iA TEXT BOO300 OF NATURAL PHILOSOPIHY: AN ACCURATE, MODERN, AND SYSTEMATIC EXPLANATION OF THE ELEMENTARY PRINCIPLES OF THE SCIENCE. ADAPTED TO USE IN THIGH SCHOOLS AND ACADEMIES. WITH 149 ILLUSTRATIONS. BY LE ROY C. COOLEY, A. M., PROFESSOR OF NATURAL SCIENCE IN THIE NEW YORK STATE NORMAL SCHOOL. "Let science, by cultivating man's intellect, elevate himn to nobler and more spiritual views of God's wisdom and power."-Cooke. NEW YORK: CHARLES SCRIBNER & CO., 654 BROADWAY. 1869. Entered accordin, to act of Congress, in the year 1865. by LE ROY C. COOLEY, in the Clerk's Office of the District Court of the United Stjates for the Northern District of New York. A I, LOl., PIllN TER. TOPICS FOuR ZIUR EVIEW. PART 1. THE PHIENOMIENA OF 3tATTER AT REST. I N TIR OD U CT I ON. The Plroperties of Jlatter.-(1.) Properties of matter-Extension-Impenetrability-Indestructibility —-Elasticity. (2.) Physical PropertiesChemical Properties. (3.) Natural Philosophy. CHAPTER I. ~ 1. The 1Fundamental Idcas. —(4.) Molecule-Inertia-AttractionRepulsion. These four ideas explain the phenomena of nature. ~ 2. Varieties of Attraction.-(5.) I. Gravitation -Universal —The first law-The second law. II. Cohesion —Its power-Through insensible distances. III. Adhesion. IV. Capillary Force - Causes liquids to penetrate porous solids-The first law —The second law.(6.) These varieties of attraction are but different manifestations of a single influence-Problems. CHAPTER II. OF THE PHYSICAL FORMS OF IATTER..ldroduction. —(7.) Application of the fundamental ideas. ~ 1. Of the Characteristic Properties of Solids. —(S.) HardnessTeuacity-fMalleability-Ductility-Crystalline Form. 1iv T O TOPICS FOR REVIEW. ~ 2. Of the Characteristic P'ropertics of Ltquids. —(9.) Attraction and repulsion nearly equal-Mobility. ~ 3. Of Liquids at Rest. (10.) Pressure equal in all directionsSurface is level-The level surface is convex. (11.) Water in pipes rises as high as its source-The supply of water to cities-SpringsArtesian wells. (12.) Pressure independent of the shape of the vessel — It depends on the depth of the liquid-To calculate the pressure.(13.) Bodies immersed are pressed upward —With force equal to the weight of fluid displaced-The solid lighter than water-The solid heavier than water. (14.) Specific gravity-I. Of gases-II. Of liquids -By direct weighing-By the hydrometer-By the use of a bulb-III. Of solids-HIeavier than water-Lighter than water-Table. (15.) The equal transmission of pressure-The shape of the vessel makes no difference-The hydrostatic press-Problems. ~ 4. Of the Prooperties of Cascs.-(] 6.) Compressibility-Expansibility -Elasticity —Weight. ~ 5. Of the Pressure of the Atmosphere.-(17.) The atmosphere exerts pressure in all directions about 15 lbs. to the square inch. (18.) I. The barometer shows the pressure of the atmosphere —The pressure of atmosphere depends upon its weight —Upon the amount of watervapor it contains-Upon the elasticity of its lower portions. II. The Common Pump. III. The Forcing Pump. IV. The Siphon. ~ 6. Of the Relation between Volume and Weight.-(19.) The volume of a given weight of air depends upon pressure and temperature —I. Pressure-Volume inversely as the pressure-Density of the atmosphere-Is greatest at the surface of the earth. II. Temperature-Heat increases the volume of air T-i of its bulk for each degree-Problems. PART II. THE PHENOMlENA OF MATTER IN MOTION. CHAPTER III. OF MOTION. Introduction.-(20.) Application of the fundamental ideas. ~ 1. Of MlIotion caused by a Single Force.-(2 1.) The first law of motion -The second law-The third law. (22.) Velocity-Uniform velocity TOPICS FO'R REVIEW. V Impulsive force-Uniform velocity produced by an impulsive forceSpace equals time multiplied by velocity. (2:1.) A constant forceUniformly accelerated velocity-Difficulties in the way of experiment -Overcome by Atwood's machine. (24.) Experiments with Atwood's machine-Proof of first principle-Proof of second principlo-Analysis of the motion of a falling body-Construction of the table-From the table obtain the laws-From the table obtain the formulas-By the formulas solve problems-Problems. ~ 2. Motion caused by more than one Force.-(25.) If a body be acted on by two forces represented by the sides of a parallelogram, they are equivalent to a single force —The resultant may be found. — (26.) Any force may be resolved —To find the component which acts in a given direction. (27.) Two forces in the same direction-The point of application —The weight of a body-The center of gravity. (28.) Curved motion —Is produced by at least two forces-One of which is constant-Projectiles-Their motion due to two forces. ~ 3. The Indestructibility of Force. —(29.) Force is indestructibleMotion can not cease without exerting the same amount of force which produced it —Suppose a body move without resistance, MomentumMotion due to an impulse meets with resistance —Suppose a constant force applied to overcome resistance, Living Force. ~ 4. Of Machle-zery.-(30.) The principle of momentum —MachinesSimple —The law of equilibrium. (31.) Levers-Three classes-Application of the principle of momentum —the compound lever-Application of the lever. (32.) The wheel and axle-Acts on the principle of the lever-Application of the principle of momentum-One wheel may t.urn another by means of cogs —By friction-By bands —Application of the wheel and axle. (33.) The pulley —Fixed and movable —The principle of momentum to the fixed pulley-To the movable pulley with one rope-To the movable pulleys with separate ropes-Applications of the pulley. (34.) The inclined plane —If the power act parallel to the length of thle plane-If it act parallel to the base of the plane-Applicalions of the inclined plane. (35.) The wedge. (3(;.) The screwApplication of the principle of momentum-Applications of the screwProblems. ~ 5. Of the Motion of Liquids.-(37.) The velocity of a jet of water the same as that of a falling body-The velocity depends upon the depth of the orifice-Calculated by the formula V- 2 1Syg. (38.) To calculate the quantity. (39.) The velocity less than the theory gives-The qli:;ntity less than the theory gives-Quantity increased by using tubes. Vi TOPICS FOR REVIEW. (40.) The undershot wheel —The ovorshot wheel —The breast wheel — The American turbine. ~ 6. Of the,1otion of Air. —(41.) Wird —The trade winds-Due to heat and the rotation of the earth. CH APTER IV. OF'MOTION.- VIBRATIONS. Introduction.-(42.) Application of the fundamental ideas. 1. Of V7ibrations of the Pendtlnm. —(43.) The pendulum —Vibrates under the influence of gravitation and inertia-The first law-The second law-The third law. (44.) The center of oscillation —The laws apply to this point. (45.) The pendulum is used to measure time-To determine the form of the earth. ~ 2. Of TVibrations of Cords. —(46.) The vibration of cords-Due to elasticity and inertia-The laws of vibration-first, second, third.(47.) Progressive vibrations-The motion appears to be lengthwise of the tube-Ventral segments. (48.) Tile cord vibrates as a whole —In ventral segments at the same time. ~ 3. Of Vibrations of Liquids and Gases.-(49.) Water waves-May interfere. (50.) The vibrations of air-Alternate rarefactions and condensations-In all directions-Different sets interfere. 4. Of Vibrations qf A]olecules.-(51.) Molecules in motion —Molecular vibrations affect our senses. C I-I APTER V. OF TIlE EFFECTS OF VIBRATIONS.-I. SOUND. ~ 1. The Origin and Transmission of Soumd. —(52.) Sound produced by vibrations. (53.) Sound waves —Are transmitted through all elastic bodies —With different velocity in different media-The first law —The second law-With uniform velocity in the same medium. ~ 2. Of Refraction and Pejflection of Sound.-(54.) Sound waves pass from one medium to another-Refraction-Sound made louder by refraction. (55.) The reflection of sound-The law —The ecllo. ~ 3. Of Jlus,'cal SonbCds.-(56.) Musical Sounds-Any noise repeated rapidly causes a continuous sound-Puffs of air made rapidly give a mllsical sound. (57.) Musical -cunds differ —I. Pitch-Pitch depends TOPICS FOR REVIEW. vii on rapidity of vibration-Intervals-The diatonic scale —Tle number of vibrations for the notes. II. Intensity. III. Quality.-(58.) Musical instruments-Stringed instruments-Pitch raised by using strings of different lengths-Of different tension-Of different weight. CHAPTER VI. OF TlE EFFECTS OF fIBRATIONS.-II. LIGHT. ~ 1. Of the Nature of Light, and the Laws of its Transmission. (59.) Light is the effect of vibrations-The ether-Luminous bodies. (60.) Rays of light —Are transmitted-In straight lines —With uniform velocity -Its intensity inversely as the square of the distance-Photometry. ~ 2. Of the Reflection of Light.-(61.) Reflection-The law. (62.) Mirrors-The effect of plane mirrors-The effect of concave mirrorsThe effect of convex mirrors. (63.) Images by reflection —Image of a point. (64.) Images by plane mirrors. (65.) Images by concave mir rors — The image of a point. (66.) Object beyond the center — Between the center and the focus-Between the focus and the mirroe.(67.) Images by convex mirrors. ~ 3. Of the Refraction of Light.-(68). Refraction-The first law-Tae second law. (69.) The index of refraction. (70TO.) Lenses-The effect of convex lenses-The effect of concave lenses. (71.) Images are formed by convex lenses-The image of a point. (72.) Object at twice the focal distance-Farther away —At a less distance-Between the focus and the lens. (73.) Images by concave lenses. ~ 4. Of the Decomposition of Light. —(74.) Prisms-Prisms refract light-Prisms decompose light. (75.) The black lines of the solar spectrum —The bright lines in spectra of artificial light. (76.) Decompo. sition by rain-drops-The primary rainbow-The red band on the out side-The colors in the form of an arch-The secondary law. (77.) De composition by refraction-The color of bodies-The color of the skyThe color of the clouds. ~ 5. Of Optical Instrusments.-(78.) The microscope-The telescopecThe magic lantern-The camera obscura-The eye. CHAPTER VII. TEE EFFECTS OF VIBRATIONS.-III. HEAT. 1~. Of the Sources and NMacure of Ieat.-(75.) The sources of heat viii TOPICS FOR REVIEW. I. The heavenly bodies-II. Mechanical action, friction-III. Chemical action. (80.) The material theory-The dynamic theory. ~ 2. Of the Transmission of Heat.-(81.) Rays of heat-Transmission of heat rays-Laws of transmission-Law of reflection —Law of refraction. (82.) The diffusion of heat-I. By conduction-Through solidsThrough liquids-Through gases. II. By convection —Air is heated in 1n other way-Liquids are heated by convection-No convection in solids. III. By radiation-It depends upon temperature-On the nature and condition of the surface. ~ 3. Of the Effects of Icat.-(83.) The action of heat is twofold-It raises temperature - It expands bodies -- Solids - Liquids - GasesTemperature is measured by expansion-The thermometer-Various forms. (84.) Temperature indicates the rapidity of molecular motionExpansion indicates a change in the relative position of moleculesSensible and latent heat-Specific heat. (85.) At the melting point -Temperature stops rising-But the expansion increases. (86.) The boiling point-Depends on the purity of the liquid-On the nature of the vessel-On pressure-At this point temperature is constant —But the expansion increases. (87.) Heat is required to expand a bodyThe same amount is given off when the body again contracts. ~ 4. Of the Steam,-Eizgiie. — (88.) The elastic force of steam-The boiler —The cylinder-Tle crank-High and low-pressur] engines. CHTIAPTER VIII. OE' ELECTRICITY. Introduction.-(89.) Application of the fundamental ideas. ~ 1. Of Frictional Electricity.-(90.) Electricity produced by frictionThe electrical machine —Electricity detected by electroscopes —Two opposite forces-Measured by electrometers-The first law-The second law. (91.) A charged body-A non-conductor —An insulated body-A charged body polarizes an insulated conductor. (92.) A series of conductors polarized-The theory of induction. (93.) The Leyden-jar-It may be charged-It may be discharged-The Leyden battery. (94.) The electricity of the atmosphere-Of the same nature as frictional eloctricity-Lightning is the discharge of oppositely charged cloudsThe aurora-Produced by electric discharges. (95.) The effect of points -Lightning-rods. (96.) The mechanical effects of electricity-Chemical cffects —Physiological efftct s. TOPICS FOR REVIEW.~ iX ~ 2. Qf Jflagetic Electricity.-(97.) AMagnets-Natural-ArtificialDifferent forms-Their force strongest at the ends. (98.) Attraction and repulsion-The law. (99.) A magnet will polarize a bar of ironSeveral bars in succession —All the molecules of a magnet are polarized. (100.) A bar magnet supported-Will point north and south-Its variation-Annual and daily. (101). The dip of the needle. ~ 3. Of Voltaic Electricity.-(102.) Voltaic electricity-The voltaic circuit-Grove's battery-Bunsen's battery. (103.) It is produced by chemical action-Resistance-Quantity and intel tity-Quantity depends on the size of the plates-Intensity depends on the number of plates.(101.) The effects of electricity —Heat-Light-Jllagyetisin, the electric telegraplh-Induction, the Ruhmkorf coil. (105.) Conclusion. TO THE PUPIL. MY DEAR FRIEND:THE most faithful efforts are sometimes followed by partial success, or, it may be, utter failure, for want of some proper method of study. I have tried to systematize the principles of Natural Philosophy, and I believe that if you reduce your efforts to a corresponding system, you will find the acquisition of this science less difficult, more pleasant, and of enduring value. Let me suggest the following plan. First, read the heading of the paragraph (numbered in parenthesis) that you may know what subject the paragraph presents. Then, look over the topics (numbered without parenthesis) and compare them with the heading, to see what are its essential thoughts. After this, study each topic in order; and finally, learn the heading and see that you can develop its topics without referring to the book. Do not be satisfied with the statement of facts alone; but carefully study the relation of thoughts. You will find the analytical contents valuable for this purpose. Finally, I hope you will not regard this little book as a commentary on the subjects it treats. You will find it profitable to have some larger work at hand in which you can find additional explanations of subjects which are of special interest to you. I have not aimed to exhaust the subject, but to give you an outline which, by present study or future reading, you will be able to fill. That your pleasure in this study shall equal that which I have felt while instructing so many classes in this science, is the desire of your friend. L. C. C. PREFACE. THrs volume is designed to be a text-bookl of natural philosophy suited to the wants of high schools and academies. The author believes that the following features of his work adapt it to the purpose for which it is designed. 1. It contains no more than can be master ed by average classes in the time usually given to this science. To this end, the polarization of light, sounding flames, and kindred subjects of a less elementary nature, are omitted. But that the pupil may have access to such important and interesting matter, an appendix has been added. 2. It presents a judicious selection of subjects. Omitting what ever is merely novel or amusing, it gives a plain and concise discussion of elementary principles, of theoretical and practical value. 3. It is an expression of modern theories. It recognizes the fact that the spirit of a new philosophy pervades every department of science, and presents the doctrines of molecules and of molecular motions, instead of the old theory of imponderables, which has been swept away. Carefully avoiding whatever is yet only probable, it seizes upon what has come to be universally accepted, and, as far as may be, adapts it to the course of ele? mentary instruction which it proposes. 4. It is logical in the arrangement and development of subjects. A single chain of thought (see Analytical Contents) binds the different branches of the science into one system of related principles. 5. It is thoroughly systnatiazd. Chapters, sections, para xii PREFACE. graphs, and topics, have been arranged with careful regard, on the one hand, to the relation of principles to each other, and on the other hand, to the best methods of conducting the exercises of the class-room. At the beginning of each paragraph is a plain and concise statement of useful facts and principles, while the paragraph itself contains the discussion of them by topics in their natural order. The mind can not work intelligently unless it has some object toward which to direct its efforts. No scientist pursues his researches by experiment, without first proposing some fact, or principle, to be tested. The discoveries of the immortal Faraday were drawn from experiments, not made at random, but conceived and executed to test the truth of theories proposed in his own mind beforehand. (See Faraday as a Discoverer, by Tyndall). The synopsis, at the beginning of each paragraph in this volume, gives the pupil a clear idea of the work proposed to be done. He is then prepared to see how the facts of observation may be used to establish the principles of physical science. Moreover, there is an increasing number of teachers who believe that oral instruction is quite as important to the pupil as the study of a text-book. These headings of the paragraphs are texts, which, taken together, give a compact view of the entire science, and which will enable the teacher to freely supplement the discussions of the book, by experimental or mathematical proofs. To facilitate this work still further, references have been given to the most accessible and reliable works wherein the subjects of the text are more exhaustively treated. The works chiefly referred to, are: Silliman's Physics, Cooke's Chemical Physics, Atkinson's Ganot's Physics, Tyndall's Lectures on Sound, and Tynd.all's Heat as a Mode of Motion. No teachler of Natural Philosophy can afford to be without these books. ANALYTICAL CONTENTS. PART I.-THE PHENOMENA OF REST. (1.) The qualities of matter are called its properties. (2.) All properties of matter are either Physical or Chemical. (3.) Natural Philosophy is the science which treats of the physical properties of matter. (4.) The FUNDAMENTAL IDEAS in Natural Philosophy are expressed by the words molecule, inertia, attraction and repulsion. Attraction is called gravitation, cohesion, adhesion, and capillary force, according to the circumstances under which it acts. (7.) Attraction and repulsion, acting upon the molecules of bodies, produce the three physical forms of matter: solid, liquid, and gaseous. The characteristic properties of solid bodies are hardness, tenacity, malleability, ductility, and crystalline form. The characteristic property of liquid bodies is mobility. The characteristic properties of gaseous bodies are expansibility and compressibility. PART II.-THE PHENOMENA OF MOTION. (20.) Read (4) and (7). Attraction and repulsion, acting upon masses of matter, determine their condition of rest or motion. Motion is uniform if produced by an impulsive force. Motion is uniformly accelerated if produced by a constant force. Motion is curved if produced by twRo forces, one, at least, of whichl is a constant force. xv ANALYTICAL CON T E T S. The force which causes motion will be reproduced whenl the motion stops: hence the principle of momentum. The principle of momentum, applied to any one of the simple machines, will determine its law of equilibrium. The free motion of liquid bodies is due to the attraction of gravitation, and must obey the laws of this force. The free motion of air, or wind. is due to the action of heat. (42.) Read (4), (7), and (20). Attraction, repulsion, and inertia, acting upon masses, or upon molecules, produce vibrationOf the pendulum. Of cords. Of liquids. Of gases. Of the molecules of all bodies. These vibrations of molecules affect our organs of sense, and give rise to the phenomenaOf sound. Of light. Of heat. (89.) A constant and opposite action of attraction and repulsion among the molecules of bodies, gives rise to the phenomena of electricity. PABlT I. THE PHENOMENA OF MATTER AT REST. NATURAL PHILOSOPHY. IN T R O DUCTI ON. THE PROPERTIES OF MATTER. (1.) THE qualities of matter are usually called its properties. Those most important for us to notice in the outset are Extension, Impenetrability, Indestructibility and Elasticity. i. The Properties of Jatter.-In what respects is a block of granite so unlike a block of wood? The granite is brittle, it may be chipped with a chisel: the wood is soft, it may be cut with a knife. The granite is heavy; to lift it may require the power of an engine: the wocd is much lighter; perhaps a single arm may move it. We are thus able to perceive a difference in bodies only because there is a difference in the qualities they possess. These qualities are called properties. 2. Extension. Every body of matter, however small, fills a portion of space. It is not possible to think of a body which should have no size. This property of matter, by virtue of which it occupies space, is called extensio.. 18 NATURAL PI[ILOSOPHY. 3. Imjpenetraballty. — Not only do all bodies occupy space, every body fills the space assigned it to the exclusion of all others. One body may not be pushed into the substance of another; it can take the place of another only when the other has been thrust away. When, for example, a nail is driven into wood, it pushes the particles of wood out of its way; and when the hand is plunged into water, the water is thrust aside to give it place. This property of matter, by virtue of which no two bodies can fill the same space at the same time, is called impenetrability. 4. Indestructibility.-A piece of gold may be cut into parts so small as to be almost invisible. It may be dissolved by acids and made to disappear, or by intense heat it may be changed into thin vapor, and hid in the air. After all these changes have been wrought upon the gold, its particles may be again collected to form a mass like the original one without the slightest diminution in weight. Amid all the changes which we witness in the forms and qualities of bodies, not a single atom is destroyed. This property of matter, by virtue of which no particle call be destroyed, is called indestructibility. 5. Elasticity. —WVhen an india rubber ball is pressed in the hand it is made smaller, but the moment the pressure is removed the ball springs back to its original size. The same quality is possessed in various degrees by all bodies. In such as lead and clay it is very slight, yet a ball made of either of these substances will spring back after having been for a moment coml1pressed. On the other hand, an ivory ball, when let fall upon a marble slab, rebounds nearly to the height from which it fell, showing that the power of restitu NATURAL PHILOSOPHY. 19 tion is, in this case, almost equal to the force of compression. This property of matter, by virtue of which it restores itself to its former condition after having yielded to some force, is called elasticity. This property of matter is more universal than is commonly supposed. Glass, although very brittle, is hig-hly elastic. A glass ball will rebound from a marble slab almost as well as one of ivory. Steel is likewise hard and brittle, yet the Damascus sword could be bent double without breaking. But should we attempt to describe all the properties of matter in detail, the time given to the study of our science would be filled with little else. The success of a student of nature depends largely upon his power to classify phenomena, and to study them in groups. (2.) All the properties of matter may be grouped in two divisions, viz.: physical properties, of which malleability and ductility are examples; and chemical properties, such as combustibility and explosibility. 1. Physical Properties.- Many of the metals may be reduced to thin plates, or leaves, by hammering them. Zinc is a familiar illustration, sheets of this metal being often placed under stoves, to protect the floor fromn heat. This property is called malleability. Gold is eminently malleable: it may be beaten into leaves so thin, that a pile of eighteen hundred of them would be no thicker than a sheet of common paper. 3Many substances may be also drawn into wire. Iron, copper, and brass wires are sufficiently familiar. The peculiar property by virtue of which they may be drawn into wire is called ductility. Glass, when heated J20 NATURAL PHILOSOPHIY. to a bright red heat, is remarkably ductile. If a point, pulled out from the mass, be fastened to the circumference of a turning wheel, a uniform thread as fine as the finest silk may be wound at the rate of a thousand yards an hour. Now fix the attention upon the fact that the wonderful malleability of gold, and the surprising ductility of glass, are shown without any change in the nature of t/ese substanees. The gold is the same material in the form of leaf as it was before it manifested its malleability. The glass in the form of thread is the identical substance which, by being drawn, manifested its ductility. All properties which, like these, a body may manifest without undergoing any change in its nature, are called fphysical properties. If now we examine those properties described in the early part of this section, we will find them all to belong to this group. Extension, impenetrability, and the rest, are properties which a body may show without any change in its nature. 2. Cliemnical P'opl)erties.-Wood, )by burning, shows that it is combustible. No substance can manifest the property of combustibility except by actually taking fire, and when it burns it changes to something else. Who, not already famrniliar with gunpowder, would suspect it to be so violently explosive? It can show that it is explosive, only by ceasing to be gunpowder, and becoming a mass of vapor. Properties like these, which a body can not manifest without changing its nature, are called c/emical p)rop)erties. This classification of properties helps us to define taccurately the science whose elements we are beginning to study. iNATURAL PHILOSOPHY 21 (3.) Natural Philosophy is the science which treats of the physical properties of matter, and of those phenomena in which there is no change in the nature of bodies. If now we look out upon the phenomena which nature presents, and will apply the test furnished by this definition, we may select, from among the multitude, those which it is the province of this science to explain. Thus, for example, we see the vapors rise; we see the rain drops fall. We listen with delight to the harmonies of music, and derive exquisite pleasure from the colors of the rainbow. In these phenomena, and in numerous others easily recognized by an attentive mind, we can detect changes in the form and place of bodies, but none whatever in their nature. But if we regard the more quiet, yet not less imposing phenomena of the seasons, we may discover a multitude whose discussion is, by the definition, excluded from this science. The young verdure of the spring-time changes at length to the matured foliage and ripening grains of summer. The fruits and hues of autumn, more somber, except where enlivened by the richly colored ripening leaves of the maple or the oak, soon afterward appear, only to be in turn displaced by the crisp and crackling snows of winter. These events are brought about by changes gradually taking place in the nature of substances, and the explanation of all such phenomena must be reserved for the science of chemistry. 22 NATURAL PHILOSOPHY. CII AP TE I. ~ 1. THE FUNDAMENTAL IDEAS. (4.) THE fundamental ideas in natural philosophy are expressed by the words molecule, inertia, attraction and repulsion. These four ideas, when fully understood, will furnish the explanations of nearly all the phenomena of which the science treats. 1. TLhe _~folecule.-A molecule is a particle of matter which can not be divided without chan,ging its nature. All bodies are made up of such particles. A piece of marble may be crushed and powdered until its particles are like the finest dust, yet, when seen through a microscope, they appear like angular blocks of stone, and may be still further divided. The same is true of a piece of ice. If its temperature be kept low enough while it is being crushed, every particle of the icepowder will still be a block of ice. By applying heat, the little block is first melted, and then changed to steam, which shows that it was composed of innumerable smaller pieces. How minute must be the particles thus made absolutely invisible! Yet each one is a fragment of the original block of ice. The heat has not changed their nature. The identical particles which make up the steam, composed the drop of water NATURAL PHIILOSOPIIY. 2. 3 and the little piece of ice. But it is thought that these particles can not be divided without chanyiwy t/hei, znatre, and they are called mzolecue8s. All bodies are made up of molecules. The size of a body depends upon their number; its shape, upon their arrangement. Whenever the term molecule is used, it should convey this idea, that every body of matter is made up of a multitude of little particles, which do not touch each other, and which can not be divided without changing their nature. 2. Inertia. —A heavy wheel requires force to put it in motion, or when in motion it requires force to stop it. It has no power to change its own condition. At rest, it would rest forever if left to itself; or once in motion it would forever move, unless acted upon by some force beyond itself. This idea, that no material body has power to change its own condition of rest or motion, is expressed by the term inertia. 3. Attraction. —When a body is not supported it falls to the ground. This familiar event illustrates the tendency of bodies to approach each other. Moreover, we have seen that bodies are composed of molecules, so small that the most powerful microscope can not reveal them, yet we must think of each as a separate body as truly as though the eye could measure its diameter. Now, by what influence are they held together? It is doubtless the same invisible force by which a body is drawn to the earth when not sup ported. It is a fact that all bodies, however large or small, have a tendency to approach each other. The force which causes this tendency is called attraction. 24 NNATURAL PHILOSOPHIIY. 4. Repulsion.-If a ball of india rubber be pressed in the hand it is made smaller-its molecules are brought nearer together. When the pressure is removed they instantly spring to their former position. While springing back the molecules are evidently being thrust away from each other. Or try the following experiment. Suspend a pith ball, or a little ball of cotton, by a fine silk thread: briskly rub a warm dry lamp chimney with a woolen cloth: bring the ball and glass together for a moment, after which it will be found that the ball will fly away from the glass, and show so strong an aversion to it that they can not be brought together. The force under whose influence bodies tend to separate is called ~repulsion. The action of repulsion among molecules is more universal than among masses. It is illustrated by many familiar facts. If, for example, a bladder be filled with cold air, and then heated, it will burst. Repulsion drives the molecules of air apart, and pushes them through the bladder. When a drop of water is heated it becomes steam, and fills a space about 1700 times larger than before. 5. T/iese Four Ideas.-Out of these four ideas may be drawn the explanation of almost all the phenomena which take place in nature. A great city, with all its various forms of architecture and machinery, is built of a few familiar substances, such as wood, and iron, and stone. This fact may excite our admiration of the intelligence and skill of man. What, then, must be our feelings when we discover that these four simple ideas are the elements out of which the sublime fabric of the universe has arisen! The whole system of material NATURAL PHILOSOPIHY. 2.5 things is simple and orderly-, displaying the infinite knowledge, power, and skill of a divine Architect. ~ 2. VARIETIES OF ATTRACTION. (5.) Attraction receives different names according to the circumstances under which it acts. Gravitationl, Cohesion, Adhesion, and Capillary Force, are its most colimmon forms. L-GRAVITATION.' A.-Gravitation is that form of attraction which is exerted upon all bodies, and throughout all distances. It is governed by two laws:1st. Its force is in proportion to the quantity of matter in the body exerting it. 2d. Its fbrce is inversely proportional to the square of the distance through which it acts. 1. Gravitation is uiiversal.-All bodies are under the influence of gravitation. The leaf, the fruit, the snow-flake, fall to the ground because they are attracted thither by gravitation. They press upon its surface because the same force continues to act after they reach the earth. No distance can outreach it, for it is the bond which holds the heavenly bodies in their orbits. Nor can any substance cut it off, or even diminish its action; for if the earth should come between the sun and moon, these two bodies would attract each other with thie same degree of' force. We come no0W to tle interesting thoughllt that this force acts writh infinite regularity and precision. 2. The rfirst lawo of gravitation.-To illustrate this Law, let us suppose two bodies, one co'ntainingl twice as 2 26 9NATURA-L PFIILOSOPHIY. much matter as the other, to attract a third. The force exerted by the first, will be twice as great as that by the other. If one body weigh nine tons and another three tons, then a third body equally distant from them will, according to the same law, receive three times as much attraction from the first as fiom the second. 3. Thie second law of eyacvitation.-To illustrate this law, suppose a body to be twice as far from the center, or source of attraction, at one time as at another. In the first position, the attraction will be only one-fourlt as strong as in the second. If the distance be three times as great, the force will be one-ninth as strong. If two distances are as 3: 4, the attractions will be to each other as 16: 9. Now, the weight of a body is due to the attraction of gravitation. Weight must, therefore, increase or diminish in exact accordance with the laws of gravitation. The greater the distance from the earth, the less will a body weigh. Now, distance from the earth is measured from its centesr. When, on the surface of the earth, a body is 4,000 miles from the center; suppose it were possible to carry the body to a height of 4,000 miles above the surface, its distance from the center would be doubled, and its weight would be reduced to one-fourthA. I. —COIESION. B. Cohesion is that form of attraction which acts between the molecules of the same body. Its power is very great, but only through insensibly small distances. 1. Cohesion.-Cohesive attraction holds the molecules of a body together, and enables it to keep its form NATURAL PHILOSOPHY. 27 and size. A cubical block of wood remains a cube only because its molecules are held together by this force. WTere it not for its action, all bodies would at once dissolve into their ultimate molecules, and vanish. 2. Its power. —The strength of cohesion is often very great. The molecules of a piece of iron are so strongly bound by it, that a weight of 500 lbs. may be lifted by mneans of a wire one-tenth of an inch in diameter. Even a strip of paper is not easily broken by a force acting exactly in the direction of its length. 3. ft acts tltro'uq insensible distances.-The distanee through which cohesion can act is quite too small to be measured. Let the parts of a body be separated, and the strength of the giant is gone. When a body is broken its parts can be made to cohere again only with great difficulty. In a few soft bodies, like wax, a slight pressure will force the nmolecules near enough together for cohesion to take hold of them; in others the pressure required is much greater, while in the majority of substances it is so great as to be practically impossible. The smith unites two pieces of iron by weldi g. iHe softens the iron by heat, then puts the two pieces toogether and unites them by the heavy blows of his sledge. Now, what he does is simply to push the yielding molecules of the two pieces of iron into very close contact; this done, cohesion grasps them, and the two pieces become one. II.-AXDUESION. C.-Adhesion is that form of attraction which acts between molecules of different bodies without changing their nature. 28 NATURAL PHILOSOPIIY. If, for example, the hand be plunged into water it comes out covered with a thin filmn of the fluid; it may be immersed in alcohol with the same effect. In these cases the fluids are held to the hand by adhesion. The hand may be withdrawn from a bath of mercury without retaining a particle of that substance, because the adhesion is too feeble to lift the fluid. This force, like cohesion, acts only through distances too small to be measured: unlike cohesion it acts between molecules of different kinds of matter. The value of glue and cement is due to the powerful adllesion which acts between them and the surfaces of solid bodies which they bind together. IV. —CAPILLARY FORCE. D.-Capillary Force is the adhesion of a liquid to a solid which is partly immersed in it. It generally causes an elevation or a depression of the liquid along the sides of the solid. It also causes a liquid to penetrate a porous solid. It is governed by two laws:ist. The heights to which a liqnid rises in different tubes of the same material are inversely proportional to the diameters of the tubes. 2d. The height to which a liquid rises between parallel plates is one-half the distance it will rise in a tube whose diameter is equal to the distance between the plates. 1. Cap'llary Force. -If small glass tubes be inserted in a vessel of water, it will be seen that the fluid instantly springs upward and remains at rest in the tubes considerably above its general level. (See Fig. 1.) Along N ATURAAL PHIILOSOPHY. 29 the outside surface of the tubes the water also climbs to a little height. Fit. 1. Fir. 2. If tubes be inserted in a vessel of mercury, this fluid will be pushed dow n. (Fig. 2.) The mercury in- side the tubes will be considerably below the gen- eral level, while the fluid against the outside is also depressed. Here are two well marked cases of capillary action. Now, when a piece of glass is plunged into water it comes out wet, but when plunged into mercury it comes out as free from the liquid as when it entered, and by repeated experiments it is shown that all liquids which will wet the sides of the tube will be bl/jtecd, while those which will not, will be pushed clown. 2. it causes liquids to penetrate porous solids.An easy experiment strikingly illustrates this action. Take a common bottle, eight or ten inches high, and wrap it in a sheet of white blotting-paper, whose edges must be secured by a bit of wax. Place the bottle, now prepared, upon a dinner-plate. Pour water upon the plate to cover the lower edge of the paper, and immediately the fluid will be seen rapidly climbing the sides of the bottle, which it will not cease to do until it has reached the top. The beauty of the experiment is enhanced by filling the bottle with some highly colored liquid. The rise of the water is due to the attraction between its particles and those of the paper and glass. This force, acting downward from each particle of the paper through the definite but imnperceptible distance 30 NATURAL PHILOSO PHY. to the one below it, lifts a particle of water. The next particle of paper above, then lifts it higher. Indeed, the successive particles of paper upward, are the successive steps of a ladder, up which the water is impelled by capillary force. Numerous familiar facts are explained by this experiment. Oil is carried up the lamp wick to supply the flame with fuel. By a similar action, water is distributed through loose soils to keep them moist and fertile. So, too, in a great degree, the sap of plants and trees is carried to their summits, and even in the animal system the circulation of blood through the minute blood-vessels is materially aided by capillary action. 3. Tlfe frst law.-In figure 1, the water is represented as being lifted to different heights in the different tubes. The height to which any fluid rises depends upon the size of the tube. If the diameter of one tube be just one-half that of another, water will invariably rise in it twice as far. If the diameters of two tubes have the ratio of 4: 3, then the water will rise in them to heights whose ratio is 3: 4. Or, in other words, the heights are inversely as the diameters of the tubes. 4. Thle seconod law.-If a plate of glass be inserted in water the liquid will rise a little distance against its sides. If two parallel plates be inserted near together, the water will rise between them, and by varying their distance from each other it may be shown that the height to whichA the liguid rises is inversely proportional to the cdistance between the plates. But if we compare the elevations whictl take place between the plates with the height to which the same liquid rises in tubes whose diameters are equal to the? NATURAL PHILOSOPHY. 31 distance between the plates, we discover that in all cases it is just one-half. (6.) We need not suppose that gravitation, cohesion, adhesion, and capillary force are so many different kinds of force. They should be regarded as but diP ferent manifestations of a single influence. One can not, it would seem, study the phenomena thns far briefly sketched without being impressed with the variety of the phlases and effects of attraction, yet wve do well to regard all these varied effects as but the different ways in which a single influence manifests itself: The differences between gravitation, cohesion, and the other forms of attraction that have been named, are apparent, not real. When bodies are separated by sensible distances, the attraction between them is called gravitation, without regard to their size; but when the bodies become very small, and the distances very minute, the force is called cohesion. Does distance alone, then, change the nature of attraction? Where shall the line be drawn at which the change occurs? Equally unreal are the differences between the other members of this group of forces, so that, looking behind the veil of appearances, we are, upon the very threshold of science, permitted to catch a glimpse of the sublime simplicity which everywhere reigns in the works of nature, and which it is the glory of scientific study to reveal. But shall we ask what is this single power whose effects are so varied and imposing? We name it attraction. Who need inquire further? The little bird that vainly beats his head against the cage bars, affords a warning to the man of science who would attempt to search for this, which God has hidden. 32 NATURAL PHILOSOPHY. PPOBLEM's ILLUsTTRTkTING TIlE LAWS OF ATTRmACTION. 1. With hlow imany times greater rorce will a body be attracted by a mass of iron weigllng 9 tons, than by a block of stone weighing 3 tons., when both are at the same distance from it? Ans. 3. 2. Two lead balls, one weighing 5 ozs. and the other 12 ozs., are hanging at a distance of 10 ft. from a third; what relative degrees of force do they exert upon it? 3. One ball of lead attracts another throungh a distance of 10 ft., with a force of S lbs.; what foree would it exert if placed at a distalnce of 20 ft Anis. 2 lbs. 4. A body is at one time 50 ft., ald at another 75 ft., from a mass of rock; what are the relative forces exerted upon it in the two positions A.rzs. 9: 4. 5. Two bodies, one weighing lbs. and the other 9 lbs., are attracting a third. The first is at a distance of 25 ft., the seconct of 50 ft.; what relative attractions do they exert? Asn,. 24: 9. 6. At the surface of the earth a body weighs 10 lbs.; what would it weighll if carried to a height of 5 miles above the surface? Ans. 9 97 lbs. 7. A glass tube - incll in diameter raigse water by capillary force about - inches; how high will water rise in a tube — IO inch diameter? Ans. 4 in. 8. htow ligh will water rise between two parallel plates I- inch apart? Ans. -2 in. 9. If between parallel plates T-a inch apart, water rises two inches; how high will it rise when the plates are 1 inch apart 1 Ans. ~ in. NATURAL PHILOSOPHY. 133 CIIAPTER II. OF THE THREE PHYSICAL FORMS OF MATTER. INTRODUCTION. APPLICATION OF THE FUNDAMENTAL IDEAS. (7.) READ (4). Attraction and repulsion acting upon the molecules of bodies, produce the three physical forms of matter: solid, liquid, and gaseous. Between the molecules of every body, two sets of forces, attraction and repulsion, are continually struggling. Just in proportion as one or the other prevails, the body will be a solid, a liquid, or a gas. In a solid body attraction prevails, and its molecules are firmly bound together. In a liquid body the attraction is almost equaled by the repulsion, and the molecules are left free to move easily among themselves. In a gaseous body the repulsion exceeds the attraction, and the molecules are driven away fiom each other to the greatest possible distance. The solid rock, the mobile water, and the rushing air, are types of these three gran'd divisions to which all bodies belong. The attraction and repulsion among the molecules of bodies are called imolecula/r forces. Cohesion, adhesion, and capillary force are molecular attractions; the force of heat is a molecular repulsion. 2* n4 N' TUR AL PIIILOSOPEY. Numerous and familiar changes of form are due to the action of heat. Ice, for example, when heated, becomes water, and water, when heated still more, rises in vapor to form the floatihg clouds. Or suppose the action to be reversed. Imparting their heat to other bodies, the clouds are changed to water, and water, again to solid ice and feathery snow. Imitating nature, we may to a limited extent, by the use of heat, change the form of various bodies, and numerous arts of life spring from the application of this power. By the repulsive force of heat the metallic ores are melted, and the usefil. metals obtained. By the same force iron is liquefied, that it may be molded into requisite.forms of strength, of beauty, or of use, demanded in the arts. The expansive force of steam is but the repulsive force of heat. ~. OF TIHE CHARACTERISTIC PROPERTIES OF SOLID BODIES. (8.) The characteristic properties of solid bodies are hardness, tenacity, malleability, ductility, and crystalline form. 1. _Iardcl7ess.-The particles of solid bodies are held together by cohesion, much more firmly in some than in others. Those in which they are held with the greatest force, will most successfully resist the pressure of others. By the term /acrdness, we refer to that property of solids which enables them to resist any action which tends to wear or scratch their particles away. Hardness does not imply strength. A piece of glass will scratch an iron hammer, which proves it to be harder than iron; yet glass is very fragile, easily broken NATURAL PHILOSOPHY~. 35 by the stroke of soft wood; indeed, by almost any thing that can inflict a blow. Neither does hardness imply density. The diamond is the hardest of substances, while gold is so soft as to be easily cut with a knife; yet gold is four times as dense as the diamond. Mercury is a fluid, and, of course, has no hardness, yet it is nearly twice as dense as the hardest steel. The process called tempering or annealing, consists in regulating the hardness of a body by the action of heat. Steel, when in its hardest condition, is too brittle to be used in the arts; but by heating it to a temperature determined by the use to be made of it, and then slowly cooling it, the steel may receive any degree of hardness desirable. It may be made almost as soft as soft iron, or it may become nearly as hard as the diamond. 2. Tenacity. —When a rod of iron is stretched in the direction of its length, it will be found that great foree is required to pull it apart. The property, in virtue of which bodies resist a force acting in the direction of their length, is called tenacity. The metals are more tenacious than other solids, and among metals, iron in the form of cast-steel, stands at the head of the list. A rod of cast-steel, the end of which has an area of one square inch, will support a weight of 134,256 pounds. It has been found by experiment that the tenacity of a bar is in proportion to the area of its cross section, and entirely independent of its length. It has also been shown that the tenacity of a metal is greatly increased by drawing it into wire, The cables of suspension bridges are, for this reason, made of fine iron wire twisted together. NATURAL PIIILOSOPHY. 3. falZZleability.-The particles of many solid bodies may be displaced witllout overcoming their cohesion. By the blows of a hammer, the molecules of many metals may be shifted about, without breaking them apart, until the bodies are reduced to the fbrm of thin plates or leaves. By passing the metal between the rollers of a rolling-mill, the great pressure exerted will produce the same effect. This property, in virtue of which a body may be hammered or rolled out into thin leaves or plates, is called imalleabilit2y. This property is possessed in a high degree by many of the metals. Under the hammer, lead is the most malleable of the useful metals; tin stands second, and gold third on the list. In the rolling-mill, gold is the most malleable, silver is second, copper third, while tin stands in the fourth place on the list. (Cooke's Chemical Physics, p. 207.) 4. Ductilit?.-If, instead of being reduced to thin plates, the substance may be drawn into wire, the property thus shown is called ductility. This property is closely allied to malleability, but metals do not possess both in an equal degree. Platinum, for exainple, which is seventh on the list of malleable metals, stands first on the list of those which are ductile. This metal has been drawn into wire finer than a spider's thread. 5. Crystalline Form. —The attraction among the molecules lhas not brought them together at random, nor in disorder. A flake of snow, when seen throughl a microscope, is found to be as symmetrically formed as a swan's feather; and water frozen on the -window panes in winter shows a beautiful variety of tree-like forms. These definite and regular forms in which solid substances occur are called crystals, and any process by NATURAL P1IlLOSOPHY. 37 which they may be obtained is called a process of crystcal'Ucatio n. In the formation of solid bodies their tendency to take a crystalline forn is almost universal. The same substance generally takes the same form, but in different substances the shape of crystals may be wonderfully unlike. Lead, in its most common ore, called yalena, is found crystallized in cubes. Specimens of these cubes are often found as perfect as could be chiseled by an artist. But the larger number of solid bodies around us do not appear to have these definite crystalline forms. They have been made solid under circumstances which did not allow the molecular forces to act freely.. In many cases, however, if we break open a body whose external form is not regular, we may discover that it is, after all, a crystallized body, by noticing that it is made up of multitudes of small crystals, very closely packed together. This is true of many rocks. Even when no indication of a crystalline structure can be seen, the substance can often be made to assume it by somle artificial process. The best mnethod is to dissolve the solid in water or some other liquid, and allow the solution to stand in a quiet place where it may evaporate slowly. Common salt and alum are substances which readily and beautifully illustrate this process. The more slowly the water evaporates, the more perfect will the crystals be. (See Cooke's Chemical Physics, pp. 119 to 185.) ~ 9. OF THE CHARAECTERISTIC PROPERTIES OF LIQUID BODIES. (9.) Liquids have elasticity and some other properties in common with solid bodies. Bat since the attrac 38 NATURAL PHILOSOPHY. tion and repulsion among their molecules are very nearly equal, we find that mobility is their characteristic property. 1. Elasticity.-Wlhern submitted to pressure liquids are compressed, and when the pressure is removed they instantly spring back to their original volume. It iequires a very great force, however, to compress a liquid in the least degree; so great, that until improved means )f experiment were contrived, liquids were thought to'e incompressible. Water, at a freezing temperature, when pressed by a force of 15 lbs. to the square inch, is condensed only.0000503 of its volume. (See Cooke's Chemical Physics, pp. 215 to 218.) The force with which a liquid springs back to its former size after being compressed, is exactly equal to the force which compressed it; it is, for this reason, said to be perfectly elastic. 2. Attraction and repulsion nearly efqal. —That the attractive and repulsive forces among the molecules of a liquid are not exactly equal may be shown by a pretty experiment. To one end of a scale-beam (Fig. 3) a disk of brass is rFi. 3. suspended, and accurately balanced by weights in the opposite scale pan. Now let the disk be brought to rest upon the surface of water in a ves__ sel, and it will be held there with considerable iorce. If the disk be two inches in diameter, weights equal to 200 grs. may lie piled upon the opposite. pan NATURAL PHILOSOPHY. 39 before it will be torn from the water. Now, notice that a film of water still adheres to the disk, having been torn away from the water beneath it. The 200 grains weight have simply overcome the coh.esionz of the water. We thus learn that the attraction is a trifle stronger than the repulsion. PBut the attractive and repulsive forces are e7tarly balanced, and if we now remember that water consists of molecules, it is not more difficult to see that there must be freedom of motion among them, than it is to see that a number of smooth balls will roll easily upon each other. 3. IJobility.-To illustrate the mobility of water, and its cause, let the following simple experiment be tried. Take three glass goblets: fill one with small marbles, one with fine shot, and the third with water. After putting a dinner-plate over each goblet, they may be inverted without spilling their contents. Now, lift the first, and the marbles will roll out upon the plate. Lift the second, and the shot roll out in the same way. A person at a distance will not be able to see tile separate shot, but will see their motion, and know it to be caused in exactly the same way as the motion of the marbles, which could be seen distinctly. NTow lift the third goblet, and the water spreads out upon the plate exactly as did the marbles and the shot. The molecules of water are balls infinitely smaller than shot; but, while the most powerful microscope fails to reveal them, the mind can see them, so small, so round and smooth, that they roll and glide among themselves with the greatest freedom. The phenomena peculiar to liquid bodies depend 40 NATURAL PHILOSOPHY. chiefly upon the mobility of their particles. Tihe phenomena of liquids at frest must be now considered: those of liquids in monoion must be reserved for a future chapter. 3 8. OF LIQUIDS AT RE:ST. (10.) At any point inside of a body of liquid there is equal pressure from all directions. -lence a fluid will rest only when its upper surface is level. And the level surface of a large body of water is convex. i. Liqigids press in all directions.-In order to see that, because the particles of a liquid are free to move, they must be exerting pressure in all directions, we will suppose a number of very smooth balls to be Fig. 4. arranged as in Fig. 4. The weight of j~ QZi~ the ball A will be a downward press-: ure upon the balls B and C. These, 0 IX-t being free to move, will be pushed -D aside. The ball B, moving toward the left, will push between the balls D and E, while the ball E, moving upward, will exert an upward pressure. Just so the small molecules of a liquid are exerting pressure downward, upward, and laterally; and, moreover, if the liquid be at rest, every point in it must be pressed equally in all these directions. An experiment may help to illustrate this principle. If a disk of metal be held in the middle of a jar of water, it is easy to see that it must be pressed downward by the weight of the water just above it; but it NATURAL PHILOSOPtHY. 41 may not be so clear that it is pushed up by an equal force. Taking a lamp chimney, and put- F 5.a ting the strinog handle of the disk C, Fig. 5, through it, hold the disk tightly against the lower end of the tube until it is pushed ti down to the middle of the water. Now _I loosen the string: the heavy disk does not,_ _ l sink, but remains tightly pressed'pwadl'd against the tube by the water. If water be allowed to enter the tube it will press down = upon the disk, and when it has filled the tube almost to a level with the water outside, then the disk falls, suggesting that the upward and downward pressures are equal. iNumerous simple experiments might be given to illustrate this important principle: one other must suffice. Glass is eminently brittle. It may be blown into sheets as thin as the finest paper cambric. In this condition, the weight of a few grains resting upon it in the air would crush it. Yet, placed near the bottom of the deepest cistern, it will support the weight of all the water above it, and remain unbroken. This could not happen, if the pressure of the water upon it was not equal from all directions. 2. The surface of water at rest is level.-The truth of this principle may be seen by attentively examining Fig. 6, which represents a section of a vessel containing water, the surface of which has for the moment been thrown into the position indicated by the line A E. Riefer to any two points in the water, as A and K. We see that the downward pressure at A, would be the weight of the water above that point-a column mz A. But the pressure at that point is equal in all dirc etions, 42 NATURAL PHILOSOPHY. Fig. 6.;!;, so that the water beA- tween A and K would ~e 1 —-- --------— n8-ad be pressed toward K by a force equal to the weight of the column in A. In 4 1 1 just the same waywemay e- show that at K, the water is being pressed toward A by a force equal to the weight of the column ma K. The column imn A is greater than nz K, and since the water is free to rnove it will yield to the greater pressure, and go toward K until the two forces are equal. The two bforces will be equal only when mn and ni are in the same level surface, a b. 3. But a level surfacte is convex.-The surface of water will be at rest when the force of gravitation acts upon all points of it alike. That the attraction of the earth may be equal on all points, they must be equally distant from the center of the earth. To be at the same distance from the center of the earth they must form a curved surface. In case of large bodies of water, of the oceans for example, the convexity can be seen. It is shown by the ancient observation that the topmast of an approaching ship is the part first seen from port. (11.) Since the surface of water at rest must be level, we infer that water confined in pipes or close channels will always rise as high as the source from which it comes. Upon this principle cities are often supplied with watel. The same principle explains the phenomena of springs and artesian wells. 1. Water in pipes will rise as Aigh as its source. NATURAL PHILOSOPHY. 13 If into one arm of a bent tube we pour water, it will flow around into the other, until it stands at the same height in both. No matter what may be the shape of the vessel, the surface of the liquid it holds must be just as high in one part of it as in another, and a pipe leading from a vessel is a part of the vessel which holds the water. 2. The.upl2)],y (f watter to citics.-A - pipe leading from a reservoir of water on a hill outside a city, may be buried in the ground, passed down the hill-side, and through the streets, and be provided with branches leading into cisterns in every dwelling. Unless these cisterns are higher than the water in the distant reservoir, the water will, flow down the hill-side, through the streets and up the branches into the dwellings, and supply them all with water. Mlany cities are, in this way, conveniently supplied with abundance of water, for private dwellings not only but for public fountains and manufacturing purposes. 3. Springs.-The rocks which compose the earth are arranged in layers, called strata, which are generally more or less oblique as represented in Fig. 7. Some of these strata will allow water to soak through them; others will not. In the figure the dotted portions a a a indicate the porous strata. Now, water falling on the surface of the earth at e, will settle through the loose or porous material until it reaches the rock, which it can not penetrate. Flowing along the surface of this rock, it will issue from the hill-side at S, and thus form a s8pring. 4. Artesian wells.-Again, the water, falling upon the surface and passing through other porous layers, comes in contact with a rock which it can not penetrate, 44 NATURAL PHILOSOP kY. and flows along its surface. The basin-shaped part, a a, of the porous layer, would thus in time become filled Fig. 7. with water; indeed the entire layer reaclling to the surface of the earth in both directions might thius be filled. If, then, a well at W be sunk through the mass down to this saturated layer, the water will rise in the well, sometimes to the surface of the ground above, and often spout in jets many feet above it. Such wells are often bored to very great depths and are called artesian wells. One of these wells was bored in Louisville, Kentucky, to the depth of 2,086 feet. Another in St. Louis has a depth of 2,199 feet. The supply of water furnished is often very abundant. The famous Grenelle well, in Paris, yields daily 600,000 gallons. (12.) The pressure of a liquid on the bottom of the vessel which holds it is independent of the shape of the vessel. It depends on the depth of the liquid, and equals the weight of a column whose base is the base -r —---- --- ~zn NATURAL PHILOSOPHY. 45 of the vessel, and whose height is the depth of the!iquid in it. 1. T/Le plessure i8s incdependent of t/te shape of the vessel. —This may be proved by experiment. Tile essential parts of an apparatus for this purpose are represented in Fig. 8. A glass tube, A B, bent twice at right angles, con- Fig. s. trains mercury. The height of the mercury - in one arm is shown / by a graduated scale, and to the other arm i forinms and heights may be attached. - A When a vessel, G, is filled with water, the fluid presses upon tile mercury at A, and pushes it up in the arm C D1; the height to which it rises being shown by the graduated scale. Now let the vessel be removed, and another, in the form shown at E, be put in its place. If water be poured into this vessel until it stands as high as it did in the other, the mercury will be seen to rise in C D to the same point as before. Vessels of various other forms may be used, but if all are of the same height the water which fills them will push the mercury to the same point on the scale. We infer that the pressure of a fluid down-ward is quite independent of the shape of the vessel and the quantity of fluid. 2. T/ie l pressure depends on the de7pth of the liquid.-. If a tube twice as high as the vessel E, in Fig. 8, be 46 NATURAL PiILOSOPHY. used and filled with water, the mercury will be seen to rise just twice as far as when the other vessels were employed, and by repeated experiment it is seen that the pressure is in proportion to the height of the column of water which exerts it. (See Cooke's Chernical Physics, p. 223). 3. To calculate tAe pre.ssure. —If the pressure depends only on the size of the base and the height of the column, then it must equal the weighyt of a column whose base is the base of the vessel, and whose height is the depth of the liquid. Now, one cubic foot of water weighs 621-lbs., and if the number of cubic feet of water which exerts the pressure be multiplied by 624, the amount of pressure in pounds will be obtained. This, suppose a vessel, represented by E F C D, in sFlg-9 Fig. 9, to be full of water: E - r' the pressure on its bottom ~}, t d is the weight of the column A BI C D. Let the area of the bottom be 3 square feet, and the depth of the water be C~' D 8 feet; then 24 cubic feet of water exerts the pressure, and 24 x 624 lbs., or 1,500 lbs. is the pressure exerted. Now, since the pressure is equal in all directions, we may obtain the amount of pressure against anFy portion of s,,6rface either in the bottom or sides of the vessel, by getting the weight of a column of water whose base is the surface pressed upon, and whose height is the depth of the water to the nidcdle point of that surface. For example, suppose we would know how much pressure is borne by one square foot of the side of a vessel at a depth of ten feet below the surface of the water. NATUR AL P-HILOSOPHY. 47 We must understand that ten feet is the distance from the top of the water to the middle point of the square foot; then the pressure will be the weight of a column of water whose base is one square foot and whose height is ten feet. Such a column will contain 10 cub. ft. of water, and its weight will be 10 x 62- lbs. (13.) A solid body when immersed in a fluid, is pushed upward by it with a force equal to the weight of the fluid it displaces. It fobllows firom this principle, 1st. That a solid body, lighter than water, will sink far enough to displace water whose weight is equal to its own. 2d. That a solid body, heavier than water, will weigh less in water than in air, the difference being the weight of the water displaced by it. 1. Solid bod'ies in water are pressed ujpwccrd.-If, for example, a piece of wood be pushed down into a vessel of water we find it struggling to rise to the surface. It is pressed upward by the water under it, and considerable force of the hand is required to keep it down. Or if a stone be suspended in water it feels lighter than when in air; the water under it pushes i upward against it, and thus supports a part of its weight. 2. TVith force equal to the weight of water displcaeed.-N ow, suppose a block of marble suspended in a e le vessel of water (Fig 10). The up- ward pressure against its lower surface, K a b, is equal to the downward pressure of the water at that depth, and this downward pressure is equal to the 4S NATURAL PHILOSOPHY. weight of the column of water, ef b a. Now tile column of water, ef c cd, is sustained by a part of this upward pressure, and the rest of it is exerted upon the marble. To sustain the column, ef c d, requires an upward pressure equal to its weight, and hence there is left a pressure against the surface, a b, equal to the weight of a,column of water, a bc c, but this water is displaced by the marble. The upward pressure against the block is, therefore, equal to the weight of the fluid displaced. We owe the discovery of this important principle to Archimedes, one of the most eminent philosophers of antiquity, and to this day it is called the prieciple of Arch/imedes. Its applications are numerous. It helps the chemist to distinguish one substance from another, and the merchant, often, to judge of the purity and value of his merchandise. In any case it enables the inquirer to determine the size or volume of a solid body, however irregular, and it has, moreover, led to valuable improvements in marine architecture and in other arts. 3. If the solid is lighter than water.-The weight of the water displaced by a block of wood will just equal the weight of the wood itself. A pound of wood will displace a pound of water, but a pound of wood is larger than a pound of water, so that only part of the wood will be immersed. A tin basin and a wooden bowl of the same size, will displace an equal volume of water, if the walls of the basin are thin enough, so that the two bodies have the same weight. Upon this principle iron ships are built. An iron ship will sink no farther than one of wood of the same size, provided the walls of iron are so thin that the two ships shall be of the same weight. NATURAL PHILOSOPHY. 49 4. If the solid is heavier than water. —If a solid be heavier than water, the upward pressure of tile fluid can support only a part of its weight. The weight supported will be the weight of the water which the solid displaces. Thus, for example, a piece of marble which weighs 10 ozs. in air, will be found to weigh only 6.3 ozs. in water. The upward pressure of the water is equal to 3.7 ozs., and this is the weight of the water which the marble displaces, and whose bulk is, of course, just equal to the bulk of the marble. (14.) The specific gravity of a substance is its weight compared to the weight of an equal bulk of some other body taken as a standard. To obtain it, different methods must be taken, according as the body is a gas, a liquid or a solid. 1. Specific Gravity.-The specific gravity of a substance shows how many times heavier it is than an equal bulk of some other body. The standards used are water and air; water for all solid and liquid bodies, and air for all gases. Then, when we say, for instance, that the specific gravity of gold is 19, we only mean that a cubic inch of gold will weigh 19 times as much as a cubic inch of water. The specific gravity of oxygen gas is 1.106: that is to say, a cubic inch of oxygen gas will weigh 1.106 as much as a cubic inch of air. The following simple rule must evidently cover all cases of getting specific gravity:-Divide the weight of the body by the weight of an equal bulk of the standard. L-.-OF GASES. A.-To obtain the specific gravity of a gas, divide 3 50 NATURAL PHILOSOPHY. the weight of a convenient portion of it by the weight of an equal portion of air. To get the weight of equal portions of gases is, however, a difficult process, requiring many precautions.' Without trying to give the details of the operation (see Cooke's Chem. Phys., pp. 93 and 667), we may describe it in general terms. A glass globe is first weighed when full of air. The air is then taken out of it by means of an air-pump, and the globe is again weighed: the difference in these weights is the weight of the globe full of air. The globe is then filled with the gas whose specific gravity is desired, and again weighed: the difference between this weight and that of the empty globe, is the weight of the globe full of gas. The specific gravity is obtained from these weights of equal volumes of gas and air. ir.-OF LIQUIDS. B.-The specific gravity of a liquid may be obtained in various ways. We may notice1. By direct weighing. 2. By an instrument called the hydrometer. 3. By the use of a solid bulb. 1. By direct weighing.-The most direct method of getting the specific gravity of a liquid, is to weigh equal quantities of it and water, and then divide the weight of the liquid by that of the water. To facilitate the operation, "specific gravity bottles" are made, which hold just 1,000 grains of pure water. The weight of the bottle being known, a single operation with the NATURAL PHILOSOPHY. 51 balance will give the weight of the liquid, and then its specific gravity may be speedily calculated. 2. By t/ze hydcroneter.-A common form of this instrument is represented in Fig. 11. It consists of a glass tube, with two bulbs near its lower end. The Fig. 11. tube and upper bulb are full of air, which A renders the instrument lighter than water. The lower and smaller bulb contains shot enough to keep the instrument in an erect position, when placed in a liquid, as shown in the figure. A graduated scale is fixed to the stem, to indicate the depth to which the instrument sinks in different liquids. The action of this instrument can be readily explained by means of a piece of wood, several inches long and an inch square, having its lower end loaded with wire. If this be put into a vessel of water, it will sink to a certain depth, and remain upright. If it sinks 10 inches, then 10 cubic inches of water are displaced by it. If now the instrument be put into a vessel of alcohol, it will sink deeper, suppose it be 12 inches; then 12 cubic inches of alcohol are displaced. But, according to the principle of Archimedes, the fluid displaced is equal in weight to the body floating in it [see (13), 1 and 2]. Hence 10 cubic inches of water have the same weight as 12 cubic inches of alcohol, or alcohol is -- as heavy as water. Its specific gravity is, therefore, -0= —.833+. >Making the instrument of glass, and giving it the form seen in Fig. 11, renders it more convenient, but does not alter the principle on which it acts. The graduation of the scale is arbitrary, and varies in different forms of the instrument. The zero usually 52 NATURAL PHILOS OPHY. marks the point to which the hydrometer sinks in pure water, and the degrees above and below show how far the instrument may sink in liquids respectively lighter and heavier than water. 3. By the itse of a bulb.-According to the principle of Archimedes, a heavy bulb of glass, or other convenient substance, when weighed in any liquid, will lose a part of its weight just equal to the weight of an equal bulk of that liquid. HIence, weigh a bulb of glass in air, afterward in water, and then in the liquid whose specific gravity is desired. The losses of weight it sustains will be the weights of equal bulks of the two liquids, and from these weights the specific gravity may be obtained, To illustrate this method, suppose the specific gravity of alcohol is to be found. A bulb of glass, weighed in air and then in water, is found to lose 325 grs. Its loss in alcohol is found to be 257 grs. Then 2 =.79 + is the specific gravity of the alcohol. III.-OF SOLIDS. C.-There are two important cases of common occurrence:1. The solid is heavier than water. 2. The solid is lighter than water. 1. Of a solid heavier than water.-Divide the weight of the body in air, by its loss of weight in water. The principle of Archimedes explains this rule. Thus the weight of marble [see (13), 4] in air being 10 ozs., and in water being 6.3 ozs., it is clear that the difference, 3.7, is the weight of a bulk of water equal NATURAL PHILOSOPHY. 53 to the size of the marble. Then, -- = 2.7 is the specific gravity of this solid. The experiment is conducted in the following manner. Let the specific Fig. 12. gravity of iron be desired. A fragment of iron of convenient size is hung from the bottom of one scale pan of a balance, and weighed. It is then immersed in a vessel of water (see Fig. 12), and _ - its weight again deter-/ mined. Now, suppose the iron weighs, in air, 360 grs., and in water, 313.85grs. Then 360 - 313.85 = 46.15 grs. is the weight of an equal bulk of water. And.6-j = 7.8 is the specific gravity of the iron. 2. Of a solid lighter than water.-If the solid be lighter than water, the operation is more complex. If the light body be compelled to sink in water by fastening to it some heavier body, their loss of weight will represent the upward pressure of the water upon them both. If the heavy body alone be weighed in water, its loss will represent the upward pressure against it. [Now, if the upward pressure against the heavy body be subtracted from the upward pressure upon both, the difference must represent the upward pressure against the light body alone, and hence, the weight of a quantity of water equal to its bulk. To illustrate this operation, suppose a body weighed, in air, 200grs. When attached to a piece of lead, both weighed 1,936 grs. in air, and 1,460 grs. in water, 54 NATURAL PHILOSOPHY. suffering a loss of 4?6 grs. The lead itself, when weighed in water, lost 152grs. The upward pressure against the light body alone must then have been, 476 - 152 = 324 grs. Then, 200 grs., the weight of the light body in air, divided by 324 grs., the weight of an equal bulk of water, is the specific gravity desired. In the following table the specific gravity of various substances are arranged for reference.. —OF GASES, AT 32~ F. BAROMETER, 30 INCHES. Names. Sp. gr. Names. Sp. gr, Air.....................1.000 Nitrogen................0.97 2 Oxygen.................1.106 Carbonic Acid..........1.529 Hydrogen............... 0.0691 Olefiant Gas.............0.978 II.-oF LIQTUIDS, AT 390 F. Names. Sp. gr. Names. Sp. gr. Water (distilled)...........1.000 Ether........0.715 Sea Water...............1.026 Naphtha................0.847 Milk..................... 1.030 Oil Turpentine...........0.869 Alcohol (absolute)......... 0.7 92 Wine of Burgundy........0.991 Olive Oil.................0.915 1l Mercury (32'F.).........13.596 III.-oF SOLIDS, AT 390 F. Names. Sp. gr. Names. Sp. gr. Platinum................. 21.5 Silver (cast)....... 10.4-7 Gold (cast)............ 19.26 Diamond.................3.50 Iron.............. 7.2 Marble................... 2.70 Steel..8....... 7.8 Ivor..................1 92 Lead (cast)..............11.3 Ice..................... 0.93 Copper "......... 8.8 Pine wood..............0.66 (15.) If an external pressure be exerted upon any portion of the surface of a liquid, the same amount of pressure will be transmitted equally in every direction. NATURAL PHILOSOPHY. 55 This is true, whatever may be the form of the vessel which contains the liquid. This is the principle applied in the hydrostatic press. 1. She equal transmission of pressure. —To illustrate the principle stated above, let a vessel, represented in section by Fig. 13, be quite filled with water. In the sides of the vessel are several Fib. 18. apertures, A, B, C, D, and E, closed with movable pistons. Let the area of each piston be 1 sqr. in., and suppose a weight of two pounds be placed upon the pis- B ton A. It will be found that a force of two pounds will be exerted against each of the other c pistons. Thus E will be pushed upward by a force of two pounds, while 13 and D will at the same time be pushed in opposite directions, each with a force of just two pounds. No matter how numerous these pistons may be, nor in what direction they may be inserted, each will be found exerting a two-pound pressure under the influence of a force of two pounds acting at A. Every square inch in the entire surface of the vessel will receive a pressure of two pounds. 2. The shape of the vessel makes no diference.The vessel may be of any shape whatever, and an equal pressure will be received on every square inch of its surface whenever an external force is applied. We will suppose, for illustration, that the vessel is a bent tube in the form of the letter U. A pressure may be exerted upon the water in one arm, by forcing the breath into the open end of the 5 G NATU RAL PHILOSOPHY. tube. The liquid will go down in that arm and rise in the other. The pressure of the breath is downward in one arm; it is lateral through the bend, and upward in the other arm. Moreover, these pressures are all exactly equal. Fi,. 14. But suppose one arm of this tube to be A ~ larger than the other. Let the vessel have the form represented in Fig. 14, the arm A being twice as large as the other. To push the water down in H G, requires no greater effort with the breath than when the arms were of equal size. The downward pressure on one square inch at H, is transmitted as an equal upward pressure on each square inch at A, and thus a column twice as o large is lifted one-half as high by the:n same force. 3. The hydrostatic pess. —The hydrostatic press acts upon the principle just explained. It is a machine by which a small force may be made to exert a great pressure. Its construction may be understood by examining Fig. 15. Two metallic cylinders, A and B, of different sizes, are joined together by a tube KI. In the small cylinder there is a piston, p, which can be moved up and down by the handle IM. In the large cylinder there is also a piston, P, having at its upper end a large iron plate which moves freely up and down in a strong firamework, Q. Between the iron plate and the top of this framework, the body to be pressed is placed. Now, when the small piston is raised, the cylinder A is filled with water drawn fiom tile reservoir H, below, and when it is tlushed down, this water is forced into NATURAL PHILOSOPHY. 57 the large cylinder, through the pipe K. There is a valve in this tube which prevents the water from returning, so that each stroke of the small piston pushes an additional quantity of water into the larger cylinder. By this means the large piston is pushed up against the body to be pressed. To calculate the pressure exerted by the large piston, we must remember that the force acting upon the pisFig. 15. A ton in A, will be exerted upon every equal amount of surface in B. To illustrate this: suppose tile area of the large piston to be ten times the area of the small one; then one pound at A will produce a pressure of ten pounds at P. The handle, MAl, increases the advantage 2* 58 NATURAL PHILOSOPHY. still more, according to the principle of the lever to be explained in a future chapter. By increasing the size of the large cylinder, and diminishing the size of the small one, the pressure exerted by a given power will be increased proportionally. The weight of a man's hand might thus be made to lift a ship with all its cargo. The only limit to the increase of power would be the strength of the material of which the machine is made. PROBLEMIS ILLUSTRATING THE LAWS OF HYDROSTATICS. 1. A cylindrical vessel, whose base is 5 sq. ft., is 10 ft. high. It is filled with water. What pressure is exerted upon the base? Ans. 3,125 lbs. 2. If the bottom of a vessel has an area of 72 sq. in., and its top an area of 96 sq. in., and it is 9 in. high; what pressure will be exerted on the bottom when the vessel is full of water? Ans. 23.43 lbs. 3. Two vessels with equal bases are filled with water, one to a height of 9 in., the other to a height of 27 in. Hiow many times more pressure on the base in the last case than in the first? Ans. 3. 4. How much pressure is being exerted against the side of a cubical vessel when full of water, its height being 18 inches a Ans. 105.46+ lbs. 5. I-ow much pressure would be exerted upon 12 sq. in. of the sides of the vessel when the middle point of this surface is 20 inches below the top of the water? Ans. 8.68 lbs. 6. IIow many cubic inches of water will be displaced by a piece of pine wood weighing just 10 lbs? [See (13.)] Ans. 276.48. NATURAL PHILOSOPHY. 59 7. How much less will a piece of marble measuring 100 cubic inches, weigh in water than in air? LSee (13.)] Ans. 3.61 lbs. 8. The specific gravity of marble being 2.7, what will be the weight of 25 cubic ft.? Ans. 4,218.75 lbs. 9. How many cubic inches in a block of ice that weighs 75 lbs..? A ns. 2,229.12. 10. What is the specific gravity of flint glass it a fragment of it weigh, in air, 4,320 grs., and in water 3,023 grs.?.Ans. 3.33. 11. The specific gravity of wax is to be found from the following data:Weight of the wax in air - - 8 oz. Weight of a piece of lead in air 16 oz. Weight of the lead in water - - 14.6 oz. Weight of wax and lead in water 13.712 oz. Ans. 0.9. 12. A bottle holding 1,000 grs. of water is found to hold only 870 grs. of oil of turpentine. What is the specific gravity of this oil? Acns. 0. 87. 13. How much pressure can be exerted upon the large piston of a hydrostatic press by applying 50 lbs. to the small piston; the area of the sn-all piston being l sq. in., that of the large piston 100 sq. in.? Ans. 10,000 lbs. ~ 4. OF THE PROPERTIES OF GASEOUS BODIES. (16.) The most characteristic properties of gases are compressibility and expansibility. Besides these properties, gases possess others common to all forms of matter, among which we notice elasticity and weight. 60 NATURAL PHILOSOPHY. 1. Compressibilzity.-Let a small glass tube be fitted to the neck of a vial by a cork, so as to make an airtight joint. Warm the vial y/ently, and then put a drop of ink into the top of the tube. As the Fig. 16. vial cools the drop slowly moves down the tube until it finally stops at some point, A (Fig. 16). There it will be held by the capillary attraction of the tube. The air in the vial and tube up to the point A will thus be separated from the air outside. Now, closing the upper end of the tube with the lips, let the breath be gently pressed against the drop; it will be pushed down, it may be, a distance of several inches. The air in the vial can not escape, and the motion of the drop therefore shows that the air is being crowded into a smaller space, in;* other words, that it is compressible. 2. Expansibility.-If the vial (Fig. 16) be warmed by grasping it in the hand, or better, by standing it in warm water, the drop of ink will move upward in the tube. The air in the vial expands and pushes the drop along. Or if, through the cork of a small bottle, a glass tube be passed, at the upper end of which is a bulb, and the lower end of which reaches down into the colored water contained in the bottle, the heat of a lamp flame may be applied to the bulb. It will be noticed that bubbles of air escape from the lower end of the tube. The air is expanded, so that the bulb and tube can no longer hold it all. When the flame is withdrawn, the bulb gradually cools, and the water will rise in the tube and stand at a certain height, as shown in Fig. 17. Now, let NATURAL PHILOSOPHY. 61 the palm of the hand be laid upon the bulb; the water is driven down the tube by the expanding air. The gentle warmth of the hand is quite sufficient to produce a very considerable expansion of the air. These two properties belong to solid and Fig. IT. liquid bodies in various slight degrees, but preeminently to gases, which seem to be compressible and expansible without limit. The force of heat in the last experiments is a repulsive force among the molecules of air, and pushes them farther apart. As long as this force increases by the action of the flame, it will push them farther and farther apart continually. In the first experiment, the slight pressure of the breath overcomes the repulsion among the molecules, and pushes them nearer together. Should the pressure be increased, we can give no reason why the molecules should not continue to approach each other. The limit of compressibility would be reached when the molecules should be brought into actual contact with each other; but to do this would doubtless require a pressure immensely greater than any at our command. 3. Elasticity.-The elasticity of air is beautifully shown by the simple apparatus already used (see Fig. 16) to illustrate the characteristic properties. When the breath is alternately pressed into and withdrawn from the tube, the air will alternately be compressed and spring back, the drop of ink jumping down and up in the tube to show it. 4. IWeight.-The air has weight. If we would show it, we may first weigh an open vessel, properly ar 62 NATURAL PHILOSOPHY. ranged, and afterward take the air out of it and weigh it again, the difference in these two weights will be the weight of the air which the vessel contains. ]But how can the air be taken out of a vessel? To answer this question we must become acquainted with Fig. 18. the air-piump. A section of the essential parts of this important instrument is represented in Fig. 18. "-. r A cylinder, A B, is joined by means of a tube, b e, to a very smooth plate, p. A piston, c, moves air-tight in the cylinder. In the piston is a valve, i,, which opens upward, and another valve at b, also opens upward from the tube into the cylinder. The vessel, d, from which the air is to be taken is placed upon the plate. Such vessels are usually called receivers. It will be seen that when the piston is raised, the valve, i, will be closed, and the air above it will be lifted out at the top of the cylinder. A vacuum would thus be formed below the piston were it not for the expansibility of the air in the receiver. This air expands, and a part of it is forced through the valve, b, into the cylinder. When the piston is pushed down, the air below it passes through the valve, i, and when by a second stroke the piston is lifted, this air is pushed out at the top of the cylinder, while another portion fiom the receiver is pressed through the tube into the cylinder below the piston. By each successive stroke, the quantity of air in the receiver is diminished, until, with a good instrument, the quantity left will be almost NATURAL PHILOSOPHY. 63 inappreciable. It is quite evident, however, that a perfect vacuum can not be obtained in this way. One form of this important instrument, complete, is represented in Fig. 19. Fig. 19. We may now attend to the process of weighing air. A hollow glass globe, with a stop-cock, is hung from one pan of a delicate balance, and its weight carefully found. It is then screwed to the opening in the plate of the airpump, and the air is exhausted. The stop-cock is then closed to prevent the air fiom returning into the globe, which is then taken from the pump and weighed. It is found to weigh less than before, and the difference must be the weight of the air which has been taken out. At the ordinary temperatures of air, 100 cubic inches weigh about 31 grains. 64 E3 NATURAL PHILOSOPHY. ~ 5. OF THE PRESSURE OF THE ATMOSPHERE. (17.) The atmosphere exerts pressure in all directions. This pressure is about 15 lbs. upon every square inch of surface. 1. /e atmosphere exerts pressure.-Since every one hundred cubic inches of air weigh about 31 grs., it is clear that the atmosphere must be exerting considerable pressure upon the surfaces of all bodies on which it rests. This pressure may be shown in various ways. Take a glass tube of convenient length, open at both ends, and insert one end in a vessel of colored water. Apply the lips to the other end, and as the air is drawn out at the top, the water will rise rapidly in the tube. What pushes the water up? The ancients called it " Nature's abhorrence of a vacuum:" many at the present day are content to say that it is " sucked up." But let it be remembered that matter never moves unless it is forced to Smtove, and that the forces of abhorrence and suction are simply fictions. The only force acting upon the water is the weight of the air resting on its surface in the vessel. This downward pressure pushes the water under the lower end and upward into the tube. A more beautiful experiment consists in causing the pressure of the air to produce a fountain playing in a vacuum. A tall glass receiver (Fig. 20) is closed at the bottom by a stop-cock which terminates in a tube extending upward a little way into the receiver. The air from this receiver being taken by an air-pump, the NATURAL PHILOSOPHY. 65 stop-cock is immersed in a vessel of water and opened. Instantly tile water leaps to the top of the receiver, and a beautiful fountain continues to play Fig. 20. until the jet pipe is covered by the falling water. 2. The _pressure is in all directions.-An experiment easily tried will show that the air is pressing equally in all directions. Stretch a piece of caoutchouc, or thin india rubber, over the large end of a lamp chim- ney, and firmly fasten it by winding a cord around it. Apply the mouth to the other end of the tube and draw the air out.! The pressure of the air pushes the rubber l\ into the tube. Hold the tube in anyyposition, and in all positions the rubber will be pushed into the tube alike. 3. Dlike pressure is 15 lbs. to the square inch.-If the air should be all taken out of our tubes used in the foregoing experiments [(17.) 1], the water would entirely fill them, and it is clear that the pressure of the atmosphere must, at least, equal the weight of the water in the tube. How much farther the water would rise if the tube was long enough, these experiments have not told. A heavier liquid will not be lifted as high as water, and will be more convenient for experiment. Mercury is a liquid metal about 131 times as heavy as water, and it is found that the air will sustain a column about 30 inches high. The experiment is conducted as follows. Take a glass tube more than 30 inches long, closed at one end, and fill it with mercury. Close the open end with the finger and invert the tube. Now place the open end in a dish of mer 66 NATURAL PHILOSOPHY. cury and withdraw the finger. It will be seen that Fig. 21. the top of the column of mercury in e aC, the tube, is about 30 inches above the surface of the mercury in the dish. ~ ll (See Fig. 21.) The space above the mercury in the tube must be a vacuum. I Now, the pressure of the atmosphere just balances the weight of this column of mercury. Tile weight of a column of mlercury 30 inches high, the area of its base being one square inch, is 15 pounds. The downward pressure of the atmosphere is therefore 15 lbs. to the square inch of surface on which it rests. (18.) The principle of atmospheric pressure is applied in the construction of many very useful instruments. We will notice the barometer, the common pump, the forcing pump, and the siphon. I.-THJE BAROMETER. A.-The barometer column always indicates the pressure of the atmosphere. But the pressure of the atmosphere depends upon1st. Its weight. 2d. The amount of water-vapor in it. 3d. The elasticity of its lower portions, due to the action of heat. 1. The barometer. —If the apparatus used to deter NATURAL PHILOSOPHY. 67 mine the pressure of the atmosphere (see Fig. 21) is inclosed for protection in a frame of' metal or wood, with a graduated scale attached, to measure the height of the column of mercury, it forms the instrument so well known as the barometer. 2. Shows the pressure of the atmosphere. —The pressure of the atmosphere is not always the same. When it is less than 15 lbs. to the inch, the column of mercury will be lower than 30 inches, and when greater, the column will be higher: indeed the height of the column will vary in exact proportion to every change in the pressure of the air which supports it. But notice that when the mercury sinks in the tube, it must rise in the cistern, and that, hence, the column must shorten at both ends, while the figures on the scale only show the change which takes place at the top: they fail to tell the true height of the column. This error is avoided in what is called Fortin's barometer, by means of a cistern with a flexible bottom (see Fig. 22). The bottom of this cistern Fig. 22. is made of deerskin, and rests upon the end of the screw C, by which it may he lowered or lifted. An ivory pointer, A, is fastened to the top of the cistern, and its lower end is the point from which the distances are measured on the scale which shows the.height of mercury in the tube. If the surface of the liquid in the cistern just touches this point, then the figures on the scale show the true height of the column, which indi-, cates the pressure of the atmosphere. 3. The pressure of the atmosphere depends upon its weight.-Consider the atmosphere as a vast ocean of 68 NATURAL PHILOSOPHY. air, whose depth (or height, since we are at the bottom of it) is thought to be about fifty miles. Its upper surface can no more be at rest than can the surface of the sea, and its billows must be more immense, because its substance is more easily moved. The barometer over which these great waves sweep to and fro, being now under the crest, and then under the depression, is subject to the pressure of columns of air of different heights, and the mercury must rise or fall accordingly. Again; the weight of the atmosphere will vary with the altitude of the place where the observation is made. When we go up a mountain-side, we leave a part of the atmosphere below us, and, of course, the height of the column above us is less. The barometer column will, therefore, be shorter. Upon this principle the barometer is used to measure the Aeight of 9nountains. If the density of the atmosphere were uniform, the fall of the mercury would be in exact ratio of the distances upward, and knowing the height required to make the mercury fall 1 of an inch, this multiplied by the number of tenths through which it is observed to sink, would tell the height of the mountain. The truth is, however, that the density of the air rapidly diminishes as we ascend. Temperature, too, affects its pressure. In spite of these difficulties, tables have been constructed, by which the height of a place above the sea-level may be calculated, by observing the height of the barometer column and the temperature of the atmosphere. (See Cooke's Chemn. Phys., p. 511.) 4. Upon the ccamount of water-vapor it contains.Mixed with the air, at all times, are considerable quantities of invisible vapor of water. If the atmosphere was pure dry air alone, it would exert a certain press NATURAL PHILOSOPHY. 6f9 ure: if it consisted wholly of water-vapor, it would exert a different amount of pressure: it does consist of a mixture of these two gases, and the pressure it exerts is'the sum of the pressures they would separately exert. It follows that the atmospheric pressure will be greatest when there is the greatest quantity of watervapor in the air; the barometer column will then rise. But let this vapor be condensed into clouds, and it will have but little force of elasticity, and will exert but a small fraction of its former pressure; hence the barometer column will stand lower in cloudy weather. On this principle the barometer is used to indicate changes in the weather. A raising Fig. 23. column indicates fair weather; a falling column indcicatesfoztl weather. S This rule is to a great extent reliable. Others are given by different A observers, but they must be taken with considerable allowance. 5. Upon the elasticity of its lower portions. —Let us approach this topic by means of an experiment. The O tube, A B, Fig. 23, having been filled with mercury and inverted, the space above A is a vacuum, and the column of mercury is sustained by the pressure of the air at B. Let this end pass, air-tight, through the stopper in the lower end of a long R glass tube C. The upper end of this tube is ground smooth, and covered with a heavy ground glass slide S. Now let the tube 70 NATURAL PHILOSOPHY. C, be heated. The air within is expanded; it can not escape at S; the entire expansive force is exerted upon the mercury at B, and the column shows this pressure by rising at A. While the heat is continued, let the slide S be drawn so as to leave a very small hole in the top of the tube C; a gradual fall of the mercury at A will show that the' pressure of the air is diminishing. Now the atmosphere is heated by coming in contact with the earth: the lower stratum is heated first, and the upper strata in succession afterward. The heated stratum is expanded like the air in the tube C, when heated. It attempts to rise, but the strata above, not yet heated, rest upon it and prevent its rising, just as the slide S keeps the air in our tube, and the expansive force of this stratum must raise the barometer column. This expansive force will, for a time, increase, until it is strong enough to lift the weight of the upper strata of air, after which it will diminish, just as it did when the slide S was removed. When the atmosphere cools, the lower stratum is first condensed, and this allows the air above to move downward. In falling it gains a certain velocity, and exerts a greater pressure: the barometer column must be raised thereby. We see, then, that as the atmosphere is daily warmed and cooled, the barometer column must rise and fall. Observation confirms this. From nine o'clock to ten in the morning, the mercury reaches its greatest height; afterward it begins to fall, and at three or four in the afternoon it reaches its lowest point. It then begins to rise again, and reaches its greatest height at nine or ten in the evening. These motions occur every day, and NATURAL PHILOSOPHY. 71 are so regular that, as Humboldt says, they might be used to indicate the time of day, only that the distance through which the column fluctuates is very small, being greatest at the equator, where it amounts to lo200 of an inch. II. —THE COMMON PUMP. This instrument, as generally made, consists of two cylinders or barrels, A and B, Fig. 24. Fig. 24, with a valve, S, at their junction, opening upward. In } the upper barrel is a piston, P, in which is a valve, 0, also opening upward. The piston is moved P by means of the handle IS, and the water may flow from the u > d spout C. When the piston islifted, the air above it will be lifted out of the barrel. A partial vacuum will thus be formed below the piston, and the pressure of the air upon the surface of the water in the A well, will push the water up the barrel A, through the valve S, into the barrel B. When the piston goes down, the valve S will close, and prevent the return of the water to the well. The -- valve in the piston will be opened, and the water will pass through it. When the piston is again lifted, the water, now above it, will be lifted to 72 NATURAL PHILOSOPHY. the spout, while the atmospheric pressure will force another portion into the barrel below the piston. At the sea-level the pressure of the air will sustain a column of mercury about 30 inches high. Since mercury is, at ordinary temperature, about 131 times heavier than water, the same force will lift a column of water 131 times as high: 13~- x 30=405; 405 in. =331ft. The lower barrel of the common pump must not exceed 331ft. in length, even at the level of the sea. III.-THE FORCING PUMP. In the forcing pump the piston has no valve, but Fig. 25, from near the bottom of the upper barrel there is a tube passing to an air-chamber, with a valve opening into the chamber. A section of this instrument is represented in Fig. 25. Reaching from near the -__ - - bottom of the air-chamber I 1K, is It ~$ Ea tube, L M, which extends to any -_____ place at which the water is to be delivered. Now, when the solid piston P, is raised, water is pressed through @ D the valve E, into the barrel B. When the piston is pushed down again, the water is driven through the tube into the air-chamber, and compresses the air in it. By every stroke, the water accumulates in the chamber, and the air is more and more compressed. The pressure of this condensed air upon the water in the chamber, pushes it up through the tube L 1Mi, to the place where it is desired. Without the NATURAL PHILOSOPHY. 73 air-chamber, the water would issue from the pipe in jets; with the chamber, the water issues in a steady stream. TV.-THE SIPHON. The siphon is an instrument by which liquids may be transferred from one vessel to another, by atmospheric pressure. It consists of a bent tube, one arm of which is longer than the other. In Fig. 26, the siphon in operation is shown. Having been first filled with water, its short armn Fig. 26. is inserted in the water to D be transferred from the yessel, C, and it is then found that the water will flow steadily, until the lower end of the short arm is left uncovered, or, in other cases, until the water in the two vessels stands at the same level.:ow, the downward pressure of the air at C, is - partly balanced by the weight of the column of water in the short arm of the tube; the excess of force will tend to push the water over through the bend. On the other hand, the atmospheric pressure at B is partly balanced by the weight of the water in the long arm: the excess will tend to push the water back through the bend toward C. It is clear that the pressure of air, minus the weight of the sworter column of water, is more than the same pressure, less the weight of the 4 NATURAL PHILOSOPHY. longer column, and hence that a greater force will be exerted to push the water from C toward B, than from B toward C: the liquid will flow in the direction of the greater force. ~ 6. OF THE RELATION BETWEEN THE VOLUME AND THE WEIGHT OF AIR. (19.) The volume of any given weight of air, or other gaseous body, will vary with every change in the pressure or the temperature to which it is subjected. I. -— PRESSURE. A. — The volume of a given weight of air will be inversely as the pressure upon it. Hence the density of the atmosphere is greatest at the surface of the earth, 1. FVoblme inversely as tke pressure. —Press the breath into the tube above the drop of ink (see Fig. 16), and the air in the bottle will be condensed. Now draw the air out of the tube, and the drop rises, showing that the air below has expandel. The same quantity of air is here seen to fill less space, when the pressure upon it is increased, and more space whlen the pressure is diminished. Now, we may prove by experiment, first, that with a double pressure, the volume will be just one-half; and, second, that with half the pressure, the volume will be just double. In the first case, we use a bent glass tube (Fig. 27), NATURAL PHILOSOPHY. 75 the short arm being closed, and the other, which should be more than 30 inches long, being open at the top. A graduated scale, to which the tube is firmly bound, measures inches from the bend. KNow, let mercury be poured into Fig. 27. the tube, until it fills the bend. The air presses upon the mercury in the long arm, and this liquid transmits the same pressure to the air in the short arm. The pressure upon the air in the short arm is, therefore, 15 lbs. to the square inch. If we fill the long arm, as shown in the figure, to the height of 30 inches, with mercury, we will be adding a pressure of 15 lbs. to the inch. The pressure upon the air in the short arm, will then be cdoutbled, and we discover that the mercury has risen, crowding the air before it, and stands at A, the air filling just half the original volume. In the second case, we take a glass tube, A B (Fig. 28), about 25 inches long, and open at both ends. Let three narrow bands of paper be pasted upon it, one at a distance of 3 inches from the top, another 6 inches frotm the top, and the third 15 inches from the second. Let another larger tube, D. about 30 inches long, be nearly filled with mercury. Insert the end A, of the small tube in the mercury of the (ceher, and push it do\eln until the upper m?-rk (3) is 'I6 NATURAL PBILOSOPHY. at the level of the mercury. Now, clasping the finger tightly over the end B, thus inclosing 3 inches Fig 28. of air in the tube, lift it until the SB third mark is brought up to the top B3 of the mercury. The air will be found ~6 n n to fill the space of 6 inches. Before the tube was lifted, the pressure 6 of the atmosphere, 15 lbs. to the inch, was exerted upon the air in it: after the tube is lifted, the atmosphere sustains a column of mercury 15 inches high. To do this takes half the pressure it can as exert, the other half is exerted upon the air above the mercury. We thus show that with half the pressure the volume will be just double. From these two experiments we infer D iiiil that the. volume of a given weight of air will be inversely as the pressure upon it, and repeated experiment confirms the inference. This law was discovered by the Abbe Mariotte in France, and is generally called Mariotte's law. (See Cooke's Chem. Phys., p. 287.) 2. The density of the atmosphere. —When a given weight of air is crowded into one-half its original volume, it must be twice as dense; and when expanded into double its first volume, it can only be half as dense. The density of air will therefore be exactly in proportion to the pressure upon it. So the atmosphere, where its pressure is greatest, will be most dense. 3. Is greatest at the surface of the earth.-The atmosphere in contact with the earth is pressed upon by NATURAL PHILOSOPHY. 77 all the air above, even to the top of the atmosphere. At a distance above the earth, the atmosphere receives less pressure, because there is less air above to exert it. Thle density being greatest where the pressure is greatest, the air at the surface must be more dense than the portions above. The air is much less dense at the top of a high mountain than at its base. II. -TEMPERATURE. B.-The volume of a given weight of air will be greater as its temperature is higher. It expands - of its bulk for every additional degree of heat. 1. Heat increases thle volume of air.-Let the palm of the hand be laid upon the bulb (Fig. 17), and the fluid in the tube descends, because the air in the bulb expands. Pour cold water upon the bulb, and the fluid ascends because the air above it is condensed. Apply the heat of the lamp flame to the bulb, and the water in the tube will be quite driven out at the bottom: let it cool again, and the water rises to its former height. These experiments show that the addition of heat expands air, and that its withdrawal contracts it. 2. At the rate of I its bulk for each degree. —The expansion of air and other gases by heat, is uniform. One degree of heat, when the temperature is low, produces the same expansion as one degree, when the temperature is high. If we have 490 cubic inches at a temperature of 32~, it will become 491 cubic inches if heated one degree, making its temperature 33~. In other words, it expands,A- of its bulk at 32~, for each additional degree of heat applied. s8 ~ iNATU'RAL PHILOSOPHY. PROBLEMS ILLUSTRATING THE LAWS OF GASEOUS BODIES. 1. What is the weight of a cubic foot of air at ordinary temperature and pressure? Ans. 535.68 grs. 2. What is the weight of 100 cub. in. of oxygen gas at ordinary temperature and pressure, its specific gravity being 1.108? Ans. 34.348 grs. 3. What is the weight of 100 cub. in. of nitrogen gas at ordinary temperature and pressure, its specific gravity being.692? 4. ~What pressure will be exerted by the atmosphere on a surface of 1 sq. ft.? [See (17.)] Ans. 2,160 lbs. 5. ~What pressure does the atmosphere exert upon a square inch suiface when the barometer column is 28 inches high? [See (18.) A. 2.] Ans. 14 lbs. 6. I-low high a column of water would the atmosphere sustain when the barometer column stands at a height of 28 inches? Ans. 31~ ft. 7. Suppose 100 cub. in. of air at a pressure of 15 lbs. to the inch is made to receive an additional pressure of 15 lbs. to the inch, what will be its volume? [See (19.) A.] Ans. 50 cub. in. 8. How much pressure must be removed from 100 cub. in. of air, at usual density, in order that it may expand to a volume of 200 cub. in.? Ans,. 7- lbs. to the inch. 9. In the air-chamber of the forcing-pump, the air is compressed into half its former bulk; how high will the water be thrown? Ans. 33i-ft. 10. If we have 500 cub. in. of air at 32~ temp., how much will there be when it is heated to a temperature of 75~? [See (19.) B.] Ans. 543.88+ cub. in. PART II. THE PHENOMENA OF BODIES IN MOTION, N'ATURAL PHILOSOPHY. 81 CHAPTER III. OF MOTION. INTRODUOTION.- APPLICATION OF THE FUNDAMENTAL IDEAS. (20.) Read (4.) and (7.)-Attraction and repulsion acting upon masses of matter determine their condition of rest or motion. 1. The motion of bodies falling to the ground is due to the attracction of gravitation. The motion of air in wind is caused chiefly by the repulsive power of heat. The bullet speeds on its mission of death, urged by the repulsive force of exploding gunpowder. The forces which produce the endless variety of motions in nature are found, when carefully studied, to be only different forms of attraction and repulsion. We speak of the forces of natzre, and call them wind, water, gravitation. This is well, because these names have been given to familiar forms of force. We will continue to use these terms: at the same time, let us do justice to the simplicity of God's stupendous works, by remembering that the forces of nature are attraction and r'epl7sion. 4* 82 N ATUR AL PHILOSOPHY. ~ 1. OF 5MOTION CAUSED BY A SINGLE FORCE. (21.) There are three important principles called the laws of motion:1st. A body at rest will remain at rest; or, if in motion, it will move forever in a straight line, unless acted upon by some force to change its condition. 2d. A given force will produce the same amount of motion, whether it act upon a body at rest, or in motion. 3d. Action and reaction are equal, and in opposite directions. 1. iThe first law. —The first law is proved when we remember, that the inertia of matter forbids that a body shall, in any way, change its own condition. Then, why are bodies so constantly changing their condition of rest or motion? Who ever saw a body in nature, moving in an absolutely straight line? Bodies are constantly under the influence of forces which do change their condition. A stone thrown froin the hand would move forever in a straight line, if it felt only the force of the hand; but gravitation, and the resistance of the air, compel it to move in a graceful curve instead. The pleasing variety of natural motions is brought about by the unceasing action of external forces. 2. DTle second law. —Let us examine this law by means of the diagram, Fig. 29. If a ball be thrllown suddenly from the point A, horizontally, it would go to the point B, if it could be let alone by other forces. So likewise if it be dropped from A, gravitation alone will carry it to C. Now, these separate effects of the two forces will be exactly produced when the forces act together. Suppose the ball to go from A to B in one NATURAL PHILOSOPHY. 83 minute, and, when dropped, to fall from A to C in the same time. Now, while the ball is moving toward B, gravitation is pulling it downward, and at the end of the minute it will be found at D, having moved to the right, a distance exactly equal to A B, and downward Fig. 29. C' through a distance exactly equal to A C; so that the force of gravitation produces the same effect, whether it act upon the ball resting at A or in motion toward B. 3. TDe third! law.-If a table be struck, the hand that strikes it receives a blow as well. The hand acts upon the table; the table reacts upon the hand. Attend, now, to the following experiment. Two ivory balls are suspended by Fig. 30. cords, and hang in con-, tact against a graduated arc. When the ball, B, is lifted up the are to D, and then allowed to swing against the other, it strikes it c and instantly stops, H I while the other ball takes up its motion, 1 and goes to the point C. The first ball acts upon the 84 NATURAL PHILOSOPHY. second; the second reacts upon the first. Now, if we notice that the motion from D to B, which is stopped by the reaction of the second ball, is just equal to the motion from A to C, which is caused by the action of the first, it becomes evident that the two forces must be equal, and exerted in opposite directions. It follows from this principle that, when two bodies come in contact, each one gives and receives an equal shock. The hand which strikes the table is itself bruised, and the bullet which shatters the bone, is itself battered and torn. (22.) The velocity of a moving body will be uniform if it be produced by an impulsive force and opposed by no resistances. The elements of motion are tim.e, space, and velocity. In uniform motion, the space is equal to the product of time multiplied by velocity. 1. Velocity.-Velocity, in a popular sense, is simply rapidity of motion, but if the term is to be of any scientific value it must be more definitely applied. Velocity is the distance passed over by a body in a,uniit of time. The velocity of a cannon ball, for example, may be 2,000 ft. a second: that of a train of cars may be 30 miles an hour. 2. Unriformn velocity.-In uniform velocity, a body moves over equal spaces in equal times. If, for instance, in each of three successive hours, a steamboat travels 15 miles, its velocity is uniform. 3. An impulsive force. —An impulsive force is one which, after acting for a time, ceases. The stroke of a bat, which knocks the ball, is an impulsive force; so are the blows of a hammer. No matter how NATURAL PHILOSOPHY. 85 long a force may have been acting, if it be suddenly withdrawn, it is at that moment an impulsive force. 4. Unioarm motion produced by acn inzpuZse. —If a body can be free from all forces but the impulse which gives it Inotion, its velocity will be uniform. This seldom occurs. I-ow rarely do we see a uniform motion produced by an impulse, either in nature or in art! It is because all bodies are under the influence of several forces at once, such as gravitation, friction, and the resistance of air, by which their velocities are changed. The motion of the earth on its axis is, however, a sublime example of uniform motion. In the arts, a uniform motion can be secured only by the constant application of power. The impulse which starts a train of cars, would make it move uniformly if it did not meet with resistances: to overcome these, a constant pressure of the steam must be applied. If this pressure be, at all times, just equal to the purpose, the motion of the train will be uniform. 5. Space equaas time multiplied by velocity.-It is evident that a train of cars, going uniformly at the rate of 25 miles an hour, will, in ten hours, go 250 miles: 250- 25 x 10, or the space is equal to the product of the two other elements, time and velocity. We may express this principle by the simple equationS — T x V: in which S stands for Space. T " " Time. V" " Velocity. Now, if any two of these elements are given, the third may be found by sustitutitng given values for 86 NATURAL PHILOSOPHY. the letters, ancd tken performing kthe operations indcicated. For example, what is the velocity of a bullet which goes 2,000 ft. in 20 seconds, supposing its velocity uniform? The value of S is 2,000 ft.; the value of T is 20 seconds. Putting these values in the equation, it becomes 2,000 - 20 x V. Hence V = 100. (23.) The motion of a body produced by the action of a constant force alone, will be uniformly accelerated. The difficulties in the way of any accurate experiment upon uniformly accelerated motion are overcome by Atwood's machine. i. A constant force.-By a constant force we mean a force which acts upon a moving body all the time alike. The force of gravitation is the most perfect examnple of a constant force. 2. Ul,.form/nly acceelerated Notion,.-The motion of a body is uniformly accelerated, when its velocity increases equally in successive units of time; as, for example: 5 ft. the first second, 8 ft. the next second, 1 ft. the third second, 14 ft. the fourth, and so on. The motion of a falling body is the most perfect example: cf lumitforly accelerated motion. It would be a perfect example were it not for the resistance of the air. 3. D "',eZ iti-s it t/tc wtcy of experiment.-Three difficlti Ds re in the way of accurate experiments upon the 1motion of a b)ody falling. 1st. It is so rapid that no accurate observations can be made. 2d. It is subject to the resistance of air, which reducesits velocity. 3d. The frictioi of any apparatus used is likely to impede it. ficulties~ ( a re, for' Ii __lt',,,~ AanParefat-, H Hi~i!] /l t tI t whichpasse over a groo~ve wheel, H' a; 1-!&Kl! li ID. Ech ed of H the ax~~~~tis ofths,,' ItI!'I I''Ii'' cicufeenes of r Y l H The standard L, is'! 1<~ iiI graduated upon t tHH'' Ii,,, H,' ~ it~ ~ ~~~~~~~~1 is a; mobl I t l II~l11ll[/ I/H'i~ ring,~ ~ ~ ~ ~~~, C, whc al j/llHi lows~~~~~~~~~~~~~, the,, weoh[ A to pass I''"i~~ttF H,~ I" tliro~~~~~~~~~~~~~~~~igh H I~~~~~~~~~~~~~~~i low, which rrests i'K IHH themtion)f the'l F1 weigh at ay deo- I'~(IHA sired point mh HItH[' ti' )'''li time~~~~~~~~~~~ of, motio i F, Hi I'vt'~,i~ measnred~~~~~~~~~~~~~~~~~1 by th ____ ___ "'HK)It pendulum~~~~~~~~~ F. _ ___ 88 NATURIAL PHILOSOPHY. Thetwo weights A and B are made exactly equal, and, of course, when left to themselves, will remain at rest. But if a small bar of brass be laid upon the weight A, motion takes place, due entirely to the action of gravitation upon the bar. Now, suppose the large weights each to be 31-~ oz., and the weight of the small bar to be 1 oz. When they all move, 64 oz. are in motion, caused by the force which acts upon the 1 oz. bar. It is evident that 64 oz. will move only m- as fast as 1 oz., with the same force. The motion of the weights is produced by a constant force, gravitation; but it is only A- as rapid as when the bodies fall freely. A slow motion is thus obtained. The resistance of the air against the small surfaces of the ends of the heavy weights, is very slight when they move slowly; the friction of the wheels at the top is trifling, and thus the three difficulties in the way of experiment are overcome. (24.) By experiments with Atwood's machine we may prove: 1st. That a body moving under the influence of gravitation during any interval of time, will gain a velocity which, acting alone, will carry the body twice as far in the next equal interval. 2d. That gravitation will add to the motion of a body just as much in every interval of time as it produced in the first. By the help of these principles we may analyze the motion of a falling body. From the diagram which represents this analysis, we may construct a table which shall contain the values of time, space, and velocity; and fromn this table obtain the laws which govern the NATURAL PHILOSOPHY. 89 motion, and the formulas by which problems may be solved. (See Cooke's Chem. Phys., p. 23.) 1. Proof of the first principle.-Let the weight A, carrying the small bar, be brought to the top of the graduated standard. Suppose that, in one second after its release, it falls to the ring 0, a distance of 3 inches. The small bar will be caught off by the ring; the weight A will pass through, and in the next second it will be found to go exactly 6 inches. By putting the ring at different places on the standard, it will be found that, in every case, as in the one just described, the body moving under the influence of gravitation during any interval of time, will gain a velocity which, alone, will carry the body twice as far in the next equal interval. 2. Proof of the second princciple. —If the weight and bar fall 3 inches in one second, they will be found to fall 12 inches in two seconds. The distance fallen in the second interval is 9 inches. If the bar were taken off at the end of the first second, the weight would go alone, 6 inches in the next. It is clear, then, that the bar acting in the last second adds a motion of 3 inches, the same amount as it produced in the first. Repeated experiments show that gravitation will add to the motion of a falling body jutst as mzuch in each second as it produced in the first. 3. Analysis of the motion of a falling body. —Now suppose a body to fall from the point A (Fig. 32), to, ward the point D. In the first second it will fall a certain distance, which we will represent by A B. For a moment suppose the force of gravity should cease to act, the body would still move on, and we know (by the first principle), that it would go in the next 90 sNATURAL PHILOSOPHY. second, just twice as far as it did in the first. Then mark below B, two spaces, each equal to A B, to represent this distance, and mark it with a heavy line, that the eye may see at a glance, that it is the distance due to velocity alone. But we know (by the second Fig. 82. principle) that gravitation in this second will add a space just equal to A B. MIarking this A space in the figure, we find that in two seconds the body will fall to C. _..| In two seconds the body has fallen 4 spaces, in the neat two seconds it will go twice as far, 8 spaces, by velocity alone. In the first of these two seconds, which is the tlird second of its fall, the body will go 4 spaces by velocity. The force of gravity adds another space, so that at the end of 3 seconds the body will be found at D. To find the distance passed in the 4th second, notice that in the first 3 seconds it has passed 9 spaces; that in the next 3 seconds it will go, by its velocity alone, 18 spaces, and that in onle of these 3 seconds, which would be the 4th second, it would go 6 spaces. Mark 6 spaces for velocity, and add one for the action of gravitation. 4. Constmcetion of th/e table.-Now, in this diagram the values of time, T. s. v. s. space and velocity stand clearly before us, and we 1 I 29 lg may put them in a tabular 2 49 4g 3S form. In the first column, 3 9 6g 5g I 16g sg 7g.D i._headed T, put the number of seconds, 1, 2, 3, 4. In the second column, NATURAL PHILOSOPHY. 91 headed S, put the total space passed over at the end of these seconds, representing the distance A B by g. In the third column, headed V, put the velocities gained at the end of eachl of the seconds. And, finally, in the fourth column, headed s, put the spaces passed in each separate second. 5. From the table obtain the laws.-The relation between time, space, and velocity, may be seen by comparing their values given in this table. ]Notice, first, that the values of S have the same ratio as the squares of the value of T. For instance, take the spaces 4g and 9g with the corresponding times 2 and 3, we find that 4g: 9:: 22: 32. Hence, the spaces passed by a f alling body rin different times are as the squares of the times. Notice, second, that the values of V have the same ratio as the values of T. Thus we find that the velocities, 4g and 6g, have the same ratio as 2 and 3, the corresponding values of time. Hence, the velocities of afalliny body at the end of successive intervals of time will vary as the time of fall. Notice, third, that the spaces _passedc in separate seconds (the values of s) are as the odd, numbers, 1, 3, 5, 7, &c. 6). Fr'omn the table also obtain the formulas. —It will be seen that by squaring any one of the values of T in the table, and then multiplying by g, the corresponding value of S will be obtained. IHence, S -= T2 (1). Again, we may discover that if the value of T in any case be multiplied by 2y the corresponding value of V will be produced. Hence, V = 2gT (2). 92 NATURAL PHILOSOPHY. V e see, again, that if the value of S in any case be multiplied by g, the square root of this product multiplied by 2, gives the value of V. Henee, V - 2 VSgq (3). Finally, a little attention will show, that if the value of T in any case be multiplied by 2, the product diminished by 1, and the remainder multiplied by g, the corresponding value of s will be obtained. Hence, = (2T - 1) g (4). 7. By theseformulas solve problems.-By the use of these four formulas all problems in uniformly accelerated motion may be solved. In all cases, g represents the distance passed by the body in the first interval of time. Its value will be different for different forces. When gravitation is the constant force which causes the motion, the value of g is 16112 feet. A single illustration will show how the formulas mnay be used. If a stone be dropped into a well whose mouth is 1444 ft. above the water, how long will it take to reach the water? Since gravitation produces this motion, the value of g is 161 ft. The 1444 ft. is the value of S, and the value of T is required. The relation between these elements is expressed by the formula S - T2g, and by substituting the given values we have 1444 = T' x 16X-N. The value of T, from this equation is 3 seconds. PROBLEMS ILLUSTRATING THE LAWS OF MOTION WHEN PRODUCED BY A SINGLE FORCE. 1. A body moves uniformly over a distance of 780 feet with a velocity or 5 feet a second: in what time did it go? Ans. 156 sec. NATURAL PHILOSOPHY. 93 2. Under the influence of an impulsive force, a body moves at the rate of 25 feet a second: how far will it go in one minute? 3. A stone dropped from the top of a tower, struck the ground in 4 seconds: how high is the tower? Ans. 2U57s feet. 4. If the tower were 257~ feet high, with what velocity would a stone strike the ground? Ans. 128] feet. 5. If the velocity of the stone should be 128}- feet a second; how long a time had it been falling Ans. 4 sec. 6. A body falls 4 seconds: how far does it go in the fourth second? Anvs. 1121-z feet. 7. Under the influence of a constant force, a body moves 3 feet the first second: how far will it go in 5 seconds? Ans. 75 feet. 8. A body is falling toward the earth; it is at the same time moving horizontally under the influence of a constant force which made it go 10 feet in the first second: how far, horizontally, did it go in 8 seconds? [See (21.) 2.] Ans. 640 feet. 9. How far did it fall in the same time? Ans. 1,029- feet. 10. With what velocity did it strike the ground? Ans. 257~ feet. 11. What velocity did it gain in a horizontal direction Ans. 160 feet. 12. How far did it go horizontally in the 5th second? Ans. 90 feet. 13. How far did it fall in the 5th second? Arns. 144-1 feet. 14. Under the influence of a constant force, a body 94 NATURAL PHILOSOPHY. goes 12 feet in the first 3 seconds; how far does it go in 18 seconds? An8. 432 ft. 15. A ball is thrown directly upward, starting with a velocity of 96 feet, to what height will it rise? Ans. 1444: ft. The motion of this ball thrown upward, will be retarc7ed by gravitation, in exactly the same ratio that it is accelercated in falling to the ground again. The height to which it rises is the same as that from which it falls. This problem may be solved exactly as if the question were: from what height would the ball fall to gain a velocity of 96~ feet a second? 16. A ball is shot upward with a velocity of 386 feet: how long will it continue to rise? Ans. 12 sec. 17. I-low high does it go? Ans. 2,316 ft. 18. 1H-ow long does it remain in the air? Ans. 24 sec. 19. How far does it rise in the last second of its ascent? Ans. 16-1 ft. 20. ITow far does it fall in the last second of its descent? Ans. 369-1 ft. 21. Suppose the large weights of Atwood's machine to be each 31~- oz., and the weight of the slnall bar to be 1 oz. We find, by experiment, that the weight and bar go 3 inches in the first second: what is the force of gravity, or, in other words, how far would gravitation cause a body moving freely to fall in one second? In this case, the whole weight moved by the force of gravitation on the bar, is 31~+31~+1 —164oz. It is clear that 64 oz. will move only ~ as far in one second as 1 oz. moved by the same force freely. Hence, 3 x 64=192 inches, would be the distance the bar NATURAL PHILOSOPHY. 95 would fall freely in one second. This distance is equal to 16 ft. When the experiment is accurate, at -the level of the sea, it is found to be 16 - ft. ~ 2. MOTION PRODUCED BY MORE THAN ONE FORCE. (25.) If a body be acted upon by two forces which, separately, would cause it to describe the adjacent sides of a parallelogram, they will be equivalent to a single force, causing it to move through the diagonal of the parallelogram. Hence the effect of two forces may be found by representing them by the two sides of a parallelogram, and then drawing the diagonal. 1. If ca body be acted on by two forces.-Forces seldom act singly. It is by the combined action of at least two, often of more, that almost every motion is produced. The action of two forces may be illustrated by a very simple experiment. Place a ball at one corner of the table. Snap it with the fingers, lengthwise of the table, and it will roll along the side; or snap it across the table, and it will roll across the end. But skillfully snap it both ways at the same time, using both hands for the purpose, and it will roll in neither of these directions, but will move obliquely -across the table. The same thing is true of the action of natural forces, such as wind and tide. A ship, driven south by a direct wind, may at the same time be drifted east by a tide moving eastward. If so, it will, at every moment, be moving south and east, or in a straight line toward the southeast. 2. Acting alonvy th.e adjacent sides of a parallelo 90 NATURAL PHILOSOPHY. gram.-The conditions of the motion of both the ball and the ship may be represented to the eye. Let A, Fig. 33, represent the original place of the ball or the ship. Suppose that while one force, if acting alone, would move the body to B, the other, if acting alone, would move it to D, in the same time; then Fig. 33. when both act at once, the body:B —-- va 8 —;7 will neither go to B nor D, but will go along the diagonal line A C, and will reach the point C in the same time it would have taken A S D to go to either B or D. 3. They are equivalent to a single force. —The two forces, acting in the directions A B and A D, produce a single motion along the line A C. A single force acting in the direction of A C would have produced the same effect. Hence two forces, acting in directions of the sides of the parallelogram, are equivalent to a single force acting in the direction of the diagonal. The separate forces are called components; the single force which would produce the same effect, is called the resultant, and the process of finding the resultant is called the composition of forces. 4. Thie resultant of forces may be found. — The resultant of two forces may be found by representing them by two adjacent sides of a parallelogram and then drawing the diagonal. The lengths of the lines represent the strength, or the intensity of the forces. In the case of the ship, for instance: suppose the wind able to drive it 10 miles, while the tide can drift it 5 miles. To find the actual path of the ship, draw the line A B, Fig. 33, to represent the 10 miles, and then NATURAL PHILOSOPHY. 97 the line A D, at right angles to it, and one hacf as lony, to represent thle 5 miles. Draw the lines B C and C D, to complete the parallelogram, and then draw the diagonal A C. This line represents the resultant of the two forces. If more than two forces act at once, the resultant of all may be found by repeating the process. Find the resultant of two of them first; then compare this resultant and a third force; this second resultant and a fourth force; and so continue until all the forces have been used; the last resultant will be the resultant of all the forces. (26.) Any force may be resolved into two others, which, acting together, would produce the same effect. This is done when we wish to know what part of a given force can be made available in a direction different froIn that in which it is exerted. 1. A force may be resolved.-To find the components of a given force, we may represent it by a line, and make this line the diagonal of a parallelogram; the adjacent sides of this parallelogram will represent the components. More than one parallelogram can be drawn on the same diagonal; so more than one set of components may be found for a single force. The process of finding the components of a single force, is called the resolution of forces. 2. To ind the component which acts in a give~n direction.-When a ball is thrown obliquely against the floor, it acts upon it with less force than when thrown perpendicularly against it. But a part of the force will still be exerted perpendicularly to the floor. To illustrate this important point, let a ball A, (Fig. 5 98 NATURAL PHILOSOPHY. 34), be thrown against the floor, striking it at C. We may let the line A C represent the force with which the ball is thrown. Now construct the parallelogram, by drawing the lines A B and C D perpendicular to the floor, and then A D parallel to it. The lines A B Fig. 34. and A D represent........ the components of the force A C. The line A B represents the amount of force exerted perpendicuclarly to the floor. To make the illustration more specific, we will suppose that, measuring the lines A C and A B, we find the latter to be 3 as long as the former; if so, then the force exerted perpendicularly to the floor, will be 3 of the force with which the ball is thrown. To find the component which acts in any given direction, we may represent the original force by a straight line, and make it the diagonal of a parallelogram, one of whose adjacent sides is in the direction given. This side will represent the force required. (27.) Two forces may act upon different points of a body inll the same direction: their resultant will be equal to their sum. The point of the body to which this resultant is applied, will be as many times nearer to the greater force than the smaller one, as the greater exceeds the smaller in intensity. The weight of a body is only the resultant of a set of parallel forces acting upon it in the same direction: and NATURAL PHILOSOPHY. 99 what is called the center of gravity, is its point of application. 1. Two forces in, the same direction. —When two forces act upon a body in the same direction, they produce the same effect as a single force equal to their sum. If two horses, for example, draw a carriage, one with a force of 200 lbs., and the other with a force of 300 lbs., it is clear that a single horse, exerting a force of 500 lbs., would produce the same effect. 2. The point of appl,)icction.-But if a single force is to take the place of two others, and produce exactly the same motion as they would when acting together, at what point of the body shall it be applied? Suppose the body represented by A B (Fig. 35), to be acted upon by two forces, represented by the lines Fig D B c and d, one just half the length of the other, the less- < er force being 25 lbs., the Id greater, 50 lbs. Then the line r, just as long as both together, will represent the resultant, a force of 75 lbs. Now, if this resultant is to move A B, exactly as the two components would, it must be applied at some point, D, as many times farther from A than from 3, as the force at A is times less than that at B. Since c is just half of d, the distance A D must be just twice as great as B ID. 3. The weigiht f a bocly.-A body falling freely, is an example of motion caused by the action of parallel components. For, since the force of gravitation acts 100 NATURAL PHILOSOPHY. upon every molecule of the body, we may regard the entire force as made up of as many separate forces as there are molecules. The sum of all these components is their resultant, and the value of this resultant is the wei/yht of the body. 4. Thie center of gravity.-The point of application of this resultant, is the center of gravity. The center of gravity is usually defined to be-that point in a body whicd, j? supportecl, the body will rest in any poosition. One can balance a book on the tip of his finger: the tip of the finger must be exactly under the center of gravity of the book. This point being supported, the whole body will rest. The center of gravity is the exact middle point of a body of uniform density; it is toward the heavier side of one that is not. (See Silliman's Physics, pp. 39 to 4a5.) A vertical line drawn through the center of gravity is called the line of direction, because it shows the direction a body will take when allowed to fall. That a body may stand upon a plane surface without falling, the line of direction must pass through its base. One body stands more firmly than another, only because it is more difficult to throw its line of direction beyond its base. A load of hay is easily overturned, because, the center of gravity being high, the line of direction may be easily thrown outside the base. A load of stone, having no greater weight, stands firm, because, the center of gravity being low, the line of direction can with difficulty be thrown beyond its base. Animals instinctively incline their bodies always in such way as to keep their center of gravity over the space between their feet. Especially is this true of man. NATURAL PHILOSOPHY. 101 A body is tottering in proportion as it has great height and a narrow base; but it is the prerogative of man to be able to support his commanding figure, erect and firm, under constant changes of position, over the very narrow base occupied by his feet. (28.) Curved motion is produced by the action of at least two forces, one of which is a constant force, the other may not be. The motion of a projectile is caused by the constant force of gravitation, and the impulse by which it is thrown. 1. Curved motion. -Whoever watches the varied and beautiful motions in nature, will find that they all take place in curves. In the ripples of the lake and the billows of the sea, he will see a wonderful variety of curved motions. The winds, and the clouds they carry, move in curves. Every swaying branch and leaf, and every nodding stalk of grass, moves in a curve. 2. Is producced by at least too forces.-The motion of a ball when fastened to the end of a string and whirled around the hand, is an example of curved motion. It is produced by the action of two forces. The impulse of the hand II (Fig. 36), Fig. 86. which starts the ball, wouldl, if it T could act alone, carry it in a straight line from A toward B. But the string HI A, held firmly by the A_ _ _d hand, is a constant force whlich pulls it away from that path. The resultant of these two forces is. D represented by the circumf'erence A B C D. 102 NATURAL PHILOSOPHY. 3. One qof w/ich is constant.-In the example just given, the force of the hand is an impulsive force; that of the string a constant force, and a curved motion is the result. Two impulsive forces will cause motion in a straight line; two egual constant forces will do the same. Two constant forces that are unequal will cause a curved motion; one, at least, of the forces must be constant. The two forces which cause curved motion are called central forces. One of them alone, acting upon the ball at B (Fig. 36), would carry it along the line B F, or if the ball has reached C, would move it toward tK. The influence of this component is to move the ball in a line which is tangent to the circle in which it revolves. This force is called the cerntrrifcyalforce. The other component, which prevents the ball from moving in a straight line from the center of motion, is called the centripetal force. A simple and pleasant experiment may be performed to illustrate the effect of centrifugal force. To the handle of a small pail, filled with water, tie a cord firmly. Grasp the cord and swing the pail, fearlessly, in a vertical circle over the head; the centrifugal force will overcome the force of gravity, so that not a drop of water will fall, even when the pail is bottom side up over the head. Circus riders incline their bodies toward the center of the ring around which they ride, that the centrifugal force may not throw them from their horses. Carriages, in rapid motion around the corner of a street, are sometimes overturned by this force. But the most wonderful examples of the action of central forces, are seen in the majestic movements of the heavenly bodies. Their orbits are ellipses. The impulse which drives the NATURAL PHILOSOPHY. 103 planets forward is the centrifugal force, while the centripetal force is the attraction of the sun, which holds them in their orbits. 4. Pr'ojectiles.-Any body thrown into the air is a projectile. The stone from the hand, the ball from the gun, and the arrow from the bow, are familiar examples of projectiles. 5. T/Cheair otion is due to two forces. - Leaving resistance of the ail out of account, the motion of a projectile is due to the action of, 1st. The izpulse, which starts it on its journey; and, 2d, the constant force of gravity. Let us suppose a cannon ball, shot from the point a (Fig. 37), to go in the direction a b. At the end of the first second, the impulse giv- Fig. 8T. en by the gunpowder would have thrown the ball to some point, as that marked I. But gravitation will, at the I/ same time, be pulling the ball toward the ground. Represent the effect of this i.r< force in the first second by I d | the line a I'. The result- ant of these two forces will carry the ball to the point e. m During the next second, the impulse acting upon the ball at e, would carry it to s, just as far as it would in the first, but gravitation would, in the same time, move it downward to d; the resultant of these two forces will carry the ball to f. In the third second, the impulse would throw the ball from f 104 NATURAL PHILOSOPHY. to m,; but gravitation would pull it down to n, theii joint action would carry it to g. Now, let us remember that gravitation acts, not only at the beginning of each second, as the figure repre sents it, but also at every other instant, so that the path of the ball will bend, not at the points e, f, and g alone, but at every point between these, thus forming a curve reaching the ground at I. The horizontal distance, a h, is called the range or the randorm of the projectile. This distance depends upon the force applied to the projectile, and the angle at which it is thrown. Theory requires that the random be greatest when the projectile is thrown at an angle of 45~; but the resistance of the air very much modifies the motion, so that, in practice, the greatest range is obtained at an angle much below 45~. The greatest range of an arrow is when the angle is about 36~. The science of gunnnery rests upon the laws of projectiles. The most skillful gunner is he who can most accurately, under all circumstances, compare and combine the forces of gunpowder, gravitation, and the resistance of the air. ~ 3. THE INDESTRUCTrBILrTY OF FORCE. (29.) Force, like matter, is indestructible. Whatever force has acted to put a body in motion, the same amount must be exerted by the moving body upon others, before it can come to rest. Three well-mlarked cases are before us: 1st. In whlich a body moves without resistance firom other bodies; NATURAL PHILOSOPHY. 105 2d. In which a body, moved by an impulsive force, meets with resistance; 3d. In which a constant force is applied to overcome the resistance. 1. Force is indestructible.-It was once thought that bodies of matter could be destroyed. It seems so yet to a careless observer; but when he has learned how to search for their scattered fragments, he finds that every atom still exists. Forces likewise vanish; but when the motions they produce have been changed to rest, and after every trace of their action seems to have been lost, they have been chased fromn their hidingplaces, until it is proved that every impulse still acts — that while it may change froml form to form, and show itself in a multitude of ways, yet not a single impulse of force can be destroyed. 2. ifotion can not cease without exerting the same amount of force which produced it.-The force of gunpowder is expended in giving motion to a ball: the ball exerts the same force upon whatever obstacles it meets. A small force will give slow motion; the body moving slowly, will, on meeting an obstacle, exert the same small force. A greater force will give a swifter motion; the body moving swiftly will strike another with the same greater force. Thus a bullet may simply bruise an arm, or it may pierce a tree, or shatter a block of the hardest stone, according to the velocity with which it strikes; and the velocity will, in turn, depend upon the force w hicl puts the ball in motion. 3. Suppose a Iody move withoutt resistance.-If a body should move without any resistance to its 106 NATURAL PHILOSOPHY. motion, until it suddenly strikes an obstacle, the force with which it would strike, would be exactly equal to that which gave it motion. If a force of tenll pounds puts a body in miotion, it rwould hit the other with a ten-pound force. The force which a body moving without resistance can exert upon an obstacle is called its monaentum. Suppose a body, weighing 1 lb., move with a velocity of 1 ft. a second. If it meet with no resistancte, it will strike another body Mwith a certain force, or momlentum, which we will call 1. The momentumn of a 2 lb. weight, Fwith the same velocity, would be twice as great; it would be 2. A weight of 1 lb. moving twice as fast, would also have twice the momentum of the first; it would be 2. A weight of 3 lbs., would have a momentum of 3, and then, if its velocity be doubled, it would, on that account, have twice as much momentum; it would be 6. The momentum of a moving body is thus seen to vary with its weight and its velocity, and we find that the momentum of a bocdy is equal to the prod-,uct of its weight multiplied by its velocity. 4. Suppose emotion due to an impulse meet with resistances.-When a moving body meets with the resistance of air, of friction, or of any other influence, before it strikes another, the force which started it will be exerted, partly upon this resistance, and partly upon the object which it finally strikes; but the su8m of these two _parts will exactly equal the force which set the body moving. Thus a stone thrown from the hand will strike a tree at a distance with much less force than it receives, but in its motion it has been compelled to move the air before it, and if the force which it exerts in this way, be added to that w-hich it exerts on the NATURAL PHILOSOPH Y. 07 tree, the aggregate will be just equal to that which the hand exerted upon the stone at first. So, if a ball be rolled upon the ground, its force must act upon the air in front of it, and upon the roughness of the ground under it: all its force is thus used, and it stops; but the total amount gradually expended in this way, must just equal the sudden impulse which started the ball upon its journey. 5. SuppOSe a constant force applied to overcome resistctnces.-When a constant force is applied to keep the body moving uniformly, in spite of resistances, the force with which it strikes an obstacle must be equal to that which acts to keep it moving. Thus, if a train of cars, kept in motion at the rate of 20 miles an hour, suddenly strike another train going with equal velocity in the opposite direction, the entire force of steam, expended to keep up the motion of both trains, will be suddenly exerted to dash them both to pieces. This force, which a body, moving against resistances with a uniform motion kept up by a constant force, will exert upon an obstacle, is called tiving force, or vis viva. Now, if the velocity of a body be doubled, the force required to keep it uniform will be four times as great. Take the case of a ship moving through water. If the velocity of the ship be doubled, twice as much water will have to be moved in the same time; it will take a double force to do this. Moreover, every particle of water will have to be moved twice as fast; it will take a double force to do this also. To do both these things at the same time, the force must be twice doubled, or made four times as great. This is true of all resistances, and for all velocities. In other words, the force 108 NATURAL PHILOSOPHY. required to keep a body moving against resistances, will be in proportion to the spquare of tihe velocity. But when, under such circumlstances, the moving body strikes an obstacle, the force which keeps it moving, must be suddenly exerted upon the body struck. It thus appears that the livingyforce of a body is in proportion to the square of its velocity. It is equal to the product of the weight multitplied by the square of the velocity. ~ 4. oF MACHINERY. (30.) The principle of momentum applied to any one of the simple machines, will determine its law of equilibrium. 1. The principle of momentlum. —Momentum has been defined to be the force which a moving body, meeting no resistances, can exert. Now, two bodies exerting equal forces upon each other in opposite directions, will, when at rest, just balance each other, or be in equilibrium. This principle is called the principle of momentum. It states briefly that two fobrces, in opposite directions, will be in equilibrium when their momenta are equal. Let us illustrate a single case by means of Fig. 38. Fig.'3.. Suppose two bodies, M and A. c N, hang from the ends of a A<~ ~ bar, A 13, which rests upon the point C, about which it r may freely turn. If it does turn, and MA goes up, N will go down, and if the distance B C is twice the distance A C, then N will go twice as fast as M. In all cases, the velocities of the two NATURAL PHILOSOPHY. 1009 bodies will have the same ratio as their distances, A 1) and B C, from the center of motion. i/Tese lines may ther be taken to represent velocities. Then the momentum of S will be M x A C, and that of TN will be iN x B C. Now if these momenta are equal, then the two bodies will be exerting equal forces upon the bar A B, and if once brought to rest, they will just balance each other. 2. iiachines. —Machines are instruments by which forces may be applied to overcome resistance, or do work. They are so made that a small force, by moving rapidly, may overcome a greater resistance, or a great force, by moving slowly, may put a small resistance in rapid motion. In all cases the momenta of the two forces must be equal. The resistance to be overcome is always called the weight: the force which overcomes it is called the power. 3. Sirplne machines. There are six simple forms of machines, usually called the mechanical powers. Out of these six simple machines all forms of machinery, complex as they may be, are made. We name them in the order which is to be followed in describing them. 1. The Lever. 4. The Inclined Plane. 2. The Wheel and Axle. 5. The Wedge. 3. The Pulley. 6. The Screw. 4. 7'e lIw of equilibrium. —By the term, law of equilibriunm, is meant a statement of the relation which must exist between the power and the weight, in order that, when at rest, they may just balance each other. (31.) Levers are of three classes. The principle of momentum applied to the ]ever, shows that the power 110 NATURAL PEIILOSOPH Y. and weight will be in equilibrium when they are to each Fig. 39. other inversely as the B' A perpendicular distances _...., from the fulcrum to the directions in which they act. A compound lever acts on the same principle. Applications of the lever are very numerous. i. levers.-A lever is an inflexible bar, able to turn freely upon one point. Thus, if the line A B (Fig. 39) represents an inflexible bar, resting upon soine support at F, upon which trig. 40. it hasfreemotion, A ~ B it represents a A lever. The point, F, aboutn which W the lever turns, P is called thefaicr'umn. 2.'hree classes of levers.-That point of a lever to Fig. 41. which the power is applied, is called X the _point of algpIication,. That on which the weight B acts is called the woriking point. N Now, the lever takes different names according to %'A/d the relative positions of the point of application, the working point, and the fulcrum. In the lever represented in Fig. 40, whose fulcrum is at I' a power (P) acts upon one XNATURAL P HILOSOPHY. 111 end of the lever (A) while a weight (W) acts upon the other (B). Thle fulcrum is between tile point of Fig. 42. Fig. 43. B F A W2w application and the working point. This is called a lever of the first claCs. Fig. 44. In the lever, Fig. 41, the wvorkirig point 13, is between the point of application A, and the fulcrum E. This is a lever of the second class. 112 NATURAL PIIILOSOPIYT. In the lever, Fig. 42, the point of application (A) is between the working point (B) and the fulcrum, F. This is a lever of the thirdc class. All levers belong to these three classes. They need not, however, be made in the simple straight form shown by the figures. In Fig. 43, the line A F B represents a lever whose arms make a right angle at the fulcrumn, F. It is a lever of the first class; so also is that shown in Fig. 41, by the curved line A F B. 3. Application of the principle of momenta. —Now if we examine the figures which represent the three classes of lever, we see that in each one, the power (P) and the weight (W) are two forces which act in opposite directions. They will be able to just balance each other, when of such strength that, when moving, their nmomenta are equal. The lines B F and A F represent their velocities [see (30.) 1]. The momentumn of the poweris therefore P x A F; that of the weight isW x B F. If equilibrium takes place only when the momenta are equal, then PxA F -WxB 3 F; hence, P: W:: BF: AF. This proportion teaches us that the power and weight will be in equilibrium, when they are to each other inversely as the distance of their points of application from the fulcrum. It may be, however, that the power and weight do not act perpendicularly upon the lever. This case is represented by Fig. 44. The lever A B has its fulcrum at F. The power (P) and the weight (W) act obliquely at B and A. Now it is evident tllhat the force of the power, acting obliquely at B, is not all expended to lower the lever [see (2(3.) 2], but that if it NATURAL PHILOSOPHY. 113 were acting upon the point N, perpendicularly, it would exert all its force to move the arm N F. So the effect of the weight acting obliquely upon A, will be the same as if it were acting perpendicularly upon an arm, 3I F. I-ience, P x N F may be taken as the momentum of the power, and W x M F as the momentum of the weight. Putting these momenta equal, P x N F:W x A F; hence, P: W::M F: N F. This proportion teaches that the power and weight will be in equdibrit-m, whienr th/e power and weig7t are rinversely as the perpendiczlar distances from the /fulcrum to the directions in whichL they act. This principle is called the law of equilibrium for the lever. It will apply to all possible forms. 4. l'he compound lever. —In a compound lever several simple levers are generally so fixed, that the short arm of one may act upon the long arm of another. Fig. 45 shows a compound Fig. 45. lever made up of two simple A'c levers having their fulcrums at F, and F'. B..!.... F In this case the momentum of the power will be equal to PxC FxB F', and that of the weight will be equal to W x D F' x A F. If these products are put into the form of an equation it will be seen that the power and weight will be in equilibrium when the power multiplied by the prodnet of all the arms on its side of the fulcrum, is equal to the weigllt multiplied by the product of all the arms on its side. The compound lever is used when a small force is required to sustain a large weight, and it is not conve 114 NATURAL PHILOSOPHY. nient to have a very long lever. If the long arms of the simple lever be 6 and S ft., and each short arm is 1 ft., then 1 lb. power at C, will balance 48 lbs. at D; while if a simple lever had been used whose long arm was as long as those two long ones together, 6 + 8 -14 ft., and whose short arm was 1 ft., then 1 lb. at C, would only be enoulgh to balance 14lbs. at D. 5. Applications of the lever.-Of levers of the first kind many familiar examples might be named. The handspike and crow-bar are levers of this class. Shears and pincers are pairs of levers, also of the first class; their fulcrums being at their joints. The bcalance is one of the most useful applications of the lever. Fig. 46 represents this instrument. Fig. 46. The beam ca b is a lever M poised at its centre, the a'- l? pivot or fulcrum c being a I little above its center of gravityS. From the ends of the beam the scale pans are hung, in one of which is put the body to be weighed, and in the other, the weights of metal to balance it. Balances are of continual use in commerce; they are indispensable in the laboratory Fig. 47. of the chemist, for whose use they are made with so great skill that a weight equal to the -U I of a grain can be easily weighed. The steelyard is also a lever of the first class, but with unequal arms. The body W, Fig. 47, to be weighed, is hung from the short arm of NATURAL PHILOSOPHY. 1ty the lever S B, and it is balanced by a small weight, P. It is clear that this small weight will balance more weight in the body AV, as it is moved farther and farther from the fulcrum C. The arm B C has notches cut upon it, and numbered, to denote the pounds or ounces in AV, balanced by P, when at these points. Levers of the second class are not so common; the whleelbarrow, however, is an example sufficiently famailiar. The axle of the wheel is the fulcrum, to the opposite ends of the handles the power is applied, while the load, or the weight, rests between these points. The oar of a boat is a lever of this kind, where, singularly enough, the unstable water serves as a fulcrum; the hand is the power at the other end of the lever, while the boat is the weight between them. Levers of the third class are often met with in the arts. The common fire-tongs and the sheep-shears are pairs of levers of this kind. Their fulcrums are at one end; the resistance to be overcome is put between their parts near the other end, while the fingers, which afford the power, are between the fulcrum and the weight. (32.) The wheel and axle acts on the principle of a lever. The power and weight will be in equilibrium when the power is to the weight as the radius of the axle is to the radius of the wheel. A compound wheel and axle acts on the same principle as a compound lever. One wheel may be made to turn another by friction, by cogs, or by bands. Applications of this machine are common and important. 116 NATURAL PHILOSOPHY. 1. T/he wheel and axle.-One form of the wheel and axle is shown in Fig. 48. It consists of a wheel (B) firmly fastened to an axle (A), and turning freely around an axis, one end of which is shown at C. The power (P) acts upon the circumferenee of the wheel, and the weight (W) acts upon the axle by means of a rope winding around it in the opposite direction. 2. It acts on the prirnciple of thle lever. —If we have an end view of the machine, it will be seen, as shown in Fig. 49, where thle large circle represents the wheel, and the small circle, the axle; the center C, being the end of the axis. At the point A, the power Fig. 49. Fig. 48. acts on the w-heel, and from the point B, on the other side of the center, the weight is suspended. Now, if a straight line A B join the points A and B, it will pass through the center, and represent a lever, whose fulcrum is at C. It is upon the ends of such a lever that the power and weight are constantly acting'. 3 A pplpicaion of the prinzcipes of momnentt2,n.The momentum of the power is P x A C; that of the weight is NV x B C. If the two forces are able to balance each other, these momenta are eclnal. Ienee, PxA C=WxBC: or, P: W:: BC: AC. NATURAL PHIL OSOPHY. 117 But, in the figlre, we notice that A C is the radius (of the whmeel, and tlhat B C is the radius of the axle, Then the proportion teaches us that the power acnd weigh7t will be in equilibrium when the power is to the weigti, s tMie radiu8s o the axle is to the radius of the wheel. If the radius of the axle is 1 ft., and that of the wheel 3 ft., then I lb will balance 3 lbs. 4. The compound wheel and axle.-Whern more than one wheel and axle are connected, so that the axle of each may act on the wheel of the next, the machine is a compound wheel and axle. Such an arrangement is shown in Fig. 50. We mayget the law of equilibrium in the samne way as in the Fig. 5. compound lever. The nmomentum of the power will C be P. multiplied by the sev- // eral radii of the wheels; that < of the weight will be W9,' mnultiplied by the several radii of the axles. If the two forces are able to balancec each other, these values must Pbe equal. Hence we learn, that in a compound wheel and axle, the power and weight will be in equilibrium, when the power multiplied by the product of the radii of the wheels, equals the weight multiplied by the product of the radii of the axles. It is easy to see that, in this way, a small power may be made to balance a muech larger weight than it could by acting upon a simple wheel and axle, unless the wheel should be so large as to be unwieldy. 118 NATURAL PHILOSOPHY. 5. One wheel may turn another by means of cos. — In Fig. 50, there may be seen projecting teeth on the circumferences of the axles, b and c, Twhich fit into equal nlotches on the circumferences of the wheels. Neithei the axles nor the wheels can turn without causing the other to turn also. This is the common and convenient method of giving motion from one wheel to another. The wheels of a clock are cog-wheels: those of a watch also beautifully illustrate this mode of communicating motion. 6. By frietion. —When the circumferences of the wheels and the axles are made smooth, they may be pressed so snugly together, that neither can turn without turning the other at the same time, in the opposite direction. In this case, the motion is communicated by the friction of the parts against each other. 7. By bands-A third method of giving motion to a train of wheel-work, consists in the use of bands or belts, which encircle the parts which are to act upon each other. In the spinning-wheel, for example, the spindle is turned by a band which passes around it and the axle of the wheel-head. Another band passes around the wheel-head and the large wheel, which is turned by the hand of the spinner. From the horse-power of a thrashing-machine, also, motion is given to the cylinder by means of a belt. 8. Al)pllications of the wheel and axle.-Many forms of the wheel and axle are in common use: the windlass is one of the most familiar, being often used to raise water from wells. One form of the windlass is represented in Fig. 48. A crank is often used in place of the wheel, B. The common grindstone is a homely illustration of the wheel and axle: the crank is in place of NATURAL PHILOSOPHY. 119 a wheel; the stone itself is the axle. The power is the force of the hand, while the weight is the resistance offered by the tool pressing onl the edge. of the stone. If the axle is in a vertical position, and the forces of power and weight act horizontally, the machine is then called a ccpstctn, and is much used on board of ships. The compound wheel and axle is used in almost every mill and factory. Two objects are sought in its use: either great resistance is to be overcome, or rapid motion is to be secured. To overcome great resistances, the power is applied to the circumference of the first wheel in the system, and the weight is acted upon by the last axle. This case is shown in Fig. 50. To secure rapid motion, the power is applied to the first axle, while the weight is acted upon by the circumference of the last wheel. The same figure illustrates this case also, if we will suppose the heavy body W, to act as a power to put the lighter body P, in motion. If we suppose the radius of each axle to be 1 ft., and of each wheel 10 ft., then P x 10 x 10 x 10=W x 1 x 1 x 1: or, 1,000 P=~W. Now, W being 1,000 times heavier than P, P must move 1,000 times faster than W. Iln this way, a great power may be changed into rapid motion. An example of this is found in the saw-mill where the slow motion of a heavy body of water, acting against a water-wheel, is given, by means of cogs and belts, from wheel to wheel, until it reappears, multiplied a thousandfold, in the buzzing saw. (33.) The pulley may be either fixed or movable. In the fixed pulley the power and weight will be in equilibrium when they are equal. In the movable pulley, with' a single rope, the 120 NATURAL PHILOSOPHY. power and weight will be in equilibrium when the power is equal to the weight, divided by the number of branches of rope which sustains the weight. In movable pulleys, with separate ropes, the power and weight will be in equilibrium when the power equals the weight, divided by 2, raised to a power, shown by the number of pulleys. The applications of the pulley are common and important. 1. Tlie _pulley.-A pulley is a grooved wheel, turning freely about its axis, with a rope passing over or around it. It is shown in Fig. 51. The grooved Fig. 51. Fig. 52.:s a:B e wheel A, moves freely upon its axis, while over its circumference goes the rope, to the ends of which the power and the weight are fastened. 2. Is either fixed or movable.-If the axis of the pulley is stationary (see Fig. 51), the pulley is called a NATURAL PHILOSOPHY. 121 ixedl pulley. The omvable pulley is one whose axis moves with the weight. This will be understood by means of Fig. 52. The wheel E, is a movable pulley. From its axis the weight is hung, while the rope, one end of which is fastened to a fixed support at D, passes under it and then over a fixed pulley A. The power is applied to this end of the rope. 3. The _Principle of momentumn aopplied to the fixed pu/lley.-The fixed pulley is shown in Fig. 51, to which we again refer. It is clear thrat, when motion occurs, the power (P) will go down with exactly the same velocity as the weight (W) goes up. To have equal momenta when the velocities are equal, the bodies must have equal weights. Hence, in the fixed pulley the potwer and weight can balance each other only when they are equal. 4. The principle of momenturn applied Fig. 53. to the movable pulley with a sincgle rope. — In the movable pulley, with a single rope E (see Fig. 52), the weight rests upon two branches of the rope, H and E, and when n it rises, both branches must be equally shortened. But the rope F P will lengthen just as much as both the branches shorten. The power (P) moves downward just twice as fast as the weight (W) goes up. Let V c o represent the velocity of the power, then V will represent the velocity of the weight, The momentum of P will be P x V, and that of W will be Wx, and the two forces can balance when P x V-=W x, or, when P-=. Now let us take another case. Suppose there are 122 NATURAL PHILOSOPHY. two movable pulleys, C and D (Fig. 53), with a single rope, one end being fastened at F, while to the other end the power P, is applied. In this case we find that the weight is supported by four branches of the rope, and we see, too, that when it rises, all four of these branches must be shortened alike. But the rope, E P, must at the same time lengthen as much as all the branches shorten, so that the velocity of P downward must be four times as great as that of WV upward. Then, if V is the velocity of P, X will be the velocity of W; and, if their momenta are equal, P x V=W x, or, P_=. In like manner, if three movable pulleys are used, we should find that, to be in equilibrium, P=-. If, now, we notice that in each of the values of P just found, the denominator of the fraction is the number of branches of the rope which supports the weight, Fig.4. we have this general principle: in "H = — K movable pulleys, with a single rope, the l 0 power and weight will be in equilibrium when the power equals the weight diC B B vicled by the nuzmber of branches which support it. 5. The movable pulley with separ'ate ropes.-When each pulley has a separate rope, the law is very different. Fig. 54 shows such a system. The three ropes, a b c, are fastened to the beam H K. The first, after passing around the pulley A, is fastened to the axis of the one above: so the rope b, after going around the pulley B, is fastened to the axis of C: but the rope c, after going over the pulley C, passes over NATURAL PHILOSOPHY. 123 a fixed pulley, and receives the power at the other end. 6. The principle of momenteua cDpplied to the qmovable pulley wit7h separate ropes.-This system is only a combination of movable pdlleys with a single rope. Suppose the pulleys A and B were taken away, the weight being hung from the axis of C, there would be left an arrangement exactly like that shown in Fig. 52. C is a movable pulley, with a single rope, to lift the pulley B. B is likewise a movable pulley, with a single rope, to lift the pulley A; while A is itself a movable pulley, with a single rope, to lift the weight W. No new application of momentum is needed. The efbect of the power (P) will be doubled by each pulley thus:W W With 1 pulley, P I -; 9 2 pulleys, P =_ 2; W W 38 — 23' If we notice that the denominator in each of these values of P, is a power of 2, whose index is the number of pulleys, we infer that, in a system of movable pulleys with separate ropes, the power and weight will be in equilibrium when the power equals the weight divided by a power of 2, whose index is the number of pulleys. For example, with a system of 5 pulleys, how much weight will a power of 10 lbs. balance? P-; or =10 -; hence W = 320lbs. 7. Application of the pulley.-No mechanical advantage is gained by the use of the fixed pulley, because the weight must move just as fast as the power, yet it 124 NATURAL PHILOSOPHY. is of great value in the arts, for changing the direction of forces. A sailor standing upon the deck of his ship may, by the use of a fixed pulley, hoist the sail to the top of the loftiest mast; or when heavy bales or boxes are to be lifted to the upper floors of warehouses, a horse, trotting along the level yard or street (Fig. 55), will lift them as effectually as though he were able to climb the perpendicular wall with the same rapidity. The movableypulleys with single rope, are in common use for moving heavy weights through considerable distances. Merchandise may be lifted by means of Fig. 5. them, from the hold of a ship to the wharf, or to the upper stories of store-houses; or by a different arrangement of the machine, the ship itself may be drawn from the water for repairs. In practice, the fixed pulleys of a system are placed side by side, and thus form what is called a block: the movable pulleys, likewise side by side, form another block. By this means the system is o - / -e made compact. r - In all pulleys there is a loss of power, due to the friction of the pulleys in the blocks, to the weight of the lower block, and to the stiffness of the ropes used; so that the weight, actually overcome by a given power, is always less than the laws of equilibrium would afford. (34.) The principle of momentum applied to the inclined plane shows: NATURAL PHIILOS OPHY. 125 lst.-That, when the power acts parallel to the length of the plane, the power and weight will be in equilibrium when the power is to the weight as the height of the plane is to its length; 2d.-That, if the power acts parallel to the base of the plane, the power and weight will be in equilibrium when the power is to the weight as the height of the plane is to its base. The applications of this machine are very numerous. 1. TALe inelined planqe.-Any plane, hard surface, placed inman oblique position, may be used as an inclined plane. In Fig. 56, A B represents an inclined plane. Fig. 56. The distance B C, is the heiyht of the plane, and A C is its base. The weight W, Inay be urged up the plane by a force acting parallel to A B, or parallel to A C, or at any angle to these. We are to notice the first two cases only. 2. If the power acts paraallel to the length of the plane.-In the figure the power P, by means of a rope going over the fixed pulley D, at the top of the plane, acts upon the weight W, in a direction (W D) parallel to the length A B, of the plane. Now, a force which will urge the weight from A to B, 126 NATURAL PHILOSOPHY. is lq;ftiny it only through the vertical height, C B. But while the weight goes from A to B, the rope passing over the pulley, will let the power down a distance equal to A B, in the same time. The velocity of the weight may, therefore, be represented by the line C B, and the velocity of the power by the line A B. The momentum of the power is, therefore, P x A B; that of the weight, W x C B. When these momenta are equal, the two forces will be able to balance each other. Thus:P x AB -=W x CB; or P W:: CB: AB. This proportion teaches us that, when in euilibrium, the power is to the weiyht as the height of the piane is to its length. Fig. 57. PR.. If, for example, the height C B, is 4 feet, and the length of the plane A B, is 16 feet, a power of 1 lb. will balance a weight of 4 lbs. Forllb.: 4lbs.:: 4ft.: 16ft. NATURAL PHILOSOPHY. 127 3. If the power acts parcallel to the base of the plane. -Let A B, Fig. 57, represent a plane whose height is C B, and whose base is A C. The power acts upon the weight by imeans of a cord passing over the pulley at C, in a direction parallel to A C. To move the weight from A to B, will be lifting it only through the vertical height, C B. If the pulley C, could be raised while the weight goes up, so as to keep the cord parallel to A C, then the cord, passing over the pulley, will let the power down a distance equal to A C. The line C B, represents the velocity of the weight, and A C the velocity of the power. The momentum of the power is therefore P x A C, and that of the weight, W x C B. If now, these momenta are equal, the power and weight will just balance each other. HTence — PxA — Wx BC; or P: W:: A B: A C. From this proportion we learn that, when the power acts parallel to the base of the plane, the power aid weight will be in eqztilibriuwn when the power is to the veight as the heigyht of the plane is to its base. Thus, if the height of the plane is 2ft. and the base is 10 ft., a power of 1 lb. will balance a weight of 5 lbs. For lb.: 5 lbs.:: 2ft.: 10 ft. 4. Application of the inclined _plane. —This machine is used to lift heavy weights through short distances. 3Many familiar examples might be named. If a barrel of merchandise is to be placed upon a wagon, it is often rolled up on a plank, one end of which rests upon the ground, the other upon the wagon. A hogshead which a dozen men could not lift, may thus be loaded by the strength of one or two. Our common stairs are, in principle, inclined planes, 128 NATURAL PHILOSOPHY. the arrangement of steps only giving a firm footing. If the distance between the floors be. the length of the stairs, then, besides the ordinary effort of walking, the person must continually, while going up, labor to lift @ of the weight of his body. (35.) The wedge, in its most common form, is made up of two inclined planes joined together at their bases. The sharper the wedge, the greater the resistance which may be overcome by it. 1. The Wedqe.-This instrument is shown in use by Fig. 58. A B is called the back of the wedge: A c Fi —58. and B c, are its sides, and e is its edge. It is generally used in cleaving timber, and very short distances. For these purposes its l edge is put into a crevice made for it, and it is then driven by blows with a sledge.. l!7I1 Since we can not calculate the force of a blow, no attempt will be here made to establish any law of equilibrium. (36.) The principle of momentum applied to the screw, shows that: — The power and weight will be in equilibrium, when the power is to the weight, as the distance between two contiguous threads is to the circumference of the circle in which the power moves. The screw is used extensively to produce great pressure: it is often used to measure delicate distances. 1. The screw.-The screw consists of a cylinder of wood or metal, with a spiral groove winding around its circumference. This grooved cylinder (C, Fig. 59) NATURAL PHILOSOPHY. 129 passes through a block N G, on the inside surface of which is a spiral groove, into which the raised parts of the cylinder exactly fit. The block is usually called the nat. The raised parts between the grooves of the cylinder are called the threacls. Suppose the nut to be stationary, then, if the screw is turned by a power acting upon the lever at B, it must advance downward at every revolution, and the pressure of the advancing screw will be exerted upon any object placed Fig. 59. under the press-board, B E F, against which the - — C end of the screw presses. 2. App2lication of te e _principle of mnonien- tum. —By one turn of!! Ti ii' the screw, it will ad vance downward a dis — tance just equal to the ____distance between two contiguous threads. The -bi, lii iii - press-board E F, which H may be regarded as the weight, will be!: li!, moved along through o (i...:;il.:, [i __!,lil a distance equal to a b, by every turn. The power acting at B will, in the same time, move through the circumference of the circle whose radius is B C. These distances, through which the power and weight pass in the same time, may represent their velocities. XHence the momentum of the power will be P x Circumference of the circle whose radius is B C, and that of the weight will be W x a b. If these momenta are equal, the tcwo 130 NATURAL PHtILOSOPHY. forces, when at rest, will be in equilibrium. Hence:P x Cire. BC V W x ctb; or P: W:: a': Cire. B C. This proportion teaches that the power and weight will be in equilibrium when the power is to the weight, as the distance between two contiguous threads is to the circulmfberence of the circle in which the power moves. Thus, if the distance between the threads is ~ in., and the circumference, traveled by the power, is 5ft., or 60 in., what weight on the nut, would 1 lb. power at B balance? llb.': V: in.: 60 in. W = 120 lbs. 3. Application of the screw.-The screw is used when great weights are to be lifted short distances, or when heavy pressure is to be exerted. By its use, cotton is pressed into bales, the juices of fruits extracted, and oils pressed from vegetable bodies, such as linseed and the almond. In contrast with these uses of the screw, depending on the immense pressure it can exert, is another, remarkable for its delicacy. It is used to measure very small distances when accuracy is required. Screws with threads of exceeding fineness are used for this purpose. Suppose a screw with 100 threads in one inch of its length; then, at every turn its end would advance just -0 of an inch, and if it carry a steel marker, spaces of that length may be marked off on any body along side of which it moves. Now let the power move in a circle 10in. in circumference, and let this circle be graduated to inches, tenths, and hundredths. If the power move one inch on this scale, the marker on the end of thlie screw will go forward only T:v of an inch. If the power goes -v inch, then the marker will advance only — r 10a of an inch, a distance quite too small to be seen except by NATURAL PHILOSOPHY. 131 the aid of a good microscope. Astronomers use the micrometer screw to measure the apparent sizes of the heavenly bodies. PROBLE3MS ILLUSTRRTING THE THEORY OF MACHINERY. 1. Suppose a body weighing 5lbs. moves without resistance, with a velocity of 20 ft. a second: what momentum w-ould it have? Ans. 100. 2. Suppose the body weighing 5 lbs. moves against resistance, with a velocity of 20 ft. a second, kept uniform by a constant force: what would be its living force Ans. 2,000. 3. Suppose two bodies, one of 5 lbs., the other of 7lbs. move, with equal velocities, 100 ft. a second, but in opposite directions, without resistance. Let them at the same instant strike a third bodcy: in which direction would the body be moved, and with what force? Ans. to 2el question, 200 lbs. 4. Two trains of cars, each moving at the rate of 30 miles an hour, or 44 ft. a second, onle weiglling 10 tons, the other 20 tons, come in collision from opposite directions: what force would be exerted to dash them to pieces? An.s. 58,080 tons a second. 5. If a power of 10 lbs. act upon the long airm of a lever, a distance from the fulcrum of 6 ft.: what weight wTould it balance at a distance of 2 ft. onil the other side of the fulcrumn Aans. 80 lbs. 6. In a lever of the second class, the power, 3 lbs., is at a distance of 1 ft. from the fulcrumn: what weight will it balance at a distance of 1 in. from the fulcrum? Ans. 36 lbs. 7. In a compound lever, the long arms are 4 ft., 5 ft., 132 NATURAL PHILOSOPHY. and 6 ft. in length; the short arms are 1 ft., 2 ft., and 3 ft. long: a weight of 2,000 lbs. is to be balanced: how much power must act upon the first long arm? Ans. 100 lbs. 8. A power of 10 lbs. lifts a weight of 500 lbs. by means of a lever whose short arm is 1 ft. long: how long is the long arm of the lever? An&. 50 ft. 9. If the 500 lbs. in the last example is to be lifted 2 ft., how far must the power move to do it? Ans. 100 ft. 10. The radius of a wheel is 30 inches; of its axle, 5 inches: a power of 100 ounces is exerted upon the wheel; how much weight will it balance at the axle? Ans. 600 oz. 11. Three wheels and axles are combined, as shown in Fig. 50; the radius of each wheel is 20 inches; of each axle, is 4 inches; a power of 2 pounds acts on the first wheel: what weight will it balance on the last axle? Ans. 250 lbs. Fitg. 60. 12. A force of 16 lbs. is applied to the last axle (Fig. 50), and moves at G the rate of 10 inches a second: how much weight at the first wheel would balance it at rest? and how much slower will it go when in motion? Ans..128 lb.; as fast. 13. With a single movable pulley a stone weighing 350 lbs. is to be lifted: X A > ~l what power must be exerted? Ans. 175 +lbs. 14. With the single movable pulley, shown in Fig. 60, what power at P would balance a weight of 250 lbs. at W? Ans. 83:- lbs. NATURAL PHILOSOPHY. 133 15. If the weight W, is lifted by the t-ower, how far would the power move to lift the weight 1 it.? Ants. 3 ft. 16. In a system of 4 movable pulleys, withl a single rope, what power would be needed to balance a w-eight of 500 lbs? Ans. 622 lbs. 11. Suppose each of the 4 pulleys has a separate rope, what power would then be needed? Ans. 311 lbs. 18. An inclined plane, 6 ft. in length and 2 ft. high, is used to put a barrel of flour upon a cart. The barrel weighs 196 lbs.: how much force must a man exert, pushing parallel to the length of the plane? Ans. 65 + lbs. 19. If the base of the plane were 5 ft., its height 2 ft., and the man pushes parallel to the base, how much force must he exert to lift the barrel of flour? -A ns. 782 + lbs. 20. The distance between the threads of a screw is 1 in., and the power of 25 lbs. moves in a circle of 3 ft. in circumference: how much weight will it balancea Ans. 900 lbs. 21. A power of 20 lbs., by means of a screw, exerts a pressure of 800 lbs. The threads are in. apart: what is the circumference of the circle in which the power moves? Ans. 20 inches. ~ 5. OF THE MOTION OF LIQUIDS. (37.) Water will issue from an opening in the side of a vessel with the same velocity which a body would gain by falling from the surface of the water to the center of the opening. Hence the velocity of the jet of water, will depend only on the distance of the orifice below the surface of 134 NATU IAL PHILOSOPHY. the water in the vessel, and may be calculated by the fbrnula, v = 2 47/Sf. 1. Thle velocity of a jet of water the srame as thatt.of a fcallinY body.-To prove this principle, we must remember: first, that water, confined in pipes, will rise as high as the source from which it comes [see (11.) 1]; second, that a body thrown upwardcl, starts with the same velocity that it has when it gets back. (See p. 94.) In Fig. 61, a bent tube (A) extends from near the Fit. 61. tbottom of a vessel of water................... The water rises as high in X!~_] E_:_ the tube as in the vessel; it ____ ____ is the upward pressure of _______ thle water at A that pushes X;A-~ it up. The same force - would Dbe exerted on the water at A, if the tube were cut off at that point, and it would, if not resisted, throw the water to the same height, as shown on the other side of the figure, at B1. But the velocity with which it must start from B to reach the level of R, is the same it would gain by falling from that level back to B. If the tube were cut off at C, the water would issue with the same force, and, therefore, with the same velocity. Hence the velocity wiith which the water issues, is the same ase thcat of a bodjy fa:llinq from the surface of the water do70wn to tihe center of thIe 0orfice. 2. The velocity of the jet defpends ol the distance of the oreice below the level, of the water. —The velocity of a falling body depends only on the height from which it has fallen. All bodies, whatever be their size NATURl,i PHILOSOPtHY. 135 or nature, fall with equal velocities. In the same man ner, all liquids, however different in nature, will issue with equal velocities, if the openings fiom which they are thlrown are at the same distance from the surface of the liquid in the reservoir. 3. Veloci-ty calculatecd by the formula, V = 2 1Sy. — ]Now, the velocity of a falling body is given by the equationl -= 2 t/'S-. [see (24,) 6], and it is clear that tile velocity of a jet of water will be given by the same formula, if S represents the distance of the orifice below the level of the water in the vessel. It, for example, we would know the velocity of a jet of water fiom an orifice 36 feet below the surface in a reservoir, we put 36 for S in the formula. It then readcs V 2 4/36 x 16. The value of V is, then, 48; the velocity of the water is 48 feet a second. (38.) The quantity of water discharged from an orifice, depends upon its velocity, the size of the orifice, and the time of flow. It may be found by multiplying the values of these three things together. i. To ca7cuZate the quant'ity.-If the orifice have an area of 1 sq. ft., then the velocity will represent the number of cubicfeet discharged in one second. MAiltiplying this by the number of square feet, or fraction of a square foot in the orifice, must show the number of cubic feet flowing from the orifice in one second, and this multiplied by the number of seconds, will tell the number of cubic feet discharged. For example, how much water will flow from an orifice of 1{ sq. ft. area, at a depth of 9 ft. below the surface of the water, in 10 seconds? At a depth of 9 ft. the water wtill issue with 136 NATURAL PHILOSOPHY. a velocity, V = 2 /9 - - 24 ft. Now, if the opening was one s8'uare foot, then 24 cubic ft. would issue in one second, and 24 x 1- x 10 = 360 cubic ft. must issue from the orifice of 1~ sq. ft. in the given time, 10 seconds. The rule is concisely expressed by the formula:Q = Vx AxT, in which Q represents the quantity of water discharged, V 6" " Velocity, A " "L lArea of the orifice, T Time of flow. In this equation there are four things, and it is clear that, any three of them being given, the fourth, whichever it may be, can be found. A single illustration will show how jthis is done. Suppose 10,000 cubic ft. of water must be discharged in 60 seconds, from an orifice so far below the surface of the water that the velocity of the jet is 250 ft. a second: hobw large must the orifice be made? In this problem, the value of V is given, 250 ft.; the value of T is 60 seconds; the value of Q is 10,000 cubic ft.; the value of A is wanted. By putting the given values into the equation it becomes:10,000 250 x x A x 60; hence, A -3 sq. ft., or 96 sq. in. (39.) The velocity of a jet of water and the quantity discharged are found in practice to be much less than the foregoing theory would give. The actual amount may be increased by using short tubes of different shapes. 1. Tle velocity in practice less than in theory.If the experiment be tried with a vessel of water, as NATURAL PHILOSOPHY. 137 shown by Fig. 61, it will be seen that the jet does not rise quite as high as the level of the water in the vessel. It does not, because the resistance of the air prevents it. From any orifice, water must issue against the resistance of air, and its motion is less rapid on that account. 2. Ttie quantity in practice less than in tkeory.If we examine a jet of water flowing from an orifice in the side of a vessel, we will see that it grows rapidly smaller, so that, at a little distance, its size is only about 2 as great as at the orifice. Beyond this point the contraction of the jet is gradual. The rapid contraction near the orifice is due to cross curreqnts, caused by the -water flowing toward the orifice from different directions in the vessel; these currents may be seen if there be any solid particles floating in the water. If the jet were the size of the orifice, the quantity of water discharged would be what the theory gives, but since it is only about two-thirds as large, there will be only about two-thirds as much water discharged. 3. lihe quantity increased by using tubes. —Short tubes inserted in the orifice are found to increase the actual flow. These tubes are either cylindrical or conical. It is found that a cylindrical tube, whose length is not more than four times its diameter, if placed in the orifice, will increase the amount discharged to about.82 of that which theory gives. In this case the water adheres to the sides of the tube, so that the contraction of the jet is prevented; the jet is the size of the orifice. By the use of conical tubes the amount discharged may be made still greater. (See Silliman's Physics, pp. 174. and 180). 138 NATURAL PHILOSOPHY. (40.) Water-wheels are turned by the power of moving water. There are several kinds: First, the underFi3. c2. shot wheel; second, the overshot wheel; third, the breast wheel; fourth, the turbine wheel. 1. TAe ulncders/ot c w w, eel. — The undershot wheel is shown in Fig. 62. Its circumference is provided with float - boards a b c, against which the running water acts. Other wheels are connected with the axle of this one by cogs and bands. This form of wheel is often placed in a horizontal position, and water from Fig. 63. the bottom of a dam guided against the float-boards of one side. 2. Tihe overshot wheel. —The overshot wheel (Fig. 63) NATUR AL PHILOSOPHY. 139 differs from the undershot, by having buckets upon its circumference, instead of float-boards. The water enters the buckets at the top of the wheel, and, filling those on one side of it, turns the wheel by its weight. The buckets all open in the same direction, so that while those on one side of the wheel are full, those on the other side will be bottom upward and empty. 3. 2he breast wheel.-The breast wheel (Fig. 64) differs from the undershot wheel only by being so Fig. 64. placed in front of a dam, that the water shall fall upon the float-boards of its circumference on a level with its axis. 4. Tl7e Anerican turbine.-The construction of the turbine is more complex than the wheels just described. Its action may be understood by a careful study of Fig. 65. This figure shows a section of the interior of the wheel, as it would, appear to one who looks down upon it as it lies in its horizontal position. In the center is a circular disk of cast iron, A B, in a horizontal position. On the upper surface of this disk 140 NATURAL PHILOSOPHY, are fastened the curved guides, a a a,. This disk is stationary. The wheel proper, C D, revolves outside of this disk. It consists of two cast-iron plates, one above Fig. 65. the other, the space between them being divided into numerous N. (.~__~channels by the curved partitions, ec c. The partitions in the wheel, _J__ii Land the guides on the __<-=- W the under plate of' this wheel is fastened a cast iron plate, which extends under the central disk A B, and to the center of this plate is attached a vertical shaft which comes up through the disk at E. The turbine, except the upper part of the shaft, is entirely under water. The weight of the column of water above the disk forces the water with great power and force out from between the curved guides of the disk, into the curved channels of the wheel, in as many different streams as there are spaces between the guides. The force of tkese streams, striking against the partitions of the wheel, turns the wheel in the direction indicated by the arrow. The vertical shaft turns with the wheel, and, by mneans of cogs, gives motion to other parts of the machinery. (See Silliman's Physics, p. 184.) Of all forms of water-wheel, the turbine is most energetic and economical. NAiTURAL PHILOSOPHY. 141 ~ 6. OF THE MOTION OF AIR. (41.) Air in motion is called wind. Winds are produced bythe action of heat and the attraction of gravitation upon the atmosphere; and, in the case of the trade winds, partly by the rotation of the earth on its axis. 1. VFind.-The motion of air, called wind, is due to a difference in the temperature of two portions of the atmosphere. Heat expands air. One hundred cubic inches of hot air will weigh less than a hundred cubic inches of cold air. Now, if a portion of hot and light air is surrounded by that which is colder and heavier, it will rise, for the same reason that a cork rises in water. It will be pushed up out of the way by the heavier air, which takes its place. Let us now suppose that, in some particular part of the country, the air becomes heated more than in surrounding portions. This heated and lighter air will )e pushed up by air moving in from all directions to take its place. This moving air is wind. People residing north of the heated place will observe a north wind, and those south of it a south wind. Now, there is an unequal distribution of heat over the surface of the earth. It is caused partly by the changes of the seasons, and partly by various local causes. To it the prodtction of winds is due. Their direction will be modified by many causes: the form of the surface over which they pass is an important one. As the same wind often blows in different directions on different sides of a house; or, as blocks of buildings compel the wind to sweep up and down the various strleets of a city, so the hills and valleys of a country, or 142 NATURAL PHILOSOPHY, the presence of forests or plains, will modify the direction of the winds that blow over them. 2. The trade wi;ncds.-The trade winds requile particular notice. They occur in the equatorial parts of the earth, ancd always blow inb the same directions. Over a surface of about 30~ of latitude on the north side of the equator, they blow from the northeast toward the southwest; while south of the equator, over about the same width of zone, they blow from the southeast tow\ard the northwest. These directions are maintained so constantly, that mariners count upon the trade winds with almost the same certainty as upon the rising and setting of the sun. 3. Due to heat atnd the rotation of the earth. —To explain this phenomenon we must remember: first, that the equatorial region is constantly heated by the sun more than parts of the earth either north or south; and second, that the earth revolves from west to east, the equatorial parts moving most swiftly. The heated air at the equator, lighter than the air either north or south of it, will be pushed up, while currents of colder air from the north and from the south, will move toward the equator. But the equatorial parts of the earth move toward the east more swiftly than other parts; the air from the north must, therefore, pass over portions of the earth which move eastward faster than itself, and it will be left behind.'We find, then, that there is a real motion from the north, and at the same time an apparent motion from the east; these two motions combined make the direction of the wind to be from the northeast. A similar explanation will show why the southern trade wind blows from the southeast toward the northwest. (See Silliman's Physics, p. 643.) NATURAL PHILOSOPHY. 143 CHAPTER IV. OF MOTION-(CONTINUED). INTRODUCTION.-APPLICATION OF THE FUNDAMENTAL IDEAS. (42.) Read (4), (7), and (20).-Attraction, repulsion, and inertia, acting upon masses, or molecules, produce vibrations. 1. Attraction, repulsion, and inertia.-We have seen that the forces of nature are only different manifestations of attraction and repulsion. [See (20.) 1.] We have also seen that a body in motion can not stop itself. [See (4.) 2.] When, therefore. a body has been put in motion, by any force, it will move in that direction, on account of its inertia, until stopped by an opposite force. Suppose the fbrce which stops it continues its action afterward, it will move the body back towardits first position, and then if the force cease, the inertia will move it onward until, again stopped by an opposite force. 2. Vibrations. — The body, thus acted upon, will swing alternately back and forth over the same path. Such a motion is called vibration. It; with the finger, we sink one scale-pan of a balance. 144: NATURAL PHILOSOPIIY. it will continue to pass alternately up and down over the same path for a long time after the finger is removed: it vibrates. Or if, instead of pushing it down we pull the scale-pan to one side and then let go of it, it will swing back and forth for a long time; this alternate motion, to and fro, is vibration. Suppose a ball, hung by a fine wire, be twirled by the fingers so as to twist the wire; let go of it, and, speedily untwisting the wire, it will go on for a time twisting it up the other way. The ball rotates, first in one direction and then in the other, and this alternate motion is vibration. Or take a bent glass tube; pour water into it until the arms are two-thirds full; tip it to one side and then suddenly bring it back to a vertical position. The water will rise and fall in the arms of the tube, and will continue this alternate motion up and down for some time. In this case a liquid vibrates. Gases may be made to vibrate in the same way. ~ 1. OF THE VIBRATIONS OF THE PENDULUM. (43.) The pendulum vibrates under the influence ot gravitation and inertia. Its vibration is governed by three laws: 1st. The time of one vibration varies as the square root of the length of the pendulum. 2d. The time of one vibration varies inversely as the square root of the force of gravity. 3d. The time of one vibration is independent of the length of the arc through which the pendulum vibrates. 1. The pendulum. —A body hanging from a fixed point by a flexible cord or wire, is called a pendulum NATURAL PHILOSOPHY. 145 In Fig. 66, the pendulum is represented as a ball B, hung from a point A. If this ball be lifted fiom the Fig. 66. point B to C, and then loosed,A from the hand, it will swing back and forth through the are D C, going a less and less distance, until finally it will stop at B. Its motion, from one end of its are D, to the, other C, is a single vibration, and the distcance D C, through 1 which it vibrates is called the amplitude of vibration. 2. It vibrates under the influence o(f gravitation and inertia.-Suppose a ball at M (Fig. 67), to represent a pendulum hung from the fixed point Fig. 67. C, by a cord X C. Now, if this ball be lifted to the point m, and, for a moment, held there, the force of gravity will act upon it in a vertical direction. We will represent this force by the line m A, and resolve it into two components [see (26.) 1], shown by the lines m D and m B. The force, m B, acts lengthwise of the string without effect to move the ball: P the other force, nID, at right angles to the first, will pull the ball toward the point M. If the ball is allowed to fall to ht, its inertia will carry it beyond that point; but gravitation will then be pulling it back with just the same power that it exerted to pull the ball from m to M. It will rise from AM to n, a distance just as far 7 146 NATURAL PHILOSOPHY. from [, as it has fallen from qn. It will there stop, and gravitation will bring it back to Mit, while its inertia will carry it up to m, and if there were no resistance to its motion it would vibrate forever through the arc n m. The resistance of the air and the friction of the cord on the hook will finally make it stop at M. 3. Zlie first law. —If two pendulums of different lengths (P and P', Fig. 68), be made to vibrate toFig. 68. gether, the short one will be seen to I vibrate much faster than the other. Ve learn from this that the time of vibration depends on the length of the pendulum. Now, let us make the pendulum P yjst four times as long as the other. With a watch in the hand, we can easily count the number of vibrations it makes in one minute, and 60 divided by this number, shows how long it takes to make one vibration. In the same way we can find the time it takes the shorter pendulum to make one vibration. Doing this, we find that the pendulum P, takes twice as long as the other to vibrate once. Being four times as long as the other, the time of vibration is two times as great. Hence, th/e time of one vibracion varies as s e square root of the length of thepend~ultnm. The length of a pendulum to vibrate in one second is about 39.1 inches; to vibrate in two seconds, it must be four times as long; to vibrate in one-half a second it must be one-fourth as long. 4. The seconZ law. —By calculating the force of NATURA L PHILOSOPHY. 147 gravity (see prob. 21, p. 94), at different distances above the level of the sea, and then, by experiment, finding the time of one vibration made by the same pendulum at those places, it will be found that the time of one vibration varies inversely as the square root of the force of gravity. 5. The third law.-Finally, if we make the pendulum P, vibrate in a large are, and find the time of one vibration, and then make it vibrate in a small are, we shall find the time of one vibration to be the same. The pendulum must vibrate in equal times, no matter whether its arc be large or small. In other words, the time of one vibration is independent of the are through which thepenvedultum vibrates. This thiMd law is absolutely true only when tile arcs compared are very small. Yet, in the latitude of I'aris, it is found that for a pendulum whose length is one meter, or 39.37 in., the time of one vibration, through an are of 8~, is only.000076 of a second longer than if its arc were infinitely small. (See Cooke's Chem. Phys. p. 69.) (44.) These laws apply to a single point in a pendulum, called the center of oscillation. 1. Thze center of oscilcation.-The different molecules of a pendulum are at different distances from the point of suspension, and hence would vibrate in different times if they were not held together by cohesion. Although they are held together, and must all move at once, yet the forces that would rmake them vibrate differently are acting just the same as if they were not. The upper parts of the pendulum are tryirng to vibrate faster, and must be pulling the lower parts along; while 148 NATURAL PHILOSOPHY. the lower parts are trying to vibrate slower, and must be pulling the upper parts back. There must be some point in the pendulum, at which these two struggles just balance each other. This point will vibrate just as fast as if it were influenced by no other molecules whatever. A point in the pendulum which vibrates as if only'under the influence of its own gyatvitation and inertia is called the center of oscillation. The center of oscillation is generally a little below the center of gravity of the pendulum ball. 2. The laws apply to this point.-The three laws, obtained in the foregoing paragraph, apply to only this pointl the center of oscillation. Indeed, whenever we speak of the pendulum we refer to this point..By the length of a pendulum we mean the distance firom the point of support to the center of oscillation, and when we use the term vibration, we refer to the motion of this one point of the pendulum. (45.) There are several uses of the pendulum; we notice only two:ist. It is used to measure time. 2d. It is used to determine the form of the earth. 1. Used to measure time.-The vibrations of a pendulumn are made in equal times. If then we know the time of one vibration, and can count the number made, we know the time during which the pendulum vibrates. Now, the common clock is an instrument in which, by weights, friction and the resistance of air are overcome, so that the pendulum shall continue its motion, and by which, the number of vibrations are at the same time recorded by the hands moving over a graduated dial. NATURAL PHILOSOPHY. 149 2. Used to determine the form of the earth.- The pendulum has been used to determine the shape of the earth. For this purpose, pendulums of the same lengthl have been made to vibrate in different latitudes. It has been fbund that the time of one vibration is less and less as the pendulum approaches the poles of the earth. lNow, to make the vibrations more rapid, the force of gravity must increase, and if this force is stronger toward the poles, the surface of the earth must be nearer the center of the earth there than at the equator. The polar diameter must, therefore, be shorter than the equatorial diameter, and the shape of the earth must be that of an oblate spheroid. ~ 2. OF TiE VIBRATIONS OF CORDS. (46.) The vibrations of cords are due to the action of elasticity and inertia. They are governed by three laws:1st. The number of vibrations in a second varies inversely as the length of the cord. 2d. The number of vibrations in a second varies directly as the square root of the weight by whicll the cord is stretched, or its tension. ad. The number of vibrations in a second varies inversely as the square root of the weight of a given length of the cord. 1. Thbe vibration of cords. —Let a cord or string be stretched between two fixed points (a and b, Fig. 69). Fig. 69. By taking hold of its middle point, the cord may be 150 NATURAL PHILOSOPHY. drawn to one side, a e b. Then loose it, and it will spriing back and go an equal distance on the other side a d b; then return, and so continue to swing rapidly back and forth until it finally stops in its first position, a c b. The motion of the cord from e to d and back again, is a complete vibration. Its motion fiom e to d, is a half vibration, or, as generally called, a single vibration. The distance from e to d, is the amplitude of vibration. 2. Due to elasticity and inertia.-When the force which stretches the string into the position a e b, is withdrawn, elasticity moves it back to its first position, a c 6, and the inertia gained by this motion, throws it forward an equal distance, to a d 6b. The elasticity of the string again pulls it back to the position, a c b, and its inertia carries it beyond, and thus, under the joint influence of elasticity and inertia, the string will swiftly vibrate, its amplitude growing less and less, on account of resistance, until at last it stops in its first position. 3. zThe laws of vibration.-The vibrations of cords are, in all cases, quite too rapid to be counted, and yet it will be impossible to establish any laws of vibration, unless we can find the number of vibrations made in a given time. How can this be done? X' However rapid the motion of the cord may be, the lightning swiftness of electricity is yet greater; so the cord, by using electricity, may register the vibrations which it makes. The apparatus used for this purpose by the author, is shown in Fig. 70, as far as necessary to illustrate the principle of the process, * The syren will be described in the chapter on sound: it seems desirable here to make the cord directly register its own vibrations, so that the laws of vibration shall stand independent of sound. NATURAL PHILOSOPHY. 151 A cord, A B, rests upon the two bridges, C and D, and passing over a pulley, B, is stretched by a weight, W. Through its middle point is a fine cambric needle n, just under the point of which stands a vessel of merFig. 70. D cury, M. From an electrical battery, G, one wire goes to the mercury, and another, after passing around an electro-magnet, E, is threaded into the eye of the needle. At P, is a sharp and soft pencil-point, and in front of it is a roller 0, over which passes a strip of paper. If now, the string vibrates up and down, the point of the needle will come in contact with the mercury below it at the end of every vibration. When the needle touches the mercury the electricity darts through the wires, and the magnet E, instantly pulls the pencil-point against the paper, and a clot is thereby made. If the paper be drawn along in front of the pencilpoint while tlhe string is vibratizgy, a series of dots will be made, and the 1number of dots shows the number of vibrations made by the string. 155 NAKTURAL PHILOSOPHY. The apparatus by which the paper is drawn along is not shown in the figure, neither is that by which time is measured. With this apparatus we proceed rapidly to verify the laws of vibration. 4. Thefilrst law.-The string C D, was taken 3 ft. in length: stretched by a weight of 56 lbs. at W, it made 420 complete or double vibrations in 3 seconds. The bridges, C and D, were then moved, so that the length of the string was 4 ft.; it then made 315 vibrations in 3 seconds. But 420 is to 315 as 4: 3. We see that when the lengths of the string are as 3: 4, the number of vibrations in the same time are as 4: 3. Hence the number of vibrations in a given time varies inversely as the lengths of the string. 5. TShe second law. —The string was again made 4 ft. long, and the weight W, 56 lbs. The vibrations in one second then numbered 105. When the weight, W, was then changed to 14 lbs., the number of vibrations in one second was, in some experiments 52, and in others 53. The instrument can not register parts of a vibration; the true number is evidently between 52 and 53; we may call it 52-. We see that when the weights are 56 and 14, or as 4: 1, the number of vibrations made in a second are 105 and 521, or as 2: 1. Hence the number of vibrations in a second, varies directly as the square root of the weight by which the string is stretched. 6. The thi/rd law.-The string which, being 4 ft. long, and stretched with a weight of 56 lbs., gave 105 vibrations a second, was found to weigh 19.4 grs. to the foot in length. Another string, weighing 43 grs. to the foot, was taken of the same length and tension as the other, and the number of vibrations in one second was, in NATURAL PHILOSOPHY. 153 some experiments 70, and in others 71. The true numbel is between these; call it T0L. Now, the weight of equal lengths of the string being 19.4: 43, the number of vibrations are found to be 105:701; but 105: 701:: 4'4: V/19.4, so nearly that we may infer, that the number of vibrations a second varies inversely as the square root of the weights of equal lengths of the string. [See (107.) 6.] (47.) In progressive vibra- Fig. 71. tions, the motion appears to be A A.A" lengthwise of the cord. A cord may divide itself into parts, vibrating separately, called ventral segments, with points of rest between them, called nodes. 1. Progressive vibrations. — Let a heavy cord, or better still, an india-rubber tube (A B, Fig. 71), several feet long, be fastened at one end to the wall or ceiling of the room. Take hold of the othler end with one hand, and by a sudden blow with the other, push the part B C aside, as shown in the figure. The little hillock thus formed will run swiftly up the tube to A, and then quickly down to the hand again. By carefully noticing the motion, it will be seen that while the hillock, running up to A, 7* 154 NATURAL PLHILOSOPHY. is on. one side of the cord or tube, that which returns Fig. 72. to the hand is on the other. HavA ing gone to the top, as seen at A', it turns as seen at A", and then comes down. Nor does it thenl stop; it nwill again and again run up and down the tube until, the height of o the hillock growing less and less, it finally disappears. This motion is progressive vibration. 2. Tihe motion cappears to be lengthwise of the tubee.-It is interM esting and important to notice that \ \ hile the motion appears to be lengthwise of the cord or tube, the only real motion of the parts, is back and forth, across their first, position. 3. Ventral sei;nments.-By starting several hillocks, one after the other quickly, the whole cord may be thrown into a series of hills and valleys, as shown in Fig. 72. ( In this case the motion between B and D, consisting of two parts, on opposite sides of the middle line, is called a wiave. Two waves are represented in the figure. By skillfully timing thle impulses of the hland, the hillocks on both sides of the middle line in Fig. 72, Inay be miade to turn themselves over at the same tinme. In that case, the tube will present the appearance shown in Fig. 72 (B), the points a b c, being alno.st stationary while the parts between are swing NATURAL PHILOSOPHY. 155 ing to and fro across the middle line, making vibrations, just as if they were separate cords. The points which appear to be at rest are called nodes, while thle vibrating parts between them, are called ventral segyments. (48.) When a cord fastened at both ends is struck, it vibrates as a whole, and in ventral segments at the same time. 1. It vibrates as a whole. —Suppose the cord shown in Fig. 69, to be struck at a point one-sixth of its length from the end b, the entire cord will swing back and forth just as represented in that figure, and the vibration of its whole length will be governed by the three laws already given, in (46). 2. Ventral segments at the same time.-The cord will at the same time divide itself into three ventral segments, each of which will make a series of separate vibrations, while taking part in the full length vibration of the cord. Now, as each segment in this case is ~ the length of the string, it must (first law) vibrate 3 times as fast. If the string is struck at Iof its length firom the end, there will be 2 segments, each ~ as long as the string, and of course, vibrating 2 times as fast. ~ 3. OF VIBRATIONS IN LIQUIDS AND GASES. (49.) Progressive vibrations are illustrated by water waves. Two sets of water waves may interfere with eacl other, and produce a single set different from either. 1. Ifater: waves.-,Let a pebble be tossed into the 156 NATURAL PHILOSOPHY. water of a lake or pond, and the tranquil surface will be carved into a series of' circular ridges and furrows, which, growing gradually larger and larger, finally break against the shore. The motion appears to be in all directions outward fiom the pebble, but the little sticks and straws that may be resting upon the water at the time, tell us, by their dancing, that the rea motion of the water is, like their own, a motion only up and down. A wave of water consists of two parts, a ridge and a furrow. 2. Water waves may inerfere.-Let two sets of water waves be started at the same time, by dropping two pebbles at a little distance from each other. The two sets of growing circles very soon cross each other, and then the smooth surface of the water will be cut up into a curious confusion of dancing hummocks. Some of these hummocks will be twice as high as the ridges of either set of waves, while others will just lift their heads above the original surface of the water. When two sets of waves are thrown together, they are said to interfere. But why are the hummocks of such different heights? It is clear that when two ridges come together their heights Awill be united, and the height of the hummock will be the sum of their separate heights. But when the ridges of one set enter the furrows of the other, the height of the resulting hummock will be equal to their difference. Now, as the waves are running across each other, the hummocks must be of various heighlts, limited on the one hand by the sumn, and on the other, by the difference in the heights of the ridges of the two sets. NATURAL PHILOSOPHY. 107 (50.) The vibrations of air consist of alternate rarefactions and condensations. In free air the waves travel outward from their source in every possible direction. Different sets must be constantly interfering. 1. Alternate rarefactions cn dc condcensctions.- YWe have seen [see (16.) 1 and 2] how easily air may be compressed, and with what promptness it springs back to its former volume when the compressing force is removed. Now, suppose that near to one end of a long tube, is a piston P (Fig. 73). By suddenly hig. 7s. pushing this piston forward to P', and then instantly pulling it back, the air in the whole length of the tube will be put in motion. Let us analyze this motion. When the piston moves from P, it crowds.::::. the air befbre it, and when it has reached P', this crowding effect will have gone forward to some point A, more or less distant. The space, P' A, is then filled with condensed k air. [Now, when the pressure of the piston is removed, the condensed air springs back. It springs both ways, backward against the piston and forward against the air at A. By its pressure against the air at A, the air in the space A B, will be condensed. The next moment this air expands, and pressing both ways, condenses the air B C, in front of it and also the air A P, behind it. These two portions will, in this way, be condensed, while the air, A B, will be rarefied. The next instant these condensed portions spring back and become rarefied, while the rarefied portion A B, and at 158 NATURaL PHILOSOPHY.' the same time, another part beyond C, will be condensed. The air is in this way thrown into a series of condensed and rarefied parts, alternately springing lbackl and forth in the direction lengthwise of the tube. We need only add, that there is no suldder transition fr'om condensed to rarefied air at the points A B and C. The mobility of air will not permit this. At the middle of the condensed part the condensation is greatest, while at the middle of the rarefied part is the greatest rarefaction, and between these points the change is gradual. A wave of air consists of two parts, a condensation and a rarefaction.. 2. WI'aves in free air yo in all directions.-The walls of the tube confine the air, and compel its waves to go in the direction of its length; in firee air the case is different. Every impulse by which the atmosphere at any point is suddenly condensed or rarefied, is the center firom which air waves go outward in all directions. Let a few grains of gunpowder be exploded. A little sph/ere of air at the point where the explosion occurs, will be, for the moment, rarefied, while by its pressure a s/ell of air outside of it will be condensed. This condensed air instantly springing back, condenses the air on both sides of it, and itself becomes rarefied. The waves will thus travel outward from the center, until the whole body of air is thrown into a series of concentric sie/CUs, alternately condensed and rarefied. HIow constant and complicated must be these vibrations of thle air! Every sudden and local puff of wind; every forcible breath exhaled firom the lungs; the fall of every stick and stone, all these are the sources of as many different sets of waves spreading in all directions, NATURAL PHILOSOPHY. 159 darting across and tihrough each other, too delicate to be seen or felt, presenting to the mind a scene of activity far exceeding the power of the senses to appreciate. 3. D),ierent saes interfere.-Suppose two sets of air waves come together; if their condensed parts coincide, a single set will be folmned whose condensations are greater tllan either. If the condensed parts of one set coincide with the rarefied parts of the other, there will be a single set whose condensations are less than either. In the first case, if the two sets are equal, the resulting waves will be doubled; if, in the other case, the two sets are equal, they will destroy each other, leaving the air without waves. ~ 4. OF THE VIBRATIONS OF fMOLECULES. (51.) The molecules of all bodies are at all times in motion. These vibrations of molecules can not be seen, yet they are able to affect our senses. Acting upon the ear they produce sound; upon the eye they are recognized as light; while upon the sense of touch they produce heat. 1. 3folectles in motion..-The molecules of bodies do not touch each other; if they did, they could never be pushed nearer together, and there could be no such thing as elasticity. They are distinct, separate bodies. Moreover, they are supp)osed to be in rcapid mnotion. Just how they move is not known. They may be swinging back and forth in straight lines, or in curves; they may be rolling on their axes to and fro, or perhaps revolving around each other: or it may be that they make several of these motions at once. Be this as it may, they are supposed to be in motion of some kind. 160 NATURAL PHILOSOPHY. The vibrations of the molecules may be increased or diminished. To illustrate: look upon a bar of iron; imagine the multitude of little molecules of which it is made; see them in rapid vibration, trembling in their little spaces. Now strike the bar with a hammer; the hammer can not stop without giving the force which moves it, to the molecules of the bar, and every molecule acted on by this force, has its vibrations thereby quickened. 2. These vi'brctton.s affect thLe senses.-The motions of the molecules are quite too delicate to be seen. They are supposed to exist, only because many effects can be explained in no other way so well as on this supposition. They are thought to be the means by which objects of matter produce effects on our senses. The organs of sense are so arranged by Him who made them, that each one receives a different effect, although the vibrations that produce it may in all cases be much alike. The ear is so made that vibrations in it produce sound. The eye is so made that vibrations are recognized as light. The sense of touch is so arranged that vibrations against it are felt as heat. The phenomena of sound and light and heat are caused by vibrations. IHow simple the means to produce such wonderful results! " Know ye, that the Lord he is God; it is ho that hath made us, and not we ourselves!" NATURAL PHILOSOPHY 161. CHAPTER V. THE EFFECTS OF VIBRATIONS.-I. SOUND. ~ 1. THE OIRIGIN AND THEI TRANSMISSION OF SOUND. (52.) IREAD (51). Sound is a sensation produced in the ear by the vibrations of external bodies. 1. Sound produced by vibrations.-Let two books be clapped together, and every ear in the room receives a shockl, to which the name of sound is given. The molecules of the books are made to vibrate by the blow, and these vibrations, acting upon the air in contact with them, produce air waves. These air waves, traveling outward in all directions, finally reach the ear, and the many parts of this organ receiving these vibrations, enable the mind to recognize the peculiar sensation which we call sound. When we listen to the sound of a church bell, we may in like manner imagine the molecules of the bell all in a state of tremulous motion, caused by the blows of the hannmer. This motion causes vibration in the air in contact with the bell. The air waves thus formed, travel in. all directions from the bell until the ear receives them. The roar of a cataract is the result of vibrations caused by the falling water. The rolling sound of 162 NATU RAL PHILOSOPHY. thunder is the effect of vibrations in air, caused by electricity. Every sound in nature, or that can be produced by art, may be traced back through the waves of some medium, to the vibrating molecules of some solid, liquid, or gaseous body. (53.) Sound waves travel through all elastic media or bodies. The velocity of sound is not the same in difi-ferent substances; it is governed by two laws:1st. The velocity of sound varies inversely as the square root of the density of the substance. 2d. The velocity of sound varies directly as the square root of the elasticity of the substance. In the same medium, the velocity of sound is uniform. 1. Sound waves. -All sounds are the effects of vibrations, but it is not true that all vibrations produce sound. There are vibrations too slow to affect the ear; such are the vibrations of a cord not over-stretched. On the other hand, there are vibrations which are too rapid to be heard. The lower limit has been fixed at 16 vibrations a second, and the higher at 38,000. Waves which occur within these limits of velocity can be heard, and are called souncz waves. It is interesting to notice that the limits of hearing are not the same in all persons. 1" Nothing can be more surprising than to see two persons, neither of them deaf, the one complaining of the penetrating shrillnecss of a sound,,while the other maintains that there is no sound at all." In the'Glaciers of the Ablps' I have referred to a case of short auditory range noticed by myself in crossing the Wengern Alp in company with a friend. The grass at each side of the path swarmed with insects which, to me, rent the air with NATURAL I PHILOSOPHY. 163 their shrill chirruping. My friend heard nothing of this, the insect music lying quite beyond his range of audition." (See Tyndall's Lect. on Sound.) 2. Are transmiltted through all elastic bodlies. —N umerous facts easily verified, prove this statement. When, for example, the blows of a hammer fall upon one end of a long wooden beam, an ear placed in contact with the other end hears the sound with surprising distinctness. The same thing is true of other solid bodies. The clatter of horses' hoofs, or the rattle of a railway train, quite inaudible to one who stands erect, is heard distinctly when the ear is placed in contact writh the ground. The solid earth transmits the sound waves. In liquids, also, sound waves travel freely. ILet two stones be struck together under water; the sound will be heard by an ear, itself under water, a long distance away. The transmission of sound waves through gases is sufficiently familiar; the sounds which throng the ear so constantly are transmitted through the atmosphere. 3. The velocity nlot thae same in all mtedlia.-The velocity of sound in a great many substances, has been found by laborious and skillful experiments (see Tyndall's Lect. on Sound, p. 26). In the following table some of these results are collected:SUBSTANCES. TEMPERATUlIE. VELOCITY. Air.......................... 32~ F. 1,092 ft. Air......................... 61 1],118 " Oxygen......................... 32' 1,040 " Hydrogeri........................ 32 4164" River Water..................... 59"i 4,714 Iron........................ 68 " 16,822" Pine Wood....................... 10,900" 164 NATURAL PHILOSOPiIY. The velocity of sound depends upon the density and the elasticity of the medium in which it travels. 4. Tlhefirst law. —The density of oxygen, other things being equal, is about 16 times that of hydrogen. But we see in the table that the velocity of sound in oxygen, is only about - as great as in hydrogen. In this case the velocity is inversely as the square root of the density of the medium. This law may be verified by repeated experiments. 5. The second law.-When air is heated in a tight vessel its elasticity is increased, while its density is unchanged. In this condition it will conduct sound more rapidly. If the elasticity of air be made 4 times as great, the velocity of sound will be doubled. The velocity of sound in this case is directly as the square root of the elasticity of the medium. It is so in all cases. It is evident that both density and elasticity must be known, before we can judge the power of a substance to conduct sound. Liquids are, for example, more dense than gases: their conducting power, on this account, would be less; but on the other hand their elasticity measured by the force required to compress t/hem is vastly greater, so that, as the table shows, water conducts sound better than air. 6. But i~n the saame vmedium velocity is unijfomz.The velocity of sound waves in air or in water, for example, is uniform. Moreover, all sounds in the same medium travel with the same velocity. When we listen to the niusic of a distant band, the various notes, high and low, loud and soft, reach the ear in the same order in which they were made. So also the shrill chirping of insects, the dull thud of a falling stone, the NATURAL PHILOSOPHY. 165 melodious songs of the birds, and the murmur of rivulets, are all borne with equal swiftness through the air. So uniform is the velocity of sound, that distances may be measured by means of it. Suppose the flash of a cannon on a distant hill was seen, and in 10 seconds afterward the report was heard, the temperature at the time being 61~ F. The velocity of sound is 1,118 ft., and the sound waves, starting when the flash was seen, took ten seconds to reach the ear. 1,118 x 10=11,180. The observer was at distance of 11,180ft. from the cannon. ~ 2. OF REFRACTION AND REFLECTION OF SOUND. (54.) Sound waves will pass from one medium to another. In this case refraction of sound occurs. Sound may be made louder, by so refracting the waves that they will be collected at the place where the sound is heard. 1. Sound waves pass from one mtedgium to another.When in a room, with doors and windows closed, we are able to hear sounds distinctly that are made in the open air. The rattling of carriages, the singing of birds, aInd the voices of friends, come freely through the solid walls of our houses. To do this, the sound waves must pass from the air outside, into the solid material of the wall, and then from this again into the air of the room. 2. -Refraction of sound. —Now, when sound waves go from one medium into another, they are beat out of the straight line in which they were moving; this is called refraction of sound. 166 NATU RAL PHILOSOPHY. To illustrate refraction: Suppose the lines B C and F H (Fig. 14) to represent two sound waves passing through Fis. 74 air and striking the surface of another substance A\\7 AA A, at the points C and H. They will not go through in straight lines to E and L, but on entering the denser medium A A, they will be bent, A.. taking' the direction C D ~ and H K, and when they emerge they will be again bent, so as to take the direction D E and K L. In this case, the refracted waves D E and K L are parallel to the original waves B C and F HI-. It will always be so when the sides of the medium, A A, are plane and parallel. 3. Souznd madce louder by refraction.-If the surfaces of the medium are curved instead of being plane and parallel, the sound waves which pass through will not come out parallel to those which enter. It may be that the waves which enter are seearating from each other, and yet those that come out are approachi~ng each other. In this way sound waves may be collected at a point, so that a sound may be heard there, which would not otlherwise be audible. This interesting fact may be illustrated by a curious experiment. A sack a m x, (Fig. 75), made of two films of collodion, or of very thin india-rubber, united at their edges by a rim of iron, is filled with carbonic acid-a gas much denser than air. A watch is placed at W, near to the sack. If now a person put his NATURAL PHILOSOPHY. 167 ear at S, it may be, a point at a distance of five or six feet on the other side of the sack, the ticking of the watch will be heard distinctly. If the ear be moved Fig. 75. firom this place ever so little, the sound will be more feeble, and if the sack be taken away the sound will not be heard at all. This experiment beautifully illustrates refraction. The sound waves which start from the watch would go in straight lines outward, farther and farther apart. But they strike the surface of the sack at points a nm, &c.; pass into it and through it, being bent from their course so as to emerge in the directions which take them all to the point S. So many vibrations are thus collected at this point that the sound is heard, whereas, if the sack were taken away, they would be so scattered that no sound would be produced. (55.) When sound waves fall upon the surface of a second medium, only a part of them enter; the rest are reflected. The reflection of sound is governed by the following law: 1E8 NATURAL PHILOSOPHY. The angle of reflection must be equal to the angle of incidence. An echo is produced by the reflection of sound. 1. The reflection of sou nd.-To illustrate the reflection of sound suppose the line I A Fig. 76. (Fig. 76) to represent the direction of several sound waves, which, passing through the air, strike a body M: M. Some of these waves will -A E: pass through the body, being refracted, but others will be thrown off in the direction A R. These are the reflected waves. Now, a person standing at R will hear the voice of another at I, when the distance is considerable, sounding as though it came from a person in the direction R A. We always judge the direction of a sounding body from us, to be that from, which the waves enter the ear. 2. Tle law of reflection. —To understand the language of this law, let us refer again to Fig. 76. The waves I A, those which fall upon the reflecting surface, are called the incident waves: the waves A R, those that are thrown off fromn the surface, are called the reflected waves, and the point, A, is called the point of incidence. Now, if a perpendicular A P, be drawn to the reflecting surface at the point of incidence, then the angle I A P, is the angle of incidence, and the angle P A R, is the angle of reflection. The law of reflection requires that these angles shall always be equal. 3. "The echo.-An echo is a repetition of sound produced by the reflection of waves from a distant object. Who, after loudly uttering a word or sentence, has not NATURAL PHILOSOrPY. 169 sometimes listened to the sound of his own voice coming back to him from a distant wood, or from the face of a cliff; or, it may be, from the wall of a distant building? Visitors to Cooperstown will not soon forget the fine echo returned from the rocky hills which skirt Otsego Lake. There, we are told by Fennimore Cooper, once dwelt Natta Bumpo, the hero in the story of the "Pioneers." Let his name be loudly called from a cer tain place upon the lake, and immediately the response — Nat-ta-Bum-po, every syllable full and clear, rings back over the water as if spoken by the hero himself from his cave in the cliffs. When two obstacles are opposite to one another, the sound may be reflected back and forth many times. Surprising repetitions of echoes are, in this way, sometimes produced. It is said that an echo near Milan repeats a single sound thirty times.' When a trumpet is sounded at the proper place in the Gap of Dunloe, the sonorous waves reach the ear after one, two, three, or more reflections from the adjacent cliffs, and thus die away in the sweetest cadences." ~ 3. ON MUSICAL SOUNDS. (56.) Musical sounds are caused by rapid vibrations which follow each other with great regularity. Any noise whatever, when repeated rapidly, will cause a continuous tone: even separate puffs of air, following each other rapidly, produce a musical sound. 1. Musical 8soundls.-When a single and intense air wave is suddenly produced, as when a gun is fired, the resulting sound is called a report. Let a series of such sounds be made in quick but irregular succession, and 8 170 NVATURAL PHILOSOPHY. the resulting sound is called noisc. But when the waves are made with regularity, and follow each other so swiftly that the ear can distinguish no interval of time between them, the result is a muszical sound. 2. Any noise reeateld ravpidly causes a continuous tone.-No matter what the source of the waves may be, nor how unmusical the separate noises, only let them be repeated with regularity and rapidity, and they will result in music. Slowly pass a piece of ivory, or even the finger nail, over the rough surface of a wound piano wire, and the sound of its strokes against the separate ridges is altogether unpleasant; but pass it quickly over tile same surface, and the ear is saluted with a musical tone of surprising shrillness and purity. If a card be pressed against the teeth of a wheel which rotates slowly, a series of distinct and unpleasant taps will be heard; but, if by means of a larger wheel and band, this wheel be made to revolve rapidly, the taps will coalesce and salute the ear with music. Fig. 17. 3. Pqfs of air macdle rapidly p2rodluce a musical sound.-The syren is an instrument by which a series of air puffs are made to produce a musical sound, and A_ by which the number of puffs made in a second are registered. Its structure may be learned from Fig. 77. - _B_ A brass tube 0, leads from a wind chest E, to a brass plate, c b, which is pierced with a /iI, series of holes arranged around the circumference of a eirc.ll. NATURAL PHILOSOPHY. 171 Above this plate is a disk c d, also perforated with holes exactly corresponding to those in the plate below. The disk is provided with a steel axis A, and is so -fixed that it may rotate with a very small amount of fiiction. The wheel work shown in the upper part of the figure registers the number of puffs made in any given time. Now, when the disk c d revolves, the holes in it will be brought alternately over the perforations in the plate (a b, and the spaces between them, so that these holes will be alternately opened and closed. When the disk is still, and the holes are open, if air be urged through the tube 0, it will escape from the top inl steady streams, but when the disk revolves these streams will be cut up into successive puffs. If the disk turns slowly, the separate puffs are heard, but as the disk is turned more and more rapidly, the air announces its escape by a musical sound of great purity and increasing shrillness. By a simple artifice, the air which gives the sound is made to turn the disk. This is done by making the holes through the plate ca b, oblique instead of vertical; those in the disk being also oblique, but inclined in the opposite direction. (57.) Mulsical sounds differ iln three respects: 1st, Pitch; 2d, Intensity; and 3d, Quality. I.-PITCH. A.-Pitch depends entirely upon the rapidity of vibrations which produce the sound. The diffe:'ence in the pitch of two sounds, is called an interval, and a series of eight sounds of differett 172 NATURAL PHILOSOPHY. pitch, has been adopted as the foundation of all music, and called the diatonic scale. The number of vibrations to produce the note a of the treble clef, is 440 a second. 1. Pitch depends on the rapidity of vibration.The pitch of sounds is that which distinguishes them as being high or low. It depends entirely upon the rapidity of vibration: the more rapid the vibrations, the higher will be the sound produced. Two sounds made by the same number of vibrations per second, however much they may differ in other respects, will have the same pitch. 2. Intervals.-When the number of vibrations which produce one sound, is twice as great as that which produces another, we must not say that the sound is twice as high, but rather that it is an octave above. The term octave, is used to designate a tone which is made by twice the number of vibrations needed to produce a lower one, called the fundamental. Other intervals will be named in the description of the scale. 3. The diatonic scale. — Now the difference in pitch, or the interval between a fundamental note and its octave, is very great. To fill up this interval, sounds have been chosen which blend, or harmonize most perfectly with the fundamental, or with each other. These, placed between the fundamental and its octave, form a series of eight notes, called the natural, or the diatonic scale. The eight notes of the scale are expressed by the following names and intervals:Names, C, D, E, F, (G, A, B, C. Intervals, 1st, 2d, 3d, 4th, 5th, 6th, 7th, 8th. NATURAL PHILOSOPHY. 173 This scale repeated about eleven times, making what is termed in music eleven octaves, will include all sounds within the range of the human ear. Only about seven octaves are available in music. The method of representing the notes in music is familiar to all. Remember that the note called A, is found in the second space of the treble clef, and the position of all others may be easily traced. 4. Number of vibrations for the notes.-The number of vibrations to produce the various notes, may be found by experiment with the syren. (See Tyndall on Sound.) It has been found that the note A, of the treble clef is made by 440 vibrations a second. (See Silliman's Phys.) In piano-fortes for private use, this note is produced by about 420 vibrations a second. If we represent the number of vibrations for the fundamental note by 1, then the several notes of the scale will be made by the following ratios:C, ), E, F, G, A, B, C. 9 43, i, 2. Now, remembering this series of fractions, and the fact that A is made by 440, the number of vibrations for all the others may be found. Thus for example, how many vibrations to give the fundamental C? The relative number of vibrations for A and C are A and 1; that is, A is produced by - as many vibrations as C; or, to reverse the ratio, C requires - as many as A, and - x 440 264. Having this number for the fundamental, multiply this by the fractions -9, a, 4, &c., and the numbers for the corresponding notes will be obtained. These multiplied by 2 will give the number for the notes in the next higher octave, or divided by 2, 174 NATURAL PHIILOSOPHY. will give the numbers for the notes in the octave below. It.-INTE1NSITY. B.-The intensity of sound is that which distinguishes it as being loud or soft. It depends entirely upon the amrplitude of the vibrations which produce it. The greater the amplitude, the louderthe sound will be. In the case of a vibrating string for example, the loudness or intensity of the sound made by it, will depend entirely upon the distance through which the string vibrates across its line of rest. III.-QUALITY. 0. —By quality, we refer to that peculiarity of sound by which we may distinguish notes of the same pitch and intensity, made on different instruments. The pitch and intensity of notes made on a violin and on a piano may not differ, and yet how easy to tell the sounds apart. We recognize the voices of friends, not by their pitch nor their intensity, but by their quality. Quality is thought to depend upon the different sets of vibration, which, in different instruments, combine with those that cause the leading tone. The material of a violin vibrates as well as the string which is stretched upon it, and the sound made by both sets of vibrations is the real tone of the instrument. The various parts of a piano vibrate as well as the piano wire, and the sound produced by all these vibrations together is the familiar sound of the instrument. Now, it is clear that the sets of vibration in these two instruments must be different, and for this cause the quality of the two tones is different. NATURAL PHtILOSOPHIY. 7 (58.) Musical instruments are, for the most part, of two classes: first, those in which the sounds are produced by vibrating strings, and, second, those in which sounds are made by vibrating columns of air. I.-STRINGED INSTRUMENTS. A.-In stringed instruments, the pitch of the different notes is obtained by using strings or wires of different lengths, of different tensions, and of different weights. 1. Strinyed nstruzents.-The violin, the guitar, and the piano, are familiar forms of stringed instruments. In every case, cords or wires are tightly stretched over some solid body having considerable surface. The music of these instruments is not made by the vibrations of their cords alone; the simple vibration of a cord is not able to produce sound of sufficient intensity, but by being stretched over hollow boxes made of elastic wood, the material of the box, and the air inside of it are made to vibrate, and these vibrations, joined with those of the cords, produce the sounds of the instrument. 2. P'iitch varied by ~using strings qf different lengths. -The pitch of any sound depends upon the rapidity of vibrations; but according to the first law of vibrating strings, the rapidity of vibration is greater as the string is made shorter. To obtain sounds of different pitch, *we may then use strings of different lengths. Now, suppose we would know the lengths of eight strings of the same weight and tension, which would give the eight notes of the scale. We lhave learned that the number of vibrations per second is inversely as the length of the cord, and we have learned also that the relative number of vibrations for the eiglht notes are 176 NATURAL PIILOSOPIIY. expressed by the series 1, -, I- 4, -,,, 2. Then invert the terms of this series, and they must express the relative lengths of cord to produce the notes. They will be 1, 1, K, A, a, -, A,. Knowing the length of the string to give the fundamental, it is easy to calculate the lengths of all the others. Let us start with a string 18 inches long for the first note; the second must be x 18; the third must be I x 18; the fourth, must be { x 18, and so on until the eighth, which must be i x 18. 3. Pitch is varied by usingy strings of d'fferent tension.-According to the second law of vibrating strings [see (46.)], the number of vibrations made in a second increases when the tension increases. Hence the pitch of sound made by the string will be higher when the tension is made greater. 4. Pitch is varied by using strings of different weights.-According to the third law of vibrating strings, the number made in one second varies inversely as the square root of the weight of the strings. IIence the pitch of the sound will be higher, when the string which makes it is lighter. II.-WIND INSTRUMENTS. B.-The organ and the clarionet are examples of wind instruments. In the organ, sounds are made by vibrating columns of air in pipes, sometimes aided by the vibrations of a slender and elastic tongue, called a reed. (See Tyndall on Sound.) In the clarionet the sounds are always made by air vibrations aided by a reed. The pitch of sounds in pipes, depends upon the lengths of the pipes. A pipe to produce the lowest note in music, must be 32 ft. in length, and the pitch of NATURAL PHILOSOPHY. 177 tones from other pipes will vary inversely as the length of the pipes. Organ pipes are sometimes open at the top, and sometimes closed. An open organ pipe yields a note an octave higher than a closed pipe of the same length. A closed pipe, to give the lowest note in music, need only be 16 ft. in length. 8*a 178 NATURAL PHILOSOPHY. CHAPTER VI. THE EFFECTS OF VIBtRATIONS.-II. LIGHT. ~ 1. ON THE NATURE OF LIGH'l' AND THE LAWS OF ITS TRANSMISSION. (59.) READ (51). Light is thought to be the effect of vibrations in an ether which fills all space not filled by other matter. These vibrations are produced by luminous bodies, and, when transmitted to the eye, cause vision. 1. Zight is the efect of vibrations.-It was once thought that light consists of minute particles of matter thrown in great abundance from the sun and some other bodies: it is now generally believed that light is the result of vibrations. But light will pass through the most perfect vacuum that can be made: what can be left to vibrate? Moreover, the atmosphere extends but a few miles above the earth, yet the light from the sun comes in floods through the vast distance which separates these bodies: what can there be between the sun and the earth, whose vibrations bring to us the sunlight? 2. The ether.-Philosophers assume that there is a thin, elastic substance called ether, much finer and rarer than air, which fills all the spaces between the he-avcnly NATURAL PH ILOSOPHY. 179 bodies, and enters into all the spaces between molecules of matter in every form. The vibrations of this ether carry light wherever it goes, through a vacuum, through celestial spaces, through bodies like glass, and through the substances of the eye, until it strikes the nerves of sight. When a gas jet is suddenly lighted in a dark room, every eye present is dazzled by the brightness of the light. The explanation is this. The heated gas makes the ether vibrate. This ether is between the particles of the air, and between the particles of the eye. Its vibrations, starting from the gas jet, go through the air and into the eye, and when they reach the delicate nerves in the back part of this organl we are made conscious of the presence of light. 3. Lumnino.s b)odies. —Bodies which shine by their own light are called lunminous bodies. They are bodies which can make the ether vibrate. Bodies which shine only by light which they receive from others are called non-lumiqwous bodies. They can not make the ether vibrate. The sun is a luminous body: so is a redhot iron ball. All flames are luminous bodies. The moon is non-luminous. Almost all bodies on the earth are non-luminous: the light which they give to us is light which the sun first gave to them. (60.) Rays of light are transmitted through some media more freely than through others but always according to two laws:1st. In a medium of uniform density, light goes in straight lines with a uniform velocity. 2d. The intensity of light varies inversely as the square of the distance from its source. .180 NATURAL PHILOSOPHY. The art of Photometry depends upon this second law. 1. Rays of light.-A single line of light, or more accurately the path of a single vibration, is called a ray of light. But the smallest portion of light which can be separated by experiment, consists of many rays. A ray of light is quite too delicate a thing to be seen. A collection of parallel rays is called a beanr of light. A collection of rays which diverge from a point, or which converge toward a point, is called a pencil of light. 2. Rays of light are trar.smittecd.-Some substances permit light to pass through them freely; they are said to be transparent. Air and water are examples of transparent bodies. Others, such as iron and wood, appear to forbid the passage of light through them: they are said to be opaque. But no substance will transmit all the light which it receives; even the air is not perfectly transparent. On the other hand, no substance will stop all the light which falls upon it; even gold, when a very thin leaf of it is examined, can be seen to transmit light. All substances are doubtless able to transmit light in somie degree. 3. L;ight moves in straight lines.-That light moves in straight lines is shown by numerous familiar facts. We can not see through a crooked tube, simply because light can not pursue a crooked path. And again: who has not seen the sunlight coming through the shutters of a half-darkened parlor, spotting the opposite wall with circles of light? The sun, the hole in the shutter, and the spot on the wall, are always in the same straight line. Let the air of the room be sprinkled with dust, NATURAL PHILOSOPHY. 181 and the paths of the sunbeams are seen streaking the air with bars of light. 4. With uriform velocity. - Light travels through space with a uniform velocity of about 192,000 miles a second. This number has been found by observing the eclipses of one of the moons of Jupiter. The time when the eclipse should begin can be calculated by an astronomer with great accuracy. But it is found that when the earth is in that part of its orbit nearest to Jupiter, the eclipse begins 16 minutes and 36 seconds sooner than it appears to when the earth is in the opposite part of its orbit. It must, therefore, take light 16 minutes and 36 seconds to go across the earth's orbit. When this distance is known and divided by the number of seconds the velocity of light is found. Calling the distance from the earth to the sun, ninety-five millions of miles, the result is about 192,000 miles a second.* For all distances on the surface of the earth, the passage of light may be considered instantaneous. It would go quite around the world almost seven times in a single second. 5. The second law.-That the intensity of light is less as we go farther from the luminous body, is a fact familiar to all: the rate at which it diminishes is not so apparent. That the intensity varies inversely as the square of the distance may be easily proved by experiment. A square piece of stiff card-board A (Fig. 78), is placed in front of another (B) very much larger. If now, a candle-flame be placed in front of the small card, a shadow will be cast upon the large one. This shadow * For Foucault's method of finding the velocity of light, see Silliman's Phys. p. 291. 182 NATURAL PHILOSOPHY. will be larger, as tile smin 11 card is moved nearer to the flame, it will be smaller as it is moved the other way. Fig. The figure is intended to show'A..................... l- the small card to A ~ - -" ~l be just I as far from the flame as Ii ) 0 4 X ~ the large one. In I this case the shad-'W___ ow will be found to be exactly 16 times as large as tile card in friont of it. Now, the same amount of light which is spread over the small card would, if it could go on, just cover the place of this shadow. Inut if the same amount of light is spread over 16 times as much surface in one case as in another, it can be only, as intense. At 4 times the distance from the luminous body, in this case, the intensity of the light is ~v as great. At 3 times the distance, the light would, in the same way, be found to be t as intense. In other words; the intensity of light varies inversely as the square of the distance from the luminous body. 6. P/ otomnery. — It is often desirable to compare the illuminatingy powers of different flames. The art of doing this is called photomerey. The simplest method is to place the two flames at such distances from a screen, that the intensities of the light they shed upon it shall be equal; the illuminating powers of the flames must then be as the squares of' these distances. Suppose, for example, that we wish to know how fiany times more light one candle will give than another of inferior quality. Let a slender rod B (Fig. 79), be put just in NATURAL PHILOSOPHY. 183 front of a white screen A, and then move the flaimes to such distances, that the two shadows of the rod, falling Fig. 79. side by side upon the scree —, shall appear to be of ea —-- side by side upon the screen, s-hall appear to be of egual darkness. The intensities of their lights on the screen must then be equal. Measure the distances from the flames to the screen: the amounts of light they give will be as the squares of their distances. One being twice as far away as the other, it gives four times as much light. ~ 2. ON THE ZREFLECTION OF LIGHT. (61.) When light in passing through one medium comes against the surface of another, only a part will be transmitted, another part will be reflected, obeying the following law:The angles of incidence and reflection must be equal, and in the same plane. 1. Refection. —The reflection of Fig. 80. light is in all respects like the reflection of sound [see (55.) 1]. The same ternms are used to describe it; the same figurre may be reproduced to illustrate it. Thus in Fig. 80, the line I A, may represent a beam of light passing through air and striking upon the surface of a plate of glass at A. One part of the 184- NATURAL PHILOSOPHY. beam will enter the glass and emerge again on the other side, but another part will be thrown back into the air in the direction A IR. The beam I A is the incident beam. The beam A RIt is the reflected beam. The point A is the point of incidence. 2. iThe claw of reflection.-The reflection of light is also governed by the same law as the reflection of sound. The angle I A P (Fig. 80), is the angle of incidence. The angle P A R is the angle of reflection. These two angles must be equal. How various and beautiful are the phenomena which this principle of reflection explains! The sky, with all its floating clouds or shining stars, is painted in every pool of water, because the light from them, falling on the surface of the water, is reflected to our eyes. Rocks, and shrubbery, and dwellings along the shore, are pictured in the quiet waters of the lake, with skill exceeding that of any human artist. Vision is produced by reflected light. How seldom do we receive the direct rays of the sun into the eye; how rarely indeed, do we look directly upon any luminous body! But in all other cases we see objects only by reflected light. The sunbeams fall upon all objects exposed to them, and, bounding from their surfaces, enter the eye, and we see them in the direction from which the reflected rays have come. (62.) The effects of mirrors are explained by reference to the law of reflection. Rays of light reflected by a plane mirror have the same relation to each other as before reflection; But the effect of a concave mirror is to collect the rays of light which are reflected by it; NATURAL PHILOSOPHY. 185 While a convex mirror always separates the rays which it reflects. 1. 3irrors.-Any surface smoothly polished that will reflect nearly all the light which falls upon it, is called a mirror. The smooth surface of quiet water is a very perfect mirror. Artificial mirrors are generally made of metal or of glass. If made of glass, a thin film of mercury is spread over one side, and the smooth surface of this metallic coating is really the reflecting surface. Mirrors are either plane or curved. Of the curved mirrors there are two varieties, the concave and the convex mirrors. 2. The efect of plane mirrors. —The rays of light which fall upon a mirror may be parallel, or converging, or diverging, but can have no other relation. Now, let the mirror be repre- Fig. 81. sented by the straight line.A B (Fig. 81), and suppose, first, that it receive two parallel rays represented by the lines a c and b d. At the point of incidence c, erect a perpendicular to the surface A B. The angle, a c g, will be the angle of incidence. Then draw the line c f, so as to make the angle of reflection, g c f, equal to the angle of incidence, and c f must be the direction of the ray reflected from the point c. Again: at the point of incidence d, erect a perpendicular and draw the line d e, making the angle of reflection equal to the angle of incidence, and this line must represent the ray reflected from the point d. It will be found that the reflected rays, c f and d e, will be parallel 186 NATURAL P HILOSOPHY. Fig. e82. Suppose, second: that two rays, a c and b d (Fig. 82), are coTverging' and strike the mirror at the points c and d. By making the angles of incidence and reflection equal, exactly as it was done in the preceding case, we find that the reflected rays will take the directions c e and d e, conver'yiny to the point e. Fig. 83. Suppose, third: that the rays are dverging. Represent them by lines a c and ad(Fig. 83). Erect the perpendiculars and construct the angles of incidence and reflection equal, and the directions of the reflected rays will be c e and df, diverging from each other. In each of these three cases, the reflected rays have the same relation as the incident rays. 3.'lie efect of concave mirrors.-We will notice only those concave mirrors whose surfaces are spherical. If -we know the direction of the incident rays, we can find the direction of the reflected rays by making the angle of reflection equal to the angle of incidence. To construct the angle of incidence, we must, as in the plane mirror, erect a perpendicular to the concave surface at the point of incidence, and all difficulty disappears when we remember that a perpencdicular to any spherical s8wrface is the radius of the sphere. NATURAL PHILOSOPHiY. 187 In Fig. 84, M N rep- Fig. A4. resents a section of a concave mirror. The point C represents the center of curvature, that is, the center of the hollow sphere, of whose concave surface the mirror is a part. Now, if E A and D B represent two _parallel incident rays, and we would find the direction they take after reflection, we may draw the radii, C A and C B, making the angles ofincidence, E A C and D B C, and then draw the lines A F and B F, so as to make the angles of reflection equal to these. By so doing, we find that the reflected rays converge and cross each other at the point F. In Fig. 85, the Fig. 85. lines, E A and D B, represent converging rays. By constructing the angles of incidence and reflection in the same way as before, we find that the reflected rays cross each other at the point F, converyizg faster after reflection than before. In the same figure, F A and F B may represent diverging rays, striking the mirror at the points A and 188 NATURAL P HILOSOPHY. B. By constructing the angles of incidence and reflection equal, we find the reflected rays taking the directions A E and B D, diverying less after reflection than before. Now, since parallel rays are made converging, and converging rays are made more converging, while diverging rays are made to diverge less, we may say that the general effect of a concave mirror is to collect rays of light. A focus is any point where rays of light cross, or appear to cross, after reflection. The points F, in Figs. 84 and 85, are foci. The axis of a mirror is a straight line drawn through the center of curvature and the middle point of. the mirror. Fig. 86- In Fig. 86, the line C A is the axis of the mirror MT N, whose center of curvature is at C. The focus of rays that are parallel to the axis, and fall upon the mirror, near its middle point, is called the principal focus. If the rays B E and D H (Fig. 86), are near to, and parallel to the axis C A, they will, after reflection, cross each other at the point F, and this point is the principal focus of the mirror. The principal focus is on the axis, half way between the center of curvature and the mirror. 4. The effect of convex mirrors.-In Fig. 87, a convex NATURAL PHILOSOPHY. 189 mirror is represented by AI N, its center of curvature by the point C. Two parallel rays of light, E A and D B, strike the mirror at the points A and B. To Fig. 8T. construct the angles of incidence, we must erect perpendiculars to the surface at these points. The perpendiculars are the radii, C A and C B, extencded beyond the convex surface of the mirror. By making the angles of reflection equal to the angles of incidence, the reflected rays are found to take the directions A F and B HI. We notice that parallel rays are rendered diverging. So we might show that diverging rays would be made more diverging, and that converging rays would be made to converge less. We say, therefore, that the general effect of a convex mirror is to separate rays of light. (63.) When the light reflected from a mirror enters the eye, we see an image of the object from which the light proceeds. 190 NATURAL PHIILOSOPIY.'The image of any point will always be found where the rays of' light which go from that point, either meet, or appear to meet, after reflection. 1. Imnayes by refection. — When a person stands b)efore a looking-glass, nnumberless rays of light from every point of his countenance fall upon it. These rays are l eflected, and many of them are thrown into the eye. Those which enter the eye, cause him to see his image in the glass. 2.:The iracge of a _point.-Now, if the rays of light, whichl form the image in the glass, were visible, the person would be able to trace thern back from. the eye, converging toward the points on the glass from which they are reflected, and they would appear as if they came fromn points in the image behind the glass. Fi. ss. This will be understood by means of Fig. 88. Let MAf N represent a plane imirror. From the point A, numberless rays fall upon the mirror, some of which, after reflection, will enter the eye, supposed to be at 0. Two of these rays are represented in the figure. The eye iwill receive these rays as if they came fromn the point a, and this point a is the image of the point A, fiom which the rays procee(l. (41.) The ilinagte iurmeed by a piane mirror is alwavs NATURAL PHILOSOPHY. 191 as far behind the mirror as the object is in front of it; the same size as the object, and erect. 1. Irmages by pla;ne mnirrors.-We are now prepared to see how looking-glasses make such perfect images of all objects placed in front of them. Suppose an Sarrow A B, placed before a mirror (Fig. 89). Let us construct its image. From the Fi. 89. vast number of rays which go from A to the glass, select two which fall upon it very near together, atf and g. By making the angles of reflection equal to the angles of incidence, we find the reflected rays taking the directions f P, and O0. Now, if the eye be placed at E, it will receive these reflected rays as if tlhey came from the point a. Again, select two rays, which, going from the other end of the arrow B, strike the mirror at points near together at c and d, so that after reflection they can enter the same eye at E. These rays will appear to have come from 7. From all points between A and B, rays of light will go to the mirror; and, being reflected(, will enter the eye at E, and appear to have come fiom points between a and b. The image of the arrowv, A B, will thus be seen at a b. We may describe this image thus: the imnage made by a _plane 7mirs'oe' is always behind the miirror, just as jfacr as the object is in front of it, of the sambe Si2Cz as the object, and erect. (65.) If an object b1e i)laced in front. of a concave 192 NATURAL PHILOSOPHY. mirror, an inverted image may be formed on the same side of the mirror. To explain this, remember that the image of any point will be, where rays of light either meet, or appear to meet, after reflection. 1. Images are formed.-The brilliant inner surface of a silver spoon shows the image of a person who looks upon it, but it will be curiously different from his image seen in a looking-glass. It is very small; it is inverted; and, moreover, by careful attention, the person sees his picture standing in the air between himself and the surface of the spoon. Nor is this all; the picture in the air will grow larger or smaller, or it may disappear altogether, as the spoon is moved toward or from the face of the observer. If a spherical concave mirror of small curvature be at hand, a beautiful experiment will illustrate its power to form images. Let a beam of sunlight pass through an opening in the shutter of a dark room. In the path of this beam, at a convenient distance from the window, place a picture of a butterfly or other object, painted in transparent colors upon glass. The concave mirror placed in front of the picture, so as to receive the light which has come through it, will reflect the rays upon the wall above the window, and if its distance from the picture is just right, a magnificent image of the butterfly, much larger than the picture, and with its head downward, will be seen upon the wall. 2. The images of points.-How is this beautiful effect produced? Can we find the images of points [see (63.) 2] of the object by tracing the reflected rays which produce them? Let M 1N (Fig. 90), represent a section of a concave mirror, and suppose an arrow, A B, in front of it. Select two rays of light which, going NATUR L PHILOSOPHY. 193 from the point A, fall upon the mirror at the points D and E. After reflection they will cross each other Fig. 90. at A'. Again select two rays, which, going fiom the point B, fall upon the mirror at the points II and F. After reflection they will cross each other at B'. Other points in the object will send rays to the mirror, which, after reflection, will cross each other at points between A' and B'. In this way a large and inverted image is made in the air at A' B'. (66.) The position and size of the image will depend upon the distance of the object from the mirror. We will notice three well-marked cases: 1st. When the object is beyond the center of curvature. 2d. When the object is between the center of curvature and the principal focus. 3d. When the object is between the principal focus and the mirror. 1. T/he object beyond t/e center.-We are now prepared to see how the mirror forms its images in the air. Let M N (Fig. 91) represent a section of a concave 9 194 NATURAL PHILOSOP HY. mirror, whose center of curvature is C, and whose principal focus is F. Suppose an arrow A 3, to be Fig. 91. put in front of the mirror, beyond the center of curvature. The rays of light from the top of the arrow A, will, after reflection from the mirror, cross each other at the point A'. Those which go from the bottom of the arrow B, will, after reflection, cross each other at B'. From points of the arrow between A and B, the light which falls upon the mirror, will be collected into corresponding points between A' and B'. A perfect image of the arrow will thus be formed at A' B'. In this case we observe that the image is between the center of curvature and the prt iceipalfocats, inverted, and snaller than the object. This case was illustrated by the experiment with the silver spoon. 2. DTe object between the center and f cces.-Now, let us suppose that in this same Fig. 91 an arrow B' A', with its head pointing downward, is placed between the center of curvature and the principal focus. The rays of light from~ the point B', striking the mirror at a and b will, after reflection, cross each other at the point B, those from A', after reflection, will cross each other at A, and the image of the arrow will be formed at A B. In this case, we observe that the image will NATURAL PI-ILOSOPRY. 195 be beyond the center of curvature, inverted, and enlarged. This case was illustrated by the experiment with the picture of the butterfly. 3. T/~he object between the focus and the mirror.When the object is gradually moved from the center toward the focus, the image will rapidly move farther and farther away, until, when the object has reached the focus, the image will be at an infinite distance in?front of tite mirror, and of course, invisible. But let the object be carried a little farther, so as to be between the focus and the mirror, and the image suddenly leaps firom its distant place in front of the mirror, to a position be/dind it. To illustrate the formation of this image behind the mirror, let A B (Fig. 92), represent an object between the focus F, and the mir- Fig. 92. ror M AI'. Two rays of light from the top of the object strike the mirror at IT, and are reflected to the point E. To an eye placed there, these rays would appear to have come from the point a behind the mirror. Two rays from the bottom of the object falling upon the mirror at K, will be reflected so as to enter the same eye at E, and will seem to have come from the point b. Joining the points a and b, we have the entire image constructed. In this case we observe that the image is behind the mirror, erect, and larger than the object. (67.) The images formed by convex mirrors are 196 NATURAL PHILOSOPHY. always behind the mirror, erect, and smaller than the object. 1. Inages by convex mirrors. —The bottom of a silver spoon will serve, in a homely way, to illustrate the effects of a convex mirror. A person looking upon it will see his own image, apparently in the metal of the spoon, erect, but very slnall. The following diagram will illustrate the formation of these images. Fig. 93. The object D E, is placed in front of the convex mirror A B, whose center of curvature is at C. Two rays of light from D, may be traced after reflection to the points H and K, and if an eye can receive these rays, they will seem to come from the point d. In like manner, rays from the point E, after reflection from the mirror, may enter the same eye, and appear to have come from e. The image of the object will thus be found at d e, 7e/imdrl the mirror, erect, and smaller titan the object. ~ 3. oxN THE REFRACTION OF LIGHT. (68.) When light passes from one medium into another of different density, it is refracted, obeying the following laws:1st. In passing into a denser medium, light is bent toward a perpendicular to the surface at the point of incidence. 2d. In passing into a rarer medium, light is bent from the perpendicular. 1. Refraction.-The refraction of light is similar to NATURAL PHILOSOPHY. 197 the refraction of sound [see (54.) 2]. The same terms are used to describe it, and the Fig. 94. same figure might be made to illustrate it. A simple experi- rT. A ment will suit our purpose better. Through a small opening in the shutter of a darkened room, let a beam of sunlight _ enter, and fall obliquely upon the surface of water held in a glass vessel (a b c d, Fig. 94). If the water has been made tur- c C D b bid by the addition of a little soap, and the air above it misty, by sprinkling into it the dust of a chalk-bruslh, the beam of light will be distinctly seen in both, absolutely straight, except at the surface of the water, where it will be very considerably bent. Its path is represented by the broken line A B D. 2. Tie frst law of refraction.-If now, a perpendicular F E, be erected to the refracting surface at the point of incidence B, we see that the rays A B, instead of moving in a straight line, onward to C, will be bent toward the perpendicular. Water is denser than air. In going from the rarer to the denser medium, the light is bent toward the perpendicular. 3. The second law of refraction. —Let us suppose that D B represents a beam of light going from the water into the air at B; it will take the direction B A, ilstead of going on in a straight line toward P, being bent from the perpendicular F E. In passing from the denser medium into the rarer, the light is bent from the perpendicular. Many phenomena in nature may be explained by 198 NATURAL PHILOSOPHY. reference to these principles. ]When, for example, an oar is dipped into clear and quiet water, it appears broken at the surface. The light comes to the eye from all points of the oar. From that part which is above water it comes in straight lines through the air, but from the part under the water the light coming up into the air, is bent at the surface. The eye which receives these bent rays traces them back in st8a;Thft lines, and the oar, from which they come, is thus made to appear to be where it really is not. (69.) Some substances refract light more than others. Their relative refracting powers are indicated by certain numbers, which are called indices of refraction. i. The index of refraction. —We may best explain the meaning of this term by means of the following diaFig. 95. grain. Suppose a small beam of light L A (Fig. 95), to be passing from air into water. It will be bent at A, and go on in the direction of A Kf.:Now, with the point A as a center, and with any convenient radius describe a circumference. Let a perpendicular B C, be erected to the surface of the water at the point A, and from the points m and p, let the lines mn n and p q, be drawn perpendicular to this line. The angle n A ins is the angle of incidence, and the angle p A q, is the angle of refraction. If now we measure the lines rn in and p q, and divide the length of m n by that of p q, we will obtain a quotient which is called the index of' refraction. It is evident that if the beam were bent still more at NATURAL PHILOSOPHY. 199 A, this quotient would be larger: the larger the index of refraction, the greater the refracting power of the substance. For water, the index of refraction is always 1.336; for crown glass, the index is 1.58; for the bisulphide of carbol, it is 1.673. (70.) The effects of lenses are explained by the principles of refraction. A convex lens collects the rays of light which pass through it. A concave lens separates the rays which pass through it. 1. Lenses.-A lens is a transparent body bounded by surfaces, one at least of which is curved. Six different varieties are used in the arts. They are usually made of glass, and their shapes are represented by sectiona in Fig. 96. The double convex lens A, is bounded by two convex surfaces. The plano-convex B, is bounded by surfaces, one of which is convex and the other plane. Fig. 96. A 3B C L:F The mnezniscus, C, has one surface convex and the other concave, the convexity being greater than the concavity. The double concave lens D, has two concave surfaces. Thepilano-concave lens E, has one surface concave and the other plane. 200 NATURAL PIIILOSOPHY. The concavo-comveex len F, has one siurface convex and the other concav-e, the convex surface being less curved than the concave surface. The first three of these varieties, A, I, C, are conveo lenses; the others, D, E, F, are concave lenses. 2. T/he effect of convex lenses.-By remembering the two laws of refraction, and that a radius of a sphere is always perpendicular to its surface, it will not be difficult to trace the rays of light as they are refracted in going through a lens. Let a section of a double convex lens be represented by M 1N, in Fig. 97. The two Fig. 97. curved surfaces are parts of the surfaces of two spheres, whose centers are at C and C'. The line C C', drawn. through these centers of curvature, is called the axis of the lens. Now suppose two rays of light, a b and c d, parallel to the axis, to fall upon the lens at the points b and d. On entering the denser medium, they will be bent toward the perpendiculars to the surface at these points. These perpendiculars are the dotted lines C' b and C' cd. The refracted rays in the leas go in the directions b h and d e. On passing out of the lens into air, they are bent from the perpenldiculars to the surface at the points h and e. These perpendiculars are the lines C A and C e, and the refiacted- rays cross each other at the point C'. Parallel rays refiac(ted by a convex lens are NATURAL PHILOSOPHY. 201 made converging. And we should find that in all cases, the rays after refraction will be nearer to each other than before. The general effect of the convex lens is to collect rays of light. The plano-convex lens and the meniscus will have the samne effect, but in a less degree. The point C' is the princ'pal focus of the lens: it is the focus of rays which are parallel to the axis. The distance of this point from the lens will depend upon the curvature of the lens, and upon the index of refraction. If the two surfaces of the lens are equally curved, and it be made of glass whose index of refraction is 1.5~, then the principal focus will be at the center of curvature, as in Fig. 97. 3. Tlke effect of concave lenses.-That concave lenses separate rays of light, may be shown by tracing the rays represented in Fig. 98. Fig. 98. Let M N represent the double concave lens, whose centers of curvature are C and C'. Two rays of light, parallel to the axis, striking the lens at the points b and d, will be bent toward the perpendiculars, and pass through the glass in the direction b i and d e. On emerging, they will be bent from the perpendicular, and go in the directions h k and e m. We thus find that parallel rays are made diverging. Diverging rays':*~~~~~~ 202 NATUR L PHIILOSOPHY. would be made more diverging, while converging rays would be made less converging. In all cases, rays refracted by a double concave lens would be separated. The plano-concave lens, and the concavo-convex lens have the same effect, but in a less degree. (71.) If an object be placed in front of a convex lens, an image of it will be formed on the other side of the lens. To explain this, remember that the image of any point will be made where rays of light going from it, either meet, or appear to meet, after refraction. 1. Inmages areformed. —If a convex spectacle glass is held in front of a window, at some distance, and a sheet of white paper is put in front of it, the light from the window will go through the glass and fall upon the paper. If the distance from the glass to the paper be just right, a very small but very perfect image or picture of the window will be seen upon it. If a good double convex lens, three or four inches in diameter be at hand, a very beautiful experiment may be made. Through an opening in a shutter of a darkened room, admit a beam of sunlight. Into this beam put any small, transparent object, it may be a picture painted on glass, or, quite as well, a wing of the dragonfly, so that the light may pass through it. If now, the lens be moved back and forth in front of this object, until just the right distance is found, a very large and perfect image will be seen inverted upon the opposite wall of the room. 2. T'he images of points.-Now let us see how these beautiful effects are produced. Suppose an arrow N S (Fig. 99), placed at some distance in front of a convex lens AI, whose centers of NATURAL PHILOSOPHY. 203 curvature aref andf.' Two rays of light from the point N, passing through the lens, will be refracted so as to cross each other at the point n. This point where Fig. 99. rays of light meet after refraction, is the image of the point N, fromn which they carme. The rays from the point S of the object, after refraction, cross each other at s, and form an image there. From points between N and S, rays of light going through the lens will be collected on corresponding points between nT and s, and thus a perfect image will be made inverted at n s. In this way, it is easy, by a diagram, to illustrate the furmation of all images by lenses. (72.) If an object be placed at a point twice the focal distance from a convex lens, an image of it will be formed at an equal distance on the other side. If the object be moved farther away, or nearer to the lens, the position and size of the image will be changed. 1. The object twice the focal dislance.-Suppose the lens to be one whose focus is at the center of curvature, and that the object is just twice that distance from the lens, as shown by the arrow N S (Fig, 100). Tworays of light from the top of the arrow go through the lens, bending according to the laws of refraction, and cross each other at the point nm. Two rays from the bottom 204 NATURAL PHILOSOPItY. of the arrow go through the lens and cross each other at the point s. Join the points n and s, and n s represents the image that is formed. This image will be at Fig. 100. twice the focal distance on the other side of the lens, of the same size as the object, and inverte 1. 2. The objectfartlher away. —This case is represented by Fig. 99. Suppose that in front of the lens MA, an arrow, with its head downward, represented by n s, is placed at more than twice the focal distance from the lens. Two rays from the arrow-head, after refraction, will be found to cross each other at N; two rays from s will, after refraction, cross each other at S. The image N S, is on the other side of the lens, at a less distance, smaller than the object, and inverted. 3. The object at a less distance.-If, in Fig. 99, we suppose N S to represent the object, outside the focus, but at less than twice the focal distance, its image will be found at n s. In this case the image will be at a greater distance on the other side of the lens, larger than the object, and inverted. 4. The object between, tAe focus and the lens. —One more ease remains to be considered. Suppose the object to be between the focus and the lens. Let M N (Fig. 101), represent a lens whlose focus is at C, and let the object A B, be placed between this point and the lens. An attentive examination of the figures show NATURAL PHTLOSOPHY. 205 that the rays of light from the point A, are diverging after refraction. And since their can never meet, it is clear that no Fig. 101. image can be formed on that side of the lens, but if an eye at E, receive these rays they will produce the same effect as if they came from A'. In like manner, the ravys from B, entering the eye at E, will seem to have come from B'. Hence an image will seem to be formed at a'! B'. This image will be on the same side of the lens as the object, erect, and larger than the object. (73.) Images are also formed by concave lenses. They are on the same side as the object, smaller, and erect. 1. Suppose an object A B (Fig. 102), in front of a Fig. 102. concave lens M N. Rays of light from A, after refraction, diverge as if they had come from a; rays froom B, after refraction, diverge as if they had come from h; the image will thus appear to be made at a b. This image 206 NATURAL PHTILOSOPHY. is on the same side of the lens, smaller than the object, and erect. ~ 4. ON TIIE DECOMIPOSITION OF LIGIIT. (74.) Prisms refract light; they also decompose it. They separate white light into rays of seven different colors, viz.: violet, indi(o, blue, green, yellow, orange, and red. 1. Prisms.-Any transparent body, two of whose sides are inclined toward each other, is a prism. The most commnon form of the prism is a triangular piece of glass. A water prism may be made by taking a threecornered vessel, with glass sides, and filling it with water. Other fluids may be used in place of water. 2. Prisms refract liygAt.-Light, in passing through prisms, must obey the laws of refraction. In Fig. 103, Fig. 103. the triangle in n o, represents a section of a prism. A ray of lig'lt srriling its surface at a, will be bent to NATURAL PHILOSOPHY. 207 ward a perpendicular on entering, and from a perpendicular on emerging, finally taking the direction b c. To the eye at c, this light would seem to come from the object at r instead of L. 3. Prisms decompose light.-The white light that comes from the sun, or fiom other luminous bodies, is really made up of seven different kinds of light. The way in which Sir Isaac Newton made this great discovery is shown in Fig. 101. In the window-shutter S, of a darkened room, he made a small hole, and Fig. 104. 0,' plaee d behind it a prism, A B C, so that the beam of sunlight D could fall obliquely upon one of its sides at E. Were it not for the prism the beam of light would go straight forward to F, where it would make a round white spot, but being reftacted by the prism, it formed above F, upon the screen MI, an oblong image containing sevenr d/Jerent colors. These colors appeared in order'from the top of the image, violet, indigo, blue, green, yellow, orange, and red. These colors are separated, it seems, because the prism has power to bend some of them more than others. The violet rays are bent most;- the red rays least. 208 NATURAL PHILOSOPHIY. The oblong image upon the screen is called the solar spectrum. The power of a prism to separate the color of white light is called dispersive power. The prism in this way enables us to analyze white light, or to find out the colors of which it is made; and now, if by any means we can unite these seven colors, we shall produce white light again. This can be done by using any irnstrunerlnt which collects rays of light. If the rays fall upon a concave mirror, they will be reflected to a focus, which will be a white spot. If the rays are received upon a double convex lens, they will be refracted to a focus, and this focus will be also white. Sir Isaac Newton collected the rays by using a second prism, exactly like the first, but placed beside it so as to bend the rays in the opposite direction: the imnage on the screen was waite. (75.) The spectrum formed by sunlight or by starlight is crossed by a great many fine black lines, while the spectra formed by light from artificial sources, are crossed by different colored bright lines. 1. The black lines.-The whole length of the solar spectrum, when seen by the naked eye, seems to be colored, but when seen through a magnifying glass. a great many fine black lines are found to cross it, as if a delicate brush, dipped in tile purest black, had been drawn across it by a skillful artist. A beam of sunlight always gives the same set of lines, holding the same relative position in the spectrum. A beam of starlight gives a different set, and the light from different stars gives each a set of its own. These lines are usually called Fraunhofer's lines, in honor of him who. first examined them carefully. NATURAL PHILOSOPHY. 209 2. The bright lines. — When the light from an artificial source is passed through a prism and its spectrum is seen through a magnitying glass, no black lines are visible, but instead of these, there will be seen lines of exceeding brightness, and of different colors. The color of these lines, and their place in the spectrum, will depend upon the substance whose flame gives the light. If, for example, a little common salt be burned in a hot gas flame, two yellow lines of surprising brightness will always appear in the yellow part of the spectrum, while the metal potassium in the flame will always give two lines, one of a brilliant crimson color, in the red end of the spectrum, the other a beautifiul blue line away off in the violet end. Each substance gives a set peculiar to itself. (76.) Drops of rain may decompose the sunlight: in this way the rainbow is produced. The primary bow consists of bands of the seven colors of the spectrum, arranged in parallel arches, with the red band on the outside. In the secondary bow the order of the colored arches is changed, the violet being on the outside. 1. The primary Fig. 105. rainbow. -This in ost A beautiful phenomenon is produced by the n action of rain drops; they decompose the sunlight and send its rich colors to the eye. To understand this action, suppose the 210 NATURAL PHIILOSOPHY. circle, whose center is at C (Fig. 105), to represent a section of a drop of water. RIays of sunlight (S A) falling upon the upper part of the drop will be refracted to the point B. At this point a part of the light will pass out into the air again, but another part will be reflected by the inner surface of the water and strike the surface at another point, D. The light which here goes out of the drop into the air, will be again refracted. Nbow the light will not oily be reftactedl, in its passage through the drop; it wNill be, at the same time decomnposel. On coninig out of' the water the red ray, bent least, will take a direction represented by D E; the violet ray, bent most, may be represented by D V; and all the other colors of the spectrum will be found between these. 2. The rede batnd on, t/le outsidce.-Now it is quite clear that if the person were standing upon tile ground in the direction of D E, so that the red rays from this drop would enter his eve, the violet rays, and indeed all the other colors, would go over hlis head. To him this drop of water would appear red. Another drop, some distance below this one, would send violet rays into the same eye. Between the drop which sends the red, and that which sends the violet, there would be Fig. 106. others from which the eye would receive tlhe other colors of the spectrurn. (Fig. 106.) *_gH IIence, when a shower of rain is flling, and the sun is at the same time shi-ling in the opposite par'- of the sky, NATURAL PHILOSOPHY. 211 so that a person looking toward the shower, will have his back turned toward the sun, he will see the seven colors of the spectrum painted upon the cloud in order, with red at the top and violet at the bottom. 3. Tie colors are i~n t/ke form of an ar)ch. —Now, suppose a line drawn from the sun through the eye of the observer, and straight onward until it reaches a point O (Fig. 105), directly under the drop C, which sends the light to the eye. If this drop sends a red ray to the eye, then all others, which like this are opposite the sun, and whose distance from O is the same, will also give red rays. If the arc of a circumference be drawn with O as a center, and with a radius C 0, all drops along this circumference will be equally distant from the center O, and will therefore give red rays. The red part of the rainbow is, for this reason, a circular arch, and for the same reason, the other colors are parallel arches below the red. 4. lhe secondary bow. —Outside of the bow just explained, another, the secondary bow is often seen. Its colors are more dim, and their order is reversed, the violet being at the top and the red at the bottom. To explain the primary bow we trace rays of light falling upon the top of the drops of water. But drops of rain in the air are entirely covered with light, and to explain the secondary Fig. 10 bow, we may trace the rays which fall upon their lower parts. The diagram (Fig. s 107) illustrates this. A beam of light S A, re- | fraected on entering the M A drop, goes through to its ~212!NATURAL PHILOSOPHY. inner surface at B, from which it is reflected. It strikes the inner surface again at D, and is again reflected. At the point F, a part of the beam will be again reflected, but another part will pass out into the air and be bent downward. In its passage through the drop the light is not only refracted; it is decolnposed. If F G represents the red ray, then F V may represent the violet ray. Now, clearly, if the red ray enters the eye, the other colors will fall belotw it, so that this drop will appear red. Other drops above this one will give the other colors in their order. Hence the outside band of the secondary bow will be violet, the inner one red. (77.) Bodies are of different colors, only because they decompose the sunlight, and reflect different parts of it to the eye. The various colors of the sky, and the clouds, are due to the decomposition of the light which comes through them from the same. 1. The color of bodies. —The sun sheds a flood of pure white light upon all bodies alike. Thlis white light is decomposed at their surfaces. Some of its colors are transmitted or absorbed by the body, while the others are reflected to the eye. One body is red because it decomposes the sunlight and reflects the red rays; another is blue, because it reflects only blue rays. The foliage of trees in the spring-time, receives the sun's white light, decomposes it, and reflects only the green rays. The petals of the violet decompose the sunlight to share with us the beautiful colors of the spectrum; it reflects the colors of the violet end, and keeps to itself those of the other. A body which NATURAL PHILOSOPIIY. 213 reflects all the color of the light it receives is white; one which reflects none is black. 2. TIte color of the sky. —The sky, when free from clouds, is blue, because the particles of the atmosphere reflect blue rays of light. If the thin air could not reflect light at all, the sky would appear black: if it reflected it without decomposition it would be white. The white sunlight falls upon its molecules, is decomposed by themn, and only those rays which make up the delicate blue color of the sky are reflected to our eyes. 3. ThAe color of the clouds.-The clouds both reflect and refract the sunlight, and all their varied colors are due to the decomposition thus produced. There can be no more gorgeous display of colors than we often see upon the clouds of the morning and the evening sky. What grand and diversified effects to be produced by means of such simple materials as light, water, and air! ~ 5. ON OPTICAL INSTRUMENTS. (78.) The microscope, the telescope, and many other instruments, help the eye to see small or distant objects, by forming large and perfect images of them near by, for it to examine. The eye itself is an optical instrument of the most perfect construction. 1. The microscope.-The simple microscope consists of a single convex lens. The lens is held in the hand at a little less than its focal distance from the obiect. The eye receives the light which comes from the object through the glass, and sees a magnified image on the other side. The operation of the compound microscope may be 214 NATURAL PHILOSOPHY. understood by means of a diagram (Fig. 103). Two convex lenses, and sometimes three, are tsed. Fig. 108. The lens A, called the object-glass, refracts the light from the object 0, placed a little beyond its focus, and forms an image inverted at 0'. The lighlt from this image is refracted by another lens 13, called the eyeglass, and if the rays are received into the eye, they will appear to llave come froim C D, which is the magnified image of the object. By means of this instrument, things otherwise too small to be seen, are made visible, and a world of wonderful creations is thus revealed for the study and admiration of man. A drop of water from a stagnant pool, is found, by mneans of the microscope, to be swarm ing with living creatures, whose forms are as perfect, and whose appetites are not unlike those of larger animals. 2. Tlie telescope.-A telescope is used for viewing distant objects. Some imes a lens is employed to form an image; sometimes the image is formed by a mirror. In the first case, the instrument is called a refracting telescope; in the second, it is called a refectiyng telescope. Of the refracting telescope there are three important forms: Galileo's, the astrolnomical, and the terrestrial. NATURAL PHILOSOPHY. 215 In Galileo's telescope there is a double convex objectglass A[ N (Fig. 109), and a double concave eye-glass, Fig. 109. E F. Rays ol ligllht from the point A of a distant object A B, after passing tllroug'h the two glasses, diverge as if they carne from the point Ca, while rays froml the point B of the object after refiraction, diverge as if fiom the point 4. An erect imnlae a b, Till be seen by holding the eye in front of the eye-glass E. The o(?7ieay-gl(,ss coilsists of' two small galilean telescopes placed side by side. In the astroononical telescope, two double convex lenses are used. Tile object-glass O (Fig. 110), forms a Fig. 110. small image a b of a distant object A B. The eyeglass (E) being so placed that its focus (F) is a little 216 NATURAL PHILOSOPHY. beyond this image, refracts the light, so that it will appear to have come from a magnified image c d. The course of the rays may be traced in the figure. In this instrument the image is always inverted. The terrestrial telescope is used for viewing distant objects upon the earth. To see them upside down, as in the astronomical telescope, is not desirable: that they may be seen right side up, two convex lenses are placed between the object-glass and the eye-glass. The arrangement of the glasses, and tlle course of the rays, are shown in Fig. 111. The object-glass 0, forms a small inverted image I, of a distant object A B, near its focus. From this image the light goes through the two lenses, m and n, to form a second image L. This image is erect with respect to the object, and it is magnified by the eyeglass E, in the usual manner. Of the reflecting telescope there are several varieties. In all of them the image of a distant object is formed by a concave mirror, and this image is magnified by a convex eye-glass. In the lHerschelia*n telescope (Fig. 112), the mirror AM N is inclined to the axis of the tube in which it is placed, so that rays of light from a distant object will be reflected to a focus near to one side of the NATURAL PHILOSOPHY. 217 tube at the other end. The observei-, looking down into the tube, holds an eye-piece, a, in his hand, through which he views a magnified image. Fig. 112. 3. The magic lantern. —The magic lantern is an instrument by which the image of a small transparent picture, painted on glass, may be thrown upon a screen, so much magnified that a whole audience may see it. It consists of a powerful lens, with objects highly illuminated by lamp-light placed so near it, that their images are formed far away. Fig. 113 shows a section of the instrument. Inside of a dark box, a strong Fig. 113. light (L) is placed. Behind this light is a concave mirror((M) and in front of it a convex lens A. This lens is at the entrance of a tube which projects from the side of the box. Inside this tube slides a smaller one, 10 2.18 NATURAL PHILOSOPHY. in which is fixed another powerful lens. The picture is placed in a slit C, provided for it in the larger tube, just in front of the first lens. The lamp fills the box with a strong light. The lens A, receiving light directly from the lamp, and reflected from the mirror, condenses it upon the object and highly illuminates it. The light from this bright object goes on through the second lens to the distant screen, and there forms a large and perfect image. This instrument is very useful to the lecturer or the teacher, who would illustrate the wonderful phenomena of nature. 1By means of small pictures, or of small transparent objects, he is able to make his audience see the relations of the heavenly bodies taught in Astronomy, or the delicate phenomena described in Natural Philosophy and Chemistry. 4. The camera obscura.-The camera obscura is an instrument by which to form miniature images of objects. It consists of a dark box, a section of which is represented by A B (Fig. 114), containing a screen S, Fig. 114. 21 _ and having a double convex lens L, filling an opening in one end. The distance of the lens from the screen may be varied by sliding the tube which carries it back and forth in the larger tube C. The light from the object O is refracted by the lens, and a beautiful imnage NATURAL PHILOSOPHY. 219 will be formed upon the screen. This image is always inverted, and smaller than the object. The camera may be illustrated by a very simple experiment. If, in a hole in the shutter of a darkened room, is placed a double convex lens, the room is itself a camera obscura, and persons present may see what takes place inside. Let a white sheet be hung in front of the lens at a proper distance, and it is at once covered with a perfect picture of whatever scenery may be outside. Houses and distant hills; the sky with its floating clouds; men and animals in the street, and even the flying birds, and the curling smoke, are painted upon the screen, with colors taken from the sun's bright rays. 5. TAe eye.-But most perfect of all optical instruments, is the eye. Who could at first believe, that in describing, as we have done, the camera obscura, we were describing a rough model of the human eye! Yet the eye is nothing but a simple camera obscura, differing from it only in its wonderful perfection. The human eye is a globular chamber, having for its outer wall a hard tough membrane called the sclerotic coat. The front part of the sclerotic coat is a transparent substance called the cornea. The chamber is lined with a more delicate membrane called the choroid, arid to insure the darkness of the place, this is covered upon the inside with a black paint. Tile front part of the choroid coat is called the iris, and in the center of this is a round hole called theppTil of the eye, through which light may pass into the dark chamber beyond. Behind this opening, is a double convex lens, very transparent and considerably hard, called the crystalline lens. Between this lens and the cornea is a limpid 220 NATURAL PHILOSOPHY. liquid called the aqueous hurnor, and filling the dark chamber, behind the lens, is another fluid, called the vitreous humor. The arrangment of these parts may be understood by attentively studying Fig. 115, which Fig, 115. S9 represents a section of the eye. S S, is the outer or sclerotic coat, sometimes called the white of the eye. C C, is the cornea; it is more convex than the sclerotic. K 1K, is the choroid, and i i, is the iris, the vertical curtain which shuts out all light, except what may get through the hole at its center —the pupil. L L, is the crystalline lens, and the large chamber V, is filled with the vitreous humor. The course of the rays of light is also shown in the figure. An inverted image of an object 0, is formed at R. It is there received upon a net-work of delicate nerve fibers called the retina, R R. The mind takes cognizance of this picture, and the person is said to see the object 0. These pictures on the retina are always smaller than the objects, and the more distant the object, the more minute the image. The diameter of the eye is little more than an inch, and yet when a person sees an extended land NATURAL PHILOSOPHY. 221 scape, every visible object, far and near, is painted upon the inner lining. If the picture in the human eye be thus minute, what must it be in the eye of a canary-bird or butterfly! 222 NATURAL PHILOSOPHY. CHAPTER VII. THE EFFECTS OF VIBRATIONS. —II. HEAT. ~ 1. OF TIIE SOURCES AND NATURE OF HEAT. (79.) TEE sources of heat may be studied in three groups. First, the heavenly bodies; second, mechanical action; and third, chemical action. I. —THE HEAVENLY BODIES. A.-The sun and the stars are sources of heat. 1. T/e sun. —Floods of heat come down with the sunlight. Upon this most familiar fact we need not dwell, further than to notice that the amount of heat received from the sun is doubtless greater than from any other source, and that as this amount varies from month to month, it allows the earth to be clothed in the snows of winter, the verdure of spring, the maturing growths of summer, and the ripening fruits of autumn. 2. 17we stars. —Heat comes with the starlight as well as with the sunlight. During the night when the stars are seen, not more than during the day when the stronger light of the sun obscures them, each star is sending its proportion of heat to warm the earth. NATURAL PHILOSOPHY. 923 II.-MECHfANICAL AC'TION. B.-No mechanical action can occur without evolving heat in the bodies which act upon each other. 1. Ilechanical action evolves beat.-When the savage lights his fire by rubbing two pieces of hard wood together, he produces heat by friction. When by repeated blows of a hammer, a nail is made too hot to handle, or when the iron-clad hoof of a horse " strikes fire" against a pavement stone, heat is evolved by percussion. And finally, when a piece of cold wood is heated by being squeezed between the plates of a hydrostatic press, heat is evolved by pressure. No two bodies can act upon each other, either by friction, by blows, or by sudden pressure without evolving heat. 2. Frietion.-By friction heat may be evolved in large quantities. Count Rumfbrd caused 18 lbs. of water-almost two gallons, to boil by the friction of a solid plunger against the bottom of an iron cylinder iminersed in the fluid. All bodies, whether solid, liquid, or gaseous, give off heat by friction. Sir Humphrey Davy quickly melted two pieces of ice by simply rubbing them together in a room whose temperature was below the freezing point. A bullet is warmed by the friction of the air through which it passes. A stream of water is warmed by friction against the sides of a channel through which it swiftly runs. lMoreover, the production of heat by friction is unzlinited; it will continue just as long as the friction is kept up. IIT.-CHEMICAL ACTION. C. —Ciemical action a source of heat.-Colnbustion 224 NATURAL PHILOSOPHY. is the most familiar form of chemical action; it is at the same time the most common source of artificial heat. Wood burns in the stove, or coal in the grate, and our houses are warmed by the heat given off by this chemical action. A chemical action takes place in the body of a person by which the food is changed to blood, and the blood again to bone and muscle: heat is evolved by this chemical action, which keeps up the constant temperature of the body. It is thought that no chemical action can take place without producing heat. (80.) The material theory of heat supposes it to be a very subtile fluid which fills the spaces between the molecules of bodies, and whose presence in larger or smaller quantities constitutes heat or cold. The dynamic theory supposes that heat is the result of vibrations among the molecules of a body: the more rapid the vibration, the higher the temperature. 1. Thee cmaterial theory.-The material theory supposes matter to consist of molecules, that these molecules do not touch each other, and that the space between them is filled by a substance called caloric, whose molecules are very much smaller than those of the body. Just as when water is poured into a barrel already filled with bullets, it runs into the spaces between them, so it is thought that the fluid caloric goes into and fills the molecular spaces. The sun and stars throw off abundance of this substance, and shoot it with the velocity of light across the spaces between them and the earth. In the cases of friction, of blows, and of pressure, the molecules of bodies are pushed nearer together, and by this means the caloric is szueczed out from betwea3n them, as, when NATURAL PHILOSOPHY. 225 a wet sponge is pressed, water flows from its interstices. In chemical action also, the particles of bodies are brought nearer together and force the heat fluid from between them. This theory, which until lately was opposed by only a few eminent men, is now almost universally discarded. 2. Thie dynamic tiheory.-It is now generally believed that heat is the result of vibrations. This theory, like the other, supposes matter to be made up of molecules separated by definite distances; it goes further, and supposes these molecules to be in motion, rapidly vibrating in the minute spaces between them. To increase the rapidity of this motion is to make a body hot; to lessen it is to make the body cold. The theory assumes also the existence of the ether, which according to the theory of light must fill all space. When we step from the shade into the sunlight, the gentle heat of its rays is instantly felt. The explanation is this: the molecules of the sun itself are in rapid vibration, they impart motion to the ether, whose vibrations dart through thie space between the sun and us, and, coming in contact with the person, impart vibration to the molecules of the sense of touch, when we become immediately conscious of the presence of heat. When bodies are heated by friction, their molecules are made to vibrate faster by the rubbing. Heat is evolved by percussion, because a blow increases the motion of the already trembling particles of the body struck. The same effect is produced by pressure. ~ 2. OF THE TRANSSMISSION OF HEAT. (81.) Rays of heat, like rays of light, pass through 10* 226 NATUItAL PHIILOSOPHY. some bodies more freely than through others. They obey the same laws of transmission, of reflection, and of refraction. 1. Rays of heat. —Since heat and light come together in the sunbeam, and since they are thought to be of the same nature, both being the result of vibrations, we may speak of rays of heat, just as we do of rayms of light. 2. Tranzsmission of tea rPays. — Just as light passes more freely through somle bodies than through others, so heat passer through different bodies with different degrees of facility. Those bodies through which it passes most freely, are sa!d to be diat/ermnic, while those through which it can go with the greatest difficulty, are said to be athertnic. Heat from different sources is transmitted in different degrees through the same substance. It is, for example, a ftmiliar fact that the glass of our windows allows the heat of the sun to enter our rooms, while it prevents the heat of the stove firom going out. Rock-salt is the most diathermic substance known; it allows heat from all sources to pass through it with the greatest freedom. 3. DLaws of transmission. —Heat passes through space with the same remarkable velocity as light. It obeys the same laws of transmission. [See (60).] 4. late of rfeection. —Ieat is also reflected in the same way that light is. For the law which it obeys, see (61). In former times, when the open fireplace was common, the housewife baked her bread by heat reflected from the top of a tin oven placed before the fire. This oven, once found in every kitchen, now only in the gar NATURAL PItILOSOPHY. 227 ret if found at all, having been pushed out by the modern stove, consisted of a tin box closed at the back and the ends, open in front, and having its top slanting at an angle of about 45~. A horizontal shelf was placed in the middle of the oven, upon which stood the loaf to be baked. Under the shelf was another slanting tin surface. The oven standing with its open face to the blazing fire, received the heat rays upon its two slanting surfaces, and reflected them against the top and bottom of the loaf. 5. Law of reractio-n.-Heat is also refracted like light. [See (C8).] The sun's heat coming through the window-glass is bent from its course. By a double convex lens it may be collected, and its intensity greatly increased. The common burning glass illustrates this. It may be a spectacle glass held by the hand in a sunbeam, and the small bright spot-the focus of light-is also the focus of heat. The other hand. held at this point will be burned; tinder will be set on fire, or gunpowder exploded. (82.) Heat tends to diffuse itself equally among all bodies. This distribution takes place in three ways; by conduction, by convection, and by radiation. 1. The eqala dicliusion of /eat. —If two bodies, one cold, the other hot, be placed near each other, it will in a short time be found that both are equally warm, The cold body has received more heat, the hot body has parted with some that it had. What is thus true of tvwo bodies is true of all. Bodies are constantly giving and receiving heat. Those whllich part with more than they receive from others, get colder; those which receive 2$28 NYATURAL PHILOSOPHY. more than they give, get warmer. Ice, for example, is giving heat to all bodies around it; it is at the same time receiving heat from them in return. Ice will actually warm a body which is colder than itself, because it will give more heat than it gets in return; it will be melted by a body warmer than itself, because it receives more than it gives. I.- CONDUCTION. A.-Heat is conducted through some bodies much more freely than through others. Among solids the metals are the best conductors. Liquids are poor conductors, and gases still poorer. i. Conduction.-Heat is transmitted by conduction when it goes to different parts of the salne body by traveling step by step from molecule to molecule. To illustrate this definition, suppose that one end of a cold iron rod is held in the flame of a lamp. The heat will travel gradually from the flame through the rod, until the distant end gets too warm to be held by the hand. Now, if we would understand how the heat has made its little journey through the rod, we must picture to ourselves the delicate motion of the molecules of the iron. Those molecules in contact with the flame are made to vibrate; they swing against their neighbors and put them also in more rapid motion; they, in turn, give motion to the next, and these to the next, until those at the distant end of the rod have finally received the shock. The vibrations of these molecules of the rod, impart motion to the molecules of the hand in contact with them; the delicate nerves of touch receive the imu NATURAL PHILOSOPHY. 229 pulses, and announce the pain. The hand is burned; the rod is hot. Some bodies conduct heat more freely than others. Those which conduct bleat freely are called conductors: those which hinder its passage much, are called poor conductors, and those which nearly or quite forbid its passage, are called non-conductors. 2. iifetals are good conductors.-Among solid bodies the metals, as a class, are the best conductors, but among metals there is great difference in conducting power. By a very simple experiment this may be illustrated. Plunge two spoons, one of silver and the other of German silver, into the same cup of hot tea; it will be found that the upper end of the silver spoon will get hot much quicker than that of the other. Among the best conductors we find silver, copper, gold, brass, tin, and iron, in the order named. 3. Conduction in liquids.-The conducting power of liquids is very feeble. Water, for example, may be boiled in a glass tube, with ice at the bottom without melting it, by applying the heat to the top of the water, or near the upper end of the tube. 4. Conduction of gyases. —Whether gases conduct heat in the least degree is doubted. Dry air is surely among the poorest conductors, and so, likewise, are all porous substances in which large quantities of air are inclosed. II. —CONVECTION. B.-Convection takes place in bodies whose particles are free to move. Air is heated in no other way. Liquids are also heated by convection, but it can not occur in solids. 230 NATURAL PIIILOSOPJIY. 1. Cornvection. —Heat is transmitted by convection when it is carried from place to place by mnoving particles of matter. The following very simple experiment will make this definition clear. Upon a plate of thick glass or a smooth block of wood put a bit of candle, lighted, and over it place a lamp-chimney so that its edge may project a little beyond the edge of the block (Fig. 116.) If the edge of the chimney fits closely upon the Fig. 16. top of the block so that no air can enter, except at the open part A, the flame will flutter violently, showing that air is forced against it. If now, some light sub-.~!!"i' 3 stance, such as down or cotton, be hung A%, from a thread acove the top of the chimney, it will be lifted away, showing that air is rising out of the chimney. ANow, we knowe already that air is expanded by the heat, and we learn from this experiment that the cold air going under the glass pushes the expanded air away from the flame, up and out at the top of the chimlney. This motion of heated air is convection. What we have seen in this experiment really takes place whenever a hot body is surrounded bv colder air. The air in contact with a hot stove, for example, is heated and expanded. The colder air then pushes it away and takes its place, only in turn to be heated and pushed away by other colder portions. The air goes to the stove, becomes heated, and moves away to other parts of the room, Car rlyinq the heat with it. This transfer of heat by the moving particles of air is called convection. 2. Air is heated in no other way.-Air is heated only by convection. The heat of a stove does not go out to NATURAL PHILOSOPHY. 231 distant parts of a room to warm the air: the air must go to the stove to get warm. So, too, the atmosphere is warmed by convection. The sunbeams coming through it do not warm it; they only warm the earth beneath it. Nor does the heat of the earth pass from particle to particle, as it may in solid bodies; the heat of the earth warms only those particles in immediate contact with it. These rise and carrv their heat with them to upper regions, while colder ones take their places in contact with the ground to get warm in turn, and then ascend. 3. lihqidc 7leated by convectvion.-Liquids are also heated by convection. A simple experiment will illustrate the convection of water. Into a flask or bottle of water put a little cochineal. Its particles are just about as heavy as those of the water, and will show by their motion whether there are currents in the water. Warrm the bottom of the bottle, and the heated water will be seen to be rapidly leaving the bottom, while other portions are moving downward to take its place. 4. No convection, in solids.-Solids can not be heated by convection simply because their particles are not free to move among themselves. III.-RADIATION. C.-I-eat is distributed by radiation from all bodies. The amount of heat which a body can radiate depends upon its temperature, its nature, and the condition of its surface. 1. Radiation.-Heat is transmitted by radiation when it goes in straight lines, in all directions, through non-conducting media. 232 NATURAL PHILOSOPHY. The air is a non-conductor, yet heat passes through it with the greatest freedom. Let a red hot iron ball be suddenly placed in a cold room; a person at a little distance will almost instantly feel its heat rays falling upon his face. The heat is not brought to him by convection, because he feels it just as well whether the ball is above his face, below it, or beside it, while the heated air can move only upwarcl. It is transmitted by radiation. The heat of the sun comes to us through space where there is no solid body to conduct it, no liquid nor gaseous substance to bring it to us by convection. It is radiated to us. It is chiefly by radiation that the general distribution of heat is accomplished. All bodies, at all temperatures, are radiating heat. That which radiates more than it receives from others, grows cold, while that which gives less than it gets, grows warm. 2. Despencls on temperalctre, nature, condition. —The higher the temperature of a body, the more heat it can radiate. Moreover, bodies of different substance, when at the same temperature, give off different quantities of heat in the same time. Thus, iron is a better radiator than gold. Still farther, the same body, at the same temperature, with a rough surface will radiate much faster than when its surface is smooth. The rough surface of a cast iron stove, for example, is a better radiator than if it were polished. ~ 3. ON THE EFFECTS OF HEAT. (83.) The action of heat is twofold; it raises the temperature of a body to which it is applied, and at the same time expands it. This is true of its action upon solid, liquid, and gaseous bodies. NATURAL PHILOSOPHY. 233 Temperature is measured by the expansion which accompanies it, in instruments called thermometers. There are three varieties of thermometers in use, the Fahrenheit, the Centigrade and the TReaumer. The air thermometer is used to show delicate changes of temperature. 1. Die action (f heat is twofold.-That the temperature of bodies is raised by the application of heat is too familiar to need illustration. That while the temperature rises, the body grows larger, is known by such facts as the following:-A ball of metal, which, when cold, just fits a ring, will be too large to enter it when hot. A clock pendulum is longer in summer than in winter. The tire of a carriage wheel is put on while hot; on cooling, it contracts and binds the parts of the wheel firmly together. 2. The exypasion of sol'ids.-To show the expansion of a metallic bar, the following beautiful experiment has been devised. A rod of metal (R, Fig. 117), is fixed at one end E, while the other end, passing freely through a post, presses against a bar of brass 13. One end of this bar is fastened by a hinge A, while upon the other end above, rests another bar D. This second bar also turns upon a hinge, and upon its other end, it carries a small plain mirror M. If a beam of sunlight S, coming through a hole in the shutter of a partially darkened room, is made to fall upon the mirror, it will be reflected, and form a white spot upon a distant wall or ceiling. This spot will be quite still as long as the mirror does not move, but when the mirror rises, the spot will move along the ceiling rapidly. Now, let the rod R, be heated, and 234 NATU RAL PHILOSOPIIY. the spot moves. The rod must be expanded, so as to push against the first bar B, the upper end of which pushes against the second bar D, and tlfts the mirror. Fig. 117. If the air in the room is dusty, the entire beam of reflected light L, can be seen, tracing a luminous path upon the ceiling, while the bar expands. Different solids expand unequally for the same increase of temperature, but each solid expands uniformly, -that is to say, two, three, or ten degrees of heat will produce respectively two, three, or ten times as much expansion as one degree. 3. Tlke expansion of liquids.-Tihe expansion of a liquid by heat, may be shown by filling a bottle with water, and then, after fitting into the cork a glass tube open at both ends, and tightly pressing the cork into the neck, standing it in a vessel of warm water. The water in the bottle will be heated, and its expansion N ATUR AL PHILO SOPHY. 2.35 will be shown by the fluid rising higher and higher in the tube. A little artifice enables one to change this slow motion into another so rapid, that it may be easily seen even by those in the most distant part of the room. A very long slender body, a rye straw full length answers the purpose admirably, is suspended by a thread tied near to one end. From this end (E, Fig. 118), is hung Fig. 118. a little cylinder of metal, of sueh weight as to be almost balanced by the long arm of the straw lever. The cylinder hangs inside of the tube of the bottle, and rests upon the water in it. Now, when the water in the bottle expands, it rises in the tube, and pushes the little cylinder up before it. While it goes up, the other end of the straw lever goes down many times faster. The rapid sinking of the straw, while the water is being heated, shows that the water is expanding. All liquids are expanded by heat, but some are much more affected than others. The expansion of liquids is much less uniform than that of solids. 4. DT/e expa)nsionz of gases.-All gases are expanded 236 NATURAL PHILOSOPHY. by heat. For illustration by experiment, of the expansion of air read (16.) 2. The expansion of gases is more nearly uniform than that of either solids or liquids, and much greater for the same addition of heat. What is more remarkable is the fact that they all erxpand at the same urate. If we have 490 cubic inches of air at a temperature of 32~ P. and add one degree of heat, there will be 491 cubic inches: it expands -- of its bulk. All gases expand at the same rate, T-X of their bulk, at 32~ for every additional degree. This fraction (Q-I0) is called the coefficient of expansion for gases. 5. Terperature mneasured by expansion.-We have found that temperature and expansion increase at the same time by the addition of heat. Moreover, in the same body a certain amount of expansion always occurs with the same increase of temperature. By seeing the expansion we may therefore judge of the increase of temperature. The expansion of solids is too slight, while that of gases is too great, to be conveniently used to measure the changing temperature of the air and other things. AMercury is a liquid metal, whose expansion is remarkably uniform, and neither too great nor too little for practical purposes. All common thermometers are made with it. 6. Tlhe thermometer.-The mercurial thermometer consists of a glass tube terminating at one end in a bulb, and sealed at the other. The bulb and lower part of the tube are filled with mercury, the space in the tube above the mercury being a vacuum. Behind the tube is a graduated scale to show the height of the column of mercury. NATURAL PHILOSOPHY. 237 7. Various forms.-There are thrlee modes of graduating the scale, and this gives rise to three varieties of mercurial thermometer. In FaAlrenheit's instrument, the zero of the scale marks the height of the mercury in the tube when the bulb is placed in a mixture of snow and salt. When the bulb is put into boiling water, the mercury in the tube runs up to a point which is marked 212 on the scale. The distance between these points is divided into 212 equal parts called degrees, and this graduation is carried above and below these points. According to this thermometer, water boils at 212~ and freezes at 320. In the centigrade thermometer, the zero point marks the height of the mercury in the tube when the bulb is placed in freezing water. The height to which it rises when the bulb is put into boiling water, is marked 100, and the distance between these points is divided into 100 equal parts. The boiling point of water is, therefore, 100~; its freezing point is 0~. In Reaumer's thermometer, the zero marks the freezing point of water; the boiling point is called 80. Degrees of temperature below the zero points are generally indicated by the minus sign (-) placed before the number. Thus, - 40~, means a temperature 40~ below zero. 8. Other forms. —Mercury freezes at about - 39~: temperatures below this point are measured by thermometers containing alcohol. Mercury boils at 660~: temperatures above this point are measured by the expansion of solid bodies. When it is necessary to show very delicate changes of temperature, the air thzermometer is used. This instrument has a variety of forms, but it consists essen 2038 NATURAL PHILOSOPHY. tially of a glass tube, terminating at one end in a bulb, the other end being open and inserted into a cistern Fig. 119. of colored liquid. (See Fig. 119.) The liquid fills a part of the tube; the rest of the tube and the bulb above is filled with air. A grad_ uated scale is placed behind the tube. The air expands or contracts with every change of temperature, and accordingly drives the colored liquid down, or allows it to rise in the tube. The motion of the liquid shows the change in the temperature. (84.) Temperature indicates the rapidity of vibration of the molecules of bodies: expansion indicates a change in their relative positions. The heat which produces the first is called sensible heat: that which produces the second is called latent heat. The sum of both quantities in any body, coinpared to the sum of both in some other body taken as a standard, is called the 111 I1 specific heat. 1. Rap2iity of motion and change of posiion.-IIe who has a clear idea of tile molecules [see (4.) 1], can distinctly imagine the multitude of these little bodies of which any larger body is made up, separated from each other by minute distances and in rapid motion. Now, heat can make them vibrate faster: it may also push them farther apart, or otherwise change their position; it can do nothing more. Then, when heat is being applied to a bar of iron, let the mind picture to itself these two effects; the molecules of the bar vibrating mnore and more swiftly, and at the same time being NATURAL PH-ILOSOPHY. 239 pushed farther and farther apart. The first of these effects is manifested as temperature, the second as expansion. 2. Sensible and latent Aeat.-The heat which is expended in raising temperature is called sensible heat; it can affect the sense of touch. That which is used to produce expansion, is called latent heat; it does not affect the sense of touch. Now, the heat that goes into, or acts upon, any body, is divided into these two portions; one part sensible, the other latent. 3. Specific heat. —But different substances do not divide it alike; that is, if the same amount be added to two substances, one of them will devote more of it to temperature and less to expansion, than the other. Let equal weights of water and mercury be placed over the same source of heat. The water divides the heat it receives into two parts, one to raise its temperature, the other to expand it. The mercury, receiving the same amount, divides it into two parts devoted to the same purposes, but the heat devoted to temperature is more than in water, while that devoted to expansion is less. We find that the temperature of mercury rises much faster than that of water: it takes thirty times as long to raise the water to a given temperature as it does the mercury. If it take thirty times as long, and one receives heat as fast as the other, there must be thirty times as much heat in the water as in the mercury when that temperature is reached by both. We see, then, that at the same temperature different substances may have very different quantities of heat in them. The relative quantities of heat in different bodies at the same temperature is called specific heals. Water is the standard of specific heat. At a given 240 NATURAL PHILOSOPHY. temperature it contains more heat than any other known substance. Its specific. heat being 1, the specific heats of all other substances are fractional. The specific heat of mercury is.03. By this is meant, that when equal weights of mercury and water are at the same temperature, the mercury will contain only.03 as much heat as the water. (85.) The expansion of a solid body will continue nearly uniform until its temperature has reached the melting point. The temperature then stops rising, while the expansion increases and continues until the solid is melted. 1. The melting point. —The temperature at which a solid body begins to melt, is called its melting point. At this point, the repulsive force of heat nearly balances the cohesion of the molecules, and enables them to move freely among themselves. The body becomes a liquid, and the change is called liquefaction. The melting point for different substances is not the same. Ice melts at 32~ F.; mercury at 39~; iron at about 3,000~ and platinum at about 5,000~. 2. The tenperature stops rising.-If heat be applied to a vessel of ice at 32~, the ice will melt and the water formed will have the same temperature, 32~. So, too, when wax, or iron, or lead is melted, the liquid will have the same temperature as the solid which is melting. 3. But the expansion increases.-But in the case of all the substances above named, except ice, the expansion is greater at the melting point than before it was reached. The liquid fills more space than the solid from which it was formed. It should be so, NATIRAL PHILOSOPHY. 241 because the heat force is all expended to change the position of the molecules, whereas, before, a part of it was used up to Froduce a rise of temperature. Ice contracts when melting; the water formed fills less space than the ice. In this case, likewise, all the heat applied is expended in chainging the _position of the molecules, but not in pushing them farther apart, for they occupy less space than before the change occurred. The change consists in throwing the molecules out of their crystalline arrangement. The water will continue to contract until it reaches a temperature of 390, after which it expands. Those who have attempted to melt ice or snow, for domestic purposes, remember how slow the process is. The amount of heat required to simply melt the snow without making it any warmer, is very great; the same amount applied to the water formed, would raise its temperature 142'. Hence the latent heat of water is said to be 142~. (86.) The expansion of a liquid will continue gradual until the boiling point is reached, a temperature depending upon the purity of the liquid, upon the nature of the vessel in which it is heated, and upon the pressure it sustains. At the boiling point, the temperature stops rising, while the expansion greatly increases, and continues until the liquid is vaporized. 1. The boiliny point.-The temperature at which a liquid begins to boil, is called its boiliqng point. At this temperature, the repulsive force of heat entirely overcomes the cohesion of the molecules, and drives them just as far apart as possible. The body rapidly becomes a vapor, and the change is called vaporization. 11 242 NATURAL PHILOSOPHY. Liquids do indeed change to vapor at all temperatures. Even from freezing water, more or less vapor is ever slowly rising. This slow change is called evaporation. The boiling point for different liquids is not the same. Water boils at 212~, Alcohol at 173~, Ether at 95~. The boiling point for the same liquid is not the same; it depends upon three circumstances. 2. It depends on the ppurity of th/e liqGid.-It is affected, first, by the presence of impurities in the liquid. The presence of some impurities raises the boiling point; of others, lowers it. Salt water, for example, boils at a higher temperature than pure water, while that which contains air, boils at a much lower temperature than that which contains none. 3. It depends on the nature of the vessel.-In an iron. vessel, water will boil at a lower temperature than in one of glass. It is so because there is a stronger adhesion between water and glass, than between water and iron. The stronger adhesion requires a stronger heat to overcome it. 4. It depends on t1he pressure.-]3ut the most important circumstance on which the boiling point of a liquid depends, is the pressure it sustains. This pressure is due to the atmosphere, to the weight of the liquid itself, and to any force which may be brought to bear upon it by artificial means. Whatever may be its cause, the effect of pressure is to raise the boiling point. It is well known that water boils at a lower temperature on the top of a mountain than at its base. It does so because the pressure of the air upon it is less. This very important principle may be easily illustrated by experiment. For this purpose take a glass NATURAL PHILOSOPHY. 243 flask, or better, a bolt head (Fig. 120), and put into it water enough to fill the stem and a small part of the bulb. Invert it so that the water may be boiled by holding the bulb over the flame of a lamp. Fig. 120. Boil it until the steam issues freely from the stem, and then, removing it from the flame, corlk the stemn at the same instant. The air has been driven out from the instrument, and nothing remains, to press upon the water, but steam. Turn the bulb upward so that the water may fill the stem; pour cold water upon the bulb, and the water inside will boil violently. Even when the tube has become so cold that it may be handled without inconvenience a fresh bath of cold water will cause the boiling to continue. It boils at the low temperature because the cold water, condensing the steam, removes the pressure from its surface. 5. The, temperature stops rising. —No matter how much heat may be applied to boiling water, its temperature can not be raised. Moreover, the temperature of the steam is always that of the water from which it is made. By the following experiment these facts may be illustrated. Water is placed in an open vessel V (Fig. 121). Into the water is plunged the bulb of an air thermometer T, whose tube is bent twice at right angles for the purpose. While the water is being heated by a lamp-flame, the gradual sinking of the fluid in the stem of the thermometer shows the increase of temperature; but when the water fairly boils, the fluid stops sinking, showing that the temperature no longer rises. 2414 NATURAL PHILOSOPHY. The fluid will remain motionless until the water in the vessel has been changed to steam. Let the bulb be lifted Fig. 121. into the steam above the water; no change occurs in tle height of the fluid in the stem, hence the'Ti' |I temperature of the steam must be the same as that of the water. 6. But the expansion increases. v/ -I ^; -If all the heat applied to a boili~ @ing liquid is expended to produce expansion, we may expect that this effect will be more rapid than when a part of it was used to raise the temperature. This inference is abundantly verified. i Tllj. -Steam fills about 1700 times as Lmuch space as the water from -wh1ich it was formed. The amount of heat required to expand water into steam, in other words, the latent heat of steam, is very great. By accurate experiment it has been found to be 972~ F. The steam and the water are of the same temperature, yet there is an excess of heat-force in an ounce of steam which, if applied to one ounce of water, would be sufficient, were it possible, to raise its temperature to 972; it will raise the temperature of nine ounces of water 108. (87.) The heat-force which has been required to produce expansion, will be reproduced when the expanded body again contracts. 1. Heat restored after being Fused.-The following experiment very satisfactorily shows that heat is re NATURAL PHILOSOPHY. 245 quired to produce expansion, and that it is again given off when contraction occurs. The bulb of an air thermometer is placed in a receiver over the plate of an air-pump; the stem, passing through the top of the receiver, is bent twice at right angles, and is filled with its colored fluid to a height very carefully marked. By a few rapid strokes of the piston, the air is partly exhausted from the receiver; that which remains expand8s, and the rising of the fluid in the thermometer shows that the bulb is at the same time cooled. It; now, air be allowed to return to the receiver, the air inside becomes more dense, and the sinking of the fluid in the thermometer shows that heat is again given off. Numerous familiar facts illustrate this principle. If water evaporates from the hand, it cools the hand, because the hand furnishes the heat to expand the water into steam; and when vapor condenses upon the hand, the hand is warmed, because the vapor gives to it all the heat which had been used to keep the water in the form of steam. Bodies in contact with melting snow or ice, are cooled, because they must furnish heat to change the solid to the liquid ibrm. But bodies near to freezing water are warmed, because the water then gives up the heat which had been needed to keep it in a fluid form. ~ 4. ON TIE STEAM-ENGINE. (88.) The elastic force of steam is applied to mechanical purposes by means of a steam-engine. The essential parts of this machine are, 1st, the boiler in which steam is generated; 2d, the cylinder in which the 246 NATURAL PHILOSOPHY. steam is made to move a piston; 3d, the crank by which the piston turns a wheel. Engines are either high-pressure or low-pressure. 1. The elastic force of steam.-W hen steam is formed at a temperature of 212~, its elastic force is just equal to the pressure of the atmosphere, or 15 lbs. to the square inch. If taken out into another vessel, preserving its temperature and density, it would exert a pressure of 15 lbs. to the inch. By subjecting water to a greater pressure, its boiling point is raised, and the elastic force of the steam will be increased. The Marcet's globe illustrates this principle. It consists of a metallic globe (Fig. 122), which is furnished with a long Fi. 122. glass tube and scale T, a stop-cock S, and a thermometer A, whose bulb is inside the globe. In the bottom of the globe is a little mercury, into which the end of the tube T dips, and above the T mercury is a quantity of water. The water is boiled until the air is driven out of the open stopcock. At this moment, the elastic force of the steam is just 15 lbs. to the inch. The stop-cock is now closed: the thermometer at once k - s shows a rise of temperature, and at the same time the mercury begins to rise in the tube, showing an increase in the ) J Alp —. force of the steam. When the temper// X at ature of the boiling water has reached 249.5, the expansive force of the steam?TV is equal to two atmospheres, or 30 lbs. to the inch, and at 306~ it is live atmospheres, or 75 lbs. to the inch. NATURAL PHILOSOPHY. 247 If, now, this elastic force of steam can be made to act alternately upon -opposite sides of a piston, it will knock it back and forth, from one end of a cylinder to the other with power enough to move any amount of other machinery. This is accomplished in the steamengine. 2. The boiler. —The boiler of a steam-engine is usually made of plates of wrought-iron riveted together in the form of a cylinder. In the best forms, there are tubes which run lengthwise through the body of the boiler, through which the flame and hot gases from the fire may pass. The water in the boiler surrounds these tubes, and is rapidly heated by them. The steam thus formed in the boiler collects above the water, and by its pressure raises the boiling point until, when its elastic force is sufficiently Fig. 123. great, the steam is allowed to n pass through a pipe to the cylinder. 3. TAhe cylinder.-The arrangement of the cylinder and piston are shown in Fig. 123. The pipe which brings the il steam from the boiler enters. i, I ii! a box d, from which two / tubes lead, one to the top, the lil other to the bottom of the me- tallic cylinder C, in whlich the F " piston P, moves. Another l, I' " i' tube leads from this box out ii into the air, or away to an-;'" other vessel, where the steam, after having moved the piston, 2-18 NATURAL PHIILOSOPHY. may be condensed. A sliding valve, Y, is so arranged in the box as to always close one of the pipes leading to the cylinder and leave the other open. If the upper tube is open, as represented in the figure, the steam will enter above the piston and push it to the bottom of the cylinder; if the lower tube is open, the steam will enter below the piston and push it to the top. In either case the steam on the opposite side of the piston will be pushed out of the cylinder, through the other tube and the pipe, 0, leading from the cavity under the sliding valve. When the steam, entering through the lower tube, has pushed the piston to the top of the cylinder, the valve is pushed down to cover the end of that tube, leaving the end of the other uncovered, so that the steam may pass through it to act above the piston. By this means the piston will be alternately pushed back and forth from one end of the cylinder to the other. 4. The crank.-By this simple motion, back and forth, the piston turns a wheel by means of a crank. To the piston-rod, A (Fig. 123), another rod is joined by a hinge; the other end of this rod turns a wheel, from which motion may be communicated to others by bands or cogs. Besides these three important parts of the steam engine, there are numerous other appendages for particular purposes, such as a safety-valve attached to the boiler to regulate the pressure of steam in it; the governor to regulate the supply of steam to the cylinder; the fly-wheel, a heavy wheel whose inertia catls.e3 the motion of the machinery to be steady. (See Silliman's Physics.) 5. Higqh and low pressure en.ginzes.-The different forms of steam-engines are almost as numerous as the NATURAL PHILOSOPHY. 249 machinists who make them, or as the variety of purposes to which they are applied. There are, however, two general classes, the Agh/T-press9ure and the low-pre&sure engines. In the high-pressure engines the steam, after moving the piston, is thrown out from the cylinder into the air. In the low-pressure engines, the steam, after moving the piston, is taken off to a vessel called the condenser, in which it is changed into water. The first is called Uig!y pressure, because the steam which moves the piston must push the steam from before the piston out into the air, which presses it back with a force of 15 lbs. to the inch. To do this evidutly requires a pressure of 15 lbs. to the inch higher than in the other class, in which the steam escapes into a vacuum, and of course exerts no pressure against the piston. 250 NATURAL PHILOSOPHY. CHAPTER VIII. ON ELECTRICITY. INTRODUCTION.-APPLICATION OF THE FUNDAMENTAL IDEAS. (89.) READ (4:). A constant and opposite action of attraction and repulsion among the molecules of bodies gives rise to the phenomena of electricity. Of the nature of electricity very little is definitely known; but since the kindred phenomena of light and heat have been found to be the result of vibratory motions among the molecules of bodies, the tendency is to regard electricity also as the effect of molecular vibrations of some kind. But whether we adopt this view, or still cling to the old theory, which regards electricity as a weightless fluid in the pores of all bodies, we may describe it truly as a manifestation of attraction and repulsion acting upon the molecules of a body, thus producing an effect upon the body itself. ~ 1. OF FRICTIONAL ELECTRICITY. (90.) Electricity may be produced by friction. The electrical machine is an apparatus for this purpose. It may be detected by instruments called electroscopes, showing its action as two opposite forces-attraction and repulsion. Its intensity may be measured by in NATURAL PHILOSOPHYII. 251 strumnents called electroleters. It is governed by two laws: 1st. Electricities of the same kind repel each other; of different kinds attract. 2d. The force of the attraction or repulsion is inversely as the square of the distance between them. 1. E'lectricity prodZceed by friction.-If a well-dried glass tube-a lamp-chimney for example-be thoroughly rubbed with a flannel cloth, it will be found to have new and curious properties. HIold it near the face, and a feeling will be experienced as if a gentle breeze were blowing against the cheek: bring it nearer, and perhaps a prickling sensation will be felt, and it may be that a crackling sound will, at the same time, be heard; or approach it toward some very light substances, such as delicate bits of loose cotton and they will rush toward it, and remain for a little time clinging to it. These various effects show the presence of electricity: the friction of the flannel upon the glass has produced it. 2. Tlie electrical rmachine.-The electrical machine is an apparatus for producing electricity by friction. It is represented in Fig. 124. Its principal parts are, 1st, a body upon whose surface electricity is to be evolved; 2d, the rubber by the friction of which electricity is produced; and 3d, the conductor on which the electricity may be accumulated. In the form shown by the figure, the first of these parts consists of a thick glass plate P, to be turned by a crank. Thle rubber t is made of leather, covered with an amalgamr made of mercury, tiln, and zinc. Two such pieces of leather are pressed, one against each side of the plate, by means of a brass clamp, which is supported 252 SNATURAL PHILOSOP HY. upon a (lass pillar. The conductor, or as usually called the Prim;e condclzctor, C, is a brass ball, or a cylinder with rounded ends, mounted on a glass support. ConFig. 124. nected with the prime conductor, is a brass fork F, one prong of which is on each side of the plate, with many sharp projecting points reaching toward the glass. By turning the crank, the friction of the rubber upon the plate evolves electricity, which remains upon the surface of the glass until it is brought around to the fork: it is there taken by the points, and it passes over the prongs to spread itself over the surface of the prime conductor. The glass support prevents it from leaving the conductor. When the machine is in operation the rubber is connected with the floor by a chain. All parts of the machine must be free from dust and thoroughly dry. NATURAL PlIILOSOPIIY. 253 When a machine of this kind, of medium size, is ill successful operation, the effects of the glass tube are experienced in a far greater degree. The face or the back of the hand will feel the breezy or prickling sensation at a distance of several inches from the conductor: all light bodies held near it, immediately fly to its surface, and if the knuckle or a brass ball be brought near, bright and zigzag sparks may be drawn through a distance of from one to two inches, the light being accompanied by a sharp report. 3. Electricity detected by electroscopes.-WVhen the force of the electricity is slight, there should be some convenient way of showing its presence. Any instrument for this purpose is called an electroscope. The simplest form is called the pit/h-ball electroscope. It consists (see Fig. 125) of a ball of pith from the cornstalk, or elder, hung by a slender silk thread from a glass support. This little ball will instantly Fig. 125. announce the presence of electricity by moving toward the body which contains it. 4. Two opposite forces.-Electricity shows its presence both by attraction and repulsion, for if the pith-ball of the electroscope be brought near to the prime conductor of the electrical machine, it will fly toward it, but on coming in contact with it, will as instantly leap away again. Now, rub a glass rod with flannel, and hold it near the pith-ball which has been repelled by the conductor; the glass rod will also repel it; but if a stick of sealing-wax be used in place of the glass tube, the pith-ball will be strongly attracted. Notice, that the pith-ball is repelled by the electricity of 254 N~ATUIRAL PHILOSOPHY. glass, and cttractd by the electricity of sealing-wax. It is thus seen that the electricities of glass and sealingwax are not alike. To distinguish them from each other, that which is produced on glass by the friction of flannel is called positive electricity; that produced upon sealing-wax is called negative electricity. It is found to be impossible to develop one of these forces without the other also. The positive force always appears on one of the bodies rubbed together, and the negative upon the other. 5. Tke forces measured by electromneters.-The sirnplest form of the electrometer is represented in Fig. 126. It consists of a brass standard, with a graduated semicircle, on the center of which moves Fig. 126. an index of' very light wood, carrying a pith-ball at its lower end. When not in use, the pith-ball hangs in contact with I! X X the standard, but when the standard is brought near to an electrified body, the pith-ball is instantly repelled. The are through which it moves is taken as the measure of the force. (See Silliman's Phys., p. 538.) 6. Tie first law.-We have seen that positive electricity is produced by friction on glass, and that the opposite force is evolved by friction on sealing-wax. Now, let two pith-balls be suspended by silk threads so as to be in contact. Thoroughly rub the glass tube; bring it in contact withl the balls; they both receive positive electricity from the tube, and it will found that they will no longer remain in contact. WVe learn from this experiment that two bodies with the same kind of electricity repel each other. NATURAL PHILOSOPHY. 255 Again: let the sealing-wax be thoroughly rubbed and brought near to the two pith-balls while they are repelling each other, and they will both fly toward it. We learn from this experiment that bodies with different kinds of electricity attrCct each othler. This law furnishes an easy test by which to find out which kind of electric force is, in any case, produced. Is the prime conducter of the electrical machine positive or negative? To decide this question, rub the glass tube; bring it in contact with the pith-ball of the electroscope; the electricity of the ball is thus known to be positive. Now, bring it near the prime conductor of the machine in operation; it is repelled. The electricity of the conductor is positive. The electricity of the rubber is negative, because, if the chain be removed, and the electrified pith-ball be brought near the brass mounting of the rubber post, it will be attracted. 7. The second law.-If the standard of the electroineter be brought in contact with an electrified body, the index will be thrown along the graduated are to a greater or less distance, as the electric force is stronger or weaker. By carefully conducted- experiments, these distances may be compared, and it is found that the strength or intensity of the force is inversally as the square of the distance. The attraction of the prime conductor for a body at a distance of two inches is only ~ as strong as at a distance of one inch. (91.) A charged or electrified body, acting through a non-conductor upon an insulated conductor, polarizes it. This action is called induction. 1. A charged body.-Whenever by friction, electricity 256 NATURAL PHILOSOPHY. is developed upon the surface of a body, the body is said to be electrified, and if, by bringing another body in contact with it, electricity is imparted, the body which receives it is said to be charged. Thus, the glass tube, when rubbed, becomes electrified; the pith-ball of the electroscope, coming in contact with the glass, takes electricity from it and becomes charged. 2. A tnon-condactor.-Some bodies allow electricity to pass freely over their surfaces; such bodies are called conductors: others will not allow electricity to pass freely over them; these are called non-conductors. If a brass rod be held in contact with the prime conductor of a machine, it will be found impossible to charge it; a glass rod held in the same way, will not prevent the charge from accumulating. The brass allows the electricity to pass into the person; the glass does not: brass is a conductor; glass is a non-conductor. The metals, as a class, are good conductors. Beside glass, we notice silk, india rubber, and dry air, as being among the best non-conductors. 3. An instlated body. —Whenever a body is quite surrounded by non-conductors, it is said to be insulated. The conductor of the machine is insulated by resting upon a glass support. A body which is not insulated can not be charged. 4. A charged body 2polarizes an insulated conductor. -A body is said to be polarized when the two opposite electricities both exist upon its surface. To illustrate this important condition, let an insulated metallic ball be connected with the prime conductor of the electrical machine, and let a small insulated conductor be placed near it (see Fig. 127). When the ball is charged, the NATURAL PHILOSOPHY. 257 motion of the pith-balls fastened to the small conductor, shows that it is also charged, and if its electricity be tested, it will be found to be positive at one end and negative at the other. Both elec- Fig. 12T. tricities are developed upon its surface at the same time, and the body + is said to be polarized. The ac-' tion of the ball, by which this body is polarized, is called iniduction.' If we examine the condition of the polarized body more carefully, we find that in the end next to the ball there is negative electricity, and in the distant end there ispositive electricity. This is always true: when a body is electrified by induction, the end or side nearest the charged body is always in a condition opposite to that which develops it. When the insulated conductor is near to the ball, the induction is strong: the greater the distance between them, the weaker it becomes, until, at a certain distance, it can no longer be detected. If, when the conductor is polarized, one end be touched with the finger, the entire surface remains charged with the opposite electricity. It will remain. charged even, when taken beyond the influence of the body which polarized it. (92.) A series of insulated conductors, placed end to end, near each other, may be all polarized by bringing a charged body near to one of them. Faraday's theory explains induction by supposing the molecules of a body to be polarized fromi each other in the same way. 1. A series of conductors poloarized. —Let a number of small insulated conductors be placed end to end, 258 NATURAL PHILOSO PIIY. near together, with one end of the first one near to Fig. 128. a brass ball connected _ — - with tthe prime conductorof the machine (see Fig. 128). The Xa motion of the pithballs will show that they are all polarized. The effect will be greater if another brass ball, connected with the rubber of the machine, is placed at the other end of the series. The positive and negative eleetricities are on opposite ends of each conductor. All the ends toward the positive ball are negative; all the ends in the other direction are positive. 2. Tlie T/heory of Iltduction.-Now the molecules of one of these conductors are as truly separate bodies as the conductors themselves, and as one electrified conductor may polarize another, so one of these molecules, acting through the minute distance between them, may polarize another. This polarizing influence passes from one molecule to another, until all the molecules of the body are thrown into this condition, each molecule having opposite electricities on its opposite sides. The theory goes further, and supposes that the molecules of conductors discharge their forces easily into one another, while those of non-conductors do not. For this reason, the molecules of the air between the charged ball and the end of the conductor are polarized and retain their electricities, while the molecules of the coilductors, as fast as they are polarized, give their electric forces to their neighbors. The positive fothrce given from one to another, in one direction, accumulates at one end of the conductor; the negative force, given fiomz one to NATURAL PHILOSOPHY. 259 another in the other direction, accumulates at the other end. (93.) The Leyden-jar is an apparatus for accumulating electricity by induction. It may be charged by bringing one of its coatings in contact with a charged body, the other being in contact with conductors. It may be discharged by making a conducting communication between its two coatings. The Leyden battery consists of several Leyden-jars connected. 1. Tlie Leyden-jar. —The Leyden-jar (Fig. 129) consists of a glass jar, coated both inside Fig. 129. and outside with tin-foil, to within a few inches of the top, and provided with a cover of hard dry wood, through which passes a brass rod, with a ball upon its upper end, and a chain reaching from its lower end to the bottom of the jar. It will be seen by this description, that in this instrument there are two condmaclill, I surlfaces, separated from each other by a fnon-conuctor. This idea may be embodied in a variety of forms, any one of which will act on the principle of the Leydenjar. Thus a pane of glass, coated with tin-foil on both sides, to within a little distance of the edge all around, has the essential parts of the Leyden-jar. A glass goblet partly full of water and grasped by the hand, illuhstrates the same idea: the glass, a non-conductor, separates two conducting surfaces-the water on the inside, and the hand upon the outside. 2. It mnaay be charged.-By bringing the ball of the Leyden-jar in contact with the prime conductor of the 260 NAT-URAL PHILOSOPHY. machille, positive electricity passes into the inside coating. This positive electricity polarizes the outside coating, causing its surface next the glass to be negative, and the other to be positive. If in contact with a conductor, this positive electricity will pass off, and thllus leave the outside coating permanently charged with negative electricity. When by this action the two coatings have opposite electricities, the jar is said to be charged. It may be removed from the prime conductor and remain charged, because the two forces hold each other by acting through the glass. The jar may be handled without danger, if care be taken not to touch the ball and the outside at the same time. The jar is charged with positive electricity when that force is upon the inside; it is charged with negative electricity when negative force is upon the inside. 3. It may be (disc/harged.-WVhen a conducting communication is made between the two coatings of the jar, the two opposite forces come together, neutralize each other, and the jar is said to be discharged. The conducting communication may be made in many ways. The discharger is a convenient instrument for the purpose. It consists of two bent brass arms, with a ball upon one end of each, the other ends being fastened by a joint to a glass handle. Taking hold of the glass handle, bring one ball in contact with the outside of the jar, and the other near to the knob; a bright spark and a sudden report announce the discharge. The coated glass plate and the goblet of water, mentioned before, may be charged and discharged in the same way as a Leyden jar. To charge the goblet, for example, let a chain from the prime conductor of the machine hang into the water; grasp the outside of the NATURAL PHILOSOPHY. 261 glass while the machine is in operation. Positive electricity will be given to the water; negative electricity will be induced upon the hand, and the goblet is thus charged. Now with the other hand try to remove the chain: the moment the chain is touched, a slight shock will be felt, announcing the discharge which occurs. 4. VTie lZeyden battery.-The larger the surface of the coatings of the jar, the more powerful will be the charge accumulated. We can obtain a larger surface by using a larger jar, or it may be done by taking several small ones and joining their surfaces by conductors. In the last case, the Leyden battery will be formed. When the inside surfaces are all connected by conductors reaching from knob to knob, and the outsides all joined by standing the jars on a metallic surface, the battery may be charged and discharged as a single jar. It is equivalent to a single jar large enough to have the smrne extent of surface. (94.) The electricity of the atmosphere is of the same nature as that produced by friction. Lightning is the discharge of oppositely charged clouds, illustrating, on a grand scale, the action of a Leyden-jar. The aurora is doubtless produced by electric discharges taking place in the rarefied air of the upper portions of the atmosphere. 1. Electricity of the atmosphere.-The atmosphere is very generally in an electrified condition. This may be shown by raising a metallic rod to a considerable height above the ground, having an electroscope fastened to its lower end, which should be insulated. A sensitive electroscope will usually indicate positive electricity, its intensity increasing as the air from which it 262 NATURAL PHILOSOPHY is drawn is higher. In its ordinary state, the electricity of the atmosphere is always positive: stronger in winter than in summer, and during the day than the night. In cloudy weather the electrical state is uncertain, sometimes changing from positive to negative and back again in a few minutes. On the approach of a thunlderstorm these changes follow each other, at times, with remarkable swiftness. 2. It is of the same nature as frictional electricity. -The bright flash and loud report which announce the discharge of a Leyden-jar or battery, can not have failed to remind one who has observed them, of the brighter flash and louder report of atmospheric lightning and thunder. These grand and sometimes awful displays of electricity, are caused by the same agent which, produced on a glass tube, lightly pricks the cheek or attracts a pith-ball. To Dr. Franklin belongs the immortal honor of proving the identity of electricity and lightning. A kite was the simple instrument employed by this man of genius. Having made a kite by stretching a silk handkerchief over two sticks in the form of a cross, he went out into a field, accompanied only by his son: raised his kite; fastened a key to the lower end of its hempen string; insulated it by fastening it to a post by means of a silk cord, and anxiously awaited the approaching storm. A dense cloud, apparently charged with lightning, soon passed over the spot where he stood, without causing his apparatus to give any sign of electricity. He was about to give up in despair, when he caught sight of some loose fibers of the hempen cord, bristling up as if repelled. I-Ie immediately presented his knuckle to the key, and received an electric spark. The string of NATURAL PHILOSOPHIY. 263 his kite soon became wet with the falling rain; it was then a better conductor, and he was able to obtain an abundance of sparks from the key. By this experiment he furnished a decisive proof of the identity of lightning and electricity. 3. igyhtzning is the discharge of oppositely charged clouds. —Clouds are often charged with electricity. When two of them, with opposite kinds of electricity, come near enough together, they will act like the two charged coatings of the Leyden-jar, the air between them being a non-conductor like the glass. When the charge rises high enough, a discharge takes place: the spark of the discharge being a flash of lightning, and its report a thunder peal. Considering the large extent of cloud surfaces discharged, we need not be surprised at the magnitude of the spark, nor at the deep intensity of the sound. When the discharge is not hidden by clouds, we can trace the whole length of the spark, and we witness chain-lightning; but at other times the- spark is behind the clouds; iwe see only the light of the discharge spread over the surface of the clouds, and this gives rise to what is called sheet-lgqhtnizg. At times the earth and a cloud are the two charged surfaces, and a discharge takes place between them. Such discharges are the source of danger to life and property. Animals, trees, buildings, all these are better conductors than air, and electricity always chooses the best conductors in its passage. In going from a cloud to the earth it takes these bodies in its way; animals are often killed, trees shattered, and buildings torn to pieces or set on fire. 4. The aurora. —This curiously beautiful phenomenon 264 NATURAL PHTILOSOPHY. consists of a diffuse light, somewhat like the morning or the evening twilight, seen in the northern sky. It exhibits a great variety of appearances. Sometimes it looks much like the dawn of morning seen in the north instead of the east. Sometimes it takes the form of anll arch, like a rainbow, but without its colors. At other times slender columns of delicate light, pointing upward from the northern horizon, not always stationary, but often, on the contrary, leaping up and down with swift and varied motions, as if engaged in a merry dance. In the southern hemisphere an aurora is also seen in the southern horizon. To distinguish these two auroras, that in the north has been called the aurora borealis, while that in the south is the aurora australis. 5..t is prodcuced by electric discharges in rarefied air.-There is still much uncertainty about the cause of the aurora, but late investigations leave no doubt as to its electrical nature. From all the facts gathered, it seems to consist of beams or discharges of electricity, between the earth and the upper regions of the atmosphere. When electricity discharges through air of the usual density, it takes the form of a spark, the light being intense and nearly white. If passed through a glass vessel, in which the air is rarefied, the light is more diffuse and tinged with a rosy hue. If the air be still further rarefied, the light becomes very diffuse, spreads readily through a great distance, and its color becomes a deep rose or purple. Now the air of the upper atmosphere is much rarefied, and we should infer that electric discharges there would give a diffuse light of various colors. Such is NiATURAL PHILOSOPHY. 265 the observed character of the aurora. (See Smithsonian Report, 1865, p. 208.) (95.) A body lhaving points projecting from its surface can not be charged even when insulated. Or if a pointed conductor be held toward its surface it will prevent a charge from accumulating, by drawing the force away silently. Upon this principle, buildings are protected from the effects of lightning by lightningrods. 1. T/te effect of p2oints. —It is found to be impossible to charge a conductor when there are sharp points on its surface, or held near to it. To illustrate this curious effect of points, fasten a pointed wire to the prime conductor of the electrical machine, and the sparks, which before could be drawn from it in abundance, cease altogether, and even pith-balls fail to detect the presence of the force. Or take the pointed wire in the hand and present its point to the prime conductor, within a few inches of its surface; not a spark can be drawn fromn it, nor will the pith-balls show either attraction or repulsion. The discharge is silently effected by the air in front of the points. Its molecules become polarized, and are first attracted to the point and then repelled. On coining in contact with the point, they take electricity from it and move away: others being polarized are attracted, receive electricity, and pass away. Thus the electricity of the body is silently carried off from the point. That such currents of air do really exist, may be proved by various experiments. If, for example, the cheek, or the back of the hand, be held near to the point, the breeze will be felt: or if the small flame of a lighted taper be held just in front of 12 266 NATURAL PHILOSOPHY. the point on the prime conductor, it will be blown away from it, and may even be extinguished. The discharge takes place from the point because the charge being more intense there than elsewhere, the polarization of the air is greater there than at any other part of the body. 2. Ligyltning -rods. —We have seen that because buildings are better conductors of electricity than air, they are liable to injury from strokes of lightning, when the discharge takes place between the cloud and the earth. But since pointed conductors silently discharge the force from a charged body, why not disarm the cloud of its lightning by the use of pointed metallic rods? This question was no sooner suggested to the practical mind of Franklin, than a trial was made, which verified his bold conjecture. Conductors for the purpose of protecting buildings from the effect of lightning, are called lightningrods. They should be made of metallic rods, pointed at the upper end, reaching several feet above the highest part of the building which they are designed to protect, and downward, without interruption, into the ground below its foundation. (96.) The effects of frictional electricity are mechanical, chemical, and physiological. 1. Mechanical efects.-WVe have already had abundant illustrations of mzotions caused by the electric forces. Poor conductors are also pierced or torn by the electric discharge. To illustrate this by experiment, let the charge of a Leyden-jar be passed through a piece of card-board; the card will be pierced with a burred or ragged perforation. This effcct is produced on a NATURAL PIILOSOPHY. 267 large scale by the lightning stroke; even rocks are sometimes shattered, while trees are often splintered from top to root, and their fragments scattered far and near in all directions. 2. C/kenizcal eifecs. —The chemical effects of electricity are shown through the agency of the heat which it develops. To illustrate by experiment: wrap the ball of a Leyden-jar with loose cotton, and sprinkle upon this, very finely powdered resin. This done, charge the jar powerfully, and then discharge it by bringing first one ball of the discharger in contact with the outside of the jar, and then the other a little above its hooded knob. The discharge takes place through the resin, and sets it on fire. Buildings are sometimes set on fire by the lightning-stroke. 3. Physiological efects.-The effect of electricity upon the human system is peculiar and startling. No description can give a correct idea of it: it must be experienced by one who would know what it is. Let a person place one hand upon the outside surface of a lightly charged Leyden-jar, and with the other hand touch its knob. He will find that his own will can no longer control his muscles: his hands are, on the instant, suddenly jerked, while a peculiar and almost indescribable sensation is felt in the wrists and arms. Many persons by joining hands may form an unbroken connection between the two coatings of the jar, and at once experience these effects. ~ 2. OF MAGNETIC ELECTRICITY. (97.) Magnets are either natural or artificial, and may be made in different forms; but in any form the 268 NATURAL PHILOSOPHY. magnetism is stronger at the ends thall in the middle. The ends are called poles. 1. fcagnets. — Bodies that attract iron in preference to other metals, are called magnets. They are usually made of steel. To illustrate their peculiar preference for iron, let some iron filings be mixed with some filings of brass; bring one end of the mnagnet among the filings, and on removing it, great numbers of the iron particles will be seen clinging to it, while the brass particles are all left behind. 2. T/he nacdratl maynet. -Fragments of an ore of iron are sometimes found which have the properties of a magnet. Such a fragment is a natucral mnagnet or loadcstone. 3. The artifcial cagynet. —If a bar of iron or steel be rubbed against a magnet it will become magnetic; it will then be an artificial magnet. Whether it remains magnetic for any length of time depends upon its hardness. Soft iron or steel will lose its magnetic properties quickly; hardened iron or steel will retain them. 4. They are made in different forms.-The two most important forms of magnet are the straight or bar magnet, and the horseshoe magnet. These names are descriptive: the bar magnet is a straight bar of steel; the horseshoe magnet is a magnet whose shape is that of a horseshoe, or the letter U; its ends are thus brought near together. 5. Their force is stronger at their ends.-If a bar magnet be rolled in a bed of iron filings, large clusters of them will be found clinging to its ends, their numbers getting less toward the middle of the bar, where very few, if any, will be held. By this experiment we NATURAL PHILOSOPHY. 269 learn that the magnetic forces are not equally distributed over the surfaces of magnets, but, on the contrary, that they are strong at the ends and weak or neutral in the middle. The ends are called poles, one being a north pole, the other a south pole. (98.) 3Magnetism shows itself both by attraction and repulsion, obeying the following law: poles of like names repel each other; those of different names attract. 1. A.ttactcnoon ancd,replsion.-Iron wrhich is not magnetic will be attracted equally by both poles of a nagnet; it is not so when two magnets act upon each other. By presenting one end of a magnet to the north pole of another, it will show an attraction for it, while the other end being presented to the same pole will repel it. Thus mnagnetism, like electricity by friction, shows itself by both attraction and repulsion. 2. The law.-When we examine the subject more closely, we find that magnetic attraction and repulsion is also governed by the same law as electricity. Thus, if we bring the north poles of two imagnets near to each other, they repel each other: two south poles manifest the same effect. But if we bring a north pole near to a south pole, an attraction instantly spring up between them, and if allowed to touch each other they will cling together: one may even lift the other by the strenrlth of the attraction. It is evident from these simple experiments that poles of the sanme name repel, while those of opposite names attract eadh other. (99.) A Inarnet, like a charged body, will polarize a bar of iron brought near to one of its poles, always in 270 NATURAL PHILOSOPHY. ducing magnetism of the opposite kind in the end next to it. The polarizing influence may extend through several bars placed end to end. It is supposed that every molecule of a magnet is in a polarized state, the north polarity being on the same side of them all, and the south polarity on the other side. I. A?mcanet will polarize a bar of iron.-If a bar of iron n s and a magnet N S (Fig. 130), be placed end Fig. to end, the iron itself becomes a magnet. That 190. it is a nmagnet may be shown by its power to'N attract or repel the poles of another magnet. Roth kinds of magnetism are developed in it, and hence we call it polarized. If now, we examine more carefully, we notice that one end of the bar is near the south pole of S-i$ tihe magnet, and we find by experiment, that the opposite end is likewise a south pole. Hence, that end of the bar next to the magnet must be s a north pole. Each pole of a magnet will always in this way induce the opposite kind of magnetism in that end of the bar nearest to it. Unlike frictional electricity, there is no discharge of magnetism when opposite kinds are brought together: the polarization takes place even when the bar is in contact with the magnet, and if the bar be made of steel, the polarity remains after the magnet is removed. 2. Several bars may be polarized.-A second bar may be placed with one end near to the first, and be found to be polarized; so a third may be polarized by the second: the series may be continued further, but the force is less in each successive magnet. To illustrate NATURAL PHILOSOPHY. 271 by experiment: from the north pole of a strong bar magnet, hang a key, from the lower end of this one a smaller key may be hlung, a third still smaller will be held by this, and a tack will cling to the lower Fig. 131. end of the last. The series of keys and nails liii s has become a series of magnets, each with its north and south pole, their north poles all directed downward (see Fig. 131). 3. All t/he molecules of ca maynet are polarized.- Now the molecules of a magnet are as truly separate from each other as the several magnets in the series just described. And it is thought that each molecule is a magnet, with its north and its south pole. Acting through the minute distances that separate them, each one is polarizing its neighbors, and hence, like the series of bars, their north poles must be all arranged in one direction, their south poles in the other. Both kinds of magnetism act upon each separate molecule, and keep it in a magnetic state. There is no transfer of the force from one molecule to another as there is of electricity in a charged body, so there can be no discharge of magnetism. A magnet, like a body charged with electricity, may polarize another, but it can not, like the charged body, become neutral by giving up its force. Why then is the middle of a magnet neutral, while only toward its ends do the forces show themselves? Not because the force of one kind leaves the molecules of one end and goes to the other, but because each molecule, from one end to the other, is exerting this force in the same direction. If a row of boys stand close together, and all push in the same direction, those at 2T2 NATURAL PHILOSOPHY. the end of the line will receive the greatest pressure; so the molecules of a magnet near the end toward which either force is acting, will be endowed with the strongest magnetism. In the middle of the series, the two forces are equal and in opposite directions, and must neutralize each other. (100.) If a bar magnet be supported so as to move fireely in a horizontal direction, it will rest only when its poles point north and south or nearly so; its variation is subject to both annual and diurnal changes. Fig. 132. 1. If a bar magnet be sl8t/oL)ted. - YE -A magnet may be supported in three ways so as to have free motion. It may be balanced upon a pivot. (See Fig. 132.) It may be hung from a fixed support by a fine C thread tied about its middle point. Fig. 13. (Fig.(Fig. 133.) Or it may be, for purposes of simple experiment, fastened to a cork and laid upon water. 2. It wmillpoint nzorth andcl south.-The magnet supported in either of the ways mentioned, will swing back and forth, until it finally settles to rest, and it will then.- be found pointing north and south. The end which points north is called the north pole: it is evident, however, that its magnetism is of the kind opposite to that of the north part of the earth. A slender bar magnet thus balanced is called a magnetic needle. Such a needle is used by mariners to direct them in their long voyages across the ocean. For NATURAL PHILOSOPHY. 273 this purpose, it is placed over a card upon which the "points of compass," north, south, east, west and others, are marked, and for protection, put into a box hung upon pivots, so that it vill keep the needle in a horiizontal position amid all the rolling or plunging motions of the ship. Sutch an arrangement is called the mariZner.'s COfiRt'S8. 3. Its vcrictlion.-VWhile it is true that the needle points in a direction which may be described as north and south, we nmust not understand that this description is exact. Indeed the needle seldom points exactly north and south. There are places at which it does; there are others at which it points east of north; and others at which it points west of the true north and south line. Its deviation, or in other words what it lacks of pointing in a true north and south line is called its uvari