- 
 
 What is meant by specific gravity ? What are the standards of com- 
 parison? Describe an apparently simple method of determining the spe- 
 cific gravity of solids. 
 
THOUSAND-GRAIN BOTTLE. 51 
 
 exact ; and the principles of hydrostatics furnish us with 
 far more accurate means for resolving such problems. 
 
 To determine the specific gravity of a solid body, it is 
 to be weighed first in air and then in water. In the latter 
 instance it will weigh less than in the former, because it 
 displaces a quantity of the water equal to its own volume, 
 and this deficit in weight is the weight of the water so 
 displaced. The weight in air and the loss in water being 
 thus determined, to find the specific gravity, " Divide the 
 weight in air by the loss in water, and the quotient is the 
 specific gravity." 
 
 If the body be lighter than water, there must be affixed 
 to it some substance sufficiently heavy to sink it, the 
 weight of which, and also its loss of weight in water are 
 previously known. Deduct this weight from the loss of 
 the bodies when immersed together, and divide the abso- 
 lute weight of the light body by the remainder ; the quo- 
 tient gives the specific gravity. 
 
 For the determination of the specific gravity of liquids 
 several methods may be resorted to. 
 One of the most simple is by the Thou- 
 sand-grain Bottle. This consists of a 
 light glass flask, <2, Fig. 56, the stopper 
 of which is also of glass with a fine per- 
 foration, b, through it. When the bot- 
 tle is filled with distilled water, and the 
 stopper inserted in its place, any excess 
 of liquid is forced through the perfora- 
 tion, and the bottle, on being weighed, 
 should be found to contain one thousand 
 grains of the liquid exactly. 
 If any other liquid be in like manner placed in this 
 bottle, by merely ascertaining its weight we at once de- 
 termine its specific gravity. Thus, if it be filled with oil 
 of vitrol or muriatic acid, it will be found to hold 1845 
 grains of the former and 1210 of the latter. Those num- 
 bers, therefore, represent the specific gravities of the 
 bodies respectively. 
 
 This instrument enables us to illustrate, in a very satis- 
 factory manner, the effect of temperature on specific grav- 
 
 Give the general hydrostatic method. What is done when the body is 
 lighter than water ? Give the method in the case of liquids by the Thou- 
 sand-grain Bottle. 
 
STANDARDS OF TEMPERATURE. 
 
 ity. It has been said that the Thousand-grain bottle is so 
 called from its containing precisely one thousand grains 
 of water ; but very superficial consideration satisfies us 
 that this can only be the case at a particular temperature. 
 Suppose the bottle is of such dimensions that at 60 Fah- 
 renheit it contains exactly one thousand grains, if we raise 
 its temperature to 70 Fahrenheit, the water will expand, 
 or if we lower it to 50 Fahrenheit it will contract exact- 
 ly as if it were a liquid in a thermometer. It is, there- 
 fore, very clear that temperature must always enter into 
 these considerations, and that before we can express the 
 relation of weight between any substance, whether solid 
 or liquid, and that of an equal volume of water, we must 
 specify at what particular temperature the experiment 
 was made. For many purposes 60 Fahrenheit is select- 
 ed, and for others 391 Fahrenheit, which is the temper- 
 ature of the maximum density of water. 
 
 There is a second method by which the specific gravity 
 of fluids may be known. It is to weigh a given solid (as 
 a mass of glass) in the fluids to be tried, and determine 
 the loss of weight in each case. Inasmuch as the solid 
 displaces its own volume of the different liquids, the losses 
 it experiences when thus weighed will be proportional to 
 the specific gravities. The following rule, therefore, ap- 
 plies : " Divide the loss of weight in the different liquids 
 by the loss of weight in water, and the quotients will give 
 the specific gravities of the liquids under trial." 
 
 For the determination of 
 the specific gravities of gases 
 a plan analogous in principle 
 to that of the Thousand-grain 
 bottle is resorted to. A light 
 glass flask, g, exhausted of air, 
 is attached by means of the 
 stop-cocks, e d, to the jar, c, 
 containing the gas to be tried. 
 This gas has been passed 
 through a drying-tube, a, by 
 means of a bent pipe, b, into 
 the jar, c, over mercury. On 
 
 Describe the effects of temperature on specific gravity. Give another 
 method for determining the density of liquids. How is that of gases dis- 
 covered ? 
 
 Fig. 57. 
 
THE HYDROMETER. 53 
 
 opening the stop-cock the gas flows into g, and its weight 
 may then be determined by the balance. 
 
 From the greater dilatation of gaes by heat, all that 
 has been just said in relation to the effect of temperature 
 on specific gravity applies here still more strongly. It is 
 to be recollected that this form of bodies is compared 
 with atmospheric air taken as the standard. 
 
 For gases another disturbing agency beside tempera- 
 ture intervenes it is pressure. Atmospheric pressure is 
 incessantly varying, and the densities of gases vary with 
 it. It is not alone the thermometer, but also the Barom- 
 eter which must be consulted, and the temperature and 
 pressure both specified. Besides, great care must be taken 
 in transferring the gas from the jars in which it is con- 
 tained, that it is not subjected to any accidental pressures 
 in the apparatus itself, and that the flask in which it is 
 weighed is not touched by the hands or submitted to any 
 other warming or cooling influences. 
 
 For the determination of the densities of liquids there 
 is still another method, often more convenient than the 
 former, and very commonly resorted to, it is by the aid 
 of instruments which pass under the name of Hydrometers 
 or Areometers. 
 
 The principle on which these act is, that when a body 
 floats upon water, the quantity of fluid displaced is equal 
 in volume to the volume of the part of the body immersed, 
 and in weight to the weight of the whole body. 
 
 Thus, a piece of cork floating on the surface of quick- 
 silver, water, and alcohol, sinks in them to very different 
 depths : in the quicksilver but little, in the water more, 
 and in the alcohol still deeper; but in every instance the 
 weight of the quantity of the liquid displaced is equal to 
 that of the cork. 
 
 It is plain, therefore, that to determine the specific 
 gravity of a liquid, we have only to determine the depth 
 to which a floating body will be immersed in it. The 
 hydrometer fulfills these conditions. It consists of a cylin- 
 drical cavity of glass, A, Fig. 58, on the lower part of 
 which a spherical bulb, B, is blown, the latter being 
 filled with a suitable quantity of small shot or quicksil- 
 
 What disturbing effects are encountered in the case of gases ? On what 
 principle is the hydrometer constructed. 
 
THE HYDROMETER. 
 
 ver. From the cylindrical portion, A, a tube, C, rises, in 
 the interior of which is a paper scale bearing the divisions. 
 Fig. 58 The whole weight of the instrument is such that 
 it floats in the liquid to be tried, and if that liquid 
 is to be compared with water, and is lighter than 
 water, the zero of the divided scale is toward the 
 lower end of the paper; but if the liquid be 
 heavier than water, the zero is toward the top of 
 the scale. Tables are usually constructed so 
 that, by their aid, when the point at which the 
 hydrometer floats in a given liquid is determined 
 in any experiment, the specific gravity is ex- 
 pressed opposite that number in the table. 
 
 Of these scale-hydrometers we have several 
 different kinds, according as they are to deter- 
 mine different liquids. Among them may be mentioned 
 Fig. 59. Beaume's hydrometer, an instrument of con- 
 stant use in chemistry. In the finer kinds of 
 areometers the weighted sphere, B, Fig. 58, 
 forms the bulb of a delicate thermometer, 
 the stem of which rises into the cavity, A. 
 This enables us to determine the temperature 
 of the liquid at the same time with its specific 
 gravity. 
 
 Nicholson's gravimeter is a hydrometer 
 which enables us to determine the density 
 either of solids or liquids. It is represented at 
 Fig. 59. 
 
 Describe the hydrometer. 
 
HYDROSTATIC PRESSURE. 
 
 55 
 
 LECTURE XIL 
 
 HYDROSTATIC PRESSURES AND FORMATION OF FOUNT- 
 AINS. Fundamental Fact of Hydrostatics holds 
 also for Gases. Illustrations of Upward Pressure. 
 . Determination of Specific Gravities of Liquids on these 
 Principles. Theory of Fountains. Cause of Natural 
 Springs. Artesian Wells. 
 
 THE fundamental fact in hydrostatics thus appears to 
 be, that as each atom of a liquid yields to the influence 
 of gravity without being restrained by any cohesive force, 
 all the particles of such a mass must press upon those 
 which are immediately beneath them, and therefore the 
 pressure of a liquid must be as its depth. 
 
 The same fact has already been recognized for elastic 
 fluids, in speaking of the mechanical properties of the 
 earth's atmosphere, which, for this veiy reason, and also 
 from the circumstance that it is a highly compressible 
 body, possesses different densities at different heights. 
 The lower regions have to sustain or bear up the weight 
 of all above them, but as we go higher and higher this 
 weight becomes less and less, until at the surface it ceases 
 to exist at all. 
 
 We have already shown from the 
 nature of a fluid such pressures are 
 propagated equally in all directions, up- 
 ward and laterally, as well as downward. 
 This important principle deserves, how- 
 ever, a still further illustration from the 
 consequences we have now to draw from 
 it. Let a tube of glass, a &, Fig. 60, have 
 its lower end, b, closed with a valve slightly 
 weighted and opening upward, the end, a, 
 being open. On holding the tube in a 
 vertical position, the valve is kept shut by 
 its own weight. But if we depress it in 
 
 What is the fundamental fact in hydrostatics ? Does this hold for elastic 
 fluids? Describe the illustration represented in Fig. GO. How may it be 
 made to prove the downward pressure of water ? 
 
 Fig. 60. 
 
56 
 
 LIQUIDS SEEK THEIR LEVEL. 
 
 a vessel of water, as soon afif a certain depth is reached 
 the upward pressure of the water forces the valve, and 
 the tube begins to fill. Still further, if before immersing 
 the tube we fill it to the height of a few inches with 
 water, we shall find that it must now be depressed to a 
 greater depth than before, because the downward pressure 
 of the included water tends to keep the valve shut. 
 
 From the same principles it follows, that whenever a 
 liquid has freedom of motion, it will tend to arrange 
 itself so that all parts of its surface shall be equidistant 
 fro A the center of the earth. For this reason the surface 
 of water in basins and other reservoir^ of limited extent 
 is always in a horizontal plane ; but when those surfaces 
 are of greater extent, as in the case of lakes and the sea, 
 they necessarily exhibit a rounded form, conforming to the 
 figure of the earth. It is also to be remembered that, when 
 liquids are included in narrow tubes, the phenomena of cap- 
 illary attraction disturb both their level and surface-figure. 
 Fig. 61. All liquids, therefore, tend to 
 
 find their own level. This fact is 
 well illustrated by the instrument, 
 fj Fig. 61, consisting of a cylinder 
 V of glass, , connected by means of 
 a horizontal branch with the tube, 
 
 b, which moves on a tight joint at, 
 
 c. By this joint, b can be set par- 
 allel to , or in any other position. 
 If a is filled with wa- 
 ter to a given height, 
 
 the liquid immediately 
 flows through the hori- 
 zontal connecting pipe, and rises to the same 
 height in b that it occupies in a. Nor does it 
 matter whether b be parallel to , or set at 
 any inclined position, the liquid spontaneously 
 adjusts itself to an equal altitude. 
 
 The same liquid always occupies the same 
 level. But when in the branches of a tube 
 we have liquids, the specific gravities of which 
 are different, then, as has already been stated in Lecture 
 
 . What is the surface-figure of liquids ? Describe the illustration given 
 51 ' 1S the laW f different Ii( l uids pressing on each other in 
 
 Fig. 62. 
 c 
 
FORMATION OF FOUNTAINS. 
 
 57 
 
 Fig. 63. 
 
 X., they rise to different heights. The law which deter- 
 mines this is, "The heights of different fluids are inversely 
 as their specific gravities'' If, therefore, in one of the 
 branches of a tube, a b, Fig. 62, some quicksilver is 
 poured so as to rise to a height of one inch, it will require 
 in the other tube, b c, a column of water 13^ inches long 
 to equilibrate it, because the specific gravities of quick- 
 silver and water are as 13^ to 1. 
 
 A very neat instrument for illustrating 
 these facts is shown in Fig. 63. It consists 
 of two long glass tubes, a b, which are con- 
 nected with a small exhausting-syringe, c, 
 their lower ends being open dip into the 
 cups, w a, in which the liquids whose spe- 
 cific gravities are to be tried are placed. Let 
 us suppose they are water and alcohol. The 
 syringe produces the same degree of partial 
 exhaustion in both the tubes, and the two li- 
 quids equally pressed up by the atmospher- 
 ic air, begin to rise. But it will be found 
 that the alcohol rises much higher than the 
 water to a height which is inversely pro- 
 portional to its specific gravity. 
 
 When in the instrument, Fig. 61, we bend 
 the tube, b, upon its joint, so that its end is 
 below the water-level in a, the liquid now be- 
 gins to spout out : or if, instead of the jointed 
 tube, we have a short tube, C e D, Fig. 64, 
 proceeding from the reservoir, A B, the wa- 
 ter spouts from its termination and forms a 
 fountain, E F, which rises nearly to the same 
 height as the water-level. The resistance of 
 the air and the descent of the falling drops 
 shorten the altitude, to which the jet rises to 
 a certain extent. On the top of the fountain 
 a cork ball, G, may be s spended by the play- 
 ing water. 
 
 The same instrument may be used to show 
 the equality of the vertical and lateral press- 
 
 Fig. 64. 
 
 
 uies at any point. For let the tube, D E, be removed so 
 
 At what heights will quicksilver and water stand ? Describe the instru- 
 ment, Fig. 63. What fact does it show ? Under what circumstances does 
 a liquid spout 1 How may a fountain be formed ? 
 
58 
 
 FORMATION OF FOUNTAINS. 
 
 as to leave a circular aperture at e ; also let C be a plug 
 closing an aperture in the bottom of exactly the same size 
 as e. Now if the reservoir, A B, be filled to the height 
 g, and kept at that point by continually pouring in water, 
 and the quantities of liquid flowing out through the lateral 
 aperture, e, and the vertical one, C, be measured, they 
 will be found precisely the same, showing, therefore, the 
 equality of the pressures ; but if an aperture of the same 
 size were made at f, the quantity would be found corre- 
 spondingly less. 
 
 It is upon these principles that fountains often depend. 
 The water in a reservoir at a distance is brought by pipes 
 Fig. 65. to the jet of the fountain, and there suffered 
 to escape. The vertical height to which it 
 can be thrown is as the height of the reser- 
 voir, and by having several jets variously ar- 
 ranged in respect of one another, the fount- 
 ain can be made to give rise to different fan- 
 ciful forms, as is the case with the public 
 fountains in the city of New York. 
 
 A simple method of exhibiting the fount- 
 ain is shown in Fig. 65. A jar, G-, is filled 
 with water, and a tube, bent as at a b c, is 
 dipped in it. By sucking with the mouth at 
 , the water may be made to fill the tube, 
 and then, on being left to itself, will play as a fountain. 
 
 On similar principles we account for the occurrence of 
 springs, natural fountains, and Artesian wells. The strata 
 composing the crust of the earth are, in most cases, in po- 
 sitions inclined to the horizon. They also differ very 
 greatly from one another in permeability to water 
 sandy and loamy strata readily allowing it to percolate 
 through them, while its passage is more perfectly resisted 
 by tenacious clays. On the side of a hill, the superficial 
 strata of which are pervious, but which rest on an imper- 
 vious bed below, the rain water penetrates, and being 
 guided along the inclination, bursts out on the sides of the 
 hill or in the valley below, wherever there is a weak place 
 or where its vertical pressure has become sufficiently pow- 
 erful to force a way. This constitutes a common spring. 
 
 Prove the equality of vertical and lateral pressures by the instrument, 
 Ftg. 64. What is the principle of fountains ? Describe the apparatus, Fig. 
 65. On what principle do springs flow from the ground ? 
 
ARTESIAN WELLS. 59 
 
 The general principle of the Artesian or overflowing 
 wells is illustrated in Fig. 66. Let b' b c d, be the sur- 
 face of a region of country the strata of which, b b' and 
 
 Fig 66, 
 
 a 
 
 d d', are more or less impervious to water, while the in- 
 termediate one, c c, of a sandy or porous constitution, al- 
 lows it a freer passage. When in the distant sandy coun- 
 try at c, the rain falls, it percolates readily and is guided 
 by the resisting stratum, d d'. Now if at a, a boring is 
 made deep enough to strike into c c or near to d on the 
 principles which we have been explaining, the water will 
 tend to rise in that boring to its proper hydrostatic level, 
 and therefore, in many instances, will overflow at its 
 mouth. The region of country in which this water ori- 
 ginally fell may have been many miles distant. 
 
 It follows, from the action of gravity on liquids, that if 
 we have several which differ in specific gravity in the 
 same vessel, they will arrange themselves according to 
 their densities. Thus, if into a deep jar we pour quick- 
 silver, solution of sulphate of copper, water, and alco- 
 hol, they will arrange themselves in the order in which 
 they have been named. 
 
 Wbat are Artesian wells ? When several liquids are in the same vessel, 
 how do they arrange themselves ? 
 
60 OF FLOWING LiaUIDS. 
 
 LECTURE XIII. 
 
 OP FLOWING LIQUIDS AND HYDRAULIC MACHINES. Laws 
 of the Flowing of Liquids. Determination of the Quan- 
 tity Discharged. Contracted Vein. Parabolic Jets. 
 Relative Velocity of the Parts of Streams. Undershot, 
 Overshot, Breast- Wheels. Common Pump. Forcing- 
 Pump. Vera's Pump. Chain-Pump. 
 
 IF a liquid, the particles of which have no cohesion, 
 flows from an aperture in the bottom of its containing ves- 
 sel, the particles so descending fall to the aperture with a 
 velocity proportional to the height of the liquid. 
 
 The force and velocity with which ,a liquid issues de- 
 pend, therefore, on the height of its level the higher the 
 level the greater the velocity. 
 
 As the pressures are equal in all directions, and as it is 
 gravity which is the cause of the flow, " The velocity 
 which the particles of a fluid acquire when issuing from an 
 orifice, whether sideways, upward, or downward, is equal 
 to that which they would have acquired in falling perpen- 
 dicularly from the level of the fluid to that of the orifice." 
 
 When a liquid flows from a reservoir which is not re- 
 plenished, but the level of which continually descends, 
 the velocity is uniformly retarded : so that an unreplen- 
 ished reservoir empties itself through a given aperture 
 in twice the time which would have been required for the 
 same quantity of water to have flowed through the same 
 aperture, had the level been continually kept up to the 
 same point. 
 
 The theoretical law for determining the quantity of wa- 
 ter discharged from an orifice, and which is, that " the 
 quantity discharged in each second may be obtained by mul- 
 tiplying the velocity by the area of the aperture" is not 
 found to hold good in practice a disturbance arising from 
 the adhesion of the particles to one another, from their 
 
 On what does the velocity of a flowing liquid depend ? What is that ve- 
 locity equal to ? What is the difference of flow between a replenished and 
 an unreplenished reservoir ? Why does not the theoretical law for the dis- 
 charge of water hold good ? 
 
THE CONTRACTED VEIN. 61 
 
 friction against the aperture, and from the formation of 
 what is designated "the contracted vein." For when wa- 
 ter flows through a circular aperture in a plate, the diam- 
 eter of the issuing stream is contracted and FI>. 67. 
 reaches its minimum dimensions at a-distance 
 about equal to that of half the diameter of the 
 aperture, as at s s', Fig. 67. This effect arises 
 from the circumstance that the flowing water is 
 not alone that which is situated perpendicularly 
 above the orifice, but the lateral portions likewise move. 
 These, therefore, going in oblique directions, make the 
 stream depart from the cylindrical form, and contract it, 
 as has been described. 
 
 By the attachment of tubes of suitable shapes to the ap- 
 erture, this effect may be avoided, and the quantity of 
 flowing water' very greatly increased. A simple aperture 
 and such a tube being compared together, the latter was 
 found to discharge half as much more water in the same 
 space of time. 
 
 As the motion of flowing liquids depends on the same 
 lav\s as that of falling solids, and is determined by gravi- 
 ty, it is obvious that the path of a spouting jet, the direc- 
 tion of which is parallel or oblique to the horizon, will bo 
 a parabola ; for, as we shall hereafter see, that is the path 
 of a body projected under the influence of gravity in vacuo. 
 When a liquid is suffered to escape in a horizontal direc- 
 tion through the side of a vessel, it may be easily shown 
 to flow in a parabolic path, as in Fig. 68. The maximum 
 distance to which a jet can 
 reach on a horizontal plane 
 is, when the opening is half 
 the height of the liquid, as 
 at C, and at points B and D 
 equidistant from C, it spouts 
 to equal distances. 
 
 To. measure the velocity 
 of flowing water, floating 
 bodies are used : they drift, 
 immersed in the stream un- 
 der examination. A bottle ____. 
 
 What is meant by the " contracted vein ?" From what does this arise ? 
 How may the quantity of flowing water be increased? What is the path 
 of a spouting jet ? 
 
62 
 
 WATER-WHEELS. 
 
 partly filled with water, so that it will sink to its neck, with 
 a small flag projecting, answers very well; or the num- 
 ber of revolutions of a wheel accommodated with float- 
 boards may be counted. 
 
 Fig. 69. In any stream the velocity is greatest 
 
 in the middle (wheve the water is deep- 
 est), and at a certain distance from the 
 surface. From this point it diminishes 
 toward the banks. Investigations of this 
 kind are best made by Pictot's stream- 
 measurer, Fig. 69. It' consists of a ver- 
 
 g tube corresponds with that outside, but 
 | the impulse of a stream causes the water 
 to rise in the tube until its vertical press- 
 ure counterpoises the force. 
 
 The force of flowing water is often 
 employed for various purposes in the 
 arts. We have several different kinds 
 of water-wheels, as the undershot, the 
 overshot, and the breast-wheel. The 
 first of these consists of a wheel or 
 drum revolving upon an axis, and on 
 the periphery there are placed float- 
 boards, a b c d, &c. It is to be fixed 
 so that its lower floats are immersed 
 in a running stream or tide, and is driven round by the 
 momentum of the current. 
 
 Fig. i\. The overshot-wheel, in 
 
 like manner, consists of a 
 cylinder or drum, with a 
 series of cells or buckets, 
 so arranged that the water 
 which is delivered by a 
 trough, A B, on the upper- 
 most part of the wheel, 
 may be held by the de- 
 scending buckets as long as possible. It is the weight 
 
 How may the velocity of flowing water be measured ? Describe the 
 stream-measurer. What is the undershot-wheel ? What is the overshot- 
 wheel? 
 
COMMON PUMP. 
 
 63 
 
 Fig. 72. 
 
 of this water that gives motion to the wheel on its 
 axis. 
 
 The breast- wheel, 
 in like manner, con- 
 sists of a drum work- 
 ing on an axis, and 
 having float -boards 
 on its periphery. It 
 is placed against a 
 wall of a circular 
 form, and the water 
 brought to it fills the buckets at the point A, and turns 
 the wheel, partly by its momentum and partly by its weight. 
 
 Of these three forms the overshot-wheel is the most 
 powerful. i*g- 73 - 
 
 There are a great many con- 
 trivances for the purpose of rais- 
 ing water to a higher level. These 
 constitute the different varieties 
 of pumps. 
 
 The common pump is repre- 
 sented in Fig. 73. It consists of 
 three parts : the suction-pipe, the 
 barrel, and the piston. The suc- 
 tion-pipe^e, is of sufficient length 
 to reach down to the water, A, 
 proposed to be raised from the 
 reservoir, L. The barrel, C B, is 
 a perfectly cylindrical cavity, in 
 which the piston, G, moves, air- 
 tight, up and down, by the rod, d. 
 It is commonly moved by a lever, 
 but in the figure a rod and han- 
 dle, D E, are represented. On >^= 
 one side is the spout, F. At !\iHl 
 the top of the suction-pipe, at 
 H, there is a valve, b, and also 
 one on the piston, at a. They 
 both open upward. When the 
 piston is raised from the bottom 
 of the barrel and again depressed, it exhausts the air in 
 
 What is the breast-wheel ? Which of these is the most powerful ? 
 Describe the lifting-pump. 
 
64 
 
 THE FORCING-PUMP. 
 
 Fiff. 74. 
 
 the suction-pipe, and the water rises from the reservoir, 
 pressed up by the atmosphere. After a few movements 
 of the piston the barrel becomes full of water, which, at 
 each successive lift, is thrown out of the spout, F. The 
 action of this machine is readily understood, after what 
 has been said of the air-pump, which it closely resembles 
 in structure. 
 
 In the forcing-pump the 
 suction pipe, e L, is commonly 
 short, and the piston, g, has 
 no valve. On the box at H, 
 there is a valve, b, as in the 
 former machine, and when 
 the piston is moved upward 
 in the barrel, C B, by the 
 handle, E, and rod, I) d, the 
 water, A, rises from the reser- 
 voir, L, and enters the barrel. 
 During the downward move- 
 ment of the piston the valve, 
 b, shuts, and the water passes 
 by a channel round m, through 
 the lateral pipe, M O M N, 
 into the air vessel, K K. The 
 entrance to this air-vessel at 
 P, is closed by a valve, #, and 
 there proceeds from it a ver- 
 tical tube, H G, open at both 
 ends. After a few movements 
 of the piston, the lower end, 
 I, of this tube becomes cov- 
 ered with water, and any fur- 
 ther quantity now thrown in 
 compresses the air in the space, H G, which, exerting its 
 elastic force, drives out the water in a continuous jet, S. 
 The reciprocating motion of the piston may, therefore, be 
 made to give rise to a continuous and uriintermitting 
 stream by the aid of the air-vessel, K K. 
 
 Among other hydraulic machines may be mentioned 
 Vera's pump, more, however, from its peculiar construc- 
 tion than for any real value it possesses. It consists of a 
 
 Describe the forcing-pump. 
 
THE CHAIN-PUMP. 
 
 65 
 
 . 75. 
 
 pair of pulleys, over which a rope is made to run rapidly, 
 the lower one is immersed in the wa- 
 ter to be raised. By adhesion a por- 
 tion of the water follows the rope in 
 its movements, and is discharged into 
 a receptacle placed above. 
 
 The chain-pump consists of a series 
 of flat plates held together by pieces 
 of metal, so arranged that, by turning 
 an upper wheel, the whole chain is 
 made to revolve, on one side ascending 
 and on the other descending. As the 
 flat plates pass upward .they move 
 through a trunk of suitable shape, and 
 therefore continually lift in it a column 
 of water. The chain-pump requires 
 deep water to work in, and cannot completely empty its 
 reservoir, but it has the advantage of not being liable to 
 be choked. 
 
 LECTURE XIV. 
 
 HYDRAULIC MACHINES. THEORY OF FLOTATION. Archi- 
 medes' Screw. The Syphon acts by the Pressure of 
 Air. The Descent, Ascent, and Flotation of Solids in 
 Liquids. Quantity of Water displaced by a Floating 
 Solid. Case where fluids of different densities are used. 
 Equilibrium of Floating Solids. 
 
 3f 
 
 THE screw of Archimedes is an ancient contrivance, 
 invented by the philosopher whose name it bears, for the 
 purpose of raising water in Egypt. It consists of a hol- 
 low screw-thread wound round an axis, upon which it 
 can be worked by means of a handle. The lower end of 
 this spiral tube dips in the reservoir from which the water 
 is to be raised, and by turning the handle the water con- 
 tinually ascends the spire and flows out at its upper 
 extremity. 
 
 The syphon is a tube with two branches, C E, D E, 
 
 What is Vera's pump ? Describe the chain-pump. Describe the screw 
 of Archimedes. What is a syphon ? 
 
66 THE SYPHON. 
 
 Fig. 76, of unequal length, often employed in the arts for 
 Fi 76 the purpose of raising or decanting 
 
 liquids. The method of using it is 
 first to fill it, and then placing the 
 shorter branch in the vessel, B, to 
 be decanted, the liquid ascends to 
 the bend and runs down the longer 
 branch. It is obvious that this mo- 
 tion arises from the inequality of 
 weight of the columns in the two 
 branches. The long column over- 
 balances the short one, and deter- 
 mines the flow ; but this cannot take 
 place without fresh quantities rising 
 through the short branch, impelled by the pressure of the 
 air. The syphon, therefore, is kept full by the pressure 
 of the air, and kept running by the inequality of the 
 lengths of the columns in its branches. 
 
 This inequality is not to be measured by the actual 
 lengths of the glass branches themselves, but it is to be 
 estimated by the difference of level, A, of the liquid in the 
 vessel to be decanted and the free end, D, of the Syphon. 
 That this instrument acts in consequence of the press- 
 ure of the air is shown by making a small one discharge 
 quicksilver under an air-pump receiver. Its action will 
 cease as soon as the air is removed. 
 
 By the aid of a syphon liquids of different specific 
 gravities may be drawn out of a reservoir without dis- 
 turbing one another, and those that are in the lower part 
 without first removing those above. Upon the same prin- 
 ciple water may also be conducted in pipes over elevated 
 grounds. 
 
 Of the Floating of Bodies in Liquids. 
 
 A solid substance will remain motionless in the interior 
 of a liquid mass when it is of the same specific gravity. 
 Under these circumstances the forces which tend to make 
 it sink are its own weight and the weight of the column 
 
 Why does water ascend in its short branch? Why does it run from 
 the longer ? How is the inequality of the branches measured ? How can 
 it be proved that its action depends on the pressure of the air ? What are 
 the uses of the syphon ? Under what circumstances will a solid remain 
 motionless in a liquid? 
 
OF FLOATING BODIES. 67 
 
 of water which is above it. But as its weight is the same 
 as that of an equal volume of the liquid in which it is 
 immersed, this downward tendency is counteracted and 
 precisely equilibrated by the upward pressure of the 
 surrounding liquid. Consequently the solid remains mo- 
 tionless in any position, precisely as a similar mass of the 
 liquid itself would be. 
 
 But if the density of the immersed body is greater than 
 that of an equal bulk of the liquid, then the downward 
 forces preponderate over the upward pressure, and the 
 solid descends. 
 
 If, on the other hand, the solid is lighter than an equal 
 volume of the liquid, the upward pressure of the sur- 
 rounding liquid overcomes the downward tendency, and 
 the body rises to the surface and floats. 
 
 In the act of floating, the body is divided into two 
 regions : one is immersed in the liquid and the rest is in 
 the air. The part which is immersed under the surface 
 of the liquid is such as displaces a quantity of that liquid 
 as is precisely equal in weight to the. 
 floating solid. This may be proved 
 experimentally. Fill a glass, A, with 
 water until it runs off through the spout, 
 a, then immerse in it a floating body, 
 such as a\ \vooden ball; the ball will 
 displace a quantity of water, which, if it 
 be collected in the receiver, B, and 
 weighed, will be found precisely equal to the weight of 
 the wood. 
 
 In any fluid a solid body will therefore sink to a depth 
 which is greater as its specific gravity more nearly ap- 
 proaches that of the liquid. As soon as the two are equal 
 the solid becomes wholly immersed. 
 
 In fluids of different densities any floating body sinks 
 deeper in that which has the smallest density. It will be 
 recollected that these are the principles which are in- 
 volved in the action of hydrometers. They are also 
 applied in the case of specific-gravity bulbs, which are 
 small glass bulbs, with solid handles, adjusted by the 
 
 Under what will it rise, and under what will it sink ? What portion of 
 the floating body is immersed ? How may this be proved ? How do the 
 specific gravities of the solid and the liquid on which it floats affect the 
 phenomenon ? 
 
68 
 
 THE BALL-COCK. 
 
 maker, so as to be of different densities. When a num- 
 ber of these are put into a liquid some will float and 
 some will sink ; but the one which remains suspended, 
 neither floating nor sinking, has the same specific gravity 
 as the liquid. That specific gravity is determined by the 
 mark engraved on the bulb. 
 
 When a body floats on the surface of water it tends to 
 take a position of stable equilibrium. The principles 
 brought in operation here will be more fully described 
 when we come to the study of the center of gravity of 
 bodies. For the present, it is sufficient to state that sta- 
 ble equilibrium ensues when the center of gravity of the 
 floating solid is in the same vertical line as the center of 
 gravity of the portion of fluid displaced, and as respects 
 position beneath it. These considerations are of great im- 
 portance in the art of ship -build ing, and also in the right 
 distribution of the cargo or ballast of a ship. 
 
 The principle of flotation is in- 
 geniously applied in the ball-cock, 
 an instrument for keeping cisterns 
 or boilers filled with a regulated 
 amount of water. Thus, suppose 
 that m n, Fig. 78, be the level of 
 the water in the boiler of a steam- 
 engine ; on its surface let there float 
 a body, B, attached by means of a 
 rod, F a, to a lever, a c b, which 
 works on the fulcrum c; on the 
 other side of the lever, at b, let 
 there be attached, by the rod b V, a valve, V, allowing 
 water to flow into the boiler, through the feed-pipe, V O. 
 Now, as the level of the water, m n, in the boiler lowers 
 through evaporation, the float, B, sinks with it, and de- 
 presses the end, a, of the lever ; but the end, b, rising, lifts 
 the valve, V, and allows the water to go down the feed- 
 pipe; and as the level again rises in the boiler the valve, V, 
 again shuts. Instead of a piece of wood or hollow cop- 
 per ball, a flat piece of stone, B, is commonly used ; and 
 to make it float it is counterpoised by a weight, W, on 
 the opposite arm of the lever. 
 
 How are specific-gravity bulbs used? What is the position of stable 
 equilibrium in a floating body ? Describe the construction and action of 
 the ball-cock. 
 
MOTION AND REST. 69 
 
 OF REST AND MOTION. 
 
 MECHANICS. 
 
 LECTURE XV. 
 
 MOTION AND REST. Causes of Motion. Classification of 
 Forces. Estimate of Forces. Direction and Intensity. 
 Uniform and Variable Motions. Initial and Final 
 Velocities. Direct, Rotatory, and Vibratory Motions. 
 
 ALL objects around us are necessarily in a condition 
 either of motion or of rest. We shall soon find that mat- 
 ter has not of itself a predisposition for one or other of 
 these states ; and it is the business of natural philosophy 
 to assign the particular causes which determine it to either 
 in any special instance. A very superficial investigation 
 soon puts us on our guard against deception. Things 
 roay appear in motion which are at rest, or at rest when 
 in reality they are in motion. A passenger in a railroad 
 car sees the houses and trees in rapid motion, though he 
 is well assured that this is a deception a deception like 
 that which occurs on a greater scale in the apparent rev- 
 olution of the stars from east to west every night the true 
 motion not being in them, but in the earth, which is turn- 
 ing in the opposite direction on its axis. 
 
 If deceptions thus take place as respects the state of 
 motion, the same holds good as respects the state of rest. 
 On the surface of the earth even those objects which seem 
 to us to be quite stationary are not so in reality. Natu- 
 ral objects, as mountains and the various works of man, 
 though they seem to maintain an unchangeable relation as 
 respects position with all the world for centuries together, 
 are but in a condition of RELATIVE REST. They are, of 
 
 What two states do bodies assume ? What deceptions may occur in re- 
 lation to motion and rest ? What is meant by relative and what by abso- 
 lute rest ? 
 
70 MOTION AND REST. 
 
 course, affected by the daily revolution of the earth on its 
 axis, arid accompany it in its annual movements round the 
 sun. Indeed, as respects themselves, their parts are con- 
 tinually changing position. Whatever has been affected 
 by the warmth of summer shrinks into smaller space 
 through the cold of winter. Two objects which maintain 
 their position toward each other are said -to be at rela- 
 tive rest ; but we make a wide distinction between this 
 and absolute rest. All philosophy leads us to suppose 
 that throughout the universe there is not a solitary parti- 
 cle which is in reality in the latter state. 
 
 Whenever an object, from a state of apparent rest, com- 
 mences to move, a cause for the motion may always be 
 assigned. And inasmuch as such causes are of different 
 kinds, they may be classified as primary or secondary 
 motive powers. The primary motive powers are utiiver^ 
 sal in their action. Such, for instance, as the general at- 
 tractive force of matter or GRAVITY. The secondary are 
 transient in their effects. The action of animals, of elas- 
 tic springs, of gunpowder, are examples. Of the second- 
 ary forces, some are momentary and others more perma- 
 nent, some giving rise to a blow or shock, and some to 
 effects of a continued duration. 
 
 Forces may be compared together as respects their in- 
 tensities by numbers or by lines. Thus one force may be 
 five, ten, or a hundred times the intensity of another, and 
 that relation be expressed by the appropriate figures. In 
 the same manner, by lines drawn of appropriate length, 
 we may exhibit the relation of forces ; and that not only 
 as respects their relative intensity, but also in other par- 
 ticulars. The direction of motion resulting from the appli- 
 cation of a given force may always be represented by a 
 straight line drawn from the point at which the motion 
 commences toward the point to which the moving body 
 is impelled. The point at which the force takes effect 
 upon the body is termed the point of application ; and 
 the direction of motion is the path in which the body 
 moves. To this special designations are given appropri- 
 
 Is any object in nature in a state of absolute rest ? How may motive 
 powers be classified ? What are primary motive powers ? Give examples 
 of some that are secondary. How may forces be compared together ? 
 How may forces be represented ? What is meant by the point of appli- 
 cation? 
 
DIFFERENT KINDS OF MOTION. 71 
 
 ate to the nature of the case, such as curvilinear, rectilin- 
 ear, &c. 
 
 Moving bodies pass over their paths with different de- 
 grees of speed. One may pass through ten feet in a sec- 
 ond of time, and another through a thousand in the same 
 interval. We say, therefore, that they have different ve- 
 locities. Such estimates of velocity are obviously^ ob- 
 tained by comparing the spaces passed over in a given 
 unit of time. The unit of time selected in natural phi- 
 losophy is one second. 
 
 A moving body may be in a state of either uniform or 
 variable motion. In the former case its velocity contin- 
 ually remains unchanged, and it passes over equal dis- 
 tances in equal times. In the latter its velocity under- 
 goes alterations, and the spaces over which it passes in 
 equal times are different. If the velocity is on the in- 
 crease it is spoken of as a uniformly accelerated motion. 
 If on the decrease as a uniformly retarded motion. In 
 these cases we mean by the term initial velocity the ve- 
 locity which the body had when it commenced moving, 
 as measured by the space it would then have passed over 
 in one second ; and, by the final velocity, that which it pos- 
 sessed at the moment we are considering it measured in 
 the same way. The flight of bomb-shells upward in the 
 air is an instance of retarded motion ; their descent down- 
 ward of accelerated motion. The movement of the fingers 
 of a clock is an example of uniform motion. 
 
 There are motions of different kinds : 1st, direct ; 2d, 
 rotatory ; 3d, vibratory. 
 
 1st. By direct motion we mean that in which all the 
 parts of the whole body are advancing in the same direc- 
 tion with the same velocity. 
 
 2d. By rotatory motion we imply that some parts of the 
 body are going in opposite directions to others. The 
 axis of rotation is an imaginary line, round which tho 
 parts of the body turn, it being itself at rest. 
 
 3d. By vibratory movement we mean that the body 
 which changes its place returns toward its original posi' 
 lion with a motion in the opposite direction. Thus, the 
 
 How are velocities measured ? What is the unit of time ? What \i 
 meant by uniform and what by variable motion ? What by initial and 
 final velocity? What varieties of motion are there? What is direct 
 motion ? What is rotatory motion ? What is vibratory motion ? 
 
72 COMPOUND MOTION. 
 
 particles of water which form waves alternately rise and 
 sink, and the pendulum of a clock beats backward and 
 forward. These are examples of vibratory or oscillatory 
 movement. 
 
 LECTURE XVI. 
 
 OP THE COMPOSITION AND RESOLUTION OF FORCES. 
 Compound Motion. Equilibrium. Resultant. The 
 Parallelogram of Forces. Case where there are more 
 Forces than Two. Parallel Forces. Resolution of 
 Forces. Equilibrium of three Forces. Curvilinear 
 Motions. 
 
 WHEN several forces act simultaneously on\a body, so 
 as to put it in motion, that motion is said to be com- 
 pound. 
 
 In cases of compound motion, if the component or con- 
 stituent forces all act in the same direction, the resulting 
 effect will be equal to the sum of all those forces taken 
 together. 
 
 If the constituent forces act in opposite directions, the 
 resulting effect will be equal to their difference, and 
 Fig. 79. its direction will be that of the 
 
 greater force. Thus, if to a 
 knot, a, Fig. 79, we attach sev- 
 eral weights, b c, by means,, of a 
 string passing over a pulley, e, 
 these weights will evidently tend 
 to pull the knot from a to e. But 
 sf if to the same knot we attach a 
 weight,j by a string passing over 
 the pulley g, this tends to draw- 
 it in the opposite direction. When the weights on each 
 side of the knot act conjointly, they tend to draw it oppo- 
 site ways, and it moves in the direction of the greater 
 force. 
 
 What is compound motion? When the component forces all act in the 
 same direction, what is their effect equal to? What is the result when 
 they act in opposite directions ? Under what circumstances are forces in 
 equilibrio ? 
 
PARALLELOGRAM OF FORCES. 73 
 
 If two forces of equal intensity, but in opposite direc- 
 tions, act upon a given point, that point remains motion- 
 less, and the forces are said to be in (equilibria. When 
 there are many forces acting upon a point in equilibrio, 
 the sum of all those acting on one side must be equal to 
 the sum of all the rest which act in the opposite direction. 
 
 By the resultant of forces we mean a single force which 
 would represent in intensity and direction the conjoint 
 action of those forces. 
 
 If the constituent forces neither act in the same nor in 
 opposite directions, but at an angle to each other, their 
 resultant can be found in the following manner : 
 
 Let a be the point on which Fig. so. 
 
 the forces act ; let one of them be ft 
 
 represented in intensity and di- .^ff- ^ 
 
 rection by the line a b, and the 
 other likewise in intensity and 
 direction by the line a c. Draw 
 the lines b d, c d, so as to com- 
 plete the parallelogram a b c d ; fc m 
 
 draw also the diagonal, a d. This c 
 
 diagonal will be the resultant of the two forces, and will, 
 
 therefore, represent their conjoint action in intensity and 
 
 direction. 
 
 The operation of 
 pairs of forces upon a 
 
 point is readily under- t^a, . . , 
 
 stood. Thus, 1st. On * 
 a point, a, Fig. 81, let 
 two forces, a b, a c, act. Complete the parallelogram 
 a b d c, and draw its diagonal, a d. This line will rep- 
 resent in intensity and direction the resultant force. 
 2d. On a point, a, Fig. 82, Fig. m. 
 
 let two forces again repre- 
 sented in intensity and di- 
 rection by the lines a b, a c, 
 act. Complete the paral- 
 lelogram abed, draw its diagonal, a d, which is the 
 resultant, as before. Now, on comparing Fig. 81 with 
 Fig. 82, it readily appears that the resultant of two forces 
 
 What is meant by a resultant ? Describe the parallelogram of forces. 
 Give illustrations of the case in which the forces act nearly in the same, 
 and also of that in which they act nearly in opposite directions. 
 
 D 
 
74 
 
 ANGULAR AND PARALLEL FORCES. 
 
 is greater as those forces act more nearly in the same 
 direction, and less as those forces act more nearly in 
 opposite directions. 
 
 Many popular illustrations of the parallelogram of 
 forces might be cited. The following may, however, 
 suffice. If a boat be rowed across a river when there is 
 no current, it will pass in a straight line from bank to 
 bank perpendicularly ; but this will not take place if there 
 is a current, for as the boat crosses it is drifted by the 
 stream, and makes the opposite bank at a point which is 
 lower according as the stream is more rapid. It moves 
 in a diagonal direction. 
 
 On the same principles we can determine the common 
 resultant of many forces acting on 
 a point. Two of the forces are 
 first taken and their resultant found. 
 This resultant is combined with the 
 third force, and a second resultant 
 found. This again is combined 
 with the fourth force, and so on, un- 
 til the forces are exhausted. The 
 final resultant represents the con- 
 joint action of all. 
 
 Thus, let there be three forces applied to the point , 
 represented in intensity and direction by the lines a b, 
 ac,ad, Fig. S3, respectively ; if a b and a c be combined, 
 they give as their resultant a e, and if this resultant, a e, be 
 combined with the third force, a d, it yields the resultant 
 af, which, therefore, represents the common action of all 
 three forces. 
 
 The resultant of two paral- 
 lel forces applied to a line, and 
 on the same side of it, is equal to 
 their sum and parallel to their 
 direction. Thus, the forces a 
 b, a' b' applied to the line a a', 
 give a resultant, p r, parallel 
 to their common direction and 
 equal to their sum. 
 
 a 
 
 Fig 84. 
 P 
 
 Give an illustration of the diagonal motion of a body under the influence 
 two forces. How may the resultant of more forces than two be found ? 
 hat is the resultant of parallel forces applied to a line on the same, and 
 
 of two forces 
 What 
 
RESOLUTION OF FORCES. 75 
 
 But when parallel forces are applied on opposite sides 
 of a line, the resultant is equal to their difference, and its 
 direction is parallel to theirs. In this, as also in the fore- 
 going case, the point at which the resultant acts is at a 
 distance from the points at which the two forces act, 
 inversely proportional to their intensities. In the fore- 
 going case this point falls between the directions of the 
 two forces, and in the latter on the outside of the direction 
 of the greater force. 
 
 The parallelogram of forces not Pig- 85. 
 
 only serves to effect the composi- 
 tion of several forces, but also the 
 resolution of any given force ; that 
 is to assign several forces which in 
 their intensities and directions shall 
 be equivalent to it. Thus, let a J] 
 Fig. 85, be the given force; by 
 making it the diagonal of a paral- 
 lelogram it may be resolved into its components, a d, a e ; 
 in the same manner, a e t may be resolved into its compo- 
 nents, a c, a b. Thus, therefore, the original force is 
 resolved into three components, a b, a c, a d. 
 
 Upon similar principles it may be readily proved that 
 two forces acting at any angle upon a point can never 
 maintain that point in equilibrio but three forces may ; 
 and in this instance, they will be represented in intensity 
 and direction by the three sides of a triangle, perpendic- 
 ular to their respective directions. 
 
 If two forces act upon a point in the direction of and in 
 magnitude proportional to the sides of a parallelogram, 
 that point will be kept in equilibrio by a third force op- 
 posed to them in the direction of the diagonal and pro- 
 portional to it. On the table, a d, place a circular piece of 
 paper, on which there is drawn any triangle, a b c, c coin- 
 ciding with the center of the table; and let us suppose 
 that the sides of this triangle are, as shown in the figure, 
 in the proportion to one another, as 2 3 4 ; draw upon the 
 paper, c e, parallel to a b, and prolong a c to d. Take three 
 strings, making a knot at the point c, and by means of the 
 
 What is meant by the resolution of forces ? How does the parallelogram 
 of forces serve for this purpose ? Can two forces acting at an angle upon 
 a point keep it in equilibrio? Can three? In this case what must be 
 their relation ? 
 
76 
 
 COMPOSITION OF FORCES. 
 
 Fig. 86. 
 
 movable pullies, 1 1 1, stretch the 
 strings over the lines c b, c d, c 
 e ; at the end of c d suspend a 
 weight of four pounds, at the 
 end of c e one of three pounds, 
 and at the end of c b one of two 
 pounds. The knot will remain 
 in equilibrio, proving, there- 
 fore, the proposition. 
 
 In the composition of forces ' 
 power must always be lost. 
 Thus, in this experiment we 
 see that a weight of three 
 pounds and one of two pounds 
 equipoise a weight of four pounds only. 
 
 If of two forces acting upon a point one is momentary 
 and the other constant, the point may move in a curve. 
 Thus, if in Fig. 87, a shot be projected obliquely up- 
 * 87 - ward from a gun, it is under the ac- 
 
 tion of two forces the momentary 
 force of the explosion of the gun- 
 powder and the constant effect of 
 the attraction of the earth. It- 
 describes, therefore, a curvilinear 
 path, a b c, the direction of which 
 continually declines toward the di- 
 rection of the constant force. 
 It is only when a force acts in a direction perpendicu- 
 lar to a body that its full effect is obtained. This is easi- 
 ly proved by resolving an oblique force into two others, 
 one of which is perpendicular and the other parallel to 
 the side of the body acted upon. This latter force is, of 
 course, lost. 
 
 Why in the composition of forces is power always lost ? What is the 
 result of the action of a momentary and a constant force upon a point? 
 In what direction must a force act to obtain its full effect ? 
 
INERTIA. 77 
 
 LECTURE XVII. 
 
 INERTIA. Inertia a Properly of Matter. Indifference to 
 Motion and Rest. Moving Masses are Motive Powers. 
 Determination of the Quantity of Motion. Momen- 
 tum. Action and Reaction. Newton's Laws of Mo- 
 tion. Bohnenbcrger's Machine. 
 
 ALL bodies have a tendency to maintain their present 
 condition, whether it be of motion or rest. It is only by 
 the exertion of force that that condition can be changed. 
 A mass of any kind, when at rest, resists the application 
 of force to put it in motion, and when in motion resists 
 any attempt to bring it to rest. This property is termed 
 INERTIA. It is illustrated by many familiar instances : 
 thus, loaded carriages require the exertion of far more 
 force to put them in motion than is subsequently required 
 to keep them going, and a train of railroad cars will run 
 for a great distance after the locomotive is detached. 
 
 Universal experience shows that inanimate bodies have 
 no power to produce spontaneous changes in their con- 
 dition. They are wholly inactive. Even when in motion 
 they exhibit no tendency whatever to alter their state. 
 Thus, the earth rotates on its axis at the same rate which 
 it did thousands of years ago, and the planetary bodies 
 pursue their orbits with an unchangeable velocity. A 
 moving mass can neither increase nor diminish its rate of 
 speed, for if it could do the former it must necessarily 
 have the power spontaneously to put itself in motion if it 
 were in a condition of rest. Nor can such a mass, if in 
 motion, change the direction of its movement any more 
 than it can change its velocity. Such a change of direc- 
 tion would imply the operation of some innate force, which 
 of itself could have put the mass in movement. When- 
 ever, therefore, we discover in a moving body changes in 
 direction or changes in velocity, we at once impute them 
 
 What is meant by the term inertia ? Give an illustration of inertia. 
 What illustration have we that when bodies are in motion they do not 
 spontaneously tend to come to rest? Can a moving mass increase or di- 
 minish its rate of speed ? Can it change its direction of itself? 
 
78 MOMENTUM. 
 
 to the agency of acting forces, and not to any innate power 
 of the moving body itself. 
 
 Fig. 88. If an ivory ball, a, Fig. 88, 
 
 be laid upon a sheet of paper, 
 
 b c, on the table, and the paper 
 
 c suddenly pulled away, the ball 
 
 does not accompany the movement but remains in the 
 same place on the table. 
 
 A person jumping from a carriage in rapid motion falls 
 down, because his body, still participating in the motion 
 of the carriage, follows its direction after his feet have 
 struck the earth. 
 
 By the MASS of a body we mean the quantity of mat- 
 ter contained in it that is, the sum of all its particles. 
 The mass of a body depends on its volume and density. 
 
 In consequence of their inertia, masses in motion are 
 
 themselves motive powers. Such a mass impinging on a 
 
 Fig. 89. second tends to set it in motion. 
 
 _ Thus, if a ball a, Fig. 89, moving 
 
 W i W toward c, impinge upon a second 
 
 ball, b, of equal weight, the two 
 
 will move together toward c, with a velocity one half of 
 that which a originally had. In this case, therefore, a has 
 acted as a motive force upon Z, and it is obvious that the 
 intensity of this action must depend on the magnitude 
 and velocity of a, increasing as they increase and dimin- 
 ishing as they diminish. The ball a is said, therefore, to 
 have a certain momentum or moment, which depends part- 
 ly upon its mass and partly upon its velocity; and the mo- 
 ments of any two bodies may be compared by multiplying 
 together the mass and velocity of each. Thus, if a body, 
 A, has twice the mass of another, B, and moves with the 
 same velocity, the momentum of A will be twice that of 
 B ; but if A, having twice the mass of B, has only half 
 its velocity the moments of the two will be equal. 
 
 It is upon this principle that heavy masses moving very 
 slowly exert a great force, and that bodies comparatively 
 light, moving with great speed, produce striking effects. 
 The battering-rams of the ancients, which were heavy 
 masses moving slowly, did riot produce more powerful 
 
 Give. an experimental illustration of inertia. How is it that moving 
 bodies are themselves motive powers ? How is the quantity of motion or 
 momentum of a body ascertained ? 
 
ACTION AND REACTION. 
 
 79 
 
 effects than cannon-shot, which, though comparatively 
 light, move with prodigious speed. 
 
 From the foregoing considerations, it therefore appears 
 that the amount of motion depends neither upon the mass 
 alone nor the velocity alone. A certain mass, A, moving 
 with a given velocity, has a certain momentum or quanti- 
 ty of motion. If to A a second equal mass, B, with a sim- 
 ilar velocity be added, the two conjointly will, of course, 
 possess double the momentum of the first the mass has 
 doubled, though the speed is the same, and therefore the 
 quantity of motion has doubled. Again, if a certain mass, 
 A, moves with a given speed, and a second one, B, moves 
 with a double speed, it is obvious that this last will have 
 twice the quantity of motion of the former. Here the 
 masses are the same, but the velocities are different. The 
 quantity of motion or momentum which a body possesses 
 is, therefore, obtained by multiplying together the num- 
 bers which express its mass and its velocity. 
 
 Action and reaction are always equal to each other. 
 The resistance which a given body exhibits is equal to 
 the effect of any force operating upon it. This equality 
 of action and reaction may be shown by an apparatus 
 represented in Fig. 90, in which Fi s- 90 - 
 
 two balls of clay or putty, a b, 
 are suspended by strings so as to 
 move over a graduated arc. If 
 one of the balls be allowed to fall 
 upon the other, through a given 
 number of degrees, it will com- 
 municate to it a pait of its mo- 
 tion, and the following facts may 
 be observed : 1st. The bodies, af- 
 ter collision, move on together, and therefore have the same 
 velocity. 2d. The quantity of motion remains unchang- 
 ed, the one having gained as much as the other has lost, 
 so that if the two are equal they will have half the veloc- 
 ity after impact that the moving one had when alone. 
 3d. If equal, and moving in opposite directions with equal 
 velocities, they will destroy each other's motions and come 
 
 Does the mass or the velocity, taken alone, measure the amount of mo- 
 tion T What is the relation between action and reaction ? What is the 
 apparatus represented in Fig. 90 intended to illustrate ? Mention some 01 
 
 the results. 
 
80 NEWTON'S LAWS. 
 
 to rest. 4th. If unequal, and moving in opposite direc- 
 tions, they will come to rest when their velocities are in- 
 versely as their masses. 
 
 The following three propositions are called "Newton's 
 laws of motion." They contain the results depending on 
 inertia : 
 
 I. Every body must persevere in its state of rest or of 
 uniform motion in a straight line, unless it be compelled 
 to change that state by forces impressed upon it. 
 
 II. Every change of motion must be proportional to 
 the impressed force, and must be in the direction of that 
 straight line in which the force is impressed. 
 
 III. Action must always be equal, and contrary to re- 
 action, or the action of two bodies upon each other must 
 be equal and directed to contrary sides. 
 
 As an example of the operation of inertia, and illustra- 
 ting the invariability of position of the axLs of the earth 
 during its revolution, I here describe 
 Bohnenberger's machine. It consists 
 of three movable rings, A A A, Fig. 
 91, placed at right angles to each other, 
 AJj {^jjfl Jf and in the smallest ring there is a heavy 
 metal ball, B, supported on an axis, 
 which also bears a little roller, c. A 
 thread being wound round this roller 
 and any particular position being given 
 to the axis, by quickly pulling the 
 thread the ball may be set in rapid ro- 
 tation. It is now immaterial in what position the instru- 
 ment is placed, its axis continually maintains the same di- 
 rection, and the ring which supports it will resist a con- 
 siderable pressure tending to displace it. 
 
 What are Newton's three laws of motion? Describe Bohnenberger's 
 machine. What does it illustrate ? 
 
GRAVITATION. 81 
 
 LECTURE XVIII. 
 
 GRAVITATION. Preliminary Ideas of Motions of Attrac- 
 tion. The Earth and Falling Bodies. Laics of At- 
 traction, as respects Mass and Distance. Nature of 
 Weight. Absolute and Specific Weight. The Plumb- 
 Line. Convergence of suck Lines toward the Earth's 
 Center. Action of Mountain Masses. 
 
 ALL material substances exert upon each other an at- 
 tractive force. To this the designation of GRAVITY or 
 GRAVITATION has been given. It was the great discovery 
 of Sir I. Newton that the same force which produces the 
 descent of a stone to the ground holds together the plan- 
 ets and other celestial bodies. 
 
 To obtain a preliminary idea of the nature and opera- 
 tion of this force, let us suppose that two balls of equal 
 weight be placed in presence of each other, and under 
 such circumstances that no extraneous agency supervenes 
 to interfere with their mutual action. Under these cir- 
 cumstances, all the phenomena of nature prove that the 
 two balls will commence moving toward each other with- 
 equal speed, their velocity continually increasing until 
 they come in contact. Inasmuch, therefore, as their 
 masses are equal and their velocities equal, the quantities 
 of motion they respectively possess will also be equal, as 
 is proved in Lecture XVII. 
 
 Again, let there be two other balls situated as before, 
 but let one of them, B, be twice as large Fig. 92. 
 
 as A. Motion will again ensue by reason 
 of their mutual attraction, and they will ^^ 
 approach each other with a velocity con- 
 tinually increasing. In this instance, 
 however, their speed will not be equal, the larger body, 
 B, having a correspondingly less velocity than the smaller 
 one, A. If, as we have supposed, it is twice as large, its 
 
 What is meant by gravity ? Give an explanation of the phenomena of 
 the attraction of two equal balls. Give a similar explanation in the case 
 where the balls are unequal. 
 
82 LAWS OF GRAVITATION. 
 
 velocity will be only one half. But in this, as in the 
 former case, the quantity of motion that each possesses 
 is the same, for that depends on velocity and mass con- 
 jointly. 
 
 Further, if of the two bodies one becomes infinitely 
 great as respects the other, then it is obvious that the lit- 
 tle one alone will appear to move. This condition is what 
 actually obtains in the case of our earth and bodies sub- 
 jected to its influence. A mass of any kind, the support 
 of which is suddenly removed, falls at once to the ground, 
 and though in reality the earth moves to meet it just as 
 much as it moves to meet the earth, the difference in 
 these masses is so immeasurably great that the earth's 
 motion is imperceptible and may be wholly neglected. 
 
 The force by which bodies are thus solicited to move 
 to the earth is called terrestrial gravity or gravitation. 
 
 The force of gravity depends on two different condi- 
 tions : 1st, the mass; 2d, the distance. 
 
 1st. The intensity of the force of gravity is directly as 
 the mass. That is to say, that, for example, in the case 
 of the earth, if its mass were twice as large its force of 
 attraction would be twice as great ; or if it were only half 
 as large its attraction would be only half as much as it is. 
 
 2d. In common with all other central forces, gravity 
 diminishes as the distance increases. The law which de- 
 termines this is expressed as follows: " The force of 
 gravity is inversely as the square of the distance ;" that 
 is to say, if a body be placed two, three, four, five times 
 its original distance from another, the force attracting 
 it will continually diminish, and in those different instances 
 will successively be four, nine, sixteen, twenty-five times 
 less than at first. 
 
 When a body, instead of being allowed to fall freely to 
 the earth, is supported, its tendency to descend is not anni- 
 hilated, but it exerts upon the supporting surface a degree 
 of pressure. This pressure we speak of as WEIGHT. And 
 inasmuch as the attractive force upon a body depends on 
 its mass, it is obvious that, if the mass is doubled, the 
 weight is doubled ; if the mass is tripled, the weight is 
 
 What is the relation in this respect between falling bodies and the earth ? 
 On what two conditions does the intensity of gravity depend ? What is 
 the law for the mass? What is the law for the distance? What is 
 
ABSOLUTE AND SPECIFIC WEIGHT. 83 
 
 tripled. Or, in other words, the weight of bodies is al- 
 ways proportional to their mass. 
 
 The absolute weight of a given body at the same place 
 on the earth's surface is always the same ; for the mass, 
 and, therefore, the attractive force of the earth never 
 changes. If by any means the attractive influence of the 
 earth could be doubled, the weight of every object would 
 change, and be doubled correspondingly. 
 
 The absolute weight of bodies is determined by bal- 
 ances, springs, steelyards, and other such contrivances, as 
 will be explained in their proper place. Different units 
 of weight are adopted in different countries, and for dif- 
 ferent purposes, as the grain, ounce, pound, gramme, &c. 
 
 In bodies of the same nature the absolute weight is pro- 
 portional to the volume. Thus a mass of iron which is 
 twice the volume of another mass will also have twice its 
 weight. 
 
 But when we examine dissimilar bodies the result is 
 very different. A globe of water compared with one of 
 copper, or lead, or wood of the same size will have a very 
 different weight. The lead will weigh more than the 
 water, and the wood less. 
 
 This fact we have already pointed out by the term 
 "specific gravity," or specific weight of bodies. And, 
 inasmuch as it is obviously a relative thing or a matter of 
 comparison, it is necessary to select some substance which 
 shall serve to compare other bodies with : for solids and 
 liquids water is taken as the unit or standard of compari- 
 son. And we say that iron is about seven, lead eleven, 
 quicksilver thirteen times as heavy as it ; or that they 
 have specific gravities expressed by those numbers. The 
 unit of comparison for gaseous and vaporous bodies is 
 atmospheric air. 
 
 When an unsupported body is allowed to fall its path 
 is in a vertical line. If a body be suspended by a thread 
 the thread represents the path in which that body would 
 have moved. It occupies a vertical direction, or is per- 
 pendicular to the position which would be occupied by 
 
 Is it constant for the same body ? How is absolute weight determined ? 
 What units are employed ? What connection is there between weight 
 and volume in bodies of the same kind ? What is meant by specific grav- 
 ity ? What substance is the unit for solids and liquids ? What is the 
 unit for gases and vapors ? 
 
84 THE PLUMB-LINE. 
 
 a surface of stagnant water. Such a thread is termed a 
 plumb-line. It is of constant use in the arts to determine 
 horizontal and vertical lines. 
 
 Fig. 93. If in two positions, A B, Fig. 93, on 
 
 the earth's surface plumb-lines were sus- 
 pended, it would be found that, though 
 they are perpendicular as respects that 
 surface, they are not parallel to one an- 
 other, but incline, at a small angle, A C 
 B, to each other. If their distance be one 
 mile this convergence would amount to 
 one minute; and if it be sixty miles the 
 convergence would be one degree. Now, 
 as the plumb-line indicates the path of a falling body, it 
 is easily understood that on different parts of the earth's 
 surface the paths of falling bodies have the inclinations 
 just described. A little consideration shows that the de- 
 scent of such bodies is in a line directed to the center, C, 
 of the earth. 
 
 That center we may therefore regard as the active 
 point, or seat of the whole earth's attractive influence. 
 
 When examinations with plumb-lines are made in the 
 neighborhood of mountain masses those masses exert a 
 disturbing agency on the plummet, drawing the line 
 from its true vertical position. But this is nothing more 
 than what ought to take place on the theory of universal 
 gravitation ; for that theory asserting that all masses ex- 
 ert an attractive influence, the results here pointed out 
 must necessarily ensue, and the lateral action of the moun- 
 tains correspondingly draw the plummet aside. 
 
 What is a plumb-line ? At considerable distances from one another are 
 plumb-lines parallel? What conclusion is drawn from this fact ? What 
 is the effect of mountain masses ? 
 
OF FALLING BODIES. 85 
 
 LECTURE XIX. 
 
 THE DESCENT OF FALLING BODIES. Accelerated Motion. 
 Different bodies fall with equal velocities. Laws of 
 Descent as respects Velocities, Spaces, Times. Prin- 
 ciple of Atticood's Machine. It verifies the Laws of 
 Descent Resistance of the Atmosphere. 
 
 OBSERVATION proves that the force with which a falling 
 body descends depends upon the distance through which 
 it has passed. A given weight falling through a space of 
 an inch or two may give rise to insignificant results ; but 
 if it has passed through many yards those results become 
 correspondingly greater. 
 
 Gravity being a force continually in operation, a falling 
 body must be under its influence during the whole period 
 of its descent. The soliciting action does not take effect 
 at the first moment of motion and then cease, but it con- 
 tinues all the time, exerting as it were a cumulative effect. 
 The falling body may be regarded as incessantly receiv- 
 ing a rapidly recurring series of impulses, all tending to 
 drive it in the same direction. The effect of each one is, 
 therefore, added to those of all its predecessors, and a uni- 
 formly accelerated motion is the result. 
 
 Falling bodies are, therefore, said to descend with a uni- 
 formly accelerated motion. 
 
 As the attraction of the earth operates with equal in- 
 tensity on all bodies, all bodies must fall with equal ve- 
 locities. A superficial consideration might lead to the 
 erroneous conclusion that a heavy body ought to descend 
 more quickly than a lighter. But if we have two equal 
 masses, apart from each other, falling freely to the ground, 
 they will evidently make their descent in equal times or 
 with the same velocity. Nor will it alter the case at all 
 if we imagine them to be connected with each other by 
 an inflexible line. That line can in no manner increase 
 or diminish their time of descent. 
 
 What is the difference of effect when bodies have fallen through differ- 
 ent spaces ? Why does gravity produce an accelerated motion '? "Do all 
 bodies fall to the earth with the same or different velocities ? 
 
86 LAWS OF FALLING BODIES. 
 
 The space through which a body falls in one second of 
 time varies to a small extent in different latitudes. It is, 
 however, usually estimated at sixteen feet and one tenth. 
 
 As the effect of gravity is to produce a uniformly 
 accelerated motion, the final velocities of a descending body 
 will increase as the times increase ; thus, at the end of two 
 seconds, that velocity is twice as great as at one ; at the 
 end of three seconds, three times as great ; at the end of 
 four, four times, and so on. Therefore the final velocity 
 at the end 
 
 Of the first second is ... 32| feet. 
 
 " second " ... 64| " 
 
 " third " ... 96| " 
 
 &c., &c. 
 
 The spaces through which the body descends in equal 
 successive portions of time increase as the numbers 1.3.5.7, 
 &c. ; that is to say, as the body descends through sixteen 
 feet and one tenth in the first second, the subsequent 
 spaces will be 
 
 For the first second 
 
 " second " ... 
 
 " third " ... 
 
 &c., 
 
 and these numbers are evidently as 1.3.5, &c. 
 
 The entire space through which a body falls increases as 
 the squares of the times. Thus, the entire space is, 
 
 For the first second . . . IGy^feet. 
 " second " 64 f " 
 
 " third " ... 144 T ^- " 
 &c., &c. 
 
 and these numbers are evidently as 1.4.9, &c., which are 
 themselves the squares of the numbers 1.2.3, &c. 
 
 If a body continued falling with the final velocity it had 
 acquired, after falling a given time, and the operation of 
 gravity were then suspended, it would descend in the same, 
 length of time through twice the space it fell through before 
 relieved from the action of gravity . 
 
 Is the space through which a body descends every where the same ? 
 What is the relation between final velocities and times ? What relation 
 is there between the spaces and times ? What between the entire spaces 
 and times? Suppose a body continues to fall, gravity being suspended, 
 what is the relation of the space through which it will move with that it 
 has already fallen through, the times being equal? 
 
ATWOOD'S MACHINE. 87 
 
 The following table imbodiee the results of the three 
 first laws. 
 
 Times 1.2.3.4.5.6.7, &c. 
 
 Final velocities 2.4.6.8.10.12.14, &c 
 
 Space for each time .... 1.3.5.7.9.11.13, &c. 
 
 Whole spaces 1.4.9.16.25.3G.49, &c. 
 
 It would not be easy to confirm these results by ex- 
 periments directly made on falling bodies, the space 
 described in the first second being so great (more than 
 sixteen feet), and the spaces increasing as the squares of 
 the times. There is an instrument, however, known as 
 Attwood's machine, in which the force of gravity being 
 moderated without any change in its essential characters, 
 we are enabled to verify the foregoing laws. 
 
 The principle of Attwood's machine is this. Over a 
 pulley, A, Fig. 94, let there pass a fine silk Fig. 94. 
 line which suspends at its extremities equal 
 weights, b c. These weights, being equally 
 acted upon by gravity, will, of course, have 
 no disposition to move ; but now to one of the 
 weights, c, let there be added another much 
 smaller weight, d, these conjointly prepon- 
 derating over b, will descend, b at the same 
 time rising. It might be supposed that the 
 small additional weight, d, under these cir- 
 cumstances, would fall as fast as if it were 
 unsupported in the air ; but we must not forget that it has 
 simultaneously to bring down with it the weight to which 
 it is attached, and also to lift the opposite one. By its 
 gravity, therefore, it does descend, but with a velocity 
 which is less in proportion as the difference between the 
 two weights to which it it affixed is less than their sum. 
 It gives us a force precisely like gravity indeed it is 
 gravity itself operating under such conditions as to allow 
 a moderate velocity. 
 
 To avoid friction of the axle of the pulley, each of its 
 ends rests upon two friction-wheels, as is shown at Q, 
 Fig. 95 ; P is the pillar which supports the pulley. Oue 
 of the weights is seen at &, the other moves in front of 
 the divided scale c d. This last weight is made to pre- 
 
 What is the principle of Attwood's machine ? Why does not the addi- 
 tional weight fall as fast as if it fell freely ? Describe the construction of 
 the machine. 
 
88 
 
 ATTWOOD S MACHINE. 
 
 Fig. 95. 
 
 ponderate by means of a rod. There is a shelf which 
 can be screwed opposite any of the di- 
 visions of the scale, and the arrival of 
 the descending weight at that point is 
 indicated by the sound arising from 
 its striking. A clock, R, indicates 
 the time which has elapsed. To en- 
 able us to fulfill the condition of sus- 
 pending the action of gravity at any 
 moment, a shelf, in the form of a ring, 
 is screwed upon the scale at the point 
 required. Through this the descend- 
 ing weight can freely pass, but the 
 rod which caused the preponderance 
 is intercepted. The equality of the 
 two weights is, therefore, reassumed, 
 and the action of gravity virtually sus- 
 pended. 
 
 By this machine it may be shown 
 that, in order that the descending 
 weight shall strike the ring at inter- 
 vals of 1, 2, 3, 4, &c., seconds, count- 
 ing from the time at which its fall 
 commences, the ring must be placed 
 at distances from the zero of the scale, 
 which are as the numbers 1, 4, 9, 16, 
 
 &c. ; and t ese are the squares of the times. And in the 
 same manner may the other laws of the falling of bodies 
 be proved. 
 
 When a body is thrown vertically upward it rises with 
 an equably retarded motion, losing 32} feet of its original 
 velocity every second. If in vacuo, it would occupy as 
 much time in rising as in falling to acquire its original 
 velocity, and the times expended in the ascent and descent 
 would be the same. 
 
 Forces which, like gravity, in this instance, produce a 
 retardation of motion are nevertheless designated as ac- 
 celerating forces. Their action is such that, if it were 
 brought to bear on a body at rest, it would give rise to an 
 accelerated motion. 
 
 Give an illustration of its use. What is the effect when a body is thrown 
 vertically upward ? Under what signification is the term " accelerating 
 forces" sometimes used ? 
 
RESISTANCE OF THE AIR. 
 
 89 
 
 In rapid movements taking place in the atmosphere, a 
 disturbing agency arises in the resistance of Fig. 96. 
 the air a disturbance which becomes the 
 more striking as the descending body is 
 lighter, or exposes more surface. If a piece 
 of gold and a feather are suffered to drop 
 from a certain height, the gold reaches the 
 ground much sooner than the feather. Thus,, 
 if in a tall air-pump receiver we allow, by 
 turning the button, a, Fig. 96, a gold coin and 
 a feather to drop, the feather occupies much 
 longer than the coin in effecting its descent ; 
 and that this is due to the resistance of the 
 air is proved by withdrawing the air from 
 the receiver, and, when a good vacuum is 
 obtained, making the coin and the feather 
 fall again. It will now be found that they 
 descend in the same time precisely. 
 ,, Nor is it alone light bodies which are subject to this 
 disturbance : it is common to all. Thus it was found that 
 a ball of lead dropped from the dome of St. Paul's Cathe- 
 dral, in London, occupied 4 seconds in reaching the 
 pavement, the distance being 272 feet. But in that time 
 it should have fallen 324 feet, the retardation being due 
 to the resistance of the air. 
 
 It has been observed that the force of gravity is not 
 the same on all parts of the earth. 
 The distance fallen through in 
 one second at the pole is 16'12 
 feet ; but at the equator it is 
 16*01 feet. This arises from the 
 circumstance, that the earth is 
 not a perfect sphere, its polar 
 diameter being shorter than its 
 equatorial and, therefore, bodies 
 at the poles are nearer to its 
 center than they are at the equator. ThusV in Fig. 97, 
 let N S represent the globe of the earth, N and S being 
 
 What cause interferes with these results ? How can it be proved that 
 these effects are due to the resistance of the air ? Is this disturbance lim- 
 ited to light bodies '! What is the distance through which a falling body 
 descends at the equator and at the poles ? What is the reason of this 
 difference? 
 
90 MOTION ON PLANES. 
 
 the north and south poles, respectively. Owing to its 
 polar being shorter than its equatorial diameter, bodies 
 situated at different points on the surface may be at very 
 different distances from the center, and the force of grav- 
 ity exerted upon them may be correspondingly very dif- 
 ferent. 
 
 LECTURE XX. 
 
 MOTION ON INCLINED PLANES. Case of a Horizontal, a 
 Vertical, and an Inclined Plane. Wright expended 
 partly in producing pressure and partly motion. Laws 
 of Descent down Inclined Planes. Systems of Planes. 
 Ascent up Planes. 
 
 PROJECTILES. Parabolic theory of Projectiles. Disturb- 
 ing agency of the Atmosphere. Resistance to Cannon- 
 shot. Ricochet. Ballistic Pendulum. 
 
 WHEN a spherical body is placed on a plane set hori- 
 zontally, its whole gravitation is expended in producing a 
 pressure on that plane. If the plane is set in a vertical 
 position the body no longer presses upon it, but descends 
 vertically and unresisted. At all intermediate positions 
 which may be given to the plane the absolute attraction 
 will be partly expended in producing a pressure upon 
 that plane, and partly in producing an accelerated de- 
 scent. The quantities of force thus relatively expended 
 in producing the pressure and the motion will vary with 
 the inclination of the plane : that portion producing press- 
 ure increasing as the plane becomes more horizontal, and 
 that producing motion increasing as the plane becomes 
 more vertical. 
 
 Let there be a ball descending on the surface of an in- 
 clined plane, A B, Fig. 98, and let the line d e represent 
 its weight or absolute gravity. By the parallelogram of 
 forces we may decompose this into two other forces, df 
 
 What are the phenomena exhibited by a spherical body placed on planes 
 of different inclinations? Into what forces may the absolute gravity of 
 the body be resolved ? 
 
MOTION DOWN INCLINED PLANES. 91 
 
 and d g, one of which is 
 perpendicular to the plane 
 and the other parallel to 
 it. The first, therefore, is 
 expended in producing 
 pressure upon the plane, 
 and the second in pro- 
 ducing motion down it. 
 
 The following are the laws of the descent of bodies 
 down inclined planes. 
 
 The pressure on the inclined plane is to the weight of 
 the body as the base, B C, of the inclined plane is to its 
 length, A B. 
 
 The accelerated motion of a descending body is to that 
 which it would have had if it fell freely as the height, A 
 
 C, of the plane is to its length, A B. 
 
 The final velocity which the descending body acquires 
 is equal to that which it would have had if it had fallen 
 freely through a distance equal to the height of the plane ; 
 and, therefore, the velocities acquired on planes of equal 
 height, but unequal inclinations, are equal. 
 
 The space passed through by a body falling freely is to 
 that gone over an inclined plane, in equal times, as the 
 length of the plane is to its height. 
 
 If a series of inclined planes be represented, in position 
 and length, by the chords of a circle termi- Fig. 99 
 rating at the extremity of the vertical diame- A 
 ter, the times of descent down each will be 
 equal, and also equal to the time of descent 
 through that vertical diameter. Thus, let A 
 
 D, A G, D B, G B be chords of a circle ter- 
 minating at the extremities, A B, of the ver- 
 tical diameter; and, regarding these as inclin- 
 ed planes, a body will descend from A to D, 
 or A to G, or D to B, or G to B in the same 
 time that it would fall from A to B. 
 
 If a body descend down a system of several planes, A 
 
 What effects do those forces respectively produce ? What relation is 
 there between the pressure on the inclined plane and the weight of the 
 body ? What is the relation between the velocities in descent down a 
 plane and free falling ? What is the final velocity equal to ? What is the 
 relation of the space passed through ? What is Fig. 99 intended, to illus- 
 trate ? 
 
92 PROJECTILES. 
 
 C, Fig. 100, with different inclinations, it will acquire 
 Fig. 100. the same velocity as it would have 
 
 had in descending through the same 
 vertical height, A B, though the 
 times of descent are unequal. 
 
 If a body which has descended 
 an inclined plane meets at the foot 
 of it a second plane of equal alti- 
 tude, it will ascend this plane with 
 the velocity acquired in coming 
 C " down the first, until it has reached 
 the same altitude from which it descended. Its velocity 
 being now expended, it will re-descend, and ascend the first 
 plane as before, oscillating down one plane, up the other, 
 and then back again. The same thing will take place 
 if, instead of being over an inclined 
 plane, the motion be made over a 
 curve, as in Fig. 101. In practice, 
 however, the resistance of the air 
 and friction soon bring these motions to an end. 
 
 In the motions of projectiles two forces are involved 
 the continuous action of gravity, and the momentary force 
 which gave rise to the impulse such as muscular ex- 
 ertion, the explosion of gunpowder, the action of a 
 spring, &c. 
 
 The resulting effects of the combination of these forces 
 will differ with the circumstances under which they act. 
 If a body be projected downward, in a vertical line, it fol- 
 lows its ordinary course of descent, its accelerated motion 
 arising from gravity being conjoined to the original pro- 
 jectile force. But if it be thrown vertically upward, the 
 action of gravity is to produce a uniform retardation. 
 Its velocity becomes less and less, until finally it wholly 
 ceases. The body then descends by the action of the 
 earth, the time of its descent being equal to that of its as- 
 cent, its final velocity being equal to its initial velocity. 
 
 But if the projectile force forms any angle with the 
 direction of gravity, the path of the body is in a para- 
 bolic curve, as seen in Fig. 102. If the direction of 
 
 Describe the phenomena of motion on curves. What forces are involv- 
 ed in the motion of a projectile ? What are the effects in vertical projec- 
 tion upward and downward? What is the theoretical path in angular 
 projection ? 
 
PARABOLIC THEORY. 93 
 
 the projection be horizontal, the 
 path described will be half a para- 
 bola. 
 
 This, which passes under the title 
 of the parabolic theory of projec- 
 tiles, is found to be entirely de- 
 parted from in practice. The curve 
 described by shot thrown from guns 
 is not a parabola, but another curve, 
 the Ballistic. In vertical projections, instead of the times 
 of ascent and descent being equal, the former is less. The 
 final velocity is not the same as the initial, but less. Nor 
 is the descending motion uniformly accelerated ; but, after 
 a certain point, it is constant. Analogous differences are 
 discovered in angular projections. 
 
 The distance through which a projectile could go upon 
 the parabolic theory, with an initial velocity of 2000 feet 
 per second, is about 24 miles : whereas no projectile has 
 even been thrown farther than five miles. 
 
 In reality, the parabolic theory of projectiles holds only 
 for a vacuum. And the atmospheric air, exerting its 
 resisting agency, totally changes all the phenomena not 
 only changing the path, but whatever may have been the 
 initial velocity, bringing it speedily down below 1280 feet 
 per second. 
 
 The cause of this phenomenon Fi s- 103> 
 
 may be understood from Fig. 
 
 103. Let B be a cannon-ball, 5^ft 
 
 moving from A to C with a ve- A- B^g C 
 
 locity more than 2000 feet per 
 second. In its flight it removes a 
 
 column of air between A and B, and as the air flows into 
 a vacuum only at the rate of 1280 feet per second, the 
 ball leaves a vacuum behind it. In the same manner it 
 powerfully compresses the air in front. This, therefore, 
 steadily presses it into the vacuum behind, or, in other 
 words, retards it, and soon brings its velocity down to 
 such a point that the ball moves no faster than the air 
 moves that is, 1280 feet per second. 
 
 Is this the path in reality ? Mention some of the discrepancies between 
 the theoretical and actual movements of projectiles. What are these dis- 
 crepancies due to? Describe the nature of the resistance exerted on a 
 cannon-shot in its passage through the air. 
 
94 
 
 MOTION ROUND A CENTER. 
 
 Fig. 104. 
 
 A shot thrown with a high initial velocity not only de- 
 viates from the parabolic path, but also to the right and 
 left of it, perhaps several times. A ball striking on the 
 earth or water at a small angle, bounds forward *or rico- 
 chets, doing this again and again until its motion ceases. 
 
 The initial velocity given 
 by gunpowder to a ball, and, 
 therefore, the explosive force 
 of that material may be de- 
 termined by the Ballistic pen- 
 dulum. This consists of a 
 heavy mass, A, Fig. 104, sus- 
 pended as a pendulum, so as 
 to move over a graduated arc. 
 Into this, at the center of per- 
 cussion, the ball is fired. The 
 pendulum moves to a corresponding extent over the grad- 
 uated arc, with a velocity which is less according as the 
 weight of the ball and pendulum is greater than the 
 weight of the ball alone. 
 
 The explosive force of gunpowder is equal to 2000 at- 
 mospheres. It expands with a velocity of 5000 feet per 
 second, and can communicate to a ball a velocity of 2000 
 feet per second. The velocity is greater with long than 
 short guns, because the influence of the powder on the 
 ball is longer continued. 
 
 LECTURE XXI. 
 
 OF MOTION ROUND A CENTER. Peculiarity of Motion on 
 a Curve. Centrifugal Force. Conditions of Free Cur- 
 vilinear Motion. Motion of the Planets. Motion in a 
 Circle. Motion in an Ellipse. Rotation on an Axis. 
 Figure of Revolution. Stability of the Axis of Rota- 
 tion. 
 
 IN considering the motion of bodies down inclined 
 planes, we have shown that the action of gravity upon 
 
 What is meant by ricochet? Describe the ballistic pendulum. What 
 is the estimate of the explosive force of gunpowder ? What is the veloci- 
 ty of its expansion ? What is the velocity it can communicate to a ball ? 
 
MOTION ON A CURVE. 95 
 
 them may be divided into two portions one producing 
 pressure upon the plane, and therefore acting perpendic- 
 ularly to its surface; the other acting parallel to the plane, 
 and therefore producing motion down it. 
 
 It has also been shown that, in some respects, there is an 
 analogy between movements over inclined planes and over 
 curved lines, but a further consideration proves that be- 
 tween the two there is also a very important difference. A 
 pressure occurs in the case of a body moving on a curve 
 which is not found in the case of one moving on a plane. 
 It arises from the inertia of a moving body. Thus, if a 
 body commences to move down an inclined plane, the 
 force producing the motion is, as we have seen, parallel 
 to the plane. From the first moment of motion to the 
 .last the direction is the same, and inasmuch as the inertia 
 of the body, when in motion, tends to continue that mo- 
 tion in the same straight line, no deflecting agency is en- 
 countered. 
 
 But it is very different with Fig. 105. 
 
 motion on a curve. Here the 
 direction of descent from A to 
 B is perpetually changing ; the 
 curve from its form resists, and 
 therefore deflects the falling 
 body. At any point its inertia 
 tends to continue its motion in 
 a straight line : thus, at A, were 
 it not for the curve it would 
 move in the line A a, at B in 
 the line B b, these lines being tangents to the curve at the 
 points A and B. The curve, therefore, continually de- 
 flecting the falling body, experiences a pressure itself a 
 pressure which obviously does not occur in the case of 
 an inclined plane. This pressure is denominated " cen- 
 trifugal force," because the moving body tends to fly from 
 the center of the curve. 
 
 In the foregoing explanation we have regarded the 
 body as being compelled to move in a curvilinear path, 
 by means of an inflexible and resisting surface. But it 
 may easily be shown that the same kind of motion will 
 
 Explain the difference between motion on inclined planes and motion on 
 curves. What is meant by centrifugal force ? Under what circumstances 
 can curvilinear motion ensue without the intervention of a rigid curve ? 
 
96 
 
 CURVILINEAR MOTION. 
 
 Fig. 106. 
 
 ensue without any such compelling or resisting surface, 
 provided the body be under the control of two forces, 
 one of which continually tends to draw it to the cen- 
 ter of the curve in which it moves, while the other, as 
 a momentary impulse, tends to carry it in a different di- 
 rection. 
 
 Thus, let there be a 
 body, A, Fig. 106, attract- 
 ed by another body, S, 
 and also subjected to a 
 projectile force tending 
 to carry it in the direction 
 A H. Under the con- 
 joint influence of the two 
 forces it will describe a 
 curvilinear orbit, A T W. 
 The point to which the 
 first force solicits the 
 body to move is termed 
 the center of gravity- 
 that force itself is desig- 
 nated the centripetal force, and the momentary force 
 passes under the name of tangential force. 
 
 The following experiment 
 clearly shows how, under 
 the action of such forces, 
 curvilinear motion arises. 
 Let there be placed upon a 
 table a ball, A, and from the 
 top of the room, by a long 
 thread, let there be suspend- 
 ed a second ball, B, the point 
 of suspension being verti- 
 cally over A. If now we re- 
 move B a short distance 
 from A, and let it go, it falls 
 at once on A, as though it 
 were attracted. It may be 
 regarded, therefore, as under 
 the influence of a centripetal force emanating from A. 
 
 Pig. 107. 
 
 
 What must the nature of the two forces be ? What is the center of 
 gravity ? What is the centripetal force ? What is the tangential force ? 
 Describe the experiment illustrated in' Fig. 107. 
 
CURVILINEAR MOTIONS. 
 
 97 
 
 But if, instead of simply letting B drop upon A, we give 
 it an impulse in a direction at right angles to the line ir 
 which it would have fallen, it at once pursues a curvilin- 
 ear path, and may be made to describe a circle or an el- 
 lipse according to the relative intensity of the tangential 
 force given it. 
 
 This revolving ball imitates the motion of the planetary 
 bodies round the sun. 
 
 To understand how these curvilinear motions arise, let 
 C be the center of gravity, and sup- 
 pose a body at the point a. Let a tan- 
 gential force act on it in such a man- 
 ner as to drive it from a to b, in the 
 same time as it would have fallen from 
 a to d. By the parallelogram offerees 
 it will move tof. When at this point, 
 f t its inertia would tend to carry it in 
 the directiony^-, a distan-ce equal to a 
 f t in a time equal to that occupied in 
 passing from a tof; but the constant 
 attractive force still operating tends to 
 bring it to h; by the parallelogram of 
 forces it therefore is carried to k ; and 
 by similar reasoning we might show 
 that it will next be found at n, and so on. But when we 
 consider that the centripetal force acts continually, and 
 not by small interrupted impulses, it is obvious that, in- 
 stead of a crooked line, the path which the body pursues 
 will be a continuous curve. 
 
 The planets move in their orbits round the sun, and 
 the satellites round their planets, in consequence of the 
 action of two forces a centripetal force, which is gravi- 
 tation, and a tangential force originally impressed on them. 
 
 The centrifugal force obviously arises from the action 
 of the tangential. It is the antagonist of the centripetal 
 force. 
 
 The figure of the curve in which a body revolves is de- 
 termined by the relative intensities of the centripetal and 
 tangential forces. If the two be equal at all points the 
 curve will be a circle, and the velocity of the body will 
 
 Explain why this curvilinear motion ensues. What forces direct the 
 motions of the planets ? What is the relation between the centripetal 
 and centrifugal force ? 
 
 E 
 
 

 98 
 
 CURVILINEAR MOTIONS. 
 
 be uniform. But if the centrifugal force at different 
 points of the body's orbit be inversely as the square of its 
 distance from the center of gravity, the curve will be an 
 ellipse and the velocity of the body variable. 
 
 In elliptical motion, which is the motion of planetary 
 bodies, the center of gravity is in one of the foci of the 
 ellipse. All lines drawn from this point to the circumfe- 
 rence are called radii vectorcs, and the nature of the mo- 
 tion is necessarily such that the radius vector connecting 
 the revolving body with the center of gravity sweeps over 
 equal areas in equal times. 
 
 The squares of the velocities are inversely as the dis- 
 tances, and the squares of the times of revolution are to 
 each other as the cubes of the distances. 
 
 Fig, 109. 
 
 Let A B D E be an elliptical orbit, as, for example, that 
 of a planet, the longest diameter being A B, and the short- 
 est D E. The points F and G are thejbci of the ellipse, 
 and in one, as F, is placed the center of gravity, which, 
 in this instance, is the sun. The planet, therefore, when 
 pursuing its orbit, is much nearer to the sun when at A 
 than when at B. The former point is, therefore, called 
 the perihelion, the latter the aphelion, and D and E points 
 
 By what circumstance is the figure of the curve determined ? Under 
 what circumstances is it a circle ? Under what an ellipse ? What is the 
 radius vector ? What are the laws of elliptic motion ? 
 
FIGURE OF REVOLUTION. 99 
 
 of mean distance. The line A B, joining the perihelion 
 and aphelion, is the line of the apsides ; it is also the great- 
 er or transverse axis of the orbit, and D E is the conju- 
 gate or less axis. A line drawn from the center of grav- 
 ity to the points D or E, as F D, is the mean distance, F 
 is the lower focus, G the higher focus, A the lower apsis, 
 B the higher apsis, and F C or G C that is the distance 
 of either of the foci from the center the excentricity. 
 
 When a body rotates upon an axis all its parts revolve 
 in equal times. The velocity of each particle increases 
 with its perpendicular distance from the axis, and, there- 
 fore, so also does its centrifugal force. As long as this 
 force is less than the cohesion of the particles, the rotating 
 body can preserve itself, but as soon as the centrifugal force 
 overcomes the cohesive, the parts of the rotating mass fly off 
 in directions which are tangents to their circular motion. 
 
 There are many familiar instances which are examples 
 of these principles. The bursting of rapidly rotating 
 masses, the expulsion of water from a mop, the projec- 
 tion of a stone from a sling. 
 
 If the parts of a rotating body have freedom of motion 
 among themselves, a change in the figure of that body 
 may ensue by reason of the difference of centrifugal force 
 of the different parts. Thus, in the case of the earth, the 
 figure is not a perfect sphere, but a spheroid, the diame- 
 ter or axis upon which it revolves, called its polar diam- 
 eter, is less than its equatorial, it having assumed a flat- 
 tened shape toward the poles and a bulging one toward 
 the equator. At the equator the centrifugal force of a 
 particle is L_ of its gravity. This 
 diminishes as we approach the 
 poles, where it becomes 0. The 
 tendency to fly from the axis of 
 motion has, therefore, given rise 
 to the force in question. 
 
 In Fig. 110, we have a repre- 
 sentation of the general figure of 
 the earth, in which N S is the 
 polar diameter and also the axis 
 of rotation, E'E, the equatorial diameter. 
 
 Define the various parts of an elliptic orbit. Describe the phenomena 
 of rotation on an axis. What figure does a movable rotating mass tend 
 to assume ? 
 
100 
 
 FIGURE OF REVOLUTION. 
 
 This may be illustrated by an instrument represented 
 Fig. in. in Fig. Ill, which consists 
 
 of a set of circular hoops, 
 made of brass or other elas- 
 tic material. They are fast- 
 ened upon an axis at the point 
 a, but at the point b can slide 
 up and down the axis. When 
 at rest they are of a circular 
 form. By a multiplying- 
 wheel a rapid rotation can 
 be given them, and when this 
 is done they depart from the 
 circular shape and assume 
 an elliptical one, the shorter 
 axis being the axis of rotation. 
 
 But if the parts of the rotating body have not perfect 
 Fie. 112. freedom of motion among themselves, 
 
 their centrifugal force gives rise to a 
 pressure upon the axis. If the mass 
 is symmetrical as respects the axis, the 
 resulting pressures compensate each 
 other. But as each one of the rotating 
 particles, by reason of its inertia, has 
 a disposition to continue its motion in 
 the same plane, it is obvious that such 
 a free axis can only be disturbed from 
 MBi^iiir.iUiiiMiiiriiiiU'iM jt s position by the exercise of a force 
 sufficient to overcome that effect. It is this result which 
 is so well illustrated by Bohnenberger's machine (Fig. 
 112), already described. 
 
 What does the instrument, Fig. Ill, illustrate? Under what circum- 
 stances does pressure on the axis take place ? For what reason does the 
 axis tend to maintain the same direction ? 
 
CAPILLARY ATTRACTION. 
 
 101 
 
 LECTURE XXII. 
 
 OF ADHESION AND CAPILLARY ATTRACTION. Adhesion of 
 Solids and Liquids. Law of Wetting. Capillary At- 
 traction. Elevations and Depressions. Relations of the 
 Diameter of Tubes. Motions by Capillary Attraction. 
 Endos7nosis of Liquids and of Gases. 
 
 To the arm of a balance, b c, Fig. 113, let there be at- 
 tached a flat circular plate of glass, Kg. 113. 
 #, arid let it be equipoised by the 
 weights in the opposite scale, d; 
 beneath it let there be brought a 
 cup of water, e, and on lowering the 
 glass plate within an inch, or even 
 within the hundredth part of an 
 inch of the water, no attraction is exhibited ; but if the 
 glass and the water are brought in contact, then it will re- 
 quire the addition of many weights in the opposite scale 
 to pull them apart. 
 
 If the cup, instead of being filled with water, is filled 
 with quicksilver, alcohol, oil, or any other liquid, or if 
 instead of a plate of glass we use one of wood or metal, 
 the same effects still ensue. The force which thus main- 
 tains the surface in contact is called " Adhesion." 
 
 Adhesion does not alone take place between bodies of 
 different forms. Two perfectly flat plates of glass or mar- 
 ble, when pressed together, can' only be separated by the 
 exertion of considerable force. In both this and the for- 
 mer case the absolute force required to effect a separa- 
 tion depends on the superficial area of the bodies in con- 
 tact. 
 
 If, on bringing a given solid in contact with a liquid, 
 the force of adhesion is equal to more than half the co- 
 hesive force of the liquid particles for one another, the 
 liquid will adhere to the solid or wet it. Thus, the adhe- 
 
 Give an example of the adhesion of a solid to a liquid. Does this take 
 place when liquids of different kinds are used ? Does it take place when 
 two solids are employed ? Under what circumstances does a liquid wet 
 or not wet a solid ? 
 
102 
 
 CAPILLARY TUBES. 
 
 Fig. 114. 
 
 sive force developed when gold is brought in contact with 
 quicksilver is more than half the cohe- 
 sion of the particles of the quicksilver 
 for each other : the quicksilver, there- 
 fore, adheres to or wets the gold. 
 
 But if the force of adhesion devel- 
 oped between a solid and liquid is 
 less than half the cohesive force of the 
 particles of the latter, the liquid does 
 not wet the solid. Thus, a piece of 
 glass in contact with quicksilver is not 
 wetted. 
 
 It is on these principles that Vera's 
 pump acts. It consists of a cord which 
 passes over two wheels, to which a 
 rapid motion can be given. The water 
 adheres to the cord and is raised by it. 
 
 If the surface of some water be dusted over with lyco- 
 podium seeds, the fingers may be plunged in it without 
 being wetted, the lycopodium preventing any adhesion 
 of the water. 
 
 But it is in the phenomena of capillary attrac- 
 tion that we see the effects of adhesion in the 
 most striking manner. These phe- 
 nomena are exhibited by tubes of 
 small diameter, called capillary tubes, 
 because their bore is as fine as a 
 hair. If such a tube, a, Fig. 115, be 
 immersed in water, the water at once 
 rises in it to a height considerably above its 
 level, in the glass cup, b. - 
 
 Or if instead of water we fill the glass cup 
 with quicksilver, and immerse the tube in it, 
 bringing it near the side so that we can see the 
 metal in the interior of the tube through the 
 glass, it will be found to be depressed be- 
 neath its proper level. 
 
 These experiments are still more conve- 
 niently made by means of tubes bent in the 
 form of a syphon, as represented in Fig. 116. 
 If one of these, A I, be partially filled with water, and 
 
 Fig. 115. 
 
 Fig. 116. 
 
 What is the principle of the action of Vera's pump ? 
 lary tube ? What phenomenon do these tubes exhibit ? 
 
 What is a capil- 
 
SURFACE OF LIQUIDS. 103 
 
 then with quicksilver, the water will be seen to rise in the 
 narrow tube, G D, above its level in the wide tube, A I, 
 and the quicksilver to be depressed. 
 
 When tubes of different diameters are used, the change 
 in the level of the liquid is different. The narrower the 
 tube the higher will water rise, and the lower will quick- 
 silver be depressed. 
 
 When tubes are very wide, or, what comes to the same 
 thins:, when liquids are contained in 
 
 i f f i Fig. 117. 
 
 bowls or basins, the surface is found not 
 to be uniformly level ; but near those 
 points where it approaches the glass, in 
 the case of water, it curves upward as 
 seen at A, Fig. 117, and in the case of 
 quicksilver it curves downward as seen 
 atB. 
 
 In tubes of the same material dipped in the same 
 liquid, the elevations or depressions are inversely as the 
 diameters of the tubes, the narrower the tube the higher 
 will water rise, and the deeper will quicksilver be de- 
 pressed. 
 
 There is a beautiful experiment which shows the con- 
 nection between the diameter of 
 the tube and the height to which 
 it will lift a liquid. Two square 
 pieces of plate glass, A B, C D, 
 Fig. 118, are arranged so that 
 their surfaces form a minute an- 
 gle. This position may be easily- 
 given them by fastening them to- 
 gether with a piece of wax or 
 cement, K. When the plates are dipped into a trough 
 of water, E F, G H, the water rises in the space between 
 them to a smaller extent where the plates are far apart, 
 and to a greater where they are closer. The upper edge 
 of the water gives the form of a hyperbola, D I A. The 
 plates may be supposed to represent a series o'f capillary 
 tubes of diameters continually decreasing, they show that 
 the narrower the intercluded space or bore of such tubes 
 the higher the liquid will rise. 
 
 The figure of the surface which bounds a liquid in a 
 
 Does this depend on the width of the tube ? How does the experiment 
 of Fig. 118 illustrate this? 
 
104 
 
 CAPILLARY MOTIONS. 
 
 Fiff 119. capillary tube is also to be remarked. 
 
 Whenever a liquid rises in a tube, its 
 bounding surface is concave upward, 
 ^ as seen in Fig. 119, where fg is the 
 tube, and a a the surface. When the 
 liquid neither rises nor sinks, the sur- 
 face a a is plane, as at d e; when the 
 liquid is depressed, the surface a a is 
 convex upward, as seen at b c. All 
 these conditions may be exhibited by 
 a glass tube properly prepared. In such a tube, when 
 quite clean, the concavity and elevation of the liquid is 
 seen ; if the interior of the tube be slightly greased, the 
 surface of the water in it is plane, and it coincides in 
 position with the level on the exterior. If it be not only 
 greased, but also dusted with lycopodium, the liquid is 
 depressed in it, and has a convex figure. 
 
 Jt may be shown, according to the principles of hydro- 
 statics, that it is the assumption of this curved surface 
 which is the cause of the elevation or depression of liquids 
 in capillary tubes. 
 
 Motions often ensue among floating bodies in conse- 
 quence of capillary attraction. At 
 first sight they might seem to indi- 
 cate the exertion of direct forces 
 of attraction and repulsion ema- 
 nating from the bodies themselves ; 
 but this in reality is not the case, 
 the motions arising in consequence 
 of a disturbance of the figure of the 
 surface on which the bodies float. Thus, if we grease 
 two cork balls, A B, and dust them with lycopodium 
 powder, they will, when set upon water, repel the liquid 
 all round, each ball reposing in a hollow space. If brought 
 iieac to each other, their repulsion exerted on the water 
 a* G makes a complete depression, and they fall toward 
 one another as though they were attracting each other. 
 It is, however, the lateral pressure of the water beyond 
 which forces them together. 
 
 Under what circumstances is the boundary surface concave, plane, and 
 convex ? What is it that determines the elevation or depression of the 
 liquid ? Describe the motions which take place in floating bodies in con- 
 sequence of these facts. 
 
ENDOSMOSIS. 105 
 
 Again, if one of the balls, E, is greased and dusted with 
 lycopodium, arid the other, D, clean, and therefore capa- 
 ble of being moistened, an elevation will exist all round 
 D, and a depression round E. When placed near to- 
 gether the balls appear to repel each other, the action 
 in this case, as in the former, arising from the figure of 
 the surface of the water. 
 
 If we take a small bladder, or any other membranous 
 Fig. 121. cavity, and having fastened it on a tube 
 open at both ends, A B, Fig. 12], fill the 
 bladder and tube to the height, C, with alco- 
 hol, and then immerse the bladder in a large 
 vessel of water ; it will soon be seen that the 
 level at C is rising, and at a short time it 
 reaches the top of the tube at B, and over- 
 flows. This motion is evidently due to the cir- 
 cumstance that the water percolates through 
 the bladder, and the phenomenon has some- 
 times been called endosmosis, or inward 
 movement. Examination proves that while 
 the water is thus flowing to the interior, a little of the al- 
 cohol is moving in the opposite way ; but as the water 
 moves quicker than the alcohol, there is an accumulation 
 in the interior of the bladder, and, consequently, a rise at C. 
 One liquid will thus intrude itself into another with 
 very great force. A bladder filled full of alcohol, and its 
 neck tightly tied, will soon burst open if it be plunged 
 beneath water. 
 
 Similar phenomena are exhibited by gases. If a jar 
 Fig. 122. De filled with carbonic acid gas, and a 
 
 piece of thin India-rubber tied over it, 
 the carbonic acid escapes into the air 
 through the India-rubber, which becomes 
 deeply depressed as at A, Fig. 122. But 
 if the jar be filled with air, and be ex- 
 posed to an atmosphere of carbonic aciu, 
 this gas, passing rapidly through it, ac- 
 cumulates in the interior of the vessel, and gives to the 
 India-rubber a convex or dome-shaped form, as seen at B. 
 Endosmosis is nothing but a complex case of common 
 capillary attraction. 
 
 Under what circumstances does repulsion take place? What is meant by 
 endosinosis ? Do gases exhibit these properties ? Give an illustration of it. 
 
106 RISE OF SAP. 
 
 The facts here described were originally discovered by 
 Priestley ; but at a later period attention was called to 
 them by Dutrochet, who, regarding them as being due to 
 a peculiar physical principle, gave to the movements in 
 question the names of endosmose and exosmose, mean- 
 ing inward and outward motion. But I have shown that 
 there is no reason to revert to any peculiar physical prin- 
 ciple, since the laws of ordinary capillary attraction ex- 
 plain every one of the facts. 
 
 The bursting of a bladder rilled with alcohol and sunk 
 under water gives us some idea of the power with which 
 the latter liquid forces its way into the membranous 
 cavity ; and it is surprising with what a degree of energy 
 these movements are often accomplished. An opposing 
 pressure of two or three atmospheres seems to offer no 
 obstacle whatever, and I have seen gases pass through 
 India-rubber to mingle with each other, though resisted 
 by pressures of from twenty to fifty atmospheres. 
 
 Whenever liquids which can commingle are placed on 
 opposite sides of a membrane or cellular body which 
 they can wet, motion ensues ; both liquids simultaneously 
 moving in opposite directions, and commonly one much 
 faster than the other. Thus, if a bladder full of gum- 
 water is immersed in common water, the latter will find 
 its way into the former against any pressure whatever. 
 
 During the growth of trees, the terminations of their 
 roots, which are of a soft and succulent nature, and which 
 pass under the name of spongioles, are filled with a gummy 
 material which originally was formed in the leaves. The 
 moist or wet soil with which the spongioles are in contact, 
 continually furnishes a supply of water which enters those 
 organs in precisely the same way that it would enter a 
 bladder full of gum-water. An accumulation takes place 
 in the organs, and the liquid rises in the vascular parts of 
 the root and the stem, which are in connection therewith. 
 To this we give the name of ascending sap. It makes its 
 way to the leaves, there to be changed into gum-water by 
 the action of the light of the sun. It is immaterial how 
 hig-l\a tree may be, the force now under consideration is 
 competent to lift the sap to any altitude. 
 
 With what degree of force are these motions accomplished ? What is 
 the cause of the rise of the sap ? 
 
PROPERTIES OF SOLIDS. 107 
 
 PROPERTIES OF SOLIDS. 
 
 LECTURE XXIII. 
 
 GENERAL PROPERTIES OF SOLIDS. Distinctive Properties. 
 Changes by particular Processes. Absolute Strength. 
 Lateral Strength. Resistance to Compression. Tor- 
 sion. Torsion Balance. 
 
 A SUBSTANCE which can of itself maintain an independ- 
 ent figure has already been defined as a solid body. This 
 peculiarity arises from the relative intensity of the attract- 
 ive and repulsive forces which obtain among its particles. 
 In solids the attractive predominates over the repulsive 
 force ; in liquids there seems to be little difference in their 
 intensity ; in gases the repulsive force prevails. It is fur- 
 ther to be observed, that portions of gas uniformly mix 
 with each other; the same also takes place with liquids 
 of a similar kind ; but when a fragment is broken from a 
 solid mass mere coaptation will not effect reunion. 
 
 The cohesive force of solids is exhibited in very dif- 
 ferent degrees some solids being brittle, and some duc- 
 tile some are hard, and others soft. Thus glass and 
 bismuth may be pulverized in a mortar; but gold can be 
 beaten out to an incredible extent by a hammer, and cop- 
 per drawn into fine wires. The diamond is the hardest 
 of all substances known, and, from their possessing the 
 same quality, rhodium and indium are used for the tips 
 of metallic pens, while other solids, such as potassium, so- 
 dium, butter, are soft, and yield to a very moderate press- 
 ure. 
 
 Mention some of the peculiarities of solid bodies. Give examples of 
 brktleness, hardness, and softness. 
 
108 STRENGTH OF MATERIALS. 
 
 It has already been stated that the special properties 
 which bodies possess can often be changed by proper 
 processes. Thus glass, by slow cooling, loses much of 
 its brittleness; and steel may be made excessively hard by 
 being ignited and then plunged in cold water. Prince 
 Rupert's drops furnish an illustration of these effects ; 
 they are made by suffering drops of melted glass to fall 
 in water. The drop takes on a pear-shaped form, ter- 
 minating in a long thread. It will stand a tolerably heavy 
 blow on the thick part, but bursts to dust if the tip of the 
 thin part is broken. 
 
 Solid substances differ very much in the important pecu- 
 liarity of STRENGTH. Of all bodies steel is the strongest. 
 The strength of materials may be considered in four 
 ways : 
 
 1st. Absolute strength, or the resistance exerted against 
 a force tending to tear asunder. 
 
 2d. Lateral or respective strength the resistance ex- 
 erted against being broken across. 
 
 3d. Resistance to compression that is to a force tend- 
 ing to crush. 
 
 4th. Strength of torsion the resistance against separa- 
 tion by being twisted. 
 
 The absolute strength of a body may be determined by 
 fastening its upper end and attaching weights to the lower 
 till it breaks. The absolute strength is not affected by* 
 the length of a body, but is proportional to the area of 
 its section. A rod of tempered steel, the area of which 
 is one inch, requires nearly 115,000 Ibs. to tear it asunder. 
 The strength of cords depends on the fineness of the 
 strands ; damp cordage is stronger than dry. Silk cords, 
 of the same diameter, have thrice the strength of those 
 of flax, and a remarkable increase of power arises from 
 gluing the threads together. A hempen cord, the 
 threads of which are glued, is stronger than the best 
 wrought-iron. 
 
 The lateral strength of a beam of the shape of a paral- 
 lelopipedon and of uniform thickness, supported at its 
 
 Can these properties be changed? What phenomenon do Prince Ru- 
 pert s drops exhibit ? What is meant by absolute strength? What by 
 lateral ? What by resistance to compression ? What by torsion ? How 
 may absolute strength be determined ? Upon what does it depend ? What 
 is the law of lateral strength of rectangular beams ? 
 
TORSION. 
 
 109 
 
 ends and loaded in the middle, is inversely as the length 
 and directly as the product of the breadth into square of 
 the depth. This strength is least when the whole weight 
 acts at the middle, and is greatest when at the ends. 
 
 The resistance to compression increases as the section 
 of the body increases, and it diminishes as the body be- 
 comes longer. When the body is only a thin plate, its 
 resistance to compression is, however, very small ; but it 
 rapidly increases with increasing thickness reaches a 
 maximum, and then diminishes as the square of the length. 
 This species of resistance is called into operation in the 
 construction of pillars or columns. 
 
 Torsion resistance is connected with the elasticity of a 
 body. As respects this force, elasticity, we have already 
 defined it, and shown that no solid substance is perfectly 
 elastic, though gases are. Each solid has its own limit 
 of elasticity, beyond which, if it be strained, it takes a 
 permanent set or it breaks. The limit of elasticity of glass 
 is the point at which it breaks, and that of iron or copper 
 being reached, the metal takes a permanent set. 
 
 The resistance arising from elasticity is proportional to 
 the displacement of the particles of the elastic body. 
 
 The application of this law is in- 
 volved in several valuable philosoph- 
 ical instruments, among which may 
 be mentioned the torsion balance, 
 used for the determination of weak 
 electric or magnetic forces. 
 
 THE TORSION BALANCE consists of 
 a delicate thread of glass or other 
 highly elastic substance, a b, Fig. 
 123, fastened at its upper end, a, to 
 a button, which turns stiffly in the 
 graduated plate, c, and to its lower 
 end at b, a lever, b d, is affixed trans- 
 versely. The thread is inclosed in 
 a glass tube, B, and the transverse 
 lever moves in a glass cylinder, A. 
 It is thus protected from the dis- 
 turbance of currents of air. Round this cylinder, from 
 
 Fig. 123. 
 
 What is the law for resistance to compression ? With what property 
 is torsion connected ? What is the law of resistance by elasticity ? De- 
 scribe the torsion balance. 
 
110 CENTER OF GRAVITY. 
 
 to 180, graduated divisions are marked, and the whole 
 instrument can be leveled by means of screwsyyi 
 
 Suppose, now, it were required to measure any feeble 
 repulsive force as the repulsion of a little electrified ball, e. 
 If this ball be introduced into the interior of the cylinder 
 through an aperture in the top, as shown in the Fig. 123, 
 the index at c and the ball at d being both at the zero of 
 their respective scales, the repulsion of e will drive the 
 movable ball d through a certain number of degrees. 
 By twisting the button at a, we can compel d to go back 
 to its original position ; and the number of degrees through 
 which the thread must be twisted to effect this, measures 
 the repulsive force for the angle of torsion is always pro- 
 portional to the force exerted. Of all methods for determ- 
 ining feeble forces in a horizontal plane, the torsion 
 balance is the most delicate and accurate. 
 
 LECTURE XXIV. 
 
 THE CENTER OF GRAVITY. Definition of the Center of 
 Gravity. Line of Direction. Position of Equilibrium. 
 Three Conditions of Support. Resulting States of 
 Equilibrium. Stability of Bodies. The Floating of 
 Bodies. 
 
 IN every solid body there exists a certain point round 
 which its material particles are arranged so as to be 
 equally acted on by gravity. The gravitating forces 
 soliciting these particles may be regarded as acting in 
 lines which are parallel to one another ; for the common 
 point of attraction, the center of the earth, is so distant, 
 that lines, drawn from it to the different particles of any 
 body on its surface, are practically parallel. To this 
 point, thus found in every body, no matter what may be 
 its figure or density, the term " Center of Gravity" is 
 applied. 
 
 A line which connects the center of gravity with the 
 centre of the earth (or, what is the same thing, a line 
 
 What is meant by the center of gravity of bodies ? 
 
CONDITIONS OF SUPPORT. Ill 
 
 drawn from the center of gravity perpendicularly down- 
 ward) is called " the line of direction." If a solid be suf- 
 fered to fall, its center of gravity moves along the line of 
 direction until it reaches the ground. 
 
 In our reasonings in relation to solids, we may regard 
 them as if all their material particles were concentrated 
 in one point that point being the center of gravity- 
 this being the point of application of the earth's attraction. 
 It follows, therefore, that if a body has freedom of motion, 
 it cannot be brought into a position of permanent equilib- 
 rium until the center of gravity is at the lowest place. 
 
 To satisfy this condition, sometimes effects which are 
 apparently contradicto- 
 tory will ensue. Thus, 
 the cylinder, m, Fig. 
 124, so constructed, by 
 being weighted on one 
 side, as to have its cen- 
 tre of gravity at the 
 point g, while its ge- 
 ometrical center is at c, will roll up an inclined plane, A 
 B, continuing its motion until, as shown at m' t where the 
 center of gravity, g', is in the lowest position. 
 
 A prop which supports the center of gravity of a body 
 supports the whole body. There are three different po- 
 sitions in which this support may be given : 
 
 1st. The prop may be applied directly to the center 
 itself. 
 
 2d. The point of support may have the center imme- 
 diately below it. 
 
 3d. The point of support may have the center imme- 
 diately above it. 
 
 In the first case, when the point of support is directly 
 applied to the center of gravity itself, the body, whatever 
 its figure may be, will remain at rest in any position as 
 is the case in a common wheel, the center of gravity of 
 which is in the center of its figure, and this being sup- 
 ported upon the axle, the wheel rests indifferently in any 
 position. 
 
 Let b a d, Fig. 125, be a brass semi-circle, weighted 
 
 What is the line of direction ? What is the position of equilibrium of 
 the center of gravity ? In what three positions may the center of gravity 
 be supported ? What phenomena arise in the first position ? 
 
112 
 
 SUPPORT OF BODIES. 
 
 Fig. 125. at the p ar ts & d to such an extent 
 
 that the center of gravity falls upon 
 the line connecting b and d. To a 
 fasten a light arm, a c, long enough 
 to reach to that line, and on this 
 arm, as shown by the figure, the 
 whole body may be balanced. 
 
 2d. The point of support may be 
 above the center of gravity. In 
 this case, if the body have freedom 
 of motion, it will not rest in equi- 
 librio until its center of gravity has 
 descended to the lowest position 
 possible, or until it is perpendicularly beneath the point of 
 Fig. 126. suspension. Thus, let there be a circular 
 plate, E c, Fig. 126, the center of gravity 
 of which is at c, and let it be suspended at 
 the point E, having freedom of motion on 
 that point. Whatever position we may 
 give it to the right or left, as shown by the 
 dotted lines, it at once moves, and is only at rest when E 
 and c are in the same perpendicular line. 
 
 In the same manner, if a ball be suspended to a point 
 by a thread, whatever position may be given it, there is 
 but one in which it will remain at rest, and that is when 
 its center of gravity is immediately beneath the point of 
 suspension, and the thread in a vertical line. 
 
 3d. The point of support may be beneath the center 
 of gravity. In this case, also, the body will be in equilib- 
 rio and at rest ; but the nature of its equilibrium differs 
 essentially from that of the foregoing case, as we shall 
 presently see. A sphere upon a horizontal plane affords 
 a case in point; and, as its center of gravity is also its 
 center of figure, it will be at rest, no matter what may 
 be the particular point of its surface to which the support 
 is applied. 
 
 Upon the principle that if a body be suspended freely, 
 and a perpendicular be drawn from the point of suspen- 
 sion, it will pass through the center of gravity, we are 
 
 What does the experiment in Fig. 125 prove? In the second position 
 of support what are the resulting phenomena ? What are those of the 
 third case of support ? How may the center of gravity of plane bodies bo 
 determined ? 
 
STABILITY OF BODIES. 113 
 
 often enabled to determine the posi- ffy. 127. 
 
 tion of that center experimentally. 
 Thus, let the plane body, ABC, Fig. 
 127, be supported by a thread attach- 
 ed to the point A, and to the same 
 point let there be attached a plumb- 
 line : this line, because it is perpen- 
 dicular, will pass through the center 
 of gravity ; let the line A m, against 
 which the plumb-line hangs, be marked 
 upon the body. Next, let it be suspended, in like man- 
 ner, by another point, B, to which the plumb-line is also 
 attached; the direction, B m', of the plumb-line will, in 
 this case, intersect its direction in the former case at some 
 point, such as G. This will be the center of gravity. 
 
 When the center of gravity is above the point of sus- 
 pension, there is produced a pressure upon that point. 
 When the center of gravity is beneath the point of sus- 
 pension, there is produced a pull upon that point. 
 
 The stability of bodies is intimately connected w r ith the 
 position of their center of gravity. A body may be in a 
 condition, 1st, of indifferent ; 2d, of stable ; 3d, of insta- 
 ble equilibrium. 
 
 Indifferent equilibrium ensues when a body is support- 
 ed upon its center of gravity ; for then it is immaterial 
 what position is given to it it remains in all at rest. 
 
 Stable equilibrium ensues when the point of support is 
 above the center of gravity. If the body be disturbed 
 from this situation, it oscillates for a time, and finally re- 
 turns to its original position. 
 
 Instable equilibrium is exhibited when the point of 
 support is beneath the center of gravity. The body being 
 movable, in this instance, it revolves upon its point of 
 support, and turns into such a position that its center of 
 gravity comes immediately beneath that point. 
 
 In the theory of the balance, hereafter to be described, 
 these facts are of the greatest importance. 
 
 When bodies are supported upon a basis, their stability 
 depends on the position of their line of direction. The 
 
 In what case does a pressure and in what a pull upon the point of sus- 
 pension arise? How many kinds of equilibrium may be enumerated? 
 tinder what circumstances do these arise? On what does the stability of 
 bodies depend ? 
 
114 
 
 STABILITY OF BODIES. 
 
 
 line of direction has already been defined to be a line 
 drawn from the center of gravity perpendicularly down- 
 ward. 
 
 If the line of direction falls within the basis of support, 
 the body remains supported. 
 
 - 128. If the. line of direction falls out- 
 
 side the basis of support, the body 
 overturns. 
 
 Thus, let there be a block of 
 wood or metal, Fig. 128, of which 
 c is the center of gravity, c d the 
 line of direction, and let it be sup- 
 ported on its lower face, a b. So 
 long as the line of direction falls within this basis, the 
 block remains in equilibrio. 
 
 Fig. 129. Again, let there be another block, 
 
 Fig. 129, of which c is the center of 
 gravity and c d the line of direction. 
 Inasmuch as this falls outside of the 
 basis, a b, the body overturns. 
 
 A ball upon a horizontal plane has 
 its line of direction within its point of 
 support; it therefore rests indifferently 
 in any position in which it may be laid. 
 But a ball upon an inclined plane has 
 its line of direction outside its point of support, and there- 
 fore it falls continually. 
 
 From similar considerations we understand the nature 
 of the difficulty of poising a needle upon its point. The 
 
 Fig. J30. 
 
 center of gravity is above 
 the point of support, and it 
 is almost impossible to ad- 
 just things so that the line 
 of direction will fall within 
 the basis. The slightest in- 
 clination instantly causes it 
 to overturn. 
 
 When the center of grav- 
 ity is very low, or near the 
 
 What is the condition for support, and what for being overturned ? Illus- 
 trate these cases in the instance of square and round blocks. Why is it so 
 difficult to poise a needle on its point ? In what circumstances is the 
 maximum stability obtained ? 
 
EaUILIBRIUM IN FLOTATION. 115 
 
 basis, there is more difficulty in throwing the line of 
 direction outside the basis than when it is high. For this 
 reason carriages, which are loaded very high, or have 
 much weight on the top, are more easily overturned than 
 those the load of which is low, and the weight arranged 
 beneath, as is shown in Fig. 130. 
 
 The stability of a body is greater according as its 
 weight is greater, its center of gravity lower, and its basis 
 wider. 
 
 The principles here laid down apply to the case of the 
 flotation of bodies. When an irregular-shaped solid mass 
 is placed on the surface of a fluid, it arranges itself in a 
 certain position to which it will always return if it be 
 purposely overset. In many such solids another position 
 may be found, in which they will float in the liquid ; 
 but the slightest touch overturns them. Bodies, there- 
 fore, may exhibit either stable or unstable flotation. A 
 long cylinder floating on one end is an instance of the 
 .latter case, but if floating with its axis parallel to the sur- 
 face of the liquid, of the former. 
 
 These phenomena depend on the relative positions of 
 the center of gravity of the floating solid, and that of the 
 portion of liquid which it displaces. The former retains 
 an invariable position as respects the solid mass, but the 
 latter shifts in the liquid as the solid changes its place. 
 
 Equilibrium takes place when the center of gravity of 
 the floating body and that of the portion of liquid dis- 
 placed are in the same line of direction. If of the two 
 the former is undermost, stable equilibrium ensues, but if 
 it is above the center of gravity of the displaced liquid, 
 unstable equilibrium takes place. To this, however, 
 there is an exception it arises when the body floats on its 
 largest surface. 
 
 There are two forces involved in the determination of 
 the position of flotation : 1st, the gravity of the body 
 downward; 2d, the upward pressure of the liquid. The 
 former is to be referred to the center of gravity of the 
 body itself, and the latter takes effect on the center of 
 gravity of the displaced liquid. If these two centers are 
 
 What is meant by stable and unstable flotation ? On what do these 
 depend ? Under what circumstances does stable equilibrium take place ? 
 Under what unstable ? What forces are involved in these results ? 
 When does rotation ensue ? 
 
116 THE PENDULUM. 
 
 in the same vertical line, they counteract each other ; but 
 in any other position a movement of rotation must ensue. 
 The solid, therefore, turns over, and finally comes into 
 such a position as satisfies the conditions of equilibrium. 
 On these principles a cube will float on any one of its 
 faces, and a sphere in any position whatever ; but if the 
 sphere be not of uniform density, one part of it being 
 heavier than the rest, motion takes place until the heaviest 
 part is lowest. A long cylinder floating on its end is 
 unstable, but when it floats lengthwise, stable. It is 
 obvious these principles are of great importance in ship- 
 building, and the loading and ballasting of ships. 
 
 LECTURE XXV. 
 
 THE PENDULUM. Simple and Physical Pendulums. 
 Nature of Oscillatory Motion. Center of Oscillation., 
 Laws of Pendulums. Cycloidal Vibrations. The 
 Seconds 1 Pendulum. Measures of Time, Space, and 
 Gravity. Compensation Pendulums. 
 
 A SOLID body suspended upon a point with its center 
 of gravity below, so that it can oscillate under the influ- 
 ence of gravity, is called a pendulum. 
 
 A simple pendulum is imagined to consist of an im- 
 ponderable line, having freedom of motion at one end, 
 and at the other a point possessing weight. 
 
 A physical pendulum consists of a heavy metallic ball 
 suspended by a thread or slender wire. 
 
 The position of rest of a pendulum is when its center 
 of gravity is perpendicularly beneath its point of suspen- 
 sion, its length, therefore, is in the line of direction. If 
 it be removed from this position, it returns to it again 
 after making several oscillations backward and forward. 
 Its descending motions are due to the gravitating action 
 of the earth, its ascending due to its own inertia. A 
 pendulum once in motion would vibrate continually were 
 it not for friction on its point of suspension, the rigidity 
 
 Give examples of the flotation of different bodies. What is a pendu- 
 lum ? What is the difference between a simple and a physical pendulum 7 
 What is the position of rest ? What is the effect of removal from that po- 
 sition ? Why does the instrument eventually come to rest ? 
 
THE PENDULUM. 
 
 117 
 
 of the thread, if it be supported by one, and the resistance 
 of atmospheric air. 
 
 The length of a pen- Fig. 131. 
 
 dulum is the distance 
 that intervenes between 
 its point of suspension 
 and its center of oscil- 
 lation. Its oscillation is 
 the extreme distance 
 through which it passes 
 from the right hand to 
 the left, or from the left 
 to the right. In Fig. 
 131, a is the point of 
 suspension, b the center 
 of oscillation ; a b the 
 length of the pendulum; 
 c b d or d b c the oscil- 
 lation ; the angle a or 
 Q is the angle of elongation ; and the time is the period 
 that elapses in making one complete oscillation. Oscilla- 
 tions are said to be isochronous when they are performed 
 in equal times. 
 
 Let a b c, Fig. 132, be a pendulous body, supported on 
 the point , and performing its oscillations fig- 132 - 
 upon that point. If we consider the motions 
 of two points, such as b and c, it will appear 
 that under the influence of gravity the point 
 
 b, which is nearer to the point of suspension, 
 would perform its oscillations more quickly 
 than the point c. But inasmuch as in the pen- 
 dulous body both are supposed to be inflex- 
 ibly connected together, by reason of the so- 
 lidity of the mass, both are compelled to per- 
 form their oscillations in the same time. The 
 
 point b will, therefore, tend to accelerate the motions of 
 
 c, and c will tend to retard the motions of b. It follows, 
 therefore, that in every pendulum there is a point the 
 velocity of which, multiplied by the mass of the pendu- 
 lum, is equal to the quantity of motion in the pendulum. 
 
 What is the length of a pendulum, the point of suspension, the oscilla- 
 tion, the angle of elongation, and the time ? 
 
118 CENTER OF OSCILLATION. 
 
 To this point the name of center of oscillation is given. 
 In a linear pendulum that is, a rod of inappreciable 
 thickness the center of oscillation is two thirds the length 
 from the point of suspension. In a right-angled conical 
 mass the center of oscillation is at the center of the base. 
 
 The center of oscillation possesses the remarkable 
 property that it is convertible with the centre of suspen- 
 sion that is to say, if a pendulum vibrates in a given 
 time, when supported on its ordinary centre of suspen- 
 sion, it will vibrate in the same time exactly if it be sus- 
 pended on its center of oscillation. Advantage has been 
 taken of this property to determine the lengths of pendu- 
 lums, with great precision, and thereby the intensity of 
 gravity and the figure of the earth. In these cases a sim- 
 ple bar of metal, of proper length, with knife-edges equi- 
 distant from its ends, has been used and adjustment made 
 until the bar vibrated equally when supported on either 
 knife edge. The distance between the knife-edges is the 
 length of the pendulum. 
 
 Pendulums of equal lengths vibrate in the same place 
 in equal times, provided their angles of elongation do not 
 exceed two or three degrees. 
 
 Pendulums of unequal lengths vibrate in unequal times 
 the shorter more quickly than the longer the times be- 
 ing to one another as the square roots of the lengths of 
 the pendulums. 
 
 fig- 133. If we take a circle, B, Fig. 
 
 3)133, and, causing it to roll 
 along a plane, B D, mark out 
 the path which is described 
 by a point, P, in its circum- 
 ference, the line so marked is designated a cycloid. 
 
 When a pendulum vibrates in a cycloid, it will describe 
 all arcs thereof in equal times ; and the time of each os- 
 cillation is to the time in which a heavy body would fall 
 through half the length of the pendulum as the circum- 
 ference of a circle is to its diameter. 
 
 The difference, therefore, between oscillation in cy- 
 
 Describe the nature of the center of oscillation. What is its position 
 in a linear pendulum and in a right-angled conical mass? What property 
 does the center of oscillation possess? What are the laws of the mo- 
 tion of pendulums ? What is a cycloid ? What property does a pendu- 
 lum vibrating in a cycloid possess ? 
 
 
LENGTH OP THE PENDULUM. 119 
 
 cloidal and circular arcs is, that in the former all oscilla- 
 tions are isochronous, but in the latter they are not ; for 
 the larger the circular arc the longer the lime of oscilla- 
 tion. And as circular movement is the only one which 
 can be conveniently resorted to in practice, it is necessa- 
 ry to reduce circular to cy cloidal oscillations by calcula- 
 tion. 
 
 When the length of the pendulum is such that its time 
 of oscillation is equal to one second, it is called a seconds' 
 pendulum. This length differs at different places. Un- 
 der the equator it is shorter than at the poles ; and this 
 evidently arises from the circumstance that the intensity 
 of gravity, as has been already explained, is different at 
 those points ; for the figure of the earth not being a per- 
 fect sphere but an oblate spheroid, its polar axis being 
 shorter than its equatorial, a body at the poles is more 
 powerfully attracted than one at the equator, it being 
 nearer the center of the earth ; and as the motion of the 
 pendulum arises from gravity, in order to make it oscil- 
 late in equal times, it is necessary to have it shorter at the 
 equator than at the pole. The length of the seconds' pen- 
 dulum in Londoa is 39.13929 inches, at a temperature of 
 60 Fahrenheit. 
 
 For many of the purposes of physical science the pen- 
 dulum is an important instrument. It affords us the best 
 measure of time, and is, therefore, used in all stationary 
 timepieces or clocks. A clock is a mechanical apparatus 
 for the purpose of registering the numbers of oscillations 
 which a pendulum makes, and at the same time of com- 
 municating to the pendulum the amount of motion it is 
 continually losing by friction on its points of support and 
 by resistance of the air. The oscillations are performed 
 in small circular arcs, so that the times are equal. 
 
 Whatever affects the length of the pendulum changes 
 the time of its motion. It is for this reason that clocks 
 go slower in summer and faster in winter the changes 
 of temperature altering the length of the pendulum. To 
 compensate this, various contrivances have been resorted 
 to with a view of securing the invariability of the instru- 
 
 What difference is there between oscillation in cycloidal and circular 
 arcs ? What is a seconds' pendulum ? Is there difference in its length at 
 different places ? From what does this arise ? What is the pendulum- 
 clock ? Why do variations of temperature change the rate of a clock ? 
 
120 
 
 THE MERCURIAL PENDULUM. 
 
 ment. The nature of these is very well illustrated by the 
 mercurial pendulum. 
 
 Fig. 134. Let A B be the pendulum-rod : at B it is 
 
 formed into a kind of rectangle, F G D E, 
 within which is placed a glass jar, G H, con- 
 taining mercury, and serving as the bulb of 
 the pendulum. When the weather becomes 
 warm, the steel-rod and rectangle elongate, 
 and therefore depress the center of oscilla- 
 tion. But simultaneously the mercury ex- 
 pands, and this motion takes place necessa- 
 rily in the upward direction. If the quan- 
 tity of mercury is properly adjusted the cen- 
 ter of oscillation is carried as far upward by 
 the mercurial expansion as downward by 
 that of the steel. Its actual position remains, 
 therefore, the same; and as the length of the 
 pendulum is the distance between the point 
 E of suspension and center of oscillation, that 
 length remains unchanged. The gridiron 
 pendulum acts on similar principles. 
 
 The pendulum is also i^sed to determine 
 the force of gravity. The nature of this ap- 
 plication has already been pointed out in 
 what has been said respecting oscillations 
 at the equator and the poles. The force of 
 gravity at any place, or the height through 
 which a body will fall in one second is de- 
 termined by multiplying the lengths of a 
 seconds' pendulum for that place by the number 4.9348. 
 The length of the seconds' pendulum being always in- 
 variable at the same place for gravity is always invaria- 
 ble may be used as a standard of measure. Thus, the 
 English inch is of such a length that 39.13939 inches are 
 equal to the length of a pendulum vibrating seconds. 
 From these measures of length, measures of capacity 
 might be derived by taking their cubes, and measures of 
 surface by taking their squares. 
 
 What contrivances have been resorted to to avoid this difficulty ( De- 
 scribe the mercurial pendulum. On what principle is the pendulum used 
 to determine the force of gravity ? Under what circumstances may the 
 pendulum be used as a standard of measure ? 
 
PERCUSSION. 
 
 LECTURE XXVI. 
 
 OF PERCUSSION. Of Impact, Central, Excentric, Direct, 
 Oblique. Inelastic and Elastic Bodies. Laws of Col- 
 lision of Inelastic Bodies. Changes of Figure of Elastic 
 Bodies. Phenomena of their Collision. Of Reflected 
 Motions. 
 
 IMPACT or percussion may take place in several differ- 
 ent ways as central, excentric, direct, oblique. 
 
 Central impact takes place when the bodies in collision 
 have their centers of gravity moving in the same right 
 line. 
 
 Excentric impact is when the directions of the motion 
 of the centers of gravity of the bodies in collision make an 
 angle with one another. 
 
 Direct impact is when the direction of the moving 
 body is perpendicular to the surface on which it impinges. 
 
 Oblique impact is when the direction of the moving 
 body makes some angle other than a right one with the 
 surface on which it impinges. 
 
 The phenomena of percussion depend greatly on the 
 physical character of the impinging bodies. The bodies 
 may either be inelastic or elastic. Masses of clay or putty 
 are illustrations of the former case, balls of ivory or steel 
 of the latter. 
 
 It has already been shown, Lecture XVII, that if two 
 inelastic bodies move in the same direction their joint mo- 
 mentum, after impact, is equal to the sum of their sepa- 
 rate momenta ; and that, if they move in opposite direc- 
 tions, it is equal to the difference. Their velocity, after 
 impact, is found by dividing their common momentum by 
 the sum of their masses. 
 
 When a hard body impinges on an immovable mass, 
 the particles of which can, however, recede, so as to ad- 
 
 What is central impact ? What are excentric, direct, and oblique ? On 
 what physical character do the phenomena of percussion, to a great ex- 
 tent depend ? Give examples of inelastic and elastic solids. What are 
 the laws of motion of inelastic bodies ? 
 
 F 
 
122 
 
 ELASTIC IMPACT. 
 
 
 mit the impinging body, the depths to which it will pene- 
 trate are as the squares of its velocity multiplied by its 
 mass. 
 
 When elastic bodies impinge on each other, there is, 
 Fig. 135. during the time of their encoun- 
 
 ter, a change of figure. Thus, 
 if we take the instrument, Fig. 
 135, and, having painted one of 
 its ivory balls, a, let the other 
 ball, b, touch it gently, the latter 
 will receive on its surface a sin- 
 gle point of paint. But if we, 
 raise this ball, and let it fall from 
 a considerable distance upon the 
 other, it will receive a circular mark of paint, showing 
 that, during the percussion, the balls lost their spherical 
 figure, and, instead of touching by a single point, they 
 touched by a surface of considerable extent. Their in- 
 stantaneous recovery of the spherical form, like the fa- 
 cility with which that form was lost, is due to their elas- 
 ticity. 
 
 Whatever tends to impair the elasticity of such balls 
 tends, therefore, to change the phenomena of impact. 
 Thus, if we make a cavity in one of them, and fill it par- 
 tially with lead, the balls, after percussion, will not re- 
 cede from one another as far as before. 
 
 The manner in which elasticity acts in these cases may 
 be understood by considering the action of a spiral spring 
 between the two balls, the length of it coinciding with 
 the direction of their motion. When the balls fall upon 
 its extremities, they give rise to compression, and the 
 spring continually resists them at each successive instant. 
 Their force, which was greatest at the moment of impact, 
 is gradually overcome by the resistance of the spring, 
 and finally vanishes. As soon as their velocity ceases, 
 the spring can undergo no further compression, and is 
 now able to begin to restore itself with a continually in- 
 creasing force. Finally, it communicates to the balls 
 the same velocity with which they originally impinged 
 upon it. 
 
 What is the nature of the change of figure which elastic bodies exhibit 
 when they encounter '>. How may this be proved ? How may it be illus- 
 trated by the action of a spring ? 
 
ELASTIC IMPACT. 
 
 123 
 
 When, therefore, a pair of elastic spherical balls are 
 made to impinge on each other, there Fig. 136. 
 
 is a compression of their particles in 
 the direction in which the motion is 
 taking place, so that the diameters, c j 
 a b, a c, Fig. 136, are less than be- 
 fore. A spheroidal form is, there- 
 fore, the necessary result. But just 
 as with the imaginary spring in the foregoing case so with 
 the compressed particles in this. As soon as the motion 
 of the bodies becomes 0, the elastic force of the compress- 
 ed particles gives rise to movement in the opposite di- 
 rection. 
 
 When two perfectly elastic bodies come in collision, the 
 force of elasticity is equal to the force of compression, and 
 the force of compression is equal to the force of the shock. 
 
 When two elastic bodies have struck each other, their 
 recession will be with the same relative velocity with 
 which they fell upon each other. 
 
 When two equal elastic bodies move toward each 
 other with equal velocities, after percussion they recede 
 from each other with the same velocity. 
 
 When of two equal elastic bodies fig- 137. 
 
 one is in motion and the other at 
 rest, the former, after collision, 
 will communicate to the other 
 all its velocity, and remain at 
 rest itself. This phenomenon, 
 and indeed much that is here 
 said in relation to the impact of 
 bodies, is well shown by an ap- 
 paratus such as Fig. 137, in 
 which let the ball, a, be at rest, and let b fall on it from 
 any height, after collision, a takes the whole velocity of 
 b, and b itself remains at rest. 
 
 When of two equal bodies, moving in the same direc- 
 tion, one overtakes the other, they exchange velocities 
 and go on as before. 
 
 When two equal bodies, moving with different veloci- 
 ties, encounter each other, they exchange, and recede from 
 one another in contrary directions. 
 
 What are the laws of motion of perfectly elastic bodies ? How may 
 these be proved experimentally ? 
 
124 ELASTIC BODIES. 
 
 If, in the instrument Fig. 137, instead of having only 
 two ivory balls, we had a large number suspended, so as 
 to touch one another, it would be found, on letting the 
 ball at one extremity impinge on the others, that all the 
 intermediate ones would remain motionless, and the one 
 at the farther extremity would rebound. The motion, 
 therefore, is transmitted through the entire series of baljs ; 
 and it is the mutual reaction of the intermediate ones which 
 keeps them at rest, the distant one rebounding because 
 there is nothing against which it can react. 
 
 Fig. 138. When an elastic ball strikes upon 
 
 c an immovable elastic plane it will 
 recoil with the same velocity with 
 which it advanced. When the 
 impact is perpendicular, the path of 
 retrocession is the same as that of 
 advance. Thus, if a b, Fig. 138, 
 be the path of the advance, per- 
 pendicular to c d, the elastic plane, 
 the recoil or retrocession will be 
 in the same path, but in the op- 
 posite direction, b a. 
 When the path of the striking body is not perpendicu- 
 lar, but at some other angle to the elastic plane the recoil 
 Fig. 139. will be under the same angle, but on the op- 
 
 \d 
 \ 
 
 \ 
 
 ja, posite side of the perpendicular. Thus/if 
 a c, Fig. 139, be the path of the striking 
 body, c, the elastic plane, the path after con- 
 -, / tact will be c, d, such that the points a c d, 
 are in the same plane, and the angle a c b is 
 equal to the angle bed. To the former of 
 these the name " angle of incidence" is given, to the lat- 
 ter " angle of reflexion." 
 
 The angle of incidence is the angle included between 
 the path of the impinging body and a perpendicular, b c, 
 drawn to the surface of impact at the point of impact 
 And the angle of reflexion is the angle included between 
 the path of the retroceding body and the same perpen- 
 dicular. 
 
 The principles given in this Lecture are applied in 
 
 What are the laws of motion of an elastic ball striking upon an immova- 
 ble elastic plane ? What is meant by the angle of incidence ? What is 
 thb angle of reflexion ? 
 
PERCUSSION. 125 
 
 many cases of practice. Thus, in the pile engine, which 
 consists of a heavy block, raised slowly by machinery be- 
 tween two uprights, and then allowed to fall suddenly on 
 the head of the pile to be driven into the ground. If the 
 block thus used as a hammer is too small, it fails to move 
 the pile ; and if its velocity is too great it splits the head 
 of the pile. A large mass, falling from a small height, is 
 therefore used. Thus it may be readily shown, that if 
 the hammer weighs 1000 pounds, and it falls through a 
 height of only four feet, the force with which it strikes 
 the pile is equal to 120,000 pounds. 
 
 When gold is beaten into thin leaves the workmen can- 
 not employ light hammers and use them quickly, for they 
 would divide or fissure the gold : they use, therefore, 
 heavier hammers, and move them more slowly. 
 
 Give some illustrations of the phenomena of impact. 
 
126 MACHINES. 
 
 THE ELEMENTS OF MACHINERY. 
 
 LECTURE XXVII 
 
 THE MECHANICAL POWERS. Definition of MacJiines. 
 Number of Mechanical Powers. Power. Weight. 
 Principle of Virtual Velocities. 
 
 THE LEVER Definition of. Three Kinds of Lever. 
 Conditions of Equilibrium. Uses of Levers. The Bal- 
 ance. Weighing Machines. 
 
 BY MACHINES are meant certain contrivances employed 
 for the purpose of changing the direction of moving pow- 
 ers, or of enabling them to produce any required velocity, 
 or to overcome any required force. 
 
 It is to be understood that the force of any moving 
 power can never be increased by the agency of any ma- 
 chine the duty of which is to transmit the effect of that 
 power unimpaired to the working point. Machinery 
 cannot create power it transmits it. Theoretically, this 
 transmission is supposed to take place without loss, but 
 practically there is always a certain degree of diminution 
 arising both from imperfections of construction and the 
 agency of such impediments to motion as friction, rigidi- 
 ty, &c., the consideration of which we shall resume in its 
 proper place. 
 
 In what follows, it will, therefore, be understood that 
 we speak of the action of machines theoretically, and 
 apart from the intervention of these disturbing causes. 
 
 All machines, no matter how complex soever their con- 
 struction may be, can be reduced to one or more of six 
 
 What is meant by a machine ? Can machines create power? What 
 is the difference between the theoretical and practical action of machines? 
 How many simple machines are there ? 
 
PRINCIPLE OF VIRTUAL VELOCITIES. 127 
 
 simpler elements, which pass under the name of the " me- 
 chanical powers." They are, 
 
 The Lever, 
 Pulley, 
 
 Wheel and axle, 
 Inclined plane, 
 Wedge, 
 Screw. 
 
 These mechanical powers, or simple machines, may, 
 indeed, be further reduced to three : 
 
 The Lever, 
 Pulley, 
 Inclined plane. 
 
 In any machine the force or original prime-mover passes 
 under the name of THE POWER. 
 
 The resistance to be overcome, or that upon which the 
 power is brought to bear through the intervention of the 
 machine, goes under the name of THE WEIGHT. 
 
 The general law which determines the equilibrium of 
 all machines, whether simple or compound, is as follows : 
 " The power multiplied by the space through which it moves 
 in a vertical direction is equal to the weight multiplied by 
 the space through which it moves in a vertical direction" 
 The principle involved in this law passes under the name 
 of " the principle of virtual velocities." 
 
 The foregoing principle expounding the conditions un- 
 der which the power and weight are in equilibrium, and 
 the machine, therefore, in a state of rest, it follows, there- 
 fore, that " if the product arising from the power multi- 
 plied by the space through which it moves in a vertical di- 
 rection, be greater than the product arising from the weight 
 multiplied by the space through which it moves in a verti- 
 cal direction, the power will overcome the resistance of the 
 weight, and motion of the machine will ensue" 
 
 THE LEVER. 
 
 The lever is the first of the elementary machines. In 
 theory, it is an inflexible and imponderable line supported 
 on one point on which it can turn. In practice, it con- 
 To what may these be further reduced ? What is the power? What 
 is the weight ? Describe the general law of equilibrium of all machines. 
 What name is given to the principle contained in this law ? Under what 
 condition does motion ensue ? What is a lever ( 
 
128 VTHE LEVER. 
 
 sists of a solid unyielding rod working upon a point 
 called a fulcrum. 
 
 Three varieties of lever are commonly enumerated. In 
 
 HO tlie ^ rst ' ttie f ulcrum F, is between the 
 
 tg ' i*' power, P, and the weight, W, as in Fig. 
 
 pi TfQ i40 t In the second, the weight is be- 
 
 Fig. MI. tween the power and the fulcrum, Fig. 
 
 fjH 141. In the third, the power is between 
 
 the weight and the fulcrum, Fig. 142. 
 
 Fig. 142. There are also other species of lever, 
 
 pa such as the bent lever, the curvilinear 
 
 lever. The mode of action and theory 
 
 of all are the same. 
 
 By the principle of virtual velocities, it appears that 
 " any lever is in equilibria when the power and the weight are 
 to each other inversely as their distances from. the fulcrum'' 
 
 As illustrative instances of this if in a lever of the 
 first kind, in equilibria, the power and the weight are equal, 
 they must be at equal distances from the fulcrum. If the 
 power is only half the weight, it must be at double the 
 distance from the fulcrum, if one third the weight, triple 
 the distance, &c. 
 
 When, therefore, it is proposed by the intervention of 
 a lever to cause a given power to overcome a given 
 weight, it is necessary that the power multiplied by its 
 distance from the fulcrum should give a greater product 
 than the weight multiplied by its distance from the ful- 
 Fiff. 143. crum. Thus, in Fig. 141, let 
 
 1 P be a power of six pounds, 
 
 w6 
 
 7 
 
 p operating on a lever of the 
 first kind, at a distance, p c, 
 from the fulcrum, c, of seven 
 inches ; let W be the weight 
 to be overcome, and let it be 
 seven pounds, with a distance, 
 W c, of six inches from the 
 
 fulcrum. Now the power multiplied into its distance 
 is equal to forty-two, and the weight multiplied into its 
 distance is also equal to forty-two ; the lever is, therefore, 
 under the law just stated in equilibrio. But if we in- 
 crease the distance of P from c, or increase P itself, or do 
 
 How many varieties of it are there ? What is the law of equilibrium of 
 the lever ? Give an illustration of it ? 
 
THE LEVER. 
 
 129 
 
 both, then the product of P into its distance from the 
 fulcrum will increase, the lever will move, and the resist- 
 ance of the weight be overcome. 
 
 Levers are used in practice for many different purposes. 
 By their agency a small power may hold in equilibrio, or 
 move a great weight; thus, the power of one man applied 
 at the end of a crowbar will overturn a heavy mass, the 
 man acting at a distance of several feet, and the mass at 
 only a few inches from the fulcrum. Of levers of the 
 first kind, crowbars and scissors are familiar examples. 
 Of those of the second kind, oars and nutcrackers ; of 
 those of the third, tongs and sheepshears. 
 
 For many of the purposes of science levers are used to 
 magnify small motions. The power causing the motion 
 is applied by a short arm near to the fulcrum of the lever, 
 
 Fig. 144. 
 
 Mention some of the applications of the lever. Give familiar instances 
 of each of the three kinds of lever. 
 
130 THE BALANCE. 
 
 and the other arm. which may be ten, twenty, or more 
 times longer, moves over a graduated scale. The py- 
 rometer is an example of this application. 
 
 The most accurate means for determining the weight 
 of bodies is by the lever. When arranged for this pur- 
 pose, it passes under the name of " The Balance." It is 
 a lever of the first kind with equal arms. Various forms 
 are given to it, and various contrivances annexed for the 
 purpose of insuring its lightness, its inflexibility, and the 
 absolute equality of the lengths of its arms. Fig. 144, 
 represents one of the best kinds : a a is the beam ; c is 
 the fulcrum, or center of motion ; d d are the scale-pans 
 in which the weights and objects to be weighed are 
 applied ; their points of suspension are at a a. With a 
 view of reducing friction, the axis of motion, c, and both 
 the points of suspension are knife-edges of hard steel 
 working on planes of agate ; and, to preserve them unin- 
 jured, the beam and the scale-pans are supported upon 
 props, except at the time a substance is to be weighed. 
 Then, by moving the handle, f, the axis of motion is de- 
 posited slowly on its agate plane, and the scale-pans on 
 their points of suspension, and the beam thrown into action. 
 
 In balances it is essential that the center of gravity 
 should have a particular position. The cause of this 
 will be appreciated from what has been said in Lecture 
 XXIV. Thus, if the center of gravity coincided with 
 the center of motion, the balance beam would not vibrate, 
 but would stand in a position of indifferent equilibrium, 
 whatever angular position might be given to its arms. 
 
 If the centre of gravity was above the axis of motion, 
 the balance would be in a condition of unstable equilib- 
 rium, and would overset by the slightest increase of 
 weight on either side, the center of gravity coming down 
 to the lowest point. But when it is beneath the axis of 
 motion, the balance vibrates like a pendulum, and neither 
 sets nor oversets. It is essential, therefore, that in all 
 these instruments the center of gravity should be below 
 the center of motion. And it might be shown that the 
 
 Give an instance of the application of the lever to magnifying small 
 motions. What is a balance ? What takes place if the center of gravity 
 coincides with the center of motion ? What is the effect when it is above 
 the axis of motion ? What when it is beneath ? With what does the 
 sensibility of the balance increase ? 
 
WEIGHING MACHINES. 
 
 131 
 
 sensibility of the balance, or, in other words, the small- 
 ness of the weight it will detect, becomes greater as 
 these two centers approach each other. 
 
 The different kinds of weighing-machines are either 
 modified levers or combinations of levers. Examples oc- 
 cur in the machine for weighing Fig. 145. 
 loaded carts, in the steelyard, 
 which is a lever of unequal arms, 
 and in the bent lever balance. 
 The latter is represented in Fig. 
 145. It consists of a bent lever, 
 ABC, the end of which, C, is 
 loaded with a fixed weight. This 
 lever works on a fulcrum, B, 
 supported on a pillar, H J. From 
 the arm, A, is suspended a scale- 
 pan, E, and to the pillar there is 
 affixed a divided scale, F G, over 
 which the lever moves. Through 
 B draw the horizontal line, G K, and let fall from it the 
 perpendiculars, A K, D C. Then, if B K and B D are 
 inversely proportional to the weight in the scale, E, and 
 the fixed weight, C, the balance will be in equilibrio ; 
 but if they are not, then the lever moves, C going farther 
 from the fulcrum, and stopping when equilibrium is at- 
 tained. The scale, F G, is graduated by previously put- 
 ting known weights in E. 
 
 LECTURE XXVIII. 
 
 THE PULLEY. Description of the Pulley. Laws of the 
 Lever apply to it. Use of the Fixed Pulley. The 
 Movable Pulley. Runners. Systems of Pulleys. 
 White's Pulley. 
 
 THE WHEEL AND AXLE. Law of Equilibrium. Advan- 
 tages over the Lever. Windlass. Capstan. Wheel- 
 work. Different kinds of TootJied-WJieels. 
 
 THE pulley is a wheel, round the rim of which a groove 
 is cut, in which a cord can work, and the center of which 
 
 Describe the bent lever balance and the steelyard, 
 sheave, and its block ? 
 
 What is a pulley, its 
 
132 THE FIXED PULLEY. 
 
 moves on pivots in a block. The wheel sometimes passes 
 under the name of a sheave. 
 
 By a fixed pulley we mean one which merely revolves 
 on its axis, but does not change its place. The power 
 is applied to one end of the cord and the weight to the 
 other. 
 
 Fig. 146. The action of the pulley may be 
 
 readily understood from that of the 
 lever. Let c, Fig. 146, be the axis 
 of the pulley, b the point to which 
 the weight is attached, a the point 
 of application of the power ; draw 
 the lines, c b, c a they represent 
 the arms of a lever and the law of 
 the equilibrium of a lever, therefore, 
 applies in this case also ; and, as 
 these arms are necessarily equal to 
 each other, the pulley will be in equilibrio when the 
 weight and power are equal. 
 
 If the direction in which the power is applied, instead 
 of being P a, is P' a, the same reasoning still holds good. 
 For, on drawing C a, as before, it is obvious that b c a 
 represents a bent lever of equal arms. The condition of 
 equilibrium is, therefore, the same. 
 
 The fixed pulley does not increase the power, but it 
 renders it more available, by permitting us to apply it in 
 any desired direction. 
 
 To prove the properties of the pulley experimentally, 
 hang to the ends of its oord equal weights ; they will re- 
 main in equilibrio. Or, if the power be increased, so as 
 to make the weight ascend, the vertical distances passed 
 over are equal. 
 
 The movable pulley is represented at Fig. 147. Its 
 peculiarity is that, besides the motion on its own axis, it 
 also has a progressive one. Let b be the axis of the pul- 
 ley, and to it the weight w is attached, the power is ap- 
 plied at a. Draw the diameter a c, then c is the fulcrum 
 of a c, which is in reality a lever of the third order in 
 which the distance, a c, of the power is twice that, b c, of 
 the weight. Consequently " the movable pulley doubles 
 
 What is a fixed pulley ? Describe the nature of its action. What is the 
 result of the action of the fixed pulley ? What is a movable pulley ? To 
 what extent does it increase the power ? 
 
SYSTEMS OF PULLEYS. 
 
 133 
 
 Fig. 147. 
 
 the effect of the power," and the dis- 
 tance traversed by the power is twice 
 that traversed by the weight. 
 
 A movable pulley is sometimes 
 called " a runner;" and, as*it would 
 be often inconvenient to apply the 
 power in the upward direction, as at 
 a P, there is commonly associated 
 with the runner a fixed pulley, which, 
 without changing the value of the 
 power, enables us to vary the direc- c 
 tion of its action. 
 
 Systems of pulleys are arrange- 
 ments of sheaves, movable and fix- 
 ed. 
 
 When one fixed pulley acts on a number of movable 
 ones, equilibrium is maintained, when the power and 
 
 Fi^. 148. Fig. 149. Fig-. 150. 
 
 i 
 
 What are systems of pulleys? 
 
134 THE WHEEL AND AXLE. 
 
 weight are to each other as 1 to that power of 2 which 
 equals the number of the movable pulleys. Thus, if 
 there be, as in Fig. 148, three movable pulleys, the 
 power is to the weight 
 
 as 1 : 2 3 that is 1:8; 
 
 consequently, on such a system, a given power will sup- 
 port an eightfold weight. 
 
 When several movable and fixed pulleys are employed, 
 as in Fig. 149, equilibrium is obtained when the power 
 equals the weight divided by twice the number of mov- 
 able pulleys. 
 
 In such systems of pulleys there is a great loss of power 
 arising from the friction of the sheaves against the sides 
 of the blocks, and on their axles. In White's pulley this 
 is, to a considerable extent, avoided. This contrivance 
 is represented in Fig. 150. It consists of several sheaves 
 of unequal diameters, all turned on one common mass, 
 and working on one common axis. The diameters of these, 
 in the upper blocks, are as the numbers 2, 4, 6, &c., and in 
 the lower 1, 3, 5, &c. ; consequently, they all revolve in 
 equal times, and the rope passes without sliding or scraping 
 upon the grooves. 
 
 THE WHEEL AND AXLE. 
 
 The wheel and axle consists of a cylinder, A, Fig. 151, 
 revolving upon an axis, and 
 having a wheel, R, of larger 
 diameter, immovably affixed 
 to it. The power is applied 
 to the circumference of the 
 wheel, the weight to that of 
 the axle. 
 
 The law of equilibrium is, 
 that " the power must le to 
 the weight as tlie radius of 
 the axle is to that of the 
 wheel" 
 
 This instrument is, evidently, nothing but a modifica- 
 tion of the lever; it may be regarded as a continuously 
 
 Give the law of equilibrium when one fixed pulley acts on a system of 
 movable ones. What is it when several movable and fixed ones are em- 
 ployed? Describe White's pulley and the difficulties it avoids. What is 
 meant by the Wtleel and axle '[ What is the law of its equilibrium ? 
 
THE WHEEL AND AXLE. 
 
 135 
 
 . 152. 
 
 acting lever. In its mode of action, the common lever 
 operates in an intermitting way, and, as it were, by small 
 steps at a time. A mass, which is forced up by a lever a 
 short distance, must be temporarily propped, and the 
 lever readjusted before it can be brought into action 
 again ; but the wheel and axle continues its operation 
 constantly in the same direction. 
 
 That this is its mode of ac- 
 tion may be understood from 
 considering Fig. 152, in which 
 let c be the common center of 
 the axle c b, and of the wheel 
 c a, a the point of application 
 of the power P, and b that of 
 the weight \V. Draw the line 
 a c b ; it evidently represents a 
 lever of the first order of which 
 the fulcrum is c, and from the 
 principles of the lever it is easy to demonstrate the law 
 of equilibrium of this machine, as just given. Further, it 
 is immaterial in what direction the power be applied, as 
 P' at the point a' for a' c b still forms a bent lever, and 
 the same principle still holds good. 
 
 Sometimes the wheel is Fi s- 154 - 
 replaced by a winch, as in 
 Fig. 153, it is then called a 
 windlass, if the motion is 
 vertical ; but if it be hori- 
 zontal, as in Fig. 154, the 
 machine is called a capstan. 
 
 Wheels and axles are often made to 
 act upon one another by the aid of cogs, as in clockwork 
 and mill machinery. In these cases the cogs on the pe- 
 riphery of the wheel take the name of teeth, those on the 
 axle the name of haves, and the axle itself is called a 
 pinion. 
 
 The law of equilibrium of such machines may be easily 
 demonstrated to be, that the power multiplied by the pro- 
 duct of the number of teeth, in all the icheels, is equal to the 
 weight multiplied by the product of the number of leaves 
 in all the pinions. 
 
 Describe its mode of action. What is a windlass and a capstan ? What are 
 teeth, leaves, and pinions ? What is the law of equilibrium of wheelwork? 
 
 Fi j 53 
 
136 
 
 WHEELWORK. 
 
 A system of wheel and pinion work is represented at 
 
 TT'.'rt. 1 K ^ T*- 4 a aror*r1 \T T>or*>ccn i*v 
 
 Fig. 155. 
 
 Fig. 155. It is scarcely necessary 
 to observe, that in it, as in all other 
 cases, the law of virtual velocities 
 holds good the power multiplied 
 by the velocity of the power is 
 equal to the weight multiplied by 
 the velocity of the weight. 
 
 In the construction of such ma- 
 chinery attention has to be paid to 
 the form of the teeth, so that they 
 may not scrape or jolt upon one another. Several of them 
 should be in contact at once, to diminish the risk of frac- 
 ture and the wear. 
 
 If the teeth of a wheel be in the direction of radii 
 from its center it is called a spur-wheel. 
 
 If the teeth are parallel to the axis of the wheel it is 
 called a crown-wheel. 
 
 If the teeth are oblique to the axis of the wheel it is 
 called a beveled-wheel. 
 
 By combining these different forms of wheel suitably 
 together, the resulting motion can be transferred to any 
 required plane. Thus, by a pair of beveled-wheels mo- 
 tion round a vertical axis may be transferred to a hori- 
 zontal one, or, indeed, one in any other direction. 
 
 When a pinion is made to work on a toothed-bar, it 
 constitutes a rack. This contrivance is under the same 
 law as the wheel and axle. 
 
 What precautions have to he used as respects the form of teeth ? What 
 is a spur, a crown, and a beveled-wheel ? How may motion be trans- 
 ferred to different planes ? What is a rack ? 
 
THE INCLINED PLANE. 137 
 
 LECTURE XXIX. 
 
 THE INCLINED PLANE. Description of the Inclined Plane. 
 Modes of Applying the Power. Conditions of Equi- 
 librium when the Power is Parallel to the Plane or Par- 
 allel to the Base. Position of Greatest Advantage. 
 
 THE WEDGE. Description and Mode of using it. 
 
 THE SCREW. -Formation of the Screw. 
 
 BY the inclined plane we mean an unyielding plane 
 surface inclined obliquely to the resist- Fig. 156 
 
 ance to be overcome. 
 
 In Fig. 156, A C represents the inclined 
 plane ; the angle at A is the elevation of 
 the plane ; the line A C is the length, C 
 B is the height, A B the base. 
 
 In the inclined plane the power may 
 be applied in the following directions : 
 
 1. Parallel to the plane ; 
 
 2. Parallel to its base ; 
 
 3. Parallel to neither of these lines. 
 
 As in the former cases, so in this ^the conditions of 
 the equilibrium may be deduced from those of the lever. 
 
 Let us take the first instance, when the power is ap- 
 plied parallel to the inclined plane. Let Q, Fig. 156, be 
 a body placed upon the plane, A C, the height of which 
 is B C, and the base A B. The weight of this body acts 
 in the vertical direction, a W; the body rests on the point, 
 c, as on a fulcrum ; and the power, P, under the supposi- 
 tion, acts on Q, in the direction a P. From the fulcrum, 
 c, draw the perpendicular, c b, to the line of direction of 
 the weight, a W ; draw also c a. Then does b c a repre- 
 sent a bent lever, the power being applied to the point 
 a, and the weight at the point, b; and, therefore, the 
 power is to the weight as b c is to a c; but the triangles, a 
 
 Describe the inclined plane. What is the angle of elevation, the length, 
 the height, and the base ? in how many directions may the power be ap 
 plied ? 
 
138 THE INCLINED PLANE. 
 
 I c, A B C, are similar to each other. Therefore, we ar- 
 rive at the following law: 
 
 When tlie power acts in a direction parallel to the in- 
 clined plane, it will be in equilibria with the weight when 
 it is to the weight as the perpendicular of the plane is to its 
 length. 
 
 In a similar manner it may be shown that when the 
 power acts parallel to the base it will be in equilibria with 
 the weight, if it be to the weight as the perpendicular of the 
 plane is to its base. 
 
 In different inclined planes the power increases as the 
 height of the plane, compared with its length, diminishes, 
 and the best direction of action is parallel to the inclined 
 plane. This is very evident from the consideration that 
 if the power be directed above the plane a portion of it 
 is expended in lifting the weight off the plane, while the 
 diminished residue draws it up. If it be directed down- 
 ward a part is expended in pressing the weight upon the 
 plane, and the diminished residue draws it up. There- 
 fore, if the power acts parallel to the plane, it operates 
 under the most advantageous condition. 
 
 Fig. 157. The laws of the inclined 
 
 plane may be illustrated by 
 an instrument, such as is rep- 
 resented in Fig. 157, in which 
 A c A' c is the plane, which 
 may be set at any angle. It 
 works upon an axis, A A'. 
 Upon the plane a roller, e, 
 moves. It has a string passing over a pulley, d, and ter- 
 minating in a scale-pan, f. in which weights may be 
 placed. The direction of the string may be varied, so as 
 to be parallel to the plane, or the base, or any other di- 
 rection. 
 
 The inclined plane is used for a variety of purposes 
 very frequently for facilitating the movements of heavy 
 loads. 
 
 THE WEDGE. 
 
 The wedge may be regarded as two inclined planes 
 
 What is the law of equilibrium when the power acts parallel to the 
 plane? What is it when the power acts parallel to the hase .' For what 
 purposes is the inclined plane used ? Describe the wedge. 
 
THE WEDGE. 
 
 139 
 
 Kg. 158. 
 A 
 
 \ 
 
 laid base to base A C D being one, and 
 A B D being the other. The planes B D 
 and C D constitute the sides or faces of the 
 wedge ; B C is its back, and A D its length. 
 The mode of employing the wedge is not 
 by the agency of pressure, but of percus- 
 sion. Its edge being inserted into a fissure, 
 the wedge is driven in by blows upon its 
 back. It is kept from recoiling by the fric- 
 tion of its sides against the surfaces past which it Fig. 159. 
 has been forced. 
 
 This mode of application of the wedge prevents 
 us from comparing its theory with that of the in- 
 clined plane a power to which it has so much 
 Fig. 161. external resemblance. 
 
 The power of the wedge in- 
 creases as the length of its back, 
 compared with that of its sides, is dimin- 
 ished. As instances of its application, we 
 may mention the splitting of timber, the 
 raising of heavy weights, such as ships. 
 Different cutting-instruments, as chisels, 
 &c., act in consequence of their wedge- 
 shaped form. 
 
 THE SCREW. 
 
 If we take a piece of paper cut into a 
 long, right-angled triangle, Fig. 160, and 
 wind it about a cylinder Fig. 161, so that 
 the height C B of the triangle is parallel 
 to the axis, the length A C will trace a 
 screw-line on the surface. The same re- 
 sults if we take a cylinder and wind upon 
 it a flexible cord, so that the strands of the 
 cord uniformly touch one another. 
 
 In any screw, the line which is thus 
 traced upon the cylinder goes under the 
 name of the "worm," or "thread," and 
 A each complete turn that it makes is called 
 
 Fig. 160, 
 
 On what principle does it act ? On what does its power depend ? How 
 may a screw-thread be represented 1 
 
140 THE SCREW. 
 
 " a spire." The distance from one thread to another, 
 which, of course, must be perfectly uniform throughout 
 the screw, is called the breadth of the worm. 
 
 In most cases the screw requires a corresponding 
 cavity in which it may work; this passes under the 
 name of " a nut." Sometimes the nut is caused to 
 move upon the screw, and sometimes the screw in 
 the nut. In either case the movable part requires a 
 lever to be attached, to the end of which the power is 
 applied. 
 
 The law of equilibrium of the screw is, that " the 
 power is to the weight as the breadth of the worm is to the 
 circumference described by that point of the lever to which 
 the power is attached. 
 
 When the end of the screw is advancing through a 
 nut, this law evidently becomes that the power is to the 
 weight as the circumference described by the power is to the 
 space through which the end of the screw advances. It is 
 obvious, therefore, that the force of the screw increases 
 as its threads are finer, and as the lever by which it is 
 urged is longer. 
 
 When the thread of a screw works in the teeth of a 
 Fig 162. wheel, as shown in Fig. 162, it 
 
 constitutes an endless screw. An 
 important use of this contrivance 
 is in the engine for dividing grad- 
 uated circles. The screw is also 
 used to produce slow motions, or to 
 measure by the advance of its point, 
 minute spaces. In the spherome- 
 ter, represented in Fig. 5, we have an example of its 
 use. 
 
 For all these purposes where slow motions have to be 
 given, or minute spaces divided, the efficacy of the screw 
 will increase with the closeness of its thread. But there 
 is soon a practical limit attained ; for, if the thread be too 
 fine it is liable to be torn off. To avoid this, and to attain 
 those objects almost to an unlimited extent, Hunter's 
 screw is often used. It may be understood from Fig. 
 163. It consists of a screw, A, working in a nut, C. 
 
 What is the worm and the spire ? What is a nut ? What is the law of 
 equilibrium of the screw? When the end of the screw advances what 
 does this law become ? Describe an endless screw. 
 
PASSIVE FORCES. 
 
 To a movable piece, D, a second 
 screw, B, is affixed. This screw 
 works in the interior of A, which 
 is hollow, and in which a corre- 
 sponding thread is cut. While, 
 therefore, A is screwed down- 
 ward, the threads of B pass up- 
 ward, and the movable piece, D, 
 advances through a space which 
 is equal to the difference of the 
 breadth of the two screws. In 
 this way very slow or minute 
 motions may be obtained with a 
 screw, the threads of which are 
 coarse. 
 
 141 
 
 Fig. 163. 
 
 LECTURE XXX. 
 
 OF PASSIVE OR RESISTING FORCES. Difference 'between 
 the Theoretical and Actual Results of Machinery. Of 
 Impediments to Motion. Friction. Sliding and Roll- 
 ing Friction. Coefficient of Friction. Action of Un- 
 guents. Resistance of Media. General Phenomena of 
 Resistance. Rigidity of Cordage. 
 
 IT has already been stated, in the foregoing Lectures, 
 that the properties of machinery are described without 
 taking into account any of those resisting agencies which 
 so greatly complicate their action. The results of the 
 theoiy of a machine in this respect differ very widely from 
 its practical operation. There are resisting forces or 
 impeding agencies which have thus far been kept out of 
 view. We have described levers as being inflexible, the 
 cords of pulleys as perfectly pliable, and machinery, gen- 
 erally, as experiencing no friction. In the case of one of 
 the powers, it is true that this latter resisting force must 
 necessarily be taken into account ; for it is upon it that 
 the efficacy of the wedge chiefly depends. 
 
 Describe Hunter's screw. What is meant by passive or resisting forces ? 
 Why does the theoretical action of a machine differ from its practical 
 operation ? 
 
142 FRICTION. 
 
 So, too, in speaking of the motion of projectiles, it has 
 been stated that the parabolic theory is wholly departed 
 from, by reason of the resistance of the air; and that not 
 only is the path of such bodies changed, but their range 
 becomes vastly less than what, upon that theory, it should 
 be. Thus, a 24-pound shot, discharged at an elevation 
 of 45, with a velocity of 2000 feet per second, would 
 range a horizontal distance of 125,000 feet were it not 
 for the resistance of the air ; but through that resistance 
 its range is limited to about 7300 feet. 
 
 Of these impediments to motion or passive or resisting 
 forces, three leading ones may be mentioned. They are, 
 1st, friction; 2d, resistance of the media moved through ; 
 3d, rigidity of cordage. 
 
 OF FRICTION. 
 
 Friction arises from the adhesion of surfaces brought 
 into contact, and is of different kinds as sliding friction, 
 when one surface moves parallel to the other, rolling 
 friction, when a round body turns upon the surface of 
 another. 
 
 By the measure of friction, we mean that part of the 
 weight of the moving body which must be expended in 
 overcoming the friction. The fraction which expresses 
 this is termed the coefficient of friction. Thus, the coef- 
 ficient of sliding friction in the case of hard bodies, and 
 when the weight is small, ranges from one seventh to one 
 third. 
 
 It has been proved by experiment that friction increases 
 as the weight or pressure increases, and as the surfaces 
 in contact are more extensive, and as the roughness is 
 greater. With surfaces of the same material it is nearly 
 proportional to the pressure. The time which the sur- 
 faces have been in contact appears to have a considerable 
 influence, though this differs much with surfaces of differ- 
 ent kinds. As a general rule, similar substances give rise 
 to greater friction than dissimilar ones. 
 
 On the contrary, friction diminishes as the pressure is 
 
 Give an illustration of resisting force in the case of projectiles. How 
 many of these impediments may be enumerated ? What varieties of fric- 
 tion are there ? What is the coefficient of friction ? Mention some of the 
 conditions which increase friction. 
 
RESISTANCE OF MEDIA. 143 
 
 less, as the polish of the moving surfaces is more perfect, 
 and as the surfaces in contact are smaller. It may also 
 be diminished by anointing the surfaces with some suita- 
 ble unguent or greasy material. Among such substances 
 as are commonly used are the different fats, tar, and black 
 lead. By such means, friction may be reduced to one 
 fourth. 
 
 Of the friction produced by sliding and rolling motions, 
 the latter, under similar circumstances, is far the least. 
 This partly arises from the fact that the surfaces in con- 
 tact constitute a mere line, and partly because the asperi- 
 ties are not abraded or pushed aside before motion can 
 ensue. The nature of this distinction may be clearly un- 
 derstood by observing what takes place when two brushes 
 with stiff bristles are moved over one another, and when 
 a round brush is rolled over a flat one. In this instance, 
 the rolling motion lifts the resisting surfaces from one 
 another ; in the former, they require to be forcibly pushed 
 apart. 
 
 Though, in many instances, friction acts as a resisting 
 agency, and diminishes the power we apply to machines, 
 in some cases its effects are of the utmost value. Thus, 
 when nails or screws are driven into bodies, with a view 
 of holding them together, it is friction alone which main- 
 tains them in their places. The case is precisely the 
 same as in the action of a wedge. 
 
 RESISTANCE OF MEDIA. 
 
 A great many results in natural philosophy illustrate 
 the resistance which media offer to the passage of bodies 
 through them. The experiment known under the name 
 of the guinea and feather experiment establishes this for 
 atmospheric air. In a very tall air-pump receiver there 
 are suspended a piece of coin and a feather in such a way 
 that, by turning a button, at a, Fig. 164, the piece on 
 which they rest drops, and permits them to fall to the 
 pump-plate. Now, if the receiver be full of atmospheric 
 air, on letting the objects fall, it will be found that, while 
 the coin descends with rapidity, and reaches, in an instant, 
 
 Mention some that diminish it. What is the difference of effect be- 
 tween sliding and rolling friction? Give an illustration of this. Under 
 what circumstances does advantage arise from friction ? 
 
144 
 
 RESISTANCE OF MEDIA. 
 
 the pump-plate, the feather comes down 
 leisurely, being buoyed up by the air, and 
 the speed of its motion resisted. But if the 
 air is first extracted by the pump, and the 
 objects allowed to fall in vacuo, both pre- 
 cipitate themselves simultaneously with equal 
 ve l c ity> ai) d accomplish their fall in equal 
 times. 
 
 In the vibrations of a pendulum, the final 
 stoppage is due partly to friction and partly 
 to this cause. And in the case of motions 
 taking place in water, we should, of course, 
 expect to find a greater resistance arising 
 from the greater density of that liquid. 
 
 The resisting force of a medium depends up- 
 on its density, upon the surface which the mov- 
 ing body presents, and on the velocity with which it moves. 
 Water, which is 800 times more dense than air, will 
 offer a resistance 800 times greater to a given motion. 
 Of the two mills represented in Fig. 36, that which goes 
 with its edge first runs far longer than that which moves 
 with its plane first. We are not, however, to understand 
 that the eifect of the medium, on a body moving through 
 it, increases directly as the transverse section of the bodv; 
 for a great deal depends upon its figure. A wedge, going 
 with its edge first, will pass through water more easily 
 than if impelled with its back first, though, in both in- 
 stances, the area of the transverse section is of course the 
 same. It is stated that spherical balls encounter one 
 fourth less resistance from the air than would cylinders 
 of equal diameter; and it is upon this principle that the 
 bodies of fishes and birds are shaped, to enable them to 
 move with as little resistance as may be through the me- 
 dia they inhabit. 
 
 The resistance of a medium increases with the velocity 
 with which a body moves through it, being as the square 
 of the velocity, so long as the motion is not too rapid ; but 
 when a high velocity is reached, other causes come into 
 operation, and disturb the result. 
 
 Describe the guinea and feather experiment. What does it prove? 
 What is the cause of the stoppage of a pendulum ? How does the density 
 of a liquid affect its resistance ? How is resistance affected by figure ? 
 How by velocity? 
 
RIGIDITY OF CORDAGE. 145 
 
 As with friction, so with the resistande of media, a 
 great many results depend on this impediment to mo- 
 tion ; among such may be mentioned the swimming of 
 fish through water, and the flight of birds through the 
 air. It is the resistance of the air which makes the para- 
 chute descend with moderate velocity downward, and 
 causes the rocket to rise swiftly upward. 
 
 RIGIDITY OF CORDAGE. 
 
 In the action of pulleys, in machinery in which the use of 
 cordage is involved, the rigidity of 
 that cordage is an impediment to 
 motion. When a cord acts round 
 a pulley, in consequence of imper- 
 fect flexibility, it obtains a leverage 
 on the pulley, as may be under- 
 stood from Fig. 165, in which let 
 C K D be the pulley working on a 
 pivot at O ; let A and B be weights 
 suspended by the rope A C K D B. 
 From what has been said respect- 
 ing the theory of the pulley, the 
 action of the machine may be regarded as that of a lever, 
 COD, with equal arms, CO, O D. Now, if the cord 
 were perfectly inflexible, on making the weight A descend 
 by the addition of a small weight to it, it would take the 
 position at A', the rope being a tangent to the pulley at 
 C' ; at the same time B, ascending, would take the position 
 B', its cord being a tangent at D'. From the new posi- 
 tions, A' and B', which the inflexible cord is thus sup- 
 posed to have assumed, draw the perpendiculars, A 7 E, 
 B' F., then will O E, O F, represent the arms of the lever 
 on which they act a diminished leverage on the, side of 
 the descending, and an increased leverage on the side of 
 the ascending weight is the result. 
 
 In practice the result does not entirely conform to the 
 foregoing imaginary case, because cords are, to a certain 
 extent, flexible. As their pliability diminishes, the dis- 
 turbing effect is greater. The degree of inflexibility de- 
 
 Mention some of the valuable results which depend on it. Give a general 
 lage 
 
 O 
 
 G 
 
 idea of the action of rigidity of cordage What takes place in case of ab- 
 solute inflexibility, as in Fig. 165? On what does inflexibility depend ? 
 
146 RIGIDITY OF CORDAGE. 
 
 pends on many casual circumstances, such as dampness 
 or dryness, or the nature of the substance of which they 
 are made. Inflexibility increases with the diameter of a 
 cord, and with the smallness of the pulley over which it 
 runs. 
 
UNDULATIONS. 147 
 
 OF UNDULATORY MOTIONS. 
 
 LECTURE XXXI. 
 
 OF UNDULATIONS. Origin of Undulations. Progressive 
 and stationary Undulation. Course of a progressive 
 Wave. Nodal Points. Three different kinds of Vibra- 
 tion. Transverse Vibration of a Cord. Vibrations of 
 Rods. Vibrations of elastic Planes. Vibrations of 
 Liquids. Waves on Water. 
 
 WHEN an elastic body is disturbed at any point, its 
 particles gradually return to a position of rest, after exe- 
 cuting a series of vibratory movements. Thus, when a 
 glass tumbler is struck by a hard body, a tremulous mo- 
 tion is communicated to its mass, which gradually declines 
 in force until the movement finally ceases. 
 
 In the same manner a stretched cord, which is drawn 
 aside at one point, and then suffered to go, is thrown into 
 a vibratory or undulatory movement ; and, according as 
 circumstances differ, two different kinds of undulation 
 may be established, 1st, progressive undulations ; 2d, sta- 
 tionary undulations. % 
 
 In progressive un Fig. 166. 
 dulations the vibra- 
 ting particles of a body 
 communicate their mo- 
 tion to the adjacent JLm ^ ^*~ > e 
 
 particles ; a succes- 
 sive propagation of < ^ 
 
 movement, therefore, ~ " G 
 
 ensues. Thus, if a 
 
 cord is fastened at one Wm. ^^^^^ sg 
 
 end, and the other is 
 
 moved up and down, y m . **"* ^ ^ e 
 
 a wave or undulation, 
 
 m D n E o, is produced. The part, m D n t is the elevation 
 
 Under what circumstances do vibratory movements arise? How many- 
 kinds of undulations are there ? Describe the nature of a progressive un- 
 dulation. 
 
148 
 
 KINDS OF VIBRATIONS. 
 
 of the wave, D being the summit, n E o is the depression, 
 E being the lowest point, D p is the height, q E the depth, 
 and m o the length of the wave. 
 
 But, under the circumstances here considered, the mo- 
 ment this wave has formed, it passes onward, and suc- 
 cessively assumes the positions indicated at I, II, III. 
 When it has arrived at the other end of the cord, it at 
 once returns with an inverted motion, as shown at IV 
 and V. This, therefore, is a progressive undulation. 
 Again, instead of the cord receiving one impulse, let it 
 Fig. 167. be agitated equally at equal inter- 
 
 vals of time; it will then divide itself, 
 as shown in Fig. 167, into equal 
 elevations and depressions with in- 
 tervening points, m n, which are at rest. These are sta- 
 tionary undulations, and the points are called nodal points. 
 The agents by which undulatory movements are estab- 
 lished are chiefly elasticity and gravity. It is the elas- 
 ticity of air which enables it to transmit the vibratory 
 motions which constitute sound, and, for the same reason, 
 steel rods and plates of glass may be thrown into musical 
 vibrations. In the case of threads and wires, a sufficient 
 degree of elasticity may be given by forcibly stretching 
 them. Waves on the surface of liquids are produced by 
 the agency of gravity. 
 
 There are three different kinds of vibrations into which 
 a stretched string may be thrown : 
 transverse, longitudinal, and twisted. 
 These may be illustrated by the in- 
 strument represented at Fig. 168. 
 It consists of a piece of spirally- 
 twisted wire, stretched from a frame 
 by a weight. If the lower end of the 
 wire be secured by a clamp, on pull- 
 ing the wire in the middle, and then 
 letting it go, it executes transverse 
 vibrations. If the weight be gently 
 lifted, and then let fall, the wire per- 
 forms longitudinal vibrations ; and if 
 
 What is meant by the height, depth, and length of a wave '/ Describe 
 the stationary vibration. By what agents are undulatory motions estab- 
 lished ? How may elasticity be communicated to cords? Into how 
 many kinds of vibration may a string be thrown ? How may this be illus- 
 trated by the apparatus represented in Fig. 168 ? 
 
 Fig. 168. 
 
TRANSVERSE VIBRATIONS. 149 
 
 the weight be twisted round, and then released, we have 
 rotatory vibrations. 
 
 If we take astring, a b, Fig.I69, and having stretched it be- 
 tween two fixed points, a Fi 169 
 and b, draw it aside, and 
 then let it go, it executes ^ 
 transverse vibrations, as a <^T 
 has already been de- 
 scribed. The cause of 
 
 its motion, from the position we have stretched it to, is its 
 own elasticity. This makes it return from the position, 
 a c b, to the straight line, afb, with a continually accel- 
 erated velocity ; but when it has arrived in afb, it cannot 
 stop there, its momentum carrying it forward to a d b, with 
 a velocity continually decreasing. Arrived in this position, 
 it is, for a moment, at rest ; but its elasticity again impels 
 it as before, but in the reverse direction to afb; and so 
 it executes vibrations on each side of that straight line 
 until it is finally brought to rest by the resistance of the 
 air. One complete movement, from a c b to a d b and 
 back, is called a vibration, and the time occupied in per- 
 forming it the time of an oscillation. 
 
 The vibratory movements of such a solid are isochro- 
 nous, or performed in equal lines. They increase in 
 rapidity with the tension that is, with the elasticity 
 being as the square root of that force. The number of 
 vibrations in a given time is inversely as the length of the 
 string, and also inversely as its diameter. 
 
 The vibrations of solid bodies may be studied best un- 
 der the divisions of cords, rods, planes, and masses. The 
 laws of the vibrations of the first are such as we have just 
 explained. 
 
 In rods the transverse vibrations are isochronous, and in 
 a given time are in number inversely as the squares of the 
 lengths of the vibrating parts. Thus, if a rod makes two 
 vibrations in one second, if its length be reduced to half 
 it will make four times as many that is, eight ; if to one 
 fourth, sixteen times as many that is, thirty-two, &c. 
 The motion performed by vibrating-rods is often very corn- 
 Describe the transverse vibration of a string. What is a vibration? 
 What is the time of an oscillation ? What is meant by isochronous vibra- 
 tions ? How are the vibrations of solid bodies divided ? What are the 
 laws for the vibrations of rods ? 
 
150 
 
 VIBRATIONS OF PLANES. 
 
 Fig 170. plex. Thus, if a bead be fastened on the free ex- 
 tremity of a vibrating steel rod, Fig. 170, it will 
 exhibit in its motions a curved path, as is seen at 
 c. Rods may be made to exhibit nodal points. 
 The space between the free extremity and the first 
 nodal point is equal to half the length contained 
 between any two nodal points, but it vibrates with 
 the same velocity. Thus, a, Fig. 171, being the 
 fixed, and b the free end Fig. rri. 
 
 of such a rod, the part 
 L ~~~*' between b and c is half a 
 the distance, c c'. 
 
 When elastic planes vibrate they exhibit nodal lines, 
 answering to the nodal points in linear vibrations ; and if 
 the plane were supposed to be made up of a series of 
 rods, these lines would answer to their nodal points. By 
 them the plane is divided into spaces the adjacent ones 
 being always in opposite phases of vibrations, as shown 
 Fig- 172. by the signs + and -7 in Fig. 
 
 172, where A B is the vibrating 
 plane. The dimensions of these 
 a spaces are regulated in the same 
 B way as the internodes of vibra- 
 ting-rods that is, the outside 
 ones, a b a b, are always half 
 the size of the interior. The 
 relation of these spaces, and 
 positions of the nodal lines may 
 be determined by making a glass 
 plate covered with dry sand vibrate. 
 
 When the surface of a liquid, as water, is touched, a 
 wave arises at the disturbed point, and propagates itself 
 into the unmoved spaces around, continually enlarging as 
 it goes, and forming a progressive undulation. 
 
 A number of familiar facts prove that the apparent ad- 
 vancing motion of the liquid on which waves are passing 
 is only a deception. Light pieces of wood are not hur- 
 ried forward on the surface of water, but merely rise up 
 and sink down alternately as the waves pass. The true 
 
 What are they for elastic planes ? How may the nodal lines be made 
 visible m the latter case ? How are waves on liquid surfaces formed ? 
 Under, such circumstances does the liquid actually advance, or is it sta- 
 
WAVES ON WATER. 151 
 
 nature of the motion is such that each particle, at the sur- 
 face of the undulating liquid, describes a circle in a verti- 
 cal plane, and in the direction in which the wave is ad- 
 vancing, the movement being propagated from each to its 
 next neighbor, and so on. And as a certain time must 
 elapse for this transmission of motion, the different parti- 
 cles will be describing different points of their circu^r 
 movement at the same moment. Some will be at the 
 highest part of their vertical circle when others are in an 
 intermediate position, and others at the lowest, giving rise 
 to a wave, which advances a distance equal to its own 
 length, while each particle performs one entire revolu- 
 tion. Thus, in Fig. 173, let there be eight particles of 
 
 Fig. 173. 
 
 water on the surface, a m, which, by some appropriate dis- 
 turbance, are made to describe the vertical circles repre- 
 sented at a b c d e f g //, moving in the direction repre- 
 sented by the darts, and let each one of these commence 
 its motion one eighth of a revolution later than the one 
 before it. Then, at any given moment, when the first one, 
 a, is in the position marked a, the second, b, will be in the 
 position marked 7, c at 6, d at 5, e at 4,y at 3, g at 2, h at 
 1 ; but m will not yet have begun to move. If, therefore, 
 we connect these various points, #7654321 w, together 
 by a line, that line will be on the surface of the wave, the 
 length of which is a m, the height or depth of which is 
 equal to the radius of the circle of each particle's revolu- 
 tion, and the time of passage through the length of one 
 wave will be equal to the time of the revolution of each 
 particle. 
 
 What is the true nature of the motion ? Describe the illustration, 
 Fig. 173. 
 
152 REFLEXION OF WAVES. 
 
 LECTURE XXXII. 
 
 UNDULATIONS (continued). Law of the Reflection of 
 Undulations. Applied in the case of a Plane , a Circle, 
 an Ellipse, a Parabola. Case of a Circular Wave on 
 a Plane. Interference of Waves. Inflexion of Waves. 
 Intensity of Waves. Method of Combining Systems 
 of Waves. 
 
 BY a ray of undulation we mean a line drawn from the 
 origin of a wave in the direction in which any given point 
 of it is advancing. A wave is said to be incident when 
 it falls on some resisting surface, and reflected when it 
 recoils from it. Incident rays are those drawn from the 
 origin toward the resisting surface, and reflected rays 
 those expressing the path of the undulating points after 
 their recoil. The angle of incidence is the angle which 
 an incident wave makes with a perpendicular drawn to 
 the surface of impact ; the angle of reflexion is the angle 
 Fig. 174. made by the reflected ray and the same per- 
 b /a pendicular. Thus, let c be a resisting sur- 
 iace of any kind, a c an incident ray, c b 
 f ' a perpendicular to the point of impact of 
 the wave, c d the reflected ray. Then a c b 
 is the angle of incidence, and deb the angle 
 of reflexion. 
 
 The general law for the reflexion of waves is, that " all 
 the points in a wave will be reflected from the surface of 
 the solid under the same angle at which they struck it." 
 
 If, therefore, parallel rays fall on a plane surface, they 
 will be reflected parallel ; if diverging, they will be re- 
 flected diverging; and if converging, converging. 
 
 If a circular wave advances from the center of a cir- 
 cular vessel, each ray falls perpendicularly on the surface 
 of the vessel, and is reflected perpendicularly that is to 
 say, back in the line along which it came. The waves, 
 
 What is meant by a ray of undulation ? What by incident and reflected 
 rays ? What is the angle of incidence, and what that of reflexion ? What 
 is the law of reflexion ? How does this apply in the case of plane sur- 
 faces ? What is the path of circular waves advancing from the center of 
 a circular vessel after reflexion ? 
 
REFLEXION OF WAVES. 
 
 153 
 
 Fig. 
 
 Fig. 176. 
 
 therefore, all return to the center from which they origi- 
 nated. 
 
 If undulations proceed from one focus of an ellipse, 
 they will, after reflection, converge to the other focus. 
 
 If a surface be a parabola, rays 
 diverging from its focal point, a, 
 will, after reflexion, pass in par- 
 allel lines, b d] c d, e d. Or if 
 the rays impinge in parallel lines, 
 they will, after reflexion, con- 
 verge to the focus. 
 
 When diverging rays of a cir- 
 cular wave fall upon a plane surface, their path, after re- 
 flexion is such as it would have been had they originated 
 from a point on the opposite side of the plane, and as far 
 distant as the point of origin itself. Thus, let c be the 
 origin of a circular wave, 
 d a g, which impinges 
 on a plane, ef, after re- 
 flexion this wave will be 
 found at e kf, as though 
 it had originated at c', a 
 point on the opposite side 
 of ef, as far as c, in front 
 of it. Now, the parts of 
 the circular wave, dag, 
 do not all impinge on the 
 plane at the same time, 
 but that at a, which 
 falls perpendicularly, im- 
 pinges first, and is first reflected ; the ray at d has to go 
 still through the distance, d e, before reflexion takes 
 place; but, in this space of time, the ray at a will have 
 returned back to k; and, in the same way, it may be 
 shown that the intermediate rays will have returned to 
 intermediate positions, and be found in the line e k f, 
 symmetrically situated, with respect to the line e n f, in 
 which they would have been had they not fallen on the 
 plane. And it further follows that the center, c', of the 
 circular wave, e kf, is as far from ef as is the centre, c, 
 of the circular wave, e nf, but on the opposite side. 
 
 How are rays reflected that come from one of the foci of an ellipse ? How 
 is it in the case of a parabola. What is the principle illustrated in Fig, 176 ? 
 
154 INTERFERENCE AND INFLEXION. 
 
 By interference we mean that two or more waves have 
 encountered one another, under such circumstances as to 
 destroy each other's effect. If on water two elevations 
 or two depressions coincide, they conspire ; but when an 
 elevation coincides with a depression, interference takes 
 place, arid the surface of the fluid remains plane. Waves 
 which have thus crossed one another continue their mo- 
 tion unimpaired. 
 
 If two systems of waves of the same length encounter 
 each other, after having come through paths of equal 
 length, they will not interfere ; nor will they interfere, 
 even though there be a difference in the length of their 
 paths, provided that difference be equal to one whole wave, 
 or two, or three, &c. 
 
 But if two systems of waves of equal length encounter 
 each other after having come through paths of unequal 
 length, they will interfere, and that interference will be 
 complete when the difference of the paths through which 
 they have come is half a wave, or one and a half, two 
 and a half, three and a half, &c. 
 
 When a circular wave impinges on a solid in which 
 Fig. 177. there is an opening, as at a, b, Fig. 
 
 177, the wave passes through, and is 
 propagated to the spaces beyond ; 
 but other waves arise from a b, as 
 centers, and are propagated as repre- 
 sented at c d e f. This is the in- 
 flexion of waves, and these new 
 waves intersecting one another and 
 the primitive one, give rise to inter- 
 ferences. 
 
 We have now traced the chief phenomena of vibrations 
 in solids and on the surface of liquids. It remains to do 
 the same for elastic bodies, such as gases. 
 
 When any vibratory movement takes place in atmos- 
 pheric air, the impulse communicated to the particles 
 causes them to recede a certain distance, condensing those 
 that are before them ; the impulse is finally overcome by 
 the resistance arising from this condensation. There, 
 
 What is meant by the interference of waves ? When will two systems 
 of waves not interfere ? When will they interfere ? What is meant by 
 the inflexion of waves ? What are the phenomena of vibrations in elastic 
 media, as atmospheric air ? 
 
INTERFERENCE OF WAVES. 155 
 
 therefore, arises a sphere of air, the superficies or shell 
 of which has a maximum density. Reaction now sets in, 
 the sphere contracts, and the returning particles come to 
 their original positions. But as a disturbance on the sur- 
 face of a liquid gives origin to a progressive wave, so does 
 the same thing take place in the air. 
 
 By the intensity of vibration of a wave we mean the 
 relative disturbance of its moving particles, or the mag- 
 nitude of the excursions they make on each side of their 
 line of rest. Thus, on the surface of water we may have 
 waves " mountains high," or less than an inch high ; the 
 intensity of vibration in the former is correspondingly 
 greater than in the latter case. 
 
 In aerial waves, precisely as in the surface-waves of 
 water, interference arises under the proper conditions. 
 Thus, let a m p h, Fig. 178, be a wave advancing toward 
 
 c, arid let m n, o p be the intensity of its vibration, or the 
 maximum distances of the excursions of its vibrating par- 
 ticles. Then suppose a second wave, originating at b (a 
 distance from a precisely equal to one wave length), the 
 intensity of vibration of which is represented by q r. The 
 motions of this second wave coinciding throughout its 
 length with the motions of the first, the force of both sys- 
 tems is increased. The intensity, therefore, of the wave, 
 arising from their conjoint action at any point, q will be 
 equal to the sum of their intensities, q r, q s that is, it 
 will be q t, and for any other point, v, it will be equal to 
 the sum of v w and v u that is, v x. So the new wave 
 will be represented by b t g x h. 
 
 Now let things remain as before, except that the point 
 of impact of the second wave, instead of being one whole 
 wave from , is only half a wave, the effects on any parti- 
 
 What is meant by the intensity of vibration ? Trace the phenomena 
 of interference represented in Figs. 178 and 179 respectively. 
 
156 
 
 INTERFERENCE OF NAVES, 
 
 cle, such as q, take place in opposite directions, the sec- 
 ond wave moving it with the intensity and direction q 
 
 fif. 17*. 
 
 r, the first with q * the resultant of its movement in in- 
 tensity and direction, will, therefore, be the difference of 
 these quantities that is, q t. And the same reasoning 
 continued gives, for the wave resulting from this conjoint 
 action, 6 t g x k c. 
 
 Under the circumstances given in Fig. ITS. the systems 
 of waves increase each other's force : under those of $f. 
 179, they diminish it : or if equal to one another counter- 
 act completely, and total interference results, 
 
 Waves in the air, as they expand, have their superfi- 
 cies continually increasing, as the squares of their radii 
 of distance from the original point of disturbance. Hence 
 the effect of all such waves is to diminish as the squares 
 of the distances incress 
 
 -v c^5 :-e 
 
ACOUSTICS. 157 
 
 THE LAWS OF SOUND. 
 
 ACOUSTICS. 
 
 LECTURE XXXIII. 
 
 PRODUCTION OF SOUND. The Note Depends on Frequen- 
 cy of Vibration. Distinguishing Powers of the Ear. 
 Soniferous Media. Origin of Sounds in the Air. Elas- 
 ticity Required and Given in the Case of Strings by 
 Stretching. Rate of Velocity of Sounds. All Sounds 
 Transmitted with Equal Speed. Distances Determined 
 by it. High and Low Sounds. Three Directions of 
 Vibration. Intensity of Sound. Quality of Sounds. 
 TJie Diatonic Scale. 
 
 WHEN a thin elastic plate is made to vibrate, one of its 
 ends being held firm and the other being free, and its length 
 limited to a few inches, it emits a clear musical note. If 
 it be gradually lengthened, it yields notes of different 
 characters, and finally all sound ceases, the vibrations be- 
 coming so slow that the eye can follow them without dif- 
 ficulty. 
 
 This instructive experiment gives us a clear insight into 
 the nature of musical sounds, and, indeed, of all sounds 
 generally. A substance which is executing a vibratory 
 movement, provided the vibrations follow one another 
 with sufficient rapidity, yields a musical sound; but when 
 those vibrations fall below a certain rate, the ear can no 
 longer distinguish the effect of their impulsions. 
 
 The number of vibrations which such a plate makes in 
 
 What is the nature of a musical sound ? Under what circumstances 
 does the sound become inaudible ? What regulates the number of vibra- 
 tions of an elastic plate ? 
 
158 SOUND ARISES IN VIBRATIONS. 
 
 a given time depends upon its length, being inversely as 
 the square of the length of the vibrating part. Thus, if 
 we take a given plate and reduce its length, the vibra- 
 tions will increase in rapidity ; when it is half as long it 
 vibrates four times as fast; when one fourth, sixteen 
 times, &c. 
 
 All sounds arise in vibratory movements, and musical 
 notes differ from one another in the rapidity of their vi- 
 brations the more rapidly recurring or frequent the vi- 
 bration the higher the note. 
 
 There is, therefore, no difficulty in determining how- 
 many vibrations are required to produce any given note. 
 We have merely to find the length of a plate which will 
 yield the note in question, knowing previously what length 
 of it is required to make a determinate number of vibra- 
 tions in a given space of time. Thus it has been found 
 that the ear can distinguish a sound made by 15 vibra- 
 tions in a second, and can still continue to hear though 
 the number reaches 48,000 per second. 
 
 That all sounds arise in these pulsatory movements 
 common observations abundantly prove. If we touch a 
 bell, or the string of a piano, or the prong of a tuning- 
 fork, we feel at once the vibratory action, and with the 
 cessation of that motion the sound dies away. 
 
 . 180. But the pulsations of such a body 
 
 are not alone sufficient to produce the 
 phenomena of sound. Media must 
 intervene between them and the or- 
 gan of hearing. In most cases the 
 medium is atmospheric air, and when 
 this is taken away the effect of the 
 vibrations wholly ceases. Thus, a 
 bell or a musical snuff-box, under an 
 exhausted receiver, as in Fig. 180, 
 can no longer be heard; but on read- 
 mitting the air the sound becomes 
 audible. The sounding body, there- 
 fore, requires a soniferous medium to propagate its im- 
 pulses to the ear. 
 
 Atmospheric air is far from being the only soniferous 
 
 How may the number of vibrations which constitute any sound be de- 
 termined ? How may it be proved that all sounds arise in vibratory move- 
 ments ? How may it be proved that a soniferous medium is required ? 
 
SONIFEROUS MEDIA. 159 
 
 medium. Sounds pass with facility through water ; the 
 scratching of a pin or the ticking of a watch may be heard 
 by the ear applied at the end of a very long plank of 
 wood. Any uniform elastic medium is capable of trans- 
 mitting sound ; but bodies which are imperfectly elastic, 
 or have not an uniform density, impair its passage to a 
 corresponding degree. 
 
 The effect of a vibrating spring, or, indeed, of any vi- 
 brating body on the atmospheric air, is to establish in it a 
 series of condensations and rarefactions which give rise 
 to waves. These, extending spherically from the point of 
 disturbance, advance forward until they impinge on the 
 ear, the structure of which is so arranged that the move- 
 ment is impressed on the auditory nerves, and gives rise 
 to the sensation which we term sound. 
 
 Both the sonorous body and the soniferous medium 
 must, therefore, be elastic, the regularity of the pulsa- 
 tions of the former depends upon the uniformity of its 
 elasticity. In the case of strings, we give them the re- 
 quisite degree of elastic force by stretching them to the 
 proper degree. And, as the undulatory movements which 
 arise in the soniferous medium are not instantaneous, but 
 successive, it follows that the transmission of sound in 
 any medium requires time. That this is the case, we 
 may satisfy ourselves by remarking the period that elapses 
 between seeing the flash of a gun and hearing the report. 
 It is greater as we are removed to a greater distance. In 
 different media, the velocity of transmission depends on 
 the density and specific elasticity. It has been found, by 
 experiment, that in tranquil air the velocity of sound at 
 60, and at an average state of moisture, is 1120 feet in 
 a second. The wind accelerates or retards sound, ac- 
 cording to its direction, damp air transmits it more slowly 
 than dry, and hot air more rapidly than cold, the velocity 
 increasing about 1*1 foot for every Fahrenheit degree. 
 
 In a soniferous medium, all sounds move equally fast ; 
 it is wholly immaterial what may be their quality or their 
 
 Mention some such soniferous media. How is it that sounds are finally 
 perceived by the ear ? What condition is required both for the sounding 
 body and soniferous medium ? How may sufficient elasticity be given in 
 the case of strings ? Does the transmission of sound require time ? What 
 is the velocity of sound per second '( What is the effect of the wind, damp- 
 ness, or change of temperature ? 
 
160 VELOCITY OF SOUND. 
 
 intensity. Thus, we know that even the most intricate 
 music executed at a distance is heard without any discord, 
 arid precisely as it would be close at hand. Nor does it 
 matter whether it be by the human voice, a flute, a.bugle, 
 or, indeed, by many different instruments at once, the 
 relation of the difference of sounds is accurately preserv- 
 ed. But this can only take place as a consequence of the 
 equal velocity of transmission ; for if some of these sounds 
 moved faster than others discord must inevitably ensue. 
 
 The experiments of Colladon and Sturm on the Lake 
 of Geneva show that the velocity in water is about four 
 times that in air, being 4708 feet in a second. With re- 
 spect to solid substances, it is stated that the velocity in 
 air being 1, that in tin is 7s, in copper 12, in glass 17. 
 
 Advantage is sometimes taken of these principles to 
 determine distances. If we observe the time elapsing 
 between the flash of a gun and hearing the sound, or be- 
 tween seeing lightning and hearing the thunder, every 
 second answers to 1120 feet. 
 
 Sounds are of different kinds : some are low or high, 
 grave or acute, according as the vibrations are slower or 
 faster. Again : the intensity of vibration or the magni- 
 tudes of the excursions which the vibrating particles 
 make determine the force of sounds, an intense vibra- 
 tion giving a loud, and a less vibration a feeble sound. 
 
 The vibrations of a soniferous body may take place in 
 three directions : they may be longitudinal, transverse, 
 or rotatory vibrations ; or, indeed, they may all co-exist. 
 Fi e- J81 - A body may be divided into vibrat- 
 
 ing parts, separated from one another 
 by nodal points or lines. Thus, if we 
 take a glass or metal plate, and having 
 strewed its surface with fine dry sand, 
 and holding it firmly at one point between the thumb 
 arid finger, or in a clamp, as represented in Fig. 181, 
 draw a violin bow across its edge, it yields a musical 
 note, and the sand is thrown off those places which are 
 in motion, and collects on the nodal points, which are 
 at rest. 
 
 The quantity, or strength, or intensity of a. sound de 
 
 What is the velocity of sounds in water 1 Into what varieties may 
 sound be divided ? In what directions may a sounding body vibrate I 
 How may nodal lines on surfaces be traced ? 
 
NATURE OF SOUNDS. 161 
 
 pends on the intensity of the vibrations and the mass of 
 the sounding body. It also varies with the distance, be- 
 ing inversely proportional to its square. 
 
 Musical sounds are spoken of as notes, or as high and 
 low. Of two notes, the higher is that which arises from 
 more rapid, and the lower from slower vibrations. 
 
 Besides this, sounds differ in their quality. The same 
 note emitted by a flute, a violin, a piano, or the human 
 voice is wholly different, and in each instance peculiar. 
 In what this peculiarity consists we are not able to say. 
 
 The several notes are distinguished by letters and 
 names ; we shall also see presently that they may be dis- 
 tinguished by numbers. They are 
 
 C D E F G A B C. 
 
 Or, ut, re, ini, fa, sol, la, si, ut. 
 
 Such a series of sounds passes under the name of the 
 diatonic scale. 
 
 LECTURE XXXIV. 
 
 PHENOMENA OP SOUND. Notes in Unison. Octave. In- 
 terval of Sounds. Melody. Harmony. The Mono- 
 chord. Length of Cord and Number of Vibrations re- 
 quired for each Note. Laws of Vibrations in Cords, 
 Rods, Planes. Acoustic Figures on Plates. Vibration 
 of Columns of Air. Interference of Sounds. Whisper- 
 ing Galleries. Echoes. Speaking and Hearing- Trum- 
 pet. 
 
 Two notes are said to be in unison when the vibrations 
 which cause them are performed in equal times. If the 
 one makes twice as many vibrations as the other, it is 
 said to be its octave, and the relation or interval there is 
 between two sounds is the proportion between their re- 
 spective numbers of vibrations. 
 
 There are combinations of sounds which impress our 
 organs of sense in an agreeable manner, and others which 
 
 On what does the intensity of sound depend ? What is it that determines 
 the highness or lowness of notes ? What is meant by the quality of sounds ? 
 How may notes be distinguished ? When are notes in unison ? What is 
 an octave ? What is the relation or interval of sounds ? 
 
162 
 
 THE MONOCHORD. 
 
 produce a disagreeable effect. In this sense, we speak 
 of the former as being in unison, and the latter as being 
 discordant. A combination of harmonious sounds is a 
 chord, a succession of harmonious notes a melody, and a 
 succession of chords harmony. 
 
 We have remarked in the last lecture that sounds may 
 be expressed by numbers as well as by letters or names, 
 and their relations to one another clearly exhibited. For 
 this purpose, we may take the monochord or sonometer, 
 C C', Fig. 182, an instrument consisting of a wire or 
 
 Fig. 182. 
 
 "n 
 
 
 
 
 TO 
 
 J C F H 
 
 
 IT F 
 
 
 
 
 M ill 
 
 
 
 
 03 
 
 catgut stretched over two bridges, F F', which are fast- 
 ened on a basis, S S' ; one end of the cord passes over a 
 pulley, M, and may be strained to any required degree 
 of weights, P. The length of the string vibrating may 
 be changed by pressing it with the finger upon a movable 
 piece, H, which carries an edge, T, and the case beneath 
 is divided into parts which exhibit the length of the vi- 
 brating part of the wire. The upper part of Fig. 182 
 shows a horizontal view of the monochord, the lower a 
 lateral view. The instrument here represented has two 
 strings, one of catgut and one of wire. 
 
 Now, it is to be understood that the number of vibra- 
 tions of such a cord are inversely as its length ; that is, 
 if the whole cord makes a given number of vibrations in 
 one second, when you reduce its length to one half it will 
 make twice as many ; if to one third, thrice as many, &c. 
 
 What is a chord, a melody, and harmony, ? Describe the monochord. 
 
VIBRATIONS OF CORDS. 163 
 
 Suppose the cord is stretched so as to give a clear sound, 
 which we may designate as C, and the movable bridge 
 is then advanced so as to obtain successively the other 
 notes of the gamut, D, E, F, G, A, B, C, it will be found 
 that these are given when the lengths of the cord, com- 
 pared with its original length, are 
 
 Name of note . . . CDEFGABC 
 Length of cord . . . 1, f, j, f, , f, T 8 5 , . 
 
 but as the number of vibrations is in the inverse ratio of 
 the lengths of the vibrating cords, we shall have for the 
 number of vibrations, if we represent by 1, the number 
 that gives C, the following for the other notes : 
 
 Name of note . . . CDEFGABC 
 Number of vibrations . 1, |, |, f, |, |, y 2. 
 
 From C to C is an octave, and from this we gather that, 
 in the octave, the higher note makes twice as many vibra- 
 tions as the fundamental note, and that between these 
 there are other intervals, which, heard in succession, are 
 harmonious ; the eight, therefore, constitute a scale, com- 
 monly called the diatonic scale. 
 
 Musical instruments are of different kinds, depending 
 on the vibrations of cords, rods, planes, or columns of air. 
 
 It has already been stated, that the number of vibra- 
 tions of a cord is inversely as its length the number also 
 increases as the square root of the force that stretches it ; 
 thus, the octave is given by the same string when stretch- 
 ed four times as strongly ; the material of the string, 
 whether it be catgut, iron, &c., also affects the note. 
 
 In rods the height of the note is directly as the thick- 
 ness, and inversely as the square of the length. The 
 quality of the material also, in respect of elasticity, deter- 
 mines the note. 
 
 The foregoing observations apply to transverse vibra- 
 tions of cords and rods ; but they may be also made to 
 execute longitudinal and torsion vibrations, the conditions 
 of which are different. 
 
 In planes held by one point, and a bow drawn across 
 at another, or struck by a blow, sounds are emitted, and 
 by the aid of sand nodal lines may be traced. Thus, in 
 Fig. 183, a is the point, in each instance, at which the 
 
 What lengths of a cord are required to give the notes of the gamut ? What 
 are the corresponding number of vibrations? What is the diatonic scale? 
 What are the laws for the vibration of cords ? What in the case of rods ? 
 
164 
 
 ACOUSTIC FIGURES. 
 
 plate is held, and b that at which the bow is applied ; the 
 sand arranges itself in the dotted lines. 
 
 The two large figures are formed by putting together 
 four smaller plates, in one instance bearing the nodal 
 lines, represented at I, and, in the other, at II. They 
 may, however, be directly generated on one" large plate 
 of glass by holding it at a, touching it at w, and drawing 
 the bow across it at b. 
 
 Circular plates, a in III, may be made to bear a four- 
 rayed star, by holding them in the center, drawing the 
 bow at any point at b, and touching the plate at a point 
 45 distant from the bow ; but if the plate be touched 30, 
 60, or 90 off, it produces a six-rayed star, Fig. IV. 
 
 Columns of air may be made to emit sounds by being 
 thrown into oscillation, as in horns, flutes, clarionets, &c. 
 In these the column of air, included in the tube of the in- 
 strument, is made to vibrate longitudinally. The height 
 of the note is inversely proportional to the length of the 
 column, and therefore different notes may be obtained 
 by having apertures, at suitable distances, in the side of 
 the tube, as in the flute. 
 
 Two sounds may be so combined together that they shall 
 
 In the case of planes how may the nodal lines be varied ? How may 
 columns of air be made to vibrate? How is the length of the vibrating 
 column varied in different wind instruments ? 
 
INTERFERENCE OF SOUNDS. 165 
 
 mutually destroy each other's effect, and silence result. 
 This arises from interference taking place in the aerial 
 waves, the laws of which are those given in Lecture XXXII. 
 The following instances will illustrate these facts. 
 
 When a tuning-fork is made to vibrate, and is turned 
 round upon its axis near the ear, four periods may be dis- 
 covered during every revolution in which the sound in- 
 creases or declines. .4 - 
 
 If we take two tuning-forks of the same note, a d t 
 Fig. 184, and fasten a circle of cardboard, Fig. 184. 
 half an inch in diameter, on one of the prongs 
 of each, and make one of the forks a little 
 heavier than the other, by putting on it a drop 
 of wax, and then filling a jar, b, to such a 
 height with water, that either of the forks, 
 when held over it, will make it resound, so 
 long as only one is held, there will be a con- 
 tinuous note, without pause or interruption ; 
 but if both are held together, there will be periods of 
 silence and periods of sound, according as the longer 
 waves, arising from one of the forks, overtakes and inter- 
 feres with the shorter waves, arising from the other. 
 
 Sounds undergo reflexion, and may therefore be directed 
 by surfaces of suitable figure. If, in the focus of a concave 
 mirror a watch be placed, its ticking may be heard at a 
 great distance in the focus of a second mirror, placed so 
 as to receive the sound-waves of the first. 
 
 On similar principles also whispering-galleries depend. 
 These are so constructed that a low whisper uttered at 
 one point is reflected to a focus at another, in which it 
 may be distinctly heard, while it is inaudible in other po- 
 sitions. The dome of St. Paul's cathedral, in London, is 
 an example. 
 
 Echoes are reflected sounds. Thus, if a person stands 
 in front of a vertical wall, and at a distance from it of 
 about 62 feet, if he utters a syllable, he will hear a sound 
 which is the echo of it. If there be a series of such ver- 
 tical obstacles, at suitable distances, the same sound may 
 be repeated many successive times. A good ear can dis- 
 tinguish nine distinct sounds in a second ; and, as a sound 
 
 Give some illustrations of the interference of sound. How may it be 
 proved that sounds undergo reflexion ? What are whispering-galleries '. 
 Under what circumstances do echoes arise ? 
 
166 
 
 ECHOES. 
 
 travels 1120 feet in the same time, for the echo to be 
 clearly distinguished from its original sound, it must travel 
 125 feet in passing to and from the reflecting surface, that 
 is, the reflector must be at least 62 feet distant. 
 
 Remarkable echoes exist in several places. One near 
 Milan repeats a sound thirty times. The ancients men- 
 tion one which could repeat the first verse of the 
 
 Fig, 185. 
 
 eight times. On the banks of rivers as, for example, on 
 the Rhine, as represented in Fig. 185 sounds are often 
 echoed from the rocks, rebounding, as at 1, 2, 3, 4, from 
 side to side. 
 
 Speaking-trumpets depend on the reflection of sound. 
 Fig. 186. The divergence 
 
 is prevented by 
 the sides of its 
 tube ; and if the 
 instrument is of 
 a suitable figure, 
 the rays of sound 
 issue from it, as 
 seen in Fig. 186, in a parallel direction. Its efficiency 
 depends on its length. It is stated that through such an 
 instrument, from 18 to 24 feet long, a man's voice can be 
 heard at a distance of three miles. Under common cir- 
 cumstances, the greatest distances at which sounds have 
 
 Why must two reflecting surfaces be at a certain distance ? What is the 
 construction of the speaking-trumpet ? 
 
HEARING-TRUMPETS 107 
 
 been heard are usually estimated as follows : the report 
 of a musket, 8000 paces; the march of a company of sol- 
 diers at night, 830 paces; a squadron galloping, 1080 ; the 
 voice of a strong man, in the open air, 230. But the ex- 
 plosions of the volcano of St. Vincent were heard at 
 Demerara, 345 miles; and, at the siege of Antwerp, the 
 cannonading was heard, in the mines of Fig. 187. 
 Saxony, 370 miles. 
 
 The hearing-trumpet is for the purpose 
 of collecting rays of sound by reflexion, 
 and transmitting them to the ear. Its 
 mode of action is represented at Fig. 187. 
 
 At what distance can sounds be heard? What is the construction of 
 the hearing-trumpet. 
 
168 OPTICS. 
 
 PROPERTIES OF LIGHT. 
 
 OPTICS. 
 
 LECTURE XXXV. 
 
 PROPERTIES OF LIGHT. Theories of the Nature of Light. 
 Sources of Light. Phosphorescence. Temperature of 
 a red Heat. Effects of Bodies on Light. Passage in 
 straight Lines. Production of Shadows. Umbra and 
 Penumbra. 
 
 HAVING successively treated of the general mechanical 
 properties of gases, liquids, solids, and the laws of motion, 
 we are led, in the next place, to the consideration of cer- 
 tain agents or forces light, heat, electricity. These, by 
 many philosophers, are believed to be matter, in an im- 
 ponderable state ; they are therefore spoken of as im- 
 ponderable substances. By others their effects are re- 
 garded as arising from motions or modifications impressed 
 on a medium everywhere present, which passes under 
 the name of THE ETHER. 
 
 Applying these views to the case of light, two different 
 hypotheses, respecting its constitution, obtain. The first, 
 which has the designation of the theory of emission, re- 
 gards light as consisting of particles of amazing minute- 
 ness, which are projected by the shining body, in all di- 
 rections, and in straight lines. These impinging eventu- 
 ally on the organ of vision, give rise to the sensation 
 which we speak of as brightness or light. To the other 
 theory, the title of undulatory theory is given ; it supposes 
 that there exists throughout the universe an ethereal me- 
 dium, in which vibratory movements can arise somewhat 
 analogous to the movements which give birth to sounds 
 
 Name the imponderable substances. What other theory is there re- 
 specting their nature ? What is the theory of emission ? What is the 
 foundation of the undulatory theory ? 
 
SOURCES OF. LIGHT. 169 
 
 in the air; and these passing through the transparent 
 parts of the eye, and falling on the retina, affect it with 
 their pulsations, as waves in the air affect the auditory 
 nerve, but in this case give rise to the sensation of light, 
 as in the other to sound. 
 
 There are many different sources of light some are 
 astronomical and some terrestrial. Among the former 
 may be mentioned the sun and the stars among the lat- 
 ter, the burning of bodies, or combustion, to which we 
 chiefly resort for our artificial lights, as lamps, candles, gas 
 flames. Many bodies are phosphorescent, that is to say, 
 emit light after they have been exposed to the sun or any 
 shining source. Thus, oyster-shells, which have been cal- 
 cined with sulphur, shine in a dark place after they have 
 been exposed to the light, and certain diamonds do the 
 same. So, too, during processes of putrefaction, or slow 
 decay, light is very often emitted, as when wood is mould- 
 ering or meat is becoming putrescent. The source of 
 the luminousness, in these cases, seems to be the same as 
 in ordinary combustions, that is, the burning away of car- 
 bon and hydrogen under the influence of atmospheric air; 
 but, in certain cases, the functions of life give rise to an 
 abundant emission of light, as in fireflies and glowworms ; 
 these continue to shine even under the surface of water, 
 and there is reason to believe that the phenomenon is to a 
 considerable extent subject to the volition of the animal. 
 All solid substances, when they are exposed to a cer- 
 tain degree of heat, become incandescent or emit light. 
 When first visible in a dark place, this light is of a red- 
 dish color, but as the temperature is carried higher and 
 higher it becomes more brilliant, being next of a yellow, 
 and lastly of a dazzling whiteness. For this reason we 
 sometimes indicate the temperature of such bodies, in a 
 rough way, by reference to the color they emit : thus we 
 speak of a red heat, a yellow heat, a white heat. I have 
 recently proved that all solid substances begin to emit 
 light at the same degree of heat, and that this answers to 
 977 of Fahrenheit's thermometer ; moreover, as the tern- 
 Mention some of the sources of light. What is meant by phospho- 
 rescence ? To what source may the light emitted during putrefaction and 
 decay be attributed ? What is there remarkable in the shining of glow- 
 worms and fireflies 1 What is meant by incandescence ? What succes- 
 sion of colors is perceived in self-luminous bodies ? At what temperature 
 do all solids begin to shine ? 
 
 H 
 
170 PATH^ OF RAYS. 
 
 perature rises the brilliancy of the light rapidly increases, 
 so that at a temperature of 2600 it is almost forty times as 
 intense as at 1900. At these high temperatures an ele- 
 vation of a few degrees makes a prodigious difference in 
 the brilliancy. Gases require to be brought to a far higher 
 temperature than solids before they begin to emit light. 
 
 Non-luminous bodies become visible by reflecting the 
 light which falls on them. In their general relations such 
 bodies may be spoken of as transparent and opaque. By 
 the former we mean those which, like glass, afford a more 
 or less ready passage to the light through them; by the 
 latter, such as refuse it a passage. But transparency and 
 opacity are never absolute they are only relative. The 
 purest glass extinguishes a certain amount of the rays 
 which fall on it, and the metals which are commonly 
 looked upon as being perfectly opaque allow light to pass 
 through them, provided they are thin enough. Thus gold 
 leaf spread upon glass transmits a greenish-colored light. 
 
 The rays of light, from whatever source they may come, 
 move forward in straight lines, continuing their course 
 until they are diverted from it by the interposition of 
 some obstacle, or the agency of some force. That this 
 rectilinear path is followed maybe proved by a variety of 
 facts. Thus, if we intervene an opaque body between 
 any object and the eye, the moment the edge of that body 
 comes to the line which connects the object and the ye 
 the object is cut off from our view. In a room into which 
 a sunbeam is admitted through a crevice, the path which 
 the light takes, as is marked out by the motes that float in 
 the air, is a straight line. 
 
 By a ray of light we mean a straight line drawn from 
 the luminous body, marking out the path along which the 
 shining particles pass. 
 
 A shining body is said to radiate its light, because it 
 projects its luminous particles in straight lines, like radii, 
 in every direction, and these falling on opaque bodies 
 and being intercepted by them, give rise to the produc- 
 tion of shadows. 
 
 At what rate does the light increase as the temperature rises? Are 
 solids or gases most readily made incandescent? How dp non-luminous 
 bodies become visible ? What classes are they divided into ? Are trans- 
 parency and opacity absolute qualities ? Prove that rays move in straight 
 lines. What is meant by radiation ? How are shadows produced ? 
 
SHADOWS. 
 
 171 
 
 If the light is emitted by a single luminous point, the 
 boundary of the shadow can be obtained by drawing 
 straight lines from the lumi- Fig. iss. 
 
 nous point to every point on 
 the edge of the body, and pro- 
 ducing them. Thus, let a, Fig. 
 188, be the luminous point, If 
 c the opaque body ; by draw- 
 ing the lines ab,ac, and pro- 
 ducing them to d and e the 
 boundary and figure of the 
 shadow may be exhibited. 
 
 But if the luminous body, 
 as in most instances is the 
 case, possesses a sensible 
 magnitude ; if it is, for example, the sun or a flame, an 
 opaque body will cast two shadows, which pass respect- 
 ively under the names of the umbra and penumbra the 
 former being dark and the latter partially illuminated. 
 This may be illustrated by Fig. 189, in Fig. 189 
 
 which a b is the flame of a candle or 
 any other luminous source, having a 
 sensible magnitude, c d the opaque 
 body. Now the straight lines, a c f, 
 a d k, drawn from the top of the flame 
 to the edges of the opaque body and 
 produced, give the shadow for that 
 point of the flame ; and the lines bee, 
 b d g, drawn in like manner from the 
 bottom of the flame, give the shadow for that point. But 
 we see that the space between g and k, which belongs to 
 the shadow for the top of the flame, is not perfectly dark, 
 because it is so situated as to be partially illuminated by 
 the bottom of the flame and a similar remark -may be 
 made as respects the space, f e, which receives light from 
 the top of the flame. But the remaining space, f g, re- 
 ceives no light whatever it is totally dark and we there- 
 fore call it the umbra, while the partially-illuminated re- 
 gions, fe and g h, are the penumbra. 
 
 Trace the shadow of a body formed by a luminous point. Trace the 
 formation of a shadow when the luminous source is of sensible size. What 
 is the umbra ? What is the penumbra ? 
 
172 PHOTOMETRY. 
 
 LECTURE XXXVI. 
 
 OF THE MEASURES OF THE INTENSITY AND VELOCITY OF 
 LIGHT. Conditions oftlie Intensity of Light. Of Pho- 
 tometric Methods. Rumford's Method by Shadows. 
 Ritchie's Photometer. Difficulties in Colored Lights. 
 Masson's Method. Velocity of Light Determined by the 
 Eclipses of Jupiter's Satellites. The same by the Aber- 
 ration of the Fixed Stars. 
 
 BY Photometry we mean the measurement of the brill- 
 iancy of light an operation which can be conducted in 
 many different ways. 
 
 It is to be understood that the illuminating power of a 
 shining body depends on several circumstances : First, 
 upon its distance for near at hand the effect is much 
 greater than far off the law for the intensity of light in 
 this respect being that the brilliancy of the light is inversely 
 as the square of the distance. A candle two feet off gives 
 only one fourth of the light that it does at one foot, at three 
 feet it gives only one ninth, &c. Secondly, it depends on 
 the absolute intensity of the luminous surface : thus we 
 have seen that a solid at different degrees of heat emits 
 very different amounts of light, and in the same way the 
 flame of burning hydrogen is almost invisible, and that 
 of spirits of wine is very dull when compared with 
 an ordinary lamp. Thirdly, it depends on the area or 
 surface the shining body exposes, the brightness being 
 greater according as that surface is greater. Fourthly, 
 in the absorption which the light suffers in passing the 
 medium through which it has to traverse for even the 
 most transparent obstructs it to a certain extent. And 
 lastly, on the angle at which the rays strike the surface 
 they illuminate, being most effective when they fall per- 
 pendicularly, and less in proportion as their obliquity in- 
 creases. 
 
 What is photometry ? Mention some of the conditions which determine 
 the brilliancy of light. What is the law of its decrease by distance? What 
 has obliquity of surfaces to do with the result ? 
 
173 INTENSITY OF LIGHT. 
 
 The first and last of the conditions here mentioned, as 
 controlling the intensity of light the effect of distance 
 and of obliquity may be illustrated as follows : 
 
 Fig. 190. 
 
 1st. That the intensity of light is inversely as the squares 
 of the distance. Let B, Fig. 190, be an aperture in a 
 piece of paper, through which rays coming from a small 
 illuminated point, A, pass ; let these rays be received on 
 a second piece of paper, C, placed twice as far from A as 
 is B, it will be found that they illuminate a surface which 
 is twice as long and twice as broad as A, and therefore 
 contains four times the area. If the paper be placed atD, 
 three times as far from A as is B, the illuminated space 
 will be three times as long and three times as broad as A, 
 and contain nine times the surface. If it be at E, which 
 is four times the distance, the surface will be sixteen times 
 as great. All this arises from the rectilinear paths which 
 the diverging rays take, and therefore a surface illumina- 
 ted by a given light will receive, at distances represented 
 by the numbers 1, 2, 3, 4, &c., quantities of light repre- 
 sented by the numbers 1, |, , T 'g-, &c., which latter are 
 the inverse squares of the former numbers. 
 
 2d. That the intensity of light is dependent on the an- 
 gle at which the rays strike the receiving surface, being 
 most effective when they fall perpendicularly, and less in 
 proportion as the obliquity increases. Let there be two 
 surfaces, D C and E C, Fig. 191, on which a beam of 
 light, A B, falls on the former perpendicularly and on the 
 latter obliquely the latter surface, in proportion to its 
 obliquity, must have a larger area to receive all the rays 
 which fall on D C. A given quantity of light, therefore, 
 
 Give illustrations of the effect of distance and of obliquity. 
 
174 RUMFORD'S PHOTOMETER. 
 
 Fig. 191. 
 
 is diffused over a greater surface when it is received ob- 
 liquely, and its effect is correspondingly less. 
 
 To compare different lights with one another, Count 
 Rumford. invented a process which goes under the name 
 of the method of shadows. The principle is very simple. 
 Of two lights, that which is the most brilliant willcast the 
 deepest shadow, and with any -light the shadow which is 
 cast becomes less dark as the light is more distant. If, 
 therefore, we wish to examine experimentally the brill- 
 iancy of two lights on Rumford's method, we take a 
 screen of white paper and setting in front of it an opaque 
 rod, we place the lights in such a position that the two 
 shadows arising shall be close .together, side by side. 
 Now the eye can, without any difficulty, determine which 
 of the two is darkest ; and by removing the light which 
 has cast it to a greater distance, we can, by a few trials, 
 bring the two. shadows to precisely the same degree of 
 depth. It remains then to measure the distances of the 
 two lights from the screen, and the illuminating powers 
 are as the squares of those distances. 
 
 Ritchie's photometer is an instrument for obtaining the 
 same result, not, however, by the contrast of shadows, 
 but by the equal illumination of surfaces. It consists of 
 a box, a Z>, Fig. 192, six or. eight inches long and one 
 broad and deep, in the middle of which a wedge of wood, 
 feg, with its angle, e, upward, is placed. This wedge 
 is covered over with clean white paper, neatly doubled to 
 a sharp line at e. In the top of the box there is a conical 
 tube, with an aperture, d, at its upper end, to which the 
 
 What is the principle of Rumford's photometric process? How is it 
 applied -in practice ? What is the illuminating power of the lights propor- 
 tional to ? Describe Ritchie's photometer. 
 
RITCHIE 3 PHOTOMETEE. 
 
 175 
 
 eye is applied, and the whole may be raised to any suitable 
 height by means of 
 the stand c. On look- 
 ing down through 
 d, having previous- 
 ly placed the two 
 lights, m n, the in- 
 tensity of which we 
 desire to determine, 
 on opposite sides of in 
 the box, they illu- 
 minate the paper 
 surfaces exposed to 
 them, e f to jn and e g to n, and the eye, at d, sees both 
 those surfaces at once. By changing the position of the 
 lights, we eventually make them illuminate the surfaces 
 equally, and then measuring their distances from e y their 
 illuminating powers are as the squares of those dis- 
 tances. 
 
 It is not possible to apply either of these methods in a 
 satisfactory manner where, as is unfortunately often the 
 case, the lights to be examined differ in color. The eye 
 can form no judgment whatever of the relation of bright- 
 ness of two surfaces when they are of different colors ; 
 and a very slight amount of tint completely destroys the 
 accuracy of these processes. To some extent, in Ritchie's 
 instrument, this may be avoided, by placing a colored 
 glass at the aperture, d. 
 
 A third photometric method has recently been intro- 
 duced ; it has great advantages over either of the fore- 
 going ; and difference of color, which in them is so se- 
 rious an obstacle, serves in it actually to increase the ac- 
 curacy of the result. The principle on which it is found- 
 ed is as follows : If we take two lights, and cause one of 
 them to throw the shadow of an opaque body upon a 
 white screen, there is a certain distance to which, if we 
 bring the second light, its rays, illuminating the screen, 
 will totally obliterate all traces of the shadow. This dis- 
 appearance of the shadow can be judged of with great 
 
 What difficulties arise when the lights and the shadows they give are 
 colored ? How may these be avoided ? Describe another process which 
 is free from the foregoing difficulties. On what principle does it de- 
 pend ? 
 
176 VELOCITY OF LIGHT. 
 
 | 
 
 accuracy by the eye. It has been found that eyes of 
 average sensitiveness fail to distinguish the effect of a 
 light when it is in presence of another sixty-four times as 
 intense. The precise number varies somewhat with dif- 
 ferent eyes ; but to the same eye it is always the same. 
 If there be any doubt as to the perfect disappearance of 
 the shadow, the receiving screen may be agitated or 
 moved a little. This brings the shadow, to a certain ex- 
 tent, into view again. Its place can then be traced ; and, 
 on ceasing the motion, the disappearance verified. 
 
 When, therefore, we desire to discover the relative in- 
 tensities of light, we have merely to inquire at what dis- 
 tance they effect the total obliteration of a shadow, and 
 their intensities are as the squares of those distances. I 
 have employed this method for the determination of the 
 quantities of light emitted by a solid at different temper- 
 atures, and have found it very exact. 
 
 Light does not pass instantaneously from one point to 
 another, but with a measurable velocity. The ancients 
 believed that its transmission was instantaneous, illustrat- 
 ing it by the example of a stick, which, when pushed 
 at one end, simultaneously moves at the other. They 
 did not know that even their illustration was false ; for a 
 certain time elapses before the farther end of the stick 
 moves ; and, in reality, a longer time than light would re- 
 quire to pass over a distance equal to the length of the 
 stick. But in 1676, a Danish astronomer, Roemer, found, 
 from observations on the eclipses of Jupiter's satellites, 
 that light moves at the rate of about 192,000 miles in one 
 second. 
 
 This singular observation may be explained as follows : 
 Let S, Fig. 193, be the sun, E the earth, moving in the 
 orbit E E', as indicated by the arrows ; let J be Jupi- 
 ter and T his first satellite, moving in its orbit round 
 him. It takes the satellite 42 hours 28 minutes 35 sec- 
 onds to pass from T to T' that is to say, through the 
 planet's shadow. But, during this period of time, the 
 earth moves in her orbit, from E to E', a space of 
 2,880,000 miles. Now, it is found, under these circum- 
 
 Does light move with instantaneous velocity ? Who discovered its pro- 
 gressive motion ? What is its actual rate ? Describe the facts by which 
 tins has been determined. By whom and under what circumstances has 
 this been verified ? 
 
ROEMER'S AND BRADLEY'S DISCOVERIES. 177 
 ptances, that the emersion of the satellite is 15 seconds 
 
 Fig. 193. 
 
 later than it should have been. And it is clear that this 
 is owing to the fact that the light requires 15 seconds to 
 pass from E to E' and overtake the earth. Its velocity, 
 therefore, in one second, must be 192,000 miles. 
 
 This beautiful deduction was corroborated by Dr. 
 Bradley, in 1725, upon totally different principles, involv- 
 ing what is termed the aberration of the stars. The prin- 
 ciple, which is somewhat dif- Fig. 194. 
 ficult to explain, is clearly il- M 
 lustrated by Eisenlohr as fol 
 lows : Let M N represent a 
 ship, whose side is aimed at 
 point blank by a cannon at a. 
 Now, if the vessel were at 
 
 rest, a ball discharged in this Mr/ 
 
 manner would pass through 
 the points b and c, so that the 
 three points, a, b, and c, would all be in the same straight 
 line. But if the vessel itself move from M toward N, 
 then the ball which entered at b would not come out at 
 the opposite point, c, but at some other point, d, as much 
 nearer to the stern, as is equal to the distance gone over 
 by the vessel, from M to N, during the time of passage 
 of the ball through her. The lines b c and b d, therefore, 
 form an angle at i, whose magnitude depends on the po- 
 sition of b c and b d. The greater the velocity of the 
 ball, as compared with the ship, the less the angle. Next, 
 
 What is meant by the aberration of the fixed stars ? Give an illustration 
 of it. What is the value of the angle of aberration ? What is the velocity 
 of light as thus determined ? 
 
178 REFLEXION OF LIGHT. 
 
 for the ship substitute in your mind the earth, and for the 
 cannon any of the fixed stars ; let the velocity, b c, of the 
 cannon-ball now stand for that of light, and let d c be the 
 velocity of the earth in her orbit. The angle d b c, is 
 called the angle of aberration. It amounts to 20 seconds 
 for all the stars ; for they all exhibit the same alteration 
 in their apparent position, being more backward than 
 they really are in the direction of the earth's annual mo- 
 tion, as Bradley discovered. By a simple trigonometri- 
 cal calculation, it appears from these facts that the velo- 
 city of light is 195,000 miles per second, a result nearly 
 coinciding with the former. 
 
 LECTURE XXXVII. 
 
 REFLEXION OP LIGHT. Different kinds of Mirrors. 
 General Law of Reflexion. Case of Parallel, Con- 
 verging, and Diverging Rays on Plane Mirrors. The 
 Kaleidoscope. Properties of Spherical Concave Mir- 
 rors. Properties of Spherical Convex Mirrors. Spheri- 
 cal Aberration. Mirrors of other Forms. Cylindrical 
 Mirrors. 
 
 WHEN a ray of light falls upon a surfaceAit may.be 
 reflected, or transmitted, or absorbed./ 
 
 We therefore proceed to the study of these three 
 incidents, which may happen to light, commencing with 
 reflexion. 
 
 Reflecting surfaces in optics are called mirrors; they 
 are of various kinds, as of polished metal or glass. They 
 differ also as respects the figure of their surfaces, \being 
 plane, convex, or concave;! and again they are divided 
 into such as arej spherical, parabolic, elliptical, &c?) 
 
 The general law which is at the foundation of this 
 part of optics the law of reflexion is as follows : 
 
 The angle of reflexion is equal to the angle of Incidence, 
 the reflected ray is in the opposite side of the perpendicular, 
 and the perpendicular, the incident, and the reflected rays 
 are all in the same plane. i 
 
 When a ray of light falls on a surface what may happen to it 1 What is 
 meant by reflecting surfaces? What is the general law of reflexion? 
 
PLANE MIRRORS. 
 
 179 
 
 Thus, let c, Fig. 195, be the reflecting sur- 
 face ; b c a perpendicular to it at any point, 
 a c a ray incident on the same point ; the 
 path of the reflected ray under the foregoing 
 law will be c d ; such, that it is on the oppo- 
 site side of the perpendicular to the incident 
 ray, that a c,cb, and c d, are all in the same 
 plane, and that the angle of incidence, a c b, is equal to 
 the angle of reflexion, bed. 
 
 Reflexion from mirror surfaces may be studied under 
 three divisions : reflexion from plane, from concave, and 
 from convex mirrors. 
 
 When parallel rays fall on a plane mirror, they will be 
 reflected parallel, and divergent and convergent rays will 
 respectively diverge and converge at angles equal to their 
 angles of incidence. 
 
 When rays diverging from a point fall on a mirror, 
 they are reflected from it in such a manner as though 
 they proceeded from a point as far behind it as it is in 
 reality before it. This principle has already been ex- 
 plained in Lecture XXXII, Fig. 
 176. It is illustrated in Fig. 196. 
 Thus, if from the point a two 
 rays, a b, a c, diverge, they will, 
 under the general law, be respect- 
 ively reflected along b d, c e ; and 
 if these be produced they will in- 
 tersect at a', as far behind the 
 mirror as a is before it. The 
 point a! is called the virtual focus, d; 
 
 From this it appears that any 
 object seen in a plane mirror ap- 
 pears to be as far behind it as it is 
 in reality before it. 
 
 If an object is placed between two parallel plane mir- 
 rors each will produce a reflected image, and will also 
 repeat the one reflected by the other. The consequence 
 is, therefore, that there is an indefinite number of images 
 produced, and in reality the number would be infinite 
 
 Illustrate this law by Fig. 195. What three kinds of mirrors are there ? 
 When parallel, divergent, or convergent rays fall on a plane mirror, what 
 happens to them after reflexion ? What does Fig. 196 illustrate ? What 
 is the effect of two parallel plane mirrors ? 
 
180 CONCAVE MIRRORS. 
 
 were the light not gradually enfeebled by loss at each 
 successive reflexion. 
 
 The kaleidoscope is a tube containing two plane mir- 
 rors, which run through it lengthwise, and are generally 
 inclined at an angle of 60. At one end of the tube is an 
 arrangement by which pieces of colored glass or other 
 objects may be held, and at the other there is a cap with 
 a small aperture. On placing the eye at this aperture 
 the objects are reflected, and form a beautiful hexag- 
 onal combination, their position and appearance may be 
 varied by turning the tube round on its axis. 
 
 Concave and convex mirrors are commonly ground to 
 a spherical figure, though other figures, such as ellipsoids, 
 parabaloids, &c., are occasionally used for special pur- 
 poses. It is the properties of spherical concaves that we 
 shall first describe. 
 
 The general action of a spherical mirror may be under- 
 197. stood by regarding 
 
 it as made up of 
 a great number of 
 small plane mirrors, 
 as A, B, C, D, E, 
 F f G,jFV#197. On 
 such a combination 
 of small mirrors, let 
 rays emanating from R impinge. The different degrees 
 of obliquity under which they fall upon the mirrors cause 
 them io follow new paths after reflexion, so that they 
 converge to the point S as to a focus. 
 
 The problem of determining the path of a ray after it 
 has been reflected is solved by first drawing a perpen- 
 dicular to the surface at the point of impact, and then 
 drawing a line on the opposite side of this perpendicular, 
 making with it an angle equal to that of the angle of 
 incidence of the incident ray. Thus, let r, s, Fig. 198, 
 be an incident ray falling on any reflecting surface at s. 
 To find the path it will take after reflexion, we first draw 
 s c, a perpendicular to the surface at the point of impact, s. 
 And then draw the line s f on the opposite side of the 
 
 What is the kaleidoscope ? What is the ordinary figure of concave and 
 convex mirrors ? How may the general action of these mirrors be con- 
 ceived? Describe the method for determining the path of rays after 
 reflexion. 
 

 CONCAVE MIRRORS. 181 
 
 perpendicular c s, such, that the angle c s f is equal to 
 the angle c s r. This is nothing but an application of 
 the general law of reflexion, that the angles of incidence 
 and reflexion are equal to one another, and are on oppo- 
 site sides of the perpendicular. 
 
 When rays of light diverge from the center of a spheri- 
 cal concave mirror, after reflexion they converge back 
 to the same point. For, from the nature of such a surface, 
 lines drawn from its center are perpendicular to the point 
 to which they are drawn, every ray, therefore, impinges 
 perpendicularly upon the surface and returns to the center 
 again. 
 
 When parallel rays of light fall on the surface of a sphe- 
 Fig, 198. rical mirror, the aper- 
 
 r ture or diameter of 
 
 ~ which is not very 
 large, they are re- 
 
 fleeted to a point half 
 
 way between the sur- 
 
 IL face and center of the 
 
 mirror. Thus, let rs 
 f f s' be parallel rays 
 falling on the mirror s s', the aperture, s s', of which is only 
 a few degrees, these rays, after reflexion, will be found 
 converging to the point f t which is called the principal 
 focus, half way between the vertex of the mirror, v, and 
 its center, c; for if we draw the radii, c s c s', these lines 
 are perpendiculars to the mirror at the points on which 
 they fall ; then make the angles c sf equal csr, and c s'f 
 equal c s' r', and it is easy to prove that the pointy is 
 midway between v and c. 
 
 But if the aperture, s s', of the mirror exceeds a few de- 
 grees, it may be proved geometrically that the rays no 
 longer converge to the focus,/) but, as the aperture in- 
 creases, are found nearer and nearer to the vertex, v, until 
 finally, were it not for the opacity of the mirror, they 
 would fall at the back of it. As this deviation is depend- 
 ent on the spherical figure of the mirror, it is termed 
 aberration of sphericity. 
 
 When rays diverge from the center of a spherical concave mirror, where 
 will they be found after reflexion ? What is the case when parallel rays 
 fall on a spherical mirror ? Why is the result limited to mirrors of small 
 aperture ? What is meant by aberration of sphericity ? 
 
182 
 
 CONCAVE MIRRORS. 
 
 Fig. 200. 
 
 Conversely, if diverging rays issue from a lucid point, 
 
 f.Fig. 198, half way 
 between the vertex 
 and center of a spheri- 
 cal mirror of limited 
 aperture, they will be 
 reflected in parallel 
 lines. 
 
 Rays coming from 
 any point, r t Fig. 199, 
 at a finite distance beyond the center of the mirror, will 
 
 be reflected so as to fall 
 between the focus, f, and 
 the center, c. 
 
 Rays coming from a point, 
 r, Fig. 200, between the 
 focus, f, and the vertex, v, 
 will diverge after reflexion. 
 Under such circumstances 
 a virtual focus, f, exists 
 at the back of the mirror. 
 
 Concave mirrors give rise 
 to the formation of images 
 in their foci. This fact may be shown experimentally by 
 placing a candle at a certain distance in front of such a mir- 
 ror and a small screen of paper at the focus. On this paper 
 will be seen an image of the flame, beautifully clear and 
 distinct, but inverted. The relative size and position of 
 this image varies according to the distance of the object 
 from the vertex of the mirror. 
 
 The second variety of curved mirrors is the convex ; 
 their chief properties are as follows : 
 
 When parallel rays fall on the surface of a convex mir- 
 ror, they become divergent after reflexion ; for let s s' be 
 such a mirror, and r s r' s' rays parallel to its axis falling 
 on it, let c be the center of the mirror, and draw c s c s', 
 which wifl be respectively perpendicular to the mirror at 
 the points s and s' ; then for the reflected rays, make the 
 
 What is the case when diverging rays issue from the focus of a spherical 
 mirror ? What when they come from a finite distance beyond the center ? 
 What when they come from between the focus and the vertex ? How may 
 it be proved that concave mirrors form images ? What is the second vari- 
 ety of mirrors ? When parallel rays fall on a convex mirror, what path 
 do they take ? 
 
CONVEX MIRRORS. 
 
 183 
 
 angle, t s p, equal to^? s r, and the angle, t' s' p' t equal to 
 p' s' r'. It may then jrer.'au. 
 
 be demonstrated, that 
 not only do these re- 
 flected rays diverge, 
 but if they be produced 
 through the mirror till 
 they intersect, they will 
 give a virtual focus at 
 ~f, half way between 
 the Vertex of the mir- 
 ror, v, and its center, c, 
 so long as the mirror is 
 of a limited aperture. 
 
 In a similar manner 
 it may be proved that diverging rays, falling on a convex 
 mirror, become more divergent. 
 
 To avoid the effect of spherical aberration, it has been 
 proposed to give to mirrors other forms than the spherical. 
 Some are ground to a paraboloidal, and others to an ellip- 
 soidal figure. . Of the properties of such surfaces I have 
 already spoken, under the theory of Undulations, in Lec- 
 ture XXXII ; and the effects remain the same, whether we 
 consider light as consisting of innumerable small particles, 
 shot forth with great velocity, or of undulations arising in 
 an elastic ether. In both cases parallel rays, falling on a 
 paraboloidal mirror, are accurately converged to the fo- 
 cus, whatever the aperture of the mirror may be ; and in 
 ellipsoidal ones, rays diverging from one of the foci, are 
 collected together in the other. Occasionally, for the pur- 
 poses of amusement, mirrors are ground to cylindrical 
 or conical figures; they distort the appearance of objects 
 presented to them, or reflect, in proper proportions, the 
 images of distorted or ludicrous paintings. 
 
 Why are paraboloidal and ellipsoidal mirrors sometimes used ? What 
 is the effect of the former on parallel rays I What of the latter on rays is- 
 suing from one of the foci ? What are the effects of cylindrical mirrors ? 
 
184 REFRACTION OF LIGHT. 
 
 LECTURE XXXVIII. 
 
 REFRACTION OF LIGHT. Refractive Action described. 
 Law of the fines. Relation of the Refractive Power 
 with other Qualities. Total Reflexion. Rays on plane 
 Surfaces. The Prism. Action of the Prism on a Ray. 
 The M.ultiplying- Glass. 
 
 WHEN a ray of light passes out of one medium into 
 another of a different density, its rectilinear progress is 
 disturbed, and it bends into a new path. This phenom- 
 enon is designated the refraction of light. 
 
 Thus, if a sunbeam, entering through a small hole in 
 the shutter of a dark room, falls on the surface of some 
 water contained in a vessel, the beam, instead of passing 
 on in a straight line, as it would have done had the water 
 not intervened, is bent or broken at the point of incidence, 
 and moves in the new direction. 
 
 Fig. 202. j n ne same way, also, if a 
 
 coin or any other object, O, 
 Fig. 202, be placed at the 
 bottom of an empty bowl, 
 A B C D, and the eye at E 
 so situated that it cannot per- 
 ceive the coin, the edge of 
 the vessel intervening, if we 
 pour in water the object comes 
 into view; and the cause of this is the same as in the for- 
 mer illustration : for while the vessel is empty the ray is 
 obstructed by the edge of the bowl, as at O Gr E, but 
 when water is poured in to the height F Gr, refraction 
 at the point L, from the perpendicular, P Q, ensues; and 
 now the ray takes the course OLE, and entering the eye 
 at E, the object appears at K, in the line E L K. 
 
 For the same reason oars or straight sticks immersed 
 in water look broken, and the bottom of a stream seems 
 at a much less depth than what it actually is. 
 
 What is meant by the refraction of light ? Explain the illustrations of 
 this phenomenon as given in Figs. 202 and 203. 
 
REFRACTION OF LIGHT. 
 
 185 
 
 The same result ensues under the circumstances repre- 
 sented in Fig. 203, in which E represents a candle, the 
 rays of which fall on a F v- 2 3 - 
 
 rectangular box, ABC 
 D, under such circum- 
 stances as to cast the 
 shadow of the side A C, 
 so as to fall at D. If the B 
 box be now filled with 
 water, every thing re- D 3 C 
 
 maining as before, the shadow will leave the point D and 
 go to d, die rays undergoing refraction as they enter the 
 liquid ; and if the eye could be placed at d, it would see 
 the candle at e, in the direction of d A produced. 
 
 Let N O, Fig. 204, be a refracting surface, and C the 
 
 G E 
 
 point of incidence of a ray, B C, C E the course of the 
 refracted ray, and C K the course the ray would have 
 taken had not refraction ensued. With the point of inci- 
 dence, C, as a center, describe a circle, N M O G, and from 
 A and R draw the lines A D, R H at right angles to the 
 perpendicular M G to the point C. Then ACM will 
 be the angle of incidence, R C G the angle of refraction ; 
 A D is the sine of the angle of incidence, and H R the 
 sine of the angle of refraction. Now in every medium 
 
 Explain Fig. 204. What is the angle of incidence ? What is the angle 
 of refraction ? Which are the sines of those angles ? 
 
186 
 
 LAW OF SINES. 
 
 Fig. 205. 
 
 these lines have a fixed relation to one another, and the 
 general law of refraction is as follows : 
 
 In each medium the sine of the angle of incidence is in a 
 constant ratio to the sine of the angle of refraction ; the in- 
 cident, the perpendicular, and the refracted ray are all in 
 the same place, which is always at right angles to the plane 
 of the refracting medium. 
 
 To a beginner, this law of 
 the constancy of sines may be 
 explained as follows : Let C 
 D, Fig. 205, be a ray falling 
 on a medium, A B, in the point 
 D, where it undergoes refrac- 
 tion and takes the direction D 
 ,E. Its sine of incidence, as 
 just explained, is C g, and its 
 sine of refraction E e; and let 
 us suppose that the medium is 
 of such a nature that the sine 
 of refraction is one half the sine of incidence that is, E 
 e is half C g. Moreover, let there be a second ray, H D, 
 incident also at the point D, and refracted along D F ; 
 H h will be its sine of incidence, and F f its sine of re- 
 fraction ; and by the law Ff will be exactly one half HA. 
 The proportion or relation between these sines differs 
 when different media are used, but for the same medium 
 it is always the same. Thus, in the case of water, the pro- 
 portion is as 1.366 to 1; for flint-glass, 1.584 to 1; for dia- 
 mond, 2.487 to 1. These numbers are obtained by ex- 
 periment. They are called the indices of refraction of 
 bodies, and tables of the more common substances are 
 given in the larger works on optics. 
 
 No general law has as yet been discovered which would 
 enable us to predict the refractive power of bodies from 
 any of their other qualities; but it has been noticed that 
 inflammable bodies are commonly more powerful than 
 incombustible ones, and those that are dense are more en- 
 ergetic than those that are rare. 
 
 When a ray of light passes out of a rare into a dense 
 
 What relation do these sines bear to one another ? Explain the law of 
 the constancy of the sines as given in Fig. 205. What is the rate for water, 
 flint-glass, and diamond ? What is meant by indices of refraction ? Is the 
 refractive power of bodies connected with any other property ? 
 
TOTAL REFLEXION. 187 
 
 medium, it is refracted toward the perpendicular. Fig. 
 203 is an illustration the rays passing from air into wa- 
 ter. But when a ray passes from a dense into a rarer 
 medium it is refracted from the perpendicular. Fig. 
 202 is an example the rays passing from water into 
 air. 
 
 In every case when a ray falls on the surface of any 
 medium whatever, it is only a portion which is transmit- 
 ted, a portion being always reflected. If in a dark room 
 we receive a sunbeam on the surface of some water, this 
 division into a reflected and a refracted ray is very evi- 
 dent : and when a ray is about to pass out of a highly re- 
 fractive medium into one that is less so, making the angle 
 of incidence so large th.at the angle of refraction is equal 
 to or exceeds 90, total reflexion ensues. This may be 
 readily shown by allowing the . Fig. 206. 
 
 rays from a candle, f t or any .^ 
 
 other object, to fall on the sec- 
 ond face, b c, of a glass prism, a & 
 b c, Fig. 2Q6 ; the eye placed atd 
 will receive the reflected ray, d 
 e, and it will be perceived that 
 the face b c of the glass, when 
 exposed to the daylight, ap- 
 pears as though it were sil- 
 vered, reflecting perfectly all objects exposed to its 
 front, a c. 
 
 As with the reflexion of light, so with refraction it is 
 to be considered as taking place on plane, convex, and 
 concave surfaces. 
 
 When parallel rays fall upon a plane refracting surface 
 they continue parallel after refraction. This must neces- 
 sarily be the case on account of the uniform action of the 
 medium. 
 
 If divergent rays fall upon a plane of greater refractive 
 power than the medium through which they have come, 
 they will be less divergent than before. Thus, from the 
 point a let the rays a b, a b' diverge ; after suffering re- 
 fraction they will pass in the paths b c, b' c', and if these 
 
 When is light refracted toward and when from the perpendicular ? Is 
 the whole of the light transmitted '( Under what circumstance does total 
 reflexion take place ? What ensues when parallel rays fall on a plane 
 surface ? What is the case with diverging ones ? 
 
188 THE PRISM. 
 
 lines be projected, they will inter- 
 sect at a', but a' b, a' b' are less 
 divergent than a b, a b'. 
 
 If, on the contrary, rays pass 
 from a medium of greater to one 
 of less refractive power, they will 
 be more divergent after refrac- 
 tion. For this reason bodies un- 
 der water appear nearer the sur- 
 face than they actually are. 
 
 When parallel rays of light pass 
 through a medium bounded .by 
 planes that are parallel, as through 
 a plate of glass, they will continue 
 still parallel to one another, and to their original direction, 
 after refraction. For this reason, therefore, we see through 
 such plates of glass objects in their natural positions and 
 relation. 
 
 The optical prism is a transparent medium, having 
 Fig. 208. plane surfaces inclined to one another. It is 
 usually a wedge-shaped piece of glass, a a, 
 a Fig. 208, which can be turned into any suita- 
 ble position, on a ball and socket-joint, c, and 
 is supported on a stand, b. As this instrument 
 is of great use in optical researches, we shall 
 describe the path of a ray of light through, it 
 more minutely. 
 
 Let, therefore, ABC, Fig. 209, be such a glass prism 
 Fi z- 209 - seen endwise, and let 
 
 a b be a ray of light 
 incident at b. As this 
 ray is passing from a 
 
 \~^K rarer to a denser me- 
 
 dium it is refracted 
 c toward the perpendic- 
 
 '"*&' ular to an extent de- 
 
 pendent on the refractive power of the glass of which the 
 prism is composed, and therefore pursues a new path, b 
 c, through the glass ; at c it again undergoes refraction, 
 and now passing from a denser to a rarer medium, takes 
 
 What is the case when parallel rays pass through media with plane and 
 parallel surfaces ? What is a prism ? Describe the path of a ray of light 
 through this instrument. 
 
MULTIPLYING-GLASS. 
 
 189 
 
 Fig, 210. 
 
 a new course, c d. To an eye placed at d, and looking 
 through the prism, an object, a, seems as though it were 
 at a', in the straight line d c continued. Through this in- 
 strument, therefore, the position of objects is changed, 
 the refracted ray, c d, proceeding toward the back, A B, 
 of the prism. 
 
 But the prism in actual practice gives rise to far more 
 complicated and interesting effects, to be described here- 
 after, when we come to speak of the colors of light. 
 
 The multiplying-glass is a 
 transparent body, having sever- 
 al inclined faces. Its construc- 
 tion and action are represented 
 at Fig. 210. Let A B be a 
 plane face, C D also plane and 
 parallel to it, but A C and D B 
 inclined. Now let rays come 
 from any object, a, those, a b, 
 which fall perpendicularly on 
 the two faces will pass with- 
 out suffering refraction ; but 
 those, ac, a d, which fall on the 
 inclined faces will be refracted 
 into new paths, c f, d f, these 
 portions acting like the prism heretofore described. Con- 
 sequently, an eye placed aty* will see three images of the 
 object in the direction of the lines along which the rays 
 have come that is, at a', a, a". Hence the term multi- 
 plying-glass, because it gives as many images of an ob- 
 ject as it has inclined surfaces. 
 
 To what other phenomenon does the prism give rise ? What is the 
 multiplying-glass? Why does it give as many images of an object as it 
 has faces ? 
 
190 
 
 LENSES. 
 
 LECTURE XXXIX. 
 
 THE ACTION OP LENSES. Different Forms of Lenses. 
 General Properties of Convex Lenses. General Proper- 
 ties of Concave Lenses. Analogy between Mirrors and 
 Lenses. Production of Images by Lenses. Size and 
 Distance of Images. Visual Angle. Magnifying Ef- 
 fects. Burning -Lenses. 
 
 TRANSPARENT media having curved surfaces are called 
 lenses. They are of six Fig. 211. 
 
 different kinds, as repre- A .^MMiiMsi^ Plano-convex. 
 sentedin Fig. 211.' The 
 plano-convex lens, A, has B 
 one surface plane and the 
 other convex, the plano- 
 concave, B, has one sur- 
 face plane and the other 
 concave ; C is the double 
 convex, I) the double con- 
 cave, E the meniscus, and 
 F the concavo-convex. 
 
 Plano-concave. 
 Double Convex. 
 Double Concave. 
 
 Meniscus. 
 Concavo-convex. 
 
 For optical uses lenses are commonly made of glass, 
 but for certain purposes other substances are employed. 
 For example, rock crystal is often used for making spec- 
 tacle lenses ; it is a hard substance, and is not, therefore, 
 so liable to be scratched or in- 
 jured as glass. 
 
 In a lens the point c is called 
 the geometrical center, for all 
 lenses are ground to spherical 
 surfaces, and c is the center of 
 their curvature ; the aperture of 
 the lens is a b, and d is its opti- 
 cal center ; f e is the axis, and any 
 ray, m n, which passes through 
 the optical center, is called a principal ray. 
 
 What are lenses ? How many kinds of lenses are there ? What are 
 they commonly made of? What other substances are sometimes used ? 
 What is the geometrical center ? What is the optical center ? What is 
 a principal ray ? What is the aperture ? 
 
ACTION OP LENSES. 
 
 191 
 
 The general action of lenses of all kinds may be under- 
 stood after what has been said in relation to the prism, of 
 which it was remarked that the refracted ray is bent toward 
 the back. Thus, if we have Fig. 213. 
 
 two prisms, a c e, b c e, 
 placed back to back, and 
 allow parallel rays of light, m 
 m n, to fall upon them, 
 these rays, after refraction, 
 being bent from their par- 
 allel path toward the back JT 
 of each prism, will inter- 
 sect each other in some 
 point, as f. Now, there is obviously a strong analogy 
 between the figure of the double convex lens and that of 
 these two prisms; indeed, the former might be regarded 
 as a series of prisms with curved surfaces, and from such 
 consideration it is clear, that when parallel rays fall on a 
 convex lens, they will converge to a focal point. 
 
 Again, let us suppose that a pair of prisms be placed 
 edge to edge, as shown in Fig. 214, and that parallel 
 rays, m n, are incident upon them. These rays undergo 
 refraction, as before, to- fig 214 
 
 ward the back of their re- 
 spective prisms, b c, d e, 
 and therefore emerge di- 
 vergent, as at f and g. n 
 Now, there is an analogy 
 between such a combina- 
 tion of prisms and a con- 
 cave lens, and we there- 
 fore see that the general 
 action of such a lens upon 
 parallel rays is to make 
 them divergent. 
 
 By the aid of the law of refraction it may be proved 
 that lenses possess the following properties. 
 
 Every principal ray which falls upon a convex lens of 
 limited thickness is transmitted without change of direc- 
 tion. 
 
 How may the general action of a double convex lens be deduced from 
 that of a pair of prisms ? Trace the same action in the case of a double 
 concave lens. 
 
192 PROPERTIES OF LENSES. 
 
 Rays parallel to the axis of a double equi-convex glass 
 lens are brought to a focus at a distance from the optical 
 center equal to the radius of curvature of the lens. But 
 if it be a plano-convex glass the focal distance is twice as 
 great. The focus for parallel rays is called the principal 
 focus. 
 
 Rays diverging from the principal focus of a convex 
 lens after refraction become parallel. 
 
 Rays diverging from a point in the axis more distant 
 than the principal focus converge after refraction, their 
 point of convergence being nearer the lens as the point 
 from which they radiated was more distant. 
 
 Rays coming from a point in the axis nearer than the 
 principal focus diverge after refraction. 
 
 With respect to concave lenses, the chief properties 
 may be described as follows : 
 
 Every principal ray passes without change of direction. 
 Fi g . 215. Rays parallel to the 
 
 axis are made diver- 
 gent. Thus, m n, Fig- 
 ure 215, being paral- 
 lel rays falling on the 
 double concave, a b, 
 diverge after refrac- 
 tion in the directions 
 g d ; and if they be 
 produced give rise to 
 a virtual or imaginary 
 focus at f. 
 
 By concave lenses diverging rays are made still more 
 divergent. 
 
 When the effects of lenses are compared with those of 
 mirrors, it will be found that there is an analogy in the 
 action of concave mirrors and convex lenses, and of con- 
 vex mirrors and concave lenses. 
 
 It has already been remarked that concave mirrors 
 give images of external objects in their focus. The same 
 holds good for convex lenses. Thus, if we take a convex 
 lens, and place behind it, at the proper distance, a paper 
 screen, we shall find upon that screen beautiful images of 
 
 What are the chief properties of convex lenses ? What are the chief 
 properties of concave lenses ? What is the relation between mirrors and 
 lenses in their effects ? 
 
FORMATION OF IMAGES. 193 
 
 all the objects in front of the lens in an inverted position. 
 The manner in which they form may be understood from 
 Fig. 216. Where L' L is a double convex lens, M N 
 
 Fig. 216. 
 
 any object, as an arrow, in front of it, the lens will give 
 an inverted image, n m, of the object at a proper distance 
 behind. From the point M all the rays, as M L, M C, 
 M L', after refraction, will converge to a focus, m ; and 
 from the point N all rays, as N L, N C, N I/, will like- 
 wise converge to a focus, n; and so, for every interme- 
 diate point between M and N, intermediate foci will form 
 between m and n, and therefore conjointly give rise to 
 an inverted image. 
 
 The images thus given by lenses or mirrors may be 
 made visible by being received on white screens or on 
 smoke rising from a combustible body, or directly by the 
 eye placed in a proper position to receive the rays. They 
 then appear as if suspended in the air, and are spoken of 
 as aerial images. 
 
 The distance of such images from a lens, and also their 
 magnitude, vary with circumstances. 
 
 If the object be very remote, it gives a minute image 
 in the focus of the lens ; as it is brought nearer, the im- 
 age recedes farther, and becomes larger ; when it is at a 
 distance equal to twice the focal distance, the image is 
 equidistant from the lens on the opposite side, and is of 
 the same size as the object. As the object approaches still 
 nearer, the image recedes, and now becomes larger than 
 the object. When it reaches the focus, the image is at 
 an infinite distance, the refracted rays being parallel to 
 one another. And, lastly, when the object comes be- 
 tween the focus and the surface of the leils, an erect and 
 
 Do convex lenses give rise to the formation of images ? How does this 
 effect arise ? How may such images be made visible ? Under what 
 circumstances do the size and distance of the image vary ? 
 
 I 
 
194 MAGNIFYING POWER. 
 
 magnified image of the object will appear on the same 
 side of the lens as the object itself. Hence, convex lenses 
 are called magnifying-glasses. 
 
 From these considerations, it therefore appears that the 
 
 magnifying power of lenses is not, as is often popularly 
 supposed, due to the peculiar nature of the glass of 
 which they are made, but to the figure of their surfaces. 
 The dimensions of all objects depend on the angles under 
 which they are seen. A coin at a distance of 100 yards 
 appears of very small size, but as it is brought nearer the 
 eye its size increases ; and when only a few inches off, it 
 can obstruct the view of large objects. Thus, if A rep- 
 resent its size at a remote distance, the angle D E F, or 
 the visual angle, is the angle under which it is seen ; when 
 brought nearer, at B, the angle is Gr E H ; and at C, in- 
 creases to I E K. In all cases the apparent size of an 
 object increases as the visual angle increases, arid all ob- 
 jects become smaller as their distances increase ; and 
 any optical contrivances, either of lenses or mirrors, which 
 can alter the angle at which rays enter the eye and make 
 it larger than it would otherwise be, magnify the objects 
 seen through them. 
 
 On these principles concave mirrors and convex 
 lenses magnify, and convex mirrors and concave lenses 
 minify. 
 
 From their property of converging parallel rays to a fo- 
 cus, convex lenses and concave mirrors have an interesting 
 application, being used for the production of high temper- 
 atures, by converging the rays of the sun. Fig. 218 repre- 
 sents such a burning-glass. The parallel rays of the sun 
 
 Why are convex lenses magnifying-glasses ? On what does this mag- 
 nifying action depend ? What is the visual angle of an object ? 
 
COLORED LIGHT. 
 
 195 
 
 Fig. 218. 
 
 falling on it are made to con- 
 verge, and this convergence 
 might be increased by a sec- 
 ond smaller lens. *At the 
 focal point any small object 
 being exposed its tempera- 
 ture is instantly raised. In 
 such a focus there are few sub- 
 stances that can withstand the 
 heat brick, slate, and other 
 such earthy matters instantly 
 boil, metals melt, and even 
 volatilize away. During the 
 last century some French chemists, using one of these 
 instruments, found that when a piece of silver is held 
 over gold, fused at the focus, it became gilded over by 
 the vapor that rose from the melted mass. And in the 
 same way gold could be whitened by the vapors of melt- 
 ed silver. The heat attained in this way far exceeds that 
 of the best constructed furnace. 
 
 LECTURE' XL. 
 
 OP COLORED LIGHT. Action of the Prism. Refraction 
 and Dispersion. The Solar Spectrum. Its Constituent 
 Rays. They pre-exist in White Light. Theory of the 
 Different Rcfrangibility of the Rays of Light. Differ- 
 ent Dispersive Powers. Irrationality of Dispersion. 
 Illuminating Effects. The Fixed Lines. Calorific 
 Effects. Chemical Effects. 
 
 IN speaking of the action of a prism, in Lect. XXXVIII., 
 it was observed, that it gives rise to many interesting 
 results connected with colored lights. These, which con- 
 stitute one of the most splendid discoveries of Newton, I 
 next proceed to explain. 
 
 Through an aperture, a, Fig. 219, in the shutter of a dark 
 room let a beam of light, a e, enter, and let it be inter- 
 cepted at some part of its course by a glass prism, seen 
 
 What is a burning glass ? Why does it give rise to the production of 
 an intense heat ? Mention some of the effects which have been obtained 
 by these instruments. Describe the action of a prism on a ray of light. 
 
196 
 
 DECOMPOSITION OF LIGHT. 
 
 endwise at b c. 
 
 Fig. 219. 
 
 The light will undergo refraction, and 
 in consequence of what has been al- 
 ready stated, will pass in a direction, 
 d, toward the back of the prism. 
 
 Now, for any thing that has yet 
 d been said, it might appear that this 
 refracted ray, on reaching the screen 
 d e, would form upon it a white spot 
 similar to that which it would have 
 given at e, had not the prism inter- 
 vened. But when the experiment is 
 made, instead of the light going as a single pencil of uni- 
 form width, it spreads out into a fan shape, as is indicated 
 by the dotted lines, and forms on the screen an oblong 
 image of the most splendid colors. 
 
 In this beautiful result, two facts, which are wholly 
 distinct, must be remarked : 1st, the light is refracted 
 or bent out of its rectilinear path ; 2d, it is dispersed into 
 an oblong colored figure. 
 
 On examining this figure or image, which passes under 
 the name of the solar spectrum, we find it divided into 
 seven well-marked regions. Its lowest portion, that is to 
 say, the part nearest to that to which the light would have 
 gone had not the prism intervened, is of a red color, the 
 most distant is of a violet, and between 'these other colors 
 may be seen occurring in the following order : 
 
 Fig. 220. 
 
 Red, 
 Orange, 
 Yellow, 
 Green, 
 
 Blue, 
 
 Indigo, 
 Violet. 
 
 truth 
 
 In Fig. 220, the order in which they occur is 
 [indicated by their initial letters, e being the point 
 to which the light would have gone had not the 
 prism intervened. 
 
 Now, from what source do these splendid colors 
 come I Newton proved that they pre-existed in 
 the white light, which, in reality, is made up of 
 I them all taken in proper proportions. 
 
 There are many ways in which this important 
 can be established. Thus, if we take a second 
 
 Is the refracted light white ? What two general facts are to he observ- 
 ed ? What color is the lowest portion of the spectrum ? What is the 
 color of the highest. What is the order of the colors ? 
 
DECOMPOSITION OP LIGHT. 
 
 197 
 
 Fig. 221. 
 
 prism, B B' S', Fig. 
 221, and put it in an in- 
 verted position, as re- 
 spects the first, A A' S, 
 so that it shall refract 
 again in the opposite 
 direction the rays re- 
 fracted by the first, 
 they will, after this 
 second refraction, reunite and form a uniform beam, M, 
 of white light, in all respects like the original beam itself. 
 
 If the production of color were due to any irregular 
 action of the faces of the first prism, the introduction of 
 two more faces in the second prism would only tend to 
 increase the coloration. But so far from this, no sooner 
 is this second prism introduced than the rays reunite and 
 recompose white light. It follows as an inevitable conse- 
 quence that ichite light contains all the seven rays. 
 
 But Newton was not satisfied with this. He further 
 collected the prismatic colored rays together into one 
 focus by means of a lens, and found that they produced 
 a spot of dazzling whiteness. And when he took seven 
 powders, of colors corresponding to the prismatic rays, 
 and ground them intimately together in a mortar, he 
 found that the resulting powder had a whitish aspect ; or 
 if, on the surface of a wheel which could be made to spin 
 round very fast on its axis, colored spaces were painted, 
 when the wheel was made to turn so that the eye could 
 no longer distinguish the separate tints, the whole as- 
 sumed a whitish-gray appearance. 
 
 By many experiments Newton proved that the true 
 cause of this development of brilliant colors from a ray 
 of white light by the prism, is due to the fact that j&afcin- 
 strument does not refract all the colors alike. Thus, it 
 could be completely shown, in the case of any transparent 
 medium, that the violet-ray was far more refrangible than 
 the red, or more disturbed by such a medium from its 
 course. In this originated the doctrine of " the different 
 refraugibility of the rays of light." 
 
 How may it be proved by two prisms that all these colors pre-exist in 
 white light ? What may be proved by reuniting the rays by a lens ? What 
 by colored powders or a painted wheel? What is the cause of this de- 
 velopment of colors? 
 
198 IRRATIONALITY OF DISPERSION. 
 
 On examining the order of colors in the spectrum, we 
 find, in reality, as in Fig. 220, that the red is least dis- 
 turbed from its course, and the other colors follow in a 
 fixed order. The red, therefore, is spoken of as the least 
 refrangible ray, the violet as the most, and the other col- 
 ors as intermediately refrangible. 
 
 We now see the cause of the development of these col- 
 ors from white light, which contains them all. If the 
 prism acted on every ray alike, it would merely produce 
 a white spot at d, analogous to that at e, Fig. 220, but as 
 it acts unequally it separates the colored rays from one 
 another, and gives rise to the spectrum. 
 
 On examining prisms of different transparent media, we 
 find that they act very differently some dispersing the 
 rays far more powerfully than others and giving rise, un- 
 der the same circumstances, to spectra of very different 
 lengths. In the treatises on optics, tables of the disper- 
 sive powers of different transparent bodies are given : 
 thus it appears that oil of cassia is more dispersive than 
 rock-salt, rock-salt more than water, and water more than 
 flu or spar. 
 
 Moreover, in many instances it has been found that if 
 we use different prisms which give spectra of equal lengths, 
 the colored spaces are unequally spread out. This shows 
 that media differ in their refracting action upon particu- 
 lar rays, some acting upon one color more powerfully 
 than another. This is called irrationality of dispersion. 
 
 The different colored rays of light are not equally lu- 
 minous that is to say, do not impress our eyes with an 
 equal brilliancy. If a piece of finely-printed paper be 
 placed in the spectrum, we can read the letters at a much 
 greater distance in the yellow than in the other regions, 
 and from this the light declines on either hand, and grad- 
 ually fades away in the violet and the red. 
 
 It has also been found that the colors are not continu- 
 ous throughout, but that when delicate means of examina- 
 tion are resorted to the spectrum is seen to be crossed with 
 many hundreds of dark lines, irregularly scattered through 
 it. A representation of some of the larger of these is 
 
 To what doctrine did this discovery give rise ? Do different media dis- 
 perse to the same or different extents ? What is meant by irrationality 
 of dispersion ? Are all the rays equally luminous to the eye ? How may 
 this be proved ? 
 
FIXED LINES. 199 
 
 given in Fig. 222. It is curious that though they exist in 
 the sun-light, and in that of the planets, they are 1^.222. 
 not found in the spectra of ordinary artificial I" 
 lights; and, indeed, the electric spark gives a light 
 which is crossed by brilliant lines instead of black 
 ones. The chief fixed lines are designated by the 
 letters of the alphabet, as shown in the figure. 
 
 The light of the sun is accompanied by heat. 
 Dr. Herschel found that the different colored pris- 
 matic spaces possess very different power over I 
 the thermometer. The heat is least in the violet,' 
 and continually increases as we descend through 
 the colors, the red being the hottest of them all. 
 But below this, and out of the spectrum, when 
 there is no light at all, the maximum of heat is] 
 found. The heat of the sunbeam is, therefore, re- j 
 frangible, but is less refrangible than the red ray 
 of light. 
 
 Late discoveries have shown that every ray of light can 
 produce specific changes in compound bodies. Thus 
 it is the yellow ray which controls the growth of plants, 
 and makes their leaves turn green; the blue ray which 
 brings about a peculiar decomposition of the iodides and 
 chlorides of silver, bodies which are used in photogenic 
 drawing. Those substances which phosphoresce after ex- 
 posure to the sun are differently affected by the different 
 rays the more refrangible producing their glow, and the 
 less extinguishing them. 
 
 Describe the fixed lines of the spectrum. How are they distinguished ? 
 What are the calorific effects of the spectrum ? Which is the hottest 
 space ? What are the chemical effects ? 
 
200 
 
 HOMOGENEOUS LIGHT. 
 
 LECTURE XLI. 
 
 OF COLORED LIGHT. Properties of Homogeneous Light. 
 Formation of Compound Colors. Chromatic Aberration 
 of Lenses. Achromatic Prism. Achromatic Lens. 
 Imperfect Achromaticity from Irrationality of Disper- 
 sion. Cause of the Colors of Opaque Objects. Effects of 
 Monochromatic Lights. Colors of Transparent Media. 
 
 EACH color of the prismatic spectrum consists of homo- 
 geneous light. It can no longer be dispersed into other 
 colors, or changed by refraction in any manner. Thus, 
 
 Fig. 223. 
 
 let a ray of light, S, Fig. 223, enter through an aperture, 
 F, into a dark room, and be dispersed by the prism, A B 
 C ; through a hole, G, in a screen, D E, let the resulting 
 spectrum pass, and be received on a second screen, d e, 
 placed some distance behind; in this let there be a small 
 opening, g, through which one of the colored rays of the 
 spectrum, formed by A B C, may pass and be received 
 on a second prisrn, a b c. It will undergo refraction, and 
 pass to the position M on the screen, N M. But it will 
 not be dispersed, nor will new colors arise from it ; and 
 it is immaterial which particular ray is made to pass the 
 opening at g, the same result is uniformly obtained. 
 
 Homogeneous or monochromatic colors, therefore, can- 
 not suffer dispersion. 
 
 By the aid of the instrument Fig. 224, which consists 
 
 How may it be proved that homogeneous light undergoes no further dis- 
 persion ? What is the use of the instrument represented in Fig. 224 ? 
 
COMPOUND COLORS. 201 
 
 of a series of little plane mirrors set upon a frame, we 
 
 fig. 224. 
 
 can demonstrate, in a very striking manner, the constitu- 
 tion of different kinds of lights ; for if this instrument be 
 placed in such a manner as to receive the prismatic spec- 
 trum, by turning its mirrors in a suitable position we can 
 throw the rays they receive at pleasure on a screen. Thus, 
 if we mix together the red and blue ray, a purple results ; 
 if the red and yellow, an orange ; and if the yellow and 
 blue, a green. It is obvious, therefore, that of the colors 
 we have enumerated in Lecture XL, as the seven pris- 
 matic rays, the green, the indigo, and violet may be com- 
 pound, or secondary ones, arising from the intermixture 
 of red, yellow, and blue, which by many philosophers are 
 looked upon as the three primitive colors. 
 
 We have already remarked that there is an analogy be- 
 tween prisms and lenses in their action on the rays of 
 light, and have shown how rays become converging or di- 
 verging in their passage through those transparent solids. 
 In the same manner it also follows, that as prisms pro- 
 duce dispersion as well as refraction, so, 
 too, must lenses: for, by considering 
 the action of pairs of prisms, as in Fig. 
 225, or as we have already done in Lec- 
 ture XXXIX., we arrive at the action of 
 concave and convex lenses, and find that 
 as refrangibility differs for different rays 
 being least for the red and most for 
 the violet a lens acting unequally will cause objects to 
 be seen through it fringed with prismatic colors. This 
 phenomenon passes under the title of chromatic aberra- 
 tion of lenses. 
 
 To understand more clearly the nature of this, let par- 
 allel rays of red light fall upon a plano-convex lens, A 
 
 Which of the colors of the spectrum maybe regarded as compound, and 
 which as simple ? How may it be shown that lenses produce colors as 
 well as prisms I 
 
 I* 
 
202 
 
 CHROMATIC ABERRATION. 
 
 B, Fig. 226, and be converged by it to a focus in the point 
 r, the distance of which from the lens is measured. Then 
 
 Fig. 226. 
 
 let parallel rays of violet light, in like manner, fall on 
 the lens, and be converged by it to a focus, v. On being 
 measured, it will be found that this focus is much nearer 
 the lens than the other; and the cause of it is plainly 
 due to the unequal refrangibility of the two kinds of light. 
 The violet is the more refrangible, and is, therefore, more 
 powerfully acted on by the lens, and made to converge 
 more rapidly. 
 
 But this which we have been tracing in the case of ho- 
 mogeneous rays must of course take place in the com- 
 pound white light. On the same principle that the prism 
 separates the white light into its constituent rays by act- 
 ing unequally on them, so, too, will the lens. Parallel 
 rays of white light falling on a lens, such as Fig. 226, are 
 not, therefore, converged to one common focus, as repre- 
 sented in Lecture XXXIX, but in reality give rise to a 
 series of foci of different colors, the red being the most 
 remote from the lens, and the violet nearest. 
 
 In some of the most important optical instruments it is 
 absolutely necessary that this defect should be avoided, 
 and that a method should be hit upon by which light 
 may be refracted without being dispersed. Newton, who 
 believed that it was impossible to succeed with this, gave 
 up the improvement of the refracting telescope, in which 
 it is required that images should be formed without chro- 
 matic dispersion, as hopeless. But, subsequently, it was 
 shown that refraction without dispersion can be effected. 
 This is done by employing two bodies having equal re- 
 fractive, but unequal dispersive powers. Those which 
 
 What is the effect of a plano-convex lens on parallel rays of red and blue 
 light, respectively ? What is the effect on white light ? 
 
ACHROMATIC PRISM AND LENS. 
 
 203 
 
 Fig. 227. 
 
 are commonly selected are crown and flint glass, which 
 refract nearly equally. The index for crown being about 
 1-53, and that of flint T60 ; but the dispersion of good 
 flint glass is twice that of crown. 
 
 If, now, \ve take two prisms, ABC, 
 Fig. 227, being of crown, and A C D, of 
 flint glass, and place them, with their bases 
 in opposite ways, the refracting angle, C,' 
 of the latter being half that of A, the 
 former, or, in other words, adjusted to 
 their relative dispersive powers, it will be found that a ray 
 of light passes through the compound prism, undergoing re- 
 fraction, and emerging without dispersion; for the incident 
 ray, in its passage through the crown prism will be dis- 
 persed into the colored rays, and these, falling on the 
 flint prism the dispersive power of which we assume to 
 be double, and acting in the opposite direction will be re- 
 fracted in the opposite direction, and emerge undispersed. 
 Such an instrument is called an achromatic prism. 
 
 The same principle can, of course, be 
 used in the construction of lenses, between 
 which and prisms there is that general 
 analogy heretofore spoken of. The achro- 
 matic lens consists of a concave lens of 
 flint and a convex one of crown, the cur- 
 vatures of each being adjusted on the same 
 principle as the angles of the achromatic 
 prism are determined. Such an arrange- 
 ment is represented in Fig. 228. It gives 
 in its focus the images of objects in 
 their natural colors, and nearly devoid of 
 fringes. 
 
 But in practice, it has been found impossible, by any 
 such arrangement, to effect the total destruction of color. 
 The edges of luminous bodies seen through such lenses 
 are fringed with color to a slight extent. This arises 
 from the circumstance that the dispersive powers of the 
 media employed are not the same for every colored ray. 
 The simple achromatic lens, Fig. 228, will collect the ex- 
 How may refraction without dispersion be performed ? Describe the 
 structure of the achromatic prism ? What is its mode of action ? Describe 
 the construction of the achromatic lens. Why are there with these lenses 
 residual fringes ? 
 
204 COLORS OF OBJECTS. 
 
 treme rays together ; but leaves the intermediate ones, 
 to a small extent, outstanding. 
 
 The theory of the compound constitution of light ena- 
 bles us to account, in a clear manner, for the colors of 
 natural objects. Those which exhibit themselves to us 
 as white merely reflect back to the eye the white light 
 which falls on them, and the black ones absorb all the in- 
 cident rays. The general reason of coloration is, there- 
 fore, the absorption of one or other tint, and the reflec- 
 tion of the rest of the spectral colors. Thus, an object 
 looks blue because it reflects the blue rays more copiously 
 than any others, absorbing the greater part of the rest. 
 And the same explanation applies to red or yellow, and, 
 indeed, to any compound colors, such as orange, green, 
 &c. That colored bodies do, in this way, reflect one class 
 of rays more copiously than others may be proved by 
 placing them in the spectrum. Thus, a red wafer seems 
 of a dusky tint in the blue or violet regions, but of a brill- 
 iant red in the red rays. 
 
 On the same principles we account for the singular re- 
 sults which arise when monochromatic lights fall on sur- 
 faces of any kind. Thus, when spirits of wine is mixed 
 with salt in a plate, and set on fire, the flame is a mono- 
 chromatic yellow that is, a yellow unaccompanied by 
 any other ray. If the variously colored objects in a room 
 are illuminated with such a light they assume an extraor- 
 dinary appearance : the human countenance, for exam- 
 ple, taking on a ghastly and death-like aspect ; the red of 
 the lips and the cheeks is no longer red, for no red light 
 falls on it ; it therefore assumes a grayish tint. 
 
 The colors of transparent bodies, such as stained glass 
 and colored solutions, arise from the absorption of one 
 class of rays and the transmission of the rest. Thus, 
 there are red glasses and red solutions which permit the 
 red ray alone to traverse them, and totally extinguish 
 every other. But, in most cases, the colors of transpa- 
 rent, and also of opaque bodies, are far from being mono- 
 chromatic. They consist, in reality, of a great number 
 
 How may the colors of natural objects be accounted for? What is the 
 cause of whiteness and blackness? How can it be proved that bodies re- 
 flect some rays in preference to others ? What is monochromatic light ? 
 What is the cause of the singular appearance of objects seen by such 
 lights ? What is the cause of the colors <jf transparent bodies 1 
 
UXDULATORY THEORY. 205 
 
 of different rays. Thus, common blue-stained glass trans- 
 raits almost all the blue light that falls upon it, and, in ad- 
 dition, a little yellow and red. 
 
 LECTURE XLII. 
 
 UNDULATORY THEORY OF LIGHT. Two Theories of Light. 
 Applications of the Corpuscular Theory. Undulatory 
 Theory. Length of Waves is the cause of Color. De- 
 termination of Periods of Vibration. Interference of 
 Light. Explanations of Newton's Rings, and Colors of 
 tJiin Plates. Diffraction of Light. 
 
 IT has been stated that there are two different theories 
 respecting the nature of light the corpuscular and the 
 undulatory. In accounting for the facts in relation to the 
 production of colors, it is assumed that, in the former, 
 there are various particles of luminous matter answering 
 to the various colors of the rays, and which, either alone 
 or by their admixture, give rise to the different tints we 
 see. In white light they all exist, and are separated 
 from one another by the prism, because of an attractive 
 force which such a transparent body exerts ; and that at- 
 tractive force being unequal for the different color-giving 
 particles, difference of refrangibility results. The colors of 
 natural objects on this theory are explained by supposing 
 that some of the col or- giving particles are reflected or 
 transmitted, and others stifled or stopped by the body on 
 which they fall. The phenomena of reflection by pol- 
 ished surfaces are therefore reduced to the impact of 
 elastic bodies ; and in the same way that a ball is repel- 
 led from a wall against which it is thrown, so these little 
 paiticles are repelled, making their angle of reflexion 
 equal to their angle of incidence. But while there are 
 many of the phenomena of light, such as reflexion, re- 
 fraction, dispersion, and coloration, which can be ac- 
 counted for on these principles, there are others which 
 
 What are the two theories of light ? What is the nature of the corpuscu- 
 lar theory ? On its principles what is the constitution of white light ? How 
 does it account for difference of refrangibility and the colors of natural 
 objects ? How does it account for the phenomena of reflexion ? 
 
206 VIBRATIONS IN THE ETHER. 
 
 the emanation or corpuscular theory cannot meet. These 
 are, however, explained in a simple and beautiful manner 
 by the other theory. 
 
 The undulatory theory rests upon the fact that there 
 exists throughout the universe an elastic medium called 
 THE ETHER, in which vibratory movements can be estab- 
 lished very much after the manner that sounds arise in 
 the air. Whatever, therefore, has been said in Lectures 
 XXXI, &c., respecting the mechanism and general princi- 
 ples of undulatory movements applies here. Waves in 
 the ether are reflected, and made to converge or di- 
 verge on the same principles that analogous results take 
 place for waves upon water or sounds in the air. It will 
 have been observed already that the reflexions of undu- 
 lations from plane, spherical, elliptic, or parabolic sur- 
 faces, as given in Lecture XXXII, are identically the 
 same as those which we have described for light in Lec- 
 ture XXXVII. 
 
 From the phenomena of sound we can draw analogies 
 which illustrate in a beautiful manner the phenomena of 
 light : for, as the different notes of the gamut arise from 
 undulations of greater or less frequency, so do the colors 
 of light arise from similar modifications in the vibrations 
 of the ether. Those vibrations that are most rapid im- 
 press our eyes with the sensation of violet, and those that 
 are slower with the sensation of red. The different col- 
 ors of light are, therefore, analogous to the different notes 
 of sound. 
 
 In Lecture XXXIII it was shown how the frequency of 
 vibration which could give rise to any musical note might 
 be determined, and it appeared that the ear could detect 
 vibrations, as sound through a range commencing with 15 
 and reaching as far as 48,000 in a second. The frequen- 
 cy of vibration in the ether required for the production 
 of any color has also been determined, and the lengths of 
 the waves corresponding. The following table gives these 
 results. The inch being supposed to be divided into ten 
 millions of equal parts, of those parts the wave lengths 
 
 On what does the undulatory theory rest? Do the general laws of undu- 
 lations apply to the phenomena of light ? What analogy is there be- 
 tween sound and light ? How do the colors of light compare with the 
 notes of sound ? 
 
TIMES OF VIBRATION. 207 
 
 For Red light 
 Orange 
 yellow 
 Green 
 Blue 
 Indigo 
 Violet 
 
 256 
 240 
 227 
 211 
 196 
 185 
 174 
 
 More recent investigations have proved the remarkable 
 fact that the length of the most refrangible violet wave 
 being taken as one, that of the least refrangible red will be 
 equal to two, and the most brilliant part of the yellow 
 one and a half. 
 
 Knowing the length of a wave in the ether required for 
 the production of any particular color of light, and the 
 rate of propagation through the ether, which is 195,000 
 miles in a second, we obtain the number of vibrations ex- 
 ecuted in one second, by dividing the latter by the former. 
 
 From this it appears that if a single second of time be 
 divided into one million of equal parts, a wave of red light 
 vibrates 458 millions of times in that short interval, and 
 a wave of violet light 727 millions of times. 
 
 Further, whatever has been said in Lectures XXXI 
 XXXII, in reference to the interference of waves, must 
 necessarily, on this theor}', apply to light. Indeed, it was 
 the beautiful manner in which some of the most incom- 
 prehensible facts in optics were thus explained, that has 
 led to its^-almost universal adoption in modern times. 
 That light added to light should produce darkness, seems 
 to be entirely beyond explanation on the corpuscular 
 theory ; but it is as direct a consequence of the undula- 
 tory, as that sound added to sound may produce silence. 
 
 From a lucid point, p, Fig. 229, let rays of light fall 
 upon a double prism, m n, the angle of which, at C, is 
 very obtuse. From what has been said respecting the 
 multiplying-glass (Lecture XXXVIII), it appears that an 
 eye applied at a would see the point p double, as at p' 
 and p". Between these images there is also perceived a 
 number of bright and dark lines perpendicular to a line 
 joining p' and p". On covering one half the prism the 
 lines disappear, and only one image is seen. 
 
 What relation of wave length exists between the least, the intermediate, 
 and the most refrangible rays? How may the frequency of vibrations be 
 determined from the wave length ? What is that frequency in the case of 
 red and 'violet light? Does interference of luminous waves take place? 
 How is this exhibited by the double prism, Fig. 229 ? 
 
208 
 
 INTERFERENCE OF LIGHT. 
 
 This alternation of light and darkness is caused by 
 ethereal waves from the points p' and^?" crossing one an- 
 other, and giving rise to interference. If, therefore, with 
 
 Fig. 229. 
 
 those points as centers, we draw circular arcs, 0, 1, 2, 
 3, 4, &c., these may represent waves, the alternate lines 
 between them being half waves. It will be perceived 
 that wherever two whole waves or two half waves en- 
 counter, they mutually increase each other's effect ; but 
 if the intersection takes place at points where the vibra- 
 tions are in opposite directions, interference, and, there- 
 fore, a total absence of light results, as is marked in the 
 figure by the large dots. 
 
 Wherever, therefore, rays of light are arranged so 
 as to encounter one another in opposite phases of vi- 
 bration, interference takes place. Thus, if we take a 
 230 convex lens, of very long focus, and 
 
 press it upon a flat glass by means of 
 screws, Fig. 230, at the point of con- 
 tact, when we inspect the instrument 
 by reflected light a black spot will be 
 seen, surrounded alternately by light 
 i<-er and dark rings. These pass under the 
 name of Newton's colored rings. When the light is ho- 
 mogeneous the dark rings are black, and the colored ones 
 of the tint which is employed, but when it is common 
 
 What is the effect of two whole or two half waves encountering? 
 When does interference take place? Describe the process for forming 
 Newton's colored rings. 
 
DIFFRACTION OF LIGHT. 209 
 
 white light the central black spot is surrounded by a se- 
 ries of colors. When the instrument is inspected by 
 transmitted light, the colors are all complementary, and 
 the central spot is of course white. These rings arise 
 from the interference of the rays reflected from the ante- 
 rior and posterior boundaries between the two glasses. 
 The colors of soap-bubbles and thin plates of gypsum, 
 are referable to the same cause. 
 
 By the diffraction of light is meant its deviation from 
 the rectilinear path, as it passes by the edges of bodies or 
 Fig. 231. through apertures. It arises from 
 
 the circumstance that when ethereal, 
 or, indeed, any kind of waves im- 
 pinge on a solid body, they give rise 
 to new undulations, originating at the 
 place of impact, and often producing 
 interference. Thus, if a diverging 
 beam of light passes through an ap- 
 erture, a b, Fig. 231, in a plate of 
 metal an eye placed beyond will dis- 
 cover a series of light and dark fringes. The cause of 
 these has been already explained in Lecture XXXII., in 
 which it was shown that from the points a and b new 
 systems of undulations arise, which interfere with one an- 
 other, and also with the original waves. 
 
 What is the cause of them ? What is the cause of the colors of soap- 
 bubbles and their films generally ? What is meant by the diffraction of 
 light? 
 
f 
 
 210 POLARIZATION OF LIGHT. 
 
 LECTURE LXIII. 
 
 OF POLARIZED LIGHT. Peculiarity of Polarized Light. 
 Illustrated by the Tourmaline. Polarization by Reflex- 
 ion. General Law of Polarization. Positions of no 
 Reflexion. Plane of Polarization. Polarization by 
 Refraction. Application of the Undulatory Theory. 
 The Polariscopc. 
 
 WHEN a ray of common light is allowed to fall on the 
 surface of a piece of glass it can be equally reflected by 
 the glass upward, downward, or laterally. 
 
 If such a ray falls upon a glass plate at an angle of 
 56, and is received upon a second similar plate at a sim- 
 ilar angle, it will be found to have obtained new proper- 
 ties : in some positions it ca.n be reflected as before, in 
 others it cannot. On examination, it is discovered that 
 these positions are at right angles to one another. 
 
 Again : if a ray of light be caused to pass through a 
 Fig. 232. plate of tourmaline, c d, Fig. 
 
 C /AM^ e A, 232 > m tne direction a b, and 
 be received upon a second plate, 
 ' placed symmetrically with the 
 first, it passes through both with- 
 out difficulty. But if the second 
 plate be turned a quarter round, as at g h, the light is 
 totally cut off. 
 
 Considering these results, it therefore appears that we 
 can impress upon a ray of light new properties by cer- 
 tain processes, and that the peculiarity consists in giving 
 it different properties on different sides. Such a ray, 
 therefore, is spoken of as a ray of polarized light. 
 
 When light is polarized by reflexion, the effect is only 
 completely produced at a certain angle of incidence, 
 which therefore passes under the name of the angle of 
 
 What is observed in the reflexion of ordinary light ? What occurs 
 when light which has already been reflected at 56 is attempted to be re- 
 flected again? Describe the action of a tourmaline. What is meant by 
 polarized light? Under what circumstances does maximum polarization 
 take place ' 
 
POLARIZATION OF LIGHT. 
 
 211 
 
 maximum polarization. It takes place when the reflected 
 ray makes, with the refracted ray, an angle of 90. 
 
 Fig. 233. 
 
 Thus, let A B, Fig. 233, be a plate of glass, a b an inci- 
 dent ray, which, at b, is partly reflected along b c and 
 partly refracted along b e, emerging therefrom at e d. 
 Now, maximum polarization ensues when c b e is a 
 right angle, from which it follows that the polarizing 
 power is connected with the refractive, the law being 
 that " the index of refraction is the tangent of the angle 
 of polarization." 
 
 Let A B, Fig. 234, be a plate of glass, on which a 
 ray of light, a b, 
 falls, and after po- 
 larization is reflect- 
 ed along be; ate let 
 it be received on a 
 second plate, C D, 
 similar to the for- 
 mer, and capable 
 of revolving on c b, 
 as it were on an 
 axis. Let us now 
 examine in what 
 positions of this 
 plate the polaiized ray, b c, can be reflected, and in what 
 it cannot. 
 
 What is the law connecting refraction and polarization? What are the 
 relative positions of the reflecting plates when the ray cannot be re- 
 flected? 
 
212 PHENOMENA OF POLARIZATION. 
 
 Experiment at once shows that when the plane of re- 
 flexion of the first mirror coincides with the plane of rc- 
 2^.235. flexion of the second, 
 
 the polarized ray un- 
 dergoes reflexion ; 
 but if they are at right 
 angles to one another, 
 it is no longer reflect- 
 ed. To make this 
 clear, let a b,Fig. 235, 
 be the first mirror, and 
 c d the second, so ar- 
 ranged as to present 
 their edges, as seen 
 depicted on this page. 
 Again : let cf be the 
 first and g li the sec- 
 
 i 1. ond, now turned half 
 
 *? way round, but still 
 presenting its edge, in 
 both those positions, 
 the planes of incidence 
 
 j | and reflexion of both 
 
 the mirrors coincid- 
 ing, the ray polarized 
 
 by a b or ef will be reflected. But if, as in i &, the sec- 
 ond mirror, I, is turned so as to present its face, or, as 
 in m n, it is turned at o, so as to present its back, in 
 these cases, the planes of incidence and reflexion of the 
 two mirrors being at right angles, the polarized ray can 
 no longer be reflected. We have, therefore, two posi- 
 tions in which reflexion is possible, and two in which it 
 is impossible, and these are at right angles to one 
 another. By the plane of polarization we mean the plane 
 in which the ray can be completely reflected from the 
 second mirror. 
 
 When a ray of light falls on the surface of a transparent 
 medium, it is divided into two portions, as has already 
 been said, one of tflese being reflected and the other re- 
 fracted. On examination, both these rays are found to 
 be polarized, but they are polarized in opposite ways, or 
 
 What is the plane of polarization 1 In the case of a transparent me- 
 dium, what is the relation between the reflected and refracted rays 1 
 
EXPLANATION OF POLARIZATION. 213 
 
 rather the plane of polarization of the refracted is at 
 right angles to the plane of polarization of the reflect- 
 ed ray. 
 
 When it is required to polarize light by refraction a 
 pile of several plates of thin glass is used, for polarization 
 from a single surface is incomplete. 
 
 On the undulatory theory we can give a very clear 
 account of all these phenomena. Common light origi- 
 nates in vibratory movements taking place in the ether ; 
 but it differs from the vibrations in the air which consti- 
 tute sound in this essential particular that, while in the 
 waves of sound the movements of the vibrating particles 
 lie in the course of the ray, in the case of light they are 
 transverse to it. This may be made plain by considering 
 the wave-like motions into which a cord may be thrown 
 by shaking it at one end, the movement being in the 
 up-and-down or in the lateral direction, while the wave 
 runs straight onward. The ethereal particles, therefore, 
 vibrate transversely to the course of the ray. But then 
 there are an infinite number of directions in which these 
 transverse vibrations may be made : a cord may be shaken 
 vertically or laterally, or in an infinite number of inter- 
 mediate angular positions, all of which are transverse to 
 its length. 
 
 Common light, therefore, arises in ethereal vibrations, 
 taking place in every possible direction transverse to the 
 path of the ray ; but in polarized light the vibrations are 
 all in one plane. Thus, in the case of the tourmaline, 
 when a ray passes through it all the vibrations are taking 
 place in one direction, and therefore the ray can pass 
 through a second plate placed symmetrically with the 
 first ; but if the second be turned a 
 quarter round the vibrations can no 
 longer pass, just in the same way th 
 a sheet of paper, c d, may be slipped 
 through a grating, a b, while its plane 
 coincides with the length of the bars; 
 but can no longer go through when it is 
 turned as at ef, a quarter round. 
 
 How is light to be polarized by refraction ? What is light according to 
 the undulatory theory? In what directions are the vibrations made? 
 How may this be illustrated by a cord? In what directions are the vibra- 
 tions of polarized light ? How is this illustrated ia Fig. 236 ? 
 
214 
 
 POLARIZED RAYS. 
 
 Fig. 237. 
 
 Again, in the case of polarization by reflexion, let A B, 
 
 Fig. 237, be the mirror on 
 which a ray of common 
 light, a b, falls at the prop- 
 er angle of polarization, 
 and is reflected in a polar- 
 ized condition along b c. 
 C D will be the plane in 
 which the ethereal parti- 
 cles vibrate after reflection, 
 and the curve line drawn 
 on it may represent .the 
 intensities of their vibra- 
 tions. 
 
 So, too, in Fig. 238, we 
 have an illustration of polarization by refraction. Let A B 
 
 Fig 238. 
 
 be a bundle of glass plates, 
 a b the incident, and c d the 
 polarized ray; the plane C D 
 at right angles to the plates 
 is the plane of polarization, 
 and the curve drawn on it 
 represents the intensities 
 with which the polarized 
 particles move. 
 
 In every instance the plane 
 of polarization is perpendic- 
 
 ular to the planes of reflexion and refraction. 
 
 Fig. 239. The polariscope is an instru- 
 
 ment for exhibiting the proper- 
 ties of polarized light. There 
 are many different forms of it : 
 Fig. 239 represents one of 
 them. It consists of a mirror 
 of black glass, a, which can be 
 set at any suitable angle to the 
 brass tube, A B, by means of a 
 graduated arc, e; it can also be 
 rotated on the axis of the tube 
 
 B A, and the amount of that rotation read off on the 
 
 What is the illustration given as respects reflected light in Fig. 237 ? 
 What is it for refracted light in Fig. 238 ? What is the constant position 
 of the plane of polarization ? Describe the polariscope. 
 
DOUBLE REFRACTION. 215 
 
 graduated circle b. At the other end of the tube there 
 is a second mirror of black glass, d, which, like a, can be 
 arranged at any required angle, and likewise turned 
 round on the axis of the brass tube, A B, the amount of 
 its rotation being ascertained by the divided circle, c. 
 Sometimes instead of this mirror of black glass, a bundle 
 of glass plates in a suitable frame is useo!. The instru- 
 ment is supported on a pillar, C. 
 
 The fundamental property of light polarized by re- 
 flexion may be exhibited by this instrument as follows : 
 Set its two mirrors, a and d, so as to receive the light 
 which falls on them at an angle of 56. Then, when the 
 first, a, makes its reflexion in a vertical plane, the light 
 can be reflected by d also in a vertical plane, upward or 
 downward. But if d be turned round 90, so as to 
 attempt to reflect the ray to the right or left in a hori- 
 zontal plane, it will be found to be impossible, the light 
 becoming extinct and in intermediate positions; as the 
 mirror revolves the light is of intermediate intensity. 
 
 LECTURE XLIV. 
 
 ON DOUBLE REFRACTION AND THE PRODUCTION OP COL- 
 ORS IN POLARIZED LIGHT. Double Refraction of Ice- 
 land Spar. Axis of the Crystal. Crystals with two 
 Axes. Production of Colors in Polarized Light. 
 Complementary Colors Produced. Colors Depend 071 
 the Thickness of the Film. Symmetrical Rings and 
 Crosses. Colors Produced by Heat and Pressure. 
 Circular and Elliptical Polarization. 
 
 BY double refraction we mean a property possessed by 
 certain crystals, such as Iceland spar, of dividing a single 
 incident ray into two emergent ones. Thus, let R r be a 
 ray of light falling on a rhomboid of Iceland spar, ABC 
 X, in the point r, it will be divided during its passage 
 through the crystals into two rays, r E, r O, the latter of 
 
 How may this instrument be used to exhibit light polarized by reflexion ? 
 What is meant by double refraction? Describe the phenomena exhibited 
 by a crystal of Iceland spar. 
 
216 
 
 DOUBLE REFRACTION. 
 
 Fig. 240. 
 
 -.N 
 
 Fig. 241. 
 
 which follows the ordi- 
 n nary law of refraction, 
 and therefore takes the 
 name of the ordinary ray, 
 the former follows a dif- 
 ferent law and is spoke 
 of as the extraordinary 
 ray. 
 
 Through such a crys- 
 tal objects appear double. 
 A line, M N, on a piece of 
 paper viewed through it is exhibited as two lines, M N,m 
 n, the amount of separation depending on the thickness 
 of the crystal. The emergent rays E e, O o, are parallel 
 after they leave the surface X. 
 
 A line drawn through the crystal from 
 one of its obtuse angles to the other is 
 called the axis of the crystal, and if arti- 
 ficial planes be ground and polished as 
 n m, op, perpendicular to this axis, a b, 
 Fig. 241, rays of light falling upon this 
 axis or parallel to it do not undergo 
 double refraction. 
 
 Fig. 242. Or, if new faces, o p, n m, Fig. 242, 
 
 I be ground and polished parallel to the 
 axis a b, a ray falling in the direction df 
 also remains single. 
 
 But if the refracting faces are neither 
 at right angles nor parallel to the axis, 
 double refraction always ensues. 
 While Iceland spar has only one axis of double refrac- 
 tion, there are other crystals, such as mica, topaz, gypsum, 
 &c., that have two. In crystals that have but one axis 
 there are differences. In some the extraordinary ray is 
 inclined from the axis in others toward it when compared 
 with the ordinary ray. The former are called negative 
 crystals, the latter positive. 
 
 The explanation which the undulatory theory gives of 
 this phenomenon in crystals having a principal axis is, 
 that the ether existing in the crystal is not equally elastic 
 
 What is the axis of the crystal ? In what cases does an incident ray not 
 undergo double refraction ? What crystals have two axes of double refrac- 
 tion ? What are negative crystals ? What are positive ones ? 
 
 ff, 
 
COLORS IN POLARIZED LIGHT. 
 
 217 
 
 in every direction. Undulations are therefore propagated 
 unequally, and a division of the ray takes place, those 
 undulations which move quickest having the less index of 
 refraction. 
 
 When the two rays emerging from a rhomb of Iceland 
 spar are examined, they afe both found to consist of light 
 totally polarized, the one being polarized at right angles 
 to the other. 
 
 We have, therefore, several different ways in which 
 light can be polarized by reflexion, refraction, absorp- 
 tion, and double refraction. 
 
 When a crystal of Iceland spar is ground to a prismatic 
 shape, and then achromatized by a prism of glass, it forms 
 one of the most valuable pieces of polarizing apparatus 
 that we have. Such a prism may be used to very great 
 advantage instead of the mirror of the apparatus, Fig. 239. 
 
 If a ray of polarized light is passed through a thin 
 plate of certain crystalized bodies, such as mica or gyp- 
 sum, and the light then viewed through an achromatic 
 prism or by reflexion from the second mirror of the 
 polarizing machine, Fig. 239, brilliant colors are at once 
 
 Fig. 243. 
 
 developed. Thus, let R A be a ray of light incident on 
 the first mirror of the polariscope, A G the resulting 
 polarized ray, and D E F G be a thin plate of gypsum 
 or mica. If, previous to the introduction of this plate, 
 the two mirrors A and C be crossed, or at right angles to 
 one another, the eye placed at E will perceive no light ; 
 
 What is the explanation of double refraction on the undulatory theory? 
 \Vhat is the condition of the emergent rays? In what ways may light 
 be polarized ? Under what circumstances are colors developed by polar- 
 ized light ? 
 
218 COLORS IN POLARIZED LIGHT. 
 
 but, on the introduction of the crystal, its surface appears 
 to be covered with brilliant colors, which change their 
 tints according as it is inclined, or as the light passes 
 through thicker or thinner places. On further examination 
 it will be found that there are two lines, D E and F G, 
 which, when either of them is parallel or perpendicular 
 to the plane of polarization, R A C or A C E, no colors 
 are produced. But if the plate be turned round in its 
 own plane a single color appears, which becomes most 
 brilliant when either of the lines a b, c d, inclined 45, to 
 the former ones are brought into the plane of polarization. 
 The former lines are called the neutral, and the latter the 
 depolarizing axes of the film. 
 
 This is what takes place so long as we suppose the two 
 mirrors, A C, fixed ; but if we make the mirror nearest 
 to the eye revolve while the film is stationary, the phe- 
 nomena are different. Let the film be of such a thickness 
 as to give a red tint, and be fixed in such a position as 
 to give its maximum coloration, and the eye-mirror to re- 
 volve, it will be found that the brilliancy of the color de- 
 clines, and it disappears when a revolution of 45 has 
 been accomplished ; and now a pale green appears, which 
 increases in brilliancy until 90 are reached, when it is at 
 a maximum. Still continuing the revolution, it becomes 
 paler, and at 135 it has ceased, and a red blush com- 
 mences, which reaches its maximum at 180 ; and the 
 same system of changes is run through in passing from 
 180 to 360 ; so that while the film revolves only one 
 color is seen, but as the mirror revolves two appear, 
 If, instead of using a mirror, we use an achromatic 
 Fig. 244. prism, we have two im- 
 
 ages of the film at the 
 same time, and we find 
 that they exhibit comple- 
 mentary colors that is, 
 colors of such a tint that 
 if they be mixed togeth- 
 er they produce white 
 light. This effect is rep- 
 resented in Fig. 244. 
 
 What are the neutral axes of the film? What are its depolarizing axes ? 
 what takes place when the film is stationary and the mirror revolves ? 
 What is the relation of the two resulting colors to each other? 
 
RINGS AND CROSSES. 
 
 219 
 
 That the particular colors which appear depend on the 
 thickness of the films, is readily established by taking a 
 thin wedge-shaped piece of sulphate of lime, and expos- 
 ing it in the polariscope ; all the different colors are then 
 seen, arranged in stripes according to the thickness of the 
 film. 
 
 When a slice of an uniaxial crystal cut at right angles 
 to the axis is used instead of the films, in the foregoing 
 experiment, very brilliant effects are produced, consisting 
 
 Fig. 245. 
 
 of a series of colored rings, arranged symmetrically and 
 marked in the middle by a cross, which may either be light 
 or dark light if the second mirror is in the proper po- 
 sition to reflect the light from the first, and dark if it be 
 at right angles thereto. 
 
 In crystals having two axes a complicated system of 
 oval rings, originating round each axis, may be perceiv- 
 
 Fig. 246. 
 
 ed, intersected by a cross. Fig. 246, represents the ap- 
 pearance in a crystal of nitrate of potash ; and in the same 
 way other figures arise with different crystals. 
 
 How can it be proved that the color is determined by the thickness of 
 the film? What phenomena are seen when slices from crystals are used ? 
 With crystals of two axes what are the results ? 
 
220 EFFECTS OF PRESSURE, ETC. 
 
 If transparent noncrystalized bodies are employed in 
 these experiments, no colors whatever are perceived. 
 
 Fig. 247. 
 
 Thus, a plate of glass placed in the polariscope, gives 
 rise to no such development ; but if the structure of the 
 glass be disturbed, either by warming it or cooling it un- 
 equally, or if it be subjected to unequal pressure from 
 screws, then colors are at once developed. This proper- 
 ty may, however, be rendered permanent in glass, by heat- 
 ing it until it becomes soft and then cooling it with rap- 
 idity. 
 
 All the phenomena here described belong to the divi- 
 sion of plane polarization but there are other modifica- 
 tions which can be impressed on light, giving rise to very 
 remarkable and intricate results : these are designated 
 circular, elliptical, &c., polarization. The mechanism of 
 the motions impressed on the ether to produce these re- 
 sults is not difficult to comprehend ; for common light, as 
 has been stated, originates in vibrations taking place in 
 every direction transverse to the ray; plane polarized light 
 arises from vibrations in one direction only : and when the 
 ethereal molecules move in circles they originate circular- 
 ly polarized light, and if in ellipses, elliptical. 
 
 When glass is unequally warmed or cooled, or subjected to unequal 
 pressure*, what is the result ? How may these effects be made perma- 
 nent? What modification of the ether gives rise to plane polarization ? 
 What to circular and what to elliptical ? 
 
THE KAINBOW. 221 
 
 LECTURE XLV. 
 
 NATURAL OPTICAL PHENOMENA. The Rainbow. Condi- 
 tions of its Appearance. Formation of the Inner Bow. 
 Formation of the Outer Bow. The Bows are Cir- 
 cular Arcs. Astronomical Refraction. Elevation of 
 Objects. The Ticilight. Reflexion from the Air. Mi- 
 rages and Spectral Apparitions, and Unusual Refraction. 
 
 THE rainbow, the moat beautiful of meteorological 
 phenomena, consists of one or more circular arcs of pris- 
 matic colors, seen when the back of the observer is turn- 
 ed to the sun, and rain is falling between him and a cloud, 
 which serves as a screen on which the bow is depicted. 
 When two arches are visible the inner one is the most 
 brilliant, and the order of its colors is the same in which 
 they appear in the prismatic spectrum the red fringing 
 its outer boundary, and the violet being within. This 
 is called the primary bow. The secondary bow, which is 
 the outer one, is fainter, and the colors are in the invert- 
 ed order. When the sun's altitude above the horizon ex- 
 ceeds 42 the inner bow is not seen, and when it is more 
 than 54 the outer is invisible. If the sun is in the hori- 
 zon, both bows are semicircles, and according as his alti- 
 tude is greater a less and less portion of the semicircle is 
 visible ; but from the top of a F - 343 
 
 mountain bows that are larger 
 than a semicircle may be seen. 
 
 These prismatic colors arise 
 from reflexion and refraction 
 of light by the drops of rain, 
 which are of a spherical figure. 
 In the primary bow there is 
 one reflexion and two refrac- 
 tions ; in the secondary there 
 
 Under what circumstances does the rainbow form? Of the two bows 
 which is the most brilliant ? What is the order of the colors ? What is 
 their order in the secondary bow ? What are the circumstances which de- 
 termine the visibility of each bow ? When are they semicircles ? When 
 more than semicircles ? How is the primary bow formed ? 
 
222 THE RAINBOW. 
 
 are two reflexions and two refractions. Thus, let S, Fig. 
 248, be a ray of light, incident on a raindrop, a ; on ac- 
 count of its obliquity to the surface of the drop, it will be 
 refracted into a new path, and at the back of the drop it 
 will undergo reflexion, and returning to the anterior face 
 and escaping it will be again refracted, giving rise to 
 violet and red and the intermediate prismatic colors 
 between, constituting a complete spectrum; and as the 
 drops of rain are innumerable the observer will see in- 
 numerable spectra arranged together so as to form a cir- 
 cular arc. 
 
 m ^g The secondary rainbow arises 
 
 " from two refractions and two re- 
 flexions of the rays. Thus, let 
 the ray S, Fig. 249, enter at the 
 bottom of the drop, it passes in 
 the direction toward I' after hav- 
 ing undergone refraction at the 
 front; from I' it moves to I", where 
 it is a second time reflected, and then emerges in front, 
 undergoing refraction and dispersion again. For the 
 same reason as in the other case, prismatic spectra are 
 seen arranged together in a circular arc and form a bow. 
 In Fig. 250, let O be the spectator and O P a line 
 drawn from his eye to the center of the bows. Then 
 rays of the sun, S S, falling on the drops ABC, will 
 produce the inner bow, and falling on D E F, the outer 
 bow, the former by one and the latter by two reflexions. 
 The drop A reflects the red, B the yellow, and C the blue 
 rays to the eye ; and in the case of the outer bow, F the 
 red, E the yellow, and D the blue. And as the color 
 perceived is entirely dependent on the angle under which 
 the ray enters the eye, as in the case of the interior bow, 
 the blue entering at the angle COP, the yellow at the 
 larger angle BOP, and the red and the largest A O P, 
 we see the cause why the bows are circular arcs. For 
 out of the innumerable drops of rain which compose the 
 shower, those only can reflect to the eye a red color 
 which make the same angle, A O P, that A does with 
 the line O P, and these must necessarily be arranged in 
 
 What are the conditions for the formation of the secondary bow ? Why 
 are both bows circular arcs ? 
 
THE RAINBOW. 
 
 223 
 
 a circle of which the center is P. And the same reason- 
 ing applies for the yellow, the blue, or any other ray as 
 
 well as the red, and also for the outer as well as the inner 
 bow. 
 
 * Another interesting natural phenomenon connected 
 with the refraction of light is what is called " astronomi- 
 cal refraction," arising from the action of the atmosphere 
 on the rays of light. It is this which so powerfully dis- 
 turbs the positions of the heavenly bodies, making them 
 appear higher above the horizon than they really are, 
 and changes the circular form of the sun and moon 
 to an oval shape. It also aids in giving rise to the twi- 
 light. 
 
 Let O be the position of an observer on the earth, Z, 
 
 What is the cause of astronomical refraction ? 
 
224 
 
 ASTRONOMICAL REFRACTION. 
 
 Fig. 251, will be his zenith, and let R be any star, the rays 
 from which come, of course, in straight lines, such as R 
 E. Now, when such a ray impinges on the atmosphere 
 Fig. 251. at s, it is refracted, and 
 
 deviates from its recti- 
 linear course. At first 
 this refraction is fee- 
 ble, but the atmos- 
 phere continually in- 
 creases in density as 
 we descend in it, and 
 therefore the deviation 
 c of the ray from its orig- 
 inal path, R E, be- 
 comes continually greater. It follows a curvilinear line, 
 and finally enters the eye of the observer at O. This may 
 perhaps be more clearly understood by supposing the 
 concentric circles, a a, b b, c c, represented in the figure, 
 to stand for concentric shells of air of the same density, 
 the ray at its entry on the first becomes refracted, and 
 pursues a new course tx> the second. Here the same 
 thing again takes place, and so with the third and other 
 ones successively. But these abrupt changes do not oc- 
 cur in the atmosphere, which does not change its density 
 from stratum to stratum abruptly, but gradually and con- 
 tinually. The resulting path of the ray is, therefore, not 
 a broken line, but a continuous curve. 
 
 Now, it is a law of vision that the mind judges of the 
 position of an object as being in the direction in which 
 the ray by which it is seen enters the eye. Consequently 
 the star, R, which emits the ray we have under consider- 
 ation, will be seen in- the direction, Or that being the 
 direction in which the ray entered the eye and, there- 
 fore, the effect of astronomical refraction is to elevate a 
 star or other object above the horizon to a higher appa- 
 rent position than that which it actually occupies. 
 
 Astronomical refraction is greater according as the ob- 
 ject is nearer the horizon, becoming less as the altitude 
 
 Trace the path of a ray of light which impinges obliquely an the at- 
 mosphere. Why is it of a curvilinear figure? How does the mind judge 
 of the position of an object ? What is, therefore, the effect of astronomical 
 refraction.'/ What is the difference in this respect between an object in 
 the horizon and one in the zenith ? 
 
ASTRONOMICAL REFRACTION. 225 
 
 increases, and ceasing in the zenith. An object seen in 
 the zenith is therefore in its true position. 
 
 On these principles, the figure of the sun and moon, 
 when in the horizon, changes to an oval shape ; for the 
 lower edge being more acted upon than the upper, is 
 therefore relatively lifted up, and those objects made less 
 in their vertical dimensions than in their horizontal. 
 
 Even when an object is below the horizon it may be 
 so much elevated as to be brought into view; for just in 
 the same way that a star, R, is elevated to r, so may one 
 beneath the horizon be elevated even to a greater extent, 
 because refraction increases as we descend to the hori- 
 zon. Stars, therefore, are visible before they have ac- 
 tually risen, and continue in sight after they have actually 
 set. They are thus lifted out of their true position when 
 in the horizon about thirty-three minutes. In the books on 
 astronomy tables are given which represent the amount 
 of refraction for any altitude. 
 
 What has been here said in relation to a star holds also 
 for the sun ; which, therefore, is made apparently to rise 
 sooner and set later than what is the case in reality. 
 From this arises the important result that the day is pro- 
 longed. In temperate climates, this lengthening of the 
 day extends only to a few minutes, in the polar regions 
 the day is made longer by a month. And it is for this 
 cause, too, that the morning does not suddenly break just 
 at the moment the sun appears in the horizon, and the 
 night set in the instant he sinks ; but the light gradually 
 fades away, as a twilight, the rays being bent from their 
 path, and the scattering ones which fall on the top of the 
 atmosphere brought in curved directions down to the 
 lower parts. 
 
 The phenomenon of twilight is not, however, wholly 
 due to refraction. The reflecting action of the particles 
 of the air is also greatly concerned in producing it. The 
 manner in which this takes place is shown in Fig. 252, 
 where A B C D represents the earth, T R P the atmos- 
 phere, and S O, S' N, S" A rays of the sun passing through 
 it. To an observer, at the point A, the sun, at S", is just 
 
 Why is the figure of the sun or moon oval in the horizon ? What is to 
 be observed as respects the rising and setting of stars? What effect has 
 the refraction of the air in producing twilight? How is it that the reflec- 
 tive power of the air aids in this effect ? 
 K* 
 
226 TWILIGHT. 
 
 set, but the whole hemisphere above him, P R T, being 
 his sky, reflects the rays which are still falling upon it, 
 and gives him twilight. To an observer, at B, the sun 
 
 Fig. 252. 
 \0 
 JM 
 
 S" 
 
 has been set for some time, and he is in the earth's shad- 
 ow, but that part of his sky which is included between P 
 Q, R x is still receiving sun-rays, and reflecting them to 
 him. To an observer atC, the illuminated portion of the 
 sky has decreased to P Q, z. His twilight, therefore, 
 has nearly gone. To an observer at D, whose horizon is 
 bounded by the line D P, the sky is entirely dark, no 
 rays from the sun falling on it. It is, therefore, night. 
 
 The action of the atmosphere sometimes gives rise to 
 curious spectral appearances such as inverted images, 
 looming, and the mirage. The latter, which often occurs 
 on hot sandy plains, was frequently seen by the French 
 during their expedition to Egypt, giving rise to a decep- 
 tive appearance of great lakes of water resting on the 
 sands. It appears to be due to the partial rarefaction of 
 the lower strata of air through the heat of the surface on 
 which they rest, so that rays of light are made to pass in 
 a curvilinear path, and enter the eye. In the same way 
 at sea, inverted images of ships floating in the air are 
 often discovered. 
 
 Thus, "On the 1st of August, 1798, Dr. Vince observ- 
 ed at Ramsgate a ship, which appeared, as at A, Fig. 253, 
 the topmast being the only part of it seen above the hori- 
 zon. An inverted image of it was seen at B, immediately 
 above the real ship, at A, and an erect image at C, both 
 of them being complete and well defined. The sea was 
 
 Describe this effect in the four positions, A, B, C, D of Fig. 252. Men- 
 tion some remarkable appearances due to unusual refraction and reflex- 
 ion of the air. 
 
THE MIRAGE. 
 
 227 
 
 Fig. 253. 
 
 distinctly seen between them, as at 
 V W. As the ship rose to the ho- 
 rizon, the image, C, gradually dis- 
 appeared ; and, while this was going 
 on, the image B, descended, but 
 the mainmast of B did not meet the 
 mainmast of A. The two images, 
 B C, were perfectly visible when 
 the whole ship was actually below 
 the horizon." 
 
 These singular appearances, which 
 have often given rise to superstitious 
 legends, may be imitated artificially. 
 Thus, if we take a long mass of hot 
 iron, and, looking along the upper 
 surface of it at an object not too 
 distant, we shall see not only the 
 object itself, but also an inverted 
 image of it below, the second im- 
 age being caused by the refraction 
 of the rays of .light as they pass through the stratum of 
 hot air, as is the case of the mirage. 
 
 The trembling which distant objects exhibit, more es- 
 pecially when they are seen across a heated surface, is, 
 in like manner, due to unusual aud irregular refraction 
 taking place in the air. 
 
 - 
 
 LECTURE XLVI. 
 
 THE ORGAN OF VISION. The Three Parts of the Eye. 
 Description of the Eye of Man. Uses of the Accessory 
 Apparatus. Optical Action of the Eye. Short and 
 Long-Sightedness. Spectacles. Erect and Double Vis- 
 ion. Peculiarities of Vision. Physiological Colors. 
 
 ALMOST all animals possess some mechanism by which 
 they are rendered sensible of the presence of light. In 
 some of the lower orders, perhaps, nothing more than a 
 diffused sensibility exists, without there being any special 
 
 How may the mirage be imitated ? How is it known that the lowest ani- 
 mals are sensible to light ? 
 
22S 
 
 THE EYE. 
 
 organ adapted for the purpose. Thus, many animalcules 
 are seen to collect on that side of the liquid in which they 
 live on which the sun is shining, and others avoid the light. 
 But in all the higher tribes of life there is a special me- 
 chanism, which depends for its action on optical laws it 
 is the eye. 
 
 This organ essentially consists of three different parts 
 an optical portion, which is the eye, strictly speaking ; a 
 nervous portion, which transmits the impressions gather- 
 ed by the former to the brain ; and an accessory portion, 
 which has the duty of keeping the eye in a proper work- 
 ing state and defending it from injury. 
 
 In man the eye-ball is nearly of a spherical figure, be- 
 
 j tl g about an inch in di- 
 ameter. As seen in front, 
 between the two eyelids, 
 d c, Fig. 254, it exhibits a 
 white portion of a porce- 
 lain-like aspect, a a; a col- 
 ored circular part, b I, 
 which continually changes 
 in width, called the iris; 
 and a central black por- 
 d tion, which is tJie pupil. 
 
 When it is removed from the orbit or socket in which 
 Fig. 255. it is placed, and dissected, the 
 
 eye is found to consist of sever- 
 al coats. The white portion 
 seen anteriorly at a a extends 
 all round. It is very tough and 
 resisting, and by its mechanical 
 qualities serves to support the 
 more delicate parts within, and 
 also to give insertion for the at- 
 tachment of certain muscles 
 which roll the eye-ball, and direct it to any object. 
 This coat passes under the name of the sclerotic. It is 
 represented in Fig. 255, at a a a a. In its front there 
 is a circular aperture, into which a transparent portion, 
 b b y resembling in shape a watch-glass, is inserted. This 
 
 Of how many parts does the eye consist ? What are the offices of 
 these parts I What is the figure and size of the eye in man ? What is 
 the iris, the pupil, and the sclerotic coat ? 
 
THE EYE. 229 
 
 This is called the cornea. It projects somewhat beyond 
 the general curve of the sclerotic, as seen at b b t in the 
 figure, and with the sclerotic completes the outer coat of 
 the eye. 
 
 The interior surface of the sclerotic is lined with a coat 
 which' seems to be almost entirely made up of blood-ves- 
 sels, little arteries and veins, which, by their internetting, 
 cross one another in evei'y possible direction. It is called 
 the choroid coat : it extends like the sclerotic as far as the 
 cornea. Its interior surface is thickly covered with a 
 slimy pigment of a black color, hence called pigmentum 
 nigrum. Over this is laid a very delicate serous sheet, 
 which passes under the name of Jacob's membrane, and 
 the optic nerve, O O, coming from the brain perforates the 
 sclerotic and choroid coats, and spreads itself out on the 
 interior surface as the retina, rrrr. The optic nerves of 
 the opposite eyes decussate one another on their passage 
 to the brain. 
 
 These, therefore, are the coats of which the eye is com- 
 posed. Let us examine now its internal structure. Be- 
 hind the cornea, b b, there is suspended a circular dia- 
 phragm, ef, black behind and of different colors in differ- 
 ent individuals in front. This is the iris. Its color is, in 
 some measure, connected with the color of the hair. The 
 central opening in it, d, is the pupil, and immediately be- 
 hind the pupil, suspended by the ciliary processes, g g, is 
 the crystaline lens, c c a double convex lens. All the 
 space between the anterior of the lens and the cornea is 
 filled with a watery fluid, which is the aqueous humor ; 
 that portion which is in front of the iris is called the an- 
 terior chamber, and that behind it the posterior. The rest 
 of the space of the eye, bounded by the crystaline lens 
 in front and the retina all round, is filled with the vitreous 
 liumor, V V. 
 
 With respect to the accessory parts, they consist chiefly 
 of the eyelids, which serve to wipe the face of the eye and 
 protect it from accidents and dust; the lachrymal appara- 
 tus, which serves to wash it with tears, so as to keep i 
 
 What is the cornea 7 What are the choroid coat, pigmentum nigrum, and 
 Jacob's membrane ? What are the optic nerve and retina ? What is the 
 position of the iris? How is the lens supported ? Where is the aqueous 
 humor? Where the vitreous ? What are the two chambers of the eye ? 
 What are the accessory parts and their uses 1 
 
230 SPECTACLES. 
 
 continually brilliant; and the muscles requisite to direct it 
 upon any point. 
 
 Of the nervous part of the eye, so far as its functions 
 are concerned, but little is known the retina receives 
 the impressions of the light, and they are conveyed along 
 the optic nerve to the brain. 
 
 Now as respects the optical action of the eye, it is ob- 
 viously nothing more than that of a convex lens, to which, 
 indeed, its structure actually corresponds : and as in ths 
 focus of such a convex lens objects form images, so by the 
 conjoint action of the cornea and crystaline, the images of 
 the things to which the eye is directed form at the proper 
 focal distance behind that is, upon the retina. Distinct 
 vision only takes place when the cornea and the lens have 
 such convexities as to bring the images exactly upon the 
 retina. 
 
 In early life it sometimes happens that the curvature 
 of these bodies is too great, and the rays converging too 
 rapidly, form their images before they have reached the 
 posterior part of the eye, giving rise to the defect known 
 as short-sightedness a defect which may be remedied by 
 putting in front of the cornea a concave glass lens of such 
 concavity as just to compensate for the excess of the con- 
 vexity of the eye. 
 
 In old age, on the contrary, the cornea and the lens be- 
 come somewhat flattened, and they cannot converge the 
 rays soon enough to form images at the proper distance be- 
 hind. This long-sightedness may be remedied by putting 
 in front of the cornea a convex lens, so as to help it in its 
 action. 
 
 Concave or convex lenses thus used in front of the 
 eyes constitute spectacles. It is believed that this appli- 
 cation was first made by Roger Bacon, and it unquestion- 
 ably constitutes one of the most noble contributions which 
 science has ever made to man. It has given sight to mil- 
 lions who would otherwise have been blind. 
 
 As the image which is formed by a convex lens is in- 
 verted as respects its object, so must the images which 
 form at the bottom of the eye. It has, therefore, been a 
 
 What is the duty of the retina, and what that of the optic nerve ? To 
 what optical contrivance is the eye analogous ? When does distihct vis- 
 ion take place? What is the cause of short-sightedness, and what is its 
 cure ? What is the cause of long-sightedness, and its cure ? 
 
PECULIARITIES OF VISION. 231 
 
 question among optical writers, why we see objects in their 
 natural position, and also why we do not see double, inas- 
 much as we have two eyes. Various explanations of these 
 facts have been offered, chiefly founded upon optical prin- 
 ciples. None, however, appear to have given general sat- 
 isfaction, and in reality the true explanation, I believe, 
 will be found not in the optical, but in the nervous part 
 of the visual organ. It is no more remarkable that we 
 see single, having two eyes, than that we hear single, hav- 
 ing two ears. It is the simultaneous arrival in the brain, 
 that gives rise out of two impressions to one perception, 
 and accordingly, when we disturb the action of one of 
 the eyes by pressing on it, we at once see double. 
 
 Among the peculiarities of vision it maybe mentioned, 
 that for an object to be seen it must be of certain magni- 
 tude, and remain on the retina a sufficient length of time; 
 arid, for distinct vision, must not be nearer than a certain 
 distance, as eight or ten inches. This distance of distinct 
 vision varies somewhat with different persons. The eye, 
 too, cannot bear too brilliant a light, nor can it distinguish 
 when the rays are too feeble ; though it is wonderful to 
 what an extent in this respect its powers range. We can 
 read a book by the light of the sun or the moon ; yet the 
 one is a quarter of a million times more brilliant than the 
 other. Luminous impressions made on the retina last for 
 a certain space of time, varying from one third to one 
 sixth of a second. For this reason, when a stick with a 
 spark of fire at the end is turned rapidly round, it gives 
 rise to an apparent circle of light. 
 
 By accidental or physiological colors we mean such as 
 are observed for a short time depicted on surfaces, and 
 then vanishing away. Thus, if a person looks steadfastly 
 at a sheet of paper strongly illuminated by the sun, and 
 then closes his eyes, he will see a black surface corre- 
 sponding to the paper. So if a red wafer be put on a sheet 
 of paper in the sun. and the eye suddenly turned on a 
 white wall, a green image of the wafer will be seen. 
 Spectral illusions in the same way often arise thus, when 
 
 Is there anything remarkable respecting erect and double vision? 
 What peculiarities respecting vision may be remarked ? What is the 
 distance of distinct vision ? To what range of intensity of light can the 
 eye adapt itself? Why does a lighted stick turned round rapidly give rise 
 to the appearance of a circle of fire ? What is meant by accidental colors ? 
 
232 OPTICAL INSTRUMENTS. 
 
 we awake in the morning, if our eyes are turned at once 
 to a window brightly illuminated, on shutting them again 
 we shall see a visionary picture of every portion of the 
 window, which after a time fades away. 
 
 LECTURE XL VII. 
 
 OF OPTICAL INSTRUMENTS. The Common Camera Ob- 
 scura. The Portable Camera. The Single Microscope. 
 The Compound Microscope. Chromatic and Spheri- 
 cal Aberration. The Magic Lantern, The Solar Mi- 
 croscope. The Oxyhydrogen Microscope. 
 
 IN this and the next Lecture I shall describe the more 
 important optical instruments. These, in their external 
 appearance, and also iri their principles, differ very much 
 according to the taste or ideas of the artist. The descrip- 
 tions here given will be limited to such as are of a simple 
 kind. 
 
 THE CAMERA OBSCURA, or dark chamber, originally con- 
 sisted of nothing more than a double convex lens, of a 
 foot or two in focus, fixed in the shutter of a dark room. 
 Opposite the lens and at its focal distance, a white sheet 
 received the images. These represent whatever is in front 
 f the lens, giving a beautiful picture of the stationary 
 and movable objects in their proper relation of light and 
 shadow, and also in their proper colors. 
 
 In point of fact, a lens is not required : for, if into a 
 
 Fig. 256. 
 
 What was the original form of the camera obscura ? 
 
CAMERA OBSCURA. 233 
 
 dark chamber, C D, Fig. 256, rays are admitted through 
 a small aperture, L, an inverted image will be formed on 
 a white screen at the back of the chamber, of whatever 
 objects are in front. Thus the object, A B, gives the in- 
 verted image, b a. These images are, however, dim, ow- 
 ing to the small amount of light which can be admitted 
 through the hole. The use of a double convex lens per- 
 mits us to have a much larger aperture, and the images are 
 correspondingly brighter. pig. 257. 
 
 The portable , 
 
 camera obscura n c 
 
 consists of an a 
 
 achromatic dou- d\ 
 ble convex lens, 
 a a', set in a brass 
 mounting in the 
 front of a box consisting of two parts, of which c c' slides 
 in the wider one, bb'. The total length of the box is ad- 
 justed to suit the focal distance of the lens. In the back 
 of the part, c c', there is a square piece of ground glass, J, 
 which receives the images of the objects to which the 
 lens is directed, and by sliding the movable part in or 
 out the ground glass can be brought to the precise focus. 
 The interior of the box and brass piece, a a', is blackened 
 all over to extinguish any stray light. 
 
 The images of the camera are, of course, inverted, but 
 they can be seen in their proper position by receiving 
 them on a looking-glass, placed so as to reflect them up- 
 ward to the eye. Objects that are near, compared with 
 objects that are distant, require the back of the box to be 
 drawn out, because the foci are farther off. Moreover, 
 those that are near the edges are indistinct, while the cen- 
 tral ones are sharp and perfect. This arises from the cir- 
 cumstance that the edges of the ground glass are farther 
 from the lens than the central portion, and, therefore, out 
 of focus. 
 
 OF MICROSCOPES. 
 
 The single microscope. When a convex lens is placed 
 
 Is it necessary to have a lens ? What advantage arises from the use of 
 one? Describe the portable camera obscura. Why does the focal dis- 
 tance vary for different objects? Why are the images on the edges indis- 
 tinct while the central ones are sharp ? 
 
234 
 
 THE MICROSCOPE. 
 
 Fig. 258. 
 
 between the eye and an object situated a little nearer than 
 its focal distance, a magnified and erect image will be seen. 
 
 The single microscope con- 
 sists of such a lens, m, Fig. 
 258, the object, b c, being on 
 one side and the eye, , at 
 the other, a magnified and 
 erect image, B C, is seen. 
 The linear magnifying pow- 
 er of such a lens is found by 
 dividing the distance of distinct vision by its focal length. 
 The co?npound microscope commonly consists of three 
 
 lenses, A B, E F, C D, 
 
 *' Fig. 259; A B being 
 
 the object-glass, E F the 
 field-glass, and C D the 
 eye-glass. Beyond the 
 object-glass is placed 
 the object, at a dis- 
 
 w tance somewhat greater 
 
 than the focal length ; a magnified image is, therefore, 
 produced, and this being viewed by the eye-glass is still 
 further magnified, and, of course, seen in an inverted po- 
 sition. The use of the field-glass is to intercept the ex- 
 treme pencils of light, n m, coming from the object-glass, 
 which would otherwise not have fallen on the eye-lens. 
 It therefore^ increases the field of view, and hence its 
 name. 
 
 In this instrument the object-glass has a very short fo- 
 cus, the eye-glass one that is much larger ; and the field- 
 glass and the eye-glass can be so arranged as to neutral- 
 ize chromatic aberration. 
 
 To determine directly the magnifying power of this in- 
 strument, an object, the length of which is known, is placed 
 before it. Then one eye being applied to the instrument, 
 with the other we look at a pair of compasses, the points 
 of which are to be opened until they subtend a space 
 equal to that under which the object appears. This space 
 being divided by the known length of the object, gives the 
 magnifying power. 
 
 Describe the single microscope. How is its magnifying power found ? 
 Describe the compound microscope. What is the use of the field lens ? 
 How may its magnifying power be found ? 
 
COMPOUND MICROSCOPE. 
 
 235 
 
 In Fig. 260, we have a representation of the compound 
 
 Fig. 260. 
 
 microscope, as commonly made. A 
 B is a sliding brass tube, which bears 
 the eye-glass ; m n is the object- 
 glass ; I K the field-glass ; S T a 
 stage for carrying the objects. It 
 can be moved to the proper focal dis- 
 tance by means of a pinion. At V 
 there is a mirror which reflects the 
 light of a lamp or the sky upward, 
 to illuminate the object. The body 
 of the microscope is supported on 
 the pillar M, and it can be turned 
 into the horizontal or any oblique po- 
 sition to suit the observer, by a joint, 
 N. To the better kind of instru- 
 ments micrometers are attached, for 
 the purpose of determining the di- 
 
 mensions of objects. These are some- LI/ 
 
 times nothing more than a piece of glass, on which fine 
 lines have been drawn with a diamond, forming divisions 
 the value of which is known. Such a plate may be placed 
 either immediately beneath the object or at the diaphragm, 
 which is between the two lenses. 
 
 In microscopes the defective action of lenses, known 
 as chromatic aberration, and described in Lecture XLL, 
 interferes, and, by imparting prismatic colors to the edges 
 of objects, tends to make them indistinct. To overcome 
 this difficulty, achromatic object-glasses are used in the 
 finer kinds of instruments. 
 
 Besides chromatic aberration, there is another defect 
 to which lenses are subject. It arises from their spheri- 
 cal figure, and hence is designated spherical aberration. 
 Let P P, Fig. 261, be a convex lens, on which rays, E P, 
 E P, E M, E M, E A, from any object, E e, are incident, 
 it is obvious that the principal ray, E A, will pass on, 
 through B, to F without undergoing refraction. Now, 
 rays which are near to this, as E M, E M, converge by 
 the action of the lens to a focus at F ; but those which 
 are more distant, and fall near the edges of the lens, as 
 
 Describe the parts of the compound microscope represented in Fig. 260. 
 What kind of micrometers may be used ? What are the effects of chro- 
 matic and spherical aberration ? 
 
236 
 
 MAGIC LANTERN. 
 
 E N, JS N, converge more rapidly, and come to a focus 
 at G-. Thus, images, F f t G g, are formed by the ex- 
 treme rays, and an intermediate series of them by the 
 
 Fig. 261. 
 
 E 
 
 intermediate rays, the whole arising from the peculiarity 
 of figure of the lens. It is, indeed, the same defect as 
 that to which spherical mirrors are liable, as explained 
 in Lecture XXXVII ; and hence, to obtain perfect action 
 with a spherical lens, as with a spherical mirror, its ap- 
 erture must be limited. 
 
 THE MAGIC LANTERN consists of a metallic lantern, 
 
 Fig. 262. 
 
 A A' Fig. 262, in front of which two lenses are placed. 
 One of these, m, is the illuminating lens, the other, n, the 
 magnifier. A powerful Argand lamp is placed at L, and 
 behind it a concave mirror, p q. In the space between 
 the two lenses the tube is widened c d, or such an arrange- 
 ment made that slips of glass, on which various figures 
 are painted, can be introduced. The action of the in- 
 strument is very simple. The mirror and the lens m 
 
 Describe the magic lantern. What is the use of its condensing lens and 
 mirror ? 
 
SOLAR MICROSCOPE. 237 
 
 illuminate the ^drawing as highly as possible ; for the 
 lamp being placed in their foci, they throw a brilliant 
 light upon it, and the magnifying lens, n, which can slide 
 in its tube a little backward and forward, is placed in 
 such a position as to throw a highly magnified image of 
 the drawing upon a screen, several feet off, the precise 
 focal distance being adjusted by sliding the lens. As it 
 is an inverted image which forms, it is, of course, neces- 
 sary to put tke drawing in the slide, c d, upside down, so 
 as to have their images in the natural position. Various 
 amusing slides are prepared by the instrument-makers, 
 some representing bodies or parts in motion. The fig- 
 ures require to be painted in colors that are quite trans- 
 parent. 
 
 THE SOLAR MICROSCOPE. This instrument, like the 
 
 magic lantern, consists of two parts one for illuminating 
 the object highly, and the other for magnifying it. It 
 consists of a brass plate, which can be fastened to an 
 aperture in the shutter of a dark room, into which a beam 
 of the sun may be directed by means of a plane mirror. 
 In Fig. 263, M is the mirror, to which movement in any di- 
 rection may be given by the two buttons, X and Y, that rays 
 from the sun may be reflected horizontally into the room. 
 They pass through a large convex lens, R, and are con- 
 converged by it ; they again impinge on a second lens, 
 U S, which concentrates them to a focus, the precise 
 point of which may be adjusted by sliding the lens to the 
 proper position by the button B. P P' is in apparatus, 
 consisting of two fixed plates, with a movable one, Q, be- 
 tween them, Q, being pressed against P' by means of 
 spiral springs. This apparatus is for the purpose of sup- 
 porting the various objects which are held by the pressure 
 
 Why must the slider be put in upside down ? What are the two parts 
 of the solar microscope? Describe the instrument as represented in 
 Fig. 263. 
 
238 OXYIIYDROGEN MICROSCOPE. 
 
 of Q, against P'. Immediately beyond this, at L, is the 
 magnifying lens, or object-glass, which can be brought to 
 the proper position from the highly illuminated object by 
 means of the button B', and the magnified image result- 
 ing is then thrown on a screen at a distance. 
 
 The solar microscope has the great advantage of ex- 
 hibiting objects to a number of persons at the same 
 time. 
 
 In principle, the oxyhydrogen microscope is the same 
 as the foregoing, only, instead of employing the light of 
 the sun, the rays of a fragment of lime ignited in the 
 flame of a oxyhydrogen blow-pipe are used. These rays 
 are converged on the object, and serve to illuminate it. 
 The advantage the instrument has over the solar micro- 
 scope is that it can be used at night and on cloudy days. 
 
 LECTURE XLVIII. 
 
 OF TELESCOPES. Refracting and Reflecting Telescopes. 
 Galileo's Telescope. The Astronomical Telescope. 
 The Terrestrial. Of Reflecting Telescopes. Hersckel's 
 Newton's, Gregory's. Determination of their Magnify- 
 ing Powers. The Achromatic Telescope. 
 
 THE telescope is an instrument which, in principle, re- 
 sembles the microscope, both being to exhibit objects to 
 us under a larger visual angle. The microscope does 
 this for objects near at hand, the telescope for those that 
 are at a distance. 
 
 Telescopes are of two kinds, refracting and reflecting. 
 Each consists essentially of two parts, the object-glass or 
 objective, and the eye-piece. In the former, the objec- 
 tive is a lens, in the latter it is a concave mirror. 
 
 The distinctness of objects through telescopes is neces- 
 sarily connected with the brilliancy of the images they 
 give, and this, among other things, depends on the size of 
 the objective. 
 
 What advantage has the solar microscope over other forms of instru. 
 ment ? What is the oxyhydrogen microscope ? What is the telescope ? 
 Of how many kinds are telescopes ? What are their essential parts ? 
 What is the objective in the refracting and reflecting telescope, re- 
 spectively ? On what does the brilliancy depend ? 
 
GALILEO S TELESCOPE. 
 
 239 
 
 There are three kinds of refracting telescopes : 1st, 
 Galileo's ; 2d, the astronomical ; 3d, the terrestrial. 
 GALILEO'S TELESCOPE, which is represented in Fig. 
 
 264, consists of a convex lens, L N, which is the objec- 
 tive, and a concave eye-glass, E E. Let O B be a dis- 
 tant object, the rays from which are received upon L N, 
 and by it would be brought to a focus, and give the im- 
 age, M I ; but, before they reach this point, they are in- 
 tercepted by the concave eye-glass, E E, which makes 
 them diverge, as represented at H K, and give an erect 
 image, i m. 
 
 This form of telescope has an advantage in the erect 
 position of its image, which is usually presented with 
 great clearness. Its field of view, by reason of the di- 
 vergence of the rays through the eye-glass, is limited. 
 When made on a small scale, it constitutes the common 
 opera-glass. 
 
 THE ASTRONOMICAL TELESCOPE differs from the former 
 
 in having for its eye-piece a convex lens of short focus 
 compared with that of the object-lens. In this, as in the 
 former instance, the office of the objective is to give an 
 image, and the eye-piece magnifies it precisely on the 
 same principle that it would magnify any object. In Fig. 
 265, L N is the objective, and E E the eye-glass ; the 
 rays from a distant object, O B, are converged so as to 
 give a focal image, M I. This being viewed through 
 the eye-lens, E E, is magnified, and is also inverted. 
 The magnifying power of the telescope is found by di- 
 
 How many kinds of refracting telescopes are there ? Describe Galileo's 
 telescope. Why has it so small a field of view ? What are the essential 
 parts of the astronomical telescope ? Why does it invert ? 
 
240 TERRESTRIAL TELESCOPE. 
 
 viding the focal length of the objective by that of the eye- 
 lens. 
 
 This telescope, of course, inverts, and therefore is not 
 well adapted for terrestrial objects ; but for celestial ones 
 it answers very well. 
 
 THE TERRESTRIAL TELESCOPE consists of an object- 
 
 Fig. 266. 
 
 O 
 
 lens, like the foregoing, but in its eye-piece are three 
 lenses of equal focal lengths. The combination is repre- 
 sented in Fig. 266, in which L N is the object lens, and 
 E E, F F, G G the eye-lenses, placed at distances from 
 each other equal to double their focal length. The prog- 
 ress of the rays through the object-lens and the first eye- 
 glass to X is the same as in the astronomical telescope ; 
 but, after crossing at X, they are received on the second 
 eye-lens, which gives an erect image of them, at i m, which 
 is viewed, therefore, in the erect position by the last eye- 
 lens, G G. 
 
 As the distance at which the image forms from the ob- 
 ject-lens is dependent on the actual distance of the object 
 itself, one which is near giving its image farther off than 
 one which is distant, it is necessary to have the means of 
 adjusting the eye-piece, so as to bring it to the proper dis- 
 tance from the image, M I. The object-lens is there- 
 fore put in a tube longer than its own focus, and in this 
 a smaller tube, bearing the three eye-lenses, immovably 
 fixed, slides backward and forward ; this tube is drawn out 
 until distinct vision of the object is attained. 
 
 REFLECTING TELESCOPES are of several different kinds. 
 They have received names from their inventors. 
 
 HERSCHEL'S TELESCOPE consists of a metallic concave 
 mirror, set in a tube in a position inclined to the axis. It 
 of course gives an inverted image of the object at its fo- 
 cus, and the inclination is so managed as to have the im- 
 age form at the side of the tube. There it is viewed by 
 
 How is its magnifying power found ? Describe the terrestrial telescope. 
 What is the action of its three eye-lenses ? Why must there be means of 
 sliding the eye-piece ? How are reflecting telescopes designated ? De- 
 scribe Herschel's telescope. 
 
NEWTON'S AND GREGORY'S TELESCOPES. 241 
 
 an eye-lens, which shows it magnified and inverted. The 
 back of the observer is turned to the object, and the in- 
 clmation of the mirror is for the purpose of avoidino- ob- 
 struction of the light by the head. 
 
 NEWTON'S TELESCOPE consists of a concave mirror A 
 R, Fig. 267, with its axis parallel to that of the tube, D E 
 
 Fig. 267 
 
 F G, in which it is set. The rays reflected from it are 
 intercepted by a plane mirror, C K, placed at an angle of 
 45, on a sliding support, m. They are, therefore, re- 
 flected toward the side of the tube, the image, i m, form- 
 ing at I M, an eye-glass at L magnifies it. 
 
 THE GREGORIAN TELESCOPE has a concave mirror, A R, 
 Fig. 268, with an aperture, L, in its center. The rays 
 
 Fif.268. 
 
 A o 
 
 from a distant object, O B, give, as before, an inverted 
 image, M I. They are then received on a small concave 
 mirror, K C, placed fronting the great one. This gives 
 an erect image, which is magnified by the eye-lens, P. 
 
 The magnifying power of any of these instruments may 
 be roughly estimated by looking at an object through them 
 with one eye, and directly at it with the other, and com- 
 paring the relative magnitude of the two images. In Her- 
 schel's telescope the back of the observer is toward the 
 object, in Newton's his side, but in Gregory's he looks di- 
 rectly at it. The latter is, therefore, by far the most 
 agreeable instrument to use. The largest telescopes hith- 
 erto constructed are upon the plan of Herschel and 
 Newton. 
 
 When Sir Isaac Newton discovered the compound na- 
 ture of light, by prismatic analysis, he came to the con- 
 In what position does the observer stand ? Describe Newton's telescope 
 Describe the Gregorian telescope. How may the magnifying power of 
 these instruments be ascertained ? 
 
242 THE ACHROMATIC TELESCOPE. 
 
 elusion that the refracting telescope could never be a per- 
 fect instrument, because it appeared impossible to form 
 an image by a convex lens, without its being colored on 
 the edges by the dispersion of light. He therefore turn- 
 ed his attention to the reflecting telescope, and invented 
 the one which bears his name. He even manufactured 
 one with his own hands. It is still preserved in the cab- 
 inet of the Royal Society of London. 
 
 But after it was discovered that refraction without dis- 
 persion can be effected, and that lenses can be made to 
 form colorless images in their foci, the principle was at 
 once applied to the telescope ; and. hence originated that 
 most valuable astronomical instrument, the achromatic 
 telescope. 
 
 - In this the object-glass is of course compound, consist- 
 ing, as represented in Fig. 269, of one crown and one 
 
 Fig. 269. Fig. 270. 
 
 flint-glass lens, or as represented in Fig. 270, of one flint 
 and two crown-glass lenses. The principle of its action has 
 been described in Lecture XLI. The great expense of 
 these instruments arises chiefly from the costliness of the 
 flint-glass, for it has hitherto been found difficult to obtain 
 it in masses of large size, perfectly free from veins or 
 other imperfections. Nevertheless, there are instruments 
 which have been constructed in Germany, with an aper- 
 ture of thirteen inches. Some of these are mounted on 
 
 .Tiiat wao it van IKU LU me adoption oi tne renecting telescope i un 
 what does the achromatic telescope depend ? Of what parts are the dou- 
 ble and triple object-glasses composed ? What is the cause of the costli- 
 
 ness of these instruments ? 
 
ACHROMATIC TELESCOPES. 243 
 
 a frame, connected with a clock movement, so that when 
 the telescope js turned to a star it is steadily kept in the 
 center of the field of view, notwithstanding the motion of 
 the earth on her axis. Several large instruments of this 
 description are now in the different observatories of the 
 United States. 
 
244 HEAT OR CALORIC. 
 
 THE PROPERTIES OF HEAT. 
 
 THERMOTICS. 
 
 LECTURE XLDL 
 
 THE PROPERTIES OF HEAT. Relations of Light and Heat. 
 Mode of Determining the Amount of Heat. The 
 Mercurial Thermometer. Its Fixed Points. Fahren- 
 keit's, Centigrade, Reaumur's Thermometers. The Gas 
 Thermometer. Differential Thermometer. Solid Ther- 
 mometers. Comparative Expansion of Gases, Liquids, 
 and Solids. 
 
 WHATEVER may be the true cause of light, whether it 
 be undulations in an ethereal medium, or particles emit- 
 ted with great velocity by shining bodies, observation has 
 clearly proved that heat is closely allied to it. 
 
 When a body is brought to a very high temperature, 
 and then allowed to cool in a dark place, though it might 
 be white-hot at first it very soon becomes invisible, losing 
 its light apparently in the same way that its loses its heat. 
 And we shall hereafter find the rays of heat which thus 
 escape from it may be reflected, refracted, inflected, and 
 polarized, just as though they were rays of light. 
 
 In its general relations heat is of the utmost importance 
 in the system of nature. The existence of life, both vege- 
 table and animal, is dependent on it; it determines the 
 dimensions of all objects, regulates the form they assume, 
 and is more or less concerned in every chemical change 
 that takes place. 
 
 Every object to which we have access possesses a cer- 
 tain amount of heat, and so long as it remains at common 
 
 What is observed during the cooling of bodies ? Why are the relations 
 of heat of such^philosophical importance ? 
 
THE THERMOMETER. 
 
 245 
 
 temperatures, may be touched without pain ; but if a larg- 
 er quantity of heat is given to it, it assumes qualities that 
 are wholly new, and if touched it burns. 
 
 To determine, therefore, with precision the quantity of 
 heat which is present in a body when it exhibits any 
 particular phenomenon, it is necessary that we should be 
 furnished with some means of effecting its measurement. 
 Instruments intended for this purpose are called ther- 
 mometers. 
 
 Of thermometers we have several different kinds. Some 
 are made of solid substances, others of liquids, and others 
 of gases. With a few exceptions, they all depend on the 
 same principle the expansion which ensues in all bodies 
 as their temperature rises. 
 
 Of these the mercurial thermometer is the most F*g- 2 71 
 common, and for the purpose of science the most' 
 generally available. It consists of a glass tube, 
 Fig, 271, with a bulb on its lower extremity. 
 The entire bulb and part of the tube are filled 
 with quicksilver, and the rest of the tube, the ex- 
 tremity of which is closed, contains a vacuum. 
 This glass portion is fastened in an appropriate 
 manner, upon a scale of ivory or metal, which 
 bears divisions, and the thermometer is said to be 
 at that particular degree against which its quick- 
 silver stands on the scale. 
 
 If we take the bulb of such an instrument in 
 the hand, the quicksilver immediately begins to 
 rise in the tube, and finally is stationary at some 
 particular degree, generally the 98th in our ther- 
 mometers. We therefore say the temperature of 
 the hand is 98 degrees. 
 
 In effecting a measure of any kind, it is neces- 
 sary to have a point from which to stait and a 
 point to which to go. The same is also necessa- 
 ry in making a scale. One of the essential qual- 
 
 ities of a thermometer is to enable observers in all parts 
 of the world to indicate the same temperature by the same 
 
 What is the use of the thermometer? What different kinds of ther- 
 mometers have we ? On what general principle do they all depend ? What 
 form of thermometer is the most common ? What are the degrees ? What 
 temperature does it indicate if held in the hand? Why are fixed points 
 necessary in forming the scale ? 
 
246 THERMOMETRIC SCALES. 
 
 degree. A common system of dividing the scale must, 
 therefore, be agreed upon, that all thermometers may cor- 
 respond. 
 
 If we dip a thermometer in melting ice or snow, the 
 quicksilver sinks to a certain point, and to this point it 
 will always come, no matter when or where the experi- 
 ment is made. If we dip it in boiling water, it at once 
 rises to another point. Philosophers in all countries have 
 agreed that these are the best fixed points to regulate the 
 scale by, and accordingly they are now used in all ther- 
 mometers. In the Fahrenheit thermometer, which is com- 
 monly employed in the United States, we mark the point 
 at which the instrument stands, when dipped in melting 
 snow, 32, and that for boiling water, 212, and divide the 
 intervening space into 180 parts, each of which is a de- 
 gree ; and these degrees are carried up to the top and 
 down to the bottom of the scale. 
 
 In other countries other divisions are used, adjusted, 
 however, by the same fixed points. The Centigrade 
 thermometer has, for the melting of ice, 0, and for the 
 boiling of water, 100, with the intervening space divid- 
 ed in 100 equal degrees. In Reaumur's thermometer, 
 the lower point is marked 0, and the upper 80. 
 
 The philosophical fact upon which the construction of 
 the thermometer reposes, is that quicksilver expands by 
 an increase of heat, and is contracted by a diminution of 
 it; and further, that these expansions and contractions are 
 in proportion to the changes of temperature. 
 
 3 ut f or particular purposes, thermometers have 
 been made of oil, of alcohol, and of a great many 
 other liquid bodies, and give rise to the same gen- 
 eral results. As an uniform law it may, therefore, 
 be asserted that all liquids dilate as their temper- 
 ature rises, and contract as it descends. 
 
 But heat determines the volume of gases as well 
 as of liquids. If we take a tube, a, Fig. 272, with 
 a bulb at its upper extremity, &, and having partly 
 filled the tube with a column of water, colored, to 
 make its movements visible, the lower end dipping 
 
 What two fixed points have been selected ? What is the Centigrade 
 scale ? What is Reaumur's scale ? What is the fact on which the con- 
 struction of the thermometer depends ? How may this be extended to 
 other liquids ? 
 
AIR THERMOMETER. ' . 247 
 
 loosely into some of the same colored water, contained in 
 a bottle, c; on touching the bulb, b, the colored liquid in 
 the tube is pressed down by the dilatation of the air, and 
 on cooling the bulb the liquid rises, because the air con- 
 tracts. And were the bulb filled with any other gaseous 
 substance, such as oxygen, hydrogen, &c., still the same 
 thing would take place. So gases, like liquids, expand 
 as their temperature rises, and contract as it descends. 
 
 Such an instrument as Fig. 272, passes under the name 
 of an air thermometer. Its indications are not altogether 
 reliable, as may be proved by putting it under an air-pump 
 receiver, when its column of liquid will instantly move as 
 soon as the least change is made in the pressure of the air. 
 It is affected, therefore, by changes of pressure as well as 
 changes of temperature. 
 
 There is, however, a form of 
 air thermometer which is free 
 from this difficulty. It is the dif- 
 ferential thermometer. This in- 
 strument consists of a tube, a 
 Fig. 273, bent at right angles to- 
 ward its ends, which terminate 
 in two bulbs, c d. In the hori- 
 zontal part of the tube is a little column of liquid marked 
 by the black line, which serves as an index. If the bulb 
 c, is touched by the hand, its air dilates and presses the 
 index column over the scale ; if d is touched the same 
 thing takes place, but the column moves the opposite 
 way ;' if both bulbs are touched at once, then the column, 
 pressed equally in opposite directions, does not move at 
 all. Of course, a similar reasoning applies to the cooling 
 of the bulbs. The instrument is, therefore, called a di 
 ferential thermometer, because it indicates the difference 
 of temperature between its bulbs, but not absolute tem- 
 peratures to which it is exposed. 
 
 In the same manner that we have thermometers, in 
 which the changes of volume of liquids and gases are 
 employed, to indicate changes of temperature, so, too, we 
 have others in which solids are used. These generally 
 consist of a strip of metal which is connected with an ar- 
 
 How may it be extended to all the gases ? Describe the air thermome- 
 ter. Describe the differential thermometer. What does this instrument 
 indicate '? 
 
248 
 
 EXPANSION OF LIQUIDS. 
 
 
 Fig. 274. 
 
 rangement of levers or wheels, by which any variations 
 in its length may be multiplied. The disturbing agencies, 
 thus introduced by this necessary mechanism, interfere 
 very much with the exactness of these instruments. And 
 hitherto they have not been employed, except for special 
 purposes, and can never supplant the mercurial thermom- 
 eter. 
 
 It being thus established that all substances, gases, 
 liquids, and solids expand as their temperature rises, and 
 contract as it falls, it may next be remarked that great 
 differences are detected when different bodies of the same 
 form are compared. There are scarcely two solid sub- 
 stances which, for the same elevation of temperature, ex- 
 pand alike. All do expand ; but some more and some 
 less. In the case of crystalline bodies, even the same 
 substance expands differently in different directions. 
 Thus, a crystal of Iceland spar dilates less in the direc- 
 tion of its longer than it does in the direction of its short- 
 er axis. The same holds good for liquids. If a number of 
 thermometers, a b c, Fig. 274, of the 
 same size be filled with different 
 liquids, and all plunged in the same 
 vessel of hot water, f, so as to be 
 warmed alike, the expansion they 
 exhibit will be very different. Until 
 recently, it was believed that .all 
 | _V- V^jl o ases expand alike for the same 
 
 ^ changes of temperature, but it is now 
 known that minute differences exist among them in* this 
 respect. For every degree of Fahrenheit's thermometer 
 atmospheric air expands T i^- of its volume at 32. 
 
 Gases, liquids, and solids compared together, for the 
 same change of temperature, exhibit very different changes 
 of volume ; gases being the most dilatable, liquids next, 
 and solids least of all. This, probably, arises from the 
 fact that the cohesive force, which is the antagonist of 
 heat, is most efficient in solids, less so in liquids, and still 
 less in gases. 
 
 Are thermometers ever made of solid bodies ? What difficulties are in 
 the way of their use ? Do bodies of the same form expand alike ? What 
 remarks may be made respecting Iceland spar? How may it be proved 
 that different liquids expand differently ? What is the expansion of air 
 for each. degree? Do other gases expand exactly like air? Of gases, 
 liquids, and solids, which expands most ? 
 
 a 
 
 '* 
 
 : b 
 
 : 
 
 c : 
 
 f 
 
 j 
 
 J 
 
 -f 
 
 . j 
 
 
RADIANT HEAT. 249 
 
 LECTURE L. 
 
 OP RADIANT HEAT. Path of Radiant Heat. Velocity 
 of Radiant Heat. Effects of Surface. Law of Reflex- 
 ion. Reflexion by Spherical Mirrors. Theory of Ex- 
 changes of Heat. Diathermanou$ and Athermanous 
 Bodies. Properties of Rock Salt. Imaginary Colora- 
 tion. 
 
 EXPERIENCE shows that whenever a hot body is freely 
 exposed its temperature descends, until eventually it 
 comes down to that of the surrounding bodies. There 
 are two causes which tend to produce this result. They 
 are radiation and conduction. 
 
 All bodies, whatever their temperature may be, radiate 
 heat from their surfaces. It passes forth in straight lines, 
 and may be reflected, refracted, and polarized like light. 
 
 The rate at which radiant heat moves is, in all proba- 
 bility, the same as the rate for light. It has been asserted 
 that its velocity is only four fifths that of light, but this 
 seems not to rest upon any certain foundation. 
 
 As respects the rapidity or facility with which radi- 
 ation takes place, much depends on the nature of the sur- 
 face. The experiments of Leslie show that, at equal 
 temperatures, such as are smooth are far less effective 
 than such as are rough. 
 This result he established 
 by taking a cubical metal- 
 lic vessel, a, filled with 
 hot water, the four verti- 
 cal sides being in differ- 
 ent physical conditions 
 one being polished, a sec- 
 ond slightly roughened, a 
 third still more so, and the fourth roughened and black- 
 ened. Under these circumstances, the rays of heat es- 
 
 What causes tend to produce the cooling of bodies ? In what direction 
 does radiant heat pass ? What is the velocity of its movement ? How is 
 the rapidity of radiation controlled by surface? Of smooth and rough 
 bodies which are the best radiators ? 
 
250 
 
 REFLEXION OF HEAT. 
 
 caping from each surface as it was turned in succession 
 toward a metallic reflector, M, raised a thermometer, d, 
 placed in the focus, to very different degrees, the polished 
 one producing the least effect. 
 
 Just as light is reflected, so, too, is heat. If we take a 
 plate of bright tin and hold it in such a position as to re- 
 flect the light of a clear fire into the face, as soon as we see 
 the light we also feel the impression of the heat. The 
 law for the one is also the law for the other, " the angle 
 of reflexion is equal to the angle of incidence," and con- 
 sequently mirrors with curved surfaces act precisely in 
 one case as they do in the other. We have already 
 shown, Lecture XXXVII, how rays diverging from tine 
 focus of a mirror are reflected parallel, and how parallel 
 rays falling on a mirror are converged. And it is upon 
 that principle that we account for the following striking 
 experiment. In the focus of a concave metallic mirror 
 
 Fig. 276. 
 
 let there be placed a red hot ball, <z, Fig. 276, the rays 
 of heat diverging from it in right lines, a c, a d, a e, af 
 will be reflected parallel in the lines c g, d h, e i,fk, and, 
 striking upon the opposite mirror, will all converge to b, 
 in its focus. If, therefore, at this point any small com- 
 bustible body, as a piece of phosphorus, be placed, it 
 will instantly take fire, though a distance of twenty or fifty 
 feet may intervene between the mirrors. Or, if the bulb 
 of an air thermometer be used instead of the phosphorus, 
 
 What is the law for the reflexion of heat ? How do curved mirrors 
 act on radiant heat ? Describe the experiment represented by Fig. 276. 
 
THEORY OF THE EXCHANGES OP HEAT. 251 
 
 it will give at once the indication of a rapid elevation of 
 temperature. 
 
 But this is not all; for, if still retaining the thermome- 
 ter in its place, we remove away the red hot ball and re- 
 place it by a mass of ice, the thermometer instantly indi- 
 cates a descent of temperature, the^production of cold. 
 At one time it was supposed that this was due to cold 
 rays which escaped from the ice, after the same manner 
 as rays of heat, but it is now admitted that the effect 
 arises from the circumstance that the thermometer bulb, 
 being warmer than the ice, radiates its heat to the ice, 
 the temperature of which ascends precisely in the same 
 manner as that in the former experiment, the red hot 
 ball being the warmer body, radiated its heat to the ther- 
 mometer. 
 
 In fact, these experiments are nothing more than illus- 
 trations of a theory which passes under the name of" the 
 Theory of the Exchanges of Heat." This assumes that 
 all bodies are at all times radiating heat to one another ; 
 but the speed with which they do this depends upon their 
 temperature, a hot body giving out heat much faster than 
 one the temperature of which is lower. If thus, we have 
 a red hot ball and a thermometer bulb in presence of one 
 another, the ball, by reason of its high temperature, will 
 give more heat to the bulb than it receives in return ; its 
 temperature will, therefore, descend, while that of the 
 bulb rises. But if the same bulb be placed in presence 
 of a mass of ice, the ice will receive more heat than it 
 gives, because it is the colder body of the two, and the 
 temperature of the thermometer therefore declines. 
 
 All bodies are at all times radiating heat, their power of 
 radiation depending on their temperature, increasing as 
 it increases, and diminishing as it diminishes. 
 
 As is the case with light, so, too, with heat : there are 
 substances which transmit its rays with readiness, and 
 others which are opaque. "We therefore speak of dia- 
 thermanous bodies which are analogous to the trans- 
 parent, and athermanous which are like the opaque. 
 
 What ensues if a piece of ice is used instead of a hot ball ? How was this 
 formerly explained ? What is the true explanation of it ? What is meant 
 by the Theory of the Exchanges of Heat ? On what does the rate of ra- 
 diation depend? What are dlathermaiious bodies ? What axe atherma- 
 nous ones? 
 
252 REFRACTION OF HEAT. 
 
 Among the former a vacuum and most gaseous bodies 
 may be numbered ; but it is remarkable that substances 
 which are perfectly transparent to light are not necessa- 
 rily so to heat. Glass, which transmits with but little 
 loss much of the light which falls on it, obstructs much of 
 the heat ; and, conversely, smoky quartz and brown mica 
 which are almost opaque to light transmit heat readily. 
 But of all solid substances, that which is most transparent 
 to heat, or most diathermanous, is rock-salt ; it has there- 
 fore been designated as the glass of radiant heat. If a 
 prism be cut from this substance, and a beam of radiant 
 heat allowed to fall upon it, it undergoes refraction arid 
 dispersion precisely as we have already described as 
 occurring under similar circumstances with a glass prism 
 for light in Lecture XL. And if convex lenses be 
 made of rock-salt they converge the rays of heat to foci, 
 at which the elevation of temperature may be detected 
 by the thermometer. Heat, therefore, can be refracted 
 arid dispersed as easily as it can be reflected. 
 
 If we take a convex lens of glass and one of rock-salt, 
 and cause them to form the image of a burning candle in 
 their foci, it will be found on examination that the image 
 through the rock-salt is hot, but that through the glass 
 can scarcely affect a delicate thermometer. This experi- 
 ment sets in a clear light the difference in the relations 
 between glass and salt, the former permitting the light 
 to pass but not the heat, the latter transmitting both 
 together. 
 
 When light is dispersed by a prism the splendid phe- 
 nomenon of the spectrum is seen. But in the case of 
 heat our organs of sight are constituted so that we cannot 
 discover its presence, and therefore fail to see the cor- 
 responding result. But it is now established beyond all 
 doubt, that in the same manner that there are modifica- 
 tions of light giving rise to the various colored rays, so, 
 too, there are corresponding qualities of radiant heat. 
 Moreover, it has been fully proved that, as stained glass 
 and colored solutions exert an effect on white Iight7 ab- 
 sorbing some rays and letting others pass, the same takes 
 place also for heat. In the case we have already con- 
 Mention some of the former. Of all solid bodies which is the most 
 diathermanous ? What is to be observed when rock-salt and glass are 
 compared? 
 
IMAGINARY COLORATION. 253 
 
 sidered of the imperfect diathermancy of glass the true 
 cause of the phenomenon is the coloration which the 
 glass possesses as respects the rays of heat, and inasmuch 
 as a substance may be perfectly transparent to one of 
 these agents and not so to the other, so, also, a body may 
 stop or absorb a given ray for the one and a totally dif- 
 ferent one for the other. Glass allows all the rays of 
 light to pass almost equally well, but it obstructs almost 
 completely the blue rays of heat. The coloration of 
 bodies, which has already been described as arising from 
 absorption, may, therefore, be wholly different in the two 
 cases ; and as our organs do not permit us to see what it 
 is in the case of heat, and we have to rely on indirect 
 evidence, we speak of the imaginary or ideal coloration 
 of bodies. 
 
 If heat like light, as there are reasons for believing, 
 arises in vibratory movements which are propagated 
 through the ether, all the various phenomena here de- 
 scribed can be readily accounted for. The undulations 
 of heat must be reflected, refracted, inflected, undergo 
 interference, polarization, &c., .as do the undulations of 
 light, the mechanism being the same in both cases. 
 
 LECTURE LI. 
 
 CONDUCTION AND EXPANSION. Good and Bad Conductors 
 of Heat. Differences among the Metals. Conduction 
 and Circulation in Liquids. Point of Application of 
 Heat. Case of Gases. Expansion of Gases, Liquids, 
 and Solids. Irregularity of Expansion in Liquids and 
 Solids. Regularity of Gases. r- Point of Maximum 
 Density of Water. 
 
 WHEN one end of a metallic bar is placed in the fire, 
 after a certain time the other has its temperature ele- 
 vated, and the heat is said to be conducted. It finds its 
 
 What reasons are there for supposing that radiant heat is colored ? Do 
 natural bodies possess a peculiar coloration for heat ? What is meant by 
 ideal or imaginary coloration ? If heat consists of ethereal undulations to 
 what effects must it be liable ? What is meant by the conduction of 
 heat? 
 
254 CONDUCTION OF HEAT. 
 
 way from particle to particle, from those that are hot to 
 those that are cold. 
 
 But if a piece of wood or of earthenware be submitted 
 to the same trial a very different result is obtained. The 
 farther end never becomes hot, proving, therefore, that 
 some bodies are good and others bad conductors of 
 heat. 
 
 The rapidity with which this conduction from particle 
 to particle takes place, depends, among other things, upon 
 their difference of temperature. Thus, when the bulb of 
 a thermometer is plunged in a cup of hot water, for the 
 first few moments its column runs up with rapidity, but 
 as the thermometer comes nearer to the temperature of 
 the water, the heat is transmitted to it more slowly. 
 
 Of the three classes of bodies solids are the best con- 
 ductors, liquids next, and gases worst of all. Of solids 
 the metals are the best, and among the metals may be 
 mentioned gold, silver, copper. Among bad solid con- 
 ductors we have charcoal, ashes, fibrous bodies, as cotton, 
 silk, wool, &c. 
 
 That the metals differ very much in this respect from 
 one another may be satisfactorily proved by taking a rod 
 of copper, one of brass, and one of iron, b c d. Fig. 277, 
 Fiff.277. of equal length and diameter, and screw- 
 ing them into a solid metallic ball, , hav- 
 ing placed on their farther extremities at 
 ^ c d, pieces of phosphorus, a very com- 
 bustible body. Now, if a lamp be placed 
 under the ball, it will be found that the 
 heat traverses the metallic bars with very 
 different degrees of facility, and the phos- 
 phorus takes fire in very different times; 
 the first that inflames is that on the copper, then follows 
 that on the brass, and a long time after that on the iron. 
 Liquids are, for the most part, very indifferent conduct- 
 ors of heat. This may be established, for example, in the 
 case of water, by taking a glass jar, a, Fig. 278, nearly 
 filled with that substance, and introducing into it the bulb 
 of a delicate air-thermometer, c, so that a very short space 
 
 How may it be proved that different bodies conduct heat with different 
 degrees of facility ? How is this affected by difference of temperature ? 
 Of the three classes of bodies which conduct heat best?. How may dif- 
 ference of conduction among metals be proved ? 
 
CIRCULATION. 255 
 
 intervenes between the top of the bulb and the 
 surface of the liquid. If now some sulphuric 
 ether be placed on that surface, and set on fire, it 
 will be found that the thermometer remains mo- 
 tionless, aod we therefore infer that the thin 
 stratum intervening between the burning ether 
 and the thermometer cuts off the passage of the 
 heat. More delicate experiments have, however, 
 proved that the liquid condition is not, in itself, a 
 necessary obstruction. Even water does conduct 
 to a certain extent; and quicksilver, which is equally a 
 liquid, conducts very well. 
 
 But experience assures us that, under common circum- 
 stances, heat is uniformly disseminated through liquids 
 with rapidity. This, however, is due to the establishment 
 of currents in their mass. We have seen how readily this 
 class of bodies expands under an elevation of tempera- 
 ture, and this explains the nature of the passage of heat 
 through them. When the source of heat is applied at the 
 bottom of a vessel containing water, those particles which 
 are in immediate contact with the bottom become warm- 
 ed by the direct action of the fice, and they therefore ex- 
 pand. This expansion makes them lighter, and they rise 
 through the stratum above, establishing a current up to 
 the surface. Meantime thetr place is occupied by colder 
 particles, which descend, and these in their turn becom- 
 ing warm follow the course of the former. Circulation, 
 therefore, takes place throughout the liquid mass, in con- 
 sequence of the establishment of these currents; pig. 279. 
 and all parts being successively brought in con- 
 tact with the hot surface, all are equally heat- 
 ed. That these movements do take place, may 
 be proved by putting into a flask of water, a, 
 Fig. 279, a number of fragments of amber, 
 adding a little glauber salt to make their spe- 
 cific gravity of the liquid more nearly that of 
 the amber, and then applying a lamp, currents 
 are soon set up, and the amber, drifting in them, 
 marks out their course in an instructive manner. 
 
 How may it be proved that liquids are bad conductors of heat ? Is the 
 liquid state a necessary obstruction ? Mention a liquid which is a good 
 conductor. How is heat then transmitted through liquids ? On what do 
 these currents depend ? How may they be illustrated by means of amber ? 
 
256 CIRCULATION IN GASES. 
 
 Such currents, however, wholly depend on the point of 
 application of the heat. If the fire, instead of being ap- 
 plied at the bottom of the vessel, is applied at the top, as 
 in Fig. 278, then the liquid can never be warmed. The 
 cause of the movements of particles is their becoming 
 lighter they therefore float upward ; but if they are al- 
 ready situated on the surface of course no movement can 
 take place. 
 
 With respect to gases we observe the same peculiari- 
 ties that we do with liquids. Strictly speaking, they are 
 Fig. 280. very bad conductors of heat; but from the mo- 
 bility of their parts, it is very easy to transfer 
 heat readily through them, provided it is right- 
 ly applied. The experiment represented in 
 Fig. 280, shows how easily circulation takes 
 place in them. If a piece of burning sulphur 
 be put in a cup, a, and ajar full of oxygen be 
 inverted over it, the combustion goes on with 
 rapidity, and the light smoke that rises marks 
 out very well the path of the moving air. It rises direct- 
 ly upward from the burning mass, until it reaches the top 
 of the jar, and then descends in circular wreaths to the 
 bottom. 
 
 On the principle of the difference of the conductibility 
 of bodies, we direct all our operations for the communi- 
 cation of heat with different degrees of rapidity. When 
 we desire to abstract the heat rapidly from bodies, we 
 surround them with good conductors ; if we wish to re- 
 tard it, we select such as are bad. And, indeed, it is in 
 this way that we regulate our changes of clothing. Thick 
 woollen articles, which are very bad conductors, are adapted 
 to the cold winter weather, when we desire to cut off the 
 escape of heat from our bodies as much as is in our pow- 
 er. Nature also resorts to the same principles the thick 
 coat of wool or of hair which serves for the covering of 
 animals protects them from the cold by its non-conduct- 
 ing power. In these instances, in reality, the action of 
 atmospheric air is brought into play, and that under the 
 
 Why do such currents depend on the point of application of the heat ? 
 Do the same laws hold in the case of gases ? How may this be proved 
 by experiment '( What applications are made of the principle of different 
 conductibility ? In the fur of animals how is the non-conducting power of 
 air called into use ? 
 
POINT OF MAXIMUM DENSITY. 257 
 
 most favorable circumstances ; for any motion of its par- 
 ticles among the thickly matted fibres is impossible, and 
 its non-conducting power, undisturbed by circulation, is 
 rendered available. 
 
 It has been stated that all bodies expand under the in- 
 fluence of heat gases being the most expansible, liquids 
 next, and solids least. But the expansion of the two lat- 
 ter classes of bodies is far irom beinij proportional to 
 their temperature; for solids and liquids expand increas- 
 ingly as their temperature rises one degree of heat, if 
 applied at 400, produces a greater dilatation than if ap- 
 plied at 100. From this irregularity it is believed that 
 gases are free they seem to expand uniformly at all tem- 
 peratures. 
 
 Besides this general irregularity which applies to all 
 solids and liquids, there are other special irregularities, 
 often of great interest. Water may afford an example. 
 If some of this liquid be taken at 32 and warmed, in- 
 stead of expanding it contracts, and continues to do so 
 until it has reached about 39 1, after which it expands. 
 It therefore follows, that if we take icater at 39^, whether 
 we warm it or cool it, it expands. At that temperature it 
 is, therefore, in the smallest space into which it can be 
 brought by cooling it has, therefore, the greatest densi- 
 ty, and 39| i& spoken of as the point of maximum density 
 of water. In the same manner several other liquids, and 
 even solids, have points of maximum density. 
 
 This fact is of considerable interest, when taken in con- 
 nection with the circulatory movements we have been de- 
 scribing. When a mass of water cools on a winter's night, 
 the colder particles do not contract and descend to the 
 bottom, but after 39| is reached, they, being the lighter, 
 float on the top, and hence freezing begins at the surface. 
 Were it otherwise, and the liquid solidified from the bot- 
 tom upward, all masses of water during the winter would 
 be converted into solid blocks of ice, instead of being 
 merely covered as they are with a screen of that sub- 
 stance, which protects them from further action. 
 
 Do solids and liquids expand with regularity ? Are there other irregu- 
 larities besides this ? What is meant by the maximum density of water .' 
 At what temperature does it take place ? How does this effect the freez- 
 ing of masses of water ? 
 
258 CAPACITY FOR HEAT. 
 
 LECTURE LII. 
 
 CAPACITY FOR HEAT AND LATENT HEAT. Illustration 
 of the Different Capacities of Bodies for Heat. Stand- 
 ards employed. Process by Melting. Process of Mix- 
 tures. Effects of Compression. Effect of Dilatation. 
 Latent Heat. Caloric of Fluidity. Caloric of Elasti- 
 city. Artificial Cold. 
 
 BY the phrase capacity of bodies for heat we allude to 
 the fact that different bodies require different degrees of heat 
 to warm them equally. 
 
 An experiment will serve to illustrate this important 
 fact. If we take two bottles as precisely alike as we can 
 obtain them, and, having filled one with water and the other 
 with quicksilver, set them before the same fire, so as to 
 receive equal quantities of heat in equal times, it will be 
 found that the water requires a very much longer expos- 
 ure, and therefore a larger quantity of heat than the quick- 
 silver to raise its temperature up to the same point. 
 
 Or if we do the converse of this, and take the two bot- 
 tles filled with their respective liquids, which, by having 
 been immersed in a pan of boiling water, have both been 
 brought to the same degree, and let them cool freely in 
 the air, it will be found that the water requires much 
 more time than the quicksilver to come down to the com- 
 mon temperatures. It contained more heat at the high 
 temperature than did the quicksilver, and required more 
 time to cool; it has, therefore, a greater capacity for heat ; 
 or, to use a loose expression, at the same temperature 
 holds more of it. 
 
 There are several different ways by which the capacity 
 of bodies for heat may be determined. Thus, we may 
 notice the times they require for warming, or those ex- 
 pended in cooling in a vacuum. Of course, we cannot 
 
 What is meant by the capacity of bodies for heat ? Illustrate this by 
 experiment. Can it be proved conversely? In what ways may the ca'- 
 pacity of bodies be determined ? Can the absolute amount of heat in 
 bodies be determined ? 
 
METHOD OF MELTING. 259 
 
 tell the absolute amount of heat which is contained in 
 any substance whatever, and these determinations are 
 hence relative different bodies being compared with a 
 given one which is taken as a standard. For these pur- 
 poses water is the substance selected for solids and liquids 
 and atmospheric air for gases and vapors. 
 
 An illustration will show the methods by which the ca- 
 pacity of bodies is determined by the process of melting. 
 Let there be provided a mass of ice, Fig. 281. 
 
 a a, Fig. 281, in which a cavity, b d, 
 has been previously made, and a slab 
 of ice, c c, so as to cover the cavity 
 completely. In a small flask, d, place 
 an ounce of water, raised to a temper- 
 ature of 200. Set this in the cavity, 
 as shown in the figure, and put on the 
 slab. The ice now begins to melt ; 
 and, as the water forms, it Collects in the bottom of the 
 cavity. When the temperature of the flask has reached 
 32 it only remains to pour out the water and measure 
 it.^ Next, let there be put in the flask an ounce of quick- 
 silver, the temperature of which is raised, as before, to 
 200 ; measure the water which it can give rise to by melt- 
 ing the ice, precisely as in the former experiment, and it 
 will be found that the water melted twenty-three times as 
 much as the quicksilver. Under these circumstances, 
 therefore, a given weight of water gives twenty-three 
 times as much heat as the same quantity of quicksilver. 
 
 There are still other means of obtaining the same re- 
 sults. Such, for instance, as by the method of mixtures. 
 If a pint of water at 50 be mixed with a pint at 100 the 
 temperature of the mixture is 75; but it a pint of mer- 
 cury, at 100, is mixed with a pint of water, at 40, the 
 temperature of the mixture will be 60, so that the 40 
 lost by mercury only raised the water 20. That this 
 result may correspond with the foregoing, it should be 
 recollected that, in this instance, we are using equal vol- 
 umes, in that equal weights. 
 
 Why is capacity a relative thing ? What is the standard for solids and 
 liquids ? What is it for gases and vapors ? Describe the process for deter- 
 mining capacities by melting. How do water and quicksilver compare ? 
 Describe the process by mixtures. In ibis, how do water and quicksilver 
 compare ? 
 
260 CHANGES OF SPECIFIC HEAT. 
 
 In this way the capacities of a great number of bodies 
 have been determined, and tables constructed in which 
 they are recorded. Such tables are given in the books 
 of chemistry. The different capacities of bodies are also 
 designated by the term specific heat, since it requires a 
 specific quantity of heat to heat bodies equally. 
 
 When a body is compressed, its specific heat or capaci- 
 ty for heat diminishes, and a portion makes itj appearance 
 as sensible heat. This may be proved by rapidly com- 
 pressing air, which will give out enough heat to set tin- 
 der on fire, or by beating a piece of iron vigorously, when 
 it may be made red hot. On the other hand, when a 
 body is dilated its capacity for heat increases. It is partly 
 for this reason that the upper regions of the atmosphere 
 are so cold the specific heat is great by reason of the rar- 
 ity. It therefore requires a large amount of heat to bring 
 the temperature up to a given point. 
 
 It has also been found that the specific heat changes 
 with the temperature, increasing therewith, so that it is 
 not constant for the same body. 
 
 There is reason to believe that the atoms of all simple 
 substances have an equal capacity for heat; and that 
 all compound bodies, composed of an equal number of 
 single atoms combined in one and the same manner, 
 have a capacity for heat which is inversely as their specific 
 gravity. 
 
 When a solid substance passes into the liquid form a 
 large quantity of heat is rendered latent that is to say, 
 undiscoverable to the thermometer. Thus, we may have 
 ice at 32 and water at 32, the one a solid and the other 
 a liquid, and the precise reason of the physical difference 
 between them is, that the water contains about 140, 
 which the ice does not a quantity which is occupied in 
 giving it the liquid state, and is insensible to the ther- 
 mometer. 
 
 For this reason the transformation of a solid into a 
 liquid is not an instantaneous phenomenon, but one requir- 
 
 What is meant by specific heat? How does specific heat change under 
 compression ? Does this take place in solids as well as gases ? What 
 reason is there for the cold in the upper regions of the air ? Does spe- 
 cific heat vary with the temperature ? What is observed respecting the 
 atoms of simple bodies ? What respecting compound ? What is latent 
 heat ? What is the latent heat of water? Why does the transformation 
 of water into ice or ice into water require time ? 
 
LATENT HEAT. 261 
 
 ing time. Ice must have its 140 degrees oflatent heat 
 before it can turn into water. And, conversely, the solid- 
 ification of a liquid is not instantaneous. It must have 
 time to give out the latent heat to which its liquid state 
 is due. 
 
 When a liquid passes into the form of a vapor it is the 
 presence of a large quantity of latent heat which gives to 
 it all its peculiarities. Thus, water in turning into steam 
 absorbs nearly 1000 oflatent heat, and when that steam 
 reverts into the liquid state the heat reappears. 
 
 To the caloric which is absorbed during fusion, the 
 designation of caloric of fluidity is given, to that which 
 gives their constitution to vapors the name of caloric of 
 elasticity. And as different bodies require during these 
 changes different quantities of heat, there are furnished 
 in the works on chemistry tables of the caloric of fluidity, 
 and caloric of elasticity of all the more common or im- 
 portant bodies. Of all known bodies water has the 
 greatest capacity for heat ; and, in consequence of the 
 great amount of latent heat it contains, it is one of the 
 great reservoirs of caloric, both for natural and artificial 
 purposes. 
 
 Hence, whenever a substance melts it absorbs heat, 
 and when it solidifies it gives out heat. When a sub- 
 stance vaporizes it absorbs heat, and when a vapor lique- 
 fies it evolves heat. 
 
 On these principles depend some of the processes re- 
 sorted to for the production of cold. If we take two 
 solid bodies, as salt and snow, which have such chemical 
 relations to one another that, when mixed, they produce 
 a forced fusion and enter on the liquid state ; before that 
 change of form can take place, caloric of fluidity must be 
 supplied, for snow cannot turn into water unless heat is giv- 
 en it. The mixture, therefore, abstracting heat from any 
 bodies around or in contact with it, brings d^wn their 
 temperature and thus produces cold. The same result 
 attends the vaporization of a liquid ; thus, ether poured 
 on the hand or on the thermometer produces a great 
 
 What is the physical difference between water and steam ? What is 
 the caloric of fluidity? What is the caloric of elasticity? What sub- 
 stance has the greatest capacity for heat ? Why is cold produced by a 
 mixture of salt and snow ? Why is it produced by the vaporization of 
 ether ? 
 
262 PHENOMENA OF BOILING. 
 
 cold, because the vapor which rises must have caloric of 
 elasticity in order to assume its peculiar form, and it 
 takes heat from the body from which it is evaporating for 
 that purpose. 
 
 LECTURE LIII. 
 
 ON EVAPORATION AND BOILING. Phenomena of Boiling. 
 Effect of the Nature of the Vessel and the Pressure. 
 Height of Mountains Determined. Effect of Increased 
 Pressure. Evaporation. Vaporization in Vacuo. 
 Effect of Temperature on a Liquid in Vacuo. Expla- 
 nation of Boiling. Nature of Vapors. 
 
 As the vaporization of liquids is connected with some 
 of the most important mechanical applications, we shall 
 proceed to consider it more minutely. 
 
 When water is placed in an open vessel on the fire the 
 temperature of the whole mass ascends on account of the 
 currents described in Lecture LI. After a time minute 
 bubbles make their appearance on the sides of the vessel; 
 these rise a little distance and then disappear, but others 
 soon take their places, and the water, being thrown into 
 a rapid vibratory motion, emits a singing sound. Imme- 
 diately after this the little bubbles make their way to the 
 surface of the liquid, and are followed by others which 
 are larger, and the phenomenon of boiling takes place. 
 The heat has now reached 212, and it matters not how 
 hot the fire may be, it never rises higher. 
 
 Different liquids have different boiling points, but for 
 the same body, under similar circumstances, the point is 
 nearly fixed. It is, indeed, in consequence of this that 
 the boiling of water is taken as the upper fixed point of 
 the thermometer. 
 
 Of the circumstances which can control the boiling 
 point, two may be mentioned : the nature of the vessel 
 and the pressure of the air. 
 
 In a polished vessel, for instance, water does not boil 
 
 Describe the different phenomena exhibited during the warming of 
 water. At what temperature does ebullition set in ? What circumstances 
 control the boiling point ? In a polished vessel what is the temperature ? 
 
EFFECT OF PRESSURE. 263 
 
 until 214 ; but if a few grains of sand or other angular 
 body is thrown in 'the temperature sinks to 212. 
 
 The absolute control which pressure exerts over the 
 boiling point may be shown in many different 
 striking ways. Thus, if a glass of warm water 
 be put under the receiver of an air-pump and 
 exhaustion made, the water enters into rapid 
 ebullition, and continues boiling until its tem- 
 perature goes down to 67. Water placed in 
 a vacuum will therefore boil with the warmth 
 of the hand. 
 
 Advantage has been taken of this fact to determine the 
 height of accessible eminences. For, as we ascend in 
 the air, the pressure necessarily becomes less; the superin- 
 cumbent column of the atmosphere being shortened, the 
 boiling point therefore declines. It has been ascertained 
 that if we ascend from the ground through 530 feet, the 
 boiling point is lowered one degree ; and formulas are 
 given by which, from a knowledge of that point, in any 
 instance the altitude may be calculated. 
 
 On the other hand, when the pressure on a liquid is 
 increased, its boiling point ascends. This may be proved 
 by taking a spherical boiler, #, properly supported over 
 a spirit lamp, there being in its top three openings ; 
 through d let a thermometer dip into some water which 
 half fills the boiler, at b let there be a stop- 
 cock which can be opened and shut at 
 pleasure, and through a third opening be- 
 tween these let a tube, c, pass, dipping down 
 nearly to the bottom of the boiler into some 
 quicksilver which is beneath the water. 
 Now let the water boil freely and the steam 
 escape through b, the thermometer will 
 mark 212. Close the stop-cock so that 
 the steam cannot get out, but, being con- 
 fined in the boiler, exerts a pressure on 
 the surface of the water, which is indicated 
 by the rise of the mercury in the tube. As the column 
 rises the boiling point rises, and if the instrument were 
 
 Prove that it is affected by pressure. At what temperature will water boi] 
 in an air-pump vacuum T How has this been applied for the determina- 
 tion of heights ? How does the boiling point vary when the pressure is 
 increased ? 
 
264 
 
 MEASURE OP ELASTIC FORCE. 
 
 adapted to show the results for high pressures, it might 
 be proved that the boiling point 
 
 For 1 atmosphere is 212 For 10 atmospheres is 358.8 
 
 2 " 250.5 15 " 392.8 
 
 3 " 275.2 20 " 418.5 
 
 4 " 293.7 40 6665 
 
 5 " 307.5 50 690.7 
 
 Besides this escape of vapor from liquids during the act 
 of boiling, the same is continually going on in a slow and 
 motionless way, at lower temperatures. If some water 
 be left in a shallow vessel exposed to the air, after a short 
 time it all disappears. To this phenomenon the term 
 evaporation is given. 
 
 At one time it was supposed that the atmospheric air 
 acted on evaporating bodies by an affinity for their vapors, 
 in the same way that a sponge will soak up water. But 
 Fig. 284. the fallacy of this idea is proved by the fact 
 that evaporation goes on more rapidly in vacuo, 
 where no body whatever is present, than in the 
 air. Thus, if into the tomcellian vacuum of 
 a barometer, we pass a little ether, alcohol, or 
 water, the moment they reach the void they 
 instantly give forth vapor, and the mercurial 
 column is depressed. With ether the depres- 
 sion is greatest, with alcohol less, and with wa- 
 ter last of all. Now when we consider the 
 nature of the barometer, and the force which 
 keeps the column of mercury suspended in it, 
 it is very clear that this simple method affords 
 
 us an easy means of knowing the elastic force of the va- 
 pors evolved from any of these substances : for the mer- 
 curial column is depressed through the operation of that 
 elastic force. It is this which forces it downward, while 
 the pressure of the air tends to force it upward. 
 
 By thus introducing liquids into- the barometric tube, 
 we have the means of determining the elastic force of the 
 vapors to which they give rise ; and very simple exper- 
 iments satisfy us that that elastic force depends upon the 
 the temperature. If we warm the tube, Fig. 284, by 
 
 Give some examples of the boiling point for different pressures. What 
 is meant by evaporation ? How can it be proved that the air does not act 
 by its porosity like a sponge ? What takes place when a liquid is passed 
 into a torricellian vacuum ? How can we measure the elastic force of the 
 vapor evolved ? 
 
EFFECT OF PRESSURE. 265 
 
 moving over it the flame of a spirit-lamp, the depression 
 becomes greater, and if we surround it by means F^.285. 
 of warm water in a wider tube, so as to be able r 
 to ascertain with accuracy the temperature ap- 
 plied, we shall discover that as the heat rises the 
 elastic force of the vapor increases, and that the 
 mercurial column is wholly depressed into the cis- 
 tern aft soon as the temperature has reached the boil- 
 ing point of the. liquid on which ice are operating. 
 
 Thus, let Abe a deep glass jar, filled to the height 
 n with mercury, and let a b be the barometric tube, 
 into the vacuum of which, at m, the liquid under 
 trial has been passed. Let a wide tube, re, capa- 
 ble of holding hot water, be adapted, by means of 
 a tight-fitting cork, at s, to the barometric tube. 
 Now if, having observed the depression which the 
 mercury exhibits at common temperatures, we fill 
 the tube, r c, with hot water, a still greater de- 
 pression is the immediate result. The tempera- 
 ture of the hot water, and, therefore, of the liquid 
 in the barometer, can easily be determined by 
 plunging a thermometer into the tube, r c. 
 
 From such experiments, therefore, we draw this im- 
 portant conclusion : The elastic force of vapor rising from 
 a liquid at its boiling point is equal to the pressure upon 
 it. If the ebullition be taking place in the open air, it is 
 therefore equal to the pressure of the air. 
 
 This principle furnishes a complete explanation of the 
 process of boiling, previously described. As the temper- 
 ature of a mass of liquid exposed to heat gradually rises, 
 the elastic force of the vapor it generates increases. Very 
 soon, therefore, on the hottest part of the vessel, that part 
 in immediate contact with the fire, the temperature reaches 
 such a point that the vapor can form, the elastic force of 
 which is just equal to the atmospheric pressure. Little 
 bubbles now rise ; but these, having to pass up through a 
 stratum above, which is of a temperature somewhat low- 
 er, are crushed in and disappear. They therefore throw 
 
 Prove that that elastic force depends on the temperature. What is the 
 elastic force when the boiling point is reached ? What is the elastic force 
 of a vapor when ebullition takes place in the air ? How are these princi- 
 ples connected with the process of boiling ? Why is a singing sound 
 emitted ? 
 
 M 
 
266 
 
 NATURE OF VAPORS. 
 
 vapors. 
 
 the liquid into a vibratory motion, and cause the singing 
 sound. But soon the whole liquid attains such a degree 
 of heat that the bubbles can make their way to the top, 
 and then bursting, the phenomenon of ebullition fairly 
 sets in. 
 
 With respect to the nature of vapors, there is a good 
 Fig. 286. deal of popular misconception. Many persons 
 suppose that they are naturally of a smoky or 
 hazy aspect. But if we repeat the experiment 
 represented in Fig. 286, and formerly described 
 in Lecture VI., we shall find that so far as the 
 vapor of ether is concerned, it is perfectly trans- 
 parent, like atmospheric air, and by proper ex- 
 amination the same may be verified for all other 
 The true peculiarity is the facility with which 
 this form of bodies assumes the liquid state. The mo- 
 ment the pressure of the air is restored, in this experi- 
 ment, the ethereal vapor collapses into the liquid condi- 
 tion. 
 
 The same fact may be illustrated in another way. If 
 Fig. 287. we take a mattrass, a, Fig. 287, and fill 
 the bulb and tube of it with water, and 
 then introduce a little sulphuric ether into 
 its upper part, the mouth dipping beneath 
 some water contained in ajar, on heating 
 the bulb by a spirit-larnp the ether pres- 
 ently vaporizes. It may now be remark- 
 ed 1st. That a vapor occupies a great 
 deal more space than the liquid from which it comes ; 2d. 
 That it has not a misty appearance, but is perfectly trans- 
 parent; 3d. That, under a reduction of temperature, it 
 collapses into the liquid state for, on removing the lamp 
 and suffering the bulb to cool, the vapor disappears. 
 
 Either by diminution of temperature or increase of 
 pressure, vapors may be condensed into the liquid state, 
 and in this consists the chief distinction between them 
 and gases. 
 
 How can it be proved that vapors are not of a misty aspect ? What is 
 their true peculiarity ? What does Fig. 287 illustrate? What three facts 
 are proved by it ? How may vapors be condensed into the liquid state ? 
 
THE STEAM ENGINE. 
 
 267 
 
 LECTURE LIV. 
 
 THE STEAM ENGINE. Elementary Steam Engine. Forms 
 of this J\Iachine. Description of the High-Pressure En- 
 gine. Principle of the Low-Pressure Engine." De- 
 scription of the Double- Acting Engine. Estimate of 
 Performance. 
 
 ON the elastic force of steam and on the rapidity with 
 which it is condensed by application of cold, the construc- 
 tion of the different forms of steam engine depends. 
 
 The instrument represented in Fig. 288 Fig- 28& 
 gives a clear idea of the elementary parts 
 of a steam engine. It consists of a cylin- 
 drical glass tube, B, terminating in a bulb, 
 A. In the tube a piston moves up and 
 down, air-tight, and a little water having 
 been placed in the bulb, it is brought to the 
 boiling point by the application of a lamp. 
 As the steam forms it presses the piston up- 
 ward by reason of its elastic force, and on 
 dipping the bulb into cold water the steam 
 condenses, and produces a partial vacuum, 
 the piston being driven downward by the 
 pressure of the air. 
 
 There are a great many modifications of 
 the steam engine. They may, however, for the most part, 
 be reduced to two kinds: 1st, high-pressure engines; 2d, 
 low-pressure engines. 
 
 The high-pressure engine, which is the simplest of the 
 two forms, consists essentially of a very strong iron ves- 
 sel or boiler, in which the steam is generated, a cylinder, 
 in which a steam-tight piston moves backward and for- 
 ward, an arrangement of valves or cocks, so adjusted as 
 alternately to admit the steam above and below the pis- 
 ton, and also alternately to let it escape into the air; 
 
 On what two principles do the different kinds of steam engine depend ? 
 Describe the instrument represented in Fig. 288. What are the chief 
 varieties of the steam engine ? Describe the high-pressure engine. 
 
268 
 
 HIGH-PRESSURE ENGINE. 
 
 and lastly, a suitable contrivance by which the oscilla- 
 tions of the piston may be converted into other kinds of 
 motion, suited to the work which the engine has to per- 
 form. 
 
 The action of the steaminoneof these machines may be 
 Fig. 289. understood from the annexed diagram, Fig. 289. 
 Let f be the cylinder, in which a solid piston, e, 
 moves, steam-tight, and let us suppose the piston 
 near to the bottom of the cylinder. The steam 
 , is now admitted through an aperture, a, and by 
 its elastic force pushes the piston to the top of 
 the cylinder. The movement of the piston-rod 
 rearranges the openings into the cylinder, clos- 
 ing at a particular moment # , through which the 
 steam has already come, and opening b; simul- 
 taneously, also, it opens c and closes d. Through 
 c, from the boiler, a fresh supply of steam ar- 
 rives, while it is shut off from a. This steam 
 cannot escape through d, because that is closed 
 it therefore takes effect upon the piston and 
 pushes it downward, all the vapor beneath es- 
 caping out into the air through b, which has 
 been opened. This downward move'ment of 
 the piston-rod rearranges all the valves, reversing the po- 
 sitions they have jusf had. It therefore opens a, shuts b, 
 opens d, and shuts c. Steam now comes in from the 
 boiler, through <z, but cannot escape through b ; it there- 
 fore pushes up the piston, driving out the steam, which is 
 on its opposite side, through d, and in this way a recip- 
 rocating motion is produced. 
 
 The means of opening and shutting the apertures lead- 
 ing into the cylinder at the proper moment differ in dif- 
 ferent engines sometimes cocks are used, and sometimes 
 sliding valves. 
 
 In this engine, therefore, the piston moves in both ways 
 against the pressure of the air. The steam must be ne- 
 cessarily raised from water at a high boiling point, and 
 hence these machines are much more liable to accident 
 than the low-pressure engine, now to be described. 
 
 The rapid condensibility of steam a principle inti- 
 
 Describe the circumstances under which the steam is alternately ad- 
 mitted above and below the piston. How are the necessary apertures 
 opened and closed ? Why must the steam be raised at high pressure 1 
 
 a 
 
CONDENSIBILITY OF STEAM. 
 
 269 
 
 mately concerned in the action of the low-pressure en- 
 gine may be illustrated in the fol- 2^.290. 
 lowing manner: Take a glass flask, a, 
 Fig. 290, and adjust to its mouth a 
 wide bent tube, b, both ends of which 
 are open, having previously placed a 
 quantity of water in the flask. Apply 
 the flame of a spirit-lamp, and bring 
 the water to the boiling point, contin- 
 uing the ebullition until all the air is 
 driven out of the flask, and nothing 
 but steam remains. Then dip the open 
 end of the tube into the jar, c, containing some cold wa- 
 ter, and remove the lamp ; the steam in the tube will at 
 once begin to condense, through the influence of the cold 
 water, which soon rises over the bent portion and precip- 
 itates itself into the flask, often with so much violence as 
 to break it to pieces. 
 
 Of the low-pressure engine we have varieties such as 
 the single-acting and the double-acting engine. In the 
 former, the piston is driven one way by means of steam 
 acting against a vacuum, returning the other way by the 
 counterpoising weight of the machinery. The machine, 
 therefore, in reality, is only in action during half its mo- 
 tion. 
 
 The double-acting engine has the steam employed to 
 produce both the ascent and descent of the piston into a 
 vacuum on the opposite side. It therefore works contin- 
 uously. 
 
 In expansive engines the supply of steam, instead of 
 being continued during the entire ascent or descent of 
 the piston, is cut off when the movement is one half or 
 one third accomplished. The expansion of that steam 
 driving the piston through the rest of the cylinder. 
 
 The following is a description of the double-acting en- 
 gine : Fig. 291 represents the boiler and its appurtenances, 
 Fig. 292 the engine. 
 
 B B, Fig. 291, is the boiler, of a cylindrical shape, the 
 fire, F F, is applied beneath, W W is the water-level, 
 and S is occupied by steam. At tt there is a bent glass 
 
 Give an illustration of the instantaneous condensation of steam. What 
 is the nature of the single-acting steam engine ? What is meant by the 
 expansive engine ? What is the double-acting engine ? 
 
270 
 
 STEAM-BOILER. 
 
 tube, open at both extremities, and so arranged that one 
 end is in the steam-space, and the other in the water; 
 
 Fig. 291. 
 
 it serves to show the level of the water in the boiler. In 
 some cases, two cocks, c and d, are inserted in the boiler, 
 one entering into the steam part and one beneath the 
 water. On opening them, if the water is at its proper 
 level, steam will escape from the upper and water from 
 the under one. If there is too much water, it escapes 
 from both ; if two little, steam escapes from both. The 
 boiler is continually replenished by the feed-pipe, the na- 
 ture of which has been explained in Lecture XIV. At 
 M there is a barometer-gauge, to show the elastic force 
 of the steam ; at e a b a safety-valve, with its weight, w ; 
 this opens upward, so that, should the elastic force in the 
 interior of the boiler become too great, the valve opens, 
 and the steam escapes. On the contrary, to prevent the 
 boiler being crushed in by the atmospheric pressure, 
 when the expansive force of the steam happens to de- 
 cline, there is a second valve at U, with its lever, a c b, 
 
 Describe the principal parts of its boiler. What are the two safety- 
 valves ? 
 
DOUBLE-ACTING ENGINE. 
 
 271 
 
 and weight, w, which opens inward, that, when the ex- 
 ternal pressure exceeds the weight, the air may find ac- 
 cess to the inside of the boiler. And, as it is necessary 
 from time to time to clear the boiler from the incrusta- 
 tions or deposits of salt and other impurities, there is an 
 opening, as at L, through which access can be had. 
 This, of course, is, at other times, securely closed. Last- 
 ly, from the boiler there passes the steam-pipe, s, which 
 is opened by the valve at N. 
 
 Fig. 292 represents the engine, properly speaking. At 
 
 Fur. 292. 
 
 z z it should be imagined as being continuous with z z 
 of Fig. 291, so that in both figures the tubes i i and s s 
 are continuous. In both s is the tube along which the 
 steam from the boiler is delivered to the cylinder. Pass- 
 ing through the four -way cock, a, either down through a 
 or up through b, into the cylinder C, in which the piston, 
 P, moves. Admission for the steam, above or below the 
 piston, is regulated by a system of levers, y y, the neces- 
 sary motion being communicated by the machine itself. 
 
 Describe the principal parts of the engine, 
 hen it leaves the cylinder ? 
 
 What becomes of the steam 
 
272 HYGROMETRY. 
 
 The piston-rod, E, is connected with the beam, B F, 
 working on the fulcrum, A. The connecting-rod is F R. 
 At R itfis attached to the crank by a pivot, H H H, being 
 the fly-wheel, the revolution of which gives uniformity to 
 the motion. The steam, after elevating or depressing 
 the piston, passes through the eduction-pipe, ff, into the 
 condenser, J, which is immersed in a cistern, L, of cold 
 water. In this it is condensed into water by a jet which 
 passes through the injection-cock. The resulting warm 
 water is pumped out by the air-pump, O, into the hot 
 well, W ; thence it is carried, by the hot-water pump, Z, 
 along the feed-pipe, i i, into the boiler. The cold-water 
 pump, S, supplies the reservoir with cold water. All the 
 pumps are worked by the beam of the engine. The sup- 
 ply of steam is regulated by the governor, G, so as to be 
 kept constant. 
 
 The performance of steam engines is commonly esti- 
 mated by horse-power. The value of the power of one 
 horse is a force sufficient to raise 33,000 pounds one foot 
 high in one minute. 
 
 LECTURE LV. 
 
 HYGROMETRY, OR THE MEASUREMENT OF THE QUANTITY 
 OF VAPOR. Hygrometers. Sponge and Paper Hy- 
 grometers. Saussure's Hair Hygrometer. Mode of 
 Graduating it. The Dew Point. Process for the 
 Dew Point. Daniel's Hygrometer. The Psychrome- 
 ter. Process for Drying Gas. 
 
 FOR many scientific purposes it is often necessary to 
 determine the amount of vapor of water in the air or in 
 various gases. We have already observed, Lecture III, 
 that the quantity of moisture in the atmosphere is con- 
 stantly changing ; and this is connected with a great num- 
 ber of interesting meteorological phenomena. 
 
 Instruments have been invented with a view of giving 
 indications of the relative degrees of dampness of the air. 
 
 What is done with the resulting hot water? How are the movements 
 of the different pumps and valves accomplished ? What is the value of a 
 horse-power ? 
 
SPONGE HYGROMETER. 
 
 273 
 
 They have received the names of hygroscopes and hy- 
 grometers. 
 
 A great many organic substances change their dimen- 
 sions according as they are exposed to various degrees 
 of moisture, expanding or contracting. Among such may 
 be mentioned ivory, hair, whalebone, wood, &c. Any of 
 these connected with a mechanism, by which the change 
 of volume might be registered, would furnish a hygrom- 
 eter. They all, however, lose their sensitiveness in the 
 course of time. Thus, it is well known that wood, when 
 it is seasoned, is much less liable to these changes than 
 when it is in a recent state. 
 
 There are other bodies, among which might be enu- 
 merated many salts, which, by absorbing moisture from 
 the air increase in weight, and by returning it back again, 
 become lighter. Most of the powerful acids, as the 
 sulphuric, also the alkalies, as potash and soda, possess 
 an intense affinity for water. Advantage has been taken 
 of this property in the construction of hygrometers, by 
 attaching a sponge, soaked in weak pearlash, to one arm 
 of a balance, the index of which plays over a graduated 
 scale, and shows the influence of the existing moisture 
 by the sponge becoming heavier or lighter. For such 
 
 . 293. 
 
 contrivances paper is a very suitable substance. Thus, 
 let G G, Fig 23Q, be a case, the front of which is of glass 
 and the sides of gauze or some other material, pervious 
 to the air; let D be the beam of a light balance suspend- 
 
 What are hygroscopes or hygrometers ? Mention some bodies which 
 change under the influence of moisture. Describe the sponge hygrometer. 
 
274 
 
 PAPER HYGROMETER. 
 
 ed within, working on the fulcrum g, and supported by 
 two brackets, A A. From the beam let there pass an index, 
 
 Fig. 294. 
 
 E, which moves over a scale, C, graduated into 100 equal 
 parts, and suspended on a support, B. From one end 
 of the beam let there hang the hygroscopic body, I, 
 which consists of a great number of round pieces of thin 
 paper, fastened together by three or more threads, form- 
 ing a column, with spaces between each of the parallel 
 pieces- of paper, that the air may have complete access to 
 the whole mass. This hygroscopic body is properly coun- 
 poised by a weight, H, in the opposite scale-pan. At F 
 there is a button, which slides upon the index ; it is to 
 be arranged in such a position that a weight of one grain 
 put on the top of the hygroscopic body will drive the 
 index from to 100 exactly. The papers are now to be 
 thoroughly dried, by placing a dish of sulphuric acid in 
 the case, or in any other suitable manner ; and when that 
 is accomplished, weights are to be added at H to bring 
 the index to 0. When, now, it is exposed to the air, the 
 papers become heavier, and the index plays over the 
 scale. The instrument, therefore, acts from the dry ex- 
 treme ; but, though its movements are interesting, for it 
 is constantly traversing, it is devoid of exactitude. 
 
 The hair hygrometer of Saussure is more simple and 
 effectual. It consists of a human hair 8 or 10 inches 
 
 Describe the hygrometer represented in Fig. 2C 
 does this instrument act? 
 
 From what extreme 
 
SAUSSURE S HYGROMETER. 275 
 
 long, b c, Fig. 295, fastened at one extremity to a screw, 
 a, and at the other passing over a pulley, c, 
 being strained tight by a silk thread and weight, F * 8 ' 295 ' 
 d. From the pulley there goes an index which 
 plays over the graduated scale e e', so that, 
 as the pulley turns through the shortening or 
 lengthening of the hair, the index moves. The 
 instrument is graduated to correspond with 
 others by first placing it under a bell jar along 
 with a dish of sulphuric acid, caustic potash, 
 chloride of calcium, or other substance having 
 an intense affinity for water, this absorbs all the 
 moisture of the air in the bell, and brings it to 
 
 absolute dryness. The hair, therefore, contracts and 
 moves the pulley and its index. When this contraction is 
 complete, the point at which the index stands is marked 0. 
 The hygrometer is then placed under a jar, the interior 
 of which is thoroughly moistened with water and set in a 
 vessel with that liquid, so as to bring the included air to 
 a condition saturated with moisture. The index moves, 
 and when it has become stationary the point opposite to 
 which it stands is marked 100. The intervening space 
 is then divided into 100 equal parts, and the instrument 
 is complete. 
 
 It is to be observed that the hair requires some pre- 
 vious preparation to give it its full hygrometric sensibility ; 
 this is accomplished by removing from it all oily matter 
 by soaking it in a weak solution of potash. 
 
 As respects the nature of the indications of this instru- 
 ment, it is to be understood, that it by no means follows 
 that, when the index stands at 25 or 50, the air contains 
 one quarter or one half the moisture it does at 100. 
 Tables have, however, been constructed, which exhibit 
 the value of its degrees. 
 
 A much more exact method is that known as the pro- 
 cess for tlie daw point. In practice it is very simple, and 
 may be thus described. If we take a glass of water, and, 
 by putting in it pieces of ice, cool it down, after a time 
 moisture will begin to dim the outside. If a thermometer 
 
 Describe the hair hygrometer of Saussure. How are its two fixed points 
 of absolute dryness and maximum moisture found '( What previous prep- 
 aration does the hair require? What is to be observed as respects its 
 indications ? 
 
276 
 
 DANIELS HYGROMETER. 
 
 is immersed in the water we may determine the precise 
 degree at which this deposit takes place; and, knowing 
 the temperature of the external air for the time being, 
 we can tell the number of degrees through which it, must 
 be cooled before the dew point (or the point at which 
 moisture deposits) is reached. Now, when the air is 
 very moist it is necessary to cool it very little before this 
 effect ensues j but when it is dry the cooling must be 
 carried to a correspondingly lower degree. If the air 
 were perfectly saturated the slightest depression of tem- 
 perature would make the moisture precipitate. Know- 
 ing, therefore, the dew point, the barometric pressure, 
 and the existing temperature, if it is required to find the 
 actual quantity of moisture in the air it can be determined 
 by calculation. 
 
 Daniel's hygrometer is a very beautiful instrument 
 
 - 296. 
 
 for determining the dew 
 point. It consists of a 
 bent tube, a c b, Fig. 
 296, at the extremities 
 of which two bulbs, a b, 
 are blown ; b is made of 
 black glass and a is cov- 
 ered over with a piece 
 of muslin. The bulb b is 
 half full of ether, and the 
 instrument -maker con- 
 trives things so that the 
 rest of the tube is void 
 of air, and contains the 
 vapor of ether only. A 
 delicate thermometer, d, 
 has its bulb dipping into 
 the ether of b. There is 
 also another thermometer attached to the stem of the 
 instrument. Under these circumstances, if the muslin 
 cover of a is moistened with a little ether, that bulb 
 becomes at once cooled by the evaporation, the vapor 
 within it condenses and a fresh quantity distils over from 
 b to supply its place. But b cannot furnish the vapor 
 without its own temperature descending, for latent heat, 
 
 Describe the process for the dew point. What is Daniel's hygrometer ? 
 How is this instrument used ? 
 
THE PSYCHROMETER. 277 
 
 is required before the vapor can form. After a time, 
 therefore, through the cooling agency dew begins to 
 deposit on the black glass, and the point at which this 
 takes place is determined by the included thermometer. 
 
 The psyckrometer consists of two delicate mercurial 
 thermometers divided into fractions of degrees, and cor- 
 responding perfectly with one another. The bulb of one of 
 them, A, Fig. 297, is covered with muslin, that of the other, 
 B, is left naked. On the central pillar there is arranged 
 a reservoir, W, of distilled water, from which a thread 
 passes to the muslin of A, and keeps it constantly moist, 
 as the water evaporates from this bulb the mercury 
 begins to fall, and the drier the air the greater the de- 
 scent. As soon as the air round the bulb is 
 saturated with moisture the point at which 
 the mercury stands is the dew point. If 
 both thermometers, the damp and the dry, 
 coincide, the air contains moisture at its 20 , 
 maximum density, and the greater the dif- 
 ference between them the dryer the air. 
 
 For many purposes in chemistry and phy- 
 sical science it is necessary to remove all 
 moisture from atmospheric air and from 
 gases. This may be done by conducting 
 them through tubes containing bodies which 
 have a strong attraction for water. The bodies com- 
 monly selected for this purpose Fig. 298. 
 are chloride of calcium, hydrate of 
 potash, phosphoric acid, and frag- 
 ments of glass or quartz moistened 
 with oil of vitriol. The process is 
 as represented in Fig. 298, where 
 a is the flask from which the gas to 
 be dried is evolved, b a bent tube 
 which conducts it into a wider tube, c, containing the 
 absorbent material. It escapes from d in a dry state. 
 
 Describe the psychrometer. Why does one thermometer commonly 
 stand lower than the other ? What substances are used in chemistry as 
 drying agents ? How are they employed ? 
 
278 MAGNETISM. 
 
 MAGNETISM. 
 
 LECTURE LVI. 
 
 MAGNETISM. The Loadstone. Artificial Magnets. Po- 
 larity. Transmission of Effect. The Poles and Axis. 
 Magnetic Curves. Law of Attraction and Repulsion. 
 Transient Magnetism of Iron. Permanent Magnet- 
 ism of Steel. Induced Magnetism. Law of Diminu- 
 tion. Simultaneous Existence of Polarities. Processes 
 for Imparting Magnetism. 
 
 MANY centuries ago it was discovered that a certain 
 ore of iron, which now passes under the name of the mag- 
 net or loadstone, possesses the remarkable quality of at- 
 tracting pieces of iron. Subsequently it was found that 
 the same power could be communicated to bars of steel, 
 by methods to be described hereafter. 
 Fig. 299. Bars of steel so prepared pass under the name 
 of artificial magnets, to distinguish them from the 
 natural loadstone. When they are of small size 
 they are commonly called needles. A magnetic 
 bar bent into the shape represented in Fig. 299, 
 is called a horse-shoe Fig. soo. 
 
 magnet, and several 
 magnets applied to- g. 
 gether take the name 
 of compound magnets, or a 
 bundle of magnets.' 
 
 The Chinese discovered 
 that when a magnetic needle 
 is poised on a pivot, as in 
 
 What is the magnet or loadstone ? What are artificial magnets ? What 
 are needles ''. What is a horse shoe magnet ? 
 
MAGNETIC POLES. 
 
 279 
 
 Fig. 300, or floated on water by a piece of cork, that it 
 spontaneously takes a direction north and south ; and if 
 purposely disturbed from that position it returns to it 
 again after a few oscillations. 
 
 By a needle so suspended, the fundamental fact of the 
 attraction of the magnet for iron is easily verified. Pre- 
 sent a mass of iron to either extremity of the needle, and 
 the needle instantly moves to meet it. 
 
 If a bar magnet is brought near a nail or a mass of 
 iron-filings, the iron will be suspended. 
 
 That these effects take place through glass, paper, and 
 solid and liquid substances generally, may be thus estab- 
 lished. A quantity of iron-filings being laid on a pane of 
 glass, if a magnet be approached beneath, the filings fol- 
 low its motions. But if a plate of iron intervenes the 
 magnetic influence is almost wholly cut off. 
 
 The power of a magnetic bar is not equal in all parts. 
 There is a point .situated near each end, which seems 
 to be the focus of action. To these points the names of 
 poles are given, and the line joining them is called the 
 axis. 
 
 If a bar magnet be rolled in 
 iron-filings, they attach them- 
 selves for the most part at the 
 two poles, d dj Fig. 301 : or, 
 if such a bar be placed under 
 the surface of which 
 filings are dusted, 
 
 Fig. 301 
 
 sheet of pasteboard, on 
 
 Fig. 302. 
 
 are 
 
 they arrange them- 
 selves in curved lines, 
 as shown in Fig. 302, 
 which are symmetri- 
 cally situated as re- 
 spects the poles, P P. 
 When a magnet is 
 freely suspended it 
 arranges itself north 
 and south, as has been stated. To that pole which is to- 
 
 How may the polarity of a needle be shown ? How may its attraction 
 for iron be shown ? Prove that these effects take place through glass, but 
 not through iron. Is the magnetic power equally diffused through a bar? 
 What are the poles ? What is the axis ? How may it be proved that the 
 poles are the foci of action ? How may the magnetic curves be exhibited? 
 
280 ATTRACTION AND REPULSION. 
 
 ward the north the name of north pole is given, the other 
 is the south pole. 
 
 When, instead of presenting to a suspended needle a 
 piece of iron, we present to it another magnet, phenom- 
 ena of repulsion as well of attraction ensue if the north 
 pole of one be presented to the north of the other, repul- 
 sion takes place, and the same occurs if two south poles 
 are presented. But if it be a north and a south pole then 
 attraction takes place. 
 
 These results may be grouped together under the sim- 
 ple law " Like poles repel and unlike ones attract." 
 
 There is, therefore, an antagonization of effect between 
 opposite magnetic poles. If a key be suspended to a 
 magnet by its north pole, on the approach of the south 
 pole of one of equal force the key drops off. 
 
 If we examine the force of a magnet, commencing at 
 either of its poles and going toward its center, the in- 
 tensity gradually declines. It ceases altogether about 
 midway between the poles. This point is termed the 
 point or line of magnetic indifference. 
 
 Magnetism may be excited in both iron and steel ; in 
 the former with greater rapidity, in the latter more slow- 
 ly. The magnetism which soft iron has received it in- 
 stantly loses on being removed from the source which has 
 given it magnetism ; but steel retains its virtue perma- 
 nently. Soft iron is, therefore, transiently hard steel 
 permanently magnetic. 
 
 When a mass of iron is in contact with the pole of a 
 magnet, it obtains the same kind of magnetism as the pole 
 with which it is in contact throughout its whole mass, and 
 can, in the same manner, communicate a similar quality 
 to a second mass brought in contact with it; and this to 
 a third, arid so on. Thus, if from the pole of a magnet a 
 key be suspended, this will suspend a second, and that a 
 third, &c., until the weight becomes too great for the mag- 
 net to hold. If, having two or three keys thus suspend- 
 ed, we take hold of the uppermost and gently slide away 
 the magnet, the moment it is removed the keys all fall 
 apart, showing the sudden loss of power in soft iron. 
 
 What is the general law of magnetic attractions and repulsions ? How 
 does the intensity vary in a magnet ? When is the point of magnetic in- 
 difference ? What is the difference between the magnetism of steel and 
 of iron ? Illustrate the communication of magnetism. 
 
MAGNETIC POLARITY. 281 
 
 But a mass of iron can receive magnetism at a distance 
 from the magnet itself. To this phenomenon the FJ^. 303. 
 name of induction is given, and the distance through 
 which this- effect can take place is called the mag- 
 netic atmosphere. The general effect of induction 
 may be exhibited by bringing a powerful magnet 
 near a large key, as in Fig. 303, when it will be 
 found that the large key will support smaller ones; 
 but as soon as it is removed from the influence of 
 the magnet these all drop off. 
 
 When magnetism is thus induced by the action of a 
 given pole, that end of the disturbed body which is near- 
 est to the pole has an opposite polarity ; but the farther 
 end has the same polarity as the disturbing pole. 
 
 The force of magnetic action varies with the distance. 
 It has been proved by Coulomb and others, that the in- 
 tensity of magnetic action is inversely proportional to the 
 square of the distance. At twice a given distance it is, 
 therefore, one fourth, at three times One ninth, &c. 
 
 Both magnetic polarities must always simultaneously 
 occur. We can never have north magnetism or south 
 magnetism alone. Thus, Fig. 304. 
 
 if we take a long mag- T& s 
 
 net, N S, Fig. 304, and f I 
 
 break it in two, we shall , , ^ g // 
 
 not insulate the north , k r j 
 
 polarity in one half and I 
 the south in the other, but each of the broken magnets 
 will be perfect, in itself, having two poles one fragment 
 being N' S'.arid the other N" S". 
 
 When the poles of a magnet are polished, and covered 
 with smooth plates of iron, the magnet is said to be armed. 
 The piece of soft iron which passes from pole to pole of 
 a horse-shoe magnet is called a keeper. The power of a 
 magnet is measured by the weight its poles are able to 
 carry. 
 
 There are many different ways in which magnetism 
 can be imparted to needles or steel bars, as, for example, 
 
 What takes place when a large key suspending several small ones is re- 
 moved from the magnetic atmosphere? What is induction? What is 
 the nature of the induced polarity? How does the force of magnetic 
 action vary ? Can one species of magnetism be separated from the other ? 
 What is meant by a magnet being armed ? What is a keeper ? 
 
282 COMMUNICATION OF MAGNETISM. 
 
 by contact, by induction, by certain movements. By the 
 aid of voltaic currents, hereafter to be described, the 
 most intense magnetic power can be communicated. 
 
 The process of magnetization by the single toucli is that 
 in which we place one pole of a magnet in the middle of 
 the steel bar, and, drawing it toward the end, then lifting 
 it up in the air return it to its former position, and repeat 
 the movement several times. The magnet is now to be 
 reversed, and in that position moved to the opposite end 
 of the bar, lifted up in the air, replaced, and the move- 
 ment many times repeated. The bar thus becomes a 
 magnet, each end having a pole opposite to that by which 
 it was touched. Or we may place two magnets with 
 their opposite poles in the middle of the bar, and then, 
 drawing them apart in opposite directions, the same 
 result arises. A still more powerful magnetism may be 
 given if the bar to be magnetized is laid on the poles of 
 two magnets, so that the contrary pole of the magnets 
 and bar coincide. 
 
 In the double touch two bar-magnets are so tied to- 
 gether that their opposite poles may be maintained a 
 short distance from one another. This combination is 
 then placed on the middle of the bar to be magnetized, 
 and drawn toward its end ; but as soon as it reaches that 
 without passing over it, it is returned to the other end 
 with a reverse motion, and then back again ; and after 
 this has been done several times the process is ended by 
 drawing the combination off sideways, when it is at the 
 middle of the bar. 
 
 Describe some of the methods by which magnetism may be imparted. 
 Describe the process by single touch. What is that by double touch? 
 
MARINER S COMPASS. 
 
 283 
 
 LECTURE LVII. 
 
 TERRESTRIAL MAGNETISM. Mariner's Compass. Mag- 
 netic Variation. Lines of Equal Declination. Dipping- 
 Ncedle. Lines of Equal Dip. Magnetic Terrestrial 
 Poles. The Earth's Inductive Action. Lines of Equal 
 Intensity. Magnetameters. Secular and Diurnal Va- 
 riation. Irregular Disturbances. Terrestrial Magnet- 
 ism due to the Heat of the Sun. 
 
 WHEN a magnetic needle is suspended on a pivot so 
 as to have freedom of motion horizontally, it sets itself 
 nearly in a direction north and south, and constitutes a 
 compass. 
 
 In the mariner's compass a light card is attached to 
 the needle; on it there is drawn a circle divided into thirty- 
 two parts. This accompanies the motion of the needle, 
 and as the instrument is constantly liable to be thrown 
 into a variety of positions by the motions of the ship, it is 
 supported in gynAals, as shown in Fig. 305. This con- 
 
 . 305. 
 
 trivance consists of two pair of pivots, E E, P P, set 
 upon rings at right angles to one another, and the bottom 
 
 What is a compass ? How is the mariner's compass arranged ? What 
 are gymbals? 
 
284 
 
 THE DIPPING-NEEDLE. 
 
 of the compass-box being heavy it is immaterial what 
 position is given to it ; it always sets itself with the card 
 in a horizontal plane. Occasionally the box is accom- 
 modated with sights, Gr H. 
 
 Accurate observations have shown that the magnetic 
 needle does not, however, point rigorously north and south, 
 except in a few restricted positions, on the earth's surface. 
 But it exhibits in most places a declination or variation 
 to the east or west of the true point. If the places in 
 which there is no declination be connected together, the 
 line running through them is called a line of no declina- 
 tion, and of these there are two, one the American and 
 the other the Asiatic. These have a general direction 
 from the north to the south. 
 
 By lines of equal declination we mean those lines 
 which pass through places where the amount of declina- 
 tion is equal. They are irregular in their form, but have 
 a relation to the magnetic poles. The position of these, 
 as well as of the former lines, is not stable : it varies in 
 the course of time. 
 
 When a needle is arranged on a horizontal axis, so as 
 
 Fig. 300. 
 
 Does the compass point accurately north and south ? What is a line of 
 no declination ? How many are there ? What is their direction ? What 
 are lines of equal declination ? Are these regular curves ? 
 
MAGNETISM OF THE EARTH. 285 
 
 to move in a vertical plane, it constitutes a dipping-needle, 
 of which a representation is given in Fig. 306. The 
 points of the needle, N S, traverse over a circle divided 
 into degrees, and the angle which such a needle makes 
 with a horizontal line is the angle of the dip. In the 
 northern hemisphere the north pole dips ; near the equa- 
 tor the needle has no dip ; and in the southern hemi- 
 sphere the south pole dips. 
 
 The dip of the needle was first discovered by Norman, 
 who noticed that, after a mariner's compass-needle was 
 magnetized it lost its horizontality, and required a little 
 wax or some small weight on the opposite side to restore 
 it to its true position. 
 
 The dip of the needle diifers in different places. Those 
 points of the earth where there is no dip being connected 
 together by a line, give what is termed the magnetic 
 equator. It is a very irregular curve which cuts the 
 geographical equator in two places, so that in the western 
 hemisphere it is south of the equator, and in the eastern 
 north. Lines which connect places where the dip is 
 equal are called lines of equal dip; they observe a. gen- 
 eral parallelism to the magnetic equator. 
 
 All the magnetic phenomena exhibited by the earth in 
 their general features answer to what ought to take place 
 were the earth itself a great magnetic mass, with its poles 
 near, but not coincident with the geographical poles. On 
 this principle the polarity and the dip of the needle are 
 both readily explained. Of course the north pole of the 
 earth possesses analogous properties to the south pole of 
 the suspended needle, and vice versa. Formerly it was 
 believed that there existed two terrestrial poles in each 
 hemisphere ; but there is reason now to suppose that 
 there is but one. That in the northern hemisphere was 
 reached by Sir James Ross in 1833. 
 
 This general similitude of the earth's action to that of 
 a magnet is still further jporne out by the inductive influ- 
 ence of the earth. This may be shown in a very striking 
 manner, by taking a bar of soft iron and bringing it near 
 
 What is a dipping-needle ? How does it act in the north and in the 
 south hemispheres? How was the dip first discovered? What is the 
 magnetic equator? What is its course ? What are lines of equal dip? 
 What do the phenomena of terrestrial magnetism answer to? How 
 many magnetic poles are there ? Has the magnetic pole ever been reached ? 
 
286 MAGNETOMETERS. 
 
 a suspended needle. So long as the bar is in a horizon- 
 tal position, and at right angles to the middle of the nee- 
 dle, the latter is unaffected ; but, on turning the bar, so 
 that its length may coincide with the line of dip, its lower 
 pole will repel the north pole of the needle, showing that 
 it has north polarity ; but it will attract the south pole. 
 And this condition remains so long as the bar remains in 
 its position ; but, on turning it over, and reversing its po- 
 sition, its magnetism is instantly reversed, showing that 
 the whole action is due to the power of the earth. 
 
 Like the declination and the dip, the absolute intensity 
 of the earth's magnetism varies very much in different 
 places ; at the magnetic equator being most feeble, and 
 gradually increasing as we go the poles. Lines connect- 
 ing places where the intensities are equal are lines of equal 
 intensity. This absolute intensity is estimated by the num- 
 ber of oscillations which a magnet makes in a given time, 
 being thus directly as the number of oscillations made in 
 one minute. The declination-needle gives us, by its os- 
 cillations, a measure of that portion of terrestrial magnet- 
 ism which acts horizontally, the dipping-needle that which 
 acts vertically ; but it may be shown that the effect of 
 either of these is proportional to the absolute intensity. 
 To measure these effects, instead of small and light nee- 
 dles being used, bars of several pounds weight are em- 
 ployed. They are called magnetometers. 
 
 The declination, the dip, and the intensity all undergo 
 variations at the same place ; some of which are regular 
 and others irregular some occurring through long pe- 
 riods of time, and others at short intervals. In the year 
 1657, the declination needle pointed due north in Lon- 
 don ; it then commenced moving westward, and contin- 
 ued to do so till the close of last century. Its variation 
 is now decreasing. The daily variation consists of an os- 
 cillation eastward or westward of the mean position, the 
 amount of which varies with the times of the day, and is 
 different in different places. Generally the greatest dec- 
 lination eastward is between six and nine in the morning, 
 
 How may the earth's inductive action be established by experiment ? Is 
 the absolute intensity variable ? How is it estimated ? What do the decli- 
 nation and dipping-needles respectively indicate ? What are magnetome- 
 ters? Are the declination, dip, and intensity constant in amount ? What 
 variations have been observed in the needle at London ? 
 
MAGNETIC DISTURBANCES. 287 
 
 and westward about one in the afternoon, returning to- 
 ward the east until eight P. M. It is never more than a few 
 minutes; and the needle is stationary at night. Changes 
 in the weather and the occurrence of storms and clouds 
 have also an influence on the needle. The dipping-nee- 
 dle exhibits similar phenomena; and, as respects the in- 
 tensity, it is greater in the evening than the morning, and 
 is less in summer than in winter. 
 
 Besides these, there are regular disturbances of the 
 earth's magnetism such, for instance, as those arising 
 from the aurora borealis, which will sometimes deflect 
 the needle several degrees. Over very extensive areas 
 simultaneous disturbances have been noticed, it having 
 been established that the minute and irregular variations 
 take effect at the Same instant in places at great distances 
 apart. 
 
 There can be no doubt that the magnetism of the earth 
 is very intimately connected with the calorific action of 
 the sun. Thus, the lines of equal dip closely correspond 
 to the lines of equal heat the northern magnetic pole 
 nearly coincides with the point of minimum heat on the 
 earth's surface. The diurnal variations, in some measure, 
 follow the temperature, as the sun shines on different parts 
 in succession ; and the same connection with inequality 
 of heating is traced in the annual variation. When we 
 come to describe thermo-electric currents currents ex- 
 cited by heat and trace the effect of these currents on 
 the suspended needle, we shall have a clearer idea of the 
 nature of these obscure phenomena. 
 
 What are the diurnal variations ? At what periods do they occur? What 
 influence does the aurora borealis exert ? What reasons have we for sup- 
 posing that the magnetism of the earth is connected with the calorific ac- 
 tion of the sun ? 
 
288 ELECTRICITY. 
 
 ELECTRICITY. 
 
 LECTURE LVIII. 
 
 ELECTRICITY. First Discoveries in Electricity. Leading 
 Phenomena. Conductors, Non-conductors, and Insula- 
 tion. Two Kinds of Electricity. Vitreous and Posi- 
 tive, Resinous and Negative. Law of Electrical Attrac- 
 tion and Repulsion. Plate Machine. Cylinder Ma- 
 chine. Miscellaneous Electrical Experiments. The 
 Two Theories of Electricity. 
 
 MORE than two thousand years ago it was discovered 
 that when amber is rubbed it acquires the property of 
 attracting light bodies. This incident has served to give 
 a name to the agent whose operations we have now to 
 explain, which has been called electricity, from TjkeiCTpov, 
 a Greek word, signifying amber. 
 
 A great number of other bodies possess the same qual- 
 ity ; among these may be mentioned glass, sealing-wax, 
 resin, silk. They, too, when rubbed, can attract light 
 substances, and, when the excitement is vigorous, emit 
 sparks like those which are seen when the back of a cat 
 is rubbed on a frosty night. It is not improbable that it 
 was from observing this singular phenomenon that the 
 Egyptians were induced to regard that animal as sacred. 
 
 If a piece of brown paper be thoroughly dried at the 
 fire until it begins to smoke, and then rubbed between 
 woollen surfaces, it will emit sparks on the approach of 
 the finger, attract pieces of light paper, and then repel 
 them. This latter phenomenon is not, however, peculiar 
 to it, but is noticed in the case of all highly-excited bodies. 
 
 When were electrical phenomena first observed? What circum- 
 stance has given to this agent a name? Mention some other electrics. 
 What experiments may be made with dry brown paper? 
 
CONDUCTORS AND NON-CONDUCTORS. 289 
 
 
 
 Electrified bodies, therefore, exhibit repulsions as well as 
 attractions. 
 
 Let there be taken a glass tube, a b, Fig. 307, an inch 
 in diameter and a foot or Fig.yn. 
 
 more long, closed at the end, a b 
 
 b, by means of a cork, into ~J_ ~~tsj QC 
 
 which there is inserted a wire 
 
 with a round ball, c. If the tube be excited by rubbing 
 with a piece of dry silk it may be shown that not only 
 does the space rubbed possess the powers of attraction 
 and repulsion, but also the cork and the ball. Nor does 
 it matter how long the wire may be, the electric power is 
 transmitted through the whole of the metal. A metal, 
 therefore, can conduct electricity. 
 
 But if, instead of a piece of metal, we terminate the 
 glass tube with a rod of glass or sealing-wax, or hang a 
 ball to it by a thread of silk, in all these cases the electric 
 power cannot pass. Such substances are, therefore, non- 
 conductors of electricity. 
 
 When electricity is communicated to a body which is 
 supported on any of these non-conducting substances, its 
 escape is cut off, and the body is said to be insulated. 
 
 From a silk thread which is fastened to a stand, c, Fig. 
 308, let there be suspended a feather, b; let Fig. MS. 
 this be electrified by a glass rod^a, highly ex- 
 cited. The feather is at first attracted and 
 then repelled. On the approach of the exci- 
 ted glass it instantly recedes, attempting, as 
 it were, to get out of its way. Now, instead 
 of the glass rod, a, let us present a stick of 
 excited sealing-wax, or a roll of sulphur the 
 feather is instantly attracted, and, therefore, this remark- 
 able experiment proves that the electric virtue which ema- 
 nates from excited bodies is not always the same, and that 
 a body which is repelled by excited glass is attracted by 
 excited wax. 
 
 Extensive inquiry has shown, that in reality there are 
 two species of electricity, to which names have therefore 
 
 What results may be shown by the instrument, Fig. 307 ? How may it 
 be shown that metals conduct electricity ? How may it be proved that 
 other bodies are non-conductors ? What is meant by insulation ? Prove 
 that there are two different sorts of electricity ? What names have been 
 given to them ? 
 
290 
 
 TWO KINDS OF ELECTRICITY. 
 
 been given. To one because it arises from the friction 
 of glass vitreous electricity ; and to the other, which 
 arises under similar circumstances from wax, resinous 
 electricity. 
 
 The relations of these electrical forces to one another, 
 as respects attraction and repulsion, constitute the funda- 
 mental law of this department of science. That general 
 law, briefly expressed, is " Like electricities repel and 
 unlike ones attract." That is to say, two bodies which 
 are both vitreously or both resinously electrified, will re- 
 pel each other; but if one is vitreous and the other res- 
 inous, attraction takes place. To the two different species 
 of electricity synonymous designations are sometimes ap- 
 plied. The vitreous is called positive, and the resinous 
 negative electricity. 
 
 For the sake of observing electrical phenomena more 
 Fig. 309. readily, instruments have been in- 
 
 vented, called electrical machines. 
 They are of two kinds : the plate 
 machine and the cylinder ; they 
 derive their names from the shape 
 of the glass employed to yield the 
 electricity. The plate machine, 
 Fig. 309, consists of a circular 
 plate of glass, a a, which can be 
 turned upon an axis, b, by means 
 of a winch, c; at d is a pair 
 of rubbers, which compress tho 
 glass between them, and a piece 
 of oiled silk extends over the glass plate, as shown at e ; 
 
 in the same manner, on 
 the opposite side of the 
 plate, there is another pair 
 of rubbers, d, and an oiled 
 silk, e; f is the prime con- 
 ductor, which gathers the 
 electricity as the plate re- 
 volves. It must be support- 
 ed on an insulated stem. 
 The cylinder machine is 
 
 What is the general law of electrical attraction and repulsion ? What 
 names are given to the two sorts of electricity? Describe the plate ma- 
 chine. Describe the cylinder machine. 
 
 c Fig. 310. 
 
ELECTRICAL MACHINES. 291 
 
 represented at Fig. 310. It consists of a glass cylinder, 
 a , so arranged that it can be turned on its axis by the 
 multiplying-wheel, b b. The rubber bears against the 
 glass on the opposite side to that seen in the figure, and 
 the oiled silk is shown at c; d is the prime conductor, 
 usually a cylinder with rounded ends, made of thin brass, 
 and e its insulating support. 
 
 Of these machines the plate is commonly the most pow- 
 erful- It is more liable to be broken than the cylinder, 
 from the disadvantageous way in which the power to 
 turn it round is applied. 
 
 To bring an electrical machine into activity, it must be 
 thoroughly dried ; but a plate machine should'never be set 
 before the fire to warm, or it will almost certainly crack. 
 The rubbers are to be spread over with a little Mosaic 
 gold, or amalgam of zinc, and the stem of the conductor 
 made dry. If the rubbers of the machine are not in con- 
 nection with the ground, there must be a chain hung from 
 them to reach the table. Then, when the instrument is 
 in activity, on presenting the finger to the prime conduct- 
 or a succession of sparks is emitted, attended with a crack- 
 ling sound. 
 
 A great many beautiful experiments may be made by 
 the aid of this machine. They are for the most part il- 
 lustrations of the luminous effects of the spark, attractions 
 and repulsions, and certain physiological results, as the 
 electrical shock. 
 
 If there be pasted on a slip of glass a continuous line 
 
 of tin foil, as shown in Fig. 311, Fg. sn. . 
 
 and then letters be cut out of it ~~ 
 with a sharp knife, on present- 
 ing the ball, G-, which commu- 
 nicates with the tin foil to the prime conductor, and touch- 
 ing the point, a, with the finger, the electric fluid will run 
 along the metallic line, leaping over each interspace, in 
 the form of a short but brilliant spark, and marking out 
 the letters in a beautiful manner. 
 
 A tube several feet long, with a ball at one end and a 
 stop- cock at the other, is to be exhausted of air. On pre- 
 senting the ball to the prime conductor, the electricity 
 
 Which of the two is more powerful ? How are they brought into ac- 
 tion ? How may words be written by the electric spark ? What phe 
 nomena are exhibited by an exhausted tube ? 
 
292 ELECTRICAL EXPERIMENTS. 
 
 passes down the whole length of the exhausted tube as a 
 pale milky flame, but giving now and then brilliant flashes, 
 especially when the tube is touched. The phenomenon 
 has some resemblance to that of the Northern lights. 
 Fig. 312. Between two metallic plates, a b, Fig. 312, of 
 which a is hung by a chain to the prime con- 
 ductor, and b supported on a conducting stand, 
 let some figures, made of paper, pith, or other 
 light body, be placed. The plates maybe three 
 or four inches apart. On throwing the machine 
 into activity the figures are alternately attracted 
 and repelled, and move about with a dancing 
 motion.. 
 
 From a brass rod, a c b, Fig. 313, which may be hung 
 by an arch, g, to the prime conductor, 
 three bells are suspended two from a 
 and b by chains, and the middle one, 
 c, by a silk thread between the bells 
 two little metallic clappers, d e, are hung 
 by silk, and from the inside of the mid- 
 dle bell a chain, f, hangs down upon the 
 table. On setting the electrical machine in activity, the 
 clappers commence moving and ring the bells. This in- 
 strument has been employed in connection with insulated 
 lightning-rods, to give warning of the approach of a thun- 
 der-cloud. 
 
 To account for the various phenomena of electricity, 
 two theories have been invented. They pass under the 
 names of Franklin's theory, or the theory of one fluid, 
 and Dufay's theory, or the theoiy of two fluids. 
 
 Franklin's theory is, that there exists throughout all 
 space an ethereal and elastic fluid, which is characterized 
 by being self-repulsive that is, each of its particles repels 
 the others ; but it is attractive of the particles of all other 
 matter. To this the name of electric fluid has been given. 
 Different bodies are disposed to assume particular or spe- 
 cific quantities of this fluid, and when they have the amount 
 that naturally belongs to them, they are said to be in a 
 natural state or condition of equilibrium. But if more than 
 
 Describe the experiment of the dancing figures. Describe the electrical 
 bells. For what purpose have they been used ? How many theories of 
 electricity are there ? What is Franklin's theory? In what consists the 
 natural, the positive, and negative state of bodies according to it ? 
 
ELECTRICAL THEORIES. 293 
 
 the natural quantity is communicated to them, they be- 
 come positively electrified; and if they have less than their 
 natural quantity, they are negatively electrified. 
 
 The theory of two fluids is, that there exists an ethere- 
 al medium, the immediate properties of which are not 
 known. It is composed of two species of electricity 
 the positive and the negative each of these being self- 
 repellent,*but attractive of the other kind. Bodies are in 
 a neutral or natural state or condition of equilibrium, 
 when they contain equal quantities of the two electrici- 
 ties ; and they are positively electrified when the positive 
 is in excess, and negative when the negative is in excess. 
 
 Of these two theories, it appears that the latter will ac- 
 count for the greater number of phenomena. 
 
 LECTURE LIX. 
 
 INDUCTION, DISTRIBUTION, AND MEASUREMENT OP ELEC- 
 TRICITY. Electrical Induction. The Ley den Jar. 
 Its Effects. Dr. Franklin's Discovery. The Light- 
 ning-Rod. Distribution of Electricity. Pointed Bodies. 
 Velocity of Electricity. Modes of Developing Elec- 
 tricity. Zamboni's Piles. Perpetual Motion. Elec- 
 troscopes. Electrometers. 
 
 BY electrical INDUCTION is meant that a body in an 
 electrified state is able to induce an analogous condition 
 in others in its neighborhood without being in immediate 
 contact with them. 
 
 This effect arises from the general law of attraction and 
 repulsion ; for the natural condition of bodies is such that 
 they contain equal quantities of positive and negative elec- 
 tricity ; and, when this is the case, they are said to be in 
 the neutral state, or in a condition of equilibrium. 
 
 When, therefore, an electrified body is brought into 
 the neighborhood of a neutral one, both being insulated, 
 disturbance immediately ensues. The electrified body 
 separates the two electricities of the neutral body from 
 
 What is Dufay's theory ? How does it account for the corresponding 
 states of bodies "? What is meant by electrical induction ? What is the 
 natural condition of bodies ? How does an electrified body disturb a neu- 
 tral one ? 
 
294 THE LBYDEN JAR. 
 
 each other, repelling that of the same kind, and attract- 
 ing that of the opposite. Thus, if a body electrified pos- 
 itively be brought near one that is neutral, the positive 
 electricity of this last is repelled to the remoter part, but 
 the negative is attracted to that part which is nearest the 
 disturbing body. 
 
 The Leyden jar, Fig. 314, is a glass jar, coated on the 
 Fig. 314. inside arid outside with tin foil to within an 
 inch OP two of the edge. Through the cork 
 which closes the mouth a brass wire reaches 
 down, so as to be in contact with the inside 
 coating, and terminates at its upper end in 
 a ball. On connecting the outside coating 
 with the ground, and presenting the ball 
 to the prime conductor, a large amount of 
 electricity is received by the machine ; and 
 -* if it be touched on the outside by one hand, 
 and communication be made with the ball by the other, 
 a very bright spark passes, and the electric shock is 
 felt. ' 
 
 The mechanical effects of lightning may be represented 
 in a small way by this instrument. On passing a strong 
 shock through a piece of wood it may be torn open, and 
 other resisting media may be burst to pieces. The shock 
 passed through a card perforates it. 
 
 Dr. Franklin discovered the identity of lightning and 
 electricity. He established this important fact by raising 
 a kite in the air during a thunder-storm. The string of 
 the kite, which was of hemp, terminated in a silken cord, 
 and at the point where the two were attached a key was 
 hung. The electricity, therefore, descended down the 
 hempen string, but was insulated by the silk, and on pre- 
 senting a finger to the key, sparks in rapid succession 
 were drawn. It is on this fact that the lightning-rod 
 for the protection of buildings depends. A metallic rod pro- 
 jects above the top of the building, and descends down 
 to a certain depth in the ground, offering, therefore, a free 
 passage for the electric fluid into the earth. 
 
 When electricity is communicated to a conducting 
 
 Describe the Leyden jar. How is it charged and discharged? What ef- 
 fects may be produced by it ? How and by whom was the identity of 
 lightning and electricity proved? What is the principle of the lightning- 
 
DISTRIBUTION OF ELECTRICITY. 295 
 
 body it resides merely upon the surface, and does not 
 penetrate to any depth within^ In the case of spherical 
 bodies, this superficial distribution is equal all over ; but 
 when the body to which the electricity is communicated 
 is longer in one direction than the other, the electricity 
 is chiefly found at its longer extremities, the quantity at 
 any point being proportional to its distance from the 
 center. 
 
 These principles may be very well illustrated by taking 
 a long strip of tin foil, so arranged as to be rolled and un- 
 rolled upon a glass axis, and connected with a pair of 
 cork balls, the divergence of which shows its electrical 
 condition. If, now, to this, when coiled up, a sufficient 
 amount of electricity is communicated to make the balls 
 diverge, on pulling out the tin foil, so as to have a larger 
 surface, they will collapse ; but on winding the foil up 
 again they will again diverge, showing that the distribu- 
 tion of electricity is wholly superficial, and that when a 
 given quantity is spread over a large surface it necessa- 
 rily becomes weaker in effect. 
 
 In the case of pointed bodies, the length of which is 
 very great compared with their other dimensions, the 
 chief accumulation of electricity takes place upon the 
 point. When a needle is fastened upon a prime con- 
 ductor, this accumulation becomes so great that the fluid 
 escapes into the air, and may be seen in the dark in the 
 form of a luminous brush. Or if, on the other hand, a 
 needle be presented to a prime conductor it withdraws 
 its electricity from it, and the point becomes gilded with a 
 little star. 
 
 The electric fluid moves with prodigious rapidity. It 
 has a Telocity greatly exceeding that of light. In a cop- 
 per wire its velocity is 288,000 miles in one second. 
 
 There are many different ways in which electricity 
 may be developed. In the processes we have hitherto 
 described it originates in friction. And, as one kind of 
 electricity can never make its appearance alone, but is 
 always accompanied with an equal quantity of the other, 
 
 Does electricity reside on the surface or in the interior of bodies ? How 
 is its distribution dependent on their figure? How may it be proved that 
 electricity is distributed superficially? What is the effect of pointed 
 bodies? How may a brush and a star of light be exhibited ? What is the 
 velocity of the electric fluid ? By what processes may electricity be devel- 
 oped ? Can one kind of electricity be obtained without the other ? 
 
296 
 
 we uniformly find that the rubber and the surface rubbed 
 are always in opposite states if the one is positive the 
 other is negative. It is on this principle that many ma- 
 chines are furnished with means of collecting the fluid 
 from the prime conductor or the rubber, and, therefore, 
 of obtaining the positive or negative electricity at pleas- 
 ure. 
 
 Electricity may also be developed by heat. The tour- 
 maline, a crystalized gem, when warmed, becomes posi- 
 tive at one end and negative at the other. Changes of 
 form and chemical changes of all kinds give rise to elec- 
 tric development. 
 
 Zamboni's electrical piles are made by pasting gold 
 leaf on one side of a sheet of paper and thin sheet zinc 
 on the other, and then punching out of it a number of 
 circular pieces half an inch in diameter. If several thou- 
 sands of these be packed together in a glass tube, so that 
 their similar metallic faces shall all look the same way, 
 Fig. 315. and be pressed tightly together at each 
 end by metallic plates, it will be found 
 that one extremity of the pile is positive 
 and the other negative ; and that the ef- 
 fect continues for a great length of time. 
 Fig. 315 represents a pair of these piles, 
 arranged so as to produce what was, at 
 one time, regarded as a perpetual motion. 
 Two piles, a Z>, are placed in such a po- 
 sition that their poles are reversed, and 
 between them a ring or light ball, c, vi- 
 brates like a pendulum on an axis, d. It 
 is alternately attracted to the one and then to the other, 
 and will continue its movements for years. A glass shade 
 is placed over it to protect it from external disturbance. 
 
 The purposes of philosophy require means for the 
 detection and measurement of electricity. The instru- 
 ments for these uses are called electroscopes and elec- 
 trometers ; they are of different kinds. 
 
 A pair of cork balls, a a, Fig. 316, suspended by cot- 
 ton threads so as to hang parallel to one another, and be 
 in metallic communication with the ball, b, furnish a sim- 
 
 What are the phenomena of the tourmaline ? "What are Zamboni's 
 electrical piles? How may these be made to furnish an apparent perpet- 
 ual motion? 
 
ELECTROMETERS. 
 
 297 
 
 pie instrument of the kind. If any electricity is commu- 
 nicated to b, the balls participate in it, and as 
 bodies electrified alike repel, these recede 
 from each other. The amount of their diverg- 
 ence gives a rough estimate of the relative 
 quantity of electricity. All delicate electrome- 
 ters should be protected from currents in the 
 air by means of a glass cylinder or shade, as c c. '' *' 
 
 The gold leaf electroscope differs from the foregoing 
 only in the circumstance that, instead of a pair of threads 
 and cork balls, it has a pair of gold leaves, the good con- 
 ducting power and extreme flexibility of which adapt 
 them well for this purpose. 
 
 The quadrant electrometer, Fig. 317, is formed 
 of an upright stem, a b, on which is fastened a 
 graduated semicircle of ivory, c, from the center 
 of which hangs a cork ball, d. As this is repelled 
 by the stem the graduation serves to show the 
 number of degrees. But no quantity of electricity 
 can ever drive it beyond 90 ; and, indeed, its 
 degrees are not proportional to the quantities of 
 electricity. 
 
 The best electrometer is Coulomb's torsion 
 
 Fig. 317. 
 
 IS 
 
 trometer, Fig. 318, of which a de- 
 scription has been given in Lecture 
 XXIII. 
 
 The best electroscope is Bohnen- 
 berger's. It consists of a small dry 
 pile, a b, Fig. 319, supported hori- 
 zontally beneath a glass shade, and 
 Fig. 319. from its extremities, 
 a b t curved wires 
 pass, which terminate 
 in parallel plates, p 
 m. One of these is, 
 therefore, the posi- 
 tive, and the other 
 the negative pole of 
 the pile. Between 
 them there hangs a 
 
 elec- 
 
 Fig. 318. 
 
 Describe the cork-ball electroscope. Describe the gold-leaf electroscope. 
 What is the quadrant electrometer? Which is the best electrometer? 
 Which is the best electroscope T Describe it. 
 
 N* 
 
298 THE VOLTAIC BATTERY. 
 
 gold leaf, d g, which is in metallic communication with die 
 plate, o n, by means of the rod, c. If the leaf hangs equally 
 between the two plates, it is equally attracted by each, and 
 remains motionless ; but on communicating the slightest 
 trace of electricity to the plate, o n, the gold leaf instantly 
 moves toward the plate which has the opposite polarity. 
 
 LECTURE LX 
 
 THE VOLTAIC BATTERY. The Voltaic Pile. The Trough. 
 Grove's Battery. Phenomena of the Battery. 
 Sparks. Incandescence. Decomposition of Water. 
 Electromotive Force. Resistance to Conduction. Power 
 of the Battery. Phenomena of a Simple Circle. 
 
 THE voltaic pile has a very close analogy in its con- 
 struction with the dry piles just described. It consists of 
 a series of zinc and copper plates, so arranged that the 
 Fig. wo. same order is continually preserved, and be- 
 tween them pieces of cloth, moistened with 
 acidulated water thus, copper, cloth, zinc ; 
 copper, cloth, zinc, &c. There should be 
 from thirty to fifty such pairs to form a pile 
 of sufficient power. 
 
 When the opposite poles or ends of this in- 
 strument are touched, a shock is at once felt. It is not 
 unlike the shock of a Leyden jar; but the pile differs from 
 the electrical machine in the circumstance that it can at 
 once recharge itself, and gives a shock of the same strength 
 as often as it is touched. 
 
 As the voltaic battery is now employed for numerous 
 purposes in science, many forms more convenient than 
 that described, have been introduced. In the voltaic 
 Fig. 321. trough the zinc and 
 
 copper plates being 
 soldered together, are 
 let into grooves in a 
 box, as shown in Fig. 
 321, the cells between 
 each pair of plates 
 
 Describe the voltaic pile. Under what circumstances does it give a 
 shock 1 What is the form given to this instrument^ the voltaic trough ? 
 
GROVE'S BATTERY. 299 
 
 serving to hold the mixture of water and sulphuric acid. 
 Such an instrument is easily brought into activity, and its 
 exciting fluid easily removed. 
 
 Of late other more powerful forms of voltaic battery 
 have been invented ; such, for instance, as Grove's and 
 Bunsen's. Grove's battery consists of a cylinder of zinc, 
 Z, Z, Fig. 322, the surface of which is amalgamated with 
 quicksilver. It is placed in a glass jar, G G. Fig . 303. 
 Within this there is a cylinder of porous earth- 
 enware, p p, in which stands a sheet of pla- z( 
 tinum, P P. In Bunsen's battery P is a cylin- 
 der of carbon, into which, at r, a polar wire 
 can be fastened. The glass cup, G G, is filled G 
 with dilute sulphuric acid (a mixture of one of 
 acid to six of water), the porous cylinder is fill- 
 ed with strong nitric acid, and the amalgamated zinc is 
 therefore in contact with dilute sulphuric acid, and the pla- 
 tinum or carbon with nitric acid. By means of the bind- 
 ing screws polar wires maybe fastened to the plates, and 
 a number of jars may be connected together so as to form 
 a compound battery. In this case, the wire coming from 
 the zinc of one cup is to be connected with the platinum 
 or carbon of the next, the same arrangement being con- 
 tinued throughout. 
 
 When several such cups are connected together, and 
 the polar wires of the terminal pairs brought in contact, 
 a bright spark, or rather flame, instantly passes, and when 
 these connecting wires are of copper the color of the light 
 is of a brilliant green. By fastening on one of the polar 
 wires conducting substances of different kinds, they burn 
 or deflagrate with different phenomena, each metal yield- 
 ing a colored light. If a fine iron or steel wire, in con- 
 tact with one of the poles, be lowered down on some 
 quicksilver into which the other is immersed, a brilliant 
 combustion ensues the iron, as it burns, throwing out in- 
 numerable sparks ; and on pointing the polar wires with 
 pieces of hard-burnt charcoal, on approaching them to 
 each other a spark passes, and the points may now be 
 drawn apart several inches, if the battery is powerful, the 
 
 Describe Grove's battery. In this battery how many metals and liquids 
 are employed ? What effect ensues when the connecting wires are brought 
 in contact ? What phenomena do the different metals exhibit during 
 combustion ? What ensues ^vhen charcoal-points are employed ? 
 
300 
 
 DECOMPOSITION OF WATER. 
 
 Fig. 323. 
 
 XTrt 
 
 flame still continuing to play between them. This flame, 
 which is arched upward, affords the most brilliant light 
 that can be obtained by any artificial process. 
 
 If, between the polar wires of a voltaic battery, a piece 
 of platinum a metal of extreme infusibility intervenes, 
 and the metal withstands fusion and is not too thick, it be- 
 comes incandescent, and continues so while the current 
 passes. 
 
 But by far the most valuable effects to which these in- 
 struments give rise are decompositions. If the poles of 
 a battery are terminated with pieces of platinum, and 
 these are dipped in some water, bubbles of gas rapidly 
 escape from each they arise from the decomposition of 
 the water. 
 
 The apparatus Fig. 323, enables us 
 to perform this experiment in a very 
 satisfactory manner. It consists of two 
 tubes, o h, which have lateral open- 
 ings,^? p, through which, by means of 
 tight corks, platinum wires, terminat- 
 ed by a little bunch of platinum, may 
 be passed. The tubes, o h, are sus- 
 pended vertically, in a small reser- 
 voir of water, g, by an upright, V. 
 They are also graduated into parts 
 of equal capacity. By means of the 
 binding screws at a and b the plati- 
 num wires may be connected with the poles of an active 
 battery. 
 
 If, now, the two tubes are filled with water and im- 
 mersed in the trough, and the communications with the 
 battery established, gas rapidly rises in each, and collects 
 in its upper part. In that tube which is in connection 
 with the positive pole of the battery oxygen accumulates, 
 in the other hydrogen. And it is to be observed that the 
 quantity of the latter is equal to twice the quantity of the 
 former gas. Water contains by volume twice as much 
 hydrogen as it does oxygen. 
 
 In any voltaic combination, the exciting cause of the 
 electricity, whatever it may be, goes under the name of 
 
 Can platinum be made continuously incandescent ? Describe the pro- 
 cess for the decomposition of water. What are the relative quantities of 
 oxygen and hydrogen gases produced in this experiment ? 
 
SIMPLE, CIRCLE. 301 
 
 the electromotive force, and the resistances, which ob- 
 struct the motion of the electricity, are termed resist- 
 ances to conduction. 
 
 The electromotive force determines the amount of elec- 
 tricity which is set in motion ; and in a voltaic battery 
 tne resistances which arise are chiefly due to the imper- 
 fect conducting power of the liquid and metalline parts. 
 
 The resistance of the metalline parts is directly as their 
 lengths and inversely as their sections. A wire two feet 
 long resists twice as^much as a wire one foot, if their sec- 
 tions are equal ; and of two wires that are of an equal 
 length that which has a double thickness or section will 
 conduct twice as well. 
 
 The resistance of the liquid parts depends on the dis- 
 tance of the plates from one another it is inversely as 
 their sections of those parts. 
 
 The total force of any voltaic battery may be ascertain- 
 ed by dividing the sum of all the electromotive forces by 
 the sum of all the resistances 
 
 The origin of the electrical action of voltaic combina- 
 tions is, in all probability, due to chemical changes 
 going on in them. The study of a simple voltaic cir- 
 cle throws much light on these facts. If we Fig. 324. 
 take a plate of amalgamated zinc, z, an inch 
 wide and six long, and a copper plate, c, of 
 equal size, and dip them in some acidulated 
 water contained in a glass jar,^ they form a 
 simple voltaic circle. It is to be understood 
 that common sheet zinc is easily covered over 
 with quicksilver, or amalgamated, by washing it 
 with sulphuric acid and water in a dish in which some 
 quicksilver is placed. 
 
 Now, so long as the two plates remain side by side 
 without touching, no action whatever takes place ; but if 
 we establish a metallic communication between them by 
 means of the wire d, innumerable bubbles of gas escape 
 from the copper, c, and the zinc in the mean time slowly 
 corrodes away. On lifting up d the action instantly ceases, 
 
 What is meant by the term electromotive force ? What by resistances 
 to conduction ? From what do the resistances chiefly arise? What is 
 the law for the resistance of the metallic parts ? What lor the liquid ? 
 How is the total force of the voltaic battery determined ? Describe the 
 apparatus, Fig. 324. 
 
302 ELECTROTYPE. 
 
 on bringing it into contact again the action is re-establish- 
 lished. And if the apparatus is in a dark place whenev- 
 er d is lifted from either plate, z or c, a small but brilliant 
 electric spark is seen, showing therefore that electricity is 
 the agent at work. 
 
 If the gas which rises from the copper plate be exam- 
 ined, it turns out to be hydrogen, and the corrosion of the 
 zinc is due to the combination of that metal with oxygen. 
 Water, therefore, must have been decomposed to furnish 
 these elements. The electric action of the common voltaic 
 circle arises from the decomposition of water. 
 
 If the wire d be a slender piece of platinum it contin- 
 ues in an ignited condition as long as the apparatus is in 
 activity. The electricity must, therefore, flow in a contin- 
 uous current ; and, as the most powerful voltaic batteries 
 are nothing but combinations of these simple ones, the 
 same reasoning applies to both, and we attribute their ac- 
 tion to the same cause chemical decompositions going 
 on in them, and giving rise to an evolution of electri- 
 city which flows in a continuous current from end to end 
 of the instrument and back through its polar wires. 
 
 A very beautiful process for working in metals, called 
 the electrotype, and founded upon the principles explain- 
 ed in this lecture, has been lately introduced into the arts. 
 When water is submitted to the influence of a voltaic 
 current we have seen that it is resolved into its constitu- 
 ent elements, oxygen and hydrogen, a total separation 
 ensuing, and each of these going to its own polar wire. 
 In the same manner, when a metalline salt transmits the 
 voltaic current, decomposition ensues, the acid part of the 
 salt being evolved at the positive and the metalline part 
 at the negative pole. When the salt has been properly 
 selected the metal is deposited as a coherent mass, and 
 faithfully copies the form of any surface in which the 
 negative pole is made to terminate. Thus, to the polar 
 wire Z, Fig. 325, of a simple voltaic battery let there 
 be attached a coin or other object, N, one surface of 
 which has been varnished or covered with some non- 
 
 What ensues when a metallic communication is made between the 
 metals ? How can it be proved that electricity is concerned in these re- 
 sults ? Why do we know that water must have been decomposed ? Why 
 do we know that there is a continuous current of electricity passing ? On 
 what principles is the electrotype process founded ? 
 
ELECTROTYPE. 
 
 303 
 
 conducting material ; to the other wire, S, let there be 
 affixed a mass of copper, C, 
 and let the trough, N C, in 
 which these are placed be filled 
 with a solution of sulphate of 
 copper. Now, when the bat- 
 tery is charged, the sulphate of 
 copper in the trough undergoes 
 decomposition, metallic copper 
 being deposited on the face of 
 the coin, N ; and as this with- 
 drawal of the metal from the so- 
 lution goes on, the mass, C, undergoes corrosion, and, dis- 
 solving in the liquid, replaces that which is continually 
 accumulating on the face of the coin. When the experi- 
 menter judges that the deposit on N is sufficiently thick, he 
 removes it from the trough, and with the point of a knife 
 splits it from the surface of the coin. The cast thus ob- 
 tained is admirably exact. 
 
 In the same manner that copper may thus be obtained 
 from the sulphate, so other metals may be used. Casts in. 
 gold and silver, and even alloys, such as brass, may be 
 obtained. There is no difficulty in gilding, silvering, or 
 platinizing surfaces, and from a single cast, by using it 
 in turn as a mould, innumerable copies may be taken. 
 
 Describe one of the methods for taking casts. Can other metals be- 
 sides copper be used ? Is this process adapted for gilding and silvering ? 
 
304 
 
 ELECTRO-MAGNETISM. 
 
 Fig. 326. 
 A 
 
 LECTURE LXI. 
 
 ELECTRO-MAGNETISM. Action of a Conducting Wire on 
 tL" Needle. Transverse Position assumed. Effects of 
 a Uent Wire. The Multiplier. Astatic Galvanometer. 
 Electro- Magnet. Rotatory Movements. Attraction and 
 Repulsion of Currents. Electro-Dynamic Helix. Elec- 
 tro-Magnetic Theory. 
 
 WHEN a magnetic needle, having freedom of motion 
 upon its center, is brought near a wire through which 
 an electric current is passing, the needle is deflected and 
 tends to move into such a position as to set itself at right 
 angles to the wire. 
 
 Thus, let there be an electric cur- 
 rent moving in the wire A B, Fig. 
 326 : in the direction of the arrow, 
 and directly over the wire and par- 
 allel to it, let there be placed a sus- 
 pended needle ; as soon as the cur- 
 rent passes in the wire, the needle 
 is deflected from its north and south 
 position, and turns round transverse- 
 ly, and if the current is strong enough 
 the needle comes at right angles to 
 the wire. 
 
 Now, every thing remaining as 
 before, let the current pass in the 
 opposite direction, the deflection 
 takes place as before, only now it is also in the opposite 
 direction. 
 
 If the needle be placed by the side of the wire the 
 same effect is observed. On one side it dips down arid 
 on the other it rises up. 
 
 What effect ensues when a magnetic needle is brought near a conduct 
 ing wire? How may it be proved that the direction of the motion de 
 pends on the direction of the current ? What takes place when the nee 
 die is at the side of the wire ? 
 
GALVANIC MULTIPLIERS. 
 
 305 
 
 In whatever position the needle is placed as respects 
 the conducting wire it tends to set itself at right angles 
 thereto. This discovery was made by Oersted in 1819. 
 
 From the foregoing experiments it will appear that if 
 a wire be bent into the Fig. 327. 
 
 form of a rectangle, as 
 represented in Fig. 327, 
 and an electric current 
 be made to flow round 
 it in the direction of the 
 arrows, all the parts of 
 the current tend to move 
 a needle in the interior 
 of such a rectangle in the same direction, and, therefore, 
 it will be much more energetically disturbed than by a 
 single straight wire. 
 
 If the wire, instead of making one convolution or turn, 
 
 Fig. 328. 
 
 A fine 
 
 Fig. 329. 
 
 is bent many times on itself, 
 so that the same current 
 may act again and again up- 
 on the needle,^ the effect of 
 a very feeble force may be 
 rendered perceptible. On 
 this principle the galvanometer is constructed, 
 copper wire, wrapped with silk, is 
 bent on itself many times, forming 
 a rectangle, d d, Fig. 328 ; the two 
 projecting ends, a a, dip into mer- 
 cury-cups, by which they may be 
 connected with the apparatus, the 
 electric current of which is to be 
 measured. In the interior of the 
 rectangle, supported on a pivot, is 
 a magnetic needle, n s, the deflec- 
 tions of which measure the current. 
 A still more delicate instrument 
 is made by placing two needles, with 
 their poles reversed, on the same 
 axis, N S, s n, suspending them by 
 a fine thread in such a way that one 
 
 By whom were these facts discovered ? What effect is there on a nee- 
 dle in the interior of a rectangle ? What is the effect when the wire 
 makes many convolutions? Describe the deflecting galvanometer. 
 
306 
 
 ELECTRO-MAGNETS. 
 
 of the needles is in the inside of the rectangle and the 
 other above. If the needles are of equal power the com- 
 bination is astatic that is, not under the magnetic influ- 
 ence of the earth ; but both of them are moved in the 
 same direction by the passage of the current. Such an 
 instrument is called an astatic galvanometer. 
 
 When an electric current, moving in a wire, is made 
 to pass round a piece of soft iron, so long as the current 
 continues the iron is magnetic ; but the moment the cur- 
 rent ceases the iron loses its magnetism. If, therefore, a 
 bar of soft iron be bent into the form N S, Fig. 330, and 
 
 Fig. 330. 
 
 b 
 
 there be wound round it a copper wire in a continuously 
 spiral course, the strands of the wire being kept from 
 touching one another, and also from contact with the iron, 
 by being covered with silk, whenever a current is passed 
 through the wires by the aid of the binding-screws, p m, 
 the iron becomes intensely magnetic. The amount of its 
 magnetism may be measured by attaching the keeper, A, 
 to the arm of a lever, a b, which works on a fulcrum, c ; 
 Ti is a hook by which weights may be suspended. In this 
 way magnets have been made which would support more 
 than a ton. 
 
 Mr. Faraday discovered that rotatory movements could 
 be produced by magnets round conducting wires ; and, 
 conversely, that conducting wires would rotate round 
 magnets. Both these facts may be proved at once by the 
 instrument Fig. 331. On the top of a pillar, gc, a strong 
 copper wire, bent as in the figure, at d f, is fastened. 
 
 Describe the astatic galvanometer. How may transient magnetism be 
 communicated to an iron bar ? Describe the instrument, Fig. 330. 
 
ELECTRO-MAGNETIC ROTATIONS. 307 
 
 To the crook aty* a fine platina wire, h, hangs by a loop, 
 on which it has perfect free- 
 dom of motion. Its lower end, 
 
 jy, on which is a small glass (Uf 
 
 bead, dips under some mer- 
 cury in a reservoir, b, in the 
 center of which a magnetiz- 
 ed sewing-needle, n, is fasten- 
 ed by means of a slip of cop- q 
 per, which communicates with 
 the binding-screw, z. On the arm, d, there is soldered 
 inflexibly another platinum wire, e, which dips into a 
 mercury reservoir, a, which is in metallic connection 
 with the binding-screw c by means of a slip of copper. 
 From the center and bottom of this reservoir a magnet- 
 ized sewing-needle is fixed by means of thin platinum 
 wire, so as to have freedom of motion round e. Under 
 these circumstances, if an electric current is passed from 
 c along d, in the direction of the arrow, to z, the magnet, 
 7tt, rotates round the fixed wire in one direction, and the 
 wire, k, round the fixed magnet n in the other. On re- 
 versing the course of the current these motions are re- 
 versed. 
 
 On similar principles all kinds of rotatory, reciproca- 
 tory, and other movements may be accomplished, magnets 
 made to revolve on their own axes, and entire galvanic 
 batteries round the poles of magnets. 
 
 In frictional electricity we have seen that the funda- 
 mental law of action is, that like electricities repel and 
 unlike ones attract. In the same way attractive and 
 repulsive motions have been discovered in the case of 
 currents. If electric currents flow in two wires which 
 are parallel to each other, and have freedom of motion, 
 the wires are immediately disturbed. If the currents 
 run in the same direction the wires move toward each 
 other, if in the opposite the wires move apart. Or, briefly, 
 " like currents attract, and unlike ones repel'' 
 
 If a wire be coiled into a spiral form, and its ends car- 
 ried back through its axis, as shown in Fig. 332, it forms 
 
 How may movements of rotation of wires and magnets round one 
 another be shown? Describe the instrument, Fig. 331. What ensues on 
 reversing the current 1 What is the action of currents on each other ? 
 What is the general law of this action ? 
 
308 THEORY OF MAGNETISM. 
 
 Fig. 332. an electro-dynamic helix. If it be sus- 
 
 pended with freedom of motion in a 
 horizontal plane, it points as a magnetic 
 needle would ii&, north and south ; or if 
 suspended, so as to move in a vertical 
 plane, it dips like a dipping-needle. 
 
 All the properties of a needle may be 
 simulated by such a helix; and if two he- 
 lices, carrying currents, are presented to 
 
 each other, they attract and repel, under 
 the same laws that two magnetic bars 
 
 would do. 
 
 If, therefore, we imagine an electric current to circu- 
 late round a magnet transversely to its axis, such a sup- 
 position will account for all its singular properties. 
 
 Anticipating what will have to be said presently as re- 
 spects thermo-electricity, it may be observed, that if we 
 take a metal ring, and warm it in one point only, by a 
 spirit-lamp, no effect ensues ; but if the lamp is moved 
 an electric current runs round the wire in the course the 
 lamp has taken. 
 
 As with this metal, wire, and lamp, so with the earth. 
 The sun, by his apparent motion, warms the parts of the 
 earth in succession, and electric currents are generated, 
 which follow his course. We must now call to mind all 
 that has been said respecting the influence of the sun's 
 heat on the magnet, in Lecture LVII. This elucidates 
 the cause of the needle pointing north and south. It 
 comes into that position because it is the position in which 
 the electric currents in it are parallel to those in the earth. 
 This is the position, as has just been explained, that cur- 
 rents will always assume. We see why, at the polar re- 
 gions, it dips vertically down. It is again that its currents 
 may be parallel with those of the earth ; for in those re- 
 gions the sun performs his daily motion in circles parallel 
 to the horizon. We see, also, that it is for the same cause, 
 in intermediate latitudes, that the needle points north and 
 also dips. 
 
 What is an electro-dynamic helix ? When two such helices act on each 
 other what phenomena arise ? What ensues when a metal ring is warm- 
 ed at one point by a lamp, and what when the lamp is moved ? How do 
 these facts bear on the polarity and dip of the needle ? Why does a mag- v 
 netic needle point north and south ? Why does it dip T 
 
MAGNETO-ELECTRICITY. 309 
 
 This prolific theory likewise includes all the phenom- 
 ena of Oersted, such as the transverse position a needle 
 takes when under the influence of a conducting-wire ; for 
 this is again the position in which the currents of the 
 needle are parallel to that in the wire. 
 
 LECTURE LXII. 
 
 MAGNETO-ELECTRICITY. THERMO-ELECTRICITY, Pro- 
 duction of Electric Currents by Magnets. Momentary 
 Nature of these Currents. They give rise to Sparks, 
 Decompositions, fyc. Magneto- Electric Machines. In- 
 duction of Currents by Currents. Electro-Magnetic Tel- 
 egraph. Production of Cold and Heat by Electric Cur- 
 rents. Thermo-electricity. Melloni's Multiplier. 
 
 IF an electric current passing round the exterior of a 
 bar ofjfsoft iron can convert it into a magnet, we should 
 expect that the converse would hold good, and a magnet 
 ought to be able to generate an electric current in a con- 
 ducting-wire. 
 
 Let there be a helix of F ig. 333. 
 
 copper wire, a, Fig. 333, 
 the successive strands of 
 which are kept from 
 touching, and let its ends 
 at b be brought in con- 
 tact. If a bar magnet, 
 N S, is introduced in the 
 axis, so long as it is in 
 
 actual movement an electric current will run through the 
 wire, but as soon as the bar comes to rest the current 
 ceases. On withdrawing the bar the current again flows, 
 but now it flows in the opposite direction. 
 If, therefore, we alternately introduce and remove with 
 rapidity a steel magnet, opposite currents will inces- 
 santly run round the helix. If we open the wire at the 
 point b, every time the current passes a bright spark is 
 
 How does this theory include Oersted's phenomena ? Can a magnet 
 develop electric currents in a wire ? Under what circumstances does this 
 take place ? How long does the current continue ? Describe the instru- 
 ment, Fig. 333. 
 
310 MAGNETO-ELECTRIC MACHINE. 
 
 seen ; or if the two separated ends dip into water it un- 
 dergoes decomposition. 
 
 Fig. 334. The same results would, of course, 
 
 occur, if, instead of introducing and 
 removing a permanent steel magnet, 
 we continually changed the polarity 
 of a stationary soft iron bar. Thus 
 if a b, Fig. 334, be a rod of soft iron, 
 surrounded by a helix, and there be 
 taken a semicircular steel magnet, 
 N c S, which can be made to revolve 
 on a pivot at c things being so ar- 
 ranged that its poles, N and S, in 
 their revolutions, just pass by the terminations of the bar, 
 a b the polarity of this bar will be reversed every half 
 revolution the magnet makes, and this reversal of polari- 
 ty will generate electric currents in the wire. To instru- 
 ments constructed on these principles the name of mag- 
 neto-electric machines is given. 
 
 The peculiarity of these currents is their momentary 
 duration. Hence they have been called momentary cur- 
 rents, and from the name of their discoverer, Faradian 
 currents. 
 
 There are a great many different forms of magneto- 
 electric machines. In some, permanent steel magnets are 
 employed; in others, temporary soft iron ones, brought 
 into activity by a voltaic battery. 
 
 Fig. 335 represents Saxton's magneto-electric machine. 
 It consists of a horse-shoe magnet, A B, laid horizontally. 
 The keeper, C D, is wound round with many coils of 
 wire, covered with silk. It rotates on an axis, E F, on 
 which it is fixed, by means of a pulley and multiplying- 
 wheel, E G. The terminations of the wire, li i, dip into 
 mercury cups at K. When the wheel is set in motion 
 the keeper rotates, its polarity being reversed every half 
 turn it makes before the magnet, and momentary currents 
 run through its wires. 
 
 If it is desirable to give the current of a magneto-elec- 
 tric machine great intensity, so as" to furnish powerful 
 shocks, or effect decompositions, the wire which is wound 
 
 What are magneto-electric machines ? What names have their cur- 
 rents received ? Describe Saxton's magneto-electric machine. What is 
 the effect of using a long thin and short thick wire ? 
 
INDUCTION OF CURRENTS BY CURRENTS. 
 
 311 
 
 round the keeper should be thin and long ; hut for pro- 
 ducing incandescence in metals, or for sparks or magnet- 
 ic operations, the wire should be short and thick. 
 
 Fig. 335. 
 
 hi? 
 
 Admitting the theory that all magnetic action arises 
 from the passage of electrical currents, it follows, from the 
 facts just detailed, that an electrical current must have 
 the power of inducing others in conducting bodies in its 
 neighborhood. Experiment proves that this conclusion 
 is correct, and currents so arising are called induced or 
 secondary currents. 
 
 Thus, when two wires are extended parallel to one an- 
 other, and through one of them an electric current is 
 passed, a secondary current is instantly induced in the 
 other; but its duration is only momentary. It flows in 
 the opposite direction to the primary one. On stopping 
 the primary current, induction again takes place in the 
 secondary wire ; but the current now arising has the same 
 direction as the primary one. The passage of an electri- 
 cal current, therefore, develops other currents in its 
 neighborhood, which flow in the opposite direction as the 
 
 How may it be proved that electric currents induce others in their neigh- 
 borhood ? What direction does the induced current take at first, and 
 what at last? 
 
312 
 
 MAGNETIC TELEGRAPH. 
 
 primary one first acts, but in the same direction as it 
 ceases. 
 
 Morse's electro-magnetic telegraph is essentially a horse- 
 shoe of soft iron, made temporarily magnetic by the pass- 
 age of a voltaic current. In Fig. 336, m m represent 
 
 Fig. 336. 
 
 the poles of the magnet, wound round with wire ; at a is 
 a keeper, which is fastened to a lever, a I, which works 
 on a fulcrum, at d; the other end of the lever bears a 
 steel point, ,?, which serves as a pen. At c is a clock ar- 
 rangement for the purpose of drawing a narrow strip of 
 paper, p p, in the direction of the arrows. W W are the 
 wires which communicate with the distant station. As 
 soon as a voltaic current is made to pass through these 
 wires, the soft iron becomes magnetic, and draws the 
 keeper, a, to its poles ; and the other end of the lever, I, 
 rising up, the point s is pressed against the moving paper 
 and makes a mark. When the lever first moves it sets 
 the clock machinery in motion, and the bell, Z, rings to 
 give notice to the observer. When the distant operator 
 stops the current, the magnetism of m m ceases, and the 
 keeper, a, rising, * is depressed from the paper. By let- 
 ting the current flow round the magnet for a short or a 
 longer time a dot or a line is made upon the paper and 
 
 Describe Morse's telegraph. How are the dots and lines which com* 
 pose the telegraphic alphabet made by the machine ? 
 
THERMO-ELECTRICITY". 313 
 
 the telegraphic alphabet consists of such a series of marks. 
 It is not necessary to use two wires to the instrument ; one 
 alone is commonly employed to carry the current to the 
 magnet ; it is brought back through the earth. 
 
 If a bar of bismuth, b, Fig. 337, and one of antimony, 
 , be soldered together at the point c, and by Fig. 337. 
 means of wires attached to the other ends, a 
 feeble voltaic current is passed from the an- 
 timony to the bismuth, heat will be genera- 
 ted at the junction, c; but if the current is 
 made to pass from the bismuth to the anti- 
 mony, cold is produced, so that if an excava- 
 tion be made at c, and a little water intro- 
 duced in it it may be frozen. 
 
 The converse of this also holds good. If we connect 
 the free terminations of a arid b, by means of a wire, and 
 raise the temperature of the junction c, an electric cur- 
 rent sets from the bismuth to the antimony; but if we 
 cool the junction the current sets in the opposite way. 
 To these currents the name of thermo-electric currents is 
 given. 
 
 Thermo-electric currents, from the circumstance that 
 they originate in good conductors, possess but very little 
 intensity. They are unable to pass through the thinnest 
 film of water, and, therefore, in operating with them it is 
 necessary that all the parts of the apparatus through which 
 they are to flow should be in perfect metallic contact. 
 The slightest film of oxide upon a wire is sufficient to 
 prevent their entrance into it. 
 
 As the effects of the voltaic circle can be increased by 
 increasing the number of pairs forming it, the same is also 
 true for thermo-electric currents. Thus, if we take a se- 
 ries of bars of bismuth and antimony, and solder their 
 alternate ends to one another, as shown pig. 338. 
 
 in Fig. 338, on warming one set of the 5 5 j & & a, 
 junctions, the current passes, and is \f\f\f\/\/J 
 greater in force according as the num- \/\/\/\/\/ 
 ber of alternations warmed is greater. a a a a, a 
 
 From their feeble intensity, these currents, when passed 
 through the wire of a multiplying galvanometer, Fig. 329, 
 
 What effects arise from passing feeble electric currents through a pair 
 of bars of bismuth and antimony ? What are thermo-electric currents ? 
 Why have they so little intensity ? How may that intensity be increased? 
 
 o 
 
314 THERMO-MULTIPLIER. 
 
 do not give rise to the same effects that are observed in 
 ordinary voltaic currents they lose as much of their force 
 by the resistance to conduction of the slender wire as they 
 gain by the effect which each coil impresses on the nee- 
 dle. A multiplier, suited for thermo-electric currents, 
 should be made of stout wire, and make but few turns 
 round the needle. 
 
 Melloni's thermo-electric pile is represented in Fig. 
 339. It consists of thirty or forty pairs of small bars of 
 
 Fig. 339. 
 
 1C A 
 
 bismuth and antimony, with their alternate ends soldered 
 together, forming a bundle, F F. The polar wires, C C, 
 projecting, are put in communication with the multiplier. 
 To each end of the pile brass caps, as seen in the figure, 
 fit. These serve to cut off the disturbing influence of 
 currents of air; and now if the hand or any other source 
 of heat be presented to one side of the pile, the needle 
 of the galvanometer immediately moves, and the amount 
 of its deflection increases with the temperature of the 
 radiant source. 
 
 It is not necessary to use many alternations, as in the 
 instrument of Melloni. Let a pair of heavy bars Fig. 340. 
 of bismuth and antimony, of the shape repre- 
 sented in Fig. 340, be soldered by the edges, 
 a b, to a circular plate of thin copper, and at 
 the others at a' b', to semicircular plates, e f, 
 having projecting pieces to communicate with 
 the wire of a galvanometer of few convolutions, 
 and the needle of which is nearly astatic. It will 
 be found that extremely minute changes of temperature 
 may be indicated the combination answering very well 
 instead of Melloni's more costly instrument. 
 
 Why does not the common galvanometer increase the effect of these 
 currents ? What ought to be the construction of a thermo-electric multi- 
 plier ? Describe Melloni's instrument. Is it necessary to use so many al- 
 ternations ? 
 
ASTRONOMY. 315 
 
 ASTRONOMY. 
 
 LECTURE LXIII. 
 
 ASTRONOMY. TJie Figure of the Earth. The Earth Ro- 
 tates on her Axis. Illustrations of Diurnal Rotation. 
 Annual Translation round the Sun. The Year. Mo- 
 tions of the Moon. Planets and Comets. Astronomical 
 Definitions. 
 
 IN the infancy of knowledge the first impression which 
 men entertained respecting the form of the earth we in- 
 habit, was that it is an indefinitely-extended plane, the 
 more central portions being the land, surrounded on all 
 sides by an unknown expanse of sea. Many natural phe- 
 nomena soon corrected these primitive ideas, and almost 
 as far back as historic records reach, philosophers had 
 come to the conclusion that our earth in reality is of a 
 round or globular form. 
 
 To this conclusion a consideration of the daily phenom- 
 ena of the starry firmament would naturally lead. Every 
 evening we see the stars rising in the east, and as the 
 night goes on, passing over the vault of the sky, and at 
 last setting in the west. During the day the same is also 
 observed as respects the sun. And as these are events 
 which are taking place day after day, in succession, and 
 no man can doubt that the objects which we see to-day 
 are those which we saw yesterday, it necessarily follows, 
 that after they have sunk under the western horizon, they 
 pursue their paths continuously, and that the earth neither 
 extends indefinitely in the horizontal direction, nor verti- 
 cally downward, but that she is of limited dimensions on 
 all sides. 
 
 What was probably the primitive idea respecting the figure of the earth ? 
 How may it be proved that the earth is limited on all sides T 
 
316 FIGURE OF THE EARTH. 
 
 Where the prospect is uninterrupted, as at sea, we are 
 further able not only to verify the foregoing conclusion, 
 but also to obtain a clearer notion of the figure of the 
 earth. Thus, as is seen in Fig. 341, let an observer be 
 
 Ffr.341. 
 
 watching a ship sailing toward him at sea. When she is 
 at a great distance, as at a, he first perceives her topmast, 
 but as she approaches from a toward b, more and more 
 of her masts come into view, and finally her hull appears. 
 When she arrives at b she is entirely visible. Now, as 
 this takes place in whatever direction she may approach, 
 whether from the north, south, east, or west, it obviously 
 points out the globular figure of the earth. In the distant 
 position, more or less of the ship is obscured by the in- 
 tervening convexity a phenomenon which never could 
 take place were the earth an extended plane. 
 
 This great truth, though admitted by philosophers in 
 ancient times, fell gradually into disrepute during the 
 middle ages ; it was re-established at the restoration of 
 learning only after a severe struggle. It is now the basis 
 of modern astronomy. 
 
 The spheroidal figure being therefore received as a 
 demonstrated fact, it is next to be observed that the earth 
 is not motionless in space, but in every twenty-four hours 
 turns round once upon her axis. That such a motion ac- 
 tually occurs is clear from the fact of the rising and set- 
 ting of the celestial bodies. 
 
 To an observer at the equator, the stars rise in the 
 eastern horizon and set in the western, continuing in view 
 for twelve hours, and being invisible for twelve. At the 
 
 What facts prove that she is of a round or globular form ? When was 
 the globular form of the earth denied, and when finally established ? Has 
 the earth a motion on her axis ? In what time is it performed ? What 
 are the phenomena of the rising and setting of the stars at the equator 
 and the poles? 
 
MOTION OF THE SUN AND MOON. 317 
 
 pole the rising or setting of a star is a phenomenon never 
 seen ; but these heavenly bodies seem to pursue paths 
 which are parallel to the horizon. In intermediate lati- 
 tudes a certain number of stars never rise or set, while 
 others exhibit that appearance. In any of these posi- 
 tions in our hemisphere the motion of the heavens seems 
 to be round one, or, rather, two points, situated in opposite 
 directions; to one of them the name of the north, and to 
 the other of the south pole is given. These are the 
 points to which the poles of the earth are directed. 
 
 When observations are made for some days or months 
 in succession, we find that there are motions among the 
 celestial bodies themselves which require to be account- 
 ed for. First, we observe that the sun does not remain 
 stationary in a fixed position among the stars, but that he 
 has an apparent motion ; and that after the lapse of a 
 little more than three hundred and sixty-five days he comes 
 round again to his original place. As with the diurnal 
 motion so with this annual. Consideration soon satisfies 
 us that it is not the sun which is in movement round the 
 earth, but the earth which is in movement round the sun. 
 To the period which she occupies in completing this rev- 
 olution the name of the year is given. Its true length is 
 three hundred and sixty-five days, five hours, forty-eight 
 minutes, forty-nine seconds. 
 
 The sun seems, in his daily motion, to accompany the 
 stars ; but if we mark the point upon the horizon at 
 which he rises or sets we find that it differs very much 
 for different times of the year. The same observation 
 may be made by observing the length of the shadow of 
 an upright pole or gnomon at midday. Such observa- 
 tions show that there is a difference in his meridian alti- 
 tude in winter and summer of forty-seven degrees. 
 
 The observation of a single night satisfies us that the 
 moon has a motion of her own round the earth. It is ac- 
 complished in twenty-seven days, seven hours, and forty 
 three minutes, and is called her periodical revolution ; 
 but, during this time, the earth has moved a certain dis- 
 tance in the same direction or, what is the same thing, 
 the sun has advanced in the ecliptic, and before the moon 
 overtakes him, twenty-nine days, twelve hours, and forty- 
 
 What other motion besides this may be discovered '( What is the year ? 
 What is the month ? 
 
318 DEFINITIONS. 
 
 four minutes elapse. This, therefore, is termed her synod- 
 ical revolution, or one month. 
 
 There are also certain stars, some of which are re- 
 markable for their brilliancy, which exhibit proper mo- 
 tions. To these the name of planets is given. And at 
 irregular intervals, and moving in different directions 
 through the sky, there appear from time to time comets. 
 Multitudes of these are telescopic, though some have ap- 
 peared of enormous magnitude. 
 
 There are several technical terms used in astronomy 
 which require explanation. 
 
 By the celestial sphere we mean a sky or imaginary 
 sphere, the center of which is occupied by the earth. On 
 it, for the purposes of astronomy, we imagine certain 
 points and fixed lines to exist. 
 
 Those circles whose planes pass through the center of 
 the sphere are called great circles. The circumference of 
 each is divided into three hundred and sixty parts, called 
 degrees, and marked (), each degree into sixty minutes, 
 marked ('), and each minute into sixty seconds, marked ("). 
 
 All great circles bisect each other. 
 
 Less circles are those whose planes do not pass through 
 the center of the sphere. 
 
 The axis of the earth is an imaginary line, drawn through 
 her center, on which she turns. The extremities of this 
 line are the poles. 
 
 A line on the earth's surface every where equidistant 
 from the poles is the equator. Circles drawn on the sur- 
 face parallel to the equator are called simply parallels, 
 arid sometimes parallels of latitude. 
 
 At sea, or where the prospect is unobstructed, the sky 
 seems to meet the earth in a continuous circle all round. 
 To this the name of sensible horizon is given. The ra- 
 tional horizon is parallel to the sensible, and in a plane 
 which passes through the center of the earth. 
 
 That point of the celestial sphere immediately overhead 
 is the zenith, the opposite point is the nadir. 
 
 A circle drawn through the two poles and passing 
 through the north and south points of the horizon is a 
 
 What are the planets ? What are comets ? What is the celestial 
 sphere ? What are great and less circles ? What is the axis of the earth ? 
 What are the poles, the equator, and parallels of latitude ? What is the 
 sensible and what the rational horizon ? What is the zenith and the nadir ? 
 
DEFINITIONS. 319 
 
 meridian. Hour circles are other great circles which pass 
 through the poles. 
 
 A circle drawn through the zenith and the east and 
 west points of the horizon is the prime vertical. Other 
 great circles passing through the zenith are vertical circles 
 or circles of azimuth. 
 
 The altitude of a body above the horizon is measured 
 in degrees upon a vertical circle. As the zenith is 90 
 from the horizon, the altitude deducted from 90 gives 
 the zenith distance. 
 
 The azimuth of a body is its distance from the north 
 or south estimated on the horizon, or by the arc of the 
 horizon intercepted between a vertical circle passing 
 through the body and the meridian. 
 
 The latitude of a place is the altitude at that place of 
 the pole above the horizon, or, what is the same thing, 
 the arc of the meridian between the zenith of the place 
 and the equator. At the earth's equator the pole is, 
 therefore, in the horizon ; at the pole it is in the zenith. 
 
 The longitude of a place on the earth is the arc of the 
 equator intercepted between the meridian of that place 
 and that of another place taken as a standard. The 
 observatory of Greenwich is the standard position very 
 commonly assumed. The longitude of a star is the arc 
 of the ecliptic intercepted between that star and the first 
 point of Aries. 
 
 The latitude of a star is its distance from the ecliptic, 
 measured on a great circle passing through the pole of 
 the ecliptic and the star. 
 
 The declination of a heavenly body is the arc of an 
 hour circle intercepted between it and the equator. 
 
 The ecliptic is the apparent path which the sun de- 
 scribes among the stars. It is a great circle which cuts 
 the equator in two points, called the equinoxial points, 
 because when the sun is in those points the nights and 
 days are equal ; one is the vernal, the other the autumnal 
 equinox. From this circumstance the equator itself is 
 sometimes called the equinoxial line. 
 
 What is a meridian ? What are hour circles ? What is the prime ver- 
 tical ? What are circles of azimuth ? What are altitude and zenith 
 distance ? What azimuth, the latitude of a place, and the declination of 
 a heavenly body ? What is the longitude of a place and that of a star? 
 What is the ecliptic ? 
 
320 DEFINITIONS. 
 
 Two points on the ecliptic, 90 distant from the equi- 
 noxial points, are the solstitial points. When the sun is 
 in one of these it is midsummer, in the other midwinter. 
 
 Motions in the direction from west to east are direct. 
 Retrograde motions are those from east to west. 
 
 The ecliptic is divided into twelve equal parts called 
 signs. They bear the following names and have the 
 following signs. 
 
 Aries C P Libra 
 
 Taurus b Scorpio HI 
 
 Gemini rj Sagittarius / 
 
 Cancer 25 Capricornus V? 
 
 Leo si Aquarius ~ 
 
 Virgo n Pisces X 
 
 Formerly these signs coincided with the constellations 
 of the same name, but owing to the precession of the 
 equinoxes, to be described hereafter, this has ceased to 
 be the case. 
 
 Two parallels to the equator one for each hemisphere 
 which touch the ecliptic, are called tropics. That for 
 the northern hemisphere is the tropic of Cancer ; that for 
 the south the tropic of Capricorn. Two other parallels 
 one for each hemisphere as far from the poles as the 
 tropics are from the equator, are the polar circles, the 
 northern one is the arctic, the southern one the antarctic. 
 
 The right ascension of a heavenly body is the distance 
 intercepted on the equator between an hour circle passing 
 through it and the vernal equinoxial point. 
 
 The astronomical day begins at noon, the civil day at 
 midnight. Both are divided into twenty-four hours, each 
 hour into sixty minutes, each minute into sixty seconds. 
 
 By the orbit of a body is meant the path it describes. 
 This, in most cases, is an ellipse. 
 
 The nodes are those points where the orbit of a planet 
 intersects the ecliptic. The ascending node is that from 
 which the planet rises toward the north, the descending 
 that from which it descends to the south; a line joining 
 the two is the line of the nodes. 
 
 What are the equinoxial and solstitial points? What are direct and 
 retrograde motions ? How is the ecliptic divided ? What are the tropics 
 and polar circles? What is right ascension? What is the difference 
 between the astronomical and civil day? What is an orbit? What are 
 the ascending and descending nodes ? 
 
MOTION OF THE SUN. 321 
 
 LECTURE LXIV. 
 
 TRANSLATION OP THE EARTH ROUND THE SUN, AND ITS 
 PHENOMENA. Apparent Motion and Diameter of the 
 Sun. Elliptical Motion of the Earth. Sidereal Year. 
 Determination of the Sun's Distance. Parallax. 
 Dimensions of the Sun. Center of Gravity of the Two 
 Bodies. Phenomena of the Seasons. 
 
 IN the last lecture it has been observed that the sun 
 has an apparent motion among the stars in a path called 
 the ecliptic. A line joining that body with the earth, and 
 following his motions, would always be found in the 
 same plane, or, at all events, not deviating from that 
 position by more than a single second. 
 
 Observation soon assures us that if we carefully ex- 
 amine the rate of the sun's motion in right ascension, it is 
 far from being the same each day. This want of uni- 
 formity might, to some extent, be accounted for by the 
 obliquity of the ecliptic; but even if we examine the 
 motion in the ecliptic itself, the same holds good. The 
 sun moves fastest at the end of the month of December, 
 and most slowly in the end of June. 
 
 Further, if we measure the apparent diameter of the sun 
 at different periods of the year, we find that it is not always 
 the same. At the time when the motion just spoken of 
 is greatest, that is during the month of December, the 
 diameter is also greatest ; and when in June the motion 
 is slowest, the diameter is smallest. These facts, there- 
 fore, suggest to us at once that the distance between the 
 earth and the sun is not constant ; but in December it is 
 least, and in June greatest, for the difference in size can 
 plainly be attributable to nothing else but difference of 
 distance. 
 
 The annual motion of the sun in the heavens, like his 
 diurnal motion, is, however, only a deception. It is not 
 
 Does the sun move with apparently equal velocity each day ? When is 
 his motion fastest and when slowest ? Is the sun always of the same 
 size ? When is he largest and when smallest ? How can we be certain 
 that the earth does not move in a circle round the sun ? 
 
322 
 
 MOTION OF THE EARTH. 
 
 the sun which moves round the earth, but the earth which 
 has a movement of translation round the sun, as well as 
 one upon her own axis. The path which she thus de- 
 scribes is not a circle, for in that case, being always at 
 the same distance, the sun would always be of the same 
 apparent magnitude, and his motion always uniform ; but 
 it is an ellipse, having the sun in one of its foci. Thus, 
 in Fig. 342, let F be the sun, A D B E the elliptic orbit of 
 the earth; it is obvious that as she moves in this path 
 
 Fig. 342, 
 
 she will be much nearer the focus F occupied by the sun 
 when she arrives at A than when she is at B. To the 
 former point, therefore, the name of perihelion, and to 
 the latter of aphelion is given ; the line A B joining them 
 is called the line of the apsides. 
 
 The periodic time occupied in one complete revolution 
 is called the sidereal year. Its length is 365 days, 6 hours, 
 9 minutes, ll seconds. 
 
 The law which regulates the velocity of motion of the 
 earth round the sun was discovered by Kepler. It has 
 already been explained, in speaking of central forces, in 
 Lecture XXI. It is " the radius vector (that is, the line 
 
 How do we know it is in an ellipse ? What are the perihelion and aphe- 
 lion points ? What is the line of the apsides ? What is the sidereal year? 
 What is Kepler's law respecting the radius vector ? 
 
PARALLAX. 
 
 323 
 
 Fig. 343. 
 
 joining the centers of the sun and earth) sweeps over 
 equal areas in equal times." 
 
 With these general ideas respecting the nature of the 
 orbit described by the earth, we proceed, in the next 
 place, to the determination of the actual size of that orbit: 
 in other words, to ascertain the distance between the earth 
 and the sun. 
 
 Let C, Fig. 343, be the center of the earth, B the po- 
 sition of an observer upon it, 
 and M the sun ; the observer, 
 B, will see the sun in the direc- 
 tion B M, and refer him in the 
 heavens to the position, . An 
 observer at C, the center of the 
 earth, would see him in the po- 
 sition C M, and refer him to 
 the point m. His apparent 
 place in die sky, will, therefore, 
 be different i the two instances. 
 This difference is called par- 
 allax ; and a little consideration shows that the amount 
 of parallax differs with the place of observation and posi- 
 tion of the body observed, being greatest under the cir- 
 cumstances just supposed, when the body is seen in the 
 horizon, and becoming when the body is in the zenith. 
 This diminution of the parallax is exemplified by sup- 
 posing the sun at M' ; the observer at B refers him to ri, 
 the observer at C to m f , but the angle B M' C is less than 
 the angle B M C. Again, if the sun be at M" that is, 
 in the zenith both observers, at B and C, refer him to 
 m", and the parallax is 0. The horizontal parallax being 
 measured by the angle, B M C is evidently the angle un- 
 der which the semidiameter of the earth appears, as seen 
 in this instance from the sun. 
 
 Although we cannot have access to the center of the 
 earth, there are many ways by which the parallax may be 
 ascertained, the result of the most exact of which has 
 fixed for the angle BMC the value of about eight sec- 
 onds and a half. Now it is a very simple trigonometrical 
 problem, knowing the value of this angle, and the length 
 
 What is parallax ? Why does the parallax become in the zenith ? 
 What is the horizontal parallax in reality ? What is the exact value of 
 the parallax ? 
 
324 DISTANCE AND SIZE OF THE SUN. 
 
 of the line B C in miles, to determine the line C M. When 
 the calculation is made, it gives about 95,000,000 miles. 
 This, therefore, is the mean distance of the earth from 
 the sun. 
 
 Knowing the apparent diameter of an object, and its 
 distance from us, we can easily determine its actual mag- 
 nitude. Seen from the earth, the sun's apparent diame- 
 ter subtends an angle of 32' 3". The true diameter, there- 
 fore, must be 882,000 miles. But the diameter of the 
 earth is short of 8000 miles. 
 
 Such, therefore, are the dimensions of the orbit of the 
 earth, and of the bodies concerned in it. We are now in. a 
 position to verify all that has been said in respect of the 
 relations of these bodies ; for, calling to mind what was 
 proved in Lecture XXI, respecting bodies situated as 
 these are, we see that in strictness the one cannot revolve 
 round the other, but both revolve round their common cen- 
 ter of gravity. Recollecting also that the center of grav- 
 ity of two bodies is at a distance inversely proportional 
 to their weights, and that the sun is 354,936 times heavier 
 than the earth, it follows that this point is only 2C7 miles 
 from his center. So, therefore, with scarce an error, the 
 center of the sun may be assumed as the center of the 
 earth's orbit, and with truth she may be spoken of as re- 
 volving around him. 
 
 Occupying such a central position, this enormous globe 
 is discovered to rotate on an axis inclined 82 40' to the 
 plane of the ecliptic, making one rotation in twenty-five 
 days and ten hours, in a direction from west to east. This 
 is proved by spots which appear from time to time on his 
 surface, and follow his movements. He is the great source 
 of light and heat to us, and determines the order of the 
 seasons. His weight is five hundred times greater than 
 that of all the planets arid satellites of the solar system. 
 though he is not of greater density than water. 
 
 In Fig. 344 we have a general representation of the 
 appearance of the solar spots. They consist of a dark 
 nucleus, surrounded by a penumbra, and are very varia- 
 
 What is the distance of the earth from the sun ? What is the actual 
 diameter of the sun ? At what distance is the center of gravity of the two 
 bodies from the sun's center ? How is it known that the sun rotates on 
 his axis ? What is the period of that rotation ? Describe the phenomena 
 of his spots. 
 
SPOTS ON THE SUN. 
 
 325 
 
 ble, both in number and size. Sometimes for a consider- 
 able period scarce any are seen, and tben they occur in 
 great numbers in irregular clusters. Their size varies 
 
 Fig. 344. 
 
 from Jj to T o- part of the sun's diameter. They are, 
 therefore, of enormous dimensions, often greatly exceed- 
 ing the surface of the earth. Their duration is also very 
 variable. Some have lasted for ten weeks, but more com- 
 monly they disappear in the course of a month or less. 
 They seem to be the seats of violent action, undergoing 
 great changes of form, not only in appearance, but also in 
 reality. On their first appearance on the sun's eastern 
 edge, they move slowly they move rapidly as they ap- 
 proach the middle of his disc, and move slowly again as 
 they pass to the western edge. This is, however, an op- 
 tical illusion, due to the globular figure of the sun. They 
 rarely appear at a greater distance than from 30 to 50 
 from the sun's equator, and cross his disc in thirteen days 
 and sixteen hours. Their apparent revolution is, there- 
 fore, twenty-seven days and eight hours ; and, making al- 
 lowance for the simultaneous movement of the earth, this 
 
326 
 
THE SEASONS. 
 
 gives for the sun's rotation on his axis twenty-five days 
 and ten hours. 
 
 To explain the occurrence of the seasons spring, sum- 
 mer, autumn, and winter it is to be understood that the 
 earth's axis of rotation, for the reasons explained in Lec- 
 ture XXI, always points to the same direction in space, 
 and, therefore, as the earth is translated round the sun, is 
 always parallel to itself. 
 
 Let, therefore, S, Fig. 345, be the sun, and E E E, &c. t 
 the positions the earth respectively occupies in the months 
 marked in the figure. Her position is, therefore, in Libra 
 at the vernal equinox, in Aries the autumnal, in Capricorn 
 at the summer, and in Cancer at the winter solstice. lu 
 these different positions, P m represents the axis of the 
 earth always parallel to itself, as has been said. Now, 
 from the globular form of the earth, the sun can only shine 
 on one half at a time. Let, therefore, the shaded portions 
 represent the dark, and the light portions the illuminated 
 halves. Further, in all the different positions, let E G 
 represent the ecliptic, P e the arctic circle, and d m the 
 antarctic. 
 
 Now, when the earth is in the position marked Aries, 
 both poles, P m, fall just with the illuminated half. It is, 
 therefore, day over half the northern and half the south- 
 ern hemispheres at once. And as the earth turns round 
 on her axis, the day and night must each be of equal 
 length that is to say, twelve hours long all over the 
 globe. Of course, precisely the same holds for the posi- 
 tion at Libra. The former corresponds to September, 
 the latter to March. 
 
 . But when the earth reaches Capricorn in June, one of 
 her poles, P, will be in the illuminated half, the other, m, 
 in the dark ; and for a space reaching from P to e, and m 
 to d, a certain portion of her surface will also be illumin- 
 ated, or also in shadow. The illuminated space, P e, as 
 the earth makes her daily rotation, will be exposed to the 
 sun all the time ; the dark space, m d, will be all the time 
 in shadow. At this period of the year the sun never sets 
 at the north polar circle, and never rises at the south. 
 And the converse of all this happens when the earth 
 moves round to Cancer, in December. 
 
 Why does the earth's axis always point in the same direction ? Ex- 
 plain the phenomena of the seasons. 
 
328 THE SOLAR SYSTEM. 
 
 The temperature of any place depends on the amount 
 of heat it receives from the sun. During the day the earth 
 is continually warming; during the night cooling. When 
 the sun is more than twelve hours above the horizon, and 
 less than twelve below, the temperature rises, and con- 
 versely. When the earth moves from Libra to Capri- 
 corn, in the northern hemisphere, the days grow longer 
 and the nights shorter, and the rise of temperature we call 
 the approach of spring. As she passes from Capricorn 
 to Aries, summer comes on. From Aries to Cancer, the 
 night becomes longer than the day, and it is autumn the 
 reverse taking place from Cancer to Libra. It is also to 
 be remarked, that similar but reverse phenomena are oc- 
 curring for the southern hemisphere. This, therefore, ac- 
 counts for the seasons, and accounts for all their attendant 
 phenomena, that the sun never sets in the polar circles 
 during summer, nor rises during winter. 
 
 LECTURE LXV. 
 
 THE SOLAR SYSTEM. The Planetary Bodies. Inferior 
 and Superior Planets. Mercury. Venus, her motions 
 and phases. Transits of Venus over the Sun. Their 
 importance. Mars, his physical appearance. 
 
 HAVING established the general relations of the earth 
 and sun, and shown how the former revolves round the 
 latter in an elliptic orbit, we proceed, in the next place, 
 to a description of the solar system, 
 
 It has already been stated that among the stars theie 
 are some which plainly possess proper motions, some- 
 times being found in one part of the heavens and some- 
 times in another. To these, from -their wandering 1 mo- 
 tion, the name of planets has been given. Like the earth, 
 they revolve in elliptic orbits round the sun. Their names, 
 commencing with the nearest to the sun, are 
 
 Mercury, Juno, Jupiter, 
 
 Venus, Ceres, Saturn, 
 
 Earth, Pallas, Uranus, 
 
 Mars, Astrea, Neptune. 
 Vesta, 
 
 On what does the temperature of any place depend ? How is this con- 
 nected with the seasons ? Wljat are the planets? Mention their names. 
 
MERCURY. 
 
 329 
 
 There are, therefore, two whose orbits are included in 
 that of the earth, the others are on the outside of it. 
 
 MERCURY always appears in the close neighborhood of 
 the sun, and hence is ordinarily difficult to be seen. In 
 the evening, after sunset, he may, at the proper time, be 
 discovered, but, soon retracing his path, is lost among the 
 solar rays. After a time he reappears in the morning, 
 and proceeding farther and farther from the sun, with a 
 velocity continually decreasing, he finally becomes station- 
 ary, and then returns, to reappear again in the evening. 
 
 The distance of this planet from the sun is more than 
 37,000,000 of miles, his diameter 3200, he turns on his 
 axis in 24h. 5' 3'', and moves in his orbit with a velocity 
 of 111,000 miles in an hour. 
 
 VENUS, which is the next of the planets, and, like Mer- 
 cury, is inferior that is, has her orbit interior to that of 
 the earth from her magnitude and position, enables us 
 to trace the phenomena of such a planet in a clear and 
 
 Fig. 346. 
 
 Under what circumstances may Mercury be seen? What is his dis- 
 tance from the sun, his diameter, and the time of his rotation ? 
 
330 VENUS. 
 
 perfect manner. She, too, is seen alternately as an even- 
 ing and morning star, being first discovered, as at A, Fig. 
 346, emerging from the rays of the sun, and moving wilh 
 considerable rapidity from A toward B. Let K be the 
 position of the observer on the earth, which, for the pres- 
 ent, we will suppose to be stationary. To such an ob- 
 server the motion of Venus, as she recedes from the sun, 
 appears to become slower and slower, then to cease. 
 And now the planet, passing from C to E, appears to 
 have a retrograde motion, the velocity of which contin- 
 ually increases, then again lessens as she moves toward 
 G, then ceases; and, lastly, the planet moves toward A 
 with a continually accelerated motion. 
 
 All this is evidently the effect which must ensue with a 
 body pursuing an interior orbit. The stationary appear- 
 ance arises from the circumstance that at one point, C, 
 she is coming toward the earth, at the opposite, Gr, re- 
 treating from it; while at A and at E she is crossing the 
 field of view. 
 
 But the planets shine only by the light of the sun. Ve- 
 nus, moving thus in an interior orbit, ought, therefore, to 
 exhibit phases. Thus, in Fig. 347, when she first emerges 
 from the rays of the sun on the opposite side, as respects 
 the earth', a position which is called her superior con- 
 junction, A, she must exhibit to us the whole of her il- 
 luminated disc ; but, as she passes from A to B, a portion 
 of her unilluminated hemisphere is gradually exposed to 
 view. This increases at D ; and at E we see half of tho 
 illuminated and half of the dark hemisphere. She looks, 
 therefore, like a little half moon. As she comes into the 
 position F Gr H we see more and more of her dark side. 
 She becomes a thinner and thinner crescent, and at I is 
 extinguished ; and, passing from this toward L M N O, 
 and from that to A, we gradually recover sight of more 
 and more of her illuminated disc. 
 
 These phenomena must necessarily hold for a planet 
 moving in an interior orbit, and were predicted before 
 the invention of the telescope. That instrument estab- 
 lished the accuracy of the prediction. 
 
 The points E and O are the points of greatest elonga- 
 tion, Ais the superior conjunction, and I the inferior. 
 
 What phenomena does Venus exhibit? How do we account for her 
 direct and retrograde motions ? Why does she exhibit phases ? 
 
PHASES OF VENUS. 
 Fif. 347. 
 
 331 
 
 Common observation shows that this planet differs very 
 much at different times in brilliancy. Two causes affect 
 her in this respect : 1st, the different amount of illumi- 
 nated surface which we perceive ; 2d, the difference of 
 apparent magnitude of the planet as she changes position 
 in her orbit. On her approach toward the earth from E 
 to H the illuminated portion visible lessens ; but then her 
 dimensions increase by reason of her proximity. The 
 
 What are the points of her greatest elongation and the superior and in- 
 ferior conjunction 1 What causes affect the brilliancy of this planet ? 
 
332 TRANSITS OF VENUS. 
 
 maximum of brilliancy takes place when she is about 40 
 from the sun. 
 
 Moreover, it is obvious that at certain intervals, at the 
 tim^ of the inferior conjunction, both this and the preceding 
 plS.net must appear to cross the face of the sun. To this 
 phenomenon the name of a transit is given. The planet 
 then appears as a round black spot or disc projected on the 
 sun. In the case of Venus, these transits take place at in- 
 tervals of about eight and one hundred and thirteen years. 
 They furnish the most exact means of determining the 
 sun's parallax. Let A B, Fig. 348, be the earth, V Ve- 
 
 . 348. 
 
 nus, S the sutn. Let a transit of the planet be observ- 
 ed by two spectators, A J>, at the opposite points of 
 that diameter of the earth, perpendicular to the ecliptic. 
 Then the spectator at A will see Venus projected on the 
 sun's disc at C, and B at D ; but the angle A V B is 
 equal to the angle C V D ; and since the distance of the 
 earth from the sun is to that of Venus from the same 
 body, as about 2| to 1, C D will occupy on the sun's disc 
 a space 2 times that under which the earth's diameter is 
 seen that is to say, five times as much as the horizontal 
 parallax. The sun's parallax, as determined from the 
 transit of 1769, is 8"-6 nearly. 
 
 The period occupied by this planet in performing her 
 revolution round the sun is 224* days, 16 hours, 42 min- 
 utes, 25.5 seconds. The orbit is inclined to the ecliptic 
 3 23' 25". She revolves on her axis in 23h 21' 19". 
 Her diameter is about 7800 miles. She is, therefore, 
 very nearly the size of the earth. 
 
 When is she most brilliant? What is a transit?. At what intervals 
 do these take place in the case of Venus? How are these used to 
 determine parallax ? What is the period of revolution of this planet ? 
 What is her diameter? 
 
MARS. 333, 
 
 MARS is the next planet, the earth intervening between 
 him and Venus, his orbit is, therefore, an exterior one, 
 and in common with the others that follow, he is desig- 
 nated as a superior planet. He is of a reddish color, and 
 sometimes appears gibbous, and both when in conjunction 
 and opposition exhibits a full disc. The diameter differs 
 very greatly according to his position, and with it, of 
 course, his brilliancy varies. The distance from the sun 
 is about 146 millions of miles, he revolves on his axis in 
 24h 31' 32", the inclination of his orbit to the ecliptic is 
 1:.F I". As with the earth his polar diameter is shorter 
 than his equatorial. 
 
 The physical appearance of Mars is somewhat remark- 
 able. His polar regions, when seen through a telescope, 
 have a brilliancy so much greater than the rest of his disc 
 that there can be little doubt that, as with the earth so 
 with this planet, accumulations of ice or snow take place 
 during the winters of those regions. In 1781 the south 
 polar spot was extremely bright ; for a year it had not 
 been exposed to the solar rays. The color of the planet 
 most probably arises from a dense atmosphere which 
 surrounds him, of the existence of which there is other 
 proof depending on the appearance of stars as they ap- 
 proach him ; they grow dim and are sometimes wholly 
 extinguished as their rays pass through that medium. 
 
 Fig. 349. 
 
 Fig. 349 represents the telescopic appearance of Mars, 
 according to Herschel ; a is the polar spot. 
 
 Why is Mars called a superior planet ? Does he exhibit phases ? What 
 is there remarkable respecting his physical appearance ? What reasons 
 are there fur supposing he has a dense atmosphere? 
 
334 
 
 THE ASTEROIDS. 
 
 LECTURE LXVI. 
 
 THE SOLAR SYSTEM. The Five Asteroids. Jupiter and 
 his Satellites. Saturn, his Rings and Satellites. 
 Uranus. Neptune. The Comets. Returns of Halley's 
 Comet. Comets of Enckc and Biela. 
 
 OUTSIDE of the orbit of Mars there occur five telescopic 
 planets closely grouped together they are VESTA. JUNO, 
 CERES, PALLAS, and ASTREA. They have all been dis- 
 covered within the present century, the last of them in 
 1846. From their smallness and distance they are far 
 from being well known. The following table contains 
 the chief facts in relation to them. 
 
 
 Period of Revolu- 
 tion. 
 
 Inclination of 
 Orbit to Ecliptic. 
 
 Distance in 
 miles. 
 
 Diameter 
 in miles. 
 
 Vesta 
 Juno 
 Ceres 
 Pallas 
 Astrea 
 
 3 yrs. 66d. 4 h. 
 4 yrs.!28d. 
 4 yrs. 
 4 yrs. 7 m. 11 d. 
 4 yrs. 2m. 4 d. 
 
 7 8' 
 13 4Y 
 ](P 37' 25" 
 34 37' 30" 
 5 2<y 
 
 225.000.000 
 256.000.000 
 264.000.000 
 267.000.000 
 250 000 000 
 
 1320 
 1320 
 1920 
 
 It has been thought that these small planets are merely 
 the fragments of a much larger one which has been burst 
 asunder by some catastrophe. There seems to be some 
 foundation for this opinion. It has been asserted that 
 they are not round, but present angular faces. They are 
 also enveloped in dense atmospheres, and in the case of 
 Juno and Pallas, their orbits are greatly inclined to the 
 ecliptic. These planets are sometimes called asteroids. 
 
 JUPITER, the largest and perhaps the most interesting 
 of the planets, has his orbit immediately beyond that of 
 the asteroids. He always presents his full disc to the 
 earth, and performs his revolution round the sun in 11 
 years 318 days, at a distance of 495 millions of miles. 
 He is nearly 1500 times the size of the earth, being 
 89,000 miles in diameter. 
 
 What planets come next in order to Mars '( What is there remarkable 
 respecting the size and orbits of these planets? Under what name do 
 they also go ? What is the position and size of Jupiter ? 
 
JUPITER. 335 
 
 Immediately after the invention of the telescope, it was 
 discovered by Galileo that Jupiter is attended by four 
 satellites or moons, which revolve round him in orbits 
 almost in the plane of his equator. Each of these satel- 
 lites revolves on its own axis in the same time that it 
 goes round its primary, so that, like our own moon, they 
 always turn the same face to the planet. Like our 
 moon, also, they exhibit the phenomena of lunar and 
 solar eclipses. Advantage has been taken of these 
 
 Fig. 350. 
 
 eclipses to determine terrestrial longitudes, and we have 
 already seen it was from them that the progressive mo- 
 tion of light was first established. 
 
 Juph^r revolves on his axis in 9h. 56'. This rapid ro- 
 tation, therefore, causes him to assume a flattened form 
 his polar axis being -fa shorter than his equatorial, and as 
 his axis is nearly perpendicular to the plane of his orbit, 
 his days and nights must be equal, and there can be but 
 little variation in his seasons. His disc is crossed by belts 
 or zones, which are variable in number and parallel to his 
 equator. 
 
 SATURN, which is the next planet, performs his revolu- 
 tion round the sun in about twenty-nine years and a half, 
 at a distance of 915 millions of miles. The inclination of 
 his orbit to the ecliptic is 2 30'. He is about 900 times 
 larger than the earth, being 79,000 miles in diameter. 
 
 How many satellites has he ? What advantage has been taken of their 
 eclipses ? What is the time of rotation of this planet on his axis ? What 
 is the relation of his equatorial to his polar diameter? What is the dis- 
 tance and size of Saturn ? 
 
336 SATURN AND URANUS. 
 
 He turns on his axis in 10 hours, and the flattening of 
 his polar diameter is y^. 
 
 Seen through the telescope, Saturn presents a most ex- 
 traordinary aspect. His disc is crossed with belts, like 
 those of Jupiter; a broad thin ring, or rather combina- 
 tion of rings, surrounds him, and beyond this seven satel- 
 lites revolve. The ring is plainly divided into two con- 
 centric portions, a b, as seen in Fig. 351, and other sub- 
 
 Fig. 351. 
 
 divisions have been suspected. The larger ring is nearly 
 205,000 miles in exterior diameter, and the space between 
 the two 2680 miles. The rings revolve on their own cen- 
 ter which does not exactly coincide with the center of 
 Saturn in about 10 hours and 20 minutes. The excen- 
 tricity of the rings is essential to their stability. 
 
 URANUS, discovered in 1781, by Herschel, revolves in 
 an orbit exterior to Saturn, in a period of about 84 years, 
 and at a distance of 1840 millions of miles. The incli- 
 nation of its orbit to the ecliptic is 46^'. It can only be 
 seen by the telescope. Its diameter is 35,000 miles. Six 
 satellites have been discovered. 
 
 By what extraordinary appendage is he attended? How many satellites 
 has he ? What is the distance of Uranus ? By whom was he discovered T 
 
NEPTUNE. 337 
 
 NEPTUNE. This planet was discovered in 1846, in con- 
 sequence of mathematical investigations made by Adams 
 and Leverrier, with a view of explaining the perturba- 
 tions of Uranus. It was also seen in 1795 by Lalande, 
 and regarded by him as a fixed star. Its period is about 
 166 years very nearly double that of Uranus. The in- 
 clination of its orbit is 1 45'. The excentricity is only 
 0.005. The orbit is, therefore* more nearly a perfect 
 circle than that of any other planet. There is reason to 
 believe that Neptune is surrounded by a ring analogous 
 to the ring of Saturn. 
 
 The planetary bodies now described, with their attend- 
 ant satellites and the sun, taken collectively, constitute 
 the solar system, a representation of which, as respects 
 the order in which the bodies revolve, is given in Fig. 
 352. In the center is the sun, and in close proximity to 
 
 Fig. 352. 
 
 him revolves Mercury, outside of whose orbit comes Ve- 
 nus. Then follows the earth, attended by her satellite, 
 
 What is the position of Neptune ? Of what is the solar system com- 
 posed ? 
 
 P 
 
338 COMETS. 
 
 the moon. Beyond the earth's orbit comes Mars ; then 
 come the asteroids, followed by Jupiter, with his four 
 moons. Still more distant is Saturn, surrounded by his 
 rings and seven satellites ; then Uranus, with six ; and 
 lastly, so far as our present knowledge extends, comes the 
 recently-discovered planet Neptune. 
 
 Such a representation as that given in Fig. 352, can 
 merely illustrate the ortftr in which the members of the 
 solar system occur, but can afford no suitable idea of their 
 relative magnitudes aud distances. Thus, in that figure, 
 the apparent diameter of the sun is about the tenth of an 
 inch, and were the proportions maintained, the diameter 
 of the orbit of the planet Neptune should be about fifty 
 feet. A similar observation might be made as respects 
 the planetary masses. 
 
 But besides these bodies, there are others now to be 
 described, which are members of our solar system. They 
 are the comets. They move in very excentric orbits, and 
 are only visible to us when near their perihelion. In ap- 
 pearance they differ very greatly from one another, but 
 
 Fig. 353. 
 
 most commonly consist of a small brilliant point, from 
 which there extends what is designated the tail. Some- 
 
 In what respects are such representations of the solar system as that in 
 Fig. 352 imperfect ? What are comets ? What is remarkable as respects 
 their physical constitution ? 
 
RETURN OF COMETS. 339 
 
 times they are seen without this remarkable appendage. 
 In other instances it is of the most extraordinary length, 
 and in former ages, when the nature of these bodies was 
 ill understood, occasioned the utmost terror, for comets 
 were looked upon as omens of pestilence and disaster. 
 The comet of 1811 had a tail nearly 95 millions of miles 
 in length that of 1744 had several, spreading forth in 
 the form of a fan. 
 
 The history of the discovery of the nature of comets is 
 very interesting. Dr. Halley, a friend of Sir I. Newton, 
 had his attention first fixed on the probability that several 
 bodies, recorded as distinct, might be the periodic returns 
 of the same identical comet, and closely examining one 
 which was seen in 1682, came to the conclusion that it 
 regularly appeared at intervals of seventy-five or seventy- 
 six years. He therefore predicted that it ought to reap- 
 pear about the beginning of the year 1759. The comet 
 actually came to its perihelion on March the 13th of that 
 year, and again, after an interval of seventy-six years, in 
 1835. 
 
 Besides the comet of Halley, there are two others, the 
 periodic returns of which have been repeatedly observed. 
 These are the comet of Encke and that of Biela. The 
 former is a small body which revolves in an elliptical or- 
 bit, with an inclination of 13 in about 1200 days. Its 
 nearest approach to the sun is about to the distance of the 
 planet Mercury; its greatest departure somewhat less 
 than the distance of Jupiter. Its motion is in the same 
 direction as that of the planets. 
 
 The comet of Biela has a period of 2460 days. It moves 
 in an elliptical orbit, the length of which is to the breadth 
 as about three to two. Its nearest approach to the sun is 
 about equal to the distance of the earth ; its greatest re- 
 moval somewhat beyond that of Jupiter. It reappears 
 with great regularity, but in the month of January, 1846, it 
 exhibited the wonderful phenomenon of a sudden division, 
 two comets springing out of one. This fact was first seen 
 by Lieutenant Maury, at the National Observatory at 
 Washington. 
 
 Nothing is known with precision respecting the nature 
 
 When was the periodic return of comets first detected ? What other 
 two comets have been frequently re-observed ? What remarkable result 
 lias been noticed respecting Biela's comet ? 
 
340 THE SECONDARY PLANETS. 
 
 of these bodies. They are apparently only attenuated 
 masses of gas, for it is said that through them stars of the 
 sixth or seventh magnitude have been seen. In the case 
 of some there appears to have been a solid nucleus of 
 small dimensions. 
 
 LECTURE LXVII. 
 
 THE SECONDARY PLANETS OR SATELLITES. The Moon, 
 her Phases, her Period of Revolution, her Physical ap- 
 pearance always presents the same face. Eclipses of the 
 Moon. Eclipses of the Sun. Recurrence of Eclipses. 
 Occultations. 
 
 THE motions of the secondary bodies of the solar sys- 
 tem, the satellites, and more especially the phenomena 
 of our own moon, deserve, from their importance, a more 
 detailed investigation. To these, therefore, I proceed in 
 this lecture. 
 
 That the moon has a proper motion in the heavens the 
 observations of a single night completely proves. She 
 is translated from west to east, so that she comes to the 
 meridian about forty-five minutes later each day, and 
 performs her revolution round the earth in about thirty 
 days, exhibiting to us each night appearances that are 
 continually changing, and known under the name of 
 phases. 
 
 First when seen in the west, in the evening, she is a 
 crescent, the convexity of which is turned to the sun. 
 From night to night the illuminated portion increases, 
 and about the seventh day she is half-moon. At this time 
 she is said to be in her quadrature or dichotomy. The 
 enlightened portion still increasing, she becomes gibbous, 
 and about the fifteenth day is full. She now rises at sun- 
 set. 
 
 From this period she continually declines, becomes gib- 
 bous, and at the end of a week half-moon. Still further 
 she is crescentic ; and at last, after twenty-nine or thirty 
 days, disappears in the rays of the sun. 
 
 What is supposed to be the physical constitution of these bodies ? What 
 is the direction of the moon's motion ? In what time is a complete revo- 
 lution completed ? What are her phases ? Describe their order. 
 
PHASES OP THE MOON. 341 
 
 At new-moon, she is said to be in conjunction with the 
 sun, at full-moon in opposition ; and these positions are 
 called syzygies; the intermediate points between the 
 svz ygies an< i quadratures are octants. 
 
 Fiff.354. 
 
 The cause of the moon's phases admits of a ready ex- 
 planation on the principle that she is a dark body, re- 
 flecting the light of the sun, and moving in an orbit round 
 the earth. Thus, let S, Fig. 364, be the sun, E the earth, 
 and a b c, &c., the moon seen in different positions of her 
 orbit. From her globular figure, the rays of the sun can 
 only illuminate one half of her at a time, and necessarily 
 that half which looks toward him. Commencing, there- 
 fore, at the position a, where both these bodies are on 
 the same side of the earth, or in conjunction, the dark 
 side of the moon is turned toward us, and she is invisi- 
 ble ; but as she passes to the position , which is the oc- 
 tant, the illuminated portion comes into view. And when 
 she has reached the position c, her quadrature, we see 
 half the shining and half the dark hemisphere. Here, 
 therefore, she is half-moon. From this point she now 
 becomes gibbous ; and at e, being in opposition, exposes 
 her illuminated hemisphere to us, and is, therefore, full- 
 mcon. From this point, as she returns through f g k t 
 she runs through the reverse changes, being in succes- 
 sion gibbous, half-moon, crescentic, and finally disappear- 
 ing. 
 
 What are the syzygies, and quadratures, and octants ? What is the ex- 
 planation of the phases ? 
 
342 . THE MOON. 
 
 Viewed through a telescope, the surface of the moon 
 is very irregular, there being high mountains and deep 
 pits upon it. These, in the various positions she assumes 
 as respects the sun, cast their shadows, which are the 
 dark marks we can discover by the eye, on her disc, and 
 which are popularly supposed to be water. 
 
 Fig. 355. 
 
 The moon's diameter, measured at different times, va- 
 ries considerably. This, therefore, proves that she is not 
 always at the same distance from the earth ; and, in fact, 
 she moves in an ellipsis, the earth being in one of the 
 foci. Her distance is about 230,000 miles. She accom- 
 panies the earth round the sun, and turns on her axis in 
 precisely the same length of time which it takes her to 
 perform her monthly revolution. Consequently, she al- 
 ways presents to us the same face. Her orbit is inclined 
 to that of the ecliptic, at an angle of little more than five 
 
 What is the appearance of the moon seen through a telescope T Is 
 her apparent diameter always the same ? What is her distance ? What 
 is her period of rotation on her axis ? Does she always present exactly 
 the same face to the earth ? 
 
ECLIPSE OF THE MOON. 843 
 
 degrees. Its points of intersection with the ecliptic are 
 the nodes. Her greatest apparent diameter is 33 min- 
 utes. The nodes move slowly round the ecliptic, in a di- 
 rection contrary to that of the sun, completing an entire 
 revolution in about eighteen years and a half. Although, 
 for the most part, she presents the same face to the earth, 
 as has been said, yet this, in a small degree, is departed 
 from in consequence of her libration. This takes place 
 both in longitude and latitude, and brings small portions 
 of her surface, otherwise unseen, into view. 
 
 The relations of the sun, the earth, and the moon to 
 one another afford an explanation of the interesting phe- 
 nomenon of eclipses. These are of two kinds eclipses 
 of the moon and those of the sun. 
 
 The earth and moon being dark bodies, which only 
 shine by reflecting the light of the sun, project shadows 
 into space. Let, therefore, A B, Fig. 356, be the sun, 
 C D the earth, and M the moon, in such a position, as 
 respects each other, that the moon, on arriving in oppo- 
 sition, passes through the shadow of the earth. The light 
 is, therefore, cut off, and a lunar eclipse takes place. 
 
 Fig. 356. 
 
 The shadow cast by the earth is of a conical foi^i, a 
 figure necessarily arising from the great size of the sun 
 when compared with that of the earth. The semi-diame- 
 ter of the shadow at the points where the moon may 
 cross it varies from about 37' to 46' that is, it may be 
 as much as three times the semidiameter of the moon. 
 A lunar eclipse may, therefore, last about two hours. 
 
 The time of the occurrence of an eclipse of the moon 
 is the same at all places at which it is visible. It is, of 
 course visible at all places where the moon is then to be 
 
 How many kinds of eclipses are there ? Under what circumstance does 
 a lunar eclipse take place ? How long may a lunar eclipse last ? How is 
 its magnitude estimated ? 
 
344 ECLIPSE OF THE SUN. 
 
 seen. The magnitude of the eclipse is estimated in digits, 
 the diameter of the moon being supposed to be divided 
 into twelve digits. 
 
 Whatever may be the circumstances under which a 
 lunar eclipse takes place, the shadow of the earth is al- 
 ways circular. Advantage has already been taken of this 
 fact in giving proof of the spherical figure of the earth. 
 
 If the plane of the moon's orbit were not inclined to 
 the ecliptic there would be a lunar eclipse every full 
 moon. It is necessary, therefore, for this to occur, that 
 the moon should be either in or near to the node, so that 
 the sun, the earth, and the moon may be in the same line. 
 It was explained in Lecture XXXV., that a body situated 
 under the same circumstances as those under which the 
 earth is now considered forms a penumbra as well as a 
 true shadow. There is, therefore a gradual obscuration 
 of light as the moon approaches the conical shadow, aris- 
 ing from its gradual passage through the penumbra. 
 
 An eclipse of the sun takes place under the following 
 circumstances. Let A B, Fig. 357, be the sun, M the 
 moon, and C D the earth. Whenever the moon passes 
 
 Kg. 357. 
 
 
 B 
 
 directly between the earth and the sun, she hides his disc 
 from us, and a solar eclipse takes place. It is partial 
 when only a portion of the sun is obscured, annular when 
 a ring of light surrounds the moon at the middle of the 
 eclipse, and total when the whole sun is covered. 
 
 As the moon is so much smaller than the earth, the 
 conical shadow which she casts can only cover a portion 
 of the earth at a time. Solar eclipses occur at different 
 times to different observers, and in this respect, therefore, 
 eclipses of the moon are more frequently observed than 
 
 What is to be observed respecting the figure of the earth's shadow ? 
 Why is there not a lunar eclipse every month ? Under what circum- 
 stance does an eclipse of the sun take place? Why is there a difference 
 between solar and lunar eclipses as respects the time at which they are 
 seen, and also as respects their relative frequency ? 
 
ECLIPSES. 345 
 
 those of the sun. Like lunar eclipses, solar ones can 
 only occur in or near one of the nodes. Solar eclipses 
 can only occur at new moon, and lunar at full moon. 
 
 Like the earth, the moon casts a penumbra ; it is a cone, 
 the axis of which is aline joining the centers of the moon 
 and sun, and the vertex of which is a point where the 
 tangents to the opposite sides of the bodies intersect. 
 
 Eclipses recur again after a period of about 1S years. 
 In each year there cannot be less than two nor more than 
 seven eclipses ^ in the former case they are both solar, in 
 the latter there must be five of the sun and two of the 
 moon. There must, therefore, be at least two eclipses 
 of the sun each year, and cannot be more than three of 
 the moon. 
 
 The satellites which move round Jupiter, Saturn, and 
 Uranus, exhibit the same phenomena of phases and 
 eclipses to the inhabitants of those bodies as are exhibited 
 to us by our moon. Advantage has been taken of the 
 eclipses of Jupiter's satellites for the purpose of deter- 
 mining longitudes upon the earth, and from them the 
 progressive motion of light was first established. 
 
 An occupation is the intervention of the moon between 
 the observer and a fixed star. Occultations may be used 
 for the determination of longitudes. 
 
 After what period do eclipses recur ? How may they occur as to num- 
 ber each year? What use is made of the eclipses of Jupiter's satellites ? 
 What is an occultation ? 
 
346 THE FIXED STARS. 
 
 LECTURE LXVIII. 
 
 THE FIXED STARS. Apparent Magnitudes. Constella- 
 tions. The Zodiac. Nomenclature of the Stars. 
 Double Stars. Parallax. Distance of the Stars. 
 Groups of Stars. Nebula. Constitution of the Uni- 
 verse. Nebular Hypothesis. 
 
 AV^iTH the exception of the sun and moon, the heavenly 
 bodies hitherto described form but an insignificant por- 
 tion of the display which the skies present to us. For, 
 besides them there are numberless other bodies of va- 
 rious sizes which, for very great periods of time, maintain 
 stationary positions, and for this reason are designated as 
 fixed stars. 
 
 The fixed stars are classed according to their apparent 
 dimensions ; those of the first magnitude are the largest, 
 and the others follow in succession ; the number increases 
 very greatly as the magnitudes are less. Of stars of the 
 first magnitude there are about eighteen, of those of th< 
 second sixty, and the telescope brings into view tens o 
 thousands otherwise wholly invisible to the human eye. 
 
 From very early times, with a view of the more ready 
 designation of the stars, they have been divided into con- 
 stellations ; that is, grouped together under some imag- 
 inary form. The number of these for both hemispheres 
 exceeds one hundred. They are commonly depicted upon 
 celestial globes. 
 
 The ecliptic passes through twelve of the constella- 
 tions, occupying a zone of sixteen degrees in breadth, 
 through the middle of which the line passes. This zone 
 is called the zodiac, and its constellations with their signs 
 are as follows : 
 
 Aries P Libra 
 
 Taurus b Scorpio ut 
 
 Gemini n Sagittarius $ 
 
 Cancer 22 Capricornus V? 
 
 Leo 1 Aquarius ~ 
 
 Virgo n Pisces X 
 
 What are the fixed stars ? How are they divided ? How many of the 
 first and second magnitudes are there ? What are constellations ? What 
 is the zodiac ? Mention the constellations of it. 
 
DOUBLE STARS. 347 
 
 The order in which they are here set down is the 
 order which they occupy in the heavens, commencing 
 with the west and going east. Motions of the sun and 
 planets in that direction are, therefore, said to be direct, 
 and in the opposite retrograde. 
 
 To many of the larger stars proper names have been 
 given. These, in many instances, are oriental, such as 
 Aldebaran, but they are chiefly designated by the aid of 
 the Greek letters, the largest star in any constellation 
 being called a, the second (3, &c., to these letters the 
 name of the constellation is annexed. 
 
 The position of any star is determined by its declina- 
 tion and right ascension, and though these positions are 
 commonly regarded as fixed, yet the great perfection to 
 which modern astronomy has arrived has shown that the 
 stars are affected by a variety of small motions, although, 
 in some instances, these may arise in extrinsic causes, 
 such, for example, as in the case of aberration, yet there 
 can now be no doubt that the stars have proper motions 
 of their own. This is most satisfactorily seen in the case 
 of double stars, of which there are several thousands. 
 These are bodies commonly arranged in pairs close to- 
 gether, the physical connection between them is established 
 by the circumstance that they revolve round one another ; 
 thus, y, Virginis, has a period of 629 years, and e, Bootis, 
 one of 1600 years. 
 
 From the planets the stars differ in a most striking 
 particular : they shine by their own light. It this respect 
 they resemble our sun, who must himself, at a suitable 
 distance, exhibit all the aspect of a fixed star. We there- 
 fore infer that the stars are suns like our own, each, 
 probably like ours, surrounded by its attendant but in- 
 visible planets ; and, therefore, though the number of the 
 stars as seen by telescopes may be countless, the number 
 of heavenly bodies actually existing, but not apparent 
 because they do not shine by their own light, must be 
 vastly greater. In our solar system there are between 
 thirty and forty opaque globes to one central sun. 
 
 It is immaterial from what part of the earth the fixed 
 
 What are direct and what retrograde motions ? How are stars designa- 
 ted ? How is their position determined ? How is it known that some of 
 them have proper motions ? What are double stars ? In what respect do 
 stars differ from planets ? 
 
348 DISTANCE OF THE STARS. 
 
 stars are seen ; they exhibit no change of position, and 
 have no horizontal parallax : an object 8000 miles in di- 
 ameter, at that distance is wholly invisible from them. 
 But more, when viewed at intervals of six months, when 
 the earth is on opposite sides of her orbit a distance of 
 190 millions of miles intervening the same result holds 
 good. To the nearest of them, therefore, our sun must 
 appear as a mere mathematical lucid point that is to 
 say, a star. 
 
 In Lecture LXV., the method of determining the dis- 
 tance of the sun has been given. The same principles 
 apply in the determination of the distance of a fixed star. 
 The horizontal parallax may be found without difficulty 
 for the bodies of our solar system : it is, in reality, the angle 
 under which the earth's semi-diameter is seen from them. 
 But when this method is applied to the fixed stars, it is 
 discovered that they have no such sensible parallax; and, 
 therefore, that the earth is, as has been observed, wholly in- 
 visible from them. This is illustrated in Fig. 358, in which 
 let S be the sun, A B C D the earth, moving in her orbit, 
 and the lines A , B b, C c, D d the axis of the earth, 
 continued to the starry heavens. This axis, we have seen 
 in Lecture XXL, is always parallel to itself; it would 
 therefore trace in the starry heavens a circle, abed, of 
 equal magnitude with the earth's orbit, ABC D that is, 
 190 millions of miles in diameter. If H be a star, when 
 the earth is at the point A of her orbit the star will be 
 distant from the pole of the heavens by the distance a H, 
 and when she is at the point C, by the distance c II. It 
 takes the earth six months to pass from A to C, ]90 mil- 
 lions of miles. But the most delicate means have hith- 
 erto failed to detect any displacement of a star, such as 
 H, as respects the pole, when thus examined semi-annu- 
 ally. It follows, therefore, that the diameter of the earth's 
 orbit is wholly invisible at those distances. 
 
 Again, let E F I G, Fig. 359, represent the orbit of the 
 earth, and K any fixed star, it is obvious that when the 
 earth is at G the star would be seen by G K, and refer- 
 red to the point, i; when the earth is" at F it would be 
 seen by F K, and referred to h, and the angle i K h, which 
 
 Have the stars any diurnal parallax ? What must be the appearance of 
 r sun to them ? Explain the illustrations given in Figs. 358 and 359 re- 
 specting parallax. 
 
ANNUAL PARALLAX. 
 
 349 
 
 Fig. 359. 
 
 is equal to F K G, would be the annual parallax, or the 
 angle under which the earth's orbit would be seen from 
 the star. But though this is 190 millions of miles, so im- 
 mense is the distance at whrch the fixed stars are placed 
 that it is wholly imperceptible. 
 
 In a few instances, however, an annual parallax has 
 been discovered. Thus, in the star 61 Cygni, amounts to 
 about one third of a second. The distance of the near- 
 est fixed star is, therefore, enormously great. 
 
 The stars are not scattered uniformly over the vault of 
 
 Have any stars an annual parallax ? 
 
350 
 
 THE MILKY WAY. 
 
 heaven, but appear arranged in collections or groups. 
 
 Just as the planets and 
 their satellites make up, 
 with our sun, one little 
 system, so too do suns 
 grouped together form 
 colonies of stars. The 
 milky way, Fig. 360, 
 which is the group to 
 which we belong, consists 
 of myriads of such suns, 
 bound together by mutual 
 attractive influences. In 
 this S may represent the 
 position of the solar sys- 
 tem, and the stars will ap- 
 pear more densely scat- 
 tered when viewed along 
 S p, than along S m, S n, 
 S c. But in other por- 
 tions of the heavens are 
 discovered small shining 
 spaces nebulce, as they 
 are called which, uncle J 
 powerful telescopes, ar 
 resolved into myriads 
 stars, Fig. 361, so far off 
 that the human eye, when 
 unassisted, is wholly una- 
 ble to individualize them, 
 and catches only the faint 
 gleam of their collected 
 lights. Of these great 
 numbers are now known. 
 Such, therefore, is the 
 system of the world. A 
 planet, like Jupiter, with 
 his attendant moons, is, as 
 it were, the point of commencement ; a collection of 
 such opaque bodies playing round a central sun is a fur- 
 ther advance a system of suns, such as form the more 
 
 a 
 
 i 
 
 What are nebulae ? What is the milky way ? 
 

 351 
 
352 THE UNIVERSE. 
 
 brilliant objects of our starry heavens and thousands of 
 such nebulae which cover the skies in whatever direction 
 we look. These, taken altogether, constitute the UNI- 
 VERSE a magnificent monument of the greatness of God, 
 and an enduring memento of the absolute insignificance 
 of man. 
 
 But though the universe is the type of Immensity and 
 Eternity, we are not to suppose that it is wholly un- 
 changeable. From time to time new stars have sudden- 
 ly blazed forth in the sky, and after obtaining wonderful 
 brilliancy have died away and also old stars have disap- 
 peared. Recent discoveries have shown that the light of 
 very many is periodic that it passes through a cycle of 
 change and becomes alternately more and less bright in 
 a fixed period of days. These intervals differ in differ- 
 ent cases, and probably all are affected in the same way. 
 There is abundant geological evidence to show that the 
 light and heat of our sun were once far greater than now 
 the luxuriant vegetation of the secondary period could only 
 have arisen in a greater brilliancy of that orb. The sun, 
 then, is one of these periodic stars. 
 
 The alternate appearance and disappearance of some 
 of the new stars may arise from their orbitual motion. 
 Thus, suppose E the earth, and A B C D the orbit of such 
 
 Fig. 362. 
 
 K 
 
 a star. If the major axis of this orbit be nearly in the 
 direction of the eye, as the star approaches to A, it will 
 rapidly increase in brilliancy, and perhaps become wholly 
 invisible at the distant point C. Such a star should, there- 
 
 What is the structure of the Universe ? What changes have been ob- 
 served in the light of some stars ? Is there reason to believe that the sun 
 is a periodic star ? Explain the probable cause of the phenomena of new 
 stars. 
 
NEBULAR HYPOTHESIS. 353 
 
 fore, be periodical ; and that this is the case there is rea- 
 son to believe as respects one which appeared in the years 
 945, 1264, 1572, in the constellation of Cassiopeia. Its 
 period seems to be 319 years. 
 
 Among the nebulae there are some which powerful tel- 
 escopes fail to resolve into stars a circumstance which 
 has caused some astronomers to suppose that they are 
 in reality diffused masses of matter which have not as 
 yet taken on the definite form of globes, but are in 
 the act of doing so. And, extending these views to all 
 systems, they have supposed that all the planetary and 
 stellar bodies are condensations of nebular matter. To 
 this hypothesis, although if admitted it will account for a 
 great many phenomena not otherwise readily explained, 
 there are many objections : and it is also to be observed 
 that every improvement which has been made in the tel- 
 escope has succeeded in resolving into stars nebula3 until 
 then supposed to be unresolvable. The inference, there- 
 fore, is. that were our instruments sufficiently powerful all 
 would display the same constitution. 
 
 LECTURE LXIX. 
 
 CAUSES OP THE PHENOMENA OF THE SOLAR SYSTEM. 
 Definitions of the Parts of an Elliptic Orbit. Laws of 
 Kepler. Conjoint Effects of a Centripetal and Projectile 
 Force. Newton's Theory of the Planetary Motions. 
 His Deductions from Kepler's Laws. Causes of Pertur- 
 bations. 
 
 HAVING, in the preceding Lectures, described the con- 
 stitution of the solar system, and of the Universe gener- 
 ally, we proceed, in the next place, to a determination of 
 the causes which give rise to the planetary movements. 
 We have to call to mind that observation proves that the 
 figure of the orbits of these bodies is an ellipse, the sun 
 
 What is meant by the nebular hypothesis ? What are the objections to 
 it ? Describe the parts of an elliptic orbit. 
 
354 ELLIPTIC ORBIT. 
 
 being in one of the foci. Thus, in Fig. 363, let F be the 
 sun, A B D E an elliptic orbit, A is the perihelion, B the 
 
 Fig. 3G3. 
 
 aphelion, F D the mean distance, and JP C, which is the 
 distance of the focus from the center, the excentricity ; 
 a line joining the sun and the planet is called the radius 
 vector. 
 
 There are three anomalies the true, the mean, and the 
 excentric. They indicate the angular distance of a planet 
 Fig. 364. from its perihelion, as seen from the sun. 
 Let A p B be the orbit of a planet, S the 
 sun, A B the transverse diameter of the 
 orbit, p the place of the planet, C the cen- 
 B ter of the orbit, with which center let there 
 be described a circle, A x B ; through p draw x p Q, and 
 suppose that while the real planet moves from A to p, 
 with a velocity which varies with its distance, an imagin- 
 ary one moves in the same orbit with an equable motion, 
 so that when the real planet is at p, the imaginary one is 
 at P, both performing their entire revolution in the same 
 time. Then A S p is the true anomaly, A S P the mean 
 anomaly, A C a; the excentric anomaly. 
 
 From an attentive study of the phenomena of planetary 
 
 What is the radius vector ? What are the true, the mean, and the ex- 
 centric anomaly ? 
 
KEPLER'S LAWS. 355 
 
 motions, Kepler deduced their laws. These pass under 
 the designation of the three laws of Kepler. They are 
 
 1st. The planets all move in ellipses, of which the sun 
 occupies one of the foci. 
 
 2d. The motion is more rapid the nearer the planet is 
 to the sun, so that the radius vector always sweeps over 
 equal areas in equal times. 
 
 3d. The squares of the times of revolution are to each 
 other as the cubes of the major axes of the orbits. 
 
 It is one of the fundamental propositions of mechanical 
 philosophy that a body must forever pursue its motion in 
 a straight line unless acted upon by disturbing causes, 
 and any deflection from a rectilinear course is the evi- 
 dence of the presence of a disturbing force. Thus, when 
 a stone is thrown upward in the air,it ought, upon these 
 principles, to pursue a straight course, its velocity never 
 changing ; but universal observation assures us that from 
 the very first moment its velocity continually diminishes, 
 and after a time wholly ceases that then motion takes 
 place in the opposite direction, and the stone falfe to the 
 surface of the earth. In former Lectures, we have already 
 traced the circumstances of these motions, and referred 
 them to an attractive force common to all matter, and to 
 which we give, in these cases, the name of universal at- 
 traction, or attraction of gravitation. 
 
 In speaking of the motions of projectiles, Lecture 
 XX, it has been shown that, under the action of a 
 force of impulse and a continuous force acting together, 
 not only may a moving body be made to ascend and de- 
 scend in a vertical line, but also in curvilinear orbits, such 
 as the parabolic, the concavity of the curve looking toward 
 the earth's center, which is the center of attraction. It 
 should not, therefore, surprise us that the moon, which 
 may be regarded in the light of a projectile, situated at 
 a great distance from the earth, should pursue a curvi- 
 linear path, constantly returning upon itself, since such 
 must be the inevitable consequence of a due apportion" 
 ment of the intensity of the projectile and central forces 
 to one another. 
 
 It is the force of gravity which, at each instant, makes 
 
 What are the three laws of Kepler ? How may it be proved that an at- 
 tractive force exists in all the planetary masses ? What is the result of 
 the action of a momentary and a continuous fore* ? 
 
356 NEWTON'S THEORY. 
 
 a cannon-ball descend a little way from its rectilinear 
 path. And it is the same force which also brings down 
 the moon from the rectilinear path she would otherwise 
 pursue, and makes her fall a little way to the earth. In 
 Lecture XXI, Fig. 107, we have shown how, under this 
 double influence, a circle, an ellipse, or other conie sec- 
 tion, must be described ; and it was the discovery of these 
 things that has given so great an eminence to Sir Isaac 
 Newton, he having first proved that it is the same force 
 which compels a projectile to return to the earth and re- 
 tains the moon in her orbit. 
 
 But more than this, extending this conclusion to the 
 solar system generally, he showed that, as the moon is 
 retained in her orbit by the attractive influence of the 
 earth, so is the earth retained in hers by the attractive 
 influence of the sun. And taking the laws of Kepler 
 as facts established by observation, he proved, from the 
 equable description of areas by the radius vector, that 
 the force acting on the planets and retaining them 
 in their orbits must be directed to the center of the 
 sun. From Kepler's first law of the description of ellip- 
 tic orbits with the sun in one of the foci, he deduced the 
 law of gravitation or of central attraction generally 
 that is, that the force of attraction on any planetary body 
 is inversely proportional to the square of its distance 
 from the sun. And from Kepler's third law that the 
 squares of the times of revolution are as the cubes of 
 the major axes, he proved that the force of attraction is 
 proportionate to the masses. 
 
 The progress of knowledge from the time of Newton 
 until now has only served to establish the truth of these 
 great discoveries, and far from restricting them to our own 
 solar system, has shown beyond doubt that they apply 
 throughout the universe. The revolutions of the double 
 stars round one another are consequences of the same 
 laws which determine the orbitual movements of the sat- 
 ellites of Jupiter round their primary, or of Jupiter him- 
 self round the sun. I 
 
 Even those outstanding facts which, at an earlier pe- 
 riod, seemed to lend a certain degree of weight against 
 
 How may this reasoning be applied to the moon ? How to the solar 
 system generally ? What did Newton deduce from Kepler's laws '( Does 
 the same theory apply beyond the solar system ? 
 
NEWTON'S THEORY. 357 
 
 the full operation of the theory of Newton have, one 
 after another, become illustrations of its truth as they 
 have in succession become better understood. 
 
 Thus, for example, the deviations which the moon ex- 
 hibits from a truly elliptic orbit in her passage round the 
 earth, and which at first sight might seem to bear against 
 Newton's theory, are, when properly considered, the in- 
 evitable consequences of it. If the motions of the moon 
 were determined by the influence of the earth's attrac- 
 tion only, her orbit must be a perfect ellipse, always in 
 the same plane, and without any retrogradation of the 
 nodes. But observation shows that this is not the case; 
 and, in reality, Newton's theory could have predicted 
 what is actually the fact ; for the moon is not alone under 
 the influence of the earth, but, like the earth, simulta- 
 neously under the influence of the sun. In her monthly 
 revolution her distance alternately varies from the latter 
 body by nearly half a million of miles, in her opposition 
 being farther off, and in her conjunction being nearer to 
 him. The law of the inverse squares, therefore, comes 
 to apply ; and the result must be in some positions an ac- 
 celeration, and in some a retardation of her motion. And, 
 as her orbit is not coincident with the plane of the eclip- 
 tic, the action of the sun must necessarily tend to draw 
 her out of that plane, and thus produce the retrograde 
 revolution of her nodes. 
 
 The summation of the theory of Newton, therefore, 
 comes to this, that all masses of matter in the universe 
 attract one another with forces, the intensities of which, 
 at equal distances, are proportional to their masses, and 
 which, with equal masses, at different distances, are in- 
 versely proportional to the squares of those distances. 
 That the elliptical motion results from a primitive projec- 
 tile impulse impressed on the heavenly bodies by the 
 Creator, conjoined with the continuous agency of the at- 
 tractive force. Upon these principles every variety of 
 motion exhibited by the celestial bodies may be expound- 
 ed, whether it be the almost circular path described by 
 
 What should the moon's motion be if under the influence of the earth 
 alone? What is it in reality? To what cause is this due? How is it 
 that the sun impresses changes of velocity on the moon's motion, and 
 makes her nodes retrograde ? What are the principal points in Newton's 
 theory ? 
 
358 THE TIDES. 
 
 the moon round the earth, the excessively eccentric ellip- 
 ses described by some comets round the sun, or the para- 
 bolic or hyperbolic orbits followed by others ; in which case 
 they enter our system but once, and, having passed their 
 perihelion, leave it forever. Moreover, these principles 
 yield us a clear explanation of other facts at first not ap- 
 parently connected with them such as perturbations gen- 
 erally, the figure of the earth, and the tides, which are 
 caused in the sea by the conjoint influence of the sun 
 and the moon, as we shall now proceed to explain. 
 
 LECTURE LXX. 
 
 THE TIDES. Flood and Ebb-Tide. Spring and Neap- 
 Tide. General Phenomena of the Tides. Connection 
 with the Position of the Moon. Effects of the Diurnal 
 Rotation. Action of the Sun. Local Tidal Effects. 
 
 BY the tide we mean an elevation and depression of 
 the waters of the sea, occurring twice during the course 
 of a day. For about six hours the sea flows from south 
 to north ; it then remains stationary for about a quarter of 
 an hour, then ebbs in the opposite direction for about 
 six hours, is then stationary again for a quarter, and then 
 recommences to flow. To this elevation and depression 
 the names of flood and ebb are given. And as the ab- 
 solute height of the tides varies, as we shall presently 
 see, at different times, the highest tide is called a spring- 
 tide, and the lowest a neap-tide. 
 
 The space of time occupied in one flow and ebb is 
 about twelve hours and twenty-five minutes. There are, 
 therefore, two tides during one lunar day or, what is the 
 same, every time the moon crosses the meridian, whether 
 superior or inferior, there is a tide ; but the actual time 
 of high water out at sea is not at the instant when the 
 the moon is upon the meridian, but about two hours 
 later. 
 
 Mention some other phenomena which this theory explains. What is 
 meant by the tide ? Describe the principal phenomena of it. What is a 
 spring and what a neap-tide? What time is occupied in one ebb and 
 flow ? What is the position of the moon at the time of high water ? 
 
ACTION OF THE MOON. 359 
 
 There can be no doubt that it is the influence of this 
 luminary that is the cause of the tides. Her attraction 
 must necessarily render those portions of the sea that are 
 immediately beneath her of less weight, and, by the laws 
 of hydrostatics, they, therefore, must rise until an equi- 
 librium be established. But on those points which are 
 in quadrature with her, the effect of her action, by reason 
 of its obliquity, is to render them heavier ; and, as re- 
 spects those which are diametrically opposite to her, on 
 the other side of the earth, she must exert on them a less 
 powerful attraction than she does on the earth's center, 
 because they are more remote than it. From this ine- 
 quality and obliquity of the moon's action there must ne- 
 cessarily ensue an elevation on those parts of the sea 
 which are immediately beneath her, and also on those 
 which are on the opposite side of the earth ; but on those 
 positions which are situated at right angles to these points 
 there must be a depression. 
 
 When these considerations are combined with the fact 
 of the diurnal rotation of the earth on its axis it will be 
 perceived that the tide thus formed must necessarily 
 follow the apparent course of the moon, and that in any 
 given locality there must be high water and low water 
 twice in every lunar day. 
 
 In Fig. 365, let a b c d be the earth and M the moon ; 
 and let the shaded line sur- Fig. 365. 
 
 rounding the earth on all sides 
 represent its surface as cover- 
 ed with a uniform sea. Now, 
 as the attractive force of the 
 moon varies inversely as the 
 squares of the distance, it must 
 be strongest at a, more feeble 
 at b and d, and still more fee- 
 ble at c. Under this attractive 
 influence the waters at a will 
 necessarily rise, and the sea, 
 losing its perfectly spherical shape, will assume that of an 
 
 To what cause is the elevation of the water due ? What is the moon's 
 action on those parts of the earth nearest and most distant from her? 
 What on those parts at quadrature with them? Why does the tide fol- 
 low the apparent course of the moon I Describe the illustration given 
 in Fig. 365. 
 
360 ACTION OF THE MOON. 
 
 ellipsoid or, in other words, a tide will form upon it. 
 Arid, as the center of the earth at o is more attracted than 
 the point c, because it is nearer the moon, it will advance 
 toward the moon more than will the water at c ; and at 
 that point an elevation forms, so that at a and at c there 
 will be high water. But as respects the points I and d, 
 which are at the quadratures, the force of the moon, by 
 reason of the obliquity under which it is acting, may there 
 be decomposed; and if this be done it will be seen that 
 a part of that force is expended in increasing the weight 
 of particles in those positions or, in other words, making 
 them tend more powerfully toward the center of the earth. 
 Under these circumstances, therefore, there being a di- 
 minished weight at a and c, and an increased one at b and 
 d, the spherical form of the shell of water is lost; there is 
 an elevation at a and c and a depression at b and d, 
 high water at the former and low water at the latter 
 places. And as the earth rotates on her axis so as to 
 bring the moon upon the meridian in about twenty-four 
 hours and fifty minutes, in that space of time there must 
 be two tides. Were it not for this diurnal rotation there 
 would only be two sets of tides in a month. 
 
 As a movement communicated to the waters cannot 
 cease at once, and as the elevation of the water is moved 
 away from the moon by the earth's revolution, the water 
 still continues to rise for a certain time, although the point 
 of elevation is no longer immediately beneath the moon. 
 So the time of high water is not coincident with the pas- 
 sage of the moon over the meridian, but occurs somewhat 
 later. 
 
 In the same way that the moon thus produces tides in 
 the sea, so, too, must the sun. And, as his attractive 
 force is much greater than hers, it might, at first sight, 
 appear that he should give rise to far higher tides. But 
 his great distance makes a wide difference in the result ; 
 so that, in point of fact, the moon is almost three times 
 as energetic as he is. We have shown, in Fig. 365, how 
 much the obliquity of the moon's action on the points in 
 quadrature has to do with the final effect. Not so with 
 the sun. His influence on the different parts of the sea 
 
 Why is not the time of high water coincident with the moon's meridian 
 passage ? Does the sun act in the same manner as the moon ? What differ- 
 ence is there between him and the moon as respects obliquity of action ? 
 
SPRING-TIDES. 361 
 
 takes place almost in parallel lines, and, therefore, the 
 effect becomes feeble. Still the sun does each day pro- 
 duce two tides as the earth revolves, though they are tides 
 of much less magnitude than the lunar ones. 
 In Fig. 366 let E be the earth, M the moon, and S the 
 
 Fig. 366. 
 
 sun ; and, as before, let the shaded line round the earth 
 represent a uniform sea. Now, it is obvious that when 
 these bodies are in the position represented in the figure 
 the action of both will coincide, and they will jointly 
 raise a higher tide. Also the same must take place when 
 the sun being at S the moon is at M'. But these posi- 
 tions are evidently those of the new and the full moon, 
 and. therefore at these times the highest tides spring- 
 tides occur. 
 
 In this case the time of the greatest elevation of water 
 does not coincide with that of the passage of both lumi- 
 naries over the meridian, but occurs some time later. A 
 certain period is required in order to communicate motion 
 to the mass of the water. 
 
 * 
 
 From what does this arise ? How many solar tides are there in a day ? 
 Describe the illustration given in Fig. 366. At what times do spring- 
 tides consequently occur ? Does the time of greatest elevation coincide 
 with that of the passage of both luminaries over the meridian ? 
 
 3 
 
362 NEAP-TIDES. 
 
 Now, let the luminaries be as is represented in Fig. 
 3G7, where S is the sun, E the earth, surrounded by its 
 ocean, and M or M' the moon in either of the quadra- 
 
 Fiff. 367 
 
 tures. In this position the effect of one of the bodies 
 counteracts that of the other. Those points which in the 
 solar tide would be high water are low water for the 
 lunar tide. Under these circumstances the sea departs 
 much less from its undisturbed position, and the tidal 
 movements are less. This condition of things corresponds 
 to the neap-tides. Neap-tides, therefore, occur when the 
 moon is in her quadratures. 
 
 The actual rise of the tide differs very much in differ- 
 ent places, being greatly determined by local circum- 
 stances. Thus, in the bay of Fundy it sometimes rises 
 as high as eighty feet ; in the West Indies it is said to be 
 scarcely more than from ten to fifteen inches. These 
 modifications arise from a great variety of disturbing 
 causes, such as the interference of successive tide-waves, 
 the configuration of coasts, the prevalence of winds, &c. 
 In inland seas and lakes there are no tides, because the 
 moon acts equally over all their surface. 
 
 How is it that neap-tides occur ? What local atrcu instances affect the 
 tides. 
 
FIGURE OF THE EARTH. 363 
 
 , f - : LECTURE LXXI. 
 
 THE FIGURE AND MOTIONS OF THE EARTH. Astronomi- 
 cal Appearances connected with the Earth's Figure. 
 
 . Determination of the Length of a Degree. Actual Di- 
 mensions of the Earth. Amount of Oblateness. Diurnal 
 Rotation proved by the Oblateness. Annual Motion 
 Round the Sun proved frtim Aberration of the Stars.- 
 Determination of Latitudes. Determination of Longi- 
 tudes. 
 
 FROM considerations connected with the appearance of 
 objects at sea, or where there is an unobstructed view of 
 the horizon, we have already deduced the fact of the 
 globular figure of the earth. If any doubt remained on 
 this point it would be entirely removed by the well 
 known circumstance that, on very many occasions, navi- 
 gators have sailed round the world. 
 
 An observer situated near the equator sees the north 
 polar star upon the horizon, but as he travels toward our 
 latitudes the star seems to rise correspondingly in the 
 sky, and if he could pursue his journey far enough would 
 finally |?e over his head. . In this fact we have another 
 proof of the spherical figure of the earth ; for, were it a 
 flattened surface or a plane, such a change in the position 
 of the stars could not take place. 
 
 Seeing, therefore, that our earth is of a spherical figure, 
 it may easily be demonstrated that for every degree that 
 we go northward upon its surface, the north pole is ele- 
 vated a degree above the horizon. This observation fur- 
 nishes us with a ready means of determining the actual 
 magnitude of our planet. 
 
 " For this purpose it would be only necessary to select 
 two positions on the same meridian, at which there was 
 a difference in the elevation of the pole of one degree ; 
 the distance between those places, if measured, would be 
 _.i_ part of the entire circumference of the earth. The 
 problem of determining the dimensions of the earth re- 
 
 What simple facts afford proof of the globular figure of the earth ? On 
 what principle may we determine its magnitude ? 
 
364 FIGURE OF THE EARTH. 
 
 solves itself, therefore, into the measurement of the length 
 of a degree. 
 
 Measurements effected on these principles give for the 
 circumference of the earth 24,880 miles, from which we 
 deduce its diameter to be 7920. _; ' 
 
 But such measurements have also proved that the 
 value of a degree is not the same in all places ; for, as we 
 leave the equator and go toward the poles, the length of 
 the degree becomes greater. This, therefore, shows that 
 though the general figure of the earth is spherical, yet it 
 is not a perfect sphere : a perfect sphere must have its 
 degrees of uniform length; and such an increase in the 
 length of the degree can be explained on one principle 
 only that the earth is flattened toward the poles. 
 
 The analogies of other bodies in the solar system illus- 
 trate this explanation : both the great planets, Jupiter and 
 Saturn, are flattened toward the 
 poles, the former having his 
 polar diameter shorter than his 
 equatorial -Jy, and the latter -Jy. 
 Such an oblate spheroidal figure 
 is presented to us in the case of 
 an orange. This flattening is 
 seen in Fig. 368, where N S is 
 the polar diameter. From trig- 
 onometrical measurements of the 
 surface of the earth, it is infer- 
 red that the flattening is about ^I F , or that the polar is 
 shorter than the equatorial diameter by about twenty- 
 six miles. The earth may be regarded, therefore, as 
 having a zone or projecting ring upon its surface, which 
 has a maximum thickness immediately under the equator. 
 From the effect of gravity varying as the inverse square 
 of the distance from the earth's center, and from the 
 figure of the earth, its polar regions being nearer the 
 center than its equatorial, the weight of bodies must 
 change as we pass from the equator to the poles. Now, 
 the number of vibrations which a pendulum of given 
 
 What are the circumference and diameter of the earth in miles ? Is the 
 length of the degree the same in all places? What follows from this as 
 respects the earth's figure ? Is this conclusion verified in the case of 
 other planets? By how much does the equatorial exceed the polar 
 diameter ? 
 
CAUSE OF OBLATENESS. 
 
 3G5 
 
 length makes in a given time depends on the intensity of 
 gravity; and when one of these instruments is examined, 
 it is found to beat more rapidly as it approaches the 
 poles. This phenomenon has already been discussed in 
 Lecture XXV, and referred to its proper cause. From 
 the oscillations of a pendulum the figure of the earth 
 may be determined. 
 
 From a variety of facts, as well as from the general 
 analogy of every body in the solar system, the sun him- 
 self not excepted, we have deduced the fact of the daily 
 revolution of the earth on her own axis. It is the prop- 
 erty of all true philosophical theories to meet with con- 
 firmation under circumstances where we might have been 
 little likely to have expected it. And so, with the diurnal 
 revolution of the earth, it might be demonstrated from 
 the oblate spheroidal figure, had we no other proof of it; 
 but having such proofs in abundance, this comes as a 
 corroborative illustration ; for, as the earth revolves on 
 her axis, it must needs follow that she, like all other 
 revolving bodies, gives rise to a centrifugal force which 
 is as. the square of the velocity of rotation. At the equa- 
 tor where the speed of rotation is the greatest, and a 
 given point passes through 25,000 miles in 24 hours that 
 is, with more than the speed of a cannon-ball the centri- 
 fugal force is at a maximum, and from this point it de- 
 clines until at the poles it ceases. Let us call to mind 
 the experiment formerly ex- 
 hibited by the machine rep- 
 resented in Figure 369, in 
 which the two brass hoops, 
 a b, bent into a circular form 
 when they are made to re- 
 volve rapidly by turning the 
 handle of the multiplying- 
 wheel, depart from their cir- 
 cular shape and bulge out 
 into that of an ellipse ; and 
 according as the velocity of. 
 rotation is greater so is the 
 elliptical figure better mark- 
 How does this affect the weight of bodies and the beating of pendulums ? 
 How does the figure of the earth prove the fact of its diurnal rotation ? 
 What is the relation of the centrifugal force at the equator and at the poles ? 
 
 Fig. 369. 
 
366 ABERRATION OF THE STARS. 
 
 ed. It is then the diurnal revolution of the earth on her 
 axis which has given her a shape flattened at the poles, 
 and in the same way in the case of all the other great 
 planets, the flattening is immediately dependent on the 
 velocity of rotation. 
 
 We have already given so many proofs of the earth's 
 orbitual motion round the sun, that any thing further might 
 seem unnecessary. I shall, however, explain what is 
 meant by the aberration of the fixed stars, not only from 
 its intimate connection with one of the fundamental facts 
 in optical science the progressive motion of light but 
 also from its being a striking exemplification of the truth 
 here more immediately under consideration, the transla- 
 tory movement of the earth round the sun. 
 
 Let A B C D, Fig. 370, be the earth's orbit, and E any 
 given star. When the earth is at A, the star will be seen 
 in the line A E, and referred on the sphere of the heav- 
 ens to G. When the earth has passed through one half 
 of her orbit, and arrived at C, the star will be seen in the 
 line C E, and referred to F. From what has already been 
 said in relation to parallax, it will be understood that this 
 shifting of the star from G to F depends on its having a 
 measurable distance from the earth. 
 
 With a view of determining the parallax of one of the 
 stars, and consequently its distance from the earth, two as- 
 tronomers during the last century commenced observa- 
 tions founded on these principles ; and selecting the star y 
 in the constellation Draco, examined its position for the 
 several months in the year. Thus, for example, the earth 
 being at C in the month of September, and the star refer- 
 red to F : six months afterward that is in March the 
 earth being at A, they expected the star would change its 
 position, and be referred to G ; but, to their surprise, they 
 found the movement was in precisely the opposite direc- 
 tion, the star being seen at K, the movement being from 
 F to K, instead of from F to G. This is what is known 
 as "the aberration of the fixed stars," and its explanation 
 depends on the fact that, owing to light moving pro- 
 gressively and not instantaneously, and the eye of the ob- 
 
 Why is the figure of a planetary body thus connected with its rotation 
 on its axis ? How was the aberration of the fixed stars first discovered f . 
 What is the direction of the apparent motion of a star compared with 
 what it should be from parallax 1 
 
ABEEEATION OP THE FIXED STARS. 367 
 
 Fig. 370. 
 
 server accompanying the earth in her orbit, the position 
 of the stars is not the same as what it would be were the 
 earth at rest. The cause of this has been explained in 
 Lecture XXXVI. 
 
 It is constantly observed of true physical theories that 
 they afford explanations of facts, and, on the other hand, 
 receive illustrations from facts with which, at first sight, 
 
 How is this motion explained ? 
 
368 LATITUDE AND LONGITUDE. 
 
 they did not seem to be connected. The aberration of 
 the fixed stars proves two of the most prominent physical 
 theories with which, at the first sight, it does not seem to 
 be in the slightest degree allied the progressive motion 
 of light, and the earth's motion round the sun. 
 
 It is often a most important problem to determine the 
 position of a given point on the earth's surface. Navi- 
 gation essentially depends on determining with precision 
 the place of a ship at sea. To effect this two problems 
 have to be solved to find the latitude and also the longi- 
 tude. 
 
 The former of these is the more easily determined of 
 the two. It may be clone in several different ways : such 
 as by the zenith distance of stars, meridian altitudes of 
 the sun, or the east and west passage of a star through the 
 prime vertical. The latitude of a place being the eleva- 
 tion of the pole above the horizon, among other methods 
 it may, therefore, be ascertained by finding the greatest 
 and least altitudes of a circurnpolar siar , naif the sum of 
 those altitudes being equal to the latitude. Of course, 
 latitude is of two kinds northern and southern. In any 
 given instance, we indicate which by the letter N or S. 
 
 In like manner, there are several ways by which the 
 longitude of a place may be determined. Longitude is 
 estimated by the number of degrees upon the equator, in- 
 tercepted between the meridian of the place of observa- 
 tion and the meridian of some other place, taken as a 
 standard or starting-point, such as the meridian of Green- 
 wich or Washington. Since a given point on the earth 
 makes one complete revolution of three hundred and sixty 
 degrees in twenty-four hours, it will describe in one hour 
 fifteen degrees. In two places which are fifteen degrees 
 of longitude apart, the sun comes on the meridian of the 
 more westerly one hour later than on that of the other. 
 To find the longitude, therefore, is to find the difference 
 of the time of day between the place of observation and 
 that taken as the standard. For this purpose chronome- 
 ters are employed. 
 
 The eclipses of Jupiter's satellites and occultations of 
 stars by the moon, are predicted in appropriate almanacs, 
 
 How is the position of a place on the earth determined ? How may the 
 latitude be found ? How is longitude estimated ? How may it be found ? 
 What use is made of the eclipses of Jupiter's satellites and occultations? 
 
PERTURBATIONS. 369 
 
 with the exact moment of their occurrence at the stand- 
 ard meridian. It is, therefore, only necessary to mark the 
 time at which one of these occurs at the place of obser- 
 vation, and the difference of the times gives the longi- 
 tude. 5 
 
 LECTURE LXXII. 
 
 OF PERTURBATIONS. Action of Three Bodies. Variation 
 from an Elliptic Orbit. Inequalities of the Moon. 
 
 Conjoint Action of the Sun and Earth upon the Moon. 
 
 Annual Equation. Change in Position of the Nodes. 
 Precession of the Equinoxes. Discovery of the Planet 
 Neptune. 
 
 ON the principles of mechanics it may be demonstrated 
 that if a solitary planet revolve round a central sun, the 
 path which it describes must be an ellipse, from which it 
 would never deviate. But if a second planet or other at- 
 tracting body be introduced, then it follows, as a direct 
 consequence of the principle of universal gravitation, that 
 disturbance will ensue, and the revolving bodies, instead 
 of moving in exact ellipses, will follow new paths accord- 
 ing as their relation of distance to each other changes. 
 
 These results, which we thus foresee theoretically, are 
 verified in the heavens. The planetary bodies of our so- 
 lar system do not, as we have heretofore supposed, pur- 
 sue invariable elliptic paths round the sun, but each plan- 
 et attracts all the rest in the same way and under the same 
 laws that the sun attracts them all. His superior mass 
 predominates, and gives its general character to the re- 
 sulting movement, but the impression which each one 
 makes upon its neighbor is plain enough to be traced. 
 
 To these disturbances the general name of perturba- 
 tions is given, and when they occur between planets and 
 satellites the name of inequalities. They are secular and 
 periodical. In every instance they compensate one an- 
 other, so that after a certain period has elapsed, the dis- 
 
 What, on the principles of mechanics, must be the path of a single 
 planet ? If, instead of two, there be three bodies, what will be the result ? 
 How does this apply to the solar system ? What is meant by perturba- 
 tions and inequalities I Of what kinds are they ? 
 Q* 
 
370 
 
 INEQUALITIES OF THE MOON. 
 
 turbances have neutralized themselves, and every thing is 
 brought back to the original condition. 
 
 The inequalities of the moon arid the earth furnish us 
 with a clear illustration of these principles. In her 
 monthly revolution round the earth, the moon alternately 
 approaches to and recedes from the sun. Her distance 
 from the earth being about 240,000 miles, her distance 
 from the sun at conjunction and opposition differs by al- 
 most half a million of miles, and under the law of the in- 
 verse squares, his attractive force upon her corresponding- 
 ly changes. When in conjunction that is, between the 
 earth and the sun, his attraction acting more powerfully 
 on her she approaches toward him, and her distance 
 from the earth therefore increases : when in opposition, 
 the earth being the nearer, is more powerfully attracted, 
 and again the distance between the two is increased. 
 Thus, let S, Fig. 371, be the sun, E the earth, and A D B 
 C the orbit of the moon. If the moon be at her quad- 
 
 Fig. 371. 
 
 \ 
 
 rature, A, the distances of the moon and earth from the 
 sun are equal, and the attractive force maybe represented 
 by the lines A S, E S. Draw A L parallel and equal to 
 E S, and complete the parallelogram E A L S. The force 
 A S may be decomposed into two, A E directed toward 
 the earth's center and A L. While A L acts parallel to 
 E S, it does not produce any disturbance, but A E act- 
 ing toward the earth's center, increases the weight or 
 gravity of the moon, and makes her fall more toward the 
 earth : and the same will take place in the other quadra- 
 ture, B. 
 
 For these reasons we see that in the moon's conjunc- 
 
 Give an illustration of these principles in the case of the sun, earth, 
 and moon. 
 
PERTURBATIONS. 371 
 
 tion and opposition her gravity toward the earth is dimin- 
 ished, but at the quadratures it is increased. So that if we 
 were to conceive the sun absent, and the moon revolving 
 round the earth in a circle, if the sun were thfen intro- 
 duced his influence would make her describe an ellipse, 
 the longest axis of which would be at the 'quadratures! 
 It may seem somewhat paradoxical that the moon should 
 come nearest the earth when her weight is least; but 
 this is only an incidental thing : it arises from the cir- 
 cumstance that her approach is the result of the great 
 curvature of her orbit at the quadratures, and arises from 
 the velocity and direction she has acquired in conjunction 
 or opposition. 
 
 Under these circumstances the velocity of her motion 
 changes. The velocity diminishes from conjunction up 
 to the first quadrature, then increases up to opposition. 
 It diminishes again to the second quadrature, and increases 
 to conjunction. 
 
 It further follows, from the same principles, that, as the 
 earth revolves in her eJKptic orbit round the sun, at one 
 time approaching to him and at another receding, new 
 variations will arise, because the relative distances of the 
 earth, the moon, and tbe sun are changed, thus giving 
 rise to another inequality, which is called the annual 
 equation. 
 
 The foregoing explanation will set in its proper light 
 the nature of perturbation, and show how it necessarily 
 arises from the theory of gravitation. The subject in it- 
 self is exceedingly complicated in its applications, and far 
 exceeds the limits which I can here give to it. Connected 
 with the foregoing we may, however, trace a second in- 
 stance. The moon's nodes, or the points where her orbit 
 intersects the ecliptic, undergo an annual change of posi- 
 tion of more than 19, making a complete revolution in a 
 little more than eighteen years and a half. This disturb- 
 ance arises from the attraction of the sun ; for as the 
 moon's orbit is inclined at an angle of five degrees to the 
 ecliptic, as she revolves round the earth and approaches 
 
 At what periods is the moon's gravity to the earth increased and at 
 what diminished ? What effect does the sun exert on the orbit of the 
 moon? What changes take place in the moon's velocity? What is meant 
 by the annual equation ? What is the cause of the retrogradation of the 
 moon's nodes ? 
 
372 PRECESSION OF THE EdUINOXES. 
 
 the plane of the ecliptic, the sun's action brings her down 
 more quickly, and makes her cross the ecliptic sooner than 
 she would otherwise have done. 
 
 The list of these perturbations to which I shall now 
 allude explains the cause of the precession of the equinoxes. 
 At the time" that names were given to the signs of the 
 zodiac the vernal equinox coincided with the first point 
 of Aries. It is now more than thirty degrees to the west- 
 ward ; for the sun crosses the equator each year at a 
 point fifty seconds west of that in which he crossed it the 
 preceding year; and thus the equinoxial points will make 
 a complete revolution in 25,867 years, the seasons then 
 having completely run through all the months of the 
 year. 
 
 This phenomenon arises from the oblate figure of the 
 earth, resulting from her rotation upon her axis, the sun's 
 attraction being exerted upon the zone of matter which 
 surrounds the earth like a protuberance at the equator, 
 and tending to make it approach the plane of the ecliptic. 
 The equinoction points the points where the ecliptic 
 and equator intersect therefore recede, and the axis of 
 rotation of the earth moves with a conical motion round 
 the axis of the ecliptic. The pole of the earth's axis 
 describes, therefore, a circular motion round the pole cf 
 the ecliptic, completing its revolution in 25,867 years. In 
 successive ages the earth's pole points to different stars, 
 which become pole-stars in succession. 
 
 These examples may afford a general idea of the nature 
 of PERTURBATIONS, and show that, though they give rise 
 to effects which might appear contradictory to the theory 
 of universal gravitation, they are in reality, as has been 
 already observed, the necessary consequences of it. The 
 cases that we have been considering are very simple ; 
 but we can understand how difficult such problems be- 
 come where more complicated systems are under investi- 
 gation as, for example, Jupiter with his four satellites, 
 or Saturn with his ring and seven. Yet to so high a de- 
 gree of perfection has modern astronomy advanced, that 
 Herschel asserts " that there is not a perturbation, great 
 
 What is meant by the precession of equinoxes ? In what time do the 
 equinoxial points make one revolution? From what does this motion 
 arise? In what direction does the earth's axis consequently move? Do 
 any known perturbations affect the validity of Newton's theory ? 
 
MEASUREMENT OF TIME. 373 
 
 or small which observation has ever detected which has 
 not been traced up to its origin in the mutual gravitation 
 of the parts of our system, and been minutely accounted 
 for in numerical amount and value by strict calculation on 
 Newton's principles !" And of late we have witnessed 
 one of the most brilliant results of modern astronomy in 
 the discovery of the planet Neptune. For it was seen 
 that Uranus exhibited disturbances in his motions not ac- 
 counted for by the action of any known body. These 
 evidently pointed to the existence of some other mass be- 
 yond him, which, though unseen, was exerting its in- 
 fluence. The magnitude of this body and the position it 
 should occupy were determined by the calculus ; and, 
 on examining the region of the heavens designated, the 
 planet was found. 
 
 LECTURE LXXIII. 
 
 OF THE MEASUREMENT OF TIME. Sidereal Day. Solar 
 Day. Sidereal Year. Equation of Time. Mean and 
 Apparent Time. Incommensurability of the Day and 
 Year. The Julian Calendar. The Gregorian Calen- 
 dar. Conclusion. 
 
 IF we examine, by proper instruments, the time which 
 elapses between the successive passages of any star what- 
 ever over the meridian, we shall find that it is uniformly 
 23 hours, 56 minutes, 4 seconds. It is immaterial what 
 star is watched ; all give the same result. To this period 
 the name of a sidereal day is given. 
 
 But if, with the same instruments, we examine the me- 
 ridian passages of the sun we find that he does not come 
 upon the meridian until 3 minutes and 56 seconds later 
 each day, the clock measuring 24 hours between each 
 passage. To this period the name of a solar day is given. 
 
 Now, the apparent revolution of the celestial bodies is 
 due to the actual rotation of _the earth on her axis. It 
 \vould seem that the sun and the stars ought all to ac- 
 complish that apparent revolution in the same space of 
 
 What is meant by a sidereal day'? What is its length? What by a 
 solar day ? What is its length ? What do we infer as respects the appa- 
 rent motion of the sun ? 
 
374 MEAN AND APPAREIVT TIME. 
 
 time. It is, therefore, obvious that the sun must move 
 every 24 hours about one degree to the east : such a mo- 
 tion accounts for his coming later on the meridian ; for 
 one degree is passed over in about four minutes of time, 
 which is very nearly the period of retardation we have 
 observed. In 90 days the sun comes on the meridian 
 six hours later than the star with which he was first com- 
 pared. In about 180 days he is 12 hours later. In a lit- 
 tle more than 365 both come on the meridian together 
 again. But this apparent easterly motion of the sun is 
 in reality the orbitual motion of the earth in the opposite 
 direction, arid the solar day differs from the sidereal by 
 reason of the revolution of the earth round the sun. If 
 that revolution did not take place, and the earth only 
 turned on her axis, the solar and sidereal days would be 
 exactly of the same length ; but that revolution existing, 
 to bring the sun upon the meridian, the earth must make 
 a little more than one revolution each day, and, at the 
 end of 365 days, must turn on her axis 366 times that 
 is to say, in a year there is one more sidereal than there 
 are solar days. The actual length of the sidereal yearis 
 366 days, 6 hours, 9 minutes, 12 seconds. 
 
 These considerations show how the measurement of 
 time becomes complicated by the annual motion of the 
 earth round the sun ; and, as the axis of the earth is in- 
 clined to her orbit, and she moves with different degrees 
 of velocity in different parts of her elliptic path, more 
 swiftly as she approaches the sun and more slowly as she 
 recedes, the length of the days will vary from time to 
 time, when compared with a clock that goes truly, giving 
 rise to a difference between the time indicated by the 
 sun and a clock a difference which is called the equa- 
 tion of time. Mean time is that indicated by the clock, 
 and apparent time that indicated by the sun. 
 
 From the inclination of the earth's axis to the ecliptic 
 it comes to pass that about the 20th of March, the 21st 
 of June, the 23d of September, and the 21st of Decem- 
 ber the sun and the clock would agree ; but between 
 March and June the sun is faster than the clock ; from 
 then until September it is slower, and so on. The differ- 
 How does his meridian passage compare with that of any given star? 
 What is the length of the sidereal day ? To what is this difference due ? 
 What is equation of time? What is mean time ? What is apparent tirrvo ? 
 
THE JULIAN CALENDAR. 375 
 
 ent velocity with which the earth moves in her orbit com- 
 plicates this, and from the two causes together the coin- 
 cidence takes place on other days on the 15th of April, 
 the 15th of June, the 31st of August, and the 24th of De- 
 cember, while the greatest difference between the sun 
 and clock, amounting to 16 minutes, takes place on the 
 1st of November. 
 
 The principal natural division of time is into days and 
 years a division which is based upon civil wants, and 
 which,' therefore, from the earliest period was adopted. 
 At a very remote time it was discovered that the year con- 
 tained about 365 days; and this was probably the first 
 exact division ; but after a while it was discovered that 
 the two periods are in reality incommensurable, and that 
 there are more than 365 and less than 366 days in a year. 
 The tropical year, as we have already stated, consists of 
 865 days, 5 hours, 48 minutes, 49 seconds. 
 
 The first great historic change in the calendar was 
 made by Julius Caesar, who, having learned in Egypt, that 
 the year really consisted of 365 days and 6 hours nearly, 
 endeavored to include these 6 hours by adding one day to 
 each fourth year. So he instituted three years of 365 days, 
 and a fourth of 366. The latter was called Bissextile. 
 The twelve months consisted, some of thirty and s^me of 
 thirty-one days, but February had only twenty-eight in 
 common years, and to it twenty-nine were given in bissex- 
 tile. This is the Julian calendar-. 
 
 It is evident, however, that Julius Caesar had thus over- 
 compensated the year. It does not consist of 365 days 
 and 6 hours, but wants 11 minutes and 11 seconds of it. 
 For a short period this small quantity may be neglected, 
 but in the course of centuries it becomes very appreciable. 
 In the year 1582 it had amounted to more than ten days. 
 At this time Pope Gregory XIII. published a bull requir- 
 ing that ten days should be cut oft from that year, and the 
 fifth of October be reckoned as the fifteenth, and by a most 
 ingenious and simple contrivance, provided against the 
 future recurrence of the difficulty. The years are to be 
 
 "On what days do the sun and the clock agree? When is there the 
 greatest difference ? What is the principal division of time ? Are the day 
 and the year commensurable ? What is the length of the tropical year? 
 What is the Julian calendar ? In what was it defective ? What was the 
 excess of compensation ? 
 
376 THE GREGORIAN CALENDAR. 
 
 enumerated by the vulgar chronology of the birth of 
 Christ, and each year, the number of which is not divisi- 
 ble by 4, is to consist of 365 days ; but every year which 
 is divisible by 4 must have 366, except it be also divisible 
 by 100. Every year which is divisible by 100, but not 
 by 400, has 365, and every year divisible by 400 has 366. 
 
 The result of this is, that in 400 years three bissextiles 
 are cut off. The year 1600 was bissextile ; 1700, 1800, 
 and 1900 are not ; but the year 2000 will be, and so per- 
 fect is this contrivance that the derangement will be less 
 than one day in the course of 3000 years. Even this 
 might be avoided if the years divisible by 4000 should 
 be made to consist of 365 days, and then, in the course of 
 one hundred thousand years, the derangement of the cal- 
 endar would not amount to a single day. This is the 
 Gregorian calendar, or new style. It is received now in 
 all Christian countries, save those in which the mode of 
 faith is according to the Greek church their years and 
 festivals occur twelve days later than ours. 
 
 It is scarcely necessary to add the subsidiary division 
 of time : The week, consisting of seven days a prime- 
 val division, which is to be traced in all countries, and 
 which has survived all legislative enactments and changes 
 of empires, because it is suitable to the wants, and com- 
 mends itself, with its seventh day of rest, to the well-be- 
 ing of man ; the month, which consists of four weeks ; 
 and the seasons, of which there are four in each year-^ 
 spring, summer, autumn, and winter. The names of the 
 seven days of the week are derived from those of the sun, 
 moon, and planets an observation which holds even for 
 modern languages. These names were imposed by pious 
 men at a very remote period ; for they, having remarked 
 the geometrical beauty of the revolutions of the stars, and 
 the amazing punctuality with which they complete their 
 periodic motions, were led to suppose that they were 
 guided by, or rather were the residences of intellectual 
 principles. They little foresaw how the great discovery 
 of Newton universal, gravitation would remove the hy- 
 pothetical beings they thus worshipped, from, the domains 
 
 By whom and when was this corrected? How did he adjust the calen- 
 dar? To what degree of perfection does this division reach ? What is 
 New Style? In what countries is it not adopted ? What other popular 
 divisions of time have we ? From what are the names of the days derived ? 
 
CONCLUSION. 377 
 
 of the solar system, and replace them by one far-reach- 
 ing mechanical principle a principle so enduring, so un- 
 changeable, that relying on it the astronomer is able to 
 look equally into the past and. the future, reproducing an- 
 cient events, or predicting those that are to take place in 
 coming centuries; and this not in a doubtful or shadowy 
 manner, but with all the precision of time, place, and cir- 
 cumstance. And this is the uniform course of human, 
 knowledge : things which are imputed by one generation 
 to special and incessant interpositions of divine agents, 
 are discovered by another to be the direct results of eter- 
 nal and uniform laws ; and the Universe, far from owing 
 its permanence and regularity to the cares of a thousand 
 gods and goddesses, contains within itself its own princi* 
 pies of conservation all its perturbations run through 
 their particular cycles, and then they compensate them- 
 selves, and every thing returns to its pristine condition. 
 It contains no element of destruction, nor even of decay, 
 and could, under the simple laws impressed upon it, con- 
 tinue its existence through all eternity, except its Al- 
 mighty Maker a monument of whose power and wisdom 
 it is should see fit to interfere. 
 
INDEX. 
 
 Aberration of light, 177. 
 stars, 367. 
 
 Accidental colors, 231. 
 Achromatic lens, 203. 
 Acoustics, 157. 
 Acoustic figures, 169. 
 Action and reaction, 79. 
 Air-pump, 17. 
 Annual parallax, 349. 
 Anomaly, 354. 
 Archimedes's screw, 65. 
 Areometers, 53. 
 Artesian wells, 59. 
 Asteroids, 334. 
 Astronomy, 315. 
 Atmosphere, 12. 
 
 color of, 13. 
 
 height of, 13. 
 A tt wood's machine, 87., 
 Aurora borealis, 287. 
 
 B. 
 
 Balance, 129. 
 Ballistic pendulum, 94. 
 Bali-cock, 68. 
 Balloon, 37. 
 Barometer, 24. 
 Beaume's hydrometer, 54. 
 Bellows, hydrostatic, 48. 
 Boiler, 270. 
 
 Bohnenberger's machine, 80. 
 Boyle's law, 31. 
 Bramah's press, 49. 
 Breast-wheel, 63. 
 Burning- lens, 195. 
 
 C. 
 
 Camera obscura, 232. 
 Capacity for heat, 258. 
 Capillary attraction, 101. 
 Cartesian images, 29. 
 Center of gravity, 110. 
 Chromatic aberration, 202. 
 Colors, 200. 
 Comets, 338. 
 Composition of forces, 73. 
 
 Compound motion, 72. 
 Compressibility of air, 14. 
 Condenser, 29. 
 Contracted vein, 61. 
 Conduction of heat, 253. 
 Cords, vibrations of, 163. 
 Currents in air, 37. 
 Cycloid, 118. 
 
 Daniel's hygrometer, 276. 
 Decomposition of water, 300. 
 Differential thermometer, 247 
 Diffraction, 209. 
 Diiftision, 39. 
 Direction of motion, 70. 
 Dispersion of light, 196. 
 Distinctive properties, 2. 
 Diving-bell, 6. 
 Divisibility, 8. 
 
 E. 
 
 Earth, figure of, 364. 
 Echoes, 166. 
 Eclipses, 343. f 
 
 Elastic impact, 122. 
 Elasticity, 7. 
 
 of air, 15,28. 
 Electricity, 288. 
 Electro-dynamic helix, 308. 
 Electrometer, 297. 
 Slectro-magnetism, 304. 
 Ulectrotype, 303. 
 Cndosmosis, 105. 
 Exchanges of heat, 251. 
 Expansion, 257. 
 Evaporation, 262. 
 xtension, 2. 
 
 F. 
 
 'ailing bodies, 85. 
 ixed lines, 199. 
 'loating bodies, 67. 
 'lorentine experiment, 43. 
 "lowing of liquids, 60. 
 >rces, 9. 
 
 composition of, 73. 
 
380 
 
 INDEX. 
 
 Forcing-pump, 64. 
 Forms of bodies, 1. 
 Fountain in vacuo, 27. 
 Fountains by pressure, 57. 
 Friction, 142. 
 
 G. 
 
 Gases, specific gravity of, 52. 
 Gravity, 70. 
 Gravitation, 80. 
 Gravimeter, 54. 
 Gregorian calendar, 376. 
 
 H. 
 
 Heat, properties of, 244. 
 Heights, determination of, 25. 
 Hydraulic press, 49. 
 Hydro-dynamics, 45. 
 Hygrometry, 272. 
 
 Impenetrability, 3. 
 Inclined plane, 137. 
 
 motion on, 90. 
 Induction, 293. 
 Inequalities, 370. 
 Inertia, 77. 
 Interference, 154. 
 
 J. 
 
 Julian calendar, 375. 
 Jupiter, 334. 
 
 K. 
 
 Kepler's laws, 355. 
 
 Latent heat, 260. 
 
 Latitude, 368. 
 
 Lenses, 190. 
 
 Level of liquids, 46. 
 
 Lever, 127. 
 
 Leyden jar, 294. 
 
 Light, properties of, 168. 
 
 theories of, 205. 
 
 velocity of, 176. 
 Liquids, properties of, 41. 
 pressures of, 56. 
 Longitude, 368. 
 
 M. 
 
 Machines, electrical, 290. 
 Magdeburg hemispheres, 22. 
 Magic lantern, 236. 
 Magnetism, 278. 
 
 terrestrial, 283. 
 
 Magneto-electricity, 309. 
 Marriotte's law, 31. 
 Mars, 333. 
 
 Mechanical powers, 126. 
 Mercurial pendulum, 120. 
 Mercury, 329. 
 Microscope, 233. 
 Mirage, 226. 
 Momentum, 78. 
 Monochord, 162. 
 Moon, 340. 
 
 Montgolfier's balloon, 37. 
 Motion, 69. 
 
 Motion round a center, 94. 
 Multiplier, 305. 
 Multiplying-glass, 189. 
 
 N. 
 
 Nebulae, 351. 
 Neptune, 337. 
 Newton's laws, 80. 
 rings, 208. 
 
 O. 
 
 Occultation, 345. 
 Oersted's machine, 44. 
 Overshot-wheel, 62. 
 
 P. 
 
 Parachute, 33. 
 Paradox, hydrostatic, 48. 
 Parallax, 323. 
 Passive forces, 141. 
 Pendulum, 116. 
 Percussion, 121. 
 Perturbations, 369. 
 Photometry, 172. 
 Planetary motions, 97. 
 Plumb-line, 84. 
 Pneumatic trough, 23. 
 Point of application, 70. 
 Polarization, 210. 
 Precession of equinox, 372. 
 Pressure of air, 21. 
 
 hydrostatic, 47. 
 
 of liquids, 56. 
 Prism, 188. 
 Projectiles, 92. 
 Psychrometer, 277. 
 Pulley, 131. 
 Pump, 63. 
 
 R. 
 
 Radiant heat, 249. 
 Radius vector, 98. 
 Rainbow, 221. 
 
INDEX. 
 
 381 
 
 Refraction, 184. 
 Refraction, double, 21 5. 
 
 of heat, 252. 
 
 atmospheric, 223. 
 Reflexion, 178. 
 Resistance of air, 32. 
 
 of media, 143. 
 Resolution of forces, 75. 
 Rest, 69. 
 Rigidity of cordage, 145. 
 
 S. 
 
 Sap, rise of, 106. 
 
 Saturn, 335. , 
 
 Saussure's hygrometer, 275. 
 
 Screw, 139. 
 
 Sea', 41. 
 
 Seasons, 326. 
 
 Shadows, 171. 
 
 Solar micrdscope, 237. 
 
 system, 337. 
 Soniferous media, 159. 
 Sound, 157. 
 
 conducted, 34, 158. 
 Specific gravity, 50. 
 Specific heat, 260. 
 Spectacles, 230. 
 Spherometer, 5. . 
 Spouting of liquids, 61. 
 Stability of bodies, 113. 
 Stars, fixed, 346. 
 Steam engine, 267. 
 Stream-measurer, 62. 
 Strength, 108. 
 Sun, 324. 
 Syphon, 66. 
 Syringe, 18. 
 
 T. 
 
 Telegraph, magnetic, 312. 
 Telescope, 238. 
 Thermo-electricity, 313. 
 Thermometer, 245. 
 Thousand-grain bottle, 51. 
 Tides, 358. 
 Time, 373. 
 Torsion balance, 109. 
 Transits, 332. 
 Trumpet, hearing, 167. 
 
 speaking, 166. 
 Twilight, 225. 
 
 Unchangeability, 4. 
 Undershot-wheel, 62. 
 Undulations, 14T. 
 Undulatory theory, 205. 
 Uranus, 336. 
 
 V. 
 
 Vapors, 265. 
 Venus, 329. 
 Vera's pump, 65. 
 Vibrations, 148. 
 Virtual velocities, 127. 
 Voltaic battery, 298. 
 
 W. 
 
 Water, compressibility of, 44. 
 Wedge, 138. 
 Weight of air, 19. 
 Wheel and axle, 134. 
 Windlass, 135. 
 
 Z. 
 
 Zaniboni's piles, 296. 
 
 THE END. 
 
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WORKS FOR COLLEGES AND DISTRICT SCHOOLS. 13 
 
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14 WORKS FOR COLLEGES AND DISTRICT SCHOOLS. 
 
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