LIBRARY OF THE UNIVERSITY OF CALIFORNIA. GIFT OF" Glass k n or THE f UNIVERSITY J *UFOBSi> NEW EDITION OF STEELE'S PHILOSOPHY. FOURTEEN WEEKS IN PHYSICS BY J. DORMAN STEELP; PH.D., F.G.S., AUTHOR OF THE FOURTEEN- WEEKS SERIES IN NATURAL SCIENCE. ' The works of Qod are fair for naught. Unless our eyes, in seeing, S&& hidden in the thing the thought That animates it* A. S. BARNES & COMPANY, NEW YORK AND CHICAGO. (Copyright, 1869, 1878.) . A POPULAR SERIES NATURAL SCIENCE, BY J. I30R1MAN STKEIvE, F*H.D., K.O.S., A uthor of the Fourteen Weeks Series in Natural Science, etc., etc. New Popular Chemistry. New Descriptive Astronomy. New Popular Physics. New Hygienic Physiology. New Popular Zoology. Popular Geology. An Introduction to Botany. The Publishers can supply (to Teachers only) a Key containing Answers to the Questions and Problems in Steele's entire Series. BARNES' HISTORICAL SERIES, ON THE PLAN OK STEELE'S FOURTEEN-WEEKS IN THE SCIENCES. A Brief History of the United States. A Brief History of France. A Brief History of Ancient Peoples. A Brief History of Mediaeval and Modern Peoples. A Brief General History. A Brief History of Greece. A Brief History of Rome. A Popular History of the United States. work has grown up in the class-room. It con- -L tains those definitions, illustrations, and applications which seemed at the time to interest and instruct the author's pupils. Whenever any explanation fixed the atten- tion of the learner, it was laid aside for future use. Thus, by steady accretions, the process has gone on until a book is the result. As Physics is generally the first branch of Natural Science pursued in schools, it is important that the beginner should not be wearied by the abstractions of the subject, and so lose interest in it at the very start. The author has therefore endeavored to use such simple lan- guage and practical illustrations as will attract the learner, while he is at once led out into real life. From the mul- titude of philosophical principles, only those have been selected which are essential to the information of ever}' well-read person. Within the limits of a small text-book, no subject can be exhaustively treated. This is, however, of less importance now, when every teacher feels that he must of necessity be above and beyond any school-work in the fulness of his information. The object of an elementary work is not to advance the peculiar ideas of any person, but simply to state the currently-accepted facts and theories. The time-honored classifications recog- nized in all scientific works, have been retained. In order 139140 PREFACE. to familiarize the pupil with the metric system, now gen- erally used by scientific men, it is continually employed in the problems. The notes contain many illustrations and additional suggestions, but their great value will appear in the descriptions of simple experiments which are within the reach of any pupil. New plates being required for this edition, the author has taken the opportunity thoroughly to revise the entire work. By carefully comparing the criticisms of teachers, he has tried to obtain the "parallax" of all its statements and methods, and to eliminate, as far as possible, the errors growing out of his "personal equation." Hearty thanks are tendered to the many friends of the book who, by their suggestions and criticisms, have so greatly added to the value of this revision. To name them all in this Preface would be impossible, and to discriminate would be invidious. The author cannot, however, allow the opportunity to pass without expressing his profound sense of obligation. By untiring study and the continued help of his friends, he hopes thus, year by year, to make the series more and more worthy the favor which his fellow-teachers have so abundantly bestowed upon it. Happy indeed will he be if he succeed in leading some young mind to become a lover and an interpreter of Nature, and thus come at last to see that Nature herself is but a "thought of God." TABLE OF CONTENTS. fAGH 1,INTRODUCTION . n MATTER , 13 II. MOTION AND FORCE . 25 THREE LAWS OF MOTION ... 28 CONSERVATION OF ENERGY ... 37 III. ATTRACTION 41 MOLECULAR FORCES . . 43 GRAVITATION 52 IV. ELEMENTS OF MACHINES . . . 67 V. PRESSURE OF LIQUIDS AND GASES 81 HYDROSTATICS 83 HYDRAULICS . 97 PNEUMATICS 103 VI. ACOUSTICS 121 VII. OPTICS . ..... 147 VIII. HEAT 181 TABLE OP TX. ELECTRICITY ' A K . 209 X, -APPENDIX 2 S5 r. QUESTIONS 257 2. TABLES ' 273 3- BLACKBOARD DRAWINGS . 275 4- INDEX 301 TO OTUDENTS are expected to obtain information from this book, *-} without the aid of questions, as they must always do in their general reading. When the subject of a paragraph is announced, the pupil should be prepared to tell all he knows about it. He should never be allowed to answer a question, except it be a short definition, in the language of the book. The diagrams and illustrations, as far as pos- sible, should be drawn upon the blackboard and explained. Although pupils may, at first, manifest an unwillingness to do this, yet in a little time it will become an interesting feature of the recitation. In his own classes, the author has been accustomed \.o place upon the blackboard the analysis of each chapter of the book, and require the piipils to recite from that, without the interposition of questions, except such as were neces- sary to bring out the topic more clearly or to throw a side light upon it. Where the analysis given in the book does not include all the minor points of the lesson, the pupils can easily supply the omission. The " Practical Questions " given at the close of each general subject have been found a profitable exercise in awakening inquiry and stimu- lating thought. They may be used at the pleasure of the instructor. The equations contained in the text are designed to be employed in the solution of the problems. It should constantly be borne in mind that, as far as possible, every question and principle should be submitted to Nature for a direct answer by means of an experiment. Pupils should be encouraged to try the simple illustrations necessary. The scholar who brings in a bit of apparatus made by himself, does better than if he were merely to memorize pages of text. The objective or inductive method has been largely adopted in this book in order to lead the pupil thus to question Nature and so verify each principle for himself. Where, however, it seemed that a subject could be more easily apprehended by using the didactic method, the author has not hesitated to adopt it. The true teacher is not the slave of any system, but employs in each case the X SUGGESTIONS TO TEACHERS. one that best subserves his end. Moreover, our pupils are not to become discoverers, and so need not necessarily pursue the oftentimes tedious path of original investigation ; while all the powers of the mind should be developed harmoniously with that of observation. Still, where the didactic method of presentation is employed, the pupil should, wherever possible, perform the experiments, and so be enabled to grasp the fact or principle as he cannot by any abstract description, however vivid. The following works, to which the author acknowledges his obliga- tion for valuable material, will be useful to teacher as well as pupil, in furnishing additional illustrations and in elucidating difficult sub- jects, viz. : Tail's Recent Advances in Physical Science ; Arnott's Ele- ments of Physics' (7th ed.) ; Stewart's Elementary Physics, Conserva- tion of Energy, and Treatise on Heat ; Atkinson's Deschanel's Natural Philosophy ; Lockyer's Guillemin's Forces of Nature ; Herschel's In- troduction to the Study of Physical Science; Tomlinson's Introduction to the Study of Natural Philosophy ; Pepper's Play-book of Science ; Beale's How to Work with the Microscope ; Schellen's Spectrum Analysis; Lockyer's The Spectroscope and Studies in Spectrum Analysis ; Airy's Geometrical Optics ; Nugent's Optics; Chevreul on Colors ; Thomson & Tail's Natural Philosophy ; Maxwell's Electricity and Magnetism ; Faraday's Forces of Matter ; Youmans's Correlation of Physical Forces ; Maury's Physical Geography of the Sea ; Atkin- son's Ganot's Physics ; Silliman's Physics ; Tyndall's Lectures on Light, Heat, Sound, Electricity, and Forms of Water; Snell's Olm- sted's Philosophy (revised edition) ; Loomis's Meteorology ; Miller's Chemical Physics; Cooke's Religion and Chemistry, and also nu- merous works named in the Reading References at the close of each general division. They may be procured of the publishers of this book. The pupil should continually be impressed with the thought that the text-book only introduces him to a subject, which he should seek every opportunity to pursue in larger works and in treatises on special topics. As heretofore, the author will be pleased to correspond with teach- ers concerning the apparatus for the performance of the experiments, or with reference to any of the " Practical Questions." THEORIES. SINCE the revision of this book in 1878 there have been many discoveries made in Physical Science. Some of these are now essential to the proper conception of even elementary principles, while others are interesting as opening up fresh fields of investigation. Experience has also suggested novel illustrations, as well as brought old truths into prominence. (P. 70.) " The arms of a lever are the two portions of it intermedi- ate, respectively, between the fulcrum and the power, and between the fulcrum and the weight. If the lever is bent, or if, though straight, it is not at right angles to the lines of action of the power and weight, it is necessary to distinguish between the arms of the lever as above defined and the arms of the power and the weight regarded as forces which have moments round the fulcrum. In this latter case the arms are the perpendicitlars dropped from the fulcrum upon the lines of action of the power and weight." (P. 130.) An interesting illustration of the reflection of sound is found at the so-called Echo River, of the Mammoth Cave, Ky. Sound- ing in succession the notes G, E, C, at the middle of the tunnel, the boatman receives the echoes, all mingled into a full chord, for eight or ten seconds afterward. (P. 164.) Langley's recent experiments near the summit of Mount Whitney place the maximum of the heat curve (Fig. 159) in the orange or orange-yellow instead of the ultra-red. " The sun's most intense radiations are not the invisible ones as has been so long supposed, but the wave-length representing the maximum of heat does not differ widely from that representing the maximum of light." While the pupil, for convenience, uses the terms heat, light, and chemical rays, he should bear in mind the-truth that these rays differ not in quality, but only in pitch. Xll FRESH FACTS AND THEORIES. (P. 174.) The full explanation of stereoscopic relief is not so sim- ple as that indicated by Fig. 172. The effect of solidity, or depth in space, is indeed due to the apparent blending of two slightly different pictures, by causing the image of one of them to be formed on one retina and of the other on the corresponding part of the other retina. But the apparent locality of the combined external picture is not deter- mined by the meeting of visual lines at C, as was long thought true. It is merely an illusion of judgment. The pictures A and B (Fig. 172) may be so far apart that the visual lines become parallel or even diver- gent. The combined image then appears still in front, but farther away, larger, and deeper. By crossing the visual lines so that the right eye is directed to A and the left eye to B (Fig. 173), the image appears smaller and nearer. The perspective is now reversed so that the tunnel appears like a mutilated cone floating in the air, with the smallest part nearest, while two companion tunnels remain, one on each side. (See art. on Stereoscope, Pop. Sc. Monthly, May & June, '82.) (P. 194.) The disks in Grookes's Radiometer are now made of aluminium rather than pith, the object being to obtain a maximum absorption of heat on one face which is covered with lamp-black, and minimum absorption on the other which is therefore best made of a bright but light metal. Mica also is used. (P. 194.) In the course of Prof. Langley's experiments upon Mount Whitney, water was boiled by exppsing it in a copper vessel covered by a pane of window-glass, to the direct rays of the sun. This shows how many of the heat-rays of the sunbeam are stricken down by the air before reaching low levels, but may be utilized at high elevations. So that, paradoxical as it may seem, it is certain that, were the atmo- sphere removed, the earth would receive far more heat and yet be much colder than now. (See American Journal of Science, March, 1883.) (P. 201.) " Numerous observations made in recent years show that the bottom of the ocean, even in equatorial regions, is at a temperature not much higher than that at which fresh water freezes. This cold water has doubtless found its way along the depths of the sea from the polar regions, while a general flow from equator to poles is taking place nearer to the surface. In connection with oceanic circulation it is to be noted that sea water (unlike fresh water), when cooled, con- tinues to contract until it reaches its freezing point." I. INT<& O 0 o of a grain of strychnine, yet this amount can be distinctly tasted. 4. Porosity is the property of having pores. By this is meant not indeed the sensible pores to which we refer when in common language we speak of a porous body, as bread, wood, unglazed pottery, a sponge, etc., but the finer or physical pores. The latter are as invisible to the eye as the * IE common language, we say a needle penetrates cloth, a nail enters wood, etc. : but a moment's examination shows that they merely push aside the fibres of the cloth or wood, and so press them closer together. With care we can drop a quarter of a pound of shingle-nails into a tumbler brimfull of water, without causing it to over- flow. The surface of the water, however, becomes convex. t Newton estimated that the film of a soap-bubble at the instant of breaking is less than 5^000 of an inch thick. Pure water will acquire the requisite viscidity for making bubbles by adding only T o part of soap. It is evident that there must be at least one molecule of soap in every cubic aa^poo of an inch of the film, and that the molecule must be smaller than one-hundredth of a cubic ^fosoos of an inc h. * -i than rTS ;i__ trillionths of a cubic inch. Now a molecule of soft-soap (if it is a pure potas- sium stearate, Chemistry, p. 219) contains 56 atoms, and this point must be reached before we come to the possible limit of divisibility. Some idea of the vastness expressed by the word trillion may be derived from the estimate that if Adam, at his creation, had commenced to count one every second of time, he would not yet have completed the first quarter of a trillion ; and if Eve had come to his relief, and they had counted day and night, they would not see the end of their task for 1U,000 years to come. (See also note on electric sparks, p. 236.) GENERAL PROPERTIES OF MATTER. 17 atoms themselves, and are caused by the fact that the mole- cules of which a body is composed are not in actual contact, but are separated by minute spaces.* Ex. : to a bowl-full of water it is easy to add a quantity of fine salt without the liquid running over. Only care must be taken to drop in the salt slowly, giving time for it to dissolve and the bubbles of air to pass off. When the water has taken up all the salt it will, we can still add other soluble solids, f In test- ing large cannon by hydrostatic pressure (p. 85), water is forced into the gun until it oozes through the thick metal and cov- ers the outside of the gun like froth, then gathers in drops and runs to the ground in streams. J The process of filtering, so much employed by druggists, depends upon this property; the liquid slowly passes through the pores of the filter, leaving the solid portions behind. Water, in Na- ture, is thus purified by perco- lating through beds of sand and * These spaces are so small that they cannot be discerned with the most power- ful microscope, yet it is thought that they are very large when compared with the size of the atoms themselves. If we imagine a being small enough to live on one of the atoms near the centre of a stone, as we live on the earth, then we are to suppose that he would see the nearest atoms at great distances from him, as we see the moon and stars, and might perchance have need of a fairy telescope to examine them, as we investigate the heavenly bodies. t In this case we suppose that the particles of salt are smaller than those of water, and those of the different substances used are smaller than those of salt. The parti- cles of salt fill the spaces between the particles of water, and the others occupy the still smaller spaces left between the particles of salt. We may better understand this if we suppose a bowl filled with oranges. It will hold a quantity of peas, then of gravel, then of fine sand, and lastly some water. % In the course of some experiments performed during the 18th centuiy at the Florence Academy, Italy, hollow globes of silver were filled with water and placed in a screw-press. The spheres being flattened, their size was diminished, and the water oozed through the pores of the metal. The philosophers of the day thought this to show that water is incompressible. We now see that it proved only that silver baa pores larger than the molecules of water. 18 . INTRODUCTION. gravel. Cisterns for filtering water have a brick partition in the middle. The water is cleansed as it soaks through the porous brick. Small filters are frequently made of a cask nearly filled with gravel and charcoal ; the water is poured in a little reservoir at the top and drawn off at the bottom by a faucet. 5. Inertia is the negative property of passiveness. * Mat- ter has no power of putting itself in motion when at rest, nor of coming to rest when in motion. A body will never change its place unless moved, and if once started will move forever unless stopped. Ex. : If we leave the room, and on our return find a book missing, we know some one has taken it the book could not have gone off of itself. 6. Indestructibility is the property which renders mat- ter incapable of being destroyed. No particle of matter can be annihilated, except by God, its creator. We may change its form, but we cannot deprive it of existence. Ex. : We cut down a tree, saw it into boards, and build a house. The house burns, and only little heaps of ashes remain. Yet in the ashes, and in the smoke of the burning building, exist the identical atoms, which have passed through these various forms unchanged, f * The common idea of inertia is that matter actively resists any change ; and that when we lift a heavy stone, for example, we must overcome the determined opposi- tion of the body to be moved. Matter possesses no such property. The seeming obstinacy is due to the fact that time is required to impart motion to a body at rest, and to overcome the momentum of a body in motion. The illustrations ordinarily given of inertia are really examples of a law of motion. We are also accustomed to think a body is more inclined to rest than to motion ; and so, while we see how a stone could not throw itself, we find it difficult to understand how, once thrown, it does not stop itself. We shall see hereafter that several forces destroy its motion and bring it to rest. (See pp. 28, 29, and Questions 55-62, p. 89.) t Walter Raleigh, while smoking in the presence of Queen Elizabeth, offered to bet her majesty that he could tell the weight of the smoke that curled upward from his pipe. The wager was accepted. Raleigh quietly finished, and then weighing the ashes, subtracted this amount from the weight of the tobacco he had placed in the pipe, thus finding the weight of the smoke. When we reach the subject of combus- tion in chemistry, we shall be able to detect Raleigh's mistake. The smoke and the ashes really weighed more than the original tobacco, since the oxygen of the air had combined with the tobacco in burning. SPECIFIC PROPERTIES OF MATTER. 19 III. SPECIFIC PROPERTIES OF MATTER. Among the most important specific properties of matter are ductility, malleability, tenacity, elasticity, hardness, and brittleness. 1. Ductility. A ductile body is one which can be drawn into wire. Fig. 3 represents a machine for making wire. B is a steel draw- ing-plate pierced Fl - 3 - with a series of gradually dimin- ishing holes. A rod of iron, A, is hammered at the end so as to pass through the larg- est. It is then grasped by a pair of pincers, 0, and, by turning the crank D, is drawn through the plate, diminished in diameter and proportionately increased in length. The tenacity of the metal is greatly improved by the process of drawing, so that a cable of fine wire is stronger than a chain or bar of the same weight. Gold, silver, and platinum are the most duc- tile metals. A silver rod an inch thick, covered with gold- leaf, may be drawn to the fineness of a hair and yet retain a perfect coating of gold, 3 oz. of the latter metal making 100 miles of the gilt-thread used in embroidery. Platinum wire has been drawn so fine that, though it is nearly three times as heavy as iron, a mile's length weighed only a single grain. (Chemistry, p. 170.) 2. Malleability. A malleable body is one which can be hammered or rolled into sheets. Ex. : Gold may be beaten until it is only ?60 i 000 of an inch thick. It would require INTRODUCTION. PIG. 4. 1800 such leaves to equal the thickness of common printing' paper.* Copper is so malleable, that a workman can ham- mer out a kettle from a solid block. 3. Tenacity. A tenacious body is one which cannot easily be pulled apart. Iron possesses this quality in a remarkable degree. Steel wire will sustain the weight of about 7-J- miles of itself . 4. Elasticity is of four kinds, according as a body tends to resume its original form when compressed, extended, twisted, or lent. (I.) ELASTICITY OF COMPRESSION. Many solids, as iron, glass, and caoutchouc, are highly elastic. Ex. : Spread 'a thin coat of oil on a smooth mar- ble slab. If an ivory ball be dropped upon it, the size of the impression will vary with the distance at which the ball is heJd above the table. This shows that the ivory is flattened, somewhat like a soap-bubble when it strikes a smooth surface and rebounds. Liquids are condensed with great difficulty, so that for a long time they were considered in- compressible. When the force is removed, they regain their exact volume, and are therefore perfectly elastic. Gases are easily compressed, and are also perfectly elastic. A pressure of 15 Ibs. to the square inch reduces the volume of * An Ingot of gold is passed many times between steel rollers, which are so ad- justed as to be constantly brought nearer together. The metal is thus reduced to a ribbon about g ^ of an inch thick. This is cut into inch squares, 150 of which are piled up alternately with leaves of stronsrpaper four inches square. A workman with a 16-lb. hammer beats the pile until the gold is spread to the size of the leaves. Each piece is next quartered, and the 600 squares are placed between leaves of goldbeaters' skin and pounded. They are then taken out, spread by the breath, cut. and the 2 400 squares pounded as before. They are finally trimmed and placed between tissue- paper in little books, each of which contains 25 gold leaves. SPECIFIC PROPERTIES OF MATTER. Fro. 5. water only 20 } 00 , whereas it diminishes the volnme of a gas . A gas may be kept compressed for years, but on being released will instantly return to its original form. (2.) ELASTICITY OF EXPANSION is possessed largely by solids, slightly by liquids, and not at all by gases. Ex..: India-rubber, when stretched, tends to fly back to its origi- nal dimensions. A drop of water hanging to the nozzle of a bottle may be touched by a piece of glass and drawn out to considerable length, but when let go it will resume its spherical form. Gases when extended manifest no tendency to return to their former shape. (3.) ELASTICITY OF TORSION is the tendency of a thread or wire which has been twisted, to un- twist again. It is a delicate test of the strength of a force (Fig. 5). (4.) ELASTICITY OF FLEXURE is the property ordinarily meant by the term elastic. Many solids possess this quality, within certain limits, to a high degree. Swords have been made which could be bent into a circle without breaking. Watch-springs, bows, cushions, etc., are useful because of their elasticity. ,5. Hardness. One body is harder than another when it will scratch or in- dent it. This property does not depend on density.* Ex. : Gold is about 2J times denser than iron, yet it is much softer. Mercury is a liquid, yet it is almost twice as dense as steel. The diamond is the hardest-known substance, yet it is not one-third as heayy as lead. 6. Brittleness. A brittle body is one that is easily broken. This property is a frequent characteristic of hard bodies. Ex. : Glass will scratch pure iron, yet it is extremely brittle. * A dense body has its molecules closely compacted. The word rare, the opposite of dense, is applied to gases. Mass, or the quantity of matter a body contains, should be distinguished from weight or size (notes, pp. 53, 2&7). 22 INTRODUCTION. SUM MARY. Matter is that which occupies space. A separate portion is called a body, and a particular kind a substance. A general property of matter belongs to all substances, and a specific one to particular kinds. Mat- ter is composed of very minute atoms. A group of atoms forms a molecule, in which reside the specific properties of a substance. A physical change never affects the molecule, but a chemical change breaks it up, and so forms a new substance. Philosophy deals with physical forces and changes ; Chemistry with chemical force or attrac- tion, and chemical changes. Extension, impenetrability, divisibility, porosity, inertia, and indestructibility are the principal general prop- erties of matter. Of these, extension is the property of occupying space ; the amount of space a body fills is its size. Impenetrability prevents two bodies from occupying the same space in the same time. Divisibility permits a body, so far as we know, to be divided infinitely. Porosity is caused by the particular structure of a body ; pores are inherent in the constitution of a body which consists of molecules that do not touch. Inertia is that property of matter which forbids its changing its state from motion to rest, or vice versa. It is like laziness in a human being. Indestructibility prevents the extinction of matter by man. Ductility, malleability, tenacity, elasticity, hard- ness, and brittleness are the principal specific properties of matter. A ductile body can be drawn into wire ; gold, silver, and platinum are the most noted for this property. A malleable body can be ham- mered into sheets ; gold possesses this quality in a remarkable degree. A tenacious body resists pulling apart ; iron is the best example. An elastic body permits a play of its particles, so that they return to their original position when the disturbing force is removed. A hard body cannot easily be indented. A brittle body is readily broken. HISTORICAL SKETCH. In ancient times, any seeker after truth was termed a philosopher (a lover of wisdom), and philosophy included all investigations concern- ing both mind and matter. In the fourth century B. C., Plato assumed that there are two principles, matter and form, which by combining produce the five elements, earth, air, fire, water, and ether. Aristotle, his pupil, established the first philosophical ideas concerning mattej HISTORICAL SKETCH. 23 and space. But the method of study generally pursued for 2000 years was one of pure metaphysical speculation. Observation had no place, but the philosophers made up a theory, and then accommodated facts to it. They guessed about the real essence of things, as to whether matter exists except when perceived by the mind,* and how a change in matter can produce a change in mind. In 1620, Bacon published his " Novum Organum," advocating the inductive method of studying nature. He argued that the philosopher should seek to benefit man* kind, and that, instead of wasting his time in sterile and ingenious theories about the world and matter, he should watch the phenomena of life, gather facts, and then reasoning from effects back to their causes, reach the general law. This work is commonly said to have established the modern method of investigation. Ptolemy, Archimedes, Galileo, and other physicists, however, had long before proved its value. The Atomic Theory was propounded by Democritus, in the fifth century B. C., and twenty-two centuries later elaborated by Dal ton, an English physicist. The grander generalization and development of this law was advanced in 1811 by Avogadro, an Italian, and afterward extended by the French philosopher, Ampere. The latter asserted that "qual volumes of all substances, when in the gaseous form and under like conditions, contain the same number of molecules." For half a century this view lay dormant. Of late it has borne fruit, and the molecular theory has become to Chemistry what the law of gravitation is to Astronomy. The labors of Thomson, Cooke, Tait and others are now building up the whole superstructure of Chemistry and Physics upon this basis. The history of the establishment of a standard of measures is a curious one. Anciently, length was referred to some portion of the human body, as the foot ; the cubit (the length of the forearm from the elbow to the end of the middle finger) ; the finger's length or breadth ; the hand's breadth ; the span, etc. In England, Henry I. (1120) ordered that the ell, the ancient yard, should be the exact length of his arm. Afterward a standard yard-stick was kept at the Exchequer in London ; but it was so inaccurate, that a commissioner, who examined it in 1742, wrote : " A kitchen poker filed at both ends would make as good a standard. It has been broken, and then repaired so clumsily that the joint is nearly as loose as a pair of tongs." In 1760, Mr. Bird carefully prepared a copy of this for the use of the Government. It was not legally adopted until 1824, when it was ordered that if destroyed, it * Dr. Johnson once remarked to a geutleman who had oeen defending the theory that there is no external world, as he was going away, ''Pray, sir, don't leave us, for we may perhaps forget to think of you, and then you will cease to e?ist." 24 HISTORICAL SKETCH. should be restored by a comparison with the length of a pendulum vibrating seconds at the latitude of London. (Third law, p. 60.) At the great fire in London, 1834, the Parliament House was burned, and with it Bird's yard-stick. Repeated attempts were then made to find the length of the lost standard by means of the pendulum. This was found impracticable, on account of errors in the original directions. At last the British government adopted a standard prepared from the most reliable copies of Bird's yard-stick. A copy of this was taken by Troughton, a celebrated instrument-maker of London, for the use of our Coast Survey.* The French had previously adopted for the length of the legal foot that of the royal foot of Louis XIV., as perishable a standard as Henry's arm. When they had established the metric system, they found that a mistake had been made in measuring the meridian. The English scientists discovered a difficulty in the calculation from the pendu- lum. So that both these attempts to fix upon an absolute unit in Nature have failed, and the French and English systems are alike founded upon arbitrary standards. Consult Cooke's " New Chemistry," chapter on Molecules, etc.; Powell's "History of Natural Philosophy"; Buckley's "History of Natural Science"; Whewell's "History of the Inductive Sciences"; Roscoe's "John Dalton and his Atomic Theory," in Manchester Science Lectures, '73-4; "Appleton's Cyclopaedia," Art. Molecules; Outerbridge's "Divisibility of Gold and Other Metals," in Popular Science Monthly, Vol. XI, p. 74 ; Crookes' " The Radiometer a fresh evidence of a Molecular Universe," Popular Science Monthly, Vol. XIII, p. 1 ; Tait's "Recent Advances in Physical Science," Chap. XII, The Structure of Matter ; Hoef er, " Histoire de la Physique et de la Chimie"; Draper's "History of Intellectual Development." * This yard is about ^s of an inch longer than the British standard. According to Act of Congress, sets of weights and measures have been distributed to the gov- ernors of the several States. The yards so furnished are equal to that of tlie Troughton scale. We have no national standard established by law. II. MOTION 3JV> FORCE. Rest is nowhere. The winds that come and go, the ocean that uneasily throbs along the shore, the earth that flies about the sun, the light that darts through space all tell of a universal law of Nature. The solidest body hides within it inconceivable velocities. Even the molecules of granite and iron have their orbits as do the stars, and revolve as ceaselessly. No energy is ever lost. It changes its form, but the eye of philosophy detects it and enables us to drive it from its hiding-place undiminished. It assumes Protean guises, but is everywhere a unit. It may disappear from the earth; still " Somewhere yet that atom's force Moves the light-poised universe? ANALYSIS. MOTION AND FORCE. r 1. DEFINITIONS. 2. RESISTANCES TO ( (*) MOTION. j ( 2 -) Resistance of air ( and water. 3. MOMENTUM. 4. COMMUNICATION OF MOTION. 5. THREE LAWS OF MOTION. 6. COMPOUND MOTION. 7. COMPOSITION OF FORCES. 8. RESOLUTION OF FORCES. 9. MOTION IN A CURVE. 10. CIRCULAR MOTION. 11. THE GYROSCOPE. 12. REFLECTED MOTION. 18. ENERGY. 14. POTENTIAL AND DYNAMIC ENERGY, 15. CONSERVATION OF ENERGY. MOTION AND FORCE. 1. Motion is a change of place. All motion, as well as rest, with which we are acquainted, is relative. Ex. : When we ride in the cars, we judge of our motion by the objects around us. A man on a steamer may be in motion with regard to the shore, but at rest with reference to the objects on the deck of the vessel. Force is that which produces or tends to produce or to destroy motion. Velocity is the rate at which a body moves. 2. The Resistances to Motion are friction and the resistance of air and water. (1.) Friction is the resistance caused by the surface over which a body moves. It is of great value in common life. "Without it, nails, screws, and strings would be useless ; engines could not draw the cars ; we could hold nothing in our hands ; and we should every- where walk as on glassy ice. (2.) The resistance which a body meets in passing through air or water is caused by the particles displaced. r It increases according to the square of the velocity.* Thus, if in running we jlouble our speed, we displace twice as much air in the same time, and give to each particle twice the velocity ; hence the resistance will be quadrupled. 3. Momentum, is the name given to the product of the mass of a body multiplied by its velocity per second, ex- pressed in feet. Ex. : A stone weighing 5 Ibs., thrown with a velocity of 20 feet per second, has 100 units of momen- tum.! * This is true at a moderate velocity, but at a high speed some of the medium is carried with the body, and the resistance increases faster than according to v 3 . t Physicists make momentum = mass x velocity. The mass of bodies (note, p. 21) is proportional to weight, at the same place on the earth's surface ; but, while the mass remains the same at different places, the weight varies (p. 53). A heavy body may move slowly and yet have an immense momentum. Ex.: An ice- berg, with a scarcely perceptible motion, will crush a man-of-war as if it were an MOTION AND FOBCB. 4. The Communication of Motion is not instanta- neous.* If I press with all my might against a rock weigh- ing a ton, I fail to move it, press I ever so long. The force is not sufficient to overcome the friction between the rock and the ground. If, however, we could conceive the rock poised in empty space, the least touch would at once move it with a velocity proportional to P ressure t if j strike one mass end of a rail a mile long, the tremor will take a definite time to reach the other end. If, on the other hand, a powerful engine suddenly pulls at one end of the rail, so as to draw it over a consi ierable distance in a second, I can imagine that the other end will move after an almost infinitely short time ; but if the engine drag the rail con- tinuously, both ends will have the same velocity, and the whole rail will move together. 5. Three Laws of Motion. FIRST. A body set in mo- tion will move forever in a straight hne, unless acted on ly some external force. This is only another statement of the passiveness of matter, or the property of inertia. Obvious- ly, no experiment will directly prove the law. There is a curious illustration, however, in the swinging of a pendulum under the receiver of an air-pump. The more perfectly the air is exhausted, the longer it will vibrate. In the best vacuum we can produce, it will swing for twenty-four hours. It is supposed that if all "resistances to motion" vere removed, the pendulum would never stop. egg-shell. Vessels lying at a wharf grind against one another with prodigious force, by the slow movement of the tide. Soldiers have thought to stop a spent cannon-ball by putting a foot against it, but have found its momentum sufficient to break a leg. On the other hand, a light body moving with a high velocity may have an enor- mous momentum. Ex. : The air in a hurricane will tear up trees by the roots and level buildings to the ground. Sand driven from a tube by steam is used for drilling, and in stone-cutting, engraving, etc. * A stone thrown against a pane of glass shatters it ; but a bullet fired through it will make only a round hole. The bullet is gone before the motion has time to past< into the surrounding particles. A fraction of time is required for a ball to receive the force of the exploding powder and to get under full headway. An instrument is used to determine the acceleration of speed before leaving the gun. LAWS OF MOTION. To this law are to be referred many ordinary illustrations of the so-called "inertia of matter." Thus, when we en- deavor to stop a moving body, as a wagon, we must over- come its momentum. The danger in jumping from a car in rapid motion lies in the fact that the body has the speed of the train, while the forward motion of the feet is checked by the contact with the ground.* SECOND LAW. A force acting upon a lody in motion or at rest, produces the same effect whether it acts alone or with other forces. Ex. : All bodies upon the earth are in constant motion with it, yet we act with the same ease that we should were the earth at rest.f We throw a stone directly at an object and hit it, yet, within the second, the mark has gone for- ward many feet.J If a cannon- ball be thrown horizontally, it will fall as fast and strike the earth as soon as if dropped to the ground from the muzzle of the gun. In Fig. 6, D is an arm driven by a wooden spring, E, and turning on a hinge at C. At D is a hollow containing a bullet, so placed that when the arm is sprung, the ball will be thrown in the line FK. At F is a * Some jnmp as nearly ua possible in the direction in which the train is moving, ami are ready to run the instant their feet touch the ground. Then with all their strength they gradually overcome the inertia of the body, and after a few rods can turn as they please. If one could jump backward with sufficient force to overcome t he forward motion of the train, it would then be possible to drop directly downward. t A ball thrown up into the air with a force that would cause it to rise 50 feet, will ascend to that height whatever horizontal wind may be blowing. While riding on a car, we throw a stone at some object at rest. The stone, having the motion of the train, strikes just as far ahead of the object as it would have gone had it remained on the train. In order to hit the mark, we should have aimed a little back of it. The circus-rider wishes, while his horse is at full speed, to jump through a hoop suspend- ed before him. He simply springs directly upward. Going forward by the momen- tum which he had acquired before he leaped from the horse, he passes through the hoop and alights upon the saddle again. A person riding in a coach drops a cent to the floor. It apparently t-trikes where it would if the coach were at rest. t The earth moves in its orbit around the sun at the rate of about 18 miles per second. See Fourteen Weeks in Astronomy, p. 106. 30 MOTIOK AND FOBOE. similar ball, supported by a thin slat, G, and so arranged that the same blow which throws the ball D, will let the bail F fall in the line FH. The two balls will strike the floor at the same instant. THIED LAW. Action is equal to reaction, and in the con- trary direction. Ex. : A bird in flying beats the air down- ward, but the air reacts and supports the bird. The powder in a gun explodes with equal force in every direction, driving the gun backward and the ball forward, with the same momentum. Their velocities vary with their weights ; the heavier the gun, the less will the recoil be noticed. When we spring from a boat, unless we are cautious, the reaction will drive it from the shore. rWhen we jump from the ground, we push the earth from us, while it reacts and pushes us from it ; we separate from each other with equal momentum, and our velocity is as much greater than that of the earth as we are lighter. We walk, therefore, by reason of the reaction of the ground on which we tread. The apparatus shown in Fig. 7 consists of ivory balls hung so as readily to vibrate.* If a ball be let fall from one side, it will strike the second ball, which will react with an equal force, and stop the motion of the first, but transmit the motion to the third ; this will act in the same manner, and BO on through the series, each acting and reactirig until the last ball is reached ; this will react and then bound off, rising as high as the first ball fell (except the loss caused by resistances to motion). If two balls be raised, two will fly off at the opposite end ; if two be let fall from one side and r one from the other, they will respond alternately. 6. Compound Motion. Let a ball at A (Fig. 8) be acted on by a force which would drive it in a given time to * The same experiments can be performed by means of glass marbles or billiard balls placed in a groove. Better still, attach strings to glass marbles by means of mucilage and bits of paper and suspend them from a simple wooden frame. COMPOUND MOTIOK. B, and also at the same instant by another which would drive it to D in the same time ; the ball will move in the direction AC. Ex. : A person wishes to row a boat across a swift cur- rent which would carry him down stream. He therefore steers toward a point above that which he wishes to reach, and so goes directly across. A bird, beating the air with both its wings, flies in a direction different from that which would be given by either one. 7. Composition of Forces. When a body is thus acted on by two forces, we draw lines representing their directions, and mark off AD and AB, whose lengths represent their comparative mag- nitudes. We next com- plete the parallelogram and draw the diagonal AC, which denotes the resultant of these forces, and gives the direction in which the body will move. If more than two forces act, we find the resultant of two, then of that resultant and a third force, and so on. ftfcW - X 8. Resolution of Forces con- sists in finding what two forces are equivalent to a given force. A par- allelogram is drawn having the given w force as a diagonal. Ex. : There is a wind blowing from the west against GH (Pig. 10), the sail of a vessel going north. We can resolve the MOTION AND FORCE. Fie. It FIG. 13. V wind-force BD into the two forces BE and BC. The former, blowing parallel to the sail, is of no use ; the latter is perpendicular to it, and drives the vessel northeast. Again, resolving BD in Fig. 11, which represents the vertical force BO in Fig. 10, we find that it is equivalent to two forces BE and BC. The former pushes the vessel sideways, but is mainly counteracted by the shape of the keel and the action of the rudder. The latter is parallel to the course of the ship, and hurries it north. By shifting the rigging, one vessel will sail into harbor while another is sail- ing out, both driven by the same wind.* Figs. 12 and 13 show how, by twice resolv- ing the force of the w . wind from the W., as in the last figures, when the sail GH is placed in the new po- sition, we have (Fig. 13) a force BO, which drives the vessel S.f If a vessel * The toy shown in Pig. 14, and easily made by any pnpil, proves how a change in the position of the sails will produce a contrary effect. Carry this wind-mill forward, and the two sets of feather -vanes will revolve swiftly in opposite directions. t In a similar manner we may resolve the three forces which act upon a kite viz., the pull of the string, the force of the wind, and its own weight. In Fig. 10, let GH represent the face of the kite. We can resolve BD, the force of the wind, into BC and BE. We next resolve BD, in Fig. 11, which corresponds to BC in Fig. 10 into BE and BC. We then have a force, BC, which overcomes the weight of the kite and also tends to lift it upward. The string pulls in the direction BD, perpendicularly to the face. The kite obeys both of these forces, and so ascends in a direction DG, between the two. It is really drawn up an inclined plane by the joint force of the wind and the string. CIRCULAR MOTIOK. 33 were to He sailed due W. against the wind, it would tack alternately K W. and SW. In this way it could go almost in the "teeth of the wind." A canal-boat drawn by horses is acted upon by a force which tends to bring it to the bank. This force may be resolved into two, one pulling toward the tow-path, and the other directly ahead. The former is counteracted by the shape of the boat and the action of the rudder ; the latter draws the boat forward. 9. Motion in a Curve.- Whenever two or more in- stantaneous forces act upon a body, the path is a straight line. When one is instantaneous and the other continuous, it is a curved line. Ex. : When a body is thrown into the air, except in a vertical line (p. 54), it is acted upon by the instantaneous force of projection and the continuous force of gravity, and so describes a line which curves toward the earth. 10. Circular Motion is produced when a moving body is drawn toward a centre by a constant force. Thus, when a sling is whirled, the stone is pulled toward the hand by the string, and as, according to the third law of motion, every action has its equal and opposite reaction, the hand is pulled toward the stone. If the string break, the stone will continue to move, according to the first law of motion, in a straight line in the direction of a tangent to the circle at that point. The tension of the string, acting inward, is called the Centripetal {centrum, the centre, peter e, to seek) force ; and the reaction of the stone^upon the string, acting outward, is termed the Centrifugal (centrum, the centre, fugere, to flee) force.* * It should be noticed that in circular motion there is bat one true force concerned. It acts, however, upon a body in motion. The so-called centrifugal force has nothing to do with the production of the motion, being merely the resistance which the body offers by its inertia to the operation of the centripetal force, and ceases the instant that force is discontinued. It does not act at right angles to the centripetal force, as is often stated, but in direct opposition. A body never flies off from the centre im- pelled by the centrifugal force, since that can never exceed the centripetal (action = reaction), and moreover the path of snch a body is in the direction of a tangent, and 34 MOTION AND FORCE. The following examples are among those usually given to illustrate the action of the centre-fleeing force : Water flies from a grindstone on account of the centrifugal force produced in the rapid revolution, which overcomes the adhesion. In factories, grindstones are sometimes re- volved with such velocity that this force overcomes that of cohesion, and the ponderous stones fly into fragments. A pail full of water may be whirled around so rapidly that none will spill out, because the centrifugal force overcomes that of gravity. When a horse is running around a small circle, he bends inward to overcome the centrifugal force. The heavenly bodies present the -o grandest example of circular motion. We may suppose the earth to have been moving originally in the direction AC. The attraction of the sun, however, drawing it in the direction BS, it passes along the line BD. If the centripe- tal force were suddenly to cease, the earth would fly oif into space along a tangent, as BO. The rapid revolution of the earth on its axis tends to throw off all bodies headlong. Ac this acts in opposition to gravity, it diminishes the weight not th* radius of a circle. Thus, when water is thrown off a grindstone in rapid rotation, th-* tendency of the water to continue to move on in the direction of the straight line in which it is going at each instant (in other words, the inertia of the water) overcomes its adhesion to the stone, and it flies off in obedience to the first law of motion. So, also, when a grindstone, driven at a high speed, breaks, and the fragments are thrown with great velocity, we are not to suppose that the centrifugal fore' impels them through the air. That force existed only while the stone was entire. It was opposed to the force of cohesion, and in the moment of its triumph ceased, and the fragments of the stone fly off in virtue of the velocity they possess at thai instant Again the so-called centrifugal force is not a real force urging bodies upward at the equator. The earth's surface is merely falling away from a tangent, and a part of the force of gravity is spent in overcoming the inertia of bodies. The ter. u centrifugal force has caused much confusion, and will doubtless soon be dis- carded. CIKCULAR MOTION. 35 FIG. 16. FIG. 17. of bodies at the equator, where it is greatest, -pfa. It also tends to drive the water on the earth from the poles toward the equator. Were the velocity of the earth's ro- tation to diminish, the water would run back toward the poles, and tend to restore the earth to a spherical form. This influence is well illus- trated by the apparatus shown in Fig. 16. The hoop is made to slide upon its axis, and if revolved rapidly it will assume an oval form, bulging out more and more as the velocity is increased.* 11. The Gyroscope beauti- fully illustrates the principle of the composition of forces in rotary motion. In Fig. 17 a wheel re- volves within a ring which is sus- tained at one end by an upright support. If the wheel is made to revolve swiftly by unwinding a string, and then placed on the sup- port, instead of falling, as one would suppose, the whole begins to revolve rapidly around the point of support, in a resultant between the force of gravity and the rotary motion of the wheel. If we attempt to raise or lower the ring, it will sen- sibly oppose the change and persist in its plane of rotation. 12. Reflected Motion is produced by the reaction of a surface against which an elastic body is cast. If a ball be thrown * This apparatus is accompanied by objects to illustrate the principle that all bodies tend to revolve about their shortest diameters, an assurance that the earth will never change its axis of rotation while it retains its present form. " Tie to FIG. 18. 36 MOTION AND fORCE. in the direction OB against the surface AC, it will rebound in the line BE. The angle OBP, that si incidence, = the angle PBR, that of reflection. 13. Energy is the power of- doing work, i. e. 9 of over- coming any kind of resistance. It is in general something put into a body by means of work, and which comes out of it when it does work. Ex. : A wound-up clock, a red-hot iron. The difference between energy and momentum is evident. When a bullet is fired from a rifle, the momenta of both are equal, but the energy of the former, i. e., its power of doing work, as piercing a board, is far greater. Energy is proportional to the square of the velocity. Thus, a cannon-ball given double speed will penetrate four times as far into a wall ; and a stone thrown upward at the rate of 96 feet per second will rise 9 times as far as with a velocity of 32 feet (p. 55). 14. Two Forms of Energy. Energy may be either active or latent. When a rock is tumbling down a moun- tain-side, it exhibits the force of gravity in full sway ; but when the rock was lodged on the mountain-top, it possessed the same energy, which could be developed at any moment by loosening it from its place. These two forms are known the middle of a lead pencil a piece of string about three feet long. Suspend so that the pencil will balance itself. Now twist the end of the string between the thumb and the first finger of the right hand, steadying and holding the string with the left hand. A circular motion will thus be communicated to the pencil, and it will revolve around the point on which it is suspended. Tie a piece of white string around the middle of the pencil, or its centre of gravity, simply to show the position of that point. Now tie the first piece of string half-way between the end of the pencil and the 'centre of gravity, an J communicate the circular motion described above, and we shall observe that the pencil will still revolve around the centre of gravity, the point marked by the white string being at rest. It can thus be shown that anything, of whatever shape, will tend to revolve on its shortest diameter. If the end links of a small steel chain (such as is often attached to purses or parasols) be hooked together, the string tied to a link, and the circular motion given, it will be observed that the chain begins to take an elliptical form, which gradually approaches that of a circle, until at last it becomes a circle, when it revolves horizontally. This shows that even a ring is subject to the same law that is, revolves on its shortest axis." ENERGY. 37 as energy of motion and energy of position, or actual and potential (possible) energy.* 15. Conservation of Energy. One kind of energy is changed into another without loss. The sum of all the energy in the universe remains the same. A hammer falls by the force of gravity and comes to rest. Its potential energy changes to kinetic and does work. Its motion as a mass is converted into one of atoms, and reveals itself to our touch as heat (p. 184). f PRACTICAL QUESTIONS. 1. Can a rifle-ball be fired through a handkerchief suspended loosely from one corner ? 2. A rifle-ball thrown against a board standing edgewise, will knock it down ; the same bullet fired at the board will pass through it without disturbing its position. Why is this ? 3. Why can a boy skate safely over a piece of thin ice, when, if he should pause, it would break under him directly. 4. Why can a cannon-ball be fired through a door standing ajar, without moving it on its hinges ? 5. Why can we drive on the head of a hammer by simply striking the end of the handle ? 6. Suppose yon were on a train of cars moving at the rate of 30 miles per hour; with what velocity would you be thrown forward if the train were * Actual energy is also styled dynamic or kinetic energy, and potential is termed static energy. In mechanics, kinetic energy is called vis viva (= ^mv 2 ), or striking force. We wind a watch, and by a few moments of labor condense in the spring a potential energy, which is doled out for 24 hours in the dynamic energy of the wheels and hands. Draw a violin bow, and the potential energy of the arm is stored up in the stretched cord. Lift a pendulum, and you thereby give the weight potential energy. Let it fall, and the potential changes gradually to dynamic. At the centre of the arc the potential is gone and kinetic is possessed. Then the kinetic changes again to potential, which increases till the end of the arc is reached and the pen- dulum ceases to rise, when the energy is that of position, not of motion. Potential energy is one that is concealed, lying in wait and ready to burst forth on the instant. It is a loaded gun prepared for the arm of the marksman. It is a river trembling on the brink of a precipice, about to take the fearful leap. It is a weight wound up and held against the tug of gravity. It is the engine on the track with the steam hissing from every crevice. It is the drop of water with a thunderbolt hidden within its crystal walls. On the contrary, dynamic energy is in full view, in actual operation. The bullet is speeding to the mark ; the river is tumbling ; the weight is falling ; the engine is flying over the rails ; and the bolt is flashing across the sky. It is heat radiating from our fires ; electricity flashing our messages over the continent ; and gravity drawing bodies headlong to the earth. t No energy in nature can be wasted. It must accomplish something. " A blow with a hammer moves the earth. A boy could in time draw the largest ship across the harbor in calm weather." " Water falling day by day Wears the hardest rock away." Statues are worn smooth by the constant kissing of enthusiastic worshippers. Stone steps are hollowed by the friction of many feet. The ocean is filled by small drops which fall from the clouds. We may notice none of these forces singly, but their effects in the aggregate startle us. 38 MOTION AND FORCE. stopped Instantly ? 7. In what line does a stone fall from the masthead of a vessel in motion ? 8. If a ball be dropped from a high tower, it will strike the ground a little qast of a vertical line. Why is this ? 9. It is stated that a suit was once brought by the driver of a light wagon against the owner of a coach for damages caused by a col- lision. The complaint was " the latter was driving so fast that when the two carriages struck, the driver of the former was thrown forward over the dashboard." On trial he was nonsuited, because his own evidence showed him to be the one who was driving at the unusual speed. Explain. 10. Suppose a train moving at the rate -of 30 miles per hour ; on the rear platform is a spring-gun aimed parallel to the track and in a direction precisely opposite to the motion of the car. Let a ball be discharged with the exact speed of the train ; where would it fall ? 11. Suppose a steamer in rapid motion, and on its deck a man jumping. Can he jump further by leaping the way the boat is moving than in the opposite direction ? 13. If a stone be dropped from the masthead of a vessel in motion, will it strike the same spot on the deck that it would if the vessel were at rest ? 14. Could a party play ball on the deck of the Great Eastern when steaming along at the rate of 20 miles per hour, without making allowance for the motion of the ship ? 15. Since action is equal to reaction, why is it not so dangerous to receive the " kick" of a gun as the force of the bullet ? 16. If you were to jump from a carriage in rapid motion, would you leap directly toward tv te spot on which you wished to alight ? 17. If you wished to shoot a bird in swift flight, would you aim directly at it ? 18. At what parts of the earth is the centrifugal force least ? 19. What causes the mud to fly from the wheels of a carriage in rapid motion ? 20. What proof have we that the earth was once a soft mass ? 81. On a curve in a railroad, one track is always higher than the other. Why is this ? 22. What is the principle of the sling? 23. The mouth of the Mississippi River is about 2 miles farther from the centre of the earth than its source. In this sense it may be said to " run up hill." What causes this apparent opposition to the attrac- tion of gravity ? 24. Is it action or reaction that breaks an egg, when I strike it against the table ? 25. Was the man philosophical who said that it " was not the falling so far, but the stopping so quick, that hurt him?" 26. If one person runs against another, which receives the greater blow ? 27. Would it vary the effect if the two persons were running in opposite directions ? In the same direction ? 28. Why can you not fire a rifle-ball around a hill? 29. Why is it that a heavy rifle "kicks" less than a light shot-gun ? 30. A man on the deck of a large vessel draws a small boat toward him. How much does the ship move to meet the boat? 31. Suppose a string, fastened at one end, will just support a weight of 25 Ibs. at the other. Unfas- ten it, and let two persons pull upon it in opposite directions. How much can each pull without breaking it ? 32. Can a man standing on a platform-scale make himself lighter by lifting up on himself? 33. Why cannot a man lift himself by pulling up on his boot-straps ? 34. If, from a gun placed vertically, a ball were fired into per- fectly still air, where would it fall ? 35. With what momentum would a steamboat weighing 1,000 tons, and moving with a velocity of 10 feet per second, strike against a sunken rock? 36. With what momentum would a train of cars weighing 100 tons, and running 10 miles per hour, strike against an obstacle ? 37. What would be the comparative striking force of two hammers, one driven with a velocity of 20 feet per second and the other 10 feet ? 38. If a 100 horse-power engine can propel a steamer 5 miles per hoar, will one of 200 horse-power double its speed T 39. Why is a bullet flattened if fired obliquely against the surface of water ? 40. Why are ships becalmed at sea often floated by strong currents into dangerous localities without the knowl- edge of the crew ? 41. A man in a wagon holds a 50-lb. weight in his hand. Suddenly the wagon falls over a precipice. Will he, while dropping, bear the strain of the weight? 42. Why are we not sensible of the rapid motion of the earth? 43. A feather is dropped from a balloon whict is immersed in and swept along by a swift current of air. Will the feather be blown away or will it appear to drop directly SUMMABT. 39 down f 44. Suppose a bomb-shell, flying through the air at the rate of 600 feet per second, explodes into two parts ot equal weight, driving one-half forward in the same direction as before, but with double its former velocity. What would become of the other half? 45. Which would have the greater penetrating power, a small cannon- ball with a high velocity, or a large one with a low velocity ? 46. There is a story told of a man who erected a huge pair of bellows in the stern of his pleasure-boat, that he might always have a fair wind. On trial, the plan failed. In which direction should he have turned the bellows ? 47. If a man and a boy were riding in a wagon, and, on coming to the foot of a hill, the man should take up the boy in his arms, would that help the horse ? 48. Why does a bird, as it begins to fly, always, if possi- ble, turn toward the wind ? 49. If we whirl a pail of water swiftly around with our hands, why will the water tend to leave the centre of the pail ? 50. Why w ill the foam collect at the hollow in the centre ? 51. If two cannon-balls, one weighing 8 Ibs. and the other 2 Ibs., be fired with the same velocity, which will go the further ? 52. Re- solve the force of the wind which turns a common wind-mill, and show how one part acts to push the wheel against its support, and one to turn it around. 63. Why is a gun firing blank cartridges more quickly heated than one firing balls ? 54. When an animal is jumping or falling, can any exertion made in mid-air change the motion of its centre of gravity ? 55. If one is riding rapidly, in which direct ion will he be thrown when the horse is suddenly stopped ? 58. When standing in a boat, why, as it starts, are we thrown backward ? 59. When carrying a cup of tea, if we move or stop quickly, why is the liquid liable to spill? 58. Why, when closely pursued, can we escape by dodging ? 59. Why is a carriage or sleigh, when sharply turning a corner, liable to tip over ? 60. Why, if you place a card on your finger and on top of it a cent, can you snap the card from under the cent, which will then drop on your finger? 61. Why is a " running jump" longer than a " standing jump" ? 62. Why, after the sail? of a vessel are furled, does it still continue to move ? and why, after the sails are spread, does it require some tune to get it under full headway ? 63. Why can a tal- low candle be fired through a board ? SUMMARY. Matter, so far as we know it, is in constant change. This change of place is termed motion. Terrestrial motion is restricted by friction, by the air, and by water. Friction is caused by the roughness of the surface over which a body moves. It may be decreased by the use of grease to fill up the minute projections, or by changing the sliding into rolling friction. Air and water must be displaced by a moving body, and the resistance they offer is increased, in general, according to the square of its velocity. Motion is governed by three laws ; viz.: A moving body left to itself tends to go forever in a straight line ; a force has the same effect whether it, acts alone or with other forces, and upon a body at rest or in motion ; and action is equal and opposed to reaction. By means of the principles of the composition and resolu- tion of forces, we can find the individual effect of a single force or the combined effect of several forces. Motion produced by two or more instantaneous forces is in a straight line ; when one is continuous, 40 MOTION AND FORCE. the result is a curved line ; and when the continuous force, directed toward a fixed point, acts upon a moving body, a circle is then described. A croquet ball struck by two mallets at the same moment, illustrates the first kind of motion ; the path of a bullet or rocket in the air exhibits the second ; and the movement of a stone whirled in a sling is an example of the third. When a rubber ball bounds back from a surface against which it is thrown, the angle of reflection equals the angle of incidence. Energy, or the power of doing work, is a general term employed to unify all the forces of nature. Out of it grows the grand law of the Conservation of Energy, which teaches that the different forces are only different forms of one all-pervading energy, and that they are mutually interchangeable, and indestructible as matter itself. HISTORICAL SKETCH. Aristotle taught that all motion is naturally circular, and this view was held by his school. He divided the phenomena of motion into two classes the natural and the violent. As an instance of the former, he gave the falling of a stone, which constantly increases in velocity ; and of the latter, a stone thrown vertically up, which being against nature, continually goes slower. Newton,^ in his " Principia " published in 1687, propounded the laws of motion as now received. Other philoso- phers, notably Galileo, Hooke, and Huygens, had anticipated much of his reasoning, yet so slowly were his opinions accepted that " at his death," says Voltaire, "he had not more than twenty followers outside of England." The law of the Conservation of Energy, Faraday, the great Eng- lish physicist, pronounced " the grandest ever presented for the con- templation of the human mind/* It has been established within the present century ; yet we now know that former scholars had inklings of the wonderful truth. It arose in connection with discoveries on the subject of Heat, and its history will be treated of hereafter. Consult Stewart's "Conservation of Energy"; Youmans's "Cor- relation of the Physical Forces"; Faraday's " Lectures on the Phys- ical Forces"; Everett's " Deschanel's Natural Philosophy"; Tait's "Recent Advances in Physical Science"; Maxwell's "Matter and Motion"; "Appleton's Cyclopaedia," Ar* Correlation of Forces, Gyroscope, etc.; Tyndall's "Crystalline and Molecular Forces," in Manchester Scienco Lectures, '73-4 ; Crane's " Ball Paradox," in Pop- ular Science Monthly, Vol. X, p, 725. III. J3.TTR ACTION. "The smallest dust which floats upon the wind Bears this strong impress of the Eternal mind : In mystery round it subtle forces roll, And gravitation binds and guides the whole. n 11 Attraction, as gravitation, is the muscle and tendon of the universe, by which its mass is held together and its huge limbs are wielded. As cohesion and adhesion, it determines the multitude of physical features of its different parts. As chemical or interatomic action, it is the final source to we trace all material changes" ARNOTT* ANAL YSIS. ' ATTRACTIVE AND REPELLENT FORCES. fc' O ^H O 1. COHESION. II. ATTRACTION OF GRAVITATION. 2. ADHESION. < f 1. Definition of Cohesion. 2. Three States of Matter. 3. Cohesion acts at Insensible Distances. 4. Liquids tend to form Spheres. 5. Solids tend to form Crystals. 6. Annealing and Tempering. 7. Rupert's Drop. f 1. Definition and Illustration of Adhesion. ( (1.) In water. 2. Capillary Attraction, 4 (2.) In mercury. 1(3.) Illustrations 3. Solution. 4 Diffusion of Liquids. 5. Diffusion of Gases. 6. Osmose of Liquids. L 7. Osmose of Gases. 1. Law of Gravitation. 2. Illustrations of Gravity. 8. Three Laws of Weight. (1.) Laws of falling bodies (2.) Equations of faUii'O bodies. (3.) To find depth of well. (4.) Bodies thrown upward. (1.) Three states of equilib- rium. (2.) To find centre of gravity. (3.) General principles. (4.) Physiological facts. (1.) Three laws. (2.) Centre of oscillation. (3.) To find centre of oscilla- tion. (4.) As time-keeper. (5.) Other use*. 4. Falling Bodies. 5. Centre of Gravity. The Pen- dulum. I. MOLECULAR FORCES. Attractive and Repellent Forces. If we take a piece of iron and attempt to pull it to pieces, we find that there is a force which holds the molecules together and resists our efforts. If we try to compress the metal, we find that there is a force which holds the molecules apart and resists our efforts as before. If, however, we apply heat, the iron expands and finally melts. So, also, if we heat a bit of ice, the attractive force is gradually overpowered, the solid becomes a liquid, and at last the repellent force predomi-. nates and the liquid passes off in vapor. In turn, we can cool the vapor, and convert it back successively into water and ice. We thus see that there are two opposing forces which reside in the molecules an attractive and a repellent force, and that the latter is heat. There are three kinds of the former, cohesion, adhesion, and chemical affinity. * 1. COHESION. 1. Cohesion is that force which holds together molecules of the same kind. 2. Three States of Matter. Matter occurs in three states solid, liquid, and gaseous. These depend on the relation of the attractive and repellent forces, cohesion and heat. If they are nearly balanced, the body is liquid; if the attractive force prevail, it is solid ; if the repellent, it is gaseous. Many substances may be made to take the three states successively. Thus, by the addition of heat, ice may be converted into water, and thence into vapor ; or vice * Chemical affinity produces chemical changes, and its consideration belongs to Chemistry. It binds together atoms of different kinds, and produces a compound unlike the original elements. 44 ATTRACTION. versa, by the subtraction of heat. Most solids pass easily to the liquid form, others go directly from the solid to the gaseous state. 3. Cohesion Acts at Insensible Distances. Take two bullets, and having flattened and cleaned one side of each, press them together with a twisting motion. They will cohere when the molecules are crowded into apparent contact. * If two globules of mercury be brought near each other, at the instant they seem to touch they will suddenly coalesce. Two freshly-cut surfaces of rubber, when warmed and pressed together, will cohere as if they formed one piece. The process of welding illustrates this principle. A wrought-iron tool being broken, we wish to mend it. So we bring the iron to a white heat at the ends which we in- tend to unite. This partly overcomes the attraction of cohesion, and the molecules will move easily upon one another. Laying now the two heated ends upon each other, we pound them until the molecules are brought near enough for cohesion to grasp them. 4. Liquids Tend to Form Spheres. Mix a glass of water and alcohol in such proportion that a drop of sweet- oil will fall half-way to the bottom. It will there form a perfect sphere. The same tendency is seen in dew-drops, rain-drops, globules of quicksilver, and in the manufacture of shot. (Chemistry, p. 174.) The reason is that the force of cohesion acts toward the centre of the drop. In a spher- ical body, every portion of the surface is equally distant from the centre ; and when that form is assumed, every molecule 011 the outside is equally attracted, and an equi- librium is established. 5. Solids Tend to Form Crystals. When a liquiu becomes a solid, the general tendency is to assume a sym- * Surfaces may appear to the eye to be in contact when they are not actually BO. Newton found, during eome experiments on light (p. 168), that a convex lens or a watch-glass laid on a flat glass does not touch it, and cannot he made to do so, even by a force of many pounds. COHESIOK. 45 metrical form. The attraction of cohesion strives to arrange the molecules in an orderly manner. Each kind of matter has its peculiar shape and angle, by which its crystals may be recognized. * When different substances are contained in the same solution, they separate on crystallization, and each molecule goes to its own. The , exquisite beauty of these crystalline forms is seen in snowflakes and the frostwork traced on a cold morning upon the windows or the stone- flagging. A beam of light passed through a block of ice reveals these crystals as a mass of star-like flowers (Fig.l9).f FIG. 19. Melted iron rapidly cooled in a mould has not time to arrange its crystals. If, however, the iron be afterward violently jarred, as when used for cannon, rail-cars, etc., the * Epsom salt crystallizes in four-sided prism?, common salt in cubes, and alum in octahedra. We can illustrate the formation of the last by adding alum to hot water until no more will dissolve. Then suspend strings across the dish and set it away to cool. Beautiful octahedral crystals will collect on the threads and sides of the vessel. The slower the process, the larger the crystals. God delights in order as in beauty. Down in the dark recesses of the earth He has fashioned, by the slow processes of His laws, the rarest gems amethysts, rubies, and diamonds. There are mountain masses transparent as glass, caves hung with, stalactites, and crevices rich with gold and silver, and lined with quartz. t It is noticeable that, as the crystals melt, at the centre of each liquid flower is a vacuum, showing that there is rot enough water formed to 11 the space occupied by the crystal, and that the solid contracts as it passes into a fluid (p. 202). This ex- periment is easily tried. The ice must be cut parallel to the plane of its freezing and be not over half an inch thick. A common oil-lamp will furnish the light. 4 ATTRACTION. molecules take on the crystalline form and the metal becomes brittle. * 6. Annealing and Tempering. If a piece of Drought- iron be heated and then plunged into water, it becomes hard and brittle. If, on the contrary, it be heated and cooled slowly, it is made tough and flexible. Strangely enough, the same process which hardens iron softens copper. Steel is tempered by heating white-hot, then cooling quickly, and afterward re-heating and cooling slowly. The higher the temperature of the second heating, the softer the steel. (Chemistry, p. 152.) 7. The Rupert's Drop is a tear of melted glass dropped into water, and cooled quickly. As there is PIG 20 no ^ ^ me * ^ or the particles to assume their -1 natural position, they exert a violent strain I \ upon one another ; and if the tail of the drop be nipped off, the tension will cause the mass yv to fly into powder with a sharp explosion. All ^^ glassware, when first made, is brittle, but it is annealed by being drawn slowly through a long oven, highly heated at one end, but quite cool at the other. During this passage, the molecules of glass have time to arrange themselves in a stable position, f PRACTICAL QUESTIONS. 1. Why can we not weld a piece of copper to one of iron? 2. Why is a bar of iron stronger than one of wood? 3. Why is a piece of iron, when perfectly welded, stronger than before it was broken ? 4. Why do drops of dif- ferent liquids vary in size ? 5. When you drop medicine, why will the last few drops contained in the bottle be of a larger size than the others ? 6. Why are the drops larger if you drop them slowly ? 7. Why is a tube stronger than a rod of the same weight? 8. Why, if you melt scraps of lead, will they form a solid mass when cooled ? 9. In what liquids is the force of cohesion greatest ? 10. Name some solids which volatilize without melting. 11. Why can glass be welded ? * On examining such a piece of iron, which can easily be procured at a car or machine-shop, we can see in a fresh fracture the smooth, shiny face of the crystals. t " The restoration of cohesion is beautifully seen in the gilding of china. A figure is drawn upon the china with a mixture of oxide of gold and an essential oil. The article is then heated, whereby the essential oil and the oxygen of the gold are expelled, and a red-brown pattern remains. This consists of pure gold in a finely- divided state, without lustre. By rubbing with a hard burnisher, the particles of gold cohere and reflect the rich yellow color of the polished metal." MOLECULAR FORCES. FIQ. 21. 2. ADHESION. 1. Adhesion is the force which holds together molecules of different kinds. Ex. : Two pieces of wood are fastened together with glue, two pieces of china with cement, two bricks with mortar, two sheets of paper with mucilage, and two pieces of tin with solder. Syrup and coal-oil are puri- fied by filtering through animal char- coal. Bubbles can be blown from soap- suds, because the soap by its adhesive force holds together the particles of water. 2. Capillary Attraction (capillus, hair) is a variety of adhesion between solids and liquids. It may be seen when two panes of glass are placed as shown in Fig. 21, but is exhibited most strik- ingly in very fine tubes, whence the name.* If we insert a glass tube in ivater, the liquid will rise in it. The finer the bore of the tube, the higher the ascent. The same in less de- gree exists between glass and alcohol. If we insert a glass tube in mercury, the capillary attraction will be reversed, and the height of the liquid will be lower than the general level. All parts of a liquid are mobile, but the surface is in a state of strain because the downward pull of the molecules beneath is not balanced. There is a tough film which is strong enough to confine the body of the liquid. It is this "surface tension "f that gives roundness to the pearly * These tubes may be drawn by the pupil to any length and size from French glass tubing in the heat of an alcohol lamp. t For discussion of surface tension, see Maxwell's Theory of Heat, p. 280 ; Descha- nel's Natural Philosophy, p. 130 ; Popular Science Monthly, Vol. IX., p. 575 ; Ameri- can Journal of Science, Dec. 1882 ; Pickering's Physical Manipulation, Vol. I., p. 102. FIG. 22. 48 ATTRACTION. dew-drop, strength to the brilliant soap-bubble, and holds up the slender column of liquid in a capillary tube. FIG. 23. ILLUSTRATIONS. The wick of a lamp or candle is a bundle of capillary tubes, which elevate the oil or melted fat and feed the flame. If the end of a towel be dipped in a basin of water, the whole towel will soon be wet by capillary action through the pores of the cloth. Blotting-paper takes up ink by capillarity. Water in the saucer of a flower- pot is elevated through the pores of the earth to the plant.* Ropes absorb water by capil- lary action, swell, and shrink often to breaking, f 3. Solution. Sugar will dissolve in water, because the adhesion between the two substances is stronger than the cohesion of the sugar, J As heat weakens cohesion, it * In the same way, water is drawn to the surface of the ground to furnish vege- tation with the materials of growth. Even in the winter, when the surface is frozen, the water still finds its way upward, and freezes into ice, which in the spring pro- duces mud, although there may have been little rain or snow. Stirring the ground causes it better to endure drought, because the size of the capillary pores is increased, thus preventing the water from being carried to the surface and evaporated. t It is 1586. The Egyptian obelisk, weighing a million pounds, is to be raised in the square of St. Peter's, Rome. Pope Sixtus V proclaims that no one shall utter a word aloud until the engineer announces that all danger is passed. As the majestic column ascends, all eyes watch it with wonder and awe. Slowly it rises, inch by inch, foot by foot, until the task is almost completed, when the strain becomes too great. The huge ropes yield and slip. The workmen are dismayed, and fly wildly to escape the impending mass of stone. Suddenly a voice breaks the silence. "Wet the ropes," rings out clear-toned as a trumpet. The crowd look. There, on a high post, standing on tiptoe, his eyes glittering with the intensity of excitement, is one of the eight hundred workmen, a sailor named Bresca di S. Remo. His voice and appearance startle every one ; but his words inspire. He is obeyed. The ropes swell and bite into the stone. The column ascends again, and in a moment more stands securely on its pedestal. The daring sailor is not only forgiven, but his descendants to this day enjoy the reward of providing the palm-branches used on Palm Sunday at St. Peter's. $ This contest between adhesion and cohesion is seen when we let fall on water a drop of oil. Adhesion tends to draw the oil to the liquid, BO as to mix thoroughly, and cohesion to prevent this. The extent to which the drop will spread will depend on the relation of the two attractions, and vary for every substance. Thus each oil nas its own COHESION FIGURE, which enables the chemist readily to detect differences and mixtures. Experiments : Dissolve a little salt in a glass of water, and touch ADHESION. 49 hastens solution, so that a substance generally dissolves more rapidly in hot water than in cold. In like manner, pulverizing a solid aids solution. Liquids also absorb gases by adhesion. Thus water contains air, which renders it pleasant to the taste. As pressure and cold weaken the repellent force, they favor the adhesion between the mole- cules of a gas and water. Soda-water receives its effervescence and pungent taste from car- bonic-acid gas, which, being absorbed under great pressure, escapes in sparkling bubbles when the pressure is removed. 4. Diffusion of Liquids. Let a jar be partly filled with water colored by blue litmus. Then, by a funnel-tube, pour clear water con- taining oil of vitriol to the bottom, beneath the colored water. At first, the two will be distinctly defined, "but in a few days they will mix, as will be seen by the change of color from blue to red. A drop of oil of vitriol may thus be distributed through a quart of water. Most liquids will mingle when brought in contact.* If, however, there is no ad- hesion between their molecules, they will not mix, and will separate even after having been thoroughly shaken together. 5. Diffusion of G-ases. Hydrogen gas is only -^ as heavy as common air. Yet, if two bottles be arranged as in Fig. 25, the lower one filled with the heavy gas, and the upper with the lighter, the gases will soon be uniformly mixed, f the surface of the liquid with a pen full of ink. The characteristic figures will quickly appear. Dissolve in water a pinch of salt and a lump of loaf-sugar. Touch the surface with lunar caustic. The figure of nitrate of silver will be seen. * A story is told of some negroes in the West Indies who supplied themselves with liquor by inverting the neck of a bottle of water in the bung-hole of a cask of rum. The water sank into the barrel, while the rum rose to take its place. t This phenomenon is explained by the theory that the molecules of all bodies are in rapid motion. As the worlds in space are clustered in mighty systems, the mem- 50 6. Osmose of Liquids. When two liquids are sepa- rated by a thin porous substance, the interchange is modified in a curious manner, according to the nature of the liquid and the substance used. At the end of a glass tube (Fig. 26) fasten a bladder of alcohol. Fill the jar with water, and mark tL* height to which the alcohol ascends in the tube. PIG. 26. FIG. 27. The column will soon begin to rise slowly. On examination, we shall see that the alcohol is passing out through the pores of the bladder and mixing with the water, while the water bers of each revolving about one another in inconceivably vast orbits, so each body is a miniature system, its molecules moving in inconceivably minute paths. In a gas, the molecular velocity is enormous. The particles of ammonia gas, for example, are flying to and fro at the rate of twenty miles per minute. " Could we, by any means," says Prof. Cooke, " turn in one direction the actual motion of the molecules of what we call still air, it would become at once a wind blowing seventeen miles per minute, and exert a destructive power compared with which the most violent tornado is feeble." Invert a bottle over a lighted candle, and the oxygen of the en- closed air being soon consumed the flame goes out. Instead of the bottle, use a foolscap-paper cone. There will be an interchange of gases through the pores of the paper and the light will burn freely. AUHES10K. 51 is coming in more rapidly. In most other cases of osmose, the flow is toward the denser liquid. The chemist uses a method of separating substances in solution, termed dialysis, that is based on their unequal diffusibility. 7. Osmose of Gases. Fit a porous cup used in Grove's Battery (p. 234) with a cork and glass tube, as in Fig. 27. Fasten the tube so that it will dip beneath the water in the glass. Then invert over the cup a jar of 'hydrogen. The gas will pass through the pores of the earthenware and down the tube so rapidly, as almost instantly to bubble up through the water.* PRACTICAL QUESTIONS. 1. Why does cloth shrink when wet? ,2. Why do sailors at a boat-race wet the sails ? 3. Why is writing-paper sized ? 4. Why does paint prevent wood from shrinking? 5. What is the shape of the surface of a glass- full of water ? Of mercury ? 6. Why can we not perfectly dry a towel by wringing? 7. Why will not water run through a fine sieve when the wires are greased ? 8. Why will camphor dissolve in alcohol, and not in water ? 9. Why will mercury rise in zinc tubes as water will in glass tubes ? 10. Why is it so difficult to lift a board out of water ? 11. Why will ink spilled on the edge of a book extend farther inside than if spilled on the side of the leaves ? 12. If you should happen to spill some ink on the edge of your book, ought you to press the leaves together ? 13. Why can you not mix water and oil ? 14. What is the object of the spout on a pitcher ? Ans. The water would run down the side of the pitcher by the force of adhesion, but the spout throws it into the hands of gravitation before adhesion can catch it. 15. Why will water wet your hand, while mercury will not? 16. Why is a pail or tub liable to fall to pieces if not filled with water or kept in a damp place ? 17. Name instances where the attraction of adhesion is stronger than that of cohesion. 18. Why does the water in Fig. 22 stand higher inside of the tube than next the glass on the outside ? 19. Why will clothes-lines tighten and sometimes break during a shower ? 20. Show that the law of the diffusion of gases aids in preserving the purity of the atmosphere. 21. In casting large cannon, the gun is cooled by a stream of cold water. Why? 22. Why does paint adhere to wood ? Chalk to the blackboard ? 23. Why does a towel dry one's face after washing? 24. Why will a greased needle float on water? 25. Why is the point of a pen slit ? 26. Why is a thin layer of glue stronger than a thick one ? * Rose balloons lose their buoyancy, because the hydrogen escapes through the pores of the rubber. If they were filled with air and placed in a jar of hydrogen, that gas would creep in so rapidly as to burst them. The quicker flow from the thinner to the thicker fluid is termed endosmose, and the opposite, slower current, exosmose, In performing the experiment shown in Fig. 27, coal-gas may be used. II. ATTRACTION OF GRAVITATION. FIG. 28. We have spoken of the attraction existing between the molecules of bodies at minute distances. We now notice an attraction which acts at all distances. 1. Law of Gravitation. Hold a stone in the hand, and you feel a power constantly drawing it to the ground. We call this familiar phenomenon weight. It is really the attraction of the earth pulling-ihe stone back to itself an instance of a general law, one operation of an ever-active force. For every particle of matter in the universe * attracts every other parti' cle, the force exerted between any tivo particles being directly proportional to the product of their masses, and inversely as the square of their distance apart. Gravitation is the general term for the attraction that exists between all bodies in the universe. Gravity is the earth's attraction for terrestrial bodies ; it tends to draw them toward the centre of the earth. Weight is the measure of the force of gravity. When we say that a body weighs 10 Ibs., we mean that the earth attracts it that amount. 2. Illustrations of Gravity. A stone falls to the ground because the * The force of gravitation resides in every particle of matter, and hence it is not confined to our own world. By its action the heavenly bodies are bound to one another, and thus kept in their orbits. It may help us to conceive how the earth is supported, if we imagine the sun letting down a huge cable, and every star in the heavens a tiny thread, to hold our globe in its place, while it in turn sends back a cable to the sun and a thread to every one of the stars. So we are bound to them and they to us. Thus the worlds throughout space are linked together by these cords of mutual attraction, which, interweaving in every direction, make the universe a unit. ATTRACTION OF GBAVITATION. 53 earth attracts it ; but in turn the stone attracts the earth. Each moves to meet the other, but the stone passes through as much greater distance than the earth as its mass is less. The mass of the earth is so gpeat that its motion is imper- ceptible. A plumb-line hanging-near a mountain is attracted from the vertical. In Fig. 28, AB represents the ordinary position of the line, while AC indicates the attractive power (exaggerated) of the mountain.* 3. Laws of "Weight. I. The iveight of a body at the centre of the earth is nothing, because the attraction there is equal in every direction. TL^Wie weight of a body above the surface of the earth decreases as the square of the distance from the centre of the earth increases.^ III. TJie weight of a body varies on different portions of the surface of the earth. \ It will be least at the equator, because (1), on account of the bulging form of our globe, a body is pushed out from the mass of the earth, and so removed from the centre of attraction ; and (2), the centrifugal force is the strongest. It will be the greatest at the poles, because (1), on account of the flattening of the earth, a body is * Maskelyne, in 1774, found the attraction of Mount Schehallien to be 12". By comparing this force with that of the earth, the specific gravity of the mountain being known, the specific gravity of the earth was estimated to be 5 times that of water. Later investigations make it 5.67. t A body at the surface of the earth (4000 miles from the centre) weiglfls 100 Ibs. What would be its weight 1000 miles above the surface (5000 miles from the centre) ? SOLUTION. (5000 mi.) a : (4000 mi.) a :: 100 Ibs. : x = 64 Ibs. Or, its weight would 4000 3 decrease in the ratio of = |g. Hence it would weigh |g x 100 Ibs. = 64 Ibs. The weight of a body below the surface of the earth is commonly said to decrease directly as the distance from the centre decreases. Thus, 1000 miles below the surface, a body would lose its weight. In fact, however, the density of the earth increases so much toward the centre, that for " T 7 o of the distance the force of gravity actually be comes stronger than on the surface." $ In these statements concerning weight, a spring-balance is supposed to be em ployed. ' With a pair of scales, the weights used would become heavier or lighter in the same proportion as the body to be weighed. If a spring-scale be graduated to indicate correctly afa medium latitude, it would show too little at the equator, and too much at the poles. In other words, a pound weighed by such a spring-scale at the equator would contain a greater mass of matter than one weighed at the polea by about jjj part, 54 ATTBACTIOH. Fio. 89. brought nearer its mass and the centre of attraction ; and (2), there is no centrifugal force at those points. 4. Falling Bodies. Since the attraction of the earth is toward its centre, bodies falling freely move in a direct line toward that point. This line is called a vertical or plumb-line. * (1.) LAWS or FALLING BODIES. I. Under the influence of gravity alone, all bodies fall with equal rapidity. This^is well illustrated by the " guinea- and-feather experiment." Let a coin and a feather be placed in a tube, and the air exhausted. Quickly invert the tube, and the two will fall in nearly the same time. Let in the air again, and the feather will flutter down long after the coin has reached the bottom, f Hence we conclude that in a vacuum all bodies descend with equal velocity, and that the resistance of the air is the cause of the variation we see between the falling of light and of heavy bodies. II. In the first second a body gains a velocity of 32 feet and falls \feet.\ This has been proved by careful experiments. Notice that 16 feet, the distance passed through the first second, is the mean between 0, the velocity at the beginning, and 32, the velocity at the close. * Prom plumbum, lead, because a lead weight is used by mechanics in finding it. All plumb-lines point very nearly toward the centre of the earth. t The same fact may be noticed in the case of a sheet of paper. When spread opt, it merely flutters to the ground ; but when rolled in a compact mass, it falls like lead. In this case we have not increased the force of attraction, but we.have diminished the resistance of the air. t More exactly, at the latitude of New York a body will fall in a vacuum 16.08 feet J)jo first second, and gain a velocity of 32.16 feet. 16 ft. =4,9 m. 32 ft. =9.8 m. =980 cm. GRAVITATION. 66 HI. At the end of any given second, the velocity is 16 feet multiplied by tivice the number of the second ; and the dis- tance passed through during that second is 16 feet multiplied by twice the number of the second minus one. In other words, the velocities are as the corresponding even numbers, 2, 4, 6, 8, etc., and the distances as the odd * numbers, 1, 3, 5, 7, etc. The body commences the second second with a velocity of 32 feet, and as gravity is a constant force, gains 32 feet during the second, making 64 feet 4 x 16 feet. It com- mences the third second with a velocity of 64 feet, and gains 32 feet, making 96 feet = 6 x 16 feet. The mean between 32 feet, the velocity at the beginning of the second second, and 64 feet, the velocity at the close, is 48 feet = 3 x 16 ft. The mean between 64 feet, the velocity at the beginning of the third second, and 96 feet, the velocity at the close, is 80 feet = 5 x 16 feet. IV. In any number of seconds a body falls 16 feet multi- plied by the square of the number of seconds. AVe have just seen that a body falls 16 feet the first second and 48 feet the next. Hence in two seconds it falls 16 feet -f- 48 feet = 64 feet = 2 2 x 16 feet. In three sec- onds it falls 16 + 48-^ 80 feet = 144 feet = 3 2 x 16 feet. (2.) EQUATIONS OF FALLING BODIES. If we represent the velocity of a falling body by v, the distance in any second by 5, the total distance by d, and the time by t, the follow- ing equations can be derived from the foregoing laws : v = 82*. .(1). d = 16 2 . . (2). - 2 = 64d. .(3). s = 16 (2t - 1). .(4). If g represent the constant force of gravity, a velocity of 32 feet per second, we have, . .(6). = ^gd ..... (8). a = %ff(2t - 1). . . .(10). * It will aid the memory, If we associate d in "distance" and ''odd," and win "velocity" and " even." To find the odd number corresponding to any second, double the number of the second and subtract one. See Explanatory Tables, p. 273. 56 ATTRACTION. (3.) To FIND THE DEPTH CF A WELL. Let a stone fall into it, and, with a watch or by the beat of the pulse, count the seconds that elapse before you hear it strike the bottom. Square the number of seconds, multiply 16 feet by the result, and the product is the depth.* (4.) WHEN A BODY is THROWN UPWARD, the same principles apply, it losing through gravity 32 feet in velocity each second. The velocity necessary to elevate it to a cer- tain point must be what it would acquire in falling that distance, f It will rise just as high in a given time as it would fall in the same time. If a ball be thrown vertically into the air, it will be as long in falling as in rising. In theory, it will strike the earth with the same velocity with which it was thrown ; in practice, however, it loses some of its velocity in rising and an equal amount in falling, owing to the resistance of the air. 5. The Centre of Gravity is that point on which, if supported, a body will balance itself. The tine of direction is a vertical drawn from the centre of gravity ; it is the line along which the centre of gravity would pass, if the body should fall. When a body is at rest, the forces which act on every mole- cule in it are said to balance one another, or to be in equilibrium. (1.) THREE STATES OF EQUILIBRIUM. 1st. A body is in stable equilibrium when the centre of gravity is below the point of support, or when any movement tends to raise the centre of gravity. In Fig. 30, the image has the centre of gravity lowered below the point of support by means of * A little time is required for the sound to come to the ear, but this is eo slight that it may be neglected. t If a body be thrown upward with a velocity of 128 feet, by applying equation (9) t = - , we find that it will rise for 4 seconds. ff GRAVITATION. 57 Fia. 31. lead balls. Remove these, and it immediately falls, but with them it is in stable equilib- rium. Any movement of the toy shown in Fig. 31 tends to raise the centre of gravity, and it returns quickly to a state of rest. A needle may be balanced on its point by a cork and two jack-knives (Fig. 32), which lower its centre of gravity. 2d. A body is said to be in unstable equilibrium when the centre of gravity is above the point of support, or when any movement tends to lower the centre of gravity. If we take the cork as arranged with the knives in Fig. 32, and invert it, we shall have difficulty in balancing the needle ; and, if we succeed, it will readily topple off, as the least motion tends to lower the centre of gravity. 3d. A body is said to be in indifferent equilibrium when the centre of gravity is at the point of support, or when any movement tends neither to ele- rate nor lower the centre of gravity. A ball of uniform density on a level surface will rest in any position, be- cause the centre of gravity moves in a line parallel to the floor. (2.) THE CENTRE OF GRAVITY MAY BE FOUND either by balancing the body, or by suspending it from two corners, successively, as in Fig. 33. By a plumb-line obtain the PIG. 33. 58 ATTRACTION. line of direction AE ; then hang the slate from another cor- ner, and mark the line of direction BD. The point 0, where the two lines cross, is the centre of gravity. (3.) GENERAL PRINCIPLES. (a.) The centre of gravity tends to seek the lowest point. (b.) A body will not tip over while the line of direction falls within the base, but will as soon as it falls without.* (c.) In general, narrowness of base combined with height of centre of gravity, tends to instability ; f breadth of base and lowness of centre of gravity, produce stability. (4.) PHYSIOLOGICAL FACTS. Our feet and the space be- tween them form the base on which we stand. By turning our toes outward, we increase its breadth. When we stand on one foot, we bend over so as to bring the line of direction within this narrower base. When we walk, we incline to the right and the left alternately. When we carry a pail of water, we balance it by leaning in the opposite direction. When we walk up hill we lean forward, and in going down hill we incline backward, in unconscious obedience to the laws of gravity. We bend forward when we wish to rise from a chair, in order to bring the centre of gravity over our feet, our muscles not having sufficient strength to raise our bodies without this aid. When we walk, we lean forward, so as to bring the centre of gravity as far in front as possi- * The Leaning Tower of Pisa, in Italy, beautifully illustrates this principle (see Frontispiece). It is about 188 feet high, and its top leans 15 feet, yet the line of direction falls so far within the base that it is perfectly stable, having stood for seven centuries. The feeling experienced by a person who for the first time looks down from the lower side of the top of this apparently impending structure is startling indeed. t This is shown by the difficulty in learning to walk upon stilts. The art of bal- ancing one's self may, however, be acquired by practice, as is seen in the Landes of southwestern France. During a portion of the year these sandy plains are half- covered with water, and in the remainder are still very bad walking. The natives accordingly double the length of their legs by stilts. Mounted on these wooden poles, which are put on and off as regularly as the other parts of their dress, they appear to strangers as a new and extraordinary race, marching with steps of six feet in length, and with the speed of a trotting-horse. While watching their flocks, they support themselves by a third staff behind, and then with their rough sheep-skin cloaks and caps, like thatched roofs, seem to be little watch-towers, or singular lofty tripods, scattered over the country. (Arnott.) GRAVITATION. 59 ble. Thus, walking is a process of falling. When we run, we lean further forward, and so fall faster. (Phys., p. 49.) 6. The Pendulum consists of a weight so suspended as to swing freely. Its move- ments to and fro are termed vibrations or oscillations. The path through which it passes is called the arc. The extent to which it goes in either direction from the lowest O point is styled its amplitude. Vibrations performed in equal times are termed i-socti- ro-nous (isos, equal ; chronos, time). (1.) THEEE LAWS. I. In the same pen- dulum, all vibrations of small amplitude are isochronous. If we let one of the balls rep- = resented fti Fig. 34 swing through a short arc, and then through a longer one, on counting the number of oscil- lations per minute, we shall find them very uniform. II. Tlie times of the vibra- tions of different pendulums are proportional to the square roots of their respective lengths.^ Ex. : A pendulum \ the length of another, will vibrate three times as fast. * Conversely, the lengths of different pendulums are proportional to the squares of their times of vibration. PIG. 35. * A pendulum which vibrates seconds must be four times as long as one which vibrates half-seconds. The apparatus rep- resented in Figs. 34 and 35 can be made by any carpenter or ingenious pupil, and will serve excellently to illustrate the three laws of the pendulum. 60 ATTRACTION. Fl6 s 6 - III. The time of the vibration of the same pendulum ivill vary at different places, since it decreases as the square root of the force of gravity increases. At the equator a pendulum vibrates most slowly, and at the poles most rap- idly. The length of a seconds-pendulum at New York is about 39^ inches. (2.) CENTRE OF OSCILLATION. The upper part of a pendulum tends to move faster than the lower part, and so has- tens the speed. The lower part of a pendulum tends to move slower than the upper part, and so retards the speed. Between these extremes is a point which is neither quickened nor impeded by the rest, but moves in the same time that it would if it were a particle swinging by an imaginary line. This point is called the centre of oscillation. It lies a little below the centre of gravity.* In Fig. 35 is shown an apparatus containing pen- dulums of different shapes, but of the same length. If they are started to- gether, they will immediately diverge, no two vibrating in the same time. As pendulums, they are not of the same length. (3.) THE CENTRE OF OSCILLATION is FOUND BY TRIAL. Huygens dis- covered that the point of suspension and the centre of oscillation are interchange- able. If, therefore, a pendulum be inverted, and a point found at which it will vibrate in the same time as before, * This determines the real length of a pendulum, which is the distance from the point of support to the centre of oscillation. The imaginary pendulum above described is known in Physics as the Simple Pendulum. 39.1 inches = 933.3 mm. GBAVITATION. 61 Fie. 37. this is the former centre of oscillation ; while the old point of suspension becomes the new centre of oscillation.* (4.) THE PENDULUM AS A TIME-KEEPER. The friction at the point of suspension, and the resistance of the air, soon destroy the motion of the pendulum. The clock is a machine for keeping up the vibration of the pendulum, and counting its beats. In Fig. 36, R is the scape-wheel driven by the force of the clock-weight or spring, and mn the escape- ment, moved by the forked arm AB, so that only one cog of the wheel can pass at each double vibration of the pendulum. Thus the oscillations are counted by the cogs on the wheel, while the friction and the resist- ance of the air are overcome by the action of the weight or spring. f As "heat expands and cold contracts," a pendulum lengthens in summer and shortens in winter. A clock, therefore, tends to lose time in summer and gain in winter. To regulate a clock, we raise or lower the pendulum-bob, L, by the nut v. The gridiron pendulum consists of brass and steel rods, so connected that the brass, h, Tc, will lengthen upward, and the steel , , c, d, downward, and thus the centre of oscillation remain unchanged. The mercu- rial pendulum contains a cup of mercury which expands upward while the pendulum- rod expands downward. (5.) OTHER USES OF THE PEHDULUM. (a.) Since the time of vibration of a pendu- * The centre of oscillation is the same as the centre of percussion. The latter is the point where we must strike a suspended body, if we wish it to revolve about its axis without any strain. If we do not hit a ball on the bat's centre of percussion, our hands " sting " with the jar. (See note, p. 260.) t The action of & clock is clearly seen by procuring the works of an old clock and watching the mcvczLccts of ike various parts. ATTRACTION. FIG. 38. lum indicates the force of gravity, and the force of gravity decreases as the square of the distance from the centre of the earth increases, we may thus find the semi-diameter of the earth at various places, and ascertain the figure of our globe. (b.) Knowing the force of gravity at any point, the velocity of a fall- ing body can be determined. (c.) The pendulum may be used as a standard of meas- ures, (d.) Foucault devised a method of showing the revolution of the earth on its axis, founded upon the fact that the pendulum vi- brates constantly in one plane.* (e.) By observing the difference in the length of a seconds-pendulum at the top of a mountain and at the level of the sea, the density of the earth may be estimated. PRACTICAL QUESTIONS. 1. When an apple falls to the ground, how much does the earth rise to meet it? 2. What causes the sawdust on a mill-pond to collect in large masses? 3. Will a body weigh more in a valley than on a mountain ? 4. Will a pound weight fall more slowly than a two-pound weight ? 5. How deep is a well if it takes three seconds for a stone to fall to the bottom ? 13. Is the centre of gravity always within a body as, for example, a pair of tongs ? 7. If two bodies, weighing respectively 2 and 4 Ibs. , be connected by a rod 2 feet long, where is the centre of gravity ? 8. In a ball of equal density throughout, where is the centre of gravity ? 9. Why does a ball roll down hill ? 10. Why is it easier to roll a round body than a square one ? 11. Why is it easier to tip over a load of hay than one of stone ? 12. Why is a pyramid such a stable structure ? 13. Where is the centre of gravity of a hollow ball? 14. Why does a rope-walkbr carry a heavy balanchig-pole ? 15. What would become of a ball if dropped into a hole bored through the centre of the earth ? 16. Would a clock lose or gain time }f carried to the top of a mountain ? If carried to the North Pole ? 17. In the winter, would you raise or lower the pendu- him-bob of your clock? 18. Why is the pendulum-bob often made flat? 19. What * A pendulum 220 feet in length was suspended from the dome of the Pantheon in Paris. The lower end of the pendulum traced its vibrations north and south upon a table beneath, sprinkled with fine sand. These paths did not coincide, but at each return to the outside, the pendulum marked a point to the right, At the poles of the earth, the pendulum, constantly vibrating in the same vertical plane, would perform a complete revolution in 24 hoars, making thus a kind of clock. At the equator it would not change east or west, as the plane of vibration would go forward with the diurnal revolution of the earth. The shifting of the plane would increase as the pen- dnlom was carried north or south from the equator. SUMMARY. 63 "beats off" the time In a watch? 20. What should be the length of a pendulum to vibrate minutes at the latitude of New York ? Solution. (1 sec.) a : (60 sec.) 8 : : 89 1 in. : x=2.2+ miles. 21. What should be the length of the above to vibrate half-seconds ? Quarter-seconds ? Hours ? 22. What is the proportionate time of vibration of two pendulums, respectively 16 and 64 inches long? 23. Why, when you are standing erect against a wall, and a piece of money is placed between your feet, can you not stoop forward and pick it up ? . 24. If a tower were 198 feet high, with what velocity would a stone, dropped from the summit, strike the ground ? 25. A body falls hi 5 seconds ; with what velocity does it strike the ground ? 26. How far will a body fall in 10 seconds? With what velocity will it strike the ground? 27. A body is thrown upward with a velocity of 192 feet the first second ; to what height will it rise? 28. A ball is shot upward with a velocity of 256 feet; to what height will it rise ? How long will it continue to ascend ? 29. Why do not drops of water, falling from the clouds, strike with a force proportional to the laws of falling bodies ? Am. Because they are so small that the resistance of the air nearly destroys their velocity. If it were not for this wise provision, a shower of rain-drops would be as fatal as one of Minie bullets. 30. Are any two plumb-lines parallel ? 31. A stone let fall from a bridge strikes the water in 3 seconds. What is the height ? 32. A stone falls from a church-steeple in 4 seconds. What is the height of the steeple ? 83. How far would a body fall in the first second at a distance of 12,000 miles above the earth's surface ? 34. A body at the surface of the earth weighs 100 tens ; what would be its weight 1,000 miles above ? 35. A boy wishing to find the height of a steeple, lets fly an arrow that just reaches the top and then falls to the ground. It is in the air 6 sec- onds. Required the height. 36. A cat let fall from a balloon reaches the grouni in 10 seconds. Required the distance. 37. In what time will a pendulum 40 feet long make a vibration ? 38^ Two meteoric bodies in space are 12 miles apart. They weigh respectively 100 and 200 Ibs. If they should fall together by their mutual attraction, what portion of the distance would be passed over by each body? 39. If a body weighs 2,000 Ibs. upon the surface of the earth, what would it weigh 2,000 miles above ? 500 miles above ? 40. At what distance above the earth will a body fall, the first second, 21 1 inches? 41. How far will a body fall in 8 seconds? In the 8th second ? In 10 seconds ? In the 30th second ?"'\42. How long would it take for a pendulum one mile in length to make a vibration ?N^3. How long must a pen- dulum be to vibrate three times in 5 seconds ? 44^(jVill a pendulum made of lead vibrate faster than one of the same length made of feathers ?^ Which would come to rest sooner ? Why ? 45. What would be ,,he time of Vibration of a pendulum 64 metres long? 46. A ball is dropped from a height of 64 feet. At the same moment a second ball is thrown upward with sufficient velocity to reach the same point. Where will the two balls pass each other ? 47. Two bodies are successively dropped from the same point with an interval of J of a second. When will the distance between them be one metre ? 48. Explain the following fact : A straight stick loaded with lead at one end, can be more easily balanced ver- tically on the finger when the loaded end is upward than when it is downward. 49. What effect would the fall of a heavy body to the earth have upon the motion of the earth in its orbit? (In answering this question, imagine the body to fall in various directions toward the earth, as opposed to the motion of the earth, in the same direction with the earth's motion, etc.) 50. If a body weighing a pound on the earth were carried to the sun it would weigh about 27 pounds. How much would it then attract the sun ? 51. Why does watery vapor float and rain fall ? 52. If a body weighs 10 kilos, on the surface of the earth, what would it weigh 1,000 kilometres above (the earth's radius being 6.366 km.) ? 53. A body is thrown vertically upward with a velocity of 100 metres ; how long before it will return to its original position ? 54. Required the time needed for a body to fall a distance of 2,000 metres. 55. If two bodies, weighing respectively 1 kilo, and 1 demi-kilo., are connected by a rod 90 centimetres long, where is the centre of gravity ? 64 ATTRACTION. SUM MARY. There are certain forces residing in molecules and acting only at insensible distances, which are known as the Molecular Forces. The one which ties together molecules of the same kind is styled cohesion. The relation between this force and that of heat determines whether a body is solid, liquid, or gaseous. Under the action of cohesion, liquids tend to form spheres ; and solids, crystals. The processes of welding and tempering, and the annealing of iron and glass, illustrate curious modifications of the cohesive force. Molecules of different kinds are held together by adhesion. Its action is seen in the use of cement, paste, etc., in the solution of solids, in capillarity, diffusion of gases, and osmose. Gravitation, though weak,* compared with cohesion, acts uni- versally. Its force is directly as the product of the attracting and attracted masses, and inversely as the square of their distance apart. Gravity makes a stone fall to the ground. The earth and a kilogram of iron in mid-air attract each other equally, but the former is so much heavier that they move toward each other with unequal velocity, and the motion of the earth is imperceptible. Weight is the resisted attraction of the earth. At the centre of the earth the weight of a body would be nothing ; at the poles it would be greatest, and at the equator least. Increase of distance above or far below the surface of the earth will diminish weight. Were the resistance of the air removed, all bodies would fall with equal rapidity. The first second a body falls 16 feet (4.9 metres), and gains a velocity of 32 feet (9.8 metres). In general, the velocity of a falling body is 16 feet, multiplied by the even number corresponding to the second, and the distance 16 feet multiplied by the odd number. The centre of gravity is the point about which the weights of all the particles composing a body will balance one another, i. e., be in equilibrium. There are three states of equilibrium stable, unstable, and indifferent according as the point of support in a body is above, below, or at the centre of grav- ity. As the centre of gravity tends to seek the lowest point, its position determines the stability of a body. The centre of gravity may be found by trial or with a plumb-line. A body suspended so as to swing freely is a pendulum. The time of a pendulum's vibration is inde- pendent of its material, proportional to the square root of its length and * As the attraction of gravitation acts so commonly upon great masses of matter, we are apt to consider it a tremendous force. We, however, readily detect its rela- tive feebleness when we compare the weight of bodies with their tenacity. Ex. : Think how much easier it is to lift an iron wire against gravity than to pull it to pieces against cohesion. HISTORICAL SKETCH. 65 variable according to the latitude. The pendulum is our time-keeper and useful in many scientific investigations. We are so accustomed to see all the objects around us possess weight, that we can hardly conceive of a body deprived of a property which we are apt to consider as an essential attribute of matter. Nothing is more natural, apparently, than the falling of a stone to the ground. "Yet," says D'Alembert, "it is not without reason that philosophers are astonished to see a stone fall, and those who laugh at their astonishment would soon share it themselves, if they would reflect on the subject." Gravity is constantly at work about us, at one moment producing equilibrium or rest, and at another, motion. When it seems to be destroyed, it is only counterbalanced for a time, and remains, apparently, as indestructible as matter itself. The stability and the incessant changes of nature are alike due to its action. Not only do rivers flow, snows fall, tides rise, and mountains stand in obedience to gravitation, but smoke ascends and clouds float through the combined influence of heat and weight. HISTORICAL SKETCH. The latter part of the sixteenth century witnessed the establish- ment of the principles of falling bodies. Galileo, while sitting in the cathedral at Pisa (see Frontispiece) and watching the swinging of an immense chandelier which hung from its lofty ceiling, noticed that its vibrations were isochronous. This was the germ-thought of the pen- dulum and the clock. Up to his time it had been taught that a 4-lb. weight would fall twice as fast as a 2-lb. one. He proved the fallacy of this view by dropping from ths Leaning Tower of Pisa balls of dif- ferent metals gold, copper, and lead. They all reached the ground at nearly the same moment. The slight variation he correctly accounted for by the resistance of the air, which was not the same for all. Newton, as the story runs, was sitting in his garden one day, and noticed the fall of an apple. Reflecting upon the force which drew it to the ground, the thought struck his mind that perhaps the same force acted upon the heavenly bodies. The moon, for example, revolves about the earth in a fixed orbit. Might it not be the attraction of the earth which causes the moon to move in this curved path? To test this, he calculated how far the moon bends from a straight line, i. e. , falls toward the earth every second. Knowing the distance a body falls in a second at the surface of the earth, he endeavored to see how far it would fall at the distance of the moon. For years he toiled over 66 ATTRACTION. this problem, but an erroneous estimate of the earth's diameter then accepted by physicists prevented his obtaining a correct result. Finally, a more accurate measurement having been made, he inserted this in his calculations. Finding the result was likely to verify his conjecture, his hand faltered with the excitement, and he was forced to ask a friend to complete the task. The truth was reached at last, and the grand law of gravitation discovered (1682). The sun-dial was doubtless the earliest device for keeping time. The clepsydra was afterward employed. This consisted of a vessel con- taining water, which slowly escaped into a dish below, in which was a float that by its height indicated the lapse of time. King Alfred used candles of a uniform size, six of which lasted a day. The first clock erected in England, about 1288, was considered of so much importance that a high official was appointed to take charge of it. The clocks of the middle ages were extremely elaborate. They indicated the motions of the heavenly bodies ; birds came out and sang songs, cocks crowed, and trumpeters blew their horns ; chimes of bells were sounded, and processions of dignitaries and military offieers, in fantastic dress, marched in front of the dial and gravely announced th3 time of day. Watches were made at Nuremberg in the fifteenth century. They were styled Nuremberg eggs. Many were as small as the watches of the present day, while others were as large as a dessert-plate. They had no minute or second hand, and required winding twice per day. On Attraction, as well as on subsequent topics treated in this book, consult Guillemin's " Forces of Nature " ; Atkinson's Ganot's Physics ; Arnott's " Elements of Physics"; SnelPs Olmstead's Natural Philosophy ; Todhunter's " Philosophy for Beginners " ; Stewart's Elementary Physics ; Silli man's Physics ; Everett's " Text-book of Physics"; Young's "Lectures on Natural Philosophy"; Thomson and Tait's "Elements of Natural Philosophy"; "Appleton's Cyclo- paedia," Articles on Clocks and Watches, Weights and Measures, Gravi- tation, Mechanics, etc. ; Peck's Ganot's Natural Philosophy ; Miller's Chemical Physics, Chap. Ill, on Molecular Force ; Weinhold's Experi- mental Physics; Pickering's " Elementary Physical Manipulation"; Fourteen Weeks in Astronomy, Sections on Galileo and Newton, pp. 29-34. The current numbers of Harper's Magazine ; Scribner's Magazine (The World's Work) ; Popular Science Monthly ; Boston Journal of Chemistry ; Scientific American ; Knowledge ; and Nature, contain the latest phases of science. IV. Nature is a reservoir of power. Tremendous forces are all about us, but they are not adapted to our use. We need to remould the energy to Jit our wants. A waterfall cannot grind corn nor the wind draw water. Yet a machine will gather up these wasted forces, and turn a grist-mill or work a pump. A kettle of boiling water has little of promise ; but husband its energy in the steam-engine, and it will weave cloth, forge an anchor, or bear our burdens along the iron track. " The hero in the fairy tale had a servant who could eat granite rocks, another who could hear the grass grow, and a third who could run a hun- dred leagues in half an hour. So man in nature is surrounded by a gang of friendly giants who can accept harder stints than these. There is no porter like gravitation, who will bring down any weight you cannot carry, and if he wants aid, knows how to get it from his fellow-laborers. Water sets his irresistible shoulder to your mill, or to your ship, or transports vast boulders of rock, neatly packed in his iceberg, a thousand miles" EMERSON CQ w <1 ANALYSIS. r THE SIMPLE MACHINES. THE LAW OF MECHANICS. 1. Definition. "(1.) 1. THE LEVER. 4. Steelyard. [jj L 5. Compound Lever. O 2. Three Classes of Levers ' (3.*) Third Class. 3. Law of Equilibrium. 2. THE WHEEL AND)*' Definition and Illustration. w AVI p { 2. Law of Equilibrium. * [ 3. Wheelwork. ft O 1 3. THE INCLINED PLANE, j 1 - Definition and Illustration. j 2. Law of Equilibrium. EH fc (^ P H w 4. THE SCREW J *' ^ enn i* ion an ^ Illustration. ( 2. Law of Equilibrium. 5 THE WEDGE j *' ^ enn i tion an ^ Illustration. i Law of Equilibrium. 1. Definition and Illustration. 6 THE PULLEY J ^' ^ xe d and Movable Pulleys, 3. Combinations of Pulleys. 4. Law of Equilibrium. 7. CUMULATIVE CONTRIVANCES. 8. PERPETUAL MOTION. ELEMENTS OF MACHINES. The Simple Machines are the elements to which all machinery can be reduced. The watch with its complex system of wheel-work, and the engine with its belts, cranks and pistons, are only various modifications of some of the six elementary forms the lever, the wheel and axle, the inclined plane, the screiv, iho^wedge, and the pulley. * They are often termed the Mechanical Powers, but they do not produce work ; they are only methods of applying it. Here again the doctrine of the Conservation of Energy holds good. The work done by the power is always equal to the resistance overcome in the weight. The Law of Mechanics is, the power multiplied ly the distance through which it moves, is equal to the weight multi- plied by the distance through which it moves, f Ex. : 1 Ib. of power moving through 10 feet = 10 Ibs. of weight moving through one foot, or vice versa. This must include the work of moving the machine as well as the weight itself. 1. The Lever is a bar turning on a pivot. The force used is termed the poiver (P), the object to be lifted the iveight (W), the pivot on which the lever turns the fulcrum (F), and the parts of the lever each side of the fulcrum the arms. THREE CLASSES OF LEVERS. In the three kinds, the fulcrum, weight and power are each respectively between the other two, as may be seen by comparing Figs. 39-41. * These six may be still further reduced to two the lever and the inclined plane. t In theory, the parts of a machine have no weight, move with no friction, and meet no resistance from the air. In practice, these influences must be considered. 70 ELEMENTS OF MACHINES. Fie. I FIG. 40. Fie. 41. FIG. 42. TV' First Class. We wish to lift a heavy stone. Accordingly we put one end of a handspike under it, and resting the bar on a block at F, bear down at P. A pump-handle is a lever of the first class. The hand is the P, the water lifted the W, and the pivot the F. A pair of scissors is a double lever of the same class. The cloth to be cut is the W, the hand the P, and the rivet the F. Second Class. We may also raise the stone, as in Fig. 43, by FIO. 43. resting one end of the lever on the ground, which acts as a fulcrum, and lifting up on the bar. An oar is a lever of the second class. The hand is the P, the boat the W, and the water the F. Third Class. The treadle of a sewing-machine is a lever of the third class. The front end resting on the ground is the F, the foot is the P, and the force is transmitted by a rod to the W, the arm above. In the fishing-rod, one hand is the F, the other the P, and the fish the W. * LAW OF EQUILIBRIUM. A force multiplied by its per- pendicular distance from a point is called the moment or turning effort of the force about that point as a pivot. In the lever, P balances W when the moments about the ful- crum are equal. Let Pd represent power's distance from * See p. xi. Fresh Facts and Theories. THE LEVER. 71 the F, and Wd weight's distance. the law of mechanics, Substituting these terms P:W::We2:P and P en at K!I fa centre above and below. The axis of the wheel is the cylinder/, from which radiate plane- floats against which the water strikes. To confine the wa- ter at the top and the bottom is a circular disk at- tached to the cyl- inder and the floats. In these disks are the swells project- ing above and below for discharging the water. They com- mence near the cylinder, and swelling outward scroll-shaped, form openings curved toward the cylinder, thus emptying the water in a direction opposite to that in which it enters the wheel. This form utilizes as high as 90 per cent, of the force. F is a band- wheel which conducts the power to the machinery. The principle of the unbalanced pressure of a column of water may also be employed. It is illustrated in the old- fashioned Barker's Mill or Reaction- Wheel.* This consists of an upright cylinder with horizontal arms, on the opposite * Revolving fire-works and the whirl-i-gig, used for watering lawns and as an ornament in foiuitains, are constructed on the same principle. An ingenious pupil HYDRAULICS. 101 FIG. 89. sides of which are small apertures. It rests in a socket, so as to revolve freely. Water is supplied from a tank above. If the openings in the arms are closed, when the cylinder is filled with water the pressure is equal in all directions and the machine is at rest. If now we open an aperture, the pressure is re- lieved on that side, and the arm flies back from the unbalanced pressure of the column of water above. 5. "Waves are produced by the friction of the wind against the sur- face of the water. The wind raises the particles of water and gravity draws them back again. They thus vibrate up and down, but do not ad- vance.* The forward movement of the wave is an illusion. The form of the wave progresses, but not the water of which it is composed, any more than the thread of the screw which we turn in our hand, or the undulations of a rope or carpet which is shaken, or the stalks of grain which bend in billows as the wind sweeps over them. The corresponding parts of different waves are said to be like phases. The distance between two like phases, or between the crests can easily construct a Reaction- wheel of straws or quills, pouring the water into the upright tube by means of a pitcher or admitting.it slowly through a siphon from a pail of water placed on a table above. * Near the shore the oscillations are shorter, and the waves unbalanced by the deep water, are forced forward till the lower part of each one is checked by the friction on the sandy beach, the front becomes well-nigh vertical, and the upper part curls over and falls beyond. The size of "mountain billows " has been exaggerated. Along the coast they may reach 90 feet, but in the open sea the highest wave, from the deepest " trough " to the very topmost " crest," rarely measures over 30 feet. 102 PRESSURE OF LIQUIDS AND GASES. of two succeeding waves, is called a wave-length. Opposite phases are those parts which are vibrating in different directions, as the point midway in the front of one wave and another midway in the rear of the next wave. A tide- wave may he setting steadily toward the west ; waves from distant storms may he moving upon this ; and above all, ripples from the breeze then blowing may diversify the FIG. 90. surface.* These different systems will be distinct, yet the joint effect may be very peculiar. If any two systems co- incide with like phases, the crest of one meeting the crest of the other, and the furrow of one meeting the furrow of the other, the resulting wave will have a height equal to the sum of the two. If any two coincide with opposite * The manner in which different waves move among and upon one another, is seen by dropping a handful of stones in water and watching the waves as they circle out from the various centres in ever-widening curves. In Fig. 90 is shown the beautiful appearance these waves present when reflected from the sides of a vessel. PNEUMATICS. 103 phases, the hollow of one striking the crest of another, the height will be the difference of the two. Thus, if in two systems having the same wave-length and height, one is exactly half a length behind the other, they will destroy each other.* This is termed the interference of waves. PRACTICAL QUESTIONS. 1. How much more water can be drawn from a faucet 8 feet than from one 4 feet below the surface of the water in a cistern 5^~2. How much water will be discharged per second from a short pipe having a diameter of 4 inches and a depth of 48 feet below the surface of the water? 3. When we pour molasses from a jug, why is the stream so much larger near the nozzle than at some distance from it? 4. Ought a faucet to extend into a barrel beyond the staves? 5. What would be the effect if both openings in one of the arms of Barker's Mill were on the same side ? III. PNEUMATICS. Pneumatics treats of the general properties and the pressure of gases. Since the molecules move among one another more freely even than those of liquids, the conclu- sions which we have reached with regard to transmission of pressure, buoyancy and specific gravity apply also to gases. As air is the most abundant gas, it is taken as the type of the class, as water is of liquids. 1 . The Air-pump is shown in its essential features in Fig. 91. A is a glass receiver stand- ing on an oiled pump-plate. The tube D, connecting the receiver with the cylinder, is closed by the valve E opening upward. There is a second * In the port of Bateha the tidal wave comes up by two distinct channels so un- equal in length that their time of arrival varies by six hours. Consequently when the crest of high water reaches the harbor by one channel, it meets the low water returning by the other, and when these opposite phases are equal, they neutralize each other so that at particular seasons there is no tide in the port, and at other times there is but one tide per day, and that equal to the differed between the ordinary morning and evening tide. Lloyd's Wave Theory. 104 PRESSURE OF LIQUIDS AND GASES. valve, P, in the piston, also opening upward. Suppose the piston is at the bottom and both valves shut. Let it now be raised, and a vacuum will be produced in the cylinder ; the expansive force of the atmosphere in the receiver will open the valve E and drive the air through to fill this empty space. When the piston descends, the valve E will close, while the valve P will open, and the air will pass up above the piston. On elevating the piston a second time, this air is removed from the cylinder, while the air from the re- ceiver passes through as before. At each stroke a portion of the atmosphere is drawn off; but the expansive force becomes less and less, until finally it is insufficient to lift the valves. For this reason a perfect vacuum cannot be obtained. 2. The Condenser, in construction, is the reverse of the air-pump. It is used to force into a vessel an increased quantity of air.* 3. Properties of Air. (1.) WEIGHT. Exhaust the air from a flask which holds 100 cubic inches, and then balance it. On turning the stop-cock, the air will rush in with a whizzing noise and the flask descend. It will require 31 grains to restore the equipoise, f * The practical applications of this pump are numerous. The soda manufacturer uses it to condense carbonic acid in soda-water reservoirs. The engineer employs it in laying the foundations of bridges. Large tubes or caissons are lowered to the bed of the stream, and air being forced in, drives out the water. The workmen are let into the caissons by a sort of trap, and work in this condensed atmosphere with comfort. Pneumatic despatch -tubes contain a kind of train holding the mail, and back of this a piston fitting the tube. Air is forced in behind the piston or ex- hausted before it, and so the train is driven through the tube at a high speed. In the Westinghouse air-brake, condensed air is forced along a tube running underneath the cars, and by its elastic force drives the brakes against the wheel. t Hermetically close one end of a piece of iron gas-pipe, and fit a stop-cock to the other. With a condenser crowd into the tube several atmospheres. Weigh the tube in a grocer's balance. Turn the stop-cock and let the air escape. Then the beam will rise. The amount of the weights required to be added to restore the equilibrium r ill show the weight of the condensed air. PNEUMATICS. 105 FIG. 93. (2.) ELASTICITY is shown in a pop-gun. We compress the atmosphere in the barrel until the elastic force drives out the stopper with a loud report. As we crowd down the piston we feel the elasticity of the air yielding to our strength, like a bent spring. The bottle-imps, or Cartesian divers, illustrate the same property. Pig. 93 represents a simple form of this apparatus. The cover of a fruit-jar is fitted with a tin tube, which is inserted in a syringe-bulb. The jar is filled with water and the diver placed within. This is a hollow image of glass, having a small opening at the end of the curved tail. If we squeeze the bulb, the air* will be forced into the jar and the water will transmit the pressure to the air in the image. This being compressed, more water will enter, and the diver will descend. On relaxing the grasp of the hand on the bulb, the air will return into it, the air in the image will expand, by its elastic force driving out the water, and the diver, thus lightened of his ballast, will ascend. The nearer the image is to the bottom, the less force will be required to move it. With a little care it can be made to respond to the slightest pres- sure, and will rise and fall as if instinct with life.* (3.) EXPANSIBILITY. Let a well-dried bladder be partly filled with air and tightly closed. Place it under the re- ceiver and exhaust the air. The air in the bladder expanding will burst it into shreds. Take two bottles partly filled with * This experiment shows also the buoyant force of liquids, their transmission of pressure in every direction, the increase of the pressure in proportion to the depth, and the principle of Barker's Mill. (See note, FIG. 94. 106 PRESSURE OP LIQUIDS AND GASES. FIG. 95. FIG. 96. colored water. Let a bent tube be inserted tightly in A and loosely in B. Place this apparatus under the receiver and exhaust the air. The expansive force of the air in A will drive the water over into B. On re- admitting the air into the receiver, the pressure will return the water into A. It may thus be driven from bottle to bottle at pleasure.* Hero* s fountain acts on the same principle, as may be seen by an examination of Fig. 96. Having removed the jet-tube, the upper globe is partly filled with water. The tube being then replaced, water is poured into the basin on top. The liquid runs down the pipe at the right, into the lower globe. The air in that globe is driven up the tube at the left, into the upper globe, and by its elas- ticity forces the wa- ter there out through the jet-tube, forming a tiny fountain. 4. Pressure of the Air. (1.) THE PROOF. If we cover a hand-glass with one hand, as in Fig. 97, on exhausting the air we shall find the pressure painful, f Tie over one FIG. 97. * Prick a hole in the small end of an egg and place the egg with the big end np in a wine-glass. On exhausting the receiver, the bubble of air in the upper pert of the egg will drive the contents down into the glass, and on admitting the air they will be forced back again. t The exhaustion of the air does not produce the pressure on the hand ; it simply reveals it. The average pressure on each person is 16 tons. It is equal, however, on all parts of the body and is counteracted by the air within. Hence we never notice it Persons who go up high mountains or g down in diving-bells feel the change in the pressure. PNEUMATICS. 107 When dry, exhaust FIG. 98. FIG. 99. end of the glass a piece of wet bladder, the air, and the mem- brane will burst with a sharp report.* The Magdeburg Hemi- spheres are named from the city in which Guer- icke, their inventor, re- sided. They consist of two small brass hemispheres, which fit closely together, but may be separated at pleasure. If, how- ever, the air be exhausted from within, several persons will be required to pull them apart, f In whatever position the hemispheres are held, the pres- sure is the same. (2. ) UPWARD PRESSURE. Fill a tumbler with water, and then lay a sheet of paper over the top. Quickly invert the glass, and the water will be supported by the up- ward pressure of the air. "Within the glass cylinder, Fig. 100, is a piston working air-tight. Connect C with the pump by a rubber tube * To show the crushing force of the atmosphere, take a tin cylinder 15 inches long and 4 inches in diameter. Fit one end with a stop-cock or merely leave a hole for the exit of the steam. Put in a little water and boil. When the air is entirely driven out, turn the stop-cock or close the opening with a bit of solder. Pour cold water over the outside to condense the steam, when the cylinder will collapse as if struck by a heavy blow. t In the Museum at Berlin the hemispheres used by Guericke in his experiments are preserved. They are of copper, and, by the author's measurements, 22 inches interior diameter with a flange an inch wide, making the entire diameter 2 feet. Accompanying is a Latin book by the burgomaster describing numerous pneumatic experiments which he had performed, and containing a wood-cut representing three spans of horses oil each side trying to separate the hemispheres. 108 PRESSURE OF LIQUIDS AND GASES. and exhaust the air. The weight will leap up as if caught by a spring. (3.) BUOYANT FORCE OF THE AIR. The law of Archi- medes (p. 93) holds true in gases. Smoke and other light substances float in the air, as wood does in water, because they are lighter and are buoyed with a force equal to the weight of the air they displace. A hollow sphere of copper, Fig. 101, is balanced in the air by a solid lead weight, but it instantly falls on being placed under the receiver and the FIG. 101. FIG. 102. air exhausted. This shows that its weight was partly sustained by the buoyant force of the air. (4.) THE PRESSURE OF THE AIR SUSTAINS A COLUMN OF MERCURY 30 INCHES HIGH, OF WATER 34 FEET HIGH, AND IS 15 LBS. PER SQUARE INCH. Take a strong glass tube about three feet in length, and j| tie over one end a piece of wet bladder. When dry, fill the tube with mercury, and invert it in a cup of the same liquid. The mercury will sink to a height of about 30 in. If the area across the tube be 1 sq. in., the metal will weigh nearly 15 Ibs. The weight of the column of mercury is equal to the downward pressure on PNEUMATICS. 109 each square inch of the surface of the mercury in the cup. Hence we conclude that the pressure of the atmosphere FlG - m is nearly 15 Ibs. per sq. in., and will balance a column of mercury 30 inches high. As water is 13 J times light- er than mercury, the same pressure would balance a column of that liquid 13 times higher, or 33} feet.* (5.) PEESSUEE OF THE AIE VAEiES.f Changes of temperature, moisture, etc., constantly vary the pressure of the air, and change the height of the column of liquid it can support. The pressure of the air also increases with the depth. Hence, in a valley its pressure is greater than on a mountain. The figures given in the last paragraph apply only to the level of the sea and a temperature of 60 F. They are the standards for reference. (6.) MAEIOTTE'S LAW. Fig. 103 represents a long, bent I * Pour OB the mercury in the cup (Fig. 102) a little water colored with red ink. Then raise the end of the tube above the surface of the metal, but not above that of the water which will rise in the tube, the mercury passing down in beautifully-beaded globules. The mercurial column is only 30 inches high, while the water will fill the tube. Finish the experiment by puncturing the bladder with, a pin, when the water will instantly fall to the cup below. t We live at the bottom of an ae'rial ocean whose depth is many times that of the deepest sea. Its invisible tides surge round us on every side. More restless than the sea, its waves beat to and fro, and never know a calm. $ By cautiously inclining the apparatus, when a little air will escape, and adding more mercury if needed, the liquid can be made to stand at zero in both arms. 110 PRESSURE OF LIQUIDS AND GASES. glass tube with the end of the short arm closed. Pour mercury into the long arm until it rises to the point marked zero. It stands at the same height in both arms, and there is an equilibrium. The air presses on the mercury in the long arm with a force equal to a column of mercury 30 inches high, and the elastic force of the air con- fined in the short arm is equal to the same amount. Now pour additional mercury into the long arm until it stands at 30 inches above that in the short arm (Fig. 104), and the pressure is doubled. In the short arm, the air is condensed to one-half its former dimensions, and the expansive force is also doubled.* We therefore conclude that the elas- ticity of a gas increases, and the volume diminishes in proportion to the pressure upon it. (7.) The BAROMETER is an instrument for measuring the pressure of the air. It consists essentially of the tube and cup of mercury in Fig. 102. A scale is attached for convenience of reference. The barometer is used (a) to indicate the weather, and () to measure the height of mountains. It does not directly foretell the weather. It simply shows the varying pressure of the air, from which we must draw our conclusions. A con- tinued rise of the mercury indicates fair weather, and a con- tinued fall, foul weather, f Since the pressure diminishes above the level of the sea, the observer ascertains the fall of * The force with which the flying molecules of air (note, p. 50) beat against the walls of any confining vessel will increase with the diminution of the space through which they can pass. If we give them only half the distance to fly through, they will strike twice as often and exert twice the pressure. t Mercury is used for filling tho barometer because of its weight and low freezing- point. It is said that the first barometer was filled with water. The inventor, Otto von Quericke, erected a tall tube reaching from a cistern in the cellar up through the roof of his house. A wooden image was placed within the tube, floating upon the water. On fine days, this novel weather-prophet would rise above the roof-top and peep out upon the queer old gables of that ancient city, while in foul weather he PNEUMATICS. 111 the mercury in the barometer, and the temperature by the thermometer ; and then, by reference to tables, determines the height. 5. Pumps. (1.) The LIFTING-PUMP contains two valves opening upward one, a, at the top of the suction-pipe, B ; the other, c, in the piston. Suppose the handle to be raised, FIG. 106. FIG. 107. FIG. 108. the piston at the bottom of the cylinder and both valves closed. Now depress the pump-handle and elevate the pis- ton. This will produce a partial vacuum in the suction- pipe. The pressure of the air on the surface of the water below will force the water up the pipe, open the valve, and would retire to the protection of the garret. The accuracy of these movements attracted the attention of the neighbors. Finally, becoming suspicious of Otto's piety, they accused him of being in league with the devil. So the offending philoso- pher relieved this wicked wooden man from longer dancing attendance upon the weather, and the staid old city was once more at peace. PRESSURE OF LIQUIDS AKD GASES. partly fill the chamber. Let the pump-handle be ele- vated again, and the piston depressed. The valve a will then close, the valve c will open and the water will rise above the piston (Fig. 107). When the pump-handle is lowered the second time and the piston elevated, the water is lifted up to the spout, whence it flows out ; while at the same time the lower valve opens and the water is forced up from below by the pressure of the air (Fig. 108).* FIG. 109. The FORCE-PUMP has no valve in the piston. The water rises above the lower valve as in the lifting-pump. When the piston de- scends, the pressure opens the valve and forces the water up the pipe D. This pipe may be made of any length, and thus the water driven to any height. (3.) The FIRE-E^GI^E consists of two force-pumps with an air-chamber. The water is driven by the pistons m, n, alter- nately, into the chamber R, whence the air, by its expansive force, throws it out in a continuous stream through the hose- pipe attached at Z (Fig. 110). 6. The Siphon is a U-shaped tube, having one arm longer than the other. Insert the short arm in the water, and then applying the mouth to the long arm, exhaust the air. The water will flow from the long arm until the end of the short arm is uncovered, f * If the valves and piston were fitted air-tight, the water could be raised 34 feet (more exactly 13^ times the height of the barometric column) to the lower valve, but owing to various imperfections it commonly reaches about 28 feet. For a similar reason we sometimes find a dozen strokes necessary to "bring water." t An instructive experiment may be given if we allow the water to run from one tumbler into another until just before the flow ceases ; then quickly elevate the glass containing the long arm, carefully keeping both ends of the siphon under the water, when the flow will set back to the first tumbler. Thus we may alternate until we PNEUMATICS. 113 Flo. 110. Fio. 111. THEORY OF THE SIPHON. The pres- sure of the air at b holds up the column of water a b, and the upward pressure is the weight of the air less the weight of the column of water a The upward pressure at d is the weight of the air minus the weight of the column see that the water flows to the lower level, and ceases whenever it reaches the same level in both glasses. It will add to the beauty of this as well as of many other experiments, to color the water with a few scales of magenta, or with red ink. 114 PEESSUEE OF LIQUIDS AND GASES. of water c d. Now c d is less than a b, and the water in the tube is driven toward the ?IG - 118 - longer arm by a force equal to the difference in the weight of the two arms. 7. The Pneumatic Inkstand can be filled only when tipped so that the nozzle is at the top. The pressure of the air will retain the ink when the stand is placed upright. When used below o, a bubble of air passes in, forcing the ink into the nozzle. 8. The Hydraulic Ram is a machine for raising water where there is a slight fall. The water enters through the FIG. 113. pipe A, fills the reservoir B, and lifts the valve D. As that closes, the shock raises the valve E and drives the water into the air-chamber G. D falls again as soon as an equi- librium is restored. A second shock follows, and more water is thrown into G. When the air in G is sufficiently condensed, its elastic force drives the water through the pipe H. 9. The Atomizer is used to turn a liquid into spray. PNEUMATICS. 115 FIG. 114. The blast of air driven from the rubber bulb, as it passes over the end of the upright tube, sweeps along the neigh- boring molecules of air and produces a partial vacuum in the tube.* The pressure of the air in the bottle drives the liquid up the tube, and at the mouth the blast of air carries it off in fine drops. The action of a current of air in dragging along with it the adjacent still atmosphere and so tending to produce a vacuum, is shown by the ap- paratus represented in Fig. 115. Tio. 118. A globe, a, is connected * In locomotives, this principle of the adhesion of gases to gases is applied to produce a draft. The waste steam is thrown into the smoke-pipe, and this current sweeps off the smoke from the fire, while the pressure of the atmosphere outside forces the air through the furnace and increases the combustion. A familiar illus- tration may be devised by taking two discs of cardboard, the lower one fitted with a quill, and the upper one merely kept from sliding off by a pin thrust through it and extending into the quill. The more forcibly air is driven through the quill against the upper disc, the more firmly it will be held to its place. See article u Ball Para- dox," in Popular Science Monthly, April, 1877. Faraday used to illustrate the prin- ciple thus : Hold the hand out flat with the fingers extended and pressed together. Place underneath a piece of paper two inches square. Blow through the opening between the index and the middle finger, and so long as the current is passing the paper will not fall. 116 PRESSURE OF LIQUIDS AND GASES. with a horizontal tube, c, containing colored water. Close the opening d with the finger, and with the mouth at b draw the air out of the globe. A slight rarefaction will cause the liquid, by the pressure of the air at the opening /, to be forced into . Now, if, instead of drawing the air out at b, a jet of air be forced through the tube and out at d, the same effect will be produced. 1C. Height of the Air. Three opposing forces act upon the air, viz. : gravity, which binds it to the earth, and the centrifugal and repellent forces, which tend to hurl it into space. There must be a point where these balance. At the height of 3.4 miles the mercury in the barometer stands at 15 inches, indicating that half the atmosphere is within about 3J miles of the earth's surface. The height of the atmosphere is variously stated at from 50 to 500 miles. PRACTICAL QUESTIONS. 1. Why must we make two openings in a barrel of cider when we tap it ? 2. What is the weight of 10 cubic feet of air ? 3. What is the pressure of the air on 1 square rod of land ? 4. What is the pressure on a pair of Magdeburg hemispheres 4 inches in diameter ? 5. How high a column of water can the air sustain when the barometric column stands at 28 inches ? 6. If we should add a pressure of two atmospheres (30 Ibs. to the square inch), what would be the volume of 100 cubic inches of common air ? 7. If, while the water is running through the siphon, we quickly lift the long arm, what is the effect on the water in the siphon ? If we lift the entire siphon ? 8. When the mercury stands at 29 inches in the barometer, how high above the surface of the water can we place the lower pump- valve ? 9. Can we raise water to a higher level by means of a siphon ? 10. If the air in the chamber of a fire engine be condensed to T V its former bulk, what will be the pressure due to the expansive force of the air on every square inch of the air- chamber ? 11. What causes the bubbles to rise to the surface when we put a lump of loaf-sugar in hot tea ? 12. To what height can a balloon ascend ? What weight can it lift ? 13. The rise and fall of the barometric column shows that the air is lighter in foul and heavier in fair weather. Why is this? Ans. Vapor of water is only half as heavy as dry air. When there is a large quantity present in the atmos- phere, displacing its own bulk of air, the weight of the atmosphere will be cor- respondingly diminished. 14. When smoke ascends in a straight line from chimneys, is it a proof of the rarity or the density of. the air? 15. Explain the action of the common leather-sucker. 16. Did you ever see a bottle really empty ? 17. Why is it so tiresome to walk in miry clay? Ans. Because the upward pressure of the air is removed from our feet. 18. How does the variation in the pressure of the air affect those who ascend lofty mountains ? Who descend in diving-bells ? 19. Explain the theory of " sucking cider " through a straw. 20. Would it make any difference in the action of the siphon if the limbs were of unequal diameter? 21. If the receiver of an air-pump is 5 times as large as the barrel, how many strokes of the piston will be needed to dimmish the air nearly one-half? 22. What would be the effect of making a small hole in the top of a diving-bell while in use ? 23. The pressure of the atmosphere being 1.03 kg. per sq. cm., what ia the amount on 1 are ? On 10 sq. metres f PNEUMATICS. 117 SUM MARY. Hydrostatics treats of the laws of equilibrium in liquids. Pres- sure is transmitted by liquids equally in every direction. Water thus becomes a " mechanical power/' as in the " Hydraulic Press." Liquids acted on by their weight only, at the same depth, press downward, upward, and sidewise with equal force. This pressure is independent of the size of the vessel, but increases with the depth. Wells, springs, aqueducts, fountains and the water-supply of cities illustrate the ten- dency of water to seek its level. The ancients understood this law, but had no suitable material for making the immense pipes needed ; just so the art of printing waited the invention of paper. Specific gravity, or the relative weights of the same bulk of different sub- stances, is found by comparing them with the weight of the same bulk of water. This is easily done, since, according to the law of Archimedes, a body immersed in water is buoyed up by a force equal to the weight of the water displaced ; i. c., it loses in weight an amount equal to that of the same bulk of water. Hence spec. grav. = - wei g htinair m A floating body displaces only its weight in air weight in water weight of liquid. This explains the buoyancy of a ship, why a floating log is partly out of water, and many similar phenomena. Hydraulics treats of moving liquids. The laws of falling bodies in the main apply. So that a descending jet of water will acquire the same velocity that a stone would in falling to the ground from the sur- face of the water; and an ascending jet would need to have the same velocity in order to reach that height. The quantity of water dis- charged through any orifice equals the area of the opening multiplied by the velocity of the stream. The chief resistance to the motion of a liquid is the friction of the air and against the sides of the pipe, and, in the case of rivers, against the banks and bottom of the channel. The force of falling water is utilized in the arts by means of water wheels. There are four kinds overshot, undershot, breast, and tur- bine. The principles of wave motion, so essential to the understanding of sound, light, etc., are easiest studied in connection with water. A stone let fall into a quiet pool sets in motion a series of concentric waves, whose particles merely rise and fall, while the movement passes to the outermost edge of the water, and is then transmitted to the ground beyond. The velocity of the particles is much less than that of the wave itself. A handful of stones acts in the same way, 118 PRESSURE OF LIQUIDS AND GASES. but sets in motion many series of waves. Hence arise the phenomena of interference. 'Pneumatics treats of the properties and the laws of equilibrium of gases. The air being composed of matter, has all the properties we associate with matter, as weight, indestructibility, extension, compres- sibility, etc. In addition, it is remarkable for its elasticity.* The elasticity of the air, according to Mariotte's (and Boyle's) law, is inversely proportional to its volume, and that is inversely proportional to the pressure upon the air ; both heat and pressure increasing the elasticity of a gas. The air, like other fluids, transmits the weight ol its own particles, as well as any outside pressure, equally in every direction ; hence the upward pressure or buoyant force of the atmos- phere. A balloon rises because it is buoyed up by a force equal to the weight of the air it displaces. It floats in the air for the same reason that a ship floats on the ocean. When smoke falls it is heavier, and when it rises it is lighter than the surrounding atmosphere. The air- pump is used for exhausting the air from, and the condenser for con- densing the air into, a receiver. A vacuum in which there remains only -unj-tmnj- of the atmosphere can be obtained by means of Spren- gel's air-pump, which acts on the principle of the adhesion of the air to a column of falling mercury. The average weight of the air being 15 Ibs. to the square inch, equals that of a column of water 34 feet, and of mercury 30 inches or 760 millimetres high. This amount varies incessantly through atmospheric changes caused by alterations in the wind, heat of the sun, etc. The barometer measures the weight of the atmosphere, and is used to determine the height of mountains and the changes of the weather. The action of the siphon, the pneumatic ink- stand, and of the different kinds of pumps, is based upon the pressure of the air. * The elasticity of the air, as well as the principles explained by the Cartesian diver, Fig. 93, may be illustrated in the following simple manner: Fill with water a wide-mouth, 8-oz. bottle, and also a tiny vial, such as is used by homceopathists. Invert the vial and a few drops of water will run out. Now put it inverted into the bottle, and if it does not sink just below the surface and there float, take it out and add or remove a little water, as may be needed. When this result is reached, cork the bottle so that the cork touches the water. Any pressure on the cork will ..hen be transmitted to the air in tb.e vial, as in the image in Fig. 93. HISTOEICAL SKETCH. 119 HISTORICAL SKETCH. ffydrostatics is comparatively a modern science. The Romans had a knowledge of the fact that " liquids rise to the level of their source," but they had no means of making iron pipes strong enough to resist the pressure.* They were therefore forced to carry water into the imperial city by means of enormous aqueducts, one of which was 63 miles long, and was supported by arches 100 feet high. The ancient Egyptians and Chaldeans were probably the first to investigate the most obvious laws of liquids from the necessity of irrigating their land. Archimedes, in the 3d century B. C., invented a kind of pump called Archimedetf Screw, demonstrated the principle of equilibrium, known now as "Archimedes' Law " (p. 117), and found out the method of obtaining the specific gravity of bodies. The discovery of the last is historical. Hiero of Syracuse suspected that a gold crown had been fraudulently alloyed with silver. He accordingly asked Archimedes to find out the fact without injuring the workmanship of the crown. One day going into a bath-tub full of water, the thought struck the philosopher that as much water must run over the side as was equal to the bulk of his body. Electrified by the idea, he sprang out and ran through the streets, shouting: "Eureka!" (I have found it !) The ancients never dreamed of associating the air with gross mat- ter. To them it was the spirit, the life, the breath. Noticing how the atmosphere rushes in to fill any vacant space, the followers of Aristotle explained it by saying, " Nature abhors a vacuum." This principle answered the purpose of philosophers for 2,000 years. In 1640, some workmen were employed by the Duke of Tuscany to dig a deep well near Florence. They found to their surprise that the water would not rise in the pump as high as the lower valve. More disgusted with nature than nature was with the vacuum in their pump, they applied to Galileo. The aged philosopher answered half in jest, we hope, certainly he was half in earnest " Nature does not abhor a vacuum beyond 34 feet." His pupil, Torricelli, how. * The ancient engineers sometimes availed themselves of this principle. Not fat from Rachel's Tomb, Jerusalem, are the remains of a conduit once used for supply- ing the city with water. The valley was crossed by means of an inverted siphon. The pipe was about two miles long and fifteen inches in diameter. It consisted of perforated blocks of stone, ground smooth at the joints, and fastened with a hard cement. 120 PBESSUEE OF LIQUIDS AND GASES. ever, discovered the secret. He reasoned that there is a force which holds up the water, and as mercury is 13 times as heavy as water, it would sustain a column of that liquid only 33 feet-r- 13^ = 30 inches high. Trying the experiment shown in Fig. 102, he verified the conclusior that the weight of the air is the unknown force. But the opinion wag not generally received. Pascal next reasoned that if the weight of the air is really the force, then at the summit of a high mountain it Ls weakened, and the column would be lower. He accordingly car- ried his apparatus to the top of a steeple, and finding a sHght fall in the mercury, he asked his brother-in-law, who lived near Puy de Dome, a mountain in Southern France, to test the conclusion. On trial, it was found that the mercury fell 3 inches. "A result," wrote Perrier, "which ravished us with admiration and astonishment." Thus was discovered the germ of our modern barometer, and the dogma of the philosophers soon gave place to the law of gravitation and our present views concerning the atmosphere. Consult Pepper's "Cyclopaedic Science"; Bert's "Atmospheric Pressure and Life," in Popular Science Monthly, Vol. XI, p. 316 ; "Appleton's Cyclopaedia," Articles on Hydromechanics, Atmosphere, Pneumatics, etc. Delaunay, " Mecanique Rationnelle"; Boutan et D' Almeida, "Cours de Physique"; Miiller, " Lehrbuch der Physik und Meteorologie"; Miiller, "Lehrbuch der Kosmischen Physik"; Wiillner, "Lehrbuch der Experimental Physik "; Mousson, "Die Physik auf Grundlage der Erfahrung " ; Beetz, " Leitfaden der Physik"; Kuelp, " Die Schule des Physikers." On the theory of Wave-Motion, and the subjects of Sound and Light, which are now to follow, consult Lockyer's " Studies in Spec- trum Analysis"; Lloyd's "Wave Theory"; Taylor's "Sound and Harmony"; Blaserna's "Theory of Sound in Relation to Music"; Tyndall's "Sound" and "Light"; Lockyer's "Water-waves and Sound-waves " in Popular Science Monthly, Vol. XIII, p. 1 66 ; Shaw's " How Sound and Words are Produced," in Popular Science Monthly, Vol. XIII, p. 43; Schellen's "Spectrum Analysis"; Airy's Optics; Lockyer's Spectroscope ; Chevreul's Colors ; Spottiswoode's " Polariza- tion of Light"; Lommers " Nature of Light"; Helmholtz's " Popular Lectures on Scientific Subjects"; "Appleton's Cyclopaedia," Articles on Sound, Light, Spectrum, Spectrum Analysis, Spectacles, Heat, etc. ; Stokes's "Absorption and Colors," and Forbes's "Radiation," in Science Lectures at South Kensington, Vol. I ; Mayer and Barnard's Light; Draper's "Popular Exposition of some Scientific Experi- ments," in Harper's Magazine for 1877 ; Core's " Modern Discoveries in Sound," in Manchester Science Lectures, '77-8 ; Dolbeare's " Art of Projecting"; Draper's "Scientific Memoirs"; Steele's Physiology, Section on Sight, pp, 187-196. VI. Oj*. So " Scitnce ought to teach us to see the invisible as well as the visible in nature : to picture to our mind's eye those operations that entirely elude the eye of the body ; to look at the very atoms of matter, in motion and in rest, and to follow them forth into the world of the senses!' TYNDALL. ANALYSIS. r 1 PRODUCTION OF SOUND. o OQ TRANSMISSION SOUND. OF (1.) Through air. (2.) In a vacuum. (3.) Velocity. (4.) Intensity. 8. REFRACTION OF SOUND. J(l.) Law of. (2.) Echoes. SOUND. (a.) Depends on what? (b.) Rate in air. (c.) Bate in water. (d.) Rate in solids. (e.) Velocity is uniform. (f.) Used to find distance. (a.) Depends what? (b.) Law of. (c.) Speaking tubes, etc. on 5. MUSICAL SOUNDS. (3.) Decrease of Intensity. (4.) Acoustic Clouds. (1.) Difference between Noise Music. (2.) Pitch. (3.) To find Number of Waves. (4.) To find Length of Waves. (5.) Unison. 6. SUPER-POSITION OF SOUND-WAVES. Definitions. (1.) Sonometer. (2.) Three Laws. (3.) Nodes. (4.) Acoustic Figures. (5.) Harmonics. (6.) Nodes of Bell. (7.) Nodes of Sounding-Board. (8.) Musical Scale. and 7. VIBRATION CORDS. OF 8. WIND INSTRUMENTS. SYMPATHETIC BRATIONS. VI- 10. THE PHONOGRAPH. 11. THE EAR. Illustrations. (1.) Sensitive Flames. (2.) Singing Flames. Description. (1.) Range of. (2.) Ability to Detect Sound. ACOUSTICS, OR THE SCIENCE OF SOUND.* 1. Production of Sound. By lightly tapping a glass fruit-dish, we can throw the sides into motion visible to the eye. Fill a goblet half -full of water, and rub a wet finger lightly around the upper edge of the glass. The sides will vibrate, and cause tiny waves to ripple the surface of the water. Hold a card close to the prongs of a vibrating tuning-fork, and you can hear the repeated taps. Place the cheek near them, and you will feel the little puffs of wind. Insert the handle between your teeth, and you will expe- rience the indescrib- able thrill J of the swinging metal. The tuning-fork may be made to draw the outline of its vibrations upon a smoked-glass. Fasten upon one prong a sharp point, and drawing the fork along, a sinuous line will show the width (amplitude) of the vibrations. * The term sound is used in two senses the subjective (which has reference to our mind) and the objective (which refers to the objects around us). (1.) Sound is the sensation produced upon the organ of hearing by vibrations in matter. In this use of the word there can be no sound where there is no ear to catch the vibrations. An oak falls in the forest, and if there is no ear to hear it there is no noise, and the old tree drops quietly to its resting-place. Niagara's flood poured over its rocky precipice for ages, but fell silently to the ground. There were the vibrations of earth and air, but there was no ear to receive them and translate them into sound. When the first foot trod the primeval solitude, and the ear felt the pulsations from the torrent, then the roaring cataract found a voice and broke its lasting silence. A trumpet does not sound. It only carves the air into waves. The tympanum is the beach on which these break into sound. (2.) Sound is those vibrations of matter capable of producing a sensation upon the organ of hearing. In this use of the word there can be a sound in the absence of the ear. An object falls and the vibrations are produced, though there may be no organ of hearing to receive an impression from them. This is the sense in which the term sound is commonly used. 124 ACOUSTICS. 2. Transmission of Sound. (1.) THROUGH AIR. The prong of a tuning-fork advances condensing the air in front, and then recedes, leaving behind it a partial vacuum. This process is repeated until the fork comes to rest, and the sound ceases. Each vibration produces a sound-wave of air, which contains one condensation and one rarefaction. In water, we measure a wave-length from crest to crest ; in air, from condensation to condensation. The condensation of the sound-wave corresponds to the crest, and the rarefac- tion of the sound-wave to the hollow of the water-wave. In JL a FIG. 117. 6' c Fig. 117, the dark spaces a, b, c, d represent the condensations, and a', b' t c' the rarefactions ; the wave-lengths are the distances ab, be, cd. If we fire a gun, the gases which are produced expand suddenly and force the air outward in every direction. This hollow shell of condensed air imparts its motion to that next, while it springs back by its elasticity FIG. 118. and becomes rarefied. The second shell rushes forward with TRANSMISSION OF SOUND. 125 FIG. 119. the motion received, then bounds back and becomes rarefied. Thus each shell of air takes up the motion and imparts it to the next. The wave, consisting of a condensation and a rarefaction, proceeds onward. It is, however, as in water- waves, a movement of the form only, while the particles vibrate but a short distance to and fro. The molecules in water-waves oscillate vertically ; those in sound-waves hori- zontally, or parallel to the line of motion. If a bell le rung, the adjacent air is set in motion ; thence, by a series of condensations and rare- factions, the vibrations are con- veyed to the ear. When we speak, we do not shoot the air we expel from our lungs into the ear of the listener. "We simply condense the air before the mouth and throw it into vibra- tion. Thus a sound-wave is formed.* This spreads in every direction in the form of a sphere of which we are the centre, f (2.) IN A VACUUM. The bell B (Fig. 119) may be set in mo- tion by the sliding-rod r. The apparatus is suspended by silk cords, that no vibration may be conducted through the pump. If the air be exhausted, the sound * A continuous blast of air produces no sound. The rush of the grand ae"rial rivers above us we never hear. They flow on in the upper regions ceaselessly hut silently. A whirlwind is noiseless. Let, however, the great billows strike a tree and wrench it from the ground, and we can hear the secondary, shorter waves which set out from the struggling limbs and the tossing leaves. t " It is marvellous," says Youmans, " how slight an impulse throws a vast amount of air into motion. We can easily hear the song of a bird 500 feet above us. For its melody to reach us it must have filled with wave-pulsations a sphere of air 1,000 feet in diameter, or set in motion 18 tons of the atmosphere. 11 12G ACOUSTICS. will become so faint that it cannot be heard, even when the ear is placed close to the receiver.* In elevated regions sounds are diminished in loudness, and it is difficult to carry on a conversation, as the voice must be raised so high. The reverse takes place in deep mines and diving-bells. The sounds then become start- lingly distinct, and workmen are enabled to converse audibly in whispers. (3.) THE VELOCITY OF SOUND depends on the ratio of the elasticity to the density of the medium through which it passes. The higher the elasticity, the more promptly and rapidly the motion is transmitted, since the elastic force acts like a bent spring between the molecules; and the greater the density, the more molecules to be set in motion, and hence the slower the transmission. Sound travels through air (at 32 F.) 1,090 feet per second. A rise in temperature diminishes the density of the air, and thus increases the velocity of sound. A difference of 1 F. makes a variation of about 1 foot. Sound also moves faster in damp than in dry air. Sound travels through water about 4^00 feet per second. Water being denser than air should convey sound more slowly ; but its high elasticity (p. 20) quadruples the rate. Sound travels through solids faster than through air. This may be illustrated by placing the ear close to the hori- zontal bar at one end of an iron fence, while a person strikes the other end a sharp blow. Two sounds will reach the ear one through the metal, and afterward another through the air. The velocity varies with the nature of the solid, f In the metals it is from 4 to 16 times that in air. * There would be perfect silence in a perfect vacuum. No pound is transmitted to the earth from the regions of space. The movements of the heavenly bodies are noiseless. In the expressive language of David, " Their voice is not heard." t Wheats tone invented a beautiful experiment to show the transmission of sound through wood. Upon the top of a music-box, he rested the end of a wooden rod reaching to the room above, and insulated from the ceiling by India rubber. A violin ^ placed on the top of the rod. the sounds from the box below filled the upper TRANSMISSION OF SOUND. 127 Different sounds travel with the same velocity.* A band may be playing at a distance, yet the harmony of the dif- ferent instruments is preserved. The soft and the loud, the high and the low notes reach the ear at the same time. Velocity of sound used to find distance. Light travels instantaneously so far as all distances on the earth are concerned. Sound moves more slowly. We see a chopper strike with his axe, and a moment elapses before we hear the blow. If one second intervenes the distance is about 1,090 feet. By means of the second hand of a watch or the beating of our pulse, we can count the seconds that elapse between a flash of lightning and the peal of thunder which follows. Multiplying the velocity of sound by the number of seconds, we obtain the distance of the thunderbolt. (4.) THE INTENSITY OF SOUND is proportional to the square of the amplitude, i. e. 9 the arc through which the molecules swing to and fro. As in a pendulum, the greater the amplitude the greater the velocity. The force of a striking body depends upon its mass and the square of its velocity (p. 36). So one sound is louder than another, be- cause the air molecules hit the ear-drum with greater force. On the top of a mountain, because of the rare atmosphere, there are fewer molecules to strike the ear ; hence, the blow is less intense. Tlie intensity of sound diminishes as the square of the distance increases.} The sound-wave expands in the form room, appearing to emanate from the violin. Take two small, round, tin boxes and pass a strong string of any length through a hole in the bottom of each, fastening it by a knot. If the string be drawn tightly, and one box be held to the mouth of the speaker and the other to the ear of the listener, the faintest whisper can be heard. * It has been said that the " heaviest thunder travels no faster than the softest whisper." Mallet, however, found that in blasting with a charge of 2,000 Ibs., the velocity was 967 feet per second, while with 12,000 Ibs. it was Increased to 1,210 feet. Parry in his Arctic travels states that, on a certain occasion, the sound of the sunset- gun reached his ears before the officer's word of command to fire, proving that the report of the cannon travelled sensibly faster than the sound of the voice. t The same proportion obtains in Gravitation, Sound, Light, and Heat. We have seen how the Pendulum Is based upon the force of Gravity, and reveals the Laws of Falling Bodies. Now we find that the Pendulum, and even the principles of Reflected 128 ACOUSTICS. of a sphere. The larger the sphere, the greater the number of air particles to be set in motion, and the feebler their vibration. The surfaces of spheres are proportional to the squares of their radii ; the radii of sound-spheres are their distances from the centre of disturbance. Hence the force with which the molecules will strike the ear decreases as the square of our distance from the sounding body. Speaking-tubes conduct sound to distant rooms because they prevent the waves from expanding and losing their intensity.* The ear-trumpet collects waves of sound and reflects them into the ear. The speaking-trumpet is based on the same principle as the speaking-tube. Probably also the sound of the voice is strengthened by the vibrations of the air in the tube. 3. Refraction of Sound. When a sound-wave goes obliquely from one medium to another, it is bent out of its course. Like light, it may be passed through a lens and FIG. 120. brought to a focus. B is a rubber globe, filled with carbonic- acid gas ; w is a watch, and /' a funnel which assists in collecting the wave at/, where the ear is placed. The ticks Motion and Momentum, are linked with the phenomena of Sound. As we progress farther, we shall find how Nature is thus interwoven everywhere with proofs of a common plan and a common Author. * Biot held a conversation through a Paris water-pipe 8,120 feet long. He says that " it was so easy to be heard, that the only way not to be heard was not to speak atalL" REFLECTION OP SOUKD. of the watch can be heard, while outside the focus they are inaudible. 4. Reflection of Sound. When a sound-wave strikes against the surface of another medium, a portion goes on while the rest is reflected. (1.) THE LAW is that of Motion ; the angle of incidence is equal to that of reflection.* If the reflecting surface be very near, the reflected sound will join the direct one and strengthen it. This accounts for the well-known fact that a speaker can be heard more easily in a room than in the open air, and that a smooth wall back of the stand re- inforces the voice. The old-fashioned "sounding-boards" were by no means inefficient, however singular may have been their appearance. Shells, by their peculiar convolu- tions, reflect the various sounds which fill even the stillest air. As we hold them to our ear, they are poetically said to "repeat the murmurs of their ocean home." (2.) ECHOES are produced where the reflecting surface is so distant that we can distinguish the reflected from the direct sound. If the sound be short and quick, this requires at least 56 feet ; but if it be an articulate one, 112 feet are necessary. One can pronounce or hear distinctly about five syllables in a second ; 1,120 ft. (the velocity at a medium temperature) -j- 5 = 224 ft.f If the wave travel 224 feet * Domes and curved walls reflect sound as mirrors do light. Thus, in the gallery under the dome of St. Paul's Cathedral, London, persons standing close to the wall can whisper to each other and be heard at a great distance. Two persons, placed with their backs to each other, at the foci of an oval room, or " Whispering Gallery," can carry on a conversation that will be inaudible to spectators standing between them. The covered recesses on the opposite sides of a street, or the arches of a stone bridge, oftentimes reflect sound so as to enable persons seated at the foci to converse in whispers while loud noises are being made in the open space between these semi-domes. t When several parallel surfaces are properly situated, the echo may be repeated backward and forward in a surprising manner. In Princeton, Ind., there is an echo between two buildings that will return the word " Knickerbocker " twenty times. So many persons yisited the place that the city council forbade the use of the echo after 9 o'clock at night. At Woodstock, England, an echo returns 17 syllables by day and 30 by night. The reflecting surface is distant about 2.300 feet, and a sharp ha! 130 ACOUSTICS. in going and returning, the two sounds will not blend, and the ear can detect an interval between them. A person speaking in a loud roice in front of a mirror 112 feet dis- tant, can distinguish the echo of the last syllable he utters ; at 224: feet, the last two syllables, etc. (3.) DECEEASE or SOUND BY KEFLECTION. If we strike the bell represented in Fig. 119, we shall find a marked dif- ference between its sound under the glass receiver and in the open air. Floors are deadened with tan-bark or mortar, since as the sound-wave passes from particle to particle of the unhomogeneous mass, it becomes weakened by partial reflection. The air at night is more homogeneous, and hence sounds are heard further and more clearly than in the day time. (4. ) ACOUSTIC CLOUDS are masses of moist air of varying density, which act upon sounds as common clouds do upon light, wasting it by repeated reflections. They may exist in the clearest weather. To their presence is to be attributed the variation often noticed in the distance at which well- known sounds, as the ringing of church bells, blowing of engine-whistles, etc., are heard at different times.* will come back a ringing ha, ha, ha /The echo is often softened, as in the Alpine regions, where it warbles a beautiful accompaniment to the shepherd's horn. The celebrated echo of the Metelli at Rome was capable of distinctly repeating the first line of the ^Eneid 8 times. In Fairfax County, Va., is an echo which will retuni 20 notes played on a flute, but supplies the place of some notes with their thirds, fifths, or octaves. The tick of a watch may be heard from one end of the Church of St. Albans to the other. At Carisbrook Castle, fele of Wight, is a well 210 feet deep and 12 feet wide, lined with smooth masonry. When a pin is dropped into the well it is distinctly heard to strike the water. In certain parts of the Colosseum at London the tearing of paper sounds like the patter of hail, while a single exclamation comes back a peal of laughter. The Dome of the Baptistry of the Cathedral at Pisa (See Frontispiece) has a wonderful echo. During some experiments there, the author found every noise, even the rattle of benches on the pavement below, to be reflected back as if from an immense distance and to return mellowed and softened into music (note, p. 131). See also p. xi., Fresh Facts and Theories. * The extinction of sound by such agencies Is iften almost incredible. Thus two observers looking across the valley of the Chickahominy at the battle of Gaines's Mill failed to hear a sound of the conflict, though they could clearly see the lines of soldiers, the batteries and the flash of the guns. These phenomena are ascribed by many (page 264) to an elevation or a depression of the wave-front so that the Bound passes above the observer or is stopped before it reaches him. See Stewart's Physics, p. 141. REFLECTION OF SOUND. 131 5. Musical Sounds. (1.) THE DIFFERENCE BETWEEN NOISE AND MUSIC is that between irregular and regular vibrations. Whatever the cause which sets the air in mo- tion, if the vibrations are uniform and rapid enough, the sound is musical. If the ticks of a watch could be made with sufficient rapidity, they would lose their individuality and blend into a musical tone. If the puffs of a locomotive could reach 50 or 60 a second, its ap- proach would be heralded by a tre- mendous organ-peal.* (2.) PITCH depends on the rapid- ity of the vibrations. Thus if we hold a card against the cogs of the rapidly-revolving wheel in the appa- ratus shown in Fig. 16, we shall ob- tain a clear tone ; and the faster the wheel turns, the shriller the tone, i. e. y the higher the pitch. (3.) THE NUMBER OF WAVES IN A SOUND is determined by an instru- ment called the Siren. is a cylin- drical box ; #, a pipe for admitting air ; db, a plate pierced with four series of holes, containing 8, 10, 12, and 16 orifices respectively ; m, n, o,p are stops for closing any series. * The pavement of London is largely composed of granite blocks, four inches in width. A cab-wheel jolting over this at the rate of eight miles per hour produces a succession of 35 sounds per second. These link themselves into a soft, deep musical tone, that will bear comparison with notes derived from more sentimental sources. This tendency of Nature to music is something wonderful. "Even friction," says Tyndall, " is rhythmic." A bullet flying through the air sings softly as a bird. The limbs and leaves of trees murmur as they sway in the breeze. The rumble of a great city, all the confused noises of Nature when softened by distance, are said to be on one pitchthe key of F. Falling water, singing birds, sighing winds, everywhere attest that the same Divine love of the beautiful which causes the rivers to wind through the landscape, the trees to bend in a graceful curve the line of beauty and the rarest flowers to bud and blossom where no eye save His may see them, delights also in the anthem of praise which Nature sings for His ear alone. 132 ACOUSTICS. FIG. 122. The rod p is bevelled at p 1 so as to turn in the socket x ; de is a disk with holes corresponding to those in the lower plate, over which it revolves. At s is an endless screw, which causes two wheels to rotate, and thus turns the hands upon the dial (Fig. 122). On this we can see the number of revolutions made by the upper disk. The holes in ab and de are inclined to each other, so that, when a current of air is forced in at t,ii passes up through the openings in the lower disk, and striking against the sides of those in the upper disk, causes it to revolve. As that turns, it alternately opens and closes the orifices in the lower disk, and thus converts the steady stream of air into uniform puffs. At first they succeed each other so slowly that they may easily be counted. But, as the motion in- creases, they link themselves to- gether, and burst into a full, melo- dious note. As the velocity aug- ments, the pitch rises, until the mu- sic becomes painfully shrill. Di- minish the speed, and the pitch falls. To find, therefore, the number of vibrations in a given sound, force the air through the Siren until the required pitch is reached. See on the dial, at the end of a minute, the number of revolutions of the disk. When the row con- taining ten holes is open, and the tone C 2 , it will indicate 1,536. There were ten puffs of air, or ten waves of sound, in each revolution. 1,536 x 10 = 15,360. Dividing this by 60, we have 256, the number per second. When the inner and outer rows of holes are opened, the ear detects the difference of an octave between the two sounds. The one containing 8 produces the lower, and 16 the higher tone. MUSICAL BOUNDS. 133 Hence an octave of a tone is caused by double the number of vibrations. (4.) To FIND THE LENGTH OF THE WAVE. Suppose the air in the last experiment was of such a temperature that the foremost sound-wave travelled 1,120 feet in a second. In that space there were 256 sound-waves. Dividing 1,120 by 256, we have 4J- feet as the length of each. We thus find the wave-length by dividing the velocity by the number of vibrations per second. As the pitch is elevated by rapidity of vibration, we perceive that the low tones in music are produced by the long waves and the high tones by the short ones.* (5.) TONES IN UNISON. If the string of a violin, the cord of a guitar, the parchment of a drum, and the pipe of an organ, produce the same tone, it is because they are exe- cuting the same number of vibrations per second. If a voice and a piano perform the same music, the steel strings of the piano and the vocal cords of the singer vibrate to- gether and send out sound-waves of the same length, f 6. Super-position of Sound-waves. The air may transmit sound-waves from a thousand instruments at once. If the condensation of one wave meet the condensation of another, the sound will be augmented, the condensations becoming more condensed and the rarefactions more rarefied (p. 102). If the condensation of one meet the rarefaction * The aerial waves are seemingly shortened when the source of sound is approach- Ing, whether by its own motion or the hearer's, and lengthened when it is receding. In the former case the tone of the sound is more acute, in the latter graver. This is strikingly illustrated when a swift train rushes past a station, the whistle blowing. While the cars are approaching, a person hears a note somewhat sharper ; after it has passed, one somewhat flatter than the true note. Still more obvious is the change when two trains pass each other. A person unfamiliar with the arrangement would suppose a different bell was rung. In one case more and in the other fewer waves reach the ears in a second. Just so a ship moving against the sea meets more waves than one moving with it. t In order to determine the number and length of the sound-waves produced by a eonorous body, we have only to bring its sound and that of the siren hi unison. " The wings of a gnat flap, in flying, at the rate of 15,000 times per second. A tired bee hums on E, while in pursuit of honey it hums contentedly on A. The common horse-fly moves its wings 335 times a second ; a honey-bee, 190 times." 134 ACOUSTICS. of the other, one wave-motion will be striving to push the air molecules forward, and the other to urge them back- ward. So that, if they meet in exactly opposite phases and the two forces are equal, they will balance each other and silence will ensue.* FIG. 123. 1HB Suppose we have two tuning-forks, A and B, a wave- length apart, and vibrating in unison. The waves will coincide, as represented by the light and dark shades in Fig. 123. The . same result would occur if they were any number of wave-lengths apart. If they are a half wave- length apart, the condensation of A will coincide with the rarefaction of B, and vice versa. The effect is represented FIG. 124. by the uniformity of the shading in Fig. 124. This is termed interference of sound-waves.] 7. Vibrations of Cords. Let ab be a stretched cord made to vibrate. The motion from e to d and back again is termed a vibration; that from e to d, a half-vibration. * Thus a sound added to a sound may produce silence. In the same way, two motions may produce rest ; two lights may cause darkness ; and two heats may produce cold. t If we strike a tuning-fork and turn it, slowly around before the ear, we shall find four points where the interference of the sound-waves neutralizes the vibrations and causes silence. Two forks or organ-pipes nearly in unison, produce the well-known - beats," a characteristic phenomenon of interference. VIBRATIONS OF CORDS. 135 The intensity of the sound depends on the width of ed, i. e., the amplitude of the vibration. (1.) THE SONOMETER is an instrument used to investigate the laws which govern the vibrations. It consists of two cords stretched by weights, P, across fixed bridges, AB. FIG. 136, The movable bridge, D, serves to lengthen or shorten the cords. Beneath is a wooden box which communicates the vibrations of the cords to the air within. This is the real sounding body. (2.) THREE LAWS. I. The number of vibrations per sec- ond increases as the length of the cord decreases. With the bow make the cord vibrate, giving the note of the entire string. Place the bridge D at the centre of the cord, and the sound will be the octave above the former. Thus by taking one-half the length of the cord we double the num- ber of vibrations. Ex. : If an entire cord make 20 vibrations per second, one-half will make 40, and one-third, 60. The violin or guitar player elevates the pitch of a string by mov- ing his finger, thus shortening the vibrating portion. In 136 ACOUSTICS. the piano, harp, etc., the long and the short strings produce the low and the high notes respectively. II. The number of vibrations per second increases as the square root of the tension. The cord when stretched by 1 Ib. gives a certain tone. To double the number of vibra- tions and obtain the octave requires 4 Ibs. Stringed instru- ments are provided with keys, by which the tension of the cord and the corresponding pitch may be increased or diminished. III. The number of vibrations per second decreases as the square root of the weight of the cord increases. If two strings of the same material be equally stretched, and one have four times the weight of the other, it will vibrate only half as often. In the violin the bass notes are produced by the thick strings. In the piano fine wire is coiled around the heavy strings. (3.) NODES. In these experiments, the cord is shortened by a movable bridge which holds it firmly. If, instead, we Fie. 127. rest a feather lightly on the string, and draw the bow over one-half, the cord will vibrate in two portions and give the octave as before. Remove the feather, and it will continue to vibrate in two parts and to yield the same tone. We can show that the second half vibrates by placing across that portion a little paper rider, On drawing the bow it will be VIBRATIONS OF CORDS. 137 thrown off. Hold the feather so as to separate one-third of the string and cause it to vibrate ; the remainder of the cord will vibrate in two segments. When the feather is removed, FIG. 128. FIG. 129. the entire cord will vibrate in three different parts of equal length, separated by stationary points called nodes. This may be shown by the riders ; the one at the node remains, while the others are thrown off. (4.) ACOUSTIC FIGURES. Sprinkle fine sand on a metal plate. Place the finger-nail on one edge to stop the vibration at that point, as the feather did in the last experiment, and draw the bow lightly across the opposite edge. The sand will be tossed away from the vibrating parts of the plate and will collect along the nodal lines, which divide the large square. It is wonderful to see how the sand will seemingly start into life and dance into line at the touch of 138 ACOUSTICS. the bow. Fig. 130 shows some of the beautiful patterns ob- tained by Chladni. (5.) HARMONICS.* Whenever a cord vibrates, it separates into segments at the same time.- Thus we have the full or fun- damental note of the entire string, and su- perposed upon it the higher notes produced by the vibrating parts. These are called overtones or "harmonics. The mingling of the two classes of vibrations determines the quality of the sound, and enables us to distinguish the music of different instruments. (6.) NODES OF A BELL. Let the heavy circle in Fig. 131 repre- sent the circumference of a bell when at rest. Let the hammer strike at #, Z>, c, or d. At one moment, as the bell vibrates, it forms an oval with ab, at the next with cd, for its longest diam- eter. When it strikes its deepest note, the bell vibrates in four segments, with n, n } n, n, as the * Press gently but firmly down the notes C, G, and C, in the octave above middle C, on the piano-forte. Without releasing these keys, give to C below middle C a quick, hard blow. The damper will fall, and the sound will stop abruptly. At the same instant a low, soft cnord will be heard. This comes from the three strings whose dampers are raised, leaving them free to sound in sympathy with the over- tones of the lower C, w'aich sounds are identical with their own. When a goblet or wine-glass is tapped with a knife-blade, we can distinguish three sounds, the fun- damental and two harmonics. VIBRATIONS OF CORDS. 139 nodal points, whence nodal lines mn up from the edge to the crown of the bell. It tends, however, to divide into a greater number of segments, especially if it is very thin, and to produce harmonics. The overtones which follow the deep tones of the bell are frequently very striking, even in a common call-belL (7.) NODES OF A SOUKDIETG-BOARD. The case of a violii or guitar is composed of thin wooden plates which divide into vibrating segments, separated by nodal lines according to the pitch of the note played. The enclosed air vibrating in unison with these, reinforces the sound and gives il fullness and richness. (8.) MUSICAL SCALE. The tone produced by an entire string is called its fundamental sound. The notes of the scale above this are given by the parts of the string indi- cated by the following fractions : C, D, E, F, G, A, B, C. iff! t t A i As the number of vibrations varies inversely as the length of the cord, we need only to invert these fractions to obtain the relative number of vibrations per second ; thus, -, f , f, |, -J, ^-, 2. Eeduced to a common denom- inator, their numerators are proportional, and we have the whole numbers which represent the relative rates of vibra- tion of the notes of the scale, viz. : 24, 27, 30, 32, 36, 40, 45, 48. The number of vibrations corresponding to the different letters is,* C, D, E, F, G, A, B, 1 C. 128, 144, 160, 170, 192, 214, 240, 256. * In this table, " C = 256 vibrations " represents the middle C of a piano-forte. This number is purely arbitrary. The so-called " concert-pitch " varies in different countries. The Stuttgart Congress of 1834 fixed the standard tuning-forkmiddle A at 440 vibrations per second, which would make middle C = 264 ; while the Paris Conservatory (1859) gave to middle A 437.5, and to middle C 261. The English tuning-fork represents C in the treble staff, and makes 528 vibrations, the pitch being the same as the Stuttgart. The ratio of the different letters is identical, whatever the pitch. 140 ACOUSTICS. FIG. 132. 8. "Wind Instruments produce musical sounds by enclosed columns of air. Sound-waves run backward and forward through the tube and act on the surrounding air like the vibrations of a cord. The sound-waves in organ- pipes are set in motion by either fixed mouth- pieces or vibrating reeds. The air is forced from the bellows into the tube P, through the vent i, and striking against the thin edge a, produces a nutter. The column of air above, thrown into vibration, reinforces the sound and gives a full musical tone. The length of the pipe determines the pitch. The variation in the quality of different wind in- struments is caused by the mingling of the harmonics with the fundamental tone. In the flute, for example, the vibrating column of air may be broken up into segments by varying the force of the breath. 9. Sympathetic Vibrations, or Res- onance. Produce a musical tone with the voice near a piano, and a certain wire will select that sound and respond to it. Change the pitch, and the first string will cease, while another replies. If a hundred tuning- forks of different tones are sounding at the foot of an organ-pipe, it will choose the one to which it can reply, and answer that alone.* Helmholtz has applied this principle to the con- struction of the resonance globe, an instrument which will respond to a particular harmonic in a compound tone, and strengthen it so as to make it audible. (1.) SENSITIVE FLAMES. Flames are sensitive to sound. At an instrumental concert the gas-lights vibrate with cer- * Two clocks set on one shelf or against the same wall, affect each other. Watches in the shop-window keep better time than when carried singly.- THE PHOKOGRAPH. 141 FIG. 133. tain pulsations of the music. This is noticeable when the pressure of gas is so great that the flame is just on the verge of flaring, and the vibration of the sound-wave is sufficient to "push it over the precipice. "* (2.) SINGING FLAMES. If we lower a glass tube over a small gas-jet, we soon reach a point where the flame leaps spontaneously into song. At first the sound seems far re- mote, but gradually approaches until it bursts into an almost intolerable scream. The length of the tube and the size of the jet determine the pitch of the note, f The flame, owing to the friction at the mouth of the pipe, is thrown into vibration. The air in the tube, being heated, rises, and not only vi- brates in unison with the jet, but, like the organ-pipe, selects the tone corresponding to its length. 1C. The Phonograph is an instrument for recording the sound vibrations. It consists of (1) an outer tube (or ear) for receiving the voice vibrations ; (2) at the bottom of this a thin plate (or membrane) which vibrates in uni- son with the voice ; (3) at the back of the membrane a * Prof. Barrett, of Dublin, describes a peculiar jet which is so sensitive that it trembles and cowers at a hiss, like a human being, beats time to the ticking of a watch, and is violently agitated by the rumpling of a silk dress. t See Chemistry, p. 55. The jets are easily made by drawing out glass tubing to a fine point over a spirit-lamp. The length of the tube may be varied, as in ie figure, by a paper tube, . DIVERSITY I ACOUSTICS. FIG. 134. lever which is moved by these vibrations ; (4) at the end of the lever a sharp point, which traces on a sheet of tin- foil marks corresponding to these vibrations; (5) a cylinder wound with a sheet of the foil, and made, by clockwork, to revolve slowly under the pen-point. After the voice has thus engraved on the foil its vibra- tions, the cylinder can be reset and the point following the indentations on the foil will move the lever, strike the membrane, and reproduce through an outer tube (or trumpet) the original sound. The sheets of foil may be taken from the cylinder and kept for any length of time, to be used when wanted. . 11. The Ear. In Fig. 134, the ear is represented (Hy- gienic Physiology, p. 216). The sound-wave passes into the auditory canal, B, which is about an inch in length, and strik- ing against the mem- brane of the tympa- num or drum, which closes the orifice of the external ear, throws it into vibration. Next, the series of small bones, 0, called re- spectively, from their peculiar form, the hammer,, anvil, and stirrup, conduct the motion to the inner ear, which is termed, from its complicated structure, the labyrinth. This is filled with liquid, and contains the semi-circular canals, D, and the cochlea (snail-shell), E, which receive the vibrations and transmit them to the auditory nerve, the fine filaments of which are spread out to catch every pulsation of the sound- wave. The middle ear, which contains the chain of small THE EAK. 143 bones, is a cavity about half ai* inch in diameter, filled with air, communicating with the mouth by the EustacMan tube, G.* Within the labyrinth are fine, elastic hair-bristles and crystalline particles among the nerve-fibres, wonderfully fitted, the one to receive and the other to prolong the vibra- tions ; and lastly, a lute of 3,000 microscopic strings, so stretched as to vibrate in unison with any sound. (1.) KANGE OF THE EAR. Helmholtz fixes the highest limit of musical sounds at 38^000 vibrations per second, and the lowest at 16. f Below this number the pulses cease to link themselves, and become distinct sounds.}; The range of the ear is thus about eleven octaves. The capacity to hear the higher tones varies in different persons. A sound audible to one may be silence to another. Some ears cannot distinguish the squeak of a bat or the chirp of a cricket, while others are acutely sensitive to these shrill sounds. Indeed, the auditory nerve seems generally more alive to the short, quick vibrations than to the long, slow ones. The whirr of a locust is much more noticeable than the sighing of the wind through the trees. * The Eustachian tube serves to connect the tnner cavity with the external atmos- phere. If at any time the pressure of the air without becomes greater or less than that within, the membrane of the tympanum feels the strain, pain is experienced, and partial deafness ensues. A forcible concussion frequently produces this result. In the act of swallowing, the tube is opened and the equilibrium restored. We may force air Into the cavity of the ear by closing the mouth and nose, and forcibly expiring the air from the lungs. This will render us insensible to low sounds, as the rumble of a railway-train, while we can hear the higher ones as usual. t A tone produced by about 16 vibrations per second may be made by inserting the finger lightly in the ear, bringing at the same time the muscles of the hand into strong contraction. A sound will be heard which is as deep as the toll of a cathedral bell. $ Our unconsciousness Is no proof of the absence of sound. There are, doubt- less, sounds in Nature of which we have no conception. Could our sense be quick- ened, what celestial harmony might thrill us I Prof. Cooke beautifully says : " The very air around us may be resounding with the hallelujahs of the heavenly host ; While our dull ears hear nothing but the feeble accents of our broken prayers." To this, however, there are remarkable exceptions. The author knows a lady who is insensible to the higher tones of the voice, but acutely sensitive to the lower ones. Thus, on one occasion, being in a distant room, she did not notice the ringing of the bell announcing dinner, but heard the noise the bell made when returned to Ub plucu ou Liic shelf. 144 ACOUSTICS. (2.) THE ABILITY OF THE EAR TO DETECT AND ANALYZE SOUND is wonderful beyond comprehension. Sound-waves chase one another up and down through the air, super- posed in entangled pulsations, yet a cylinder not larger than a quill conveys them to the ear, and each string of that wonderful harp selects its appropriate sound, and re- peats the music to the soul within. Though a thousand instruments be played at once, there is no confusion, but each is heard, and all blend in harmony.* PRACTICAL QUESTIONS. 1. Why cannot the rear of a long column of soldiers keep time to the music in front ? 2. Three minutes elapse between the flash and the report of a thunderbolt ; how for distant is it ? 3. Five seconds expire between the flash and the report of a gun ; what is its distance 7 4. Suppose a speaking-tube should connect two villages ten miles apart ; how long would it take the sound to travel ? 5. The report of a pistol-shot was returned to the ear from the face of a cliff in four seconds ; what was the distance ? 6. What is the cause of the difference between the voice of man and woman ? A base and a tenor voice ? 7. What is the number of vibrations per second necessary to produce the fifth tone of the scale oi C ? 8l What is the length of each sound-wave in that tone when the temperature is at zero r 9. What is the number of vibrations in the fourth tone above middle C ? 10. A meteor of Nov. 13, 1868, exploded at a height of 60 miles ; what time was needed for its sound to reach the earth ? ll^j A stone is let fall into a well, and in four seconds is heard to strike the bottom ; how deep is the well ? ; 12. What time would be required for a sound to travel five miles in the still wafer of a lake ? 13. How much louder will be the report of a gun to an observer at a distance of 20 rods than to one at half a mile ? 14. Does sound travel faster at the foot than at the top of a mountain ? 15. Why is an echo weaker than the original sound ? 16. Why is it so fatiguing to talk through a speaking-trumpet ? 17. Why will the report of a cannon fired in a valley be heard on the top of a neighboring mountain, better than one fired on the top of a mountain will be heard in the valley? 18. Why do our footsteps in unfurnished dwellings sound so startlingly distinct ? 19. Why do the echoes of an empty church disappear when the audience assemble ? 20. What is the object of the sounding-board of a piano ? 21. During some experiments, Tyndall found that a certain sound would pass through twelve folds of a dry silk handkerchief, but would be stopped by a single fold of a wet one. Explain. 22. What is the cause of the musical murmur often heard near telegraph lines ? 23. Why will a variation in the quantity of water in the goblet, when made to sound, in the experiment described on p. 123, cause a difference in the tone ? 24. At what rate (in metres) will sound move through air, the temperature being 20 C. t * " Is not the ear the most perfect sense ? A needle woman will distinguish by the sound whether it is silk or cotton that is torn. Blind people recognize the age of persons by their voices. An architect, comparing the length of two lines sepa- rated from each other, if he estimate within &, we deem very accurate ; but a musician would not be considered very precise who estimated within a quarter of a note (128 -- 30 = 4 nearly). In a large orchestra, the leader will distinguish each note of each instrument. We recognize an old-time friend by the sound of his voice, when the other senses utterly fail to recall him. The musician carries in his ear the idea of the musical key and every tone in the scale, though he is constantly hearing a multitude of sounds. A tune once learned, will be remembered when the words of the song are forgotten." SUMMARY. 145 SUMMARY. Sound is produced by vibrations. These are transmitted in waves through the air (60 F.) at the rate of 1120 feet per second ; through water four times, and through iron fifteen times as fast. In gen- eral, the velocity depends on the relation between the density and the elasticity of the medium; and the intensity is proportional to the square of the amplitude of the molecular vibrations. Sound, like light, may be reflected and refracted to a focus. Echoes * are produced by the reflection of sound from smooth surfaces, not less than 112 feet (about 33 metres) distant. Rapidly-repeated vibrations make a contin- uous sound ; regular and rapid vibrations produce music ; irregular ones cause a noise. 'S The pitch of a sound .depends on the rapidity of the vibrations. The number of waves, and their consequent length in a given sound, is found by means of the siren. Unison is produced by identical wave-motions. Any number of sound-waves may traverse the air, as any number of water-waves may the surface of the sea, without losing their individuality. The motion of each molecule of air is the algebraic sum of the several motions it receives. Two systems of waves may therefore destroy or strengthen each other, according as their several condensations or rarefactions coalesce. Interference is the mutual destruction of two systems of waves. " Beats " is the effect produced by two musical sounds of nearly the same pitch, which alternately interfere and coincide. The vibrations of a cord .produce a musical sound, which is reinforced by a sounding-board. The rate of vibration and consequent pitch depends on the length, the tension, and the weight of the cord. Sounding bodies tend to vibrate in seg- ments. The harmonics thus produced give the quality (timbre) of different sounds. The various notes in the musical scale are deter- * Several acoustic phenomena have become of historical interest. (1.) Near Syracuse, Sicily, is a cave known as the Ear of Dionysius. A whisper at the farther end of the cavern is easily heard by a person at the entrance, though the distance is 200 feet. Tradition says that the Tyrant of Syracuse used this as a dungeon, and was thus enabled to listen to the conversation of his unfortunate prisoners. (2.) On the banks of the Nile, near Thebes, is a statue 47 feet high, and extending 7 feet below the ground. It is called the Vocal Memnon. Ancient writers tell us that about sunrise each morning, there issued from this gigantic monolith a musical sound resembling the breaking of a harp-string. It is now believed that this was produced by strong currents of air (due to the change of temperature in the early morning) passing through crevices in the stone. (3.) Near Mount Sinai, in Arabia, remarkable sounds are produced by the sand falling down a declivity. The sand, which is very white, fine and dry, lies at such an angle as to be easily set in motion by any cause, such as scraping away a little at the foot of the slope. The sand then rolls down with a sluggish motion, causing at first a low moan, that gradually swells to a roar like thunder, and finally dies away as the motion ceases. 146 ' ACOUSTICS. mined by fixed portions of the length of the cord. The music of a wind-instrument is produced by vibrating columns of air. Resonance is a sympathetic vibration caused by one sonorous body in another, as seen in sensitive flames, the resonance globe, etc. The voice is a reed instrument, with its vibrating cords and resonant cavity. The ear collects the sound-waves and transmits the motion to the brain. It consists of the outer ear, the drum and the labyrinth. HISTORICAL SKETCH. The ancients knew that without air we should be plunged in eternal silence. "What is the sound of the voice," cried Seneca, "but the concussion of the air by the shock of the tongue ? What sound could be heard except by the elasticity of the aerial fluid ? The noise of horns, trumpets, hydraulic organs, is not that explained by the elastic force of the air ? " Pythagoras, who lived in the 6th century before Christ, conceived that the celestial spheres are separated from each other by intervals corresponding with the relative lengths of strings arranged to produce harmonious tones. In his musical investigations he used a monochord, the original of the sonometer now employed by physicists, and wished that instrument to be engraved on his comb. Pythagoras held that the musical intervals depend on mathematics ; while his great rival, Aristoxenes, claimed that they should be tested by the ear alone. The theories of these two philosophers long divided the attention of the scientific world. Many centuries elapsed before any marked advance was made. Galileo called attention to the sonorous waves traversing the surface of a glass of water, when the glass is made to vibrate. Newton believed sound to be transmitted by aerial waves, and estimated the rate. The present century has witnessed a more complete demonstration of the laws of the vibrations of cords and the general principles of sound. In 1822, Arago, Gay-Lussac and others decided the velocity of sound to be 337 metres at 10 C. Savart invented a toothed wheel by which he determined the number of vibrations in a given sound ; Latour discovered the siren, which gave still more accurate results ; Colladon and Sturm, by a series of experiments at Lake Geneva, found the velocity of sound in water ; Helmholtz made known the laws of harmonics ; Lissajous, by means of a mirror attached to the vibrating body, threw the vibrations on a screen in a series of curves, and so rendered them visible ; while Tyndall has investigated the causes modifying the propagation of sound, as acoustic clouds, fogs, etc.* and poj ularized the whole subject of acoustics. (References, p. 120.) VII. O JV L I G- H T. TIu sunbeam comes to the earth as simply motion of ether-waves, yet it is the grand source of beauty and power. Its heat, light, and chemical force work everywhere the miracle of life and motion. In the growing plant, the burning coal, the flying bird, the glaring lightning, the blooming flower, the rushing engine, the roaring cataract, the pattering rain we see only itvritj manifestations of this one all-energizing force. ANALYSIS. 'on: 1. DEFINITIONS. 2. VISUAL ANGLE, 3. LAWS OF LIGHT. 4. VELOCITY OF LIGHT. 5. THEORY OF LIGHT. ri. DEFINITION AND LAW. j_! 3. ACTION OF ROUGH AND POLISHED SURFACES. I g i(a.) Effect of. (b.) Image seen. u. o (c.) Image behind mirror. z (d.) Multiple images. O 8. (e.) Images in water. h- O LU (2.) Con- ((a.) J^srf o/. cave. | (b.) Image seen. tr (3.) Con- ((a.) Effect of . vex. j (b.) Image seen. k 4. TOTAL REFLECTION. ^ f i DEFINITION AND ILLUSTRATIONS. 02 OfJ 2'. LAWS OF REFRACTION AND ILLUSTRATIONS. M I-I og f (1.) Con- ( (a.) Effect of. E< Ll_ .^ 3. LENSES < vex< < ^^ /ma ^ e seen ' ES ' ] (2.) Con- ] (a.) Effect of . So (. cave. 1 (b.) Image seen. 4. ABERRATION. CO I 5 - MIRAGE. ' j < SOLAR SPECTRUM. Lu 2. THREE CLASSES OF RAYS. o 3. THREE KINDS OF SPECTRA. z 4. THE SPECTROSCOPE. . C (1.) Formation of. -53; RATxrorvcir J (2.) Primary Bow. o S2 . )W ' 1 (3.) Secondary Bow. Q__J I (4.) Why the Bow is Circular, 6. COMPLEMENTARY COLORS. 7. INTERFERENCE OF LIGHT. . 8. COLOR. 9. POLARIZATION OF LIGHT. 1. MICROSCOPE. 2. TELESCOPE. 3. OPERA GLASS. 4. STEREOSCOPE. 5. MAGIC LANTERN. 6. CAMERA. 7. EYE. OPTICS, OR THE SCIENCE OF LIGHT. 1. PRODUCTION AND TRANSMISSION OF LIGHT. 1. Definitions. A luminous body is one that emits light. A medium is any substance through which light passes. A transparent * body is one that obstructs light so little that we can see objects through it. A translucent body is one that lets some light pass, but not enough to render objects visible through it. An opaque body is one that does not transmit light. A._ray of light is a single line of light ; it may be traced in a dark room into which a sunbeam is admitted by the floating particles of dust which reflect the light to the eye. K pencil or learn of liglit is a collection of rays, which may be parallel, diverging or converging. 2. The Visual Angle is the angle formed at the eye by rays coming from the extremities of an object. The angle AOB is the angle of vision subtended by the object FIG. 185. AB. The size of this angle varies with the distance of the body. AB and A'B' are of the same length, and yet the angle A'OB' is smaller than AOB, and hence A'B' will seem * The terms transparent and opaque are relative. No substance is perfectly transparent, or entirely opaque. Glass obstructs some light. According to Miller 7 feet of the clearest water will arrest one-half the light which fall? upon it. While Young asserts that the beam of the setting sun, passing through 200 miles of air, loses &g of its force. On the other hand, gold, beaten into leaf, becomes translucent, and of a feint green color; and scraped horn is semi-transparent 150 OPTICS. shorter than AB. The distance and the size 01 objects are intimately connected, since by experience we have learned to associate them. Knowing the distance of an object, we immediately determine its size from the visual angle.* 3. Laws of Light. I. Light passes off from a lumi- nous body equally in every direction. II. Light travels through a uniform medium in straight lines. III. The intensity of light decreases as the square of the distance V increases. 4. The Velocity of Light has been determined in various ways. The following was the first method : The planet Jupiter has four moons. As these revolve around the planet, they are eclipsed at regular intervals. In the cut, let J represent Jupiter, e one of the moons, S the sun, FIG. 136. and T and t different positions of the earth in its orbit around the sun. When the earth is at T, the eclipse occurs 16 min. and 36 sec. earlier than at t. That interval of time is required for the light to travel across the earth's orbit, giving a velocity of about 186,000 miles per second, f 5. TJncUilatory Theory of Light. There is supposed to be a fluid, termed ether, constituting a kind of universal atmosphere, diffused through space. It is so subtle that it * We can vary the apparent size of any body at which we ars looking by increasing or diminishing this angle a principle that will be found of great importance in the formation of images by mirrors and lenses. . t This rate is so great that for all distances on the earth it is instantaneous. A sunbeam would girt the globe quicker than we can wink. REFLECTION OF LIGHT. 15-1 glides among the molecules of bodies as the air does among the branches and the foliage of trees. It fills the pores of all substances, eludes all chemical tests, passes in through the receiver, and remains -even in the vacuum of an air-pump. A luminous body sets in motion waves of ether, which go off in every direction. They move at the rate of 186,000 miles per second, and breaking upon the eye, give the im- pression of sight. The wave-motion is like that of sound, except that the vibrations are transverse (crosswise).* 2. REFLECTION OF LIGHT. 1. Definition. Light falling on a surface is divided into two portions. One enters the body ; the other is re- flected f according to the familiar law of Motion and of Sound : The angle of incidence = that of reflection. 2. Action of Bough and Polished Surfaces. When the surface is rough, the numerous little elevations scat- j, ter the reflected rays in every direction, forming diffused [, light. Such a body can be seen from any point. "When the Jl surface is polished, the rays are uniformly reflected in particular directions, and bring to us the images of other objects. We thus see non-lurninous objects by irregularly- reflected (diffused) light, and images of objects by regularly- reflected light. J 3. Mirrors. All highly-reflecting surfaces are mirrors. These are of three kinds plane, concave and convex. The \! * Thus, if we suppose a star directly overhead and a ray of light coming down to us, we should conceive that the particles which compose the waves are vibrating N. S. E. W., and toward every other point of the compass all at once. t The amount of light reflected varies with the angle at which light falls. Thus, if we look at the images of objects in etill water, we notice that those near us are not as distinct as those on the opposite bank. The rays from the latter striking the water more obliquely are more perfectly reflected to the eye. Fill a sheet-iron or any dark-colored pail with water tinted with bluing or red ink. The color will be quite invisible to a spectator at a little distance. Now insert in the water a plate. This will reflect the transmitted light and reveal the hue of the water. J The most perfectly polished substance, however, diffuses some light enough to enable us to trace its surface ; were it not so, we should not be aware of its exist, ence. The deception of a large plate-glass mirror is often nearly complete ; but dust or vapor, increasing the irregular reflection, will bring its surface to view. 152 ornos. FIG. 187. first has a flat surface ; the second, one like the inside, and the third, one like the outside of a watch-crystal. The general principle of mirrors is that the image is s-een in the direction of the reflected ray as it enters the eye. (1.) PLANE MIBKOBS. Kays of light retain their relative direction after reflection from a plane surface.* An image seen in a plane mirror is therefore erect and of the same size as the object. It is, however, reversed right and left. Why the image is as far behind the mirror as the object is in front. Let AB be an arrow held in front of the mirror MN. Rays of light from the point A striking upon the mirror at C, are reflect- ed, and enter the eye as if they came from a. Eays from B seem to come from T). Since the image is seen in the direction of the re- flected rays, it appears at ab, a point which can easily be proved to be as far be- hind MN as the arrow is in front of it. Such an image is called a virtual one, as it has no real existence. Why ive can see several images of an object in a mirror. Metallic mirrors form only a single image. If, however, we look obliquely at the image of a candle in a looking-glass, we shall see several images, the first feeble, the next bright, and the others diminishing in intensity. The ray from A is in part reflected to the eye from the glass at b, and gives rise to the image a ; the re- mainder passes on and is reflected from the metallic surface * The perpendiculars are not given in the figures of the book, as the pupil at red tation should draw all the cuts on the blackboard, erect the perpendiculars and demon- strate the locati&n of the reflected ray. It wiil aid in drawing the perpendicular to a FIG. 136. REFLECTION OF LIGHT. 153 at c, and coming to the eye forms a second image a'. The ray cd, when leaving the glass at d, loses a part, which is reflected back to form a third image. This ray in turn is divided to form a fourth, and so on.* Images seen in water are symmetrical, but inverted. The reason of this can be understood by holding an object in front of a horizontal looking-glass and noticing the angle at which the rays must strike the surface in order to be re- flected to the eye. When the moon is high in the heavens, we see the image in the water at only one spot, while the rest of the surface appears dark. The light falls upon all parts, but the rays are reflected from only one point at the convex or concave surface, to remember that it is a radius of the sphere of which the mirror forms a part. A book held in various positions before a looking-glass illus- trates the action of plane mirrors. A beam of light admitted into a dark room and reflected from a mirror will show that the angles of incidence and reflection are in the same plane. Many of the grotesque effects of concave and convex mirrors may be seen on the inner and outer surfaces of a bright spoon, call-bell, or metal cup (see Mayer & BarnarcTs Light for inexpensive experiments). * To illustrate the formation of multiple images, place two small mirrors as in Fig. 139, where two coincident images are produced by second partial reflections. To vary the experiment hold the mirrors to- FIG. 139. getherlike the covers of a book placed on end, and put the can- dle between them on the table,openingand shutting the mirror- cover so as to vary the angle ; or hold the mirrors parallel to each other with the light between them. When the mirrors are inclined at 90, three images are -formed ; at 60% five images ; and at 45, seven im- ages. As the angle increases, thenumbcr diminishes. The im- ages are upon the cir- cumference of a circle whose centre is on a line in which the reflecting surfaces would Intersect if produced. Where the mirrors are parallel the images are in a straight line. They become dim- mer as they recede, light being lost at each reflection. The Kaleidoscope contains three mirrors set at an angle of 60. Small bits of colored glass at one end reflect to the eye at the other multiple images, which change in varying patterns as the tube is revolved. 154 OPTICS. right angle to reach the eye. Each observer sees the image at a different place. When the surface of the water is ruf- Fio. 140. FIG. 141. fled, a tremulous line of light is reflected from the side of each tiny wave that is turned towards us. As every little billow rises, it flashes a gleam of light to our eyes, and then sinking, comes up beyond, to reflect another ray. (2.) A CON- CAVE MlKEOR tends to collect the rays of light. * Thus in Fig. 141, parallel rays f all- ing upon the mir- * This statement is convenient as it is true in the practical use of the mirror, but does not obtain in every possible position. Thus, if a light be placed between A and F the rays would be scattered, as can easily be shown by a diagram. Again, in elementary optics it is supposed that MCN, known as the angular aperture of the mirror, does not exceed 8 or 10. When greater, the rays reflected near the edge of the mirror meet the principal axis AL, nearer the mirror than F. This is called the aberration of the mirror (p. 161). The reflected rays will then cross at points in a curved surface called a caustic. A section of such a curve can be seen when the light of a candle is reflected from the inside of a cup partly full of milk. REFLECTION OF LIGHT. 155 ror MN are reflected to the point F, the principal focus (focus, a hearth). This is half way between the mirror and C, the centre of curvature, i. e. the centre of the hollow sphere of which the mirror is a part. AF is the focal dis- tance ; CB, CD, etc., are radii of the sphere (perpendiculars, to find the angle of incidence) ; and the angles HBO, GDC, etc., are equal respectively to FBC, FDC, etc. A light held at C will have its rays brought to a focus at C, where a real image will be formed ; while one at F will be reflected in a beam of parallel rays. Images formed ly concave mirrors. Hang a concave mir- ror against the wall, and stand closely to it between the mirror and the principal focus. The image is erect, virtual, FiO. 142. and larger than life. The ray a falls upon the mirror, is reflected and strikes the eye as if it came from A. In the same manner I is seen at B. The visual angle is increased the nearer we approach the mirror, and hence the larger the image appears. We now walk back. When we reach the focus, the image dis- appears. We are in the position of the candle ab (Fig. 143) and the real image is behind us at AB. A few of the parallel rays, however, enter the eye, and an indistinct image is formed. Retiring still further, we come to the centre of curvature, Here we find no distinct image, although por 156 OPTICS. tions of our figure, as we catch snatches of the rays forming the image AB, are seen grotesquely magnified. As we con- tinue to recede, we reach a point beyond the centre of FIG. 143. curvature. Here we occupy the position AB (Fig. 143), and see the image at rib inverted, as the rays have crossed. The points occupied by the two candles, db and AB, are termed conjugate foci, because a light at either one is brought to a focus at the other. FIG. 145. FIG. 144. (3.) A CONVEX MIBROE tends to scatter the rays of light. The par-' illel rays AD and BK (Fig. 144), are reflected in the diverging lines DE and KH. An eye receiving these rays will perceive the image of AB at ab, virtual, erect, and smaller than life. Whatever may be the position of the object, the image being always between the object and the centre of curvature is smaller than the object. 4. Total Reflection. When we look obliquely into n REFRACTION OF LIGHT. 157 pond, we cannot see the bottom, because the rays of light from belo\v are reflected downward at the surface of the water. Hold a glass of water above the level of the eye, and the upper part will gleam like burnished silver. * Thus the internal surface of a transparent body becomes a mirror. This occurs when light would pass very obliquely from a denser to a rarer medium. 3. REFRACTION OF LIGHT. 1. Definition. When a ray of light passes obliquely | from one medium to another of different density, it is I refracted or bent out of its course. Ex. : A spoon in clear tea appears bent. An oar dipping in still water seems to break at the point where it enters the 'water. f Put a cent in a bowl. Standing where you cannot see the coin, let another person pour water into the vessel, when the coin * Place a "bright spoon in the glass and notice its image reflected from the surface of the water. The apparently increased size of the spoon, the broken handle, etc., will be understood after reading the next subject. Turn the spoon about in the glass and, changing the angle of observation, notice the effect. The real handle may ap- parently be attached to the image in the water. The spoon will soon be covered with bubbles of air shining, like pearls, from total reflection. This shows also the presence of air in water and the adhesion of gases to solids. FIG. 146. The goblet, if filled with cold water, will "sweat," as it is called, from the condensed moisture of the atmosphere. t Fish seem nearer the sur- face than they really are, and Indians, who spear them, try to strike perpendicularly, or else aim lower than they apparently lie. In Fig. 146, the man on the bridge sees the fish in its true place : but the boy on the bank sees the 'fish at a, while the fish sees the boy at c. Water is deeper than it appears. Look obliquely into a pail of water, then place your finger on the outs' de where the bottom seems to be ; you will be surprised to find the real bottom is several inches below. Fill a glass dish with water, and, darkening the windows, let a sunbeam fall upon the surface. The ray will bend as it enters. Dust scattered through the air will make the beam distinct. 158 OPTICS. will be lifted into view. Fie. 147. To understand the apparent ^ change of position, re- member that the object is seen in the direction of the refracted ray as it enters the eye. Let L, Fig. 148, be a body be- neath the water. A ray, LA, coming to the surface, is bent downward toward C, FIO. 148. and strikes the eye as if it came from L'. The object will there- fore apparently be elevated above its true place. 2. Laws of Refraction. I. In passing into a rarer medium, the ray is bent from the perpendicular. II. In passing into a denser medium, the ray is bent toward the perpendicular.* ILLUSTRATIONS. Path of rays through a window-glass. When a ray enters a window-glass, it is refracted toward the perpen- dicular (2d law), and on leaving, is refracted from the perpendicular (1st law). The general direction of objects is therefore unchanged. A poor quality of glass produces distortion by its unequal density and uneven surface. /IU Path of rays through a prism. A ray of light, on entering and on leaving a prism, is refracted as by a window-glass. The inclination of the sides causes the ray * Both the Incident and the refracted ray lie in the same plane as the normal (perpendicular). The ratio between the sines of the incident and refracted angles is termed the index of refraction. It varies with the media. Ex. : From air to water ii la land from air to glass | . FIG. 149. ff BKFRACTIOH OF LlGflT. to be bent twice in the same direction. The candle L will therefore appear to be at r. 3. Lenses, A lens is a transparent body, with at least one curved surface. There are two gen- eral classes of lenses, concave and convex.* (See Fig. 151.) FIG. 151. (1.) THE DOUBLE-COKVEX LENS has two convex surfaces. Its action on light is like that of a concave mirror. A ray FIG. 152. X striking perpendicularly, is not refracted. The parallel rays M, L, etc., are refracted both on entering and on leav- ing the lens, and are converged at F, the focus, f If a light be placed at F, its rays will be made parallel. * Forms of lenses: M, double-convex; N, plano-convex ; O, meniscus (crescent); P, double-concave ; Q, plano-concave ; R, concavo-convex. The first three are styled magnifiers, and the second, diminishers. t The convex lens is sometimes termed a burning-glass, being used, like the 160 OPTICS. The image formed by a convex lens is like that of a con- cave mirror. If we hold a lens above a printed page, when we obtain the focal distance correctly, we shall find the let- Fio. 153. ters right-side up and highly magnified. In Fig. 153 we see how the converging power of the lens increases the visual angle, and makes the object AB appear the size ah. FIG. 154. Moving the lens back from the page, the letters entirely dis- appear as we pass the principal focus. At length they reappear again, but smaller and inverted (Fig. 154). (2.) THE DOUBLE-CONCAYE LENS has two concave sur- faces. Its action on light is like that of a convex mirror. Thus, diverging rays from L (Fig. 155) are rendered more diverging, and, to an eye which receives the rays MN", the candle would seem to be at Z, where the image is seen. concave mirror, for collecting the sun's rays. Lenses have been manufactured of sufficient power to melt a stone by sunheat. Even glass-globes of water, puch as are used for gold fishes or in the windows of drug stores, may fire adjacent objects. REFRACTIOH OF LIGHT. FIG. 155. 163 The image formed by a concave lens, like that of a convex mirror, is virtual, erect, and diminished in size (Fig. 156). FIG. 156. 4. Aberration. Bays which pass through a lens near the edge are brought to a focus sooner than those near the centre. Therefore, when the border of an image is clear, the centre will be indistinct, and vice versa. This wander- ing of the rays from the focus is termed spherical aberration. The different refrangibility of the colors which compose white light (p. 163) produces chromatic aberration. The violet, being bent most, comes to a focus sooner than the red, which is bent least. This causes the play of colors seen around the image produced bv an ordinary lens. The defect 162 OPTICS. is remedied by a second lens of different dispersive power, which counteracts the effect of the first. Such a compound lens is said to be achromatic (colorless). 5. Mirage. In the heated deserts of Africa, the trav- eller sometimes sees in the distance quiet lakes with the shadows of trees in their cool waters. Rushing forward to slake his eager thirst, he finds only the barren waste of sand. The mariner often recognizes in the sky the images of ships, and the far-distant coast, with its familiar cliffs. The cause / of these phenomena is the refraction and reflection of the ( rays of light traversing layers of air of unequal density. FIG. 157. Sometimes a layer of air high up in the sky acts as a reflector, and sends down inverted images of ships which are beyond the horizon. In Fig. 157, rays of light from a clump of trees are refracted more and more until finally they are reflected from a layer at a, and enter the eye of the Arab as if they came from the surface of a quiet lake. The deception is made complete by the fact that the sandy desert, shimmering in the hot sun, often has in the distance the aspect of tranquil water.* * Hold a pane of glass horizontally above the eyes. The inverted images of objects in front may be seen, reflected from the surface of the glass. COMPOSITION OF LIGHT. 163 4. THE COMPOSITION OF LIGHT. 1. Solar Spectrum. When a sunbeam shines through a prism, the ray is not only bent from its course, but is also spread out, fan-like, into a band of rainbow-colors the solar spectrum. It contains the seven primary colors violet, indigo, blue, green, yellow, orange, red.* If we receive the spectrum on a concave mirror, or pass it through a convex lens, it will form a white spot. We therefore con- clude that white light is composed of seven colors. They are separated because the prism bends them unequally. The violet is most refracted, and the red least. FIG. 158. 2. Three classes of rays exist in the solar spectrum , viz. : the heat rays ; luminous rays ; and actinic rays.f If~we examine the prismatic spectrum with a very delicate thermometer, we find that the heat increases from the violet to the red end, and becomes the greatest in the dark space just beyond. If we test with a paper containing * Notice that the initial letters spell the mnemonic word, Vib-gy-or, \ The classification into three kinds of rays is retained as it is etill common in scientific books. Draper has shown that the effects described above are due merely to an unequal distribution of the ether- waves by the prism. Rays of all colors have the same light, heat, and chemical power, and the same cause radiant energy. We call this one thing, light, heat, or actinism, according to the means used to reveal its presence (pp. 183-4). See also p. xi. Fresh Facts, etc. chloride of silver, it will blacken least in the red, most toward the violet, and some in the dark space beyond. Be- tween these two extremes lie the rays which strongly affect the eye. All are mingled in the normal spectrum. 3. Three Kinds of Spectra. I. When the light of a solid or liquid body, as iron white-hot, is passed through a prism, the spectrum is continuous and consists of the familiar colors of the rainbow. II. When the light of a burning gas is passed through a prism, the spectrum is not con- tinuous, but consists of bright-colored lines copper giving a set of green lines, and zinc one of bright -blue and red. Each element produces a series which can be recog- nized as its test. III. When a light of the first kind is passed through one of the second at a lower temperature, the spectrum is crossed ly dark lines. Thus, when the light of white hot lime shines through a flame of burning sodium, instead of the two Tivid yellow lines so characteristic of that metal, two black lines occupy their place. In general, a gaseous flame absorbs rays of the same color that it emits.* FIG. 160. * Imagine a room filled with piano- wires, stretched in every direction and tuned to one key. Now let a person at one end of the room play a tune. Another per- OF LIGHT. 165 4. The Spectroscope is an instrument for examining spectra. The rays of light (Fig. 161) enter through a nar- row slit in the tube at A, and are rendered parallel by an object-glass. They then pass through the prisms at 0, are separated into the different colors, and entering the tele- scope at D, fall upon the eye at B. Any substance may be placed in the flame in front of A and its spectrum examined.* 5. The Rainbow is formed by the refraction and re-- flection of the sunbeam in drops of falling water. The wHIte light is thus decomposed into its simple colors. The son at the opposite end of the room would hear the tune perfectly except when the particular note which belonged to the wires was struck, when that would be sifted out. * On the uses of the spectroscope, examine Astroncmy, p. 286, and Chemistry, p. 145. The frontispiece of the latter gives a colored illustration of the spectra. The solar spectrum is crossed by dark lines known as FraunJiofer's lines. The most prominent are marked for convenience of reference (A, B, C, etc., Fig. 160). The spectroscope affords an unrivalled mode of analysis. No cLemical test is so delicate. Strike together two books near the light at the slit of the spectroscope, and the dust blown into the flame will contain enough sodium (the basis of common salt) to cause the yellow D lines its test to flash out distinctly. (Seo note on spectroscope, p. 226.) A very effective spectroscope may be contrived thus: Cut a slit not over 3>o inch wide and 2 inches long in a piece of tinfoil, and guia it on a pane of glass. Hold this before a flame and look at it through a prism. 166 OPTICS. inner arch is termed the primary bow ; the outer or fainter arch, the secondary. PEIMAKY Bow. A ray of light, S", enters, and is bent downward at the top of a falling drop, passes to the opposite side, is there reflected, then passing out of the lower side, is bent upward. By the refraction the ray of white light is decomposed, so that when it emerges it is spread out fan-like, as in the solar spectrum. Suppose that the eye of a spectator is in a proper position to receive the red ray, he cannot receive any other color from the same drop, because the red is bent upward the least, and all the others will pass directly over his head. He sees the violet in a drop below. Intermediate drops furnish the other colors of the spectrum. FIG. 163. SECONDARY Bow. A ray of light, S, strikes the bot- tom of a drop, v, is refracted upward, passes to the oppo- site side, where it is twice reflected, and thence passes out at the upper side of the drop. The violet ray being most refracted, is bent down to the eye of the spectator. Another drop, r, refracting another ray of light, is in the right posi- tion to send the red ray to the eye. COMPOSITION OF LIGHT. 167 WHY THE Bow is OIECULAE. When the red ray of the primary bow leaves the drop, it forms an angle with the sun's ray, S'V, of about 42, and the violet 40. These angles are constant. Let ab be a straight line drawn from the sun through the observer's eye. If produced, it would pass through the centre of the circle of which the rainbow is an arc. This line is termed the visual axis. It is parallel to the rays of the sun ; and when it is also parallel to the horizon, the rainbow is a semicircle. Suppose the line Ey in the primary bow to be revolved around E#, keeping the angle #Ev unchanged ; the point v would describe a circle on the sky, and every drop over which it passed would be at the proper angle to send a violet ray to the eye at E. Imagine the same with the drop r. We can thus see (a) the bow must be circular ; (b) when the sun is high in the heavens, the whole bow sinks below the horizon ; (c) the lower the sun the larger is the visible circumference ; and (d) on lofty mountains a perfect circle may some- times be seen.* GREENISH 10WISH OREEN BLUE YELLOW ORANGE H ORANGE 6. Complementary Colors. Two colors, which by their mixture produce white light, are termed complementary to each other. Thus, if we sift the red rays out of a beam of light and bring the remainder to a focus, a green image will be formed, f In Fig. 163 the colors opposite each other are complementary. Place a red and a * Halos, coronas, sundogs, circles about the moon, and the tinting at sunrise and sunset, are produced by the refraction and reflection of the sun's rays by the clouds. The phenomenon known as the " sun's drawing water," consists of the long shadows of broken clouds. Twilight and kindred topics are treated in Astronomy. t Certain substances are able to split a ray of light into its complementary colors. Thus gold-leaf reflects the red and transmits the green. 168 OPTICS. blue ribbon side by side. The former will take on a yellow and the latter a green tint. Lay a piece of tissue paper upon black letters printed on colored paper. The dark letters will appear of a color complementary to that of the background.* 7. Interference of Light (Netvton's Rings). Let the convex side of a plano-convex lens be pressed down upon a plane of glass. The two surfaces will apparently touch at the centre. If different circles be described around this point, at all ^^^ FlG ' 164 ' ^^ "OtlluS 01 GtLC-Ll Gi.l*C-L6 "LUG SU-J/IclC'tJo AVJ.-L1 \y///////////////.' , /. ' ''/////////////////////////ih be the same distance apart, and the larger the circle the greater the distance. Now let a beam of red light fall upon the flat surface. A black spot is seen at the centre ; around this a circle of red light, then a dark ring, then another circle of red light, and so alternating to the circumference. The distances between the surfaces of the glass, where the successive dark rings appear, are pro- portional to the numbers 0, 2, 4 , and the bright circles to 1, 3, 5 This fact suggests the cause. There are two sets of waves, one reflected from the upper surface of the plane glass, and the other from the lower surface of the convex glass. These alternately interfere, producing darkness, and combine, making an intenser color, f To de- * A color is heightened when placed near its complement. A red apple is the brighter for the contrast of the green leaf. Observe a white cloud through a bit of red glass with one eye and through green glass with the other eye. After some moments, transfer both eyes to the red glass, opening and closing them alternately. The strengthening of the red color in the eye fatigued by its complementary green, is very striking. In examining ribbons of the same color, the eye becomes v/earied and unable to detect the shade, because of the mingling of the complementary hue. t The play of colors in mother-of-pearl is due to the interference of light in its thin overlapping plates. In a similar manner the plumage of certain birds reflects changeable hues. A metallic surface ruled with fine parallel lines not more than 55 Vo of an inch apart, gleams with brilliant colors. Thin cracks in plates of glass or quartz, mica when two layers are slightly separated, even the scum floating in stagnant water, breaks up the white light of the sunbeam and reflects the varying tints of the rainbow. The rich coloring of a soap-bubble is caused by the interfer- ence of the rays reflected from the upper and lower surfaces of the bubble. DIFFRACTION is a kind of interference produced by a beam of light passing along the edge of an opaque body or through a small opening. Ex. : If we hold a fine needle close to one eye and look toward the window, we see several needles. Place the COMPOSITION OF LIGH-T. 169 termine the length of a wave of red light, we have only to measure the distance between the two glasses at the first ring. When beams of light of the various colors are used cor- responding circles are obtained, having different diameters ; red light gives the !argest, and violet the smallest. We hence conclude that red waves are the longest, and violet the shortest. The minuteness of these waves passes com- prehension. About 40,000 red waves and 60,000 violet ones are comprised within a single inch. Knowing the velocity of light, we can calculate how many of these tiny waves reach our eyes each second. When we look at a violet object, 757 million million of ether-waves break on the retina every moment ! 8. Color is analogous to pitch, violet corresponding to the high and red to the low sounds in music. Intensity of color, as of sound, depends on the amplitude of the vibra- tions. When a body absorbs all the colors of the spectrum except blue, but reflects that to the eye, we call it a blue body; when it absorbs all but green, we call it a green body.* Red glass has the power of absorbing all except the red rays, which it transmits. When a substance reflects all the colors to the eye, it seems to us white. If it absorbs all the colors, it is black. Thus color is not an inherent prop- erty of objects, f In darkness all things are colorless. blades of two knives closely together and hold them up to the sky: waving lines of interference will shade the open space. Look at the sky through the meshes of a veil, or at a lamp-light through a bird-feather or a fine slit in a card, and delicate colors will appear. * Some eyes are blind to certain colors, as some ears are deaf to certain sounds. " Color-blindness " generally exists as to red. Such a person cannot by the color distinguish ripe cherries from the leaves. Doubtless railway accidents have occurred through this inability to apprehend signals. Dr. Mitchell mentions a naval officer who chose a blue coat and red waistcoat, believing them of the same color ; a tailor who mended a black silk waistcoat with a piece of crimson ; and another who put a red collar on a blue coat. Dalton could see in the solar spectrum only two colors, blue and yellow, and having once dropped a piece of red sealing-wax in the grass, he could not distinguish it. t Moisten a swab with alcohol saturated with common salt. On igniting the 170 OPTICS. FIG. 165. 9. Polarization of Light (Double Refraction). If we could loolf~at ihe end of a ray of light as we can at the end of a rod, we should see the particles of ether swimming swiftly to and fro in the direction of all the diameters (Fig. 165). Certain crystals have the power of sifting and arranging these vibra- tions into two sets at right angles to each other, making ;t ray of the form seen in Fig. 166. As one set is more refracted than the other, the ray is divided into two the ordinary and the extraordinary. Rays which have thus been sifted constitute polarized light. Iceland spar possesses the FIG. 166. FIG. 167. property of double refraction in a remarkable degree. An object viewed through it appears double. If the crystal be placed on a dot and slowly turned round, two dots will be seen, the second revolving about the first. Objects seen by polar- ized light present curious changes. A crystal of quartz reveals beautiful colors due to interference. Looking at a lamp-light through a piece of thin mica, we see a series of polarised rays having a star-like form. When polarized light is passed through common glass no change is noticed, but on slight pressure a system of variegated colors appears. Polarized light therefore affords a delicate means of determining the molecular structure of a body.* * Some substances have the power of twisting the plane of the polarized light. Cane-sugar turns it to the right, and fruit-sugar to the left (Chemistry, p. 190). The French government uses a polarizing instrument, in which this principle 10 applied to test the quality of sugar. OPTICAL INSTRUMENTS. 5. OPTICAL INSTRUMENTS. 171 1. Microscopes (to see small things) are of two kinds, simple and compound. The former consists of one or more convex lenses through which the object is seen directly : the latter contains a simple magnifier for viewing the image of Fia 168. an object produced by a second lens. Fig. 168 represents a compound microscope. At M is a mirror which reflects the rays of light through the object a. The object-lens (objec- tive) o forms, in the tube above, a magnified, inverted image of the object. The eye-lens (ocular) magnifies this image. 172 OPTICS. The magnifying power of the instrument is nearly equal to the product of that of the two lenses. If a microscope in- creases the apparent diameter of an object 100 times, it is said to have a power of 100 diameters, the surface being magnified 100 2 =10,000 times. The eye-piece may be only a single lens, and is really a simple microscope. The object- lens often consists of several lenses, and each one of a com- bination (p. 161) to prevent aberration. 2. Telescopes (to see afar off) are of two kinds, reflect- ing and refracting. The former contains a large metallic mirror (speculum) which reflects the rays of light to a focus. The observer stands at the side and examines the image with an eye-piece.* The Refracting Telescope contains an object-lens o which forms an image ab. This is viewed through the eye-piece 0, which produces a magnified, inverted image cd. The latter unage is as much larger than the former as the focal distance FIG. 169. of the eye-piece is less than that of the object-glass. The larger the object-lens the more light is collected with which to view the image. The magnifying power is principally due to the eye-piece, f The apparent inversion of the object is * The largest reflecting telescope is that of Lord Kosse (See Frontispiece to Astronomy). Its speculum is 6 feet in diameter and gathers about 120,000 times as much light as would ordinarily enter the eye. t The Washington Observatory telescope has an object-glass 26 inches in diam- eter, and of excellent defining power. The Chicago telescope has a lens of 18 inches diameter. It collects * 5000 times as much light as the unaided pupil "equivalent to increasing the astronomer's eye to that size. The use of the telescope depends upon (1st) its light-collecting and (2d) its magnifying power. Thus Herschel, illus- trating the former point, says that once he told the time of night from a clock on a steeple invisible on account of the darkness. It is noticeable that while in the com- pound microscope the image is as much larger than the object as the image is further OPTICAL INSTRUMENTS. Pie. 170. 173 CAMBRIDGE EQUATORIAL. of no importance for astronomical purposes. In terrestrial observations additional lenses are used to invert the image. 3. The Opera-glass contains an object-glass and an FIG. 171. than the object from the object-glass, in the telescope the image is as much smaller than the object as it is nearer than the object to the object-glass ; while in both cases the image is examined with a magnifier. If a power of 1000 be used in looking at the sun, we shall evidently see the sun as if it were only 93,000 miles away, or less than one-half the distance of the moon. The same power used upon the moo vould bring that body apparently to within 240 miles of us. 174 OPTICS. Tie. 178. opticon, contains a light (Fig. 174) upon the object magnified image produced by two to melt into each eye-piece o. The latter is a double- concave lens ; this increases the visual angle by diverging the rays of light, which would otherwise come to a focus beyond the eye-piece. An erect and magnified image is seen at db. 4. The Stereoscope contains por- tions of two convex lenses (Fig. 172). Two photographs A and B are taken by two cameras inclined to each other. This produces two pictures like the views we obtain of an object by the use of each eye alternately. The blending at C causes the appearance of solidity.* 5. The Magic Lantern, or Stere- a reflector M, which condenses the rays of upon a lens L. They are there converged db. Thence a double lens m throws a on the screen AB. Dissolving views are lanterns containing the scenes which are other. FIG. 173. * In Pig. 173 there are two views of a tunnel. In one the opening is at the left of the centre and in the other at the right. If the view be held about 4 inches from the eyes three engravings will be seen, the middle one formed by the mental blend- ing of the other two. By closing either eye alternately one view will disappear. See also p. xii. Fresh Facts and Theories OPTICAL INSTRUMENTS. 175 FIG. 175. 6. The Camera, used by photographers, contains a double-convex lens, A, which throws an inverted image of the object upon the ground-glass screen EB. When the focus has been obtained, the screen is removed and a slide, con- taining a sensitive film, is inserted in its place. ( Chem- istry, p. 167.) 7. The Eye is a unique optical instrument resembling a camera. It is rarely, if ever, troubled by spherical or chromatic aberration, and is self- focusing. The outer membrane is termed the sclerotic coat, S. It is tough, white, opaque, and firm. A little portion in front, called the cornea, c, is more convex and perfectly transparent. The middle or choroid coat, C, is soft and delicate, like velvet. It lines the inner part of the eye and is covered with a black pigment, which absorbs the super- fluous light. Over it the optic nerve, which enters at the rear, expands in a net-work of delicate fibres termed the 176 OPTICS. retina, the seat of vision. Back of the cornea is a colored curtain, hi, the iris (rainbow), in which is a round hole called the pupil. The crystalline lens, o, is a double- convex lens, composed of concentric layers somewhat like an onion, weighing about 4 grains and transparent as glass. Between the cornea and the crystalline lens is a limpid fluid Fie. 176. termed the aqueous humor; while the vitreous humor, a transparent, jelly-like liquid, fills the space back of the crystalline lens. Let AB represent an object in front of the eye. Rays of light are first refracted by the aqueous humor, next by the crystalline lens, and last by the vitreous humor, forming on the retina an image, ab,* which is real, inverted, and smaller than the object. To render vision distinct, the rays must be accurately focused on the retina. If we gaze steadily at an object near by, and then suddenly observe a distant one, we find our vision blurred. In a few moments it becomes clear again, showing that the eye has the power of adapting itself to the varying distances of objects. This is done by a change in the convexity of the crystalline lens. When * The diameter of the eye is less than an inch ; yet, as we look over an extended landscape, every feature, with all its variety of shade and color, is repeated in miniature on the retina. Millions upon millions of ether waves, converging from every direction, break on that tiny beach, while we, oblivious to the marvellous nature of the act, think only of the beauty of the revelation. Yet in it the physicist sees a new illustration of the simplicity and perfection of the laws and methods of the Divine Workman, and a continued reminder of His forethought and skill. OPTICAL INSTRUMENTS. 177 the distance at which the clearest vision occurs is less than ten or twelve inches, the person is near-sighted, and when greater, far-sighted. Too great flatness or convexity of the cornea or crystalline lens will produce this result. The defect, however, often lies in the shape of the eyeball. In far-sightedness the ball is too flat, and the retina too near the lens ; in near-sightedness the ball is elongated, so that the retina is too distant. The former can be remedied by convex glasses, which bring the rays to a focus sooner, and the latter by concave, which throw the focus further back. The retina retains an impression about one-eighth of a second. * This explains why a wheel, when rapidly revolved, appears solid, or a lighted brand like a ring of fire. On the other hand, it requires a moment for an impression to be made. Thus a wheel may be whirled so swiftly that its spokes become invisible. PRACTICAL QUESTIONS. 1. Why is the secondary bow fainter than the primary ? Why are the colors reversed ? 2. Why can we not see around the corner of a house, or through a bent tube ? 3. What color would a painter use if he wished to represent an opening into a dark cellar ? 4. Is white a color ? Is black ? 5. By holding an object nearer a light, will it increase or diminish the size of the shadow ? 6. What must be the size of a glass in order to reflect a full-length image of a person ? Ans. Half the person's height. 7. Where should we look for a rainbow in the morning ? 8. Can two spectators see the same bow ? 9. Why, when the drops of water are falling through the air, does the rainbow appear stationary ? 10. Why can a cat see in the night ? 11. Why cannot an owl see in daylight ? 12. Why are we blinded when we pass quickly from a dark into a lighted room ? 13. If the light of the sun upon a distant planet is ^ of that which we receive, how does its distance from the sun compare with ours ? 14. If, when I sit six feet from a candle, I receive a certain amount of light, how much shall I diminish it if I move back six feet further ? 15. Why do drops of rain, in falling, appear like liquid threads ? 16. Why does a towel turn darker when wet ? 17. Does color exist in the object, or in the mind of the observer ? 18. Why is lather opaque, while air and a solution of soap are each transparent ? 19. Why does it whiten molasses candy to u pull it " f 20. Why does plastering become lighter in color as it dries ? 21. Why does the pho- tographer use a kerosene-oil lamp in the ll dark room " ? 22. Is the common division of colors into "cold " and "warm" verified in philosophy? 23. Why is the image on the camera, Fig. 175, inverted '{ 24. Why is the second image seen in a mirror, Fig. 138, brighter than the first ? 25. Why does a blow on the head make one u see stars " 1 Ans. The blow excites the optic nerve, and so produces the sensation of light. 26. What is the principle of the kaleidoscope ? 27. Which can be seen at * When one is riding slowly on the cars and looking at the landscape between the upright fence-boards, he catches only glimpses of the view; but when moving rapidly, these snatches uoitt combine to form a perfect landscape, which has, however. a grayish tint, owing to the decreased amount of light reflected to the eye. 178 OPTICS. the greater distance gray or yellow ? 28. Look down Into the glass of water shown in Pig. 145, and, at a certain angle, you will see two spoons, one small and having the real handle of the spoon, though apparently bent, and the real spoon with no handle. Explain. 29. When a star is near the horizon, does it seem higher or lower than its true place ? 30. Why can we not see a rainbow at midday ? 31. What con- clusion do we draw from the fact that moonlight shows the same dark lines as sun- light ? 32. Why does the bottom of a ship seen under water appear flatter than it really is ? 33. Of what shape does a round body appear in water ? 34. Why is rough glass translucent while smooth glass is transparent? 85. Why are some bodies brilliant and others dull ? 36. Why can a carpenter, by looking along the edge of a board, tell whether it is straight ? 88. Why can we not see out of the window after we have lighted the lamp in the evening ? 38. Why does a ground-glass globe soften the light ? 39. Why can we not see through ground-glass or paiutod windows ? 40. Why does the moon's surface appear flat? 41. Why can we see farther with a telescope than with the naked eye ? 42. Why is not snow transparent, like ice ? 43. Are there rays hi the sunbeam which we cannot perceive with the eye ? 44 Why, when we press the finger on one eyeball, do we see objects double ? 45. Why does a distant light, in the night, seem like a star? 46. Why does R bright light, in the night, seem so much nearer than it is ? 47. What color predominates in artificial lights ? Ans. Yellow. 48. Why does yellow seem white, and blue green, when seen by artificial light ? 49. Why are we not sensible of darkness when we wink? 50. Why is the lens of a fish's eye (seen in the eye-socket of a boiled fish) so convex ? 51. When do the eyes of a portrait seem to follow a spectator to all parts of a room ? 52. Why does the dome of the sky seem flattened ? 53. Why do the two parallel tracks of a railroad appear to approach in the distance ? 54. Why does a fog mag- nify objects ? 55. If you sit where you cannot see another person's image, why cannot that person see yours ? 56. Why can we see the multiple images in a mirror better if we look into it very obliquely ? 57. Why is an image seen in water inverted? 58. Why is the sun's light fainter at sunset than at midday? 59. Why can we not see the fence-posts when we are riding rapidly? 60. Ought a red flower to be placed in a bouquet by an orange one ? A pink or blue with a violet one ? 61. Why are the clouds white while the clear sky is blue? 62. Why does skim- milk look blue and new milk white ? 63. What would be the effect of filling the basin, in the experiment shown in Fig. 147, with salt water ? 64. Why is not the image of the sun in water at midday so bright as near sunset ? 65. Why is the rainbow always opposite the sun ? SUMMARY. Eight comes from the sun and other self-luminous bodies. It is transmitted by means of vibrations in ether, according to the principles of wave-motion. It radiates equally in all directions, travels in straight lines, decreases as the square of the distance, and moves 186,000 miles per second. Light falling upon a body may be absorbed, transmitted or reflected. If the surface be rough, the irregularly- reflected light enables us to see the body ; if it be smooth and highly polished, the rays are reflected so nearly as they fall that they form an image of the original object. Surfaces producing such images are SUMMARY. 179 termed mirrors plane, concave, or convex. The image is seen in the line of the reflected ray, and, in a plane mirror, as far behind the mirror as the object is in front. Multiple images are produced by repeated reflections, as in the kaleidoscope. A concave mirror, as generally used, collects the rays, and serves to magnify an object or to throw a parallel beam of light. A convex mirror scatters the rays, and apparently diminishes the size of an object. When a ray enters or leaves a transparent body obliquely it is refracted ; if passing into a rarer medium it is bent from, and if into a denser, toward a perpendicular. A transparent body with one or more curved surfaces is a lens. There are two classes convex and concave. The former lens, as generally used, tends, like a concave mirror, to collect the rays of light, and is known as a "magnifier"; the latter, like a convex mirror, scatters the rays of light, and is known as a "diminisher." Mirage is an optical delusion caused by reflection and refraction of light in passing through air composed of strata of unequal density. Owing to the varying refrangibility of the different constituents of the sunbeam, a prism can disperse them into a colored band called the solar spectrum. The spectrum shows white light to consist of seven elementary colors, and that the sunbeam con- tains, in addition to the luminous rays, heat and chemical rays. By means of the spectroscope we can examine the spectrum of a flame, and find whether it is a burning gas or an incandescent solid. Each substance gives a spectrum with its peculiar lines of color. A gas absorbs the same rays that it is capable of emitting ; hence we have absorption spectra, which contain dark instead of colored lines. A delicate mode of analysis is thus furnished, whereby the elements even of the distant stars can be detected. The rainbow is formed by the refraction and reflection of the sunbeam in raindrops. Light, when reflected by or transmitted through bodies, is so modified, chiefly by absorption, as to produce the varied phenomena of color. Each color has its own wave-length, the minuteness of which is almost incredible. Different systems of light, as of sound waves, may co- exist. But if any two coincide with similar phases they will strengthen each other ; and if with opposite phases, weaken each other. Inter- ference of light, as thus produced, causes the play of colors in the soap-bubble, mother-of-pearl, etc. Polarized light is that in which the molecular vibrations are made in the same plane. It is of use in determining the internal constitution of a body. The principal optical instruments, including the eye, are adapted to produce and examine the image formed by a lens. In the magic- lantern, stereopticon, and solar microscope, the image is thrown on a screen in a dark room lamplight being used in the first, the calcium light in the second, and sunlight in the third. In the refracting tele- 180 OPTICS. scope and the microscope, the image is formed in a tube Toy a lens at one end and looked at from behind by a lens at the other end. In the eye, which is a small camera-obscura, the image is formed on the retina, whence the sensation is carried by the optic nerve to the brain. HISTORICAL SKETCH. The ancients knew that light is propagated in straight lines. They deduced the laws of reflection, and we read that Archimedes set fire to the Roman ships off Syracuse by means of concave mirrors. Euclid and Plato, however, thought that the ray of light proceeds from the eye to the object, an error that was long of correction. One thousand years did not pursue the subject into other departments. The Arabian philosopher, Alhazen, who lived in the eleventh century, discovered the phenomenon shown in Fig. 147. About 1608 the telescope was invented by the Dutch.* Jansen, Metius and Lippersheim each claimed the honor, and the legend is that the discovery grew out of some children at play, accidentally arranging two watch-glasses so as to magnify a distant object. In fact, however, the action of the convex lens was already known, the compound microscope had been in- vented by Jansen 20 years previously, and the simple microscope was known to the ancient Chaldeans. In 1621 Snell discovered the law of refraction. By its aid Descartes explained the rainbow. Half a cen- tury of waiting, and Newton published his investigations in the decomposition of light. He, however, believed in what is known as the "corpuscular theory," that light consists of minute particles of mat- ter radiated in straight lines from a luminous object. In 1676 Roemer, by observing Jupiter's moons (p. 150), found out the velocity of light, which up to that time had been considered instantaneous. A little later, Huygens advanced the undulatory theory, which was applied with singular skill by Young and Fresnel, in the first quarter of the present century, to explain all optical phenomena. (See list of books for additional information, on p. 120.) * " In 1609, the government of Venice made a considerable present to Signer Galileo, of Florence, Professor of Mathematics at Padua, and increased his annual stipend by 100 crowns, because, with diligent study, he found out a rule and measure by which it is possible to see places 30 miles distant as if they were near, and, on the other hand, near objects to appear much larger than they are before our eyes." From an old paper in the Library of Heidelberg University. VIII. " The combustion of a single pound of coal, supposing it to take place in a minute, is equivalent to the work of three hundred horses ; and the force set free in the burning of 300 Ibs. of coal is equivalent to the work of an able-bodied man for a lifetime" ANALYSIS. EH'