GIFT OF Berkeley Public Library r l X jJLc*~s<^^ *&**& ~*~ >J& ; ( ^ THE NEW TEXT-BOOK OF PHYSICS AN ELEMENTARY COURSE IN NATURAL PHILOSOPHY DESIGNED FOR USE IN HIGH SCHOOLS AND ACADEMIES BY LE ROY C. COOLEY, PH.D. PROFESSOR OF PHYSICS AND CHEMISTRY IN VASSAR COLLEGE IVISON, BLAKEMAN, TAYLOR, AND COMPANY, NEW YORK AND CHICAGO. COPYBIGHT, 1868. COPTBIQHT, 1880, BY LE ROY C. COOLEY, PEEFAOE. THE Text-book of Natural Philosophy, first published in 1868, is now thoroughly revised; and an essentially New Text-Book of Physics is offered with the hope that it will prove to be still more worthy of the esteem of the friends of sound learning, and still more useful to the very large num- ber of science-teachers who have so long employed the older book. That which chiefly distinguishes this New Text-Book is V the prominence which it gives to the principle of energy. ' Physics has come to be universally regarded by scientists as "the science of matter and energy;" and I have felt, , that, unless I could fairly present the principle of energy as / the most vital element of the system, my work would be / altogether out of harmony with the later views, and unworthy I to be used in the education of the young, because it would / fail to give the student any adequate idea of the presentj state of the science. Various changes in the arrangement of subjects have been accordingly made ; and the doctrine of energy, in an element- ary form such as it must take in so elementaiy a work, will be found giving tone to all departments of the course. The first three chapters, treating of MATTER and MOTION, will abundantly prepare the student for the study of ENERGY in the fourth ; while, in the remaining chapters, he will be able to trace the exhibition of energy as seen in the phenomena of sound, heat, light, electricity, and machinery. R&4.392 IV PREFACE. Much new matter has been introduced, as, for example, on the subject of electrical induction, the telephone, the phono- graph, and other discoveries and applications which the late progress of science has made fit subjects for an elementary course. Among the new features designed to adapt the work to the actual wants of the class-room, is the Review at the end of every chapter. These reviews consist of Summaries of Prin- ciples, Summaries of Topics, and Problems. The summaries of principles are not simply a re-statement of principles in the order of their previous discussion : they are constructed in a way to show these truths in new rela- tions, and to supplement the synopses of the paragraphs in giving clear but concise statements of the most vital prin- ciples of the science. The summaries of topics follow, and suggest to the mind all the points in the discussion of the subject of every paragraph. And finally the problems tend to make the student's knowledge more exact by requiring him to apply it mathematically. The References which accompany the synopsis of each subject are specific, not simply to a book by title, but to the particular paragraph of the book where the desired in- formation ma} r be found ; and not to many and inaccessible authors, but, throughout, to two, one or the other of which, or both, may be in the hands of the teacher or pupil. Ganot's Physics is selected because of its excellent and thorough discussions, and Arnott's because of the appro- priate and interesting illustrations in which it abounds. These references are designed for the actual use of the student who is advanced enough and has time to extend his study beyond the elementary course in this work, and of the teacher who desires to bring additional matter into the class-room to elucidate or extend these elementary texts. If circumstances permit the use of a larger number of PREFACE. V reference-books, I would mention Deschanel's Natural Phi- losophy, by Everett ; Lardner's volumes on Mechanics and Optics ; Silliman's Physics ; Olmstead's Natural Philosophy, by Kimball . Mayer's works on Sound and Light ; Sylvanus P. Thompson's Electricity and Magnetism ; and Tyndall's several volumes on Sound, Heat, Light, and Electricity, as among those likely to prove most generally useful. The character of the work is still further indicated by the following extracts from the preface to the first edition : This volume is designed to be a text-book of natural philosophy suited to the wants of high schools and acade- mies. 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 mastered by average classes in the time usually given to this science. 2. It presents a judicious selection of subjects. Omitting whatever 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 mole- cules and of molecular motions, instead of the old theory of imponderables, which has been swept away. Carefully avoid- ing 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 elementary instruction which it proposes. 4. It is logical in the arrangement and development of subjects. A single chain of thought binds the different branches of the science into one system of related principles. 5. It is thoroughly systematized. Chapters, sections, paragraphs, and topics have been arranged with careful regard, on the one hand, to the relation of principles to VI PREFACE. 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. 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 relia- ble works wherein the subjects of the text are more exhaust- ively treated. LEll. C. C. JUNE, 1880. CONTENTS. CHAPTER I. ON MATTER AND FORCE. SECTION. PAGE. I. NATURAL PHILOSOPHY DEFINED 1 II. ON MATTER AND FORCE 6 III. ON THE FUNDAMENTAL IDEAS 16 IV. REVIEW .... 17 CHAPTER II. ON THE THREE PHYSICAL FORMS OF MATTER. I. ON THE APPLICATION OF THE FUNDAMENTAL IDEAS, 20 II. ON THE CHARACTERISTIC PROPERTIES OF SOLIDS . 21 III. ON THE CHARACTERISTIC PROPERTIES OF LIQUIDS . 24 IY. ON THE PRESSURE OF LIQUIDS 26 V. ON THE CHARACTERISTIC PROPERTIES OF GASES . 43 YI. ON ATMOSPHERIC PRESSURE 48 VII. ON "THE THREE LAWS" FOR GASES ... 57 VIII. REVIEW 62 CHAPTER III. ON MOTION. I. ON MOTION PRODUCED BY A SINGLE FORCE . . 67 II. ON MOTION PRODUCED BY MORE THAN ONE FORCE . 77 III. ON THE MOTION OF LIQUIDS 86 IV. ON THE MOTION OF AIR 90 V. ON VIBRATION 92 VI. ON UNDULATIONS 103 VII. REVIEW 109 vii Vlll CONTENTS. CHAPTER IV. ON ENERGY. SECTION. PAGE. I. ON DEFINITIONS AND MEASURES 114 II. ON THE CONSERVATION OF ENERGY . . . .123 III. ON THE RECOGNITION OF ENERGY BY THE SENSES . 126 IV. REVIEW 129 CHAPTER V. ON MOLECULAR ENERGY, OR HEAT. I. ON CONDUCTION AND CONVECTION .... 132 II. ON THE EFFECTS OF HEAT 135 III. REVIEW 146 CHAPTER VI. ON UNDULATORY ENERGY, OR SOUND. I. ON TRANSMISSION AND REFLECTION OF SOUND . . 148 II. ON MUSICAL SOUNDS 153 III. ON MUSICAL AND SENSITIVE FLAMES . . . .163 IV. REVIEW 167 CHAPTER VII. ON RADIANT ENERGY, OR LIGHT. I. ON TRANSMISSION 169 II. ON REFLECTION 172 III. ON REFRACTION 184 IV. ON DISPERSION ........ 194 V. ON OPTICAL INSTRUMENTS ...... 209 VI. ON DOUBLE REFRACTION AND POLARIZATION . . 216 VII. REVIEW 220 CHAPTER VIII. ON ELECTRICAL ENERGY. I. ON FRICTION AL ELECTRICITY 224 II. ON MAGNETIC ELECTRICITY 241 III. ON DYNAMIC ELECTRICITY 247 IV. REVIEW 269 CONTENTS. IX CHAPTER IX. ON MACHINERY SECTION. PAGE. I. ON THE SIMPLE MACHINES 274 II. ON WATER-POWER 293 III. ON THE STEAM-ENGINE 296 IV. REVIEW ........ , 300 PHYSICS, OR NATURAL PHILOSOPHY. CHAPTER I. ON MATTER AND FORCE. SECTION I. \ , ? Y. : *;. ; .; % " ; NATURAL PHILOSOPHY DEFINED. 1. THE qualities of matter are usually called its properties. Extension, Impenetrability, Indestructibility, and Elasticity are examples. The Properties of Matter. In what respects is a block of granite so unlike a block of wood ? The granite is brit- tle ; 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 re- quire the power of an engine : the wood is much lighter ; perhaps a single arm is able to 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. 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 EXTENSION. 2 NATURAL PHILOSOPHY. Measurement of Extension. Every body of matter must have length, breadth, and thickness. The amount of space which a body fills is found by measuring these three dimensions. In England and the United States the yard is adopted as the unit of length. Feet, inches, rods, and miles are the divisions and multiples of the yard. In France and man}' other countries the metric measures are employed, in which the unit is called the meter. The meter is the forty-millionth part of that meridian of our globe which passes through Paris. It is equal to 39.37 inches. In the metric system smaller units are obtained by dividing the meter into tenths, hundredths, and thousandths ; and larger ones, by multiplying it by ten, one hundred, and one thousand. The names and values of the smaller units are 'given on page x, : Fig. 1 . r Volume* - Tlie amount of space which a body occupies c is 'Called ,its VOLUME/ For bodies of small size the volume is ^measured In \3ubic inches, or, by the metric system, in cubic centimeters. For bodies of larger size a larger unit is more convenient ; and their volumes are measured in cubic feet, or cubic yards, and by the metric system, in cubic meters. Impenetrability. 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. 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 NATtJRAL PHILOSOPHY. 8 be again collected to form a mass like the original one with- out the slightest diminution in weight. Amid all the changes which we witness in the forms and qualities of bodies, not a single atom is destro} r ed. This property of matter, by virtue of which no particle can be destroyed, is called INDESTRUCTI- BILITY. Elasticity. When 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 compressed. 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- tion is, in this case, almost equal to the force of compression. Tliis property of matter, by virtue of which it restores itself to its former condition after having yielded to some force, is called ELASTICITY. Are all Bodies elastic? This property of matter is possessed by all bodies. Some are very slightly elastic ; such are lead and clay. Glass, although very brittle, is highly 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, which was made of steel, 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 explosjbility. 4 NATURAL PHILOSOPHY. I. -PHYSICAL PROPERTIES. Malleability. Many of the metals may be reduced to thin plates, or leaves, by hammering them. Zinc is a famil- iar illustration, sheets of this metal being often placed under stoves to protect the floor from 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. Ductility. Many substances ma}' be also drawn into wire. Iron, copper, and brass wires are sufficiently familiar. The peculiar property by virtue of which the}' may be drawn into wire is called DUCTILITY. Glass, when heated 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 ma}' be wound at the rate of a thousand yards an hour. Physical Properties. 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 these substances. 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 with- out undergoing any change in its nature, are called PHYSICAL PROPERTIES. If now we examine those properties described in the early part of this section, we shall find them all to belong to this group. Extension, Impenetrability, and the rest, are proper- ties which a body may show without any change in its nature. II. CHEMICAL PROPERTIES. Chemical Properties. 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. NATURAL PHILOSOPHY. 5 Who, not already familiar 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 CHEMICAL PROPERTIES. This classification of properties w T ill help us to define accu- rately the science whose elements we are beginning to study. 3. Natural Philosophy, or Physics as it is now more gen- erally called, is the science which treats of the physical prop- erties of matter, and of those phenomena in which there is no change in the nature of bodies. Illustrations. 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 raindrops 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. We therefore expect to learn the explanation of them in the study of physics. But if we regard the more quiet yet not less impos- ing phenomena of the seasons, we may discover a multitude whose discussion is, by the definition, excluded from this science. The young verdure of the springtime 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 dis- placed by the 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. 6 NATURAL PHILOSOPHY. SECTION II. ON MATTER AND FORCE. 4. Matter, with respect to its Divisibility, may be consid- ered either as Masses, Molecules, or Atoms. (O. 2, 3 ; A. 1, 2, 7-10. 1 ) Divisibility. Every body of matter may be cut or broken into pieces. This quality or property of matter is called DIVISIBILITY. Examples of minute Division. There are bodies all around us so small that we can not see them. They are in the air we breathe, and the water we drink ; some of them are so minute that only the most powerful microscope can enable us to discover them. Common salt can be detected by chemical means in the air, even at great distances from the sea, and when the air is perfectly transparent. There are living creatures so small that a million indi- viduals together would be no larger than a mustard-seed. Yet each one must be made up of parts, else it could not move about, and take its food, as all of them can do. A grain of cochineal dissolved in water will impart a dis- tinct color to a whole gallon. That it may do this, it is esti- mated that the grain must be divided into not less than six million pieces. Masses. A mass is any separate portion of matter, whether large or small. A block of marble or a particle of the dust into which it may be crushed, the grain of cochineal or one of its six million pieces, is a MASS. Molecules. But there is a limit bej'ond which a mass can not be divided without changing the nature of its sub- 1 Books of reference are indicated as follows : {?., Ganot's Physics, by Atkinson, 8th ed., 1877 ; A., Arnott's Physics, by Bain and Taylor, 7th ed., 1877. Numbers refer to paragraphs, not to pages. The dash between two numbers means that all the paragraphs between are included : e.g., " 7-10 " refers to paragraphs 7, 8, 9, and 10. NATURAL PHILOSOPHY. 7 stance. A block of ice, for example, may be crushed until its particles are like the finest dust, but, if its temperature be kept low enough while it is being crushed, every particle of the ice-powder 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 abso- lutely 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 and the little piece of ice. But it is thought that these particles can not be divided without changing their nature, and they are called MOLECULES. A molecule is a particle of matter which can not be divided without changing its chemical character. All bodies are made up of molecules. The size of a body depends upon their number ; its shape, upon their arrange- ment. Atoms. If the molecules are broken or divided, the character of the substance is changed. Let steam, for ex- ample, be passed into a red-hot gun-barrel : that which issues from the other end is not steam, but hydrogen gas, while another gas, oxygen, combines with the iron of the gun- barrel. The molecules of steam are broken into pieces, but the substance is no longer steam. These smaller parts are particles of hydrogen and oxygen. The chemist finds that there are two pieces of hydrogen and one of oxygen obtained whenever a molecule of water is divided. But no way has yet been found to carry the division any further; and these, the smallest of all frag- ments into which matter can be divided, are called ATOMS. By combining trigitbflr, atoms form molecules. An atom is the smallest portion of matter that can enter into combination. What is Inertia ? Masses of matter have no power to move themselves, nor to stop themselves when once in motion. 8 NATURAL PHILOSOPHY. 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. Molecules and atoms also are powerless to change their own condition. It is believed that the molecules of every body are in motion always, but no molecule can in any way change its own velocity or direction. Inertia is the property of matter which does not allow a body to change its own con- dition of rest or motion. 5. Forces are either attractive or repellent. (6r. 26.) Force. Bodies are sometimes in motion, and sometimes at rest. Their motion is at one time swift, at another slow. Now, inertia prevents any body from causing these changes in itself, and we must attribute them to the influence of other bodies. Whatever this influence may be, it is called FORCE. Force is the name given to the influence which tends to pro- duce or diminish or in any way change the motion of bodies. 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 supported. 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. 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 NATURAL PHILOSOPHY. 9 spring to their former position. While springing back the molecules are evidently being thrust away from each other. Or try the following experiment (Fig. 2) : Suspend a pith-ball, or a little ball of cotton, by a fine silk thread : briskly rub a warm dry strip of glass 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. That which keeps them apart is called REPULSION. Fig An influence under which bodies tend to separate is called REPULSION. Molecular Repulsion. The action of repulsion among molecules is more universal than among masses. It is illus- trated by man}' familiar facts. If, for example, a bladder be filled with cold air, and then heated, it will burst. Repul- sion 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 seventeen hundred times larger than before. 10 NATURAL PHILOSOPHY. Notice that in these examples the separation of the mole- cules is due to heat. It is believed that all molecular repulsion is the same influence as that which shoivs itself as HEAT. The Forces of Mature. We speak of the forces of nature, 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 all the forces of nature are only different manifestations of attraction and repulsion. 6. Attraction receives different names according to the cir- cumstances under which it acts. Gravitation, Cohesion, Ad- hesion, and Chemism are its most common forms. (G. 84-87 ; A. 18-28, 86, 87.) I. GRAVITATION. Gravitation denned. Gravitation is that form of at- traction which is exerted upon all bodies, and throughout all distances. 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 an}^ substance cut it off, or even diminish its action ; for, if the earth should come between the sun and moon, these two bodies would still attract each other with the same degree of force. Governed by two Laws. The intensit} T of gravitation between bodies depends on two things, the quantity of matter contained in them, and the distance between their centers. The "law of gravitation," discovered by Newton, consists of two parts which express these two relations. We may study them as two laws. The First Law of Gravitation. Suppose two bodies, one containing twice as much matter as the other, to attract NATURAL PHILOSOPHY. 11 a third. The force exerted by the first will be twice as great as that by the other. If one body weighs nine tons and another three tons, then a third body equally distant from them will receive three times as much attraction from the first as from the second. These facts illustrate the law that the force of gravitation varies directly as the quantity of matter exerting it. The Second Law of Gravitation. 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-fourth as strong as in the second. If the dis- tance 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. These facts illustrate the law that the force of gravitation varies inversely as the square of the distance through which it acts. Weight. The weight of a body is the downward press- ure which it is able to exert. It is due to the attraction of gravitation exerted by the earth. Weight must therefore increase or diminish in exact accordance with the laws of gravitation. Is proportional to the Quantity of Matter. Accord- ing to the first law, a double quantity of matter is attracted by the earth with a double force, and it therefore weighs twice as much. For the same reason, if the quantities of matter in two bodies are as 1 : 4, their weights must also be as 1 : 4. That is : the weights of bodies are proportional to the quanti- ties of matter in them. And inversely proportional to the Square of the Dis- tance from the Earth's Center. According to the second law, the greater the distance from the earth, the less will a body weigh. Now, distance from the earth is measured from its center. When on the surface of the earth, a body is four thousand miles from the center ; suppose it were possible to carry the body to a height of four thousand miles above the surface, its distance from the center would be doubled, and its weight would be reduced to one-fourth. 12 NATURAL PHILOSOPHY. Not limited to Bodies on the Earth. Since the laws of gravitation are universal, a body on the moon or an}' other heavenly body has weight. Not the same as Mass. By mass, we mean the quantity of matter in a bod} r . We speak of the body itself as a mass to distinguish it from molecules and atoms ; but the mass of a bod} 7 is the quantity of matter it contains. A body on the moon, for example, would have the same quantity of matter in it as if upon the earth. Yet the moon could exert much less attraction than the earth, and hence the weight of the bod} 7 would be less. Mass is the quantity of matter in a body ; weight is the force of attraction ex- erted on it. The mass of a bod} T is everywhere the same ; its weight is different at different places. Bat at any one place the weights of all bodies are proportional to their masses; and for this reason we can compare the quantities of matter in bodies b} r weighing them. II. COHESION. Cohesion defined. Cohesive attraction holds the mole- cules of a body together, and enables it to keep its form and size. A cubical block of wood remains a cube only because its molecules are held together by this force. Were it not for its action, all bodies would at once dissolve into their ultimate molecules, and vanish. COHESION is that form of attraction which acts between the molecules of the same body. Its Power is very great. 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 five hundred pounds may be lifted by means of a wire one-tenth of an inch in diameter. Even a strip of paper is not easily broken b} T a force acting exactly in the direction of its length. But it acts through Insensible Distances. The dis- tance 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. NATURAL PHILOSOPHY. 13 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 molecules 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. Welding-. The smith unites two pieces of iron by weld- ing. He softens the iron by heat, then puts the two pieces together, and unites them by the heavy blows of his sledge. All that 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. III. ADHESION. Adhesion defined If the hand be plunged into water, it comes out covered with a thin film of the fluid ; it may be immersed in alcohol with the same effect. When one writes upon the blackboard, he leaves fine particles of the crayon clinging to the surface of the board. In all such cases we notice that there is an attraction between particles of different kinds of matter. Attraction between particles of unlike kinds is called ADHESION. By what Experiment may we illustrate it? A very pret- ty experiment is shown in Fig. 3. It illustrates the adhesion between water and brass. A round plate of brass, having a handle fastened to its center, is laid flat upon the surface of water, and then slowly and gently lifted. The water un- der it is also lifted a little, as the picture shows it to be. You can use a plate of wood or of glas. in the same way. Adhesion of Solids to Solids. The value of glue and 14 NATURAL PHILOSOPHY. cement is due to the powerful adhesion which acts between them and the surfaces of solid bodies which they bind to- gether. Adhesion of Liquids to Solids. 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. 4.) Along the outside surface of the tubes the water also climbs to a little height. If tubes be inserted in a vessel of mercury, this fluid will be pushed down. (Fig. 5.) The mercury inside the Fig. 4. Fig. 5. tubes will be considerably be- low the general level, while the fluid against the outside is also depressed. Here are two well-marked cases of the action of adhesion. Whenever 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 experi- ments it is shown that all liquids which will wet the sides of the tube will be lifted, while those which will not will be pushed down. Capillarity. The elevation or depression of fluids in small tubes is called CAPILLARITY. The attraction causing it is, however, nothing different from adhesion. It causes Liquids to penetrate Porous Solids. An eas3 r 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. NATURAL PHILOSOPHY. 15 Explanation. The rise of the water is due to the at- traction between its particles and those of the paper and glass. This force, acting downward from each particle of the paper through the definite but imperceptible distance 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 lad- der, up which the water is impelled by capillary force. Familiar Examples. Numerous familiar facts are ex- plained by this experiment. Oil is carried up the lamp-wick to supply the flame with fuel. Ity 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. Tlie Law. In Fig. 4, the water is represented as being lifted to different heights in the 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. These facts illustrate the law that the heights to which a liquid rises in different tubes of the same material are inversely proportional to the diameters of the tubes. A tube one-hundredth of an inch in diameter will lift water to a height of about four inches. IV . CHEMISM. Chemism defined. When coal burns, the carbon of which it is composed combines with the oxygen of the air. They form a new substance called in chemistry carbonic di- oxide. The properties of carbonic dioxide are very unlike those of either coal or oxygen. This action occurs among the atoms of coal and oxygen. 16 NATURAL PHILOSOPHY. Under the influence of the heat these unlike atoms are drawn together, and then so firmly held that they seem to be one body. They form molecules of carbonic dioxide. The attraction which holds the atoms together in a mole- cule is called CHEMISM. Chemical affinity is another and an older name for it. SECTION III. ON THE FUNDAMENTAL IDEAS. 7. The fundamental ideas in regard to matter and force are suggested by the words, Molecules, Inertia, Attraction, and Repulsion. These terms have been already defined; but they may suggest to the mind much more of what is believed about the minute constitution of matter than their definitions con- tain. Principle suggested by the Term Molecule. Every body of matter is made up of a multitude of little particles, which do not touch each other, which are forever in motion, and which can not be divided without changing their nature. Principle suggested by the Term Inertia. No body of matter a mass, a molecule, nor an atom has power to change its own condition of rest or motion. Principle suggested by the Term Attraction. All bodies of matter masses, molecules, and atoms tend to approach one another. Principle suggested by the Term Repulsion. There is also an influence under which molecules tend to separate, and which forbids their actual contact in a body. Of these four Ideas. These four ideas may be so com- bined as to yield the explanation of almost all the phenom- ena which appear in nature. A great city, with all its various forms of architecture and machinery, is built of a NATURAL PHILOSOPHY. 17 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 things is simple and orderly, dis- playing the infinite knowledge, power, and skill of a divine Architect. SECTION IV. REVIEW. I. SUMMARY OF PRINCIPLES. In the foregoing chapter we have found that : All properties of matter are either physical or chemical. Physics or 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 substances. Matter may be considered as consisting of masses, mole* cules, and atoms. Forces are either attractive or repellent. Attraction is called Gravitation, when it acts between masses ; Cohesion or adhesion, when it acts between molecules ; Chemism, when it acts between atoms. The force of gravitation varies directly as the quantity of matter exerting it, and inversely as the square of the dis- tance through which it acts. Volume is the space occupied by a body. Mass is the quantity of matter in a. body. Weight is the pressure of a body downward, caused by the attraction of the earth. The fundamental ideas of matter and force are suggested by the words, Molecule, Inertia, Attraction, and Repul- sion. 18 NATURAL PHILOSOPHY. II. SUMMARY OF TOPICS. 1. Properties of matter. Extension. Impenetrability. Indestructibility. Elasticity. 2. Malleability. -- Ductility. Definition of physical properties. Definition of chemical properties. 3. Definition of Physics. Illustrations. 4. Divisibility. Examples. Masses. Molecules. Atoms. Inertia. 5. Force. Attraction. Repulsion. Molecular repul- sion. 6. Gravitation described. Governed by two laws. The first law. The second law. Weight defined. It is proportional to quantity of matter. Inversely propor- tional to square of the distance from the earth. Not limited to bodies on the earth. Not the same as mass. Cohesion defined. Its power. At insensible distances. Weld- ing. Adhesion defined. Experiment. Of solids to solids. Of liquids to solids. Capillarity. Familiar ex- amples. .The law. Chemism defined. 7. The fundamental idea suggested by the term Molecule. By the term Inertia. By the term Attraction. By the term Repulsion. III. PROBLEMS. 1 . With how many times greater force will a body be at- tracted by a mass of iron weighing 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 ounces and the other 12 ounces, are hanging at a distance of 10 feet from a third ; what relative degrees of force do they exert upon it ? 3. One ball of lead attracts another through a distance of 10 feet with a force of 8 pounds ; what force would it exert if placed at a distance of 20 feet? Ans. 2 pounds. 4. A body is at one time 50 feet, and at another 75 feet, NATURAL PHILOSOPHY. 19 from a mass of rock ; what are the relative forces exerted upon it in the two positions? Ans. 9 : 4. 5. Two bodies, one weighing 6 pounds, and the other 9 pounds, are attracting a third. The first is at a distance of 25 feet, the second of 50 feet ; what relative attractions do they exert ? 6 9 72 : if/)25 which, reduced, is the Ans. 8:3. 6. At the surface of the earth a body weighs 10 pounds ; what would it weigh if carried to a height of 5 miles above the surface? Ans. 9.975 pounds. (4005 miles) 2 : (4000 miles) 2 : : 10 pounds : x. x = 9.975 pounds. 20 NATURAL PHILOSOPHY. CHAPTER II. THE THREE PHYSICAL FORMS OF MATTER. SECTION I. APPLICATION OF THE FUNDAMENTAL IDEAS. 8. ATTRACTION and REPULSION acting upon the molecules of bodies produce the three physical forms of matter, Solid, Liquid, and Gaseous. The Action of the Molecular Forces. Between the molecules of every body, two sets of forces, attractive and repellent, 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 from each other to the greatest possible dis- tance. The solid rock, the mobile water, and the rushing air are types of these three grand divisions to which all bodies belong. Changes of Condition in Nature. Numerous and fa- miliar 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 floating clouds. In this case molecular repulsion is increased until it is stronger than molecular attraction. Or, suppose the action to be reversed. Imparting their heat to other bodies, the NATURAL PHILOSOPHY. 21 clouds are changed to water, and water again to solid ice and feathery snow. In this case molecular repulsion is dimin- ished until it is weaker than attraction. Artificial Changes. Imitating nature, we may to a limited extent, by the use of heat, change the form of vari- ous bodies ; and numerous arts of life spring from the appli- cation of this power. By the repulsive force of heat, the metallic ores are melted, and the useful metals obtained. By the same force iron is liquefied, that it may be molded into requisite forms of strength, of beaut} r , or of use, demanded in the arts. The expansive force of steam is but the repul- sive force of heat. SECTION II. ON THE CHARACTERISTIC PROPERTIES OF SOLIDS. 9. The characteristic properties of solid bodies are Hard- ness, Tenacit}^, Malleability, Ductility, and Crystalline Form. (G. 93-95 ; A. 59-64.) Hardness. The particles of solid bodies are held to- gether 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 HARDNESS, 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 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 ; }*et gold is four times as dense as the diamond. Mercury is a fluid, and, of course, has no hard- ness ; yet it is nearly twice as dense as the hardest steel. 22 NATURAL PHILOSOPHY. Tempering. The process called tempering, or anneal- ing, consists in regulating the hardness of a bod}* 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 tempera- ture 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. Tenacity. When a rod of iron is stretched in the direc- tion of its length, it will be found that great force is required to pull it apart. The property, in virtue of which a body resists a force which tends to pull its parts asunder, is called TENACITY. Of Metals. 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. Malleability. The particles of many solid bodies may be displaced without overcoming their cohesion. By the blows of a hammer, the molecules of many metals ma}' be shifted about, without breaking them apart, until the bodies are reduced to the form 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 prop- erty, in virtue of which a body may be hammered or rolled out into thin leaves or plates, is called MALLEABILITY. Of Metals. This property is possessed in a high degree by many of the metals. Under the hammer, lead is the HATTTRAL PHILOSOPHY. 23 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. (Silliman's Physics, p. 138.) Ductility. 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 example, 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. Crystalline Form. The attraction among the molecules has not brought them together at random, nor in disorder. A flake of snow, when seen through 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 beauti- ful variety of tree-like forms. These definite and regular forms in which solid substances occur are called CRYSTALS ; and any process by which they may be obtained is called a process of CRYSTALLIZATION. In Nature. In the formation of solid bodies their tend- ency to take a crystalline form is almost universal. The same substance generally takes the same form, but in differ- ent substances the shapes of crystals may be wonderfully unlike. Lead, in its most common ore, called galena, 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 freety. 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, 24 NATURAL PHILOSOPHY. Made artificially. Even when no indication of a crys- talline structure can be seen, the substance can often be made to assume it by some artificial process. The best method 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. SECTION III. ON THE CHARACTERISTIC PROPERTIES OF LIQUIDS. 10. Liquids have elasticity and some other properties in common with solid bodies. But, since the attraction and repulsion among their molecules are very nearly equal, we find that Mobility is their characteristic property. (G. 97, 98 ; A. 74.) Elasticity. When submitted to pressure, liquids are com- pressed ; and when the pressure is removed they instantly spring back to their original volume : the}' are elastic. 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. Compressibility. It re- _ quires a very great force, how- - ever, to compress a liquid in the least degree ; so great, that, until improved means of experiment were contrived, liquids were thought to be incompressible. Water at a freezing temperature, when pressed by a force of fifteen pounds to the square inch, is condensed only .0000503 of its volume. NATURAL PHILOSOPHY, 25 Attraction and Repulsion nearly equal. That the attractive and repulsive forces among the molecules of a liquid are not exactly equal, ma}* be shown by a pretty ex- periment. To one end of a scale-beam (Fig. 6) a disk of brass is suspended, and accurately balanced by weights in the oppo- site scale-pan. Then let the disk be brought to rest upon the surface of water in a vessel, and it will be held there with considerable force. If the disk be two inches in diam- eter, weights equal to two hundred grains may be placed upon the opposite pan before it will be torn from the water. But we notice that a film of water still adheres to the disk, having been torn away from the water beneath it. The weight of two hundred grains has simpty overcome the cohe- sion of the water. We thus learn that the attraction is a trifle stronger than the repulsion. Mobility. But the attractive and repulsive forces are nearly balanced ; and, if we now remember that water con- sists of molecules, it is not more" difficult to see that there must be freedom of motion among them, than it is to see that shot, or smooth balls of any other kind, will roll easily upon each other. 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. This freedom of motion among the molecules of a substance is called MOBILITY. Mobility is the property of a liquid which makes it differ from a solid. Destroy the mobility of water, and it becomes a solid, ice. Impart mobility to a solid, and it ceases to be a solid ; it becomes a liquid, as when ice is melted. 26 NATURAL PHILOSOPHY. SECTION IV. ON THE PRESSURE OF LIQUIDS. 11. At any point inside of a body of liquid at rest, there is equal pressure from all directions. Hence a fluid will rest only when its upper surface is level ; but the level surface of a large body of water is convex. (G. 105, 108, 110; A. 304.) Liquids 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 arranged as in Fig. 7. The weight of the ball A will be a downward pressure upon the balls B and C. These, being free to move, will be pushed 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. This pressure is due to gravitation. Moreover, the pressure of the liquid must be exerted Equally in all Directions. For, if the pressure at any point were greater in one direction than another, the liquid would move in that direction on account of its mobility. If, then, the liquid is at rest, the pressures in all directions must be just balanced. Experimental Illustration. 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 may not be so clear that it is pushed upward by an equal force. Taking a lamp-chimney, and putting the string NATURAL PHILOSOPHY. 27 handle of the disk (Fig. 8) through it, hold the disk tightly against the lower end of the tube until it is pushed down to the middle of the water. Now drop the string : the heavy disk does not sink, but remains tightly pressed upward against the tube by the water. If water be al- lowed 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 out- side, then the disk falls, suggesting that the upward pressures Fig. 8. and downward are equal. Another Illustration. Numerous simple experi- ments might be given to illustrate this important principle : one other must suffice. Glass is eminently brittle. It ma}' 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 B will support the weight of all the water above it, and re- main unbroken. This could E not happen if the pressure of the water upon it were not equal from all directions. The Surface of Water at Fig. 9. Rest is level. The truth of this principle may be seen by attentively examining Fig. 9, which represents a section of a vessel containing water, the surface of which has for the moment been thrown into 28 NATURAL PHILOSOPHY. the position indicated by the line A E. Refer to an} T two points in the water, as h and K. We see that the down- ward pressure at h would be the weight of the water above that point, a column m h. But the pressure at that point is equal in all directions, so that the water between h and K would be pressed toward K by a force equal to the weight of the column m h. In just the same way we may show that at K the water is being pressed toward h by a force equal to the weight of the column n K. The column m h is greater than n K ; and, since the water is free to move, it will yield to the greater pressure, and'go toward K until the two forces are equal. The two forces will be equal only when m and n are in the same level surface, a b. But a level Surface 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. 12. Since the surface of water at rest must be level, we infer that water confined in pipes or close channels will always rise in them as high as the source from which it comes. Upon this principle cities are often supplied with water. The same principle explains the phenomena of springs and artesian wells. Water in Pipes will rise as high as its Source. No matter what ma}' 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. Moreover, a pipe leading from a vessel is a part of the vessel which holds the water. NATUBAL PHILOSOPHY. 29 The vessel shown in Fig. 10 has a very irregular shape. There is first the large vase at the left hand, then the horizontal tube, and finally the tubes reaching upward from the last ; yet it is all one vessel, because the water can pass freely from one part to another. If water is poured into the vase, it will rise just as fast in the tubes, and will at last stand at the same height in all parts, as the picture shows it to be. The Supply of Water to Cities. A pipe leading from a reservoir of water on a hill outside a city may be buried Fig. 10. in the ground, passed down the hillside 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 hillside, through the streets, and up the branches, into the dwellings, and supply them all with water. Many cities are in this way convenient!}' supplied with abundance of water, not only for private dwellings, but also for public foun- tains and manufacturing purposes. Springs. The rocks which compose the earth are ar- 30 NATURAL PHILOSOPHY. ranged in layers, called strata, which are generally more or less oblique as represented in Fig. 1 1 . 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 c 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 hillside at S, and thus form a spring. Artesian Wells. Again, the water, falling upon the Fig. 11. surface, and passing through other porous layers, at length comes in contact with a rock which it can not penetrate, and flows along its surface. The basin-shaped part, a a, of the porous layer, would thus in time become filled with water ; indeed, the entire layer reaching to the surface of the earth in both directions might thus be filled. If, then, a well as W be sunk through the mass down to this saturated layer, the water will collect in the well, and rise sometimes to the surface of the ground above, and sometimes it even spouts in jets many feet above the surface. Such wells are often bored to very great depths, and are NATURAL PHILOSOPHY. 31 called artesian wells. One of these wells was bored in Louisville, Ky., to the depth of 2,086 feet. Another in St. Louis has a depth of 2,199 feet. The supply of water fur- nished is often very abundant. The famous Grenelle well, in Paris, yields daily 600,000 gallons. 13. 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 the area of the bottom of the vessel. It equals the weight of a column whose base is the base of the vessel, and whose height is the depth of the liquid. (G. 104; A. 303.) The Pressure is independent of the Shape of the Vessel. This may be proved by experiment. The essen- tial parts of an apparatus for this purpose are represented in Fig. 12. A glass tube, A B, bent twice at right angles, contains mercu- ry. The height of mer- cury in one arm is shown by a graduated scale, and to the other arm vessels of various forms and heights may be at- tached. When a vessel, G, is filled with water, the fluid presses upon the mercury at A, and pushes it up in the arm C D ; 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 Fig. 12. 32 NATURAL PHILOSOPHY. which fills them will push the mercury to the same point on the scale. We infer that the pressure of a fluid downward is quite independent of the shape of the vessel and of the quantity of fluid it contains. The Pressure depends on the Depth of the Liquid If a tube twice as high as the vessel E, in Fig. 12, be 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 found that the pressure is in pro- portion to the height of the column of water which exerts it. The Pressure depends also on the Area of Base. In these experiments the area receiving the pressure at the bot- tom of the vessels is the same for all. If next we suppose the bottom of the vessel to be made just twice as large, there would be just twice as much water resting upon it, and therefore just twice the downward pressure. In any case, the pressure is in proportion to the area of the base of the vessel. To calculate the Pressure. If the pressure depends only on the size of the base and the height of the column, then it must equal the weight 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 62J pounds ; and, if the number of cubic feet of water which exerts the pressure be multiplied by 62^, the amount of pressure in pounds will be obtained. Illustration. Thus, suppose a vessel, represented by E F C D in Fig. 13, to be full of water : the pressure on its bottom is the weight of the column A B C D. Let the area of the bottom be three square feet, and the depth of the water be eight feet ; then the pressure is the weight of 24 cubic feet of water, and 24 X 62J pounds, or 1,500 pounds, is the pressure exerted. Since the pressure is equal in all directions, we may NATURAL PHILOSOPHY. 33 obtain the amount of pressure against any portion of sur- face, either in the bottom or sides of the vessel, by finding 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 middle 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. We must under- stand 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 con- tain ten cubic feet of water, and its weight will be 10 x 62^ pounds. 14. 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 follows from this principle : 1st, That a solid body, lighter than water, will sink far enough to displace a quantit}* of water just equal to its own weight. 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. (G. 116, 119 ; A. 320, 325-327.) Solid Bodies in Water are pressed upward. If, for example, a piece of wood be pushed dowi> 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 is lighter than when in air : the water under it pushes upward against it, and thus supports a part of its weight. With Force equal to the Weight of Water displaced. Let us suppose that a block of marble is suspended in a 34 NATURAL PHILOSOPHY. Fig. 14. vessel of water (Fig. 14). The upward pressure against its lower surface, a 6, is equal to the downward pressure of the water at that depth ; and this downward pressure is equal to the weight of the column of water, efba. Now, a part of this upward pressure sus- tains the column of water, efcd, and the rest of it is exerted upon the marble. To sustain the column, efcd requires an upward pressure equal to its weight ; and hence there is left a pressure against the surface a 6, equal to the weight of a column of water, a b c d, but this water is dis- placed by the marble. The upward pressure against the block is therefore equal to the weight of the fluid displaced. The Principle of Archimedes. 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 PRINCIPLE OF ARCHIMEDES. 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 ena- bles the inquirer to determine the size or volume of a solid body, however irregular ; and it has, moreover, led to valua- ble improvements in marine architecture and in other arts. 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 im- mersed. 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. KATUKAL PHILOSOPHY. 35 If the Solid is heavier than Water, If a solid is heavier than water, the upward pressure of the fluid can support only a part of its weight. The weight supported will be equal to the weight of the water which the solid displaces. Thus, for example, a piece of marble which weighs 10 ounces in air will be found to weigh only 6.3 ounces in water. The upward pressure of the water is equal to the difference, 3.7 ounces; 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. 15. The specific gravity of a substance is its weight com- pared to the weight of an equal volume 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. (G. 123, 125, 130.) Specific Gravity. The specific gravity of a substance shows how many times heavier it is than an equal volume of some other body. The standards used are water and air; water for all solid and liquid bodies, and air for all gases. In chemistry hydrogen instead of air is the standard for gases. Then, when we say, for instance, that the spe- cific 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. Or, compared with Irydrogen, its specific gravity is 16 : that is to say, a cubic inch of oxy- gen weighs 16 times as much as a cubic inch of Irydrogen. The following simple rule must evidently cover all cases of finding specific gravity : Divide the weight of the body by the weight of an equal volume of the standard. How shall these two Weights be found? The weight of the body whose specific gravity is sought can be found 36 NATURAL PHILOSOPHY. directly with the balance, but the weight of an equal volume of the standard can not. It is not easy to know the exact volume of the body, which is often very irregular in shape. Different methods of experiment must be used in different cases. I. OF GASES. How may the Specific Gravity of a Gas be found ? To obtain the specific gravity of a gas, divide the weight of a convenient portion of it by the weight of an equal portion of air or hydrogen. To get the weight of equal portions of gases, is, however, a difficult process, requiring many precautions. Without trying ^o give the details of the operation, we may describe it in general terms. A glass globe is first weighed when full of air (Fig. 15). 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 gravit} T is de- sired, and again weighed. The difference between this weight and that of the empty globe is the weight of the globe-full of gas. The spe- cific gravity is obtained from these weights of equal volumes of gas and air. II. OF LIQUIDS. How may the Specific Gravity of a Liquid be found ? To obtain the specific gravity of a liquid, divide the weight of a convenient volume of it by the weight of an equal vol- ume of water. Pig. 15. NATURAL PHILOSOPHY. 37 The experiments by which to find the weights of equal vol- umes of the two liquids may be made, 1st, With a balance. 2d, With a hydrometer. 3d, With a solid bulb. With a Balance. 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 one thousand grains of pure water. The weight of the bottle being known, a single operation with the balance will give the weight of the liquid, and then its specific gravity may be speedily calculated. With a Hydrometer. A common form of this instru- ment is represented in Fig. 16. It consists of a glass tube, with two bulbs near its lower end. The tube and upper bulb are full of air, which 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. Explain the Action of this Instrument. The action of the Irydrometer can be read- ily explained by means of a piece of wood, several inches long and an inch square, hav- ing 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 ten inches, then ten cubic inches of water are displaced by it. If the instrument be put into a vessel of alcohol, it will sink deeper : suppose it be twelve inches ; thf^. twelve cubic inches of alcohol are dis- placed. But, according to the principle of Archimedes, the fluid displaced is equal in weight to the body floating in it, 38 NATURAL PHILOSOPHY. Hence ten cubic inches of water have the same weight as twelve cubic inches of alcohol ; or alcohol is |f as heavy as water. Its specific gravit}- is, therefore, ^f = .833 + . Making the instrument of glass, and giving it the form seen in Fig. 16, renders it more convenient and more ac- curate, but does not alter the principle on which it acts. The Graduation. The graduation of the scale is arbi- trary, and varies in different forms of the instrument. The zero usually 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. By the Use of a Bulb. According to the principle of Archimedes, a heavy bulb of glass, or other convenient sub- stance, when weighed in an}' liquid, will lose a part of its weight just equal to the weight of an equal bulk of that liquid. Hence, 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 gravit} T ma}' 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 grains. Its loss in alcohol is found to be 257 grains. Then J|-Jr= .79+ is the specific gravity of the alcohol. Alcohol, with this specific gravity contains no water : a higher specific gravity shows the pres- ence of water. III. OF SOLIDS. How may the Specific Gravity of a Solid be found ? To find the specific gravity of a solid body, divide the weight of a convenient portion of it by the weight of an equal volume of water. There are two important cases of common occurrence : 1st, The solid is heavier than water. 2d, The solid is lighter than water. KATURAL PHILOSOPHY. 39 Of a Solid heavier than Water. Divide the weight of the body in air, by its loss of weight in water. The princi- ple of Archimedes explains this rule. Thus the weight of a piece of marble in air is ten ounces, and in water it is 6.3 ounces: the difference, 3.7 ounces, is the weight of a bulk of water equal to the size of the marble. Then, |? = 2.7 is the specific gravity of this solid. Describe the Experiment. The experiment is con- ducted in the following manner : Let the specific 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. 17), and its weight again de- termined. Of a Solid lighter than Water If the solid be light- er than water, the operation is more complex. If the light body be compelled to sink in water by fastening to it some heavier bod} r , 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 alone. If the upward pressure against the heavy body be subtracted from the upward pressure against 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. Illustration. A body weighed 200 grains in air. When attached to a piece of lead, both weighed 1,936 grains in air, and 1,460 grains in water; suffering a loss of 476 grains. The lead itself, when weighed in water, lost 152 grains. The upward pressure against the light body alone must have been Fig. 17. 40 NATURAL PHILOSOPHY. 476 152 = 324 grains. Then, 200 grains, the weight of the light bod}' in air, divided by 324 grains, the weight of an equal bulk of water, is the specific gravity desired. In the following table the specific gravities of several im- portant substances are arranged for reference. I. Of Gases, at 32 F. Barometer, 30 inches. NAMES. SPECIFIC GRAVITY. NAMES. SPECIFIC GRAVITY. Air . ... 1.000 Nitrogen 972 OxVfifen 1 106 Carbonic acid 1 529 Hydrogen 0.0692 Olefiant gas 978 II. Of Liquids, at 39 F. NAMES. SPECIFIC GRAVITY. NAMES. SPECIFIC GRAVITY. Water (distilled) 1 000 Ether 723 Sea-water Milk 1.026 1.030 Naphtha. . . . Oil turpentine 0.847 0.870 Alcohol (absolute) . . Olive-oil 0.792 0.915 Wine of Burgundy . Mercury (32 F.) . . 0.991 13.598 III. Of Solids, at 39 F. NAMES. SPECIFIC GRAVITY. NAMES. SPECIFIC- GRAVITY. Platinum (rolled) . . Gold (stamped) . . . 22.069 19.362 7 2 Silver (cast) . . . Diamond .... Marble 10.47 3.50 2 837 Steel 7 8 1.92 Lead (cast) .... Copper " 11.3 8 78 Flint-glass .... Ice . . 3.329 0.93 Brass 8 38 Pine wood .... 0.66 NATURAL PHILOSOPHY. 41 16. If an external pressure be exerted anywhere upon a liquid, the same amount of pressure will be transmitted in eveiy direction. It will act with the same force on equal surfaces, and in directions at right angles to them. This principle is known as PASCAL'S LAW. (G. 99, 109 ; A. 298, 299.) The equal Transmission of Pressure. To the principle stated above, let a vessel, represented in section by Fig. 18, be quite filled with water. In the sides of the vessel are several apertures, A, B, C, D, and E, closed with movable pis- tons. Let the area of each piston be one square inch, and suppose a weight of two pounds be placed upon the pis- ton A. It will be found that the pressure on each piston will be increased by a illustrate Fig. 18. force of just two pounds. Thus E will be pushed upward by a force of two pounds, while B 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 in- serted, each will be found exerting a two-pound pressure greater than before 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. Experiment. Then, suppose two C3 T linders, one just twice as large as the other, to be joined together by a tube at their bottoms (Fig. 19), and let there be a piston fitting each cylinder exactly, and carrying a table as shown in the picture. Now, Fig. 19. 42 NATURAL PHILOSOPHY. according to the principle just learned, if a one-pound weight be put upon the small table, it will balance a two-pound weight upon the other. If one cylinder be one hundred times larger than the other, then one pound on the small table will balance one hun- dred pounds on the large one. The experiment shows that if an external pressure be made on any part of the surface of a fluid, the pressure received by any other part of the surface will be in proportion to its area. Fig. 20. Application of this Principle. 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. 20. Two metallic cylinders, A and B, of different sizes, are NATURAL PHILOSOPHY. 43 joined together by a tube K. In the small cylinder there is a piston, p, which can be moved up and down by the handle M. 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 framework, Q. Between the iron plate and the top of this framework, the body to be pressed is placed. When the small piston is raised, the cylinder A is filled with water drawn from the reservoir H, below ; and, when it is pushed down, this water is forced into 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 piston in A will be exerted upon every equal amount of surface in B. To illustrate this, suppose the 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. By increasing the size of the large cylinder, and diminish- ing the size of the small one, the pressure exerted by a given power is increased proportionally. The weight of a man's hand may thus be made to lift a ship with all its cargo. The only limit to the increase of power is the strength of the material of which the machine is made. SECTION V. ON THE PROPERTIES OF GASEOUS BODIES. 17. The most characteristic properties of gases are Com- pressibility and Expansibility. Besides these, gases possess other properties common to all forms of matter, among which we notice Elasticity, Weight, and Mobility. 44 NATURAL PHILOSOPHY. Compressibility. The compressibility of air is prettily shown by the apparatus represented in Fig. 21. It consists ^^ of a glass tube with a bulb at the upper end, and with its lower end joined to another glass tube b}' a piece of rubber tubing. A colored liquid fills the bend, and stands at equal heights in the glass tubes. Closing the upper end of the open tube with the lips, let the breath be gentl}* blown into it ; the fluid will be seen to rise in the other tube, it may be a distance of several inches. The air in the bulb can not escape, and the mo- tion of the liquid shows that the air is being crowded into a smaller space ; in other words, that it is com- pressible. Expansibility. If the bulb (Fig. 21) be warmed by grasping it in the hand, the colored liquid will move downward in the tube. The air in the bulb expands, and pushes the liquid along. Or if, through the cork of a small bottle, a lg ' ' 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 rises in the tube, and stands at a certain height, as shown in Fig. 22. Now let 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 Properties are characteristic. Solids and liquids likewise possess the properties of compressibility and expansibility in various slight degrees. All gaseous bodies NATURAL PHILOSOPHY. 45 possess them in very high degree. There seems to be no limit to the expansibility of gases, and the limit of com- pressibility is reached only when the gas is reduced to the liquid state. By combined pressure and cold, all gases have been changed into liquids. Elasticity. The elasticity of air is beautifully shown by the simple apparatus already used (see Fig. 21) to illustrate the characteristic properties. Let the breath be alternately pressed into and with- drawn from the tube, the air will alternately be com- pressed, and spring back, which will be shown by the alternate motion up and down of the liquid in the tube. Weight. The air has weight. If we would show it, we may first weigh a closed vessel, prop- erly arranged, 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 con- tains. But how can the Air be taken out of a Vessel ? To answer this question, we must become acquainted with the air-pump. A section of the essential parts of this impor- tant instrument is represented in Fig. 23. 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 C3 7 linder. The vessel, taken, is placed upon the plate. called receivers. Fig. 23. from which the air is to be Such vessels are usually 46 NATURAL PHILOSOPHY. It will be seen that when the piston is raised, the valve, z, will be closed, and the air above it will be lifted out of 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, 6, 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 from the w Fig. 24. receiver is pressed through the tube into the cj'linder 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 inappreciable. It is quite evident, however, that a perfect vacuum can not be obtained in this way. One form of this important instrument, com- plete, is represented in Fig. 24. To weigh Air. We may now attend to the process of weighing air. A hollow glass globe, with a stop-cock, is NATURAL PHILOSOPHY. 47 hung from one pan of a delicate balance, and its weight carefuQy found. It is then screwed to the opening in the plate of the air-pump, and the air is exhausted. The stop- cock is then closed to prevent the air from returning into the globe, which is then taken from the pump, and weighed. It Fig. 25. 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 temperature of air, one hundred cubic inches weigh about thirty-one grains. Mobility. The molecules of air and other gases move among themselves with the most perfect freedom. Their 48 NATURAL PHILOSOPHY. mobility exceeds that of liquids, because there is no cohesion at all to be overcome in them. Pascal's law and the principle of Archimedes are therefore as applicable to gases as the}' are to liquids. The Ascent of a Balloon is an exhibition of the principle of Archimedes. The balloon is filled with coal-gas or hydro- gen, and it is lighter than an equal volume of air. It is therefore lifted by a pressure equal to the difference between the weight of the balloon with its contents, and that of an equal volume of air. Absolute Weight. Bodies show less than their real weight when weighed in air. The}' lose an amount equal to the weight of an equal volume of air. To obtain their true weights, bodies must be weighed in vacuo. SECTION VI. ON ATMOSPHERIC PRESSURE. 18. The atmosphere exerts pressure in all directions. This pressure is about fifteen pounds upon every square inch of surface. (G. 156, 157 ; A. 423, 424, 426). The Atmosphere exerts Pressure. Since every one hundred cubic inches of air weigh about thirty-one grains, 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. 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 be seen to 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 move, and that the forces NATURAL PHILOSOPHY. 49 of abhorrence and suction are simply fictions. The only force acting upon the water is the weight of the air resting upon its surface in the vessel. This downward pressure pushes the water under the lower end and upward into the tube. It may be shown in another Way. A more beautiful experiment consists in causing the pressure of the air to pro- Fig. 26. duce a fountain playing in a vacuum. A tall glass receiver (Fig. 26) , closed at the bottom, has a stop-cock from which a tube extends upward a little way into the interior. This receiver is first exhausted by an air-pump, then fixed upon its base, and placed standing in a vessel of water ; the stop- cock is opened, when instantly the water leaps to the top of the receiver, and a beautiful fountain continues to play until the jet-pipe is covered by the falling water. 50 NATURAL PHILOSOPHY. 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-rub- ber, over the large end of a lamp-chimney, 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 into the tube. Hold the tube so that the caoutchouc shall be above, or below, or side wise in an}- direction, and in all direc- tions alike the rubber will be pushed into the tube. The Pressure is fifteen Pounds to the square Inch. If the air should be all taken out of our tubes used in the foregoing experiments, to show that the atmosphere exerts pressure, 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 which it lifts into the tube. How much farther the water would rise if the tube were long enough, these experiments have not told. A heavier liquid will not be lifted as high as water, and will be more convenient for ex- periment. Mercur} r is a liquid metal about thirteen and a half times as heavy as water, and it is found that the air will sustain a column of mercuiy about thirty inches high. The experiment is conducted as follows : Take a glass tube more than thirty inches long, closed at one end, and fill it with mercury. Close the open end with the finger, and invert the tube. Next place the open end in a dish of mercurj 7 , and withdraw the finger. It will be seen that the top of the column of mercury in the tube is only about thirty inches above the surface of the mercury in the dish. (See Fig. 27.) The space above the mercury in the Fig. 27. NATURAL PHILOSOPHY. 51 tube must be a vacuum. The experiment was first made by Torricelli, and this vacuum is called the TORRICELLIAN VACUUM. Now, the pressure of the atmosphere just balances the weight of this column of mercury. But the weight of a column of mercury thirty inches high, the area of its base being one square inch, is fifteen pounds. The downward pressure of the atmosphere is therefore fifteen pounds to the square inch of surface on which it rests. A Unit of Pressure. Any pressure of fifteen pounds to a square inch of surface is called a pressure of ONE ATMOS- PHERE. Heavy pressures are measured by this unit. A pressure of " four atmospheres " is a pressure of 4 x 15 = 60 pounds to a square inch. At a temperature of 140 C. below zero, oxygen gas under a pressure of 320 atmospheres becomes a colorless liquid. What is this pressure in pounds ? The Kinetic Theory of Gases. It is believed that the distances between the molecules of a gas are very many times greater than the diameters of the molecules themselves. Within these spaces the little molecules are darting about in all directions ; but each one moves in a straight line until it strikes a neighboring molecule, or the side of the vessel in which the gas is held. On striking another, each molecule bounds away in another straight line until its course is again changed by another collision. Pressure is the Energy of these Blows. It is easy to see, that, if this theory is true, the molecules of air must be continually pounding against the walls of the vessel which contains it ; or, indeed, against every thing which it touches. Every little blow exerts a little pressure, and such a multi- tude of swift blows is a constant pressure. Indeed, we be- lieve that the pressure of air is nothing more than the energy of these molecular blows. The Radiometer. In the radiometer of Crookes (Fig. 28) this molecular energy actually turns a little wheel. The 52 NATURAL PHILOSOPHY. radiometer is a small glass globe with a very light vane resting on a pivot in the center. Each one of the four arms of the vane carries a disk of aluminum which is white on one side and black on the other. The air in the globe is exhausted to a very per- fect vacuum. Of course there are then so few molecules, that the}' are able to fly in straight lines much farther before their path is changed b} r collision with one an- other. Now the sunbeam, or a candle-flame, will heat the black faces of the disks more than the white ones, and will make the vane whirl in a surprising manner, by thus increasing the energy of the molecular motion against the black faces. 19. The principle of atmospheric press- ure is applied in the construction of many very useful instruments. We will notice the Barometer, the Common Pump, the Forcing Pump, and the Siphon. Fig. 28. I. THE BAROMETER. The barometer-column always indicates the pressure of the atmosphere. But the pressure of the atmosphere depends upon 1st, Its height. 2d, The amount of water- vapor in it. (G. 162-167.) The Barometer. If the apparatus used to determine the pressure of the atmosphere (see Fig. 27) is inclosed for protection in a frame of metal or wood, with a graduated scale attached to measure the height of the column of mercuiy, it forms the instrument so well known as the BAROMETER. Shows the Pressure of the Atmosphere. The press- ure of the atmosphere is not alwa} T s the same. When it is NATURAL PHILOSOPHY. 53 less than fifteen pounds to the inch, the column of mercuiy will be lower than thirty inches, and, when greater, the col- umn 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. If the top of the mercury stands at 28 on the scale, the pressure of the atmosphere is f f x 15 pounds to the inch, nearly. A Correction necessary. We say nearly in this ex- ample, because the number on the scale at the top of the mercury column does not show exactly the true height. For we should notice that when the mercury sinks in the tube, it must rise in the cistern, so that the column must shorten at both ends. The figures on the scale, however, only show the change which takes place at the top : they fail to tell the true height of the column. Made by Fortin's Cistern. This error is avoided in what is called Fortin's barometer, by means of a cistern with a flexible bottom. (See Fig. 29.) The bottom of this cis- tern is made of deer-skin, and rests upon the end of the screw C, by which it may be 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 cis- tern just touches this point, then the figures on the scale show the true height of the column, which indicates the pressure of the atmosphere. The Pressure of the Atmosphere depends upon its Height. 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. Hence the weight of the atmosphere will vary with the alti- tude of the place where the observation is made, and on this account the height of the barometer column will be differ- ent at different distances above the sea-level. Fig. 29. 54 NATURAL PHILOSOPHY. To Measure Heights of Mountains. Upon this princi- ple the barometer is used to measure the heights of mountains. If the density of the atmosphere were uniform, the fall of the mercury would be in the exact ratio of the distances up- ward ; and, knowing the height required to make the mercury fall one-tenth 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. Tempera- ture, 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 atmos- phere. Pressure depends also upon the Amount of Water- Vapor present. Mixed with the air, at all times, are con- siderable quantities of invisible vapor of water. If the at- mosphere were pure dry air alone, it would exert a certain pressure ; 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 water-vapor 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. To predict Weather Changes. On this principle the barometer is used to indicate changes in the weather. A rising column indicates fair weather; a falling column indi- cates foul weather. This rule is to a great extent reliable. Others are added by different observers, but they must be taken with consider- able allowance. NATURAL PHILOSOPHY. II. THE COMMON PUMP. D'-scriptioii. This instrument, as general!}' made, con- sists of two cylinders or barrels, A and B, Fig. 30, with a valve, S, at their junction, opening up- ward. In the upper barrel is a piston, P, in which is a valve, O, also opening upward. The* piston is moved by means of the handle H, and the water may flow from the spout C. Explanation. When the piston is lifted, 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 well will push the ft r ater up the barrel A, through the valve S, into the barrel B. When the piston goes down, the valve S will "lose, 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 the spout, while the atmospheric pressure will force another portion into the barrel below the piston. Fig. 30. Limit of Height. ^ At the sea-level the pressure of the air wall sustain a column of mercury about thirty inches high. Since mercury is, at ordinary temperature, about 13| times heavier than water, the same force will lift a column of water 131 times as high : 13| X 30 = 405 ; 405 in. = 33| feet. The atmosphere can not lift water in the common pump to a greater height than this, even at the level of the sea. In practice the valve S must be less than 33J feet above the water. 56 NATUBAL PHILOSOPHY, III. THE FORCING PUMP. Description. In the forcing pump the piston has ho valve, but 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. 31. Reaching from near the bottom of the air-chamber, I K, is a tube, L M, which extends to any place K at which the water is to be delivered. Explanation. Now, when the sol- id piston P is raised, water is pressed through 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. B}' eveiy 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 M, to the place where it is desired. Without the air-chamber, the water w r ould issue from the pipe in jets : with the cham- ber, the water issues in a steady stream. IY. THE SIPHON. Description. The siphon is an instrument b} r which liquids may be transferred from one vessel to another, by at- mospheric pressure. It consists of a bent tube, one arm of which is longer than the other. In Fig. 32 the siphon in operation is shown. Having been first filled with water, its short arm is inserted in the water to be transferred from the vessel C, and it is then found that the water will flow stead- ily 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. NATURAL PHILOSOPHY. 57 Explanation. The downward pressure of the air at C is partly balanced by the weight of the column of water, C D, in the short arm of the tube ; the excess of pressure will tend to push the water over through the bend toward B. On the other hand, the atmospheric pressure at B is parti}- balanced by the pressure of the water in the long arm, which is equal to the weight of a column A B ; 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 shorter column of water, is more than the same pressure, minus the weight of the 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, up the short arm, over the bend, M, and out at B. Fig. 32. SECTION VII. ON "THE THREE LAWS." There are three fundamental principles which apply to all true gases. They are known as The Law of Boyle or Harriot te, The Law of Charles, The Law of Avogadro. L THE LAW OF BOYLE. 20. The volume of a given weight of air will be inversely as the pressure upon it. (G. 174, 175 ; A. 412, 458.) 58 NATURAL PHILOSOPHY. Volume depends upon the Pressure. Press the breath into the open tube of the apparatus represented in Fig. 21, and the liquid flows toward the bulb, showing that the air in the bulb is condensed. Next draw the air out of the tube, and the liquid flows away from the bulb, showing that the air within is expanded. The same quantity of air is here seen to fill less space when the pressure upon it is increased, and more space when the pressure is diminished. Plan for further Experiment. 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. Pressure greater than one Atmos- phere. In the first case, we use a bent glass tube (Fig. 33), the short arm being closed, and the other, which should be more than thirty inches long, being open at the top. A graduated scale, to which the tube is firmly bound, measures inches from the bend. Now let mercury be poured into 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, fifteen pounds to the square inch. If we fill the long arm with mer- cury, as shown in the figure, to the height of thirty inches above the level of the mer- cury in the other, we shall be adding a Fig. 33. pressure of fifteen pounds to the inch. The pressure upon the air in the short arm will then be doubled; and we shall discover that the mercury has risen, crowding the air before it, and stands at A, the air having just half its original volume. NATURAL PHILOSOPHY. 59 Pressures less than one Atmosphere. In the second case, we take a glass tube (A B, Fig. 34), about twenty- five inches long, and open at both ends. Let three narrow bands of paper be pasted upon it, the first at a distance of three inches from the top, the second six inches from the top, and the third fifteen inches from the second. Let another larger tube, D, about thirty inches long, be nearly filled with mercuiy. Insert the end, A, of the small tube, in this mercury, and push it down until the upper mark (3) is at the level of the mercury. Now, clasping the finger tightly over the end B, thus inclosing three inches of air in the tube, lift it until the third mark is brought up to the top of the mercur}-. The air will be found to fill the space of six inches. Before the tube was lifted, the whole press- ure of the atmosphere, fifteen pounds to the inch, was exerted upon the air within : after the tube was lifted, the atmosphere sustained a column of mercuiy fifteen inches high. To do this, required half the pressure it can exert : the other half was exerted upon the six inches of air above the mercury. We thus show that with half the pressure the volume will be just double. What is true in both Cases ? In these two experiments we find that the volume of a given weight of air is inversely as the pressure upon it; and repeated experiment confirms the inference that the same principle holds true for other pressures. This law was discovered independently by Robert Boyle in England, and the Abbe Marriotte in France. 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 Fig. 34. 60 NATURAL PHILOSOPHY. 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 own pressure is great- est, will be most dense. Is greatest at tlie Surface of the Earth The at- mosphere in contact with the earth is pressed upon by all the air above, even to the top of the atmosphere. At a dis- tance above the earth, the atmosphere receives less pressure, because there is less air above to exert it. The 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. THE LAW OF CHARLES. 21. The volume of a given weight of air will be greater as its temperature is higher. It expands J T of its bulk at 32 for every additional degree Fahrenheit, or ^^ of its bulk at for each degree Centigrade. Charles's law declares that the volume of a given weight of gas is directly as its absolute temperature. Heat increases the Volume of Air. Let the palm of the hand be laid upon the bulb (Fig. 22), 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. At the Bate of T ^y 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 491 cubic inches at a temperature of 32, it will become 492 cubic inches if heated one degree, making its NATURAL PHILOSOPHY. 61 temperature 33. In other words, it expands ^-Jy of the vol- ume at 32, for each additional degree of heat applied. If the Centigrade scale of temperature be used, then the illustration is as follows : 273 cubic inches of gas at will become 274 cubic inches if heated to 1. That is to say, it expands ^ 3- of its volume at for each additional degree. One hundred cubic inches of air at 32 F. will be expanded at 60 F. to be 100 + -?fc X 100 = 105.7 cubic inches. The Effect of Cooling- -- Conversely each degree of heat taken awaj r from a gas, beginning at C. or 32 F., will reduce its volume at the same rates. 273 cubic inches at C. will be 272 cubic inches at 1 C., and 271 cubic inches at 2 C. The gas would go on losing ^^ of its volume for each degree of lower temperature. Then How many Deg rees can be withdrawn ? Not more than 273, because it would be impossible for the gas to con- tract more than f^-f of its volume. If the law holds good at such low temperature, then at 273 C. the volume of a gas would be infinitely small, and it would be impossible to conceive it airy colder. Absolute Temperature. This point on the Centigrade s^-ale, 273, is called the absolute zero, and temperatures measured from this point are called the absolute temperatures. Absolute temperatures are obtained by adding 273 to the temperature on the Centigrade scale. Thus 60 is 333 on the absolute scale, and 40 is 233. The Law of Charles declares that the volume of a given weight of gas, the pressure being unchanged, will vary directly as the absolute temperature. III. THE LAW OF AVOGADRO. 22. Equal volumes of all gases, at the same temperature and pressure, contain the same number of molecules. Illustration. It is believed that there are just as many molecules in a cubic inch of oxj'gen as there are in a cubic 62 NAtUHAL PHILOSOPHY. inch of hydrogen, when these gases are under the same pressure and* at the same temperature. The prftdf of this law is found in the stud}' of mathemat- ical ph}'sics and of the science of chemistry. We must therefore omit the demonstration now ; but the law itself should be remembered with those of Boyle and Charles, because these three laws together define tho truly gaseous condition of matter. SECTION VIII. REVIEW. I. SUMMARY OF PRINCIPLES. The solid, liquid, and gaseous conditions depend on the relative strength of attraction and repulsion between the molecules of the body. Hence, Hardness, tenacit}', malleability, ductilit}', and crystalline form are properties of solids only ; while Mobility is the characteristic property of liquids, and Compressibility and expansibility are the characteristic properties of gases. The pressure of a liquid at rest is due to gravitation, and is exerted equally in all directions. For this reason, The surface of water at rest must be level. The liquid will always rise to the same height in all tubes or reservoirs which communicate with one another. The pressure of a liquid on the base of the vessel contain- ing it depends upon two things only, the area of the base, and the height of the liquid above the base. It is equal to the weight of a column as large as the base of the vessel and as high as the surface of the liquid. A bod}' immersed in fluid, either liquid or gaseous, is pressed both upward and downward ; but the upward press- ure is the greater. Hence a 'body loses weight when im- mersed, and its loss is just equal to the weight of the fluid it displaces. NATURAL PHILOSOPHY. - 68 A fluid, either liquid or gaseous, transmits external press- ure in every direction, and allows it to act -with the same energy on eveiy equal amount of surface. * II. SUMMARY OF TOPICS. 8. The molecular forces. Illustrated in natural changes in condition. In artificial changes. 9. Hardness. Tenacit} r . Malleability. Ductility. Cr}'stalline form. These properties characteristic of solids. 10. Elasticity of liquids. Attraction and repulsion nearly equal. Mobility. Characteristic property. 11. Liquids press in all directions. Equall}'. The sur- face at rest must be level. Level surface convex. 12. Water in pipes rises as high as its source. The sup- ply of water to cities. Springs. Artesian wells. 13. Pressure independent of the shape of the vessel. It depends on the depth of the liquid. On the area of the base. To calculate the pressure. Against any surface. 14. Bodies immersed are pressed upward. With force equal to the weight of fluid displaced. The solid lighter than water. The solid heavier than water. 15. Specific gravity. Of gases. Of liquids. By di- rect weighing. B}' the hydrometer. By the use of a bulb. Of solids. Heavier than water. Describe the experi- ment. Lighter than water. Table. 1C. The equal transmission of pressure. Experiment. The shape of the vessel makes no difference. The hydro- static press. 17. Of the properties of gases. Compressibilit}'. Ex- pansibilitj'. These properties characteristic. Elasticity. Weight. The air-pump. To weigh air. Mobility. Ascent of a balloon. Absolute weight. 18. The atmosphere exerts pressure. Shown loy experi- ment. In all directions. About fifteen pounds to the square inch. Unit of pressure. The Kinetic theory. The radiometer. 64 NATURAL PHILOSOPHY. 19. The barometer. Shows the pressure of the atmos- phere. Correction needed. Made by Fortin's cistern. The pressure of the atmosphere depends upon its height. Measurement of mountains. Upon the amount of water- vapor it contains. To predict changes in the weather. The common pump. The forcing-pump. The siphon. 20. Volume of gas depends on pressure. Plan for experi- ment. Pressure greater than one atmosphere. Pressure less than an atmosphere. Law deduced. Densit}' of the atmosphere. Density greatest at surface of the earth. 21. Heat increases the volume of air. At the rate of 4^Y of its bulk for each degree. The effect of cooling. How many degrees can be withdrawn ? Absolute tempera- ture. Law of Charles. 22. Law of Avogadro. Illustration. III. PROBLEMS. Problems illustrating the Laws of Hydrostatics. 1. A C3*lindrieal vessel, whose base is 5 square feet, is 10 feet high. It is filled with water. What pressure is exerted upon the base? Ans. 3125 pounds. 2. If the bottom of a vessel has an area of 72 square inches, and its top an area of 96 square inches, and it is 9 inches high, what pressure will be exerted on the bottom when the vessel is full of water? Ans. 23.43+ pounds. 3. Two vessels with equal bases are filled with water, one to a height of 9 inches, the other to a height of 27 inches. How man}' times more pressure on the base in the last case than in the first? Ans. 3. 4. How much pressure is exerted against the side of a cubical vessel which is full of water, its height being 18 inches? Ans. 105. 46 -f- pounds. 5. How much pressure would be exerted upon 12 square inches 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 pounds. NATURAL PHILOSOPHY. 65 6. How many cubic inches of water will be displaced by a piece of pine wood weighing just 10 pounds? Ans. 276.48. 7. How much less will a piece of marble measuring 100 cubic inches weigh in water than in air? Ans. 3.61 pounds. 8. The specific gravity of marble being 2.7, what will be the weight of 25 cubic feet? Ans. 4218.75 pounds. 9. How man}' cubic inches in a block of ice that weighs 75 pounds? Ans. 2229.67. 10. What is the specific gravity of flint-glass if a frag- ment of it weigh, in air, 4320 grains, and in water 3023 grains? Ans. 3.33. 11. The specific gravity of wax is to be found from the following data : Weight of the wax in air .... 8 ounces. Weight of a piece of lead in air . . 16 ounces. Weight of the lead in water . . . .14.6 ounces. Weight of wax and lead in water . 13.712 ounces. Ans. 0.9. 12. A bottle holding 1000 grains of water is found to hold only 870 grains of oil of turpentine. What is the spe- cific gravity of this oil? Ans. 0.87. 13. How much pressure can be exerted upon the large piston of a hydrostatic press by applying fifty pounds to the small piston ; the area of the small piston being one-half square inch, that of the large piston 100 square inches? Ans. 10000 Ibs. 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 grains. . 2. What is the weight of 100 cubic inches of oxygen gas at ordinary temperature and pressure, its specific gravity being 1.106? Ans. 34.286 grains. 3. What is the weight of 100 cubic inches of nitrogen gas at ordinary temperature and pressure, its specific gravity being .972? 66 NATURAL PHILOSOPHY. 4. What pressure\will be exerted by the atmosphere on a surface of one square foot ? Ans. 2,160 pounds. 5. What pressure does the atmosphere exert upon a square Inch surface when the rkrometer column is 28 inches trigh ? Ans. 14 pounds. 6. How high a column of water would the atmosphere sustain when the barometer column stands at a height of 28 inches? Ans. 31^ feet. 7. Suppose 100 cubic inches of air at a pressure of 15 pounds to the inch is made to receive an additional pressure of 15 pounds to the inch : what will be its volume? Ans. 50 cubic inches.' 8. How much pressure must be removed from 100 cubic inches of air, at usual density, in order that it may expand to a volume of 200 cubic inches ? Ans. 7jj pounds to the inch. 9. In the air-chamber of the forcing-pump the air is com- pressed into half its former bulk ; how high will the w r ater be thrown? Ans. 33f feet. 10. If we have 500 cubic inches of air at 32 F. tempera- ture, how much will there be when it is heated to a tem- perature of 75? Ans. 543.78-f cubic inches. NATURAL PHILOSOPHY. . 67 CHAPTER III. OX MOTION. 23. The Fundamental Ideas. ATTRACTION and REPUL- SION acting upon masses or MOLECULES of matter determine their condition of rest or motion. Illustration. The motion of bodies falling to the ground is due to the attraction of gravitation. The motion of air in wind is caused chiefly by the repulsive power of heat. The bullet speeds on its wa}-, urged by the repulsive force of exploding gunpowder. The forces which produce the endless variet}' of motions in nature are found, when care- fully studied, to be only different forms of attraction and repulsion. SECTION I. ON MOTION CAUSED BY A SINGLE FORCE. 24. There are three important principles known as New- ton's 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 bod} r at rest or in motion. 3d, Action and reaction are equal, and in opposite direc- tions. (A. 154-157, 168.) The first Law. The truth of the first law is seen when we remember that the inertia of matter forbids that a body shall, in any way, change its own condition. 68 KATtJEAL PHILOSOPHY. Then, why are bodies so constantly changing their condi- tion of rest or motion? We rarely see a bod}* in nature, moving in an absolutely straight line ? The reason is this : bodies are constantly under the influence of forces which do change their condition. A stone thrown from 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. The second Law. Let us examine this law by means of the diagram, Fig. 35. If a ball be thrown suddenly from the point A, hori- A ( ^--, ~| B zontall}', it would go to the point B, if it could be let alone by other for- ces. So likewise, if it be dropped from A, gravitation ^' alone will cany it ll ' ig ' 35 ' 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 minute, and, when dropped, to fall from A to C in the same time. 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 exacth* equal to AB, and downward through a distance exactly equal to A C ; so that the force of gravi- tation produces the same effect, whether it act upon the ball resting at A or in motion toward B. The 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 NATURAL PHILOSOPHY, 69 cords, and hang in contact against a graduated arc. When the ball B is lifted up the arc to D, and then allowed to swing against the other, it strikes it, and instantly stops, while the othefball takes up its motion, nnd goes to the point C. The first ball acts upon the second ; the second re- acts upon the first. Now, if we notice that the mo- tion 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 ac- tion 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. 25. The velocity of a moving bod} 7 will be uniform if it be produced by an impulsive force, and opposed by no resist- ances. The elements of motion are Time, Space, and Velocity. In uniform motion, the space is equal to the product of time multiplied by velocity. (G. 25 ; A. 105, 110.) Velocity. Velocity, in a popular sense, is simpty rapid- ity 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 unit of time. The velocity of a cannon-ball, for example, may be two thousand feet a second ; that of a train of cars may be thirty miles an hour. Uniform Velocity. In uniform velocity, a body moves 70 NATURAL PHILOSOPHY. over equal spaces in equal times. If, for instance, in each of three successive hours, a steamboat travels fifteen miles, its velocity is uniform. 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 long a force may have been acting, if it be suddenly withdrawn, it is at that moment an impulsive force. Uniform Motion produced by an Impulse. If a body can be free from all forces but the impulse which gives it motion, its velocity will be uniform. This seldom occurs. How rarel}' do we see a uniform motion produced b} T an im- pulse, either in nature or in art ! This is because all bodies are under the influence of several forces at once, such as gravi- tation, friction, and the resistance of air, b}* 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 enough to accomplish that purpose, the motion of the train will be uniform. Space equals Time multiplied by Velocity. It is evident that a train of cars, going uniformly at the rate of 25 miles an hour, will in 10 hours go 250 miles. But we see that 250 = 25 x 10, or, that the space is equal to the product of the two other elements, time and velocity. We n,ay express this principle by the simple equation, S = T x V: in which S stands for Space ; T stands for Time ; V stands, for Velocit}'. Now, if any two of these elements are given, the third may be found by substituting the given values for the letters, NATUEAL PHILOSOPHY. 71 and then performing the operations indicated. For example, what is the velocity of a bullet which flies 2,000 feet in 20 seconds, supposing its velocity uniform? The value of S is 2,000 feet; the value of T is 20 seconds. Putting these values in the equation, it becomes 2,000 = 20 x V. Hence V = 100. 26. 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 uni- formly accelerated motion are overcome by At wood's ma- chine. (G. 27, 77, 78 ; A. 132-135.) A constant Force. Bj* 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 example of a constant force. Uniformly accelerated Motion. The motion of a body is uniformly accelerated, when its velocity increases equally in successive units of time , as, for example, five feet the first second, eight feet the next second, eleven feet the third second, fourteen feet the fourth, and so on. The motion of a falling body is the most perfect example known of uniformly accelerated motion. It would be a perfect example, were it not for the resistance of the air. Difficulties in the way of Experiment. But there are three difficulties in the way of accurate experiments upon the motion of a body falling. 1st, This motion is so rapid that no accurate observations can be made. 2d, It is sub- ject to the resistance of air, which reduces its velocity. 3d, The friction of an} T apparatus used is likely to impede it. These Difficulties overcome by Atwood's Machine. These difficulties are, for the most part, overcome by Atwood's machine (Fig. 37). . Two heavy weights, A and B, are fastened to the ends of a small cord which passes over a grooved wheel, D. Each end of the axis of this wheel rests on the circumferences of two other wheels. This set 72 NATURAL PHILOSOPHY. Fig. 37. of wheels may be supported by a bracket firmly fixed to the wall of a room, several feet above .the floor. The standard C L, reaching to the floor, is graduated ; upon it is a movable ring, which allows the weight A to pass through it ; and a table below, which arrests the motion of the weight at any desired point. The time of motion is meas- ured by the pendulum F. The two weights A and B are made exactly equal, and of course, when left to themselves, will re- main 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^ ounces, and the weight of the small bar to be one ounce. When they all move, 64 ounces are in motion, but this mo- tion is caused by the force which acts upon the one-ounce bar. It is evident, that, if the force is the same, 64 ounces will move only -^ as fast as one ounce. The motion of the weights is produced by a constant force, gravitation ; but it is only -fa as rapid as when the bodies fall freely. A sloiu motion is thus obtained. The resistance of the air against the small sur- faces of the ends of the heavy NATURAL PHILOSOPHY. 16 weights is very slight when they move slowly. The friction of the wheels at the top is trifling. And thus the three diffi- culties in the way of experiment are overcome. 27. By experiments with At wood's machine we may prove : 1st, That a body moving under the influence of gravita- tion 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 from this table obtain the Laws which govern the motion, and the Formulas by which problems may be solved. Proof of the first Principle, Let the weight A, carry- ing the small bar, be brought to the top of the gradu- ated standard, and let the ring C be placed three inches below. Suppose that, in one second after its release, A falls to the ring. 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 six 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 tvhich, alone, will carry the body twice as far in the next equal interval. Proof of the second. Principle. If the weight and bar fall three inches in one second, they will be. found by experi- ment to fall twelve inches in two seconds. Hence the dis- tance fallen in the second interval is nine inches. If the bar were taken off at the end of the first second, we know that the weight would go alone six inches in the next. It is clear, 74 NATURAL PHILOSOPHY. then, that the bar acting in the last second adds a motion of three inches, the same amount as it produced in the first. Repeated experiments show that gravitation will add to the motion of a falling body just as much in each second as it produced in the first. Analysis of the Motion of a falling- Kody. Now sup- pose a body to fall from the point A (Fig. 38), toward 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 bod}* would still move on, and we know (b} T the first principle) that it would go in the next 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 ma} T see at a glance that it is the distance due to velocnyy alone. But we know (b} T the second principle) that gravitation in this second will add a space just equal to A B. Marking this additional space in the figure, we find that in two seconds the bod}' will fall to C. In two seconds the body has fallen four spaces : in the next two seconds it will go twice as far, eight spaces, by velocity alone. In the first of these two seconds, which is the third second of its fall, the body will go one half that distance, or four spaces, by velocity. The force of gravity adds another space, so that at the end of three seconds the body will be found at D. To find the distance passed in the fourth second, notice .that in the first three seconds it has passed D "j 1 "" nine spaces ; that in the next three seconds it will go, by its velocity alone, eighteen spaces, and that lg ' ' in one of these three seconds, which would be the fourth second, it would go six spaces. Mark six spaces for velocity, and add one for the action of gravitation. T. Id 3d NATURAL PHILOSOPHY. 75 Construction of the Table. Now, in this diagram the values of time, space, and velocity, stand clearly before us, and we may put them into a tabular form. In the first column, headed T, put the number of seconds, 1, 2, 3, 4. In the second column, headed S, put the total space passed over at the end of these seconds, representing the distance A B by d. In the third column, headed V, put the velocities gained at the end of each of the seconds. And, finally, in the fourth column, headed s, put the spaces passed in each separate second. From the Table obtain the Laws. The relation be- tween 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 4c and 9cZ, with the corresponding times 2 and 3, we find that 4 d : 9 d : : 2' 2 : 3 2 . Hence the spaces passed by a falling body in 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 4d and 6d have the same ratio as 2 and 3, the corresponding values of time. Hence the velocities of a falling body at the end of successive intervals of time ivill vary as the time of fall. Notice, THIRD, that the spaces passed in separate seconds (the values of s) are as the odd numbers, 1, 3, 5, 7, &c. From the Table also obtain Formulas. It will be seen, that by squaring any one of the values of T in the table, and then multiplying by d, the corresponding value of S will be obtained. Hence, S-T 2 d. (1.) Again, we may discover that if the value of T in any case be multiplied by 2 d, the corresponding value of V will be produced. Hence, V = 2dT. (2.) 76 NATURAL PHILOSOPHY. We see, again, that if the value of S in any case be mul- tiplied by cZ, the square root of this product, multiplied by 2, gives the value of V. Hence, V=2VS^. (3.) Finally, a little attention will show, that if the value of T in an}^ case be multiplied by 2, the product diminished by 1, and the remainder multiplied by d, the corresponding value of s will be obtained. Hence, s= (2 T- 1) d. (4.) Acceleration. The velocity added in each interval of time is called the ACCELERATION. The acceleration is always represented by the letter g. The diagram shows that d = \g- Let us put ^ g, which is the value of cZ, in place of c?, and the four formulas become, S=i?T 2 . (1.) V = gT^_ (2.) V = V*S0. (3.) s=Jgr(2T-l). (4.) The Value of e acted on by two Forces. Forces sel- dom act singly. It is b}' 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 experi- ment. 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 wa} T s 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 north by a direct wind, ma}* at the same time be drifted east by a tide moving eastward. If so, it will at every mo- s c ment be moving north and east, or in a straight line toward the north-cast. Acting along- the adjacent Sides of a Parallelogram. The condi- tions of the motion of both the ball and the ship may be represented to the Fig ' 39 * eye. Let A (Fig. 39) represent the original place of the ship. Suppose that while the wind, if acting alone, would move the ship to B, the force of the stream, if acting alone, 78 NATURAL PHILOSOPHY. would move it to D in the same time: then, when both act at once, the body 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 to go to either B or D. They are equivalent to a single Force. The two forces, acting in the directions A B and A D, produce a sin- gle motion along the line AC. A single force acting in the direction of A C would have produced the same effect. Hence two forces, acting in the 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 COMPO- SITION OF FORCES. The Resultant of two Forces may be found. The resultant of two forces ma}' be found by representing them by two adjacent sides of a parallelogram, and then drawing the diagonal. The lengths of the lines rep- resent the strength, or the intensity, of the forces. In the case of the ship, for instance, suppose the wind able to drive it ten miles, while the tide can drift it five miles. To find the actual path of the ship, draw the line A B (Fig. 40), to represent the ten miles, and then the line A D, at right angles to it, and one- half as long, to represent the five miles. Fig. 40. Draw the lines B C and C D, to complete the parallelogram, and then draw the diagonal A C. This line represents the path of the ship, or the resultant of the two forces. The Resultant of more than 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 NATURAL PHILOSOPHY. 79 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. 29. 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 from that in which it acts. A Force may be resolved. To find the components of a given force, we ma}* 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. To find the Component which acts in a given Direc- tion. When a ball is thrown obliquely against the floor, it acts upon it with less force than when thrown perpen- dicularly against it. But a part of the force will still be exerted perpendicularly against the floor. To illustrate this important point, let a ball, A (Fig. 41), 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 Fig ' 41 ' to the floor, and then A D parallel to it. The lines A B and A D represent the components of the force A C. The line A B represents the amount of force exerted per' 80 NATURAL PHILOSOPHY. pendicularly against 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 f as long as the former ; if so, then the force exerted perpendicular to the floor will be f of the force with which the ball is thrown. To find the component which acts in any given direction, we ma}' represent the original force by a straight line, and make it the diagonal of a parallelogram, one of whose adja- cent sides is in the direction given. This side will represent the force required. 30. Two forces may act upon different points of a body in the same direction : their resultant will be equal to their sum. The point of the bod}' 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 bod}' is only the resultant of a set of par- allel forces acting upon it in the same direction ; and what is called the center of gravity is the point of application of this resultant. (G. 69 ; A. 202, 207, 210.) 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 two hundred pounds, and the other with a force of three 4 D JK hundred pounds, it is clear that a single horse exerting a force of five hundred pounds would produce the same effect. The Point of Application. But if a single force is to take the place of two others, and produce exactly the same Flg * 42 ' motion as they would when act- Ing together, at what point of the body shall it be applied ? Suppose the body represented by A B (Fig. 42), to be NATURAL PHILOSOPHY. 81 acted upon by two forces, represented by the lines c and d, one just half the length of the other, the lesser force being twenty-five pounds, the greater fifty pounds. Then the line r, just as long as both together, will represent the resultant, a force of seventy-five pounds. 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 B 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 D. The Weight of a Body. A body falling freely is an example of motion caused by the action of parallel compo- Fig. 43. nents. For, since the force of gravitation acts upon every molecule of the bod} T , 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 weight of the bod}\ The Center of Gravity. The point of application of this resultant is the center of gravity. The center of grav- ity is usually defined to be that point in a body, which being supported, the body will rest in any position. One can bal- ance 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 82 NATURAL PHILOSOPHY. of uniform density ; it is toward the heavier side of one that is not. In Fig. 43 the center of gravity in each bod}- is at G. What is the Line of Direction ? Now imagine a ver- tical line drawn through the center of gravity* , as shown by the vertical dotted lines in Fig. 43. This line will show the direction in which the body would fall if it were left without support ; and it is called the line of direction. Principle of Stability That a body may stand upon a plane surface without falling, the line of direction must pass through its base. Fig. 44. 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 cen- ter 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. Carriages may lean considerably to one side without over- turning (Fig. 44) ; but an accident is sure to happen if they lean so far as to throw the line of direction beyond the lower side of the wheel. NATURAL PHILOSOPHY. 83 Animals instinctively incline their bodies always in such a way as to keep their center of gravit}* over the space between their feet. The showman offers a gold coin to the boy who will stand with his heels pressed against the wall of a room, and then pick it from the floor in front of him without falling. He is perfectly safe in making the offer. For no one can stoop without falling, unless, when he throws his head forward, he can, at the same time, throw some other part of his body backward far enough to keep his center of gravity over his feet. He can not do this with his heels pressed against a wall, and therefore can not win the coin. 31. 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. (Gr. 53; A. 159, 1G4.) 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 wall see a wonderful variety of curved motions. The winds, and the clouds they cany, move in curves. Every swaying branch and leaf, and every nodding stalk of grass, moves in a curve. Is produced by at least Two For- ces. The motion of a ball when fast- ened 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 H (Fig. 45), which starts the ball, would, if it could act alone, carry it in a straight line from A toward E. But the string H A, held firmly by the hand, is a constant force 4 NATURAL PHILOSOPHY. which pulls it away from that path. The resultant of these two forces is represented by the circumference A B C D. One of which 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 equal 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. Tlic Central Forces. These two forces by which curved motion is produced are called the CENTRAL FORCES. One of them always acts toward the center of the circle around which the bod}' is moving, and the other always in the direc- tion of a tangent. The force which acts toward the center of the circle around which the body moves is called the CENTRIPETAL FORCE. The force of the string which holds the ball in its circuit is the centripetal force. Let the centripetal force be destroyed, and the other cen- tral force will cause the ball to fry in a straight line, as B F or C K. 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 planets forward, and the attraction of the sun, are the cen- tral forces which hold them in their oroits. Centrifugal Force. The ball, when moving in the cir- cle, is trying all the time to move in a straight line instead. This is the effect of its inertia. The string must overcome this inertia at every point, and this resistance of the ball is a pull lengthwise of the string outward. This resistance to deflection from a straight line is called the CENTRIFUGAL FORCE. This force takes no part in the production of the curved motion. It is simply the re-action of the moving bod}' against the centripetal force. Experiment. A simple and pleasant experiment may be performed to illustrate the effect of centrifugal force. To NATURAL PHILOSOPHY. 85 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. Illustration*. Circus-riders incline their bodies toward the center of the ring around which the}" ride, that the cen- trifugal force may not throw them from their horses. Car- riages, in very rapid motion around the corner of a street, are in danger of being overturned by this force. Projectiles Any body thrown into the air is a pro- jectile. The stone from the hand, the ball from the gun, and the arrow from the bow, are familiar examples of projectiles. Their Motion is due to two Forces. Leaving resist- ance of the air out of account, the motion of a projectile is due to the action of, 1st, The impulse which starts it on its journey ; and, 2d, the constant force of gravity. Range. The horizontal distance is called the RANGE y 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 b}^ percussion. And, finally, when a piece of cold wood is heated by being squeezed be- tween 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. The Dynamic Theory. It is now generally believed that heat is a kind of vibration, whose energy can affect the sense of touch. This theory supposes matter to be made up of molecules separated by definite distances ; it goes fur- ther and supposes these molecules to be in motion, rapidly vibrating in the minute spaces between them. To increase this molecular motion, is to make a body hot ; to lessen it, is to make the body cold. The theory assumes also the exist- ence 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 instantty felt. The explanation is this : The molecules of the sun itself are in rapid vibration ; they impart motion to the ether, whose undulations dart through NATURAL PHILOSOPHY. 127 the space between the sun and us, and, coming in contact with the person, impart their energy to the organ 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. II. SOUND. Hearing produced by Vibrations. Let two books be clapped together, and every ear in the room receives a shock, to which the name of " sound " is given. The molecules of the books are made to vibrate by the blow, and these vibra- tions, acting upon the air in contact w r ith them, produce air- waves. These air-waves, traveling outward in all directions, finally reach the ear ; and the many parts of this organ, receiving the energy of these undulations, 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 hammer. This motion causes undulation in the air in contact with the bell. The air-waves thus formed travel in all directions from the bell until they impart their energy to the ear. The roar of a cataract is the result of vibrations caused by the falling water. The rolling sound of 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 mole- cules of a solid, liquid, or gaseous body. Sound. In the study of physics, the word " sound " re- fers to the undulations outside, rather than to the sensation in, the ear. Sound is an undulatory motion in an elastic medium whose energy can affect the ear. 128 NATURAL PHILOSOPHY. III. LIGHT. Light is undulatory Motion. 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 a kind of undulation. But light will pass through the most perfect vacuum that can be made. 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 undulations bring to us the energy of sunlight? 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 heavenly bodies, and enters into all those between the molecules of matter in every form. The undulations of this ether pass through a vacuum, through celestial spaces, through bodies like glass, and through the substances of the eye, until they strike the nerves of sight. Vision. When a gas-jet is suddenty 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 in contact with it vibrate. This ether is between the particles of the air, and between the molecules of the substance of the eye. Its undulations, starting from the gas- jet, go through the air and into the eye ; and, when these undulations of the ether impart their energj- to the delicate nerves in the back part of this organ, we are made conscious of the presence of light. Luminous Bodies. Bodies which shine by their own light are called LUMINOUS bodies. They are bodies which can start undulations in the ether. Bodies which shine only by light which they receive from others are called NON- LUMINOUS bodies : they can not start undulations in the ether. The sun is a luminous body : so is a red-hot iron NATURAL PHILOSOPHY. 129 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. Light. Light is the undulation of the ethereal medium whose energy produces vision. Manifestations of Energy. All the phenomena of heat and sound and light can be best explained by regarding them as only so many different exhibitions of molecular and radi- ant energy. SECTION IV. REVIEW. I. SUMMARY OF PRINCIPLES. Force is that which in any way tends to affect the condi- tion of a body as to rest or motion. Work is the overcoming of resistance. Energy is the ability to do work. The unit of force is the force needed to move a unit of mass at the rate of one foot a second. The unit of work is the work done in lifting one pound to a height of one foot. The unit of energy is the energy expended in lifting one pound a foot high in one second. To find the numerical value of a force, multiply the mass which the force moves, by the velocity with which it is moved. This product, viz., mxv, is called the MOMENTUM of the body. The momentum of a moving bod}' is a measure of the force which is moving it. To find the work done in lifting a bod}*, multiply the weight of the body by the vertical height to which it is lifted. To find the energy in a moving body, multiply the weight 130 NATURAL PHILOSOPHY. of the body by the square of its velocity, and divide by Kinetic energy is the ability of a moving body to over- come resistance. Potential energy is the ability of a body at rest when in some high or advantageous position, to overcome resistance- Energy of these two types is mechanical, molecular, chem- ical, radiant, or electrical, taking its name from the kind of work in which it appears. All physical phenomena are only different exhibitions of energy. PHYSICS is THE SCIENCE OF MATTER AND ENERGY. II. SUMMARY OF TOPICS. 45. Mass and its measure. 46. Force and its measure. 47. Work. The unit. The French unit. Rule for calculating work. Work independent of time. When the body is not lifted verticall}-. 48. Energy defined. Energy depends on mass and ve- locity. The law. Illustrated. Relation of energy to work. Comparison of units. To compute energy. 49. Kinetic energy. Potential energ}". The advanta- geous position. Another definition of potential energy. 50. Mechanical energy*. Molecular energy. Chemical energy. Radiant energ}'. Electrical energ}'. 51. Energy may be transmitted. Energy may be trans- muted. No loss of energy in the changes. The mechan- ical equivalent of heat. The three essentials in the law of conservation. 52. Mechanical action evolves heat. The dynamic theo- ry. Hearing produced by vibrations. Sound. Light is undulatoiy motion. The ether. Vision. Luminous bodies. Light defined. Manifestations of energy. NATURAL PHILOSOPHY. 131 III. PROBLEMS. 1 . What FORCE is required to put a ball of iron weighing one pound in motion, with a velocity of one foot a second? Ans. 1 unit. 2. What is the MOMENTUM of one pound moving with a velocity of one foot a second? Ans. 1 unit. 3. A locomotive weighing ten tons is to be put in motion with a velocity of thirty feet a second : what FORCE must the steam exert? Ans. 600000 units. 4. What is the MOMENTUM of a ball weighing ten pounds, and flying with a velocity of seventy-five feet a second ? Ans. 750 units. 5. How much WORK must be done to lift a bucket filled with water, weighing twenty pounds, from the bottom to the top of a well which is fifteen feet deep ? Ans. 300 foot-pounds. 6. A person whose weight is 120 pounds ascends a flight of stairs, reaching between two floors, which are 12 feet apart : how much WORK does he do ? Ans. 1440 foot-pounds. 7. Find the ENERGY of a body weighing five pounds, and moving at the rate of 45 feet a second. Ans. 157.38-j- foot-pounds. 8. What is the ENERGY of a locomotive whose weight is ten tons, and which is moving at the rate of thirty miles an hour? Ans. 601865.28+ foot-pounds. 9. Suppose the locomotive whose energy is found in the preceding problem should meet another having the same weight and velocity, what amount of energy would be ex- pended to dash them to pieces? Ans. 1203730.56 foot-pounds. 10. Suppose it were possible to convert the energy of the collision of these two locomotives into heat, how much water would the heat produced be able to raise from 32 F. to 212 F.? Ans. 8.66+ pounds. 132 NATURAL PHILOSOPHY. CHAPTER V. ON MOLECULAR ENERGY: HEAT. SECTION I. ON CONDUCTION AND CONVECTION. 53. 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. (G. 392, 394-398 ; A. 601, 602.) Conduction. 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 becomes too warm to be held by the hand. The heat travels step by step from molecule to molecule to the end. This mode of transmitting heat is called CONDUCTION. Explanation. : 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 ; the} T 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 energy of these molecules of the rod is intercepted b} r the hand in contact with them ; the delicate nerves of touch receive the impulses, and announce the pain. Definitions. Some bodies conduct heat more freely than others. Those which conduct heat freely are called NATURAL PHILOSOPHY. 133 CONDUCTORS ; those which hinder its passage much are called POOR CONDUCTORS ; and those which nearly or quite forbid its passage are called NON-CONDUCTORS. The prop- ert^y in virtue of which bodies conduct heat is called CON- DUCTIVITY. Metals 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 become hot much quicker than that of the other. Among the best conductors we find silver, cop- per, gold, brass, tin, and iron, in the order named. The Conductivity of Liquids. The con- ducting power of liq- u i d s is very feeble. Wa t e r , for example , in a glass tube, with ice at the bottom, may be boiled without melting the ice, by applying the heat to the top of the water, or near the upper end of the tube. (Fig. 60.) The Conductivity of Gases. Whether gases conduct heat in the least degree, is doubted. Dry air is surely among the poorest conductors ; and so, likewise, are all Fig. 60. porous substances in which large quantities of air are in- closed. 134 KATtJ&AL PHILOSOPHY. 54. Convection takes place in bodies whose particles arc free to move. Air is heated in no other way. Liquids are also heated by convection : solids never are. Convection. Heat is transmitted by convection when it is carried from place to place by moving 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 be} r ond the edge of the block (Fig. 61). If the edge of the chimney fits closely upon the top of the block, so that no air can enter except at the open part A, the flame will flut- ter violently, showing that air is forced against it. If some light substance, such as down or cotton, be hung from a thread above the top of the chimney, it will be lifted away, showing that air is rising out of the chimney. Now, we lg ' ' know alread}' 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 chimne}*. What we have seen in this experiment really takes place whenever a hot body is surrounded by colder air. The air in contact with a hot stove, for example, is heated and ex- panded. 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, carrying the heat with it. This transfer of heat by the moving particles is called CONVECTION. Air is heated in no other Way. Air is heated only by convection. The heat of a stove does not go out to dis- tant parts of a room to warm the air : the air must go to the stove to be warmed. So, too, the atmosphere is warmed by convection. The sunbeams coming through it do not warm KATUBAL PHILOSOPHY. 135 it : they only warm the earth beneath it. Nor does the heat of the earth pass from particle to particle of the air, as it may in solid bodies : the heat of the earth warms only those particles in immediate contact with it. These rise and carry 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. liquids heated by Convection. Liquids are also heat- ed 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 current^ in the water. Warm the bottom of the bottle, and the heated water will be seen to be rapidly leav- ing the bottom, while other portions are moving downward to take its place. No Convection in Solids. Solids can not be heated by convection, simpl} 7 because their particles are not free to move among themselves. SECTION II. ON THE EFFECTS OF HEAT. 55. The action of heat is twofold : it raises the tempera- ture 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. (G-. 303, 304, 309, 310 ; A. 660.) The Action of Heat is Twofold. That the temper- ature 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-pendu- lum 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. 136 NATURAL PHILOSOPHY. The Expansion of Solids. The expansion of a solid b}' heat may be shown by an experiment. A ball of iron or of brass is taken, just large enough to pass easily through a ring of the same material. The ball is then heated by a lamp, after which it will be too large to go through the ring. It will rest upon the ring (Fig. 62) until it is cold again, when it once more passes easily as at first. We see that heat makes this ball larger. And it has the same effect upon other solids. 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 respec- Fig. 62. tivety two, three, or ten times as much expansion as one degree. Expansion of Liquids. To show the expansion of a liquid a glass bulb with a long open stem is used. The bulb is filled with water, and the stem partty filled, after which, if the bulb is plunged into hot water (Fig. 63), the water in the stem will be seen slowly rising. Illustrations. A kettle very nearly full of cold water will be quite full when the water is heated : the water will run over long before it boils. Twenty gallons of alcohol in midwinter will become about twenty-one gallons in midsummer. NATURAL PHILOSOPHY. 137 The Expansion of Gases. 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 expand at the same rate. If we have 491 cubic inches of air at a tem- perature of 32 F., and add one degree of heat, there will be 492 cubic inches : it expands ^y of its bulk. All gases ex- pand at the same rate, 4^ of their bulk at 32, for every additional de- gree. This fraction (^Jy) of its volume at 32 F., which a gas expands for every degree of tempera- ture, is called the CO- EFFICIENT OF EXPANSION for gases. 56. Temperature is measured by the expan- sion which accompanies Flg ' 63 ' it, in instruments called thermometers. There are three varieties of thermometers in use, the Fahrenheit, the Centigrade, and the Reaumur. The air-thermometer is used to show delicate changes of temperature. (G. 287-293.) Temperature measured by Expansion. We have found that temperature and expansion increase at the same time by the addition of heat. Moreover, in the same body 138 NATURAL PHILOSOPHY. 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. Mercury 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. The Thermometer. The mercurial thermometer con- sists of a glass tube terminating at one end in a bull), 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. There are three modes of graduating the scale, and this gives rise to three varieties of mercurial thermometer. Fahrenheit. In the Fahrenheit thermometer, 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 32. Centigrade. 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. R&uimur. In the Reaumur thermometer, the zero marks the freezing point of water ; the boiling point is marked 80. Below Zero. Degrees of temperature below the zero NATURAL PHILOSOPHY. 139 point are generally indicated by the minus sign ( ) placed before the number. Thus, 40 means a temperature 40 below zero. Otlior Forms. Mercury freezes at about 39 F. Temperatures below this point are measured by thermometers containing alcohol. Mercury boils at 660 F : tern- /"~"\ peratnres above this point are measured by the ex- I ) pansion of solid bodies. When it is necessary to show very delicate changes of temperature, the air-thermometer .is used. This instrument has a variety of forms, but it consists essentially of a glass tube, terminating at one end in a bulb, the other end being open, and inserted into a cistern of colored liquid. (See Fig. 64.) The liquid fills a part of the tube : the rest of the HO tube and the bulb above is filled with air. A gradu- ated scale is placed behind the tube. The air ex- pands or contracts with every change of tempera- ture, 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. 57. Temperature is the manifestation of kinetic energy : expansion, of potential. The first affects the touch, and is called SENSIBLE HEAT. The sec- ond does not affect the touch, and is called LATENT J I KAT. (G. 434, 435* 438, 439, 443 ; A. 670.) Rapidity of Motion, and Change of Position. He who has a clear idea of the molecules 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 140 NATURAL PHILOSOPHY. more and more swiftly, and at the same time being pushed farther and farther apart. The first of these effects is mani- fested as temperature, the second as expansion. In the first we have molecules in motion, or kinetic energy. In the second we have molecules separated, or potential energ} 7 . Sensible and Latent Heat. The heat which is ex- pended in raising temperature is called SENSIBLE HEAT : it can affect the sense of touch. That which is used to pro- duce expansion or change the positions of the molecules of a body 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. Specific Heat. But different substances do not divide it alike ; that is, if the same amount be added to two sub- stances, one of them will devote more of it to temperature, and less to expansion, than the other. Let equal weights of water and mercuiy be placed over the same source of heat. The water divides the heat it re- ceives 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 tempera- ture of mercury rises much faster than that of water : it takes thirt} 7 times as long to raise the water to a given temperature as it does the mercuiy. 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 mercuiy when that temperature is reached by both. We see, then, that at the same temperature different substances may have very differ- ent quantities of heat in them. The relative quantities of heat in different bodies, at the same temperature, is called SPECIFIC HEATS. Water is the Standard of Specific Heat. At a given NATURAL PHILOSOPHY. 141 temperature water 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 mer- cury and water are at the same temperature, the mercury will contain only .03 as much heat as the water. 58. 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 in- creases and continues until the solid is melted. (6r. 327- 329, 335, 336.) The Melting 1 Point. The temperature at which a solid body begins to melt is called its MELTING POINT. At this temperature, 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 from the solid to the liquid form is called LIQUEFAC- TION. The melting-point for different substances is not the same. Ice melts at 32 F. ; mercuiy at .39 ; iron at about 3000, and platinum at about 5000. The Temperature 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 tem- perature as the solid which is melting. 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, because the heat is all expended to change the position of the molecules, whereas, before, a part of it was used up to produce a rise of temperature. An Exception. Ice contracts when melting ; the water formed fills less space than the ice. In this case, likewise, all the heat applied is expended in changing the position of 142 NATURAL PHILOSOPHY. 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 39, after which it expands. Those who have attempted to melt ice or snow, for domes- tic purposes, remember how slow the process is. The amount of heat required to simpty melt the snow, without making it any warmer, is very great ; the same amount applied to the water formed would raise its temperature 142. This is the amount of heat which is used up in changing the relative positions of the molecules, and becomes latent. Hence the latent heat of water is said to be 142. 59. 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 ex- pansion greatly increases, and continues until the liquid is vaporized. (G. 351, 352, 354, 358 ; A. 684.) The Boiling Point. The temperature at which a liquid begins to boil is called its BOILING POINT. At this tempera- ture, the body rapidly becomes a vapor, and the change is called VAPORIZATION. Evaporation. 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 EVAPORA- TION. The boiling point for different liquids is not the same. Water boils at 212 F., alcohol at 173, ether at 95. The boiling point for the same liquid is not always the same : it depends upon three circumstances. The Boiling Point depends on the Purity of the Liquid. It is affected, first, b} r the presence of impurities in the liquid. The presence of some impurities raises the boiling point ; of others, lowers it. Salt water, for example, NATURAL PHILOSOPHY. 143 boils at a higher temperature than pure water, while that which contains air boils at a much lower temperature than that which contains none. 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. It depends on the Pressure. But the most impor- tant 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 ma}^ 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 flask, or, better, a bolt head (Fig. 65), 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. Boil it until the steam issues freely from the stem, and then, removing it from the flame, cork the stem at the same instant. The air has been driven out from the instrument, and noth- ing 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 tem- perature because the cold water, condensing the steam, re- moves the pressure from its surface. >144 NATUEAL PHILOSOPHY. The Temperature stops rising. No matter how much heat may be applied to boiling water, its temperature is not raised. Moreover, the temperature of the steam is always that of the water from which it is made. By the following experiment these facts maybe illustrated. Water is placed in an open vessel V (Fig. 66). 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 rise of tem- perature ; but, when the water fairly boils, the fluid stops sinking, showing that the temperature no longer rises. The fluid will remain motionless until the water in the vessel has been changed to steam. Let the bulb be lifted into the steam above the water ; no change occurs in the height of the fluid in the stem, hence the temperature of the steam must be the same as that of the water. But the Expansion increases. If all the heat applied to a boiling 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 in- ference is abundantly verified. Steam fills about 1,700 times as much space as the water from which it was formed. The Latent Heat of Steam. The amount of heat re- quired to expand water into steam, in other words, the latent heat of steam, is very great. Bj 7 accurate experiment it has been found to be 972 F. The steam and the boiling water are ot the same temperature, } T et there is an excess of heat in an ounce of steam, which, if applied to one ounce of water, Fig. 66. NATURAL PHILOSOPHY. 145. would be sufficient, were it possible, to raise its temperature to 972 ; it will raise the temperature of nine ounces of water 108. 60. The heat which has been required to produce expan- sion will be reproduced when the expanded body again contracts. Heat restored after being used. The following ex- periment very satisfactorily shows that heat is required to produce expansion, and that it is again given off when con- traction occurs. The bulb of an air-thermometer is placed in a receiver over the plate of an air-pump ; the stem, pass- ing 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 expands, and the rising of the fluid in the thermometer shows that the bulb is at the same time cooled. If, now, air be allowed to return to the receiver, the air inside be- comes more dense, and the sinking of the fluid in the ther- mometer shows that heat is again given off. Illustrations. 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 form. But bodies near to freezing water are warmed, because the water, while freezing, gives up the heat which had been needed to keep it in a fluid form. Steam-Heating-. In the production of steam the kinetic energy of the fuel, burning in the furnace, becomes potential energy in the expanded steam. Let this steam be condensed 146 NATURAL PHILOSOPHY. in pipes, and its potential energ}^ is changed back again to kinetic energy, and the pipes show it by being hot. This principle is largely applied in the warming of buildings by steam. REVIEW. I. SUMMARY OF PRINCIPLES. Conductivity is that quality of a substance which allows heat to pass from molecule to molecule through the bod} T . Convection is the transmission of heat by moving parti- cles or currents in the substance. Solids are the best conductors, liquids stand next in order, and gases last. Gases are heated by convection only, liquids by convection chiefly, and solids by convection never. With few exceptions the volume of a body increases with the temperature. Solids expand least, liquids more, and gases most, by the same increment of heat. Thermometers are instruments for measuring temperature. 180F. = 100 C. = 80 R. Fahrenheit=f Cent . + 32, = f Reaumur -f32. Sensible heat is the kinetic energy of the molecular motion. Latent heat is the potential energy due to the separation of molecules by heat. Sensible heat becomes latent during the melting of a solid and the boiling of a liquid. Latent heat becomes sensible during the liquefaction of vapors and the solidifj'ing of liquids. Equal weights of any two substances at the same tempera- ture contain different quantities of heat. The total heat in a body compared with that in the same weight of water at the same temperature is its specific heat. The boiling point of a liquid depends on its purity, on the nature of the vessel containing it, and on the pressure upon it. NATURAL PHILOSOPHY, 147 II. SUMMARY OF TOPICS. 53. Conduction of heat. Explanation. Definitions. Conductivity of metals. Of liquids. Of gases. 54. Convection illustrated. Defined. Of air. Of liquids. Of solids. 55. The twofold action of heat. Expansion of solids. Of liquids. Of gases. 56. Temperature measured by expansion. The ther- mometer. Fahrenheit's. Centigrade. Reaumur's. Degrees below zero. Other forms. 57. Effect of heat on the motion and position of mole- cules. Sensible and latent heat. Specific heat. 58. The melting point. No rise of temperature while melting. But an increased expansion. Except in the case of ice. The latent heat of water. 59. The boiling point. Depends on the purity of the liquid. On the nature of the vessel. And on the press- ure. No rise of temperature during ebullition. But an increased expansion. The latent heat of steam. 60. Heat restored after being used. Illustrations. Steam-heating. 148 NATURAL PHILOSOPHY. CHAPTER VI. ON UNDULATORY ENERGY: SOUND. SECTION I. ON THE TRANSMISSION AND REFLECTION OF SOUND. 61. SOUND -WAVES travel through all elastic media. The Velocity of sound is not the same in different substances ; it is governed b} T 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. (G. 226, 227; A. 489-491.) Sound -Waves. All sounds are undulations, but it is not true that all undulations are sound. Some are too slow to affect the ear : such are those produced by the vibrations of a cord not over- stretched. On the other hand, there are undulations which are too rapid to be heard. The lower limit has been fixed at sixteen a second, and the higher at 38,000. The energy of waves which occur within these limits of velocity can affect the ear, and such waves are called SOUND-WAVES, or simply, SOUND. It is interesting to notice that the limits of hearing are not the same in all persons. " Nothing can be more surprising than to see two persons, neither of them deaf, the one -com- plaining of the penetrating shrillness of a sound, while the other maintains that there is no sound at all." "In the NATUBAL PHILOSOPHY. 149 * Glaciers of the Alps ' 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 their shrill chirruping. My friend heard nothing of this, the insect-music tying quite bej'ond his range of audi- tion." (See Tyndall's Lectures on Sound.) Are transmitted through all elastic Bodies. Nu- merous facts, easily verified, prove that sound-waves can traverse all elastic bodies. 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 sur- prising distinctness. The same thing is true of other solid bodies. The clatter of horses' hoofs, or the rattle of a rail- way-train, quite inaudible to one who stands erect, is heard distinctly when the ear is placed in contact with the ground. The solid earth, in this case, transmits the sound-waves. In liquids, also, sound-waves travel freely. Let 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 suffi- ciently familiar ; the sounds which throng the ear so con- stantty are transmitted through the atmosphere. The Velocity not the same in all Media. The velo- city of sound in a great many substances has been found by laborious and skillful experiments (see T}*ndairs Lectures on Sound). In the following table some of these results are collected : SUBSTANCES. TEMPERATURE. VELOCITY. Air 32 F. 61 32 32 ' 59 ' 68 1,092 fe 1,118 1,040 4,164 4,714 16,822 10,900 c j t p< >rsec. Air . ... River-water Pine Wood 150 NATURAL PHILOSOPHY. The velocity of sound depends upon the density and the elasticity of the medium in which it travels. The first Law. The density of oxygen, other things being equal, is about sixteen times that of h}'drogen. But we see in the table that the velocity of sound in oxygen is only about one-fourth as great as in hydrogen. In this case the velocity is inversely as the square root of the density of the medium. It is always so. The law has been verified by repeated experiments. 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 four 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. Density and Elasticity. 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 elas- ticit}^ measured by the force required to compress them is vastly greater, so that, as the table shows, water conducts sound better than air. But in the same Medium Velocity is Uniform. 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 velocit} 7 . 1 When we listen to the music 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 melodious songs of the birds, and the murmur of rivulets, are all borne with equal swift- ness through the air. 1 There is reason to believe that very loud sounds do travel a very little faster than feeble ones. NATURAL PHILOSOPHY. 151 Application. So uniform is the velocit} 7 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 ten sec- onds afterward the report was heard, the temperature at the time being 61 F. The velocity of sound is 1,118 feet ; and the sound-waves, starting when the flash was seen, took ten seconds to reach the ear. 1,118x10 = 11,180. The ob- server was at a distance of 11,180 feet from the cannon. The Formula. The two laws of velocity are expressed in the formula : V= fl Nd The Effect of Temperature. The heating of air ex- pands it : its elasticity is thereby increased, and its density diminished. But to increase the value of e, and lessen that of (> d, would, in both cases, increase the value of the fraction - . Hence a rise of temperature must increase the velocity of sound. This is verified by experiment. Notice the two velocities of air in the table. * M 62. 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 : The angle of reflection must be equal to the angle of incidence. An Echo is produced by the reflection of sound. (G. 231, 232 ; A. 495, 496.) The Reflection of Sound. To illus- trate the reflection of sound, suppose the line I A (Fig. 67) to represent the direction of several sound-waves, which, passing through the air, strike a body M M. Some of these waves will pass through the body, but others will be Fig. 67. 152 NATURAL PHILOSOPHY. 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. The Law of Reflection. To understand the language of this law, let us refer again to Fig. 67. 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 from 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 IN- CIDENCE, and the angle P A R is the ANGLE OF REFLECTION. The law of reflection requires that these angles shall always be equal. 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 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 Coopers- town, N.Y., will not soon forget the fine echo returned from the rocky hills which skirt Otsego Lake. There, we are told by Fenimore Cooper, once dwelt Natty Bumpo, the hero in the story of " The Pioneers." Let his name be loudly called from a certain place upon the lake, and immediately the re- sponse, "Nat-ty-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. Multiple Echo. When two obstacles are opposite to one another, the sound ma} r 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 NATURAL PHILOSOPHY. 153 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." SECTION II. ON MUSICAL SOUNDS. 63. Musical sounds are caused by rapid vibrations which follow each other with great regularity. Any noise what- ever, when repeated rapidly, will cause a continuous tone : even separate puffs of air, following each other rapidl}', pro- duce a musical sound. (G. 236, 237 ; A. 512.) Musical Sounds. 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 the resulting sound is called NOISE. 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 MUSICAL SOUND. Any Noise repeated rapidly causes a continuous Tone. No matter what the source of the waves maybe, 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 the 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 unpleas- ant 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. 154 NATURAL PHILOSOPHY. Even Puffs of Air : the Siren. The siren is an in- strument by which ;i scries of air-putt's arc, made to produce a musical sound, and by which the number of puffs made in a second are registered. Its structure may be learned from Fig. 68. Description. A brass tube, O, leads from a wind-chest, E, to a brass plate, B, which is pierced with a series of holes arranged around the cir- cumference of a circle. Above this plate is a disk, also per- forated with holes exactly cor- responding to those in the plate below. The disk is provided with a vertical steel axis, and is so fixed that it may rotate with a very small amount of friction. The wheel-work shown in the upper part of the figure registers the number of puffs made in any given time. Its Action. Now, when the disk revolves, the holes in it will be brought alternately over the perforations in the plate 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 O, it will escape from the top in steady streams, but when the disk revolves these streams will be cut up into successive puffs. If the disk turns slowly, the sepa- rate 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 B oblique instead of vertical ; those in the disk being also oblique, but inclined in the opposite direction. Pig. 68. NATURAL PHILOSOPHY. 155 64. Musical sounds differ in throe respects: in 1'itch ; in Intensity; and, in Quality. I. PITCH. Pitch depends entirely upon the rapidity of vibrations which produce the sound. The difference in the pitch of two sounds is called an IN- II.UVAL; and a series of eight sounds of different 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. (G. 243-248 ; A. 520.) 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 vibra- tion : 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. Intervals. When the number of vibrations which pro- duce one sound is twice as great as that which produces another, we must not say that the sound is twice as //,/>/ A, 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 fun- damental. Other intervals will be named in the description of the scale. 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 tones, called the NATURAL or the DIATONIC SCALE. The eight notes of the scale are expressed by the follow- ing names and intervals : 156 NATURAL PHILOSOPHY. Names, C, D, E, F, G, A, B, C. Intervals, 1st, 2d, 3d, 4th, 5th, 6th, 7th, 8th. This scale repeated about eleven times, making what is termed in music eleven octaves, will include all sounds with- in the range of the human ear. Only about seven octaves are used 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. Number of Vibrations for the Notes. The num- ber of vibrations to produce the various notes may be found by experiment with the siren. (See Tyndall on Sound.) Or it may be found with the greatest ac- curacy by means of the electric register (Fig. 52). Fig. 69 shows how the standard tuning-fork is made to open and close the electric circuit. 1 1 From the prong of the fork a silk fiber stretches across to a slender vertical spring, s, fixed at the lower end, while its upper end rests against the end of a set screw, t. The two surfaces in contact are platinized. The spring is slightly bent; and the set screw, pressing against its upper end, holds it in constant tension, and thus forbids it vibrating, except in unison with the fork. Every vibration of the prong is transmitted by the fiber, and compels the spring away from contact with the screw. Putting this break-circuit in place of the monocord, represented in Fig. 52, between the pendulum P and the register R, the vibrations of the fork record themselves upon the moving paper. Noticing that the accuracy of Koenig's tuning-forks is questioned by Mr. Ellis (Nature, xvi., p. 85), I fancied that the testimony of this method would not be with- out interest. Seizing the earliest opportunity, therefore, I submitted the C^sfork, bearing Koenig's monogram, to careful examination. The pendulum was accurately adjusted to hold the circuit one-half a second. The iodide-starch solution, with a battery of ten Bunsen's immersion cells, was used. Fifteen perfectly distinct and easily counted records were taken. Every one of these autographs was found to consist of 128 dots, representing 128 complete vibrations per half-second, or 256 per second, testifying to the exactness of Koenig's stamu. Jour- Jfrank. Ind. vol. Ixxii. NATURAL PHILOSOPHY. 157 On the English standard of pitch, the note A of the treble clef is made by 440 vibrations a second. On the French standard the rate for the same note is 435. Relative Kates. If we represent the number of vibra- tions for the fundamental note by 1, then the several notes of the scale will be made by the following ratios : C, D, E, F, G, A, B, C. i * f> t f> * -> 2 - Absolute Rates. 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 -| and 1 ; that is, A is produced *by f as many vibrations as C ; or, to reverse the ratio, C requires |- as many as A, and -|x440 = 264. Having this number for the fundamental, multiply this by the fractions , j, f , &c. , and the numbers for the cor- responding notes will be obtained. These multiplied by 2 will give the numbers for the notes in the next higher octave ; or, divided by 2, will give the numbers for the notes in the octave below. II. INTENSITY. Definition. The intensity of sound is that which dis- tinguishes it as being loud or soft. It is the energy of the waves against the ear. It depends entirely upon the ampli- tude of the vibrations which produce it. The greater the amplitude, the louder the 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. (G. 222, 223.) The Law. If this distance be doubled, then the velocity of a string will be doubled also. But a body with double velocity has a quadruple energy. Hence the intensity of sound varies as the square of the amplitude. 158 NATURAL PHILOSOPHY. III. QUALITY. Definition. 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 rec- ognize the voices of friends, not by their pitch nor their intensity, but by their quality. (G. 249, 253-255 ; A. 523- 526.) Compound Sounds. A musical sound is rarely made by a single undulation : several, with different rates and amplitudes, are combined in almost every tone we hear. Fig. 70 Illustration. If a plate of brass is fastened at its cen- ter, and covered with a sprinkling of fine sand, and then if a violin-bow is drawn across its edge (Fig. 70), a shrill tone is produced. The sand at the same time dances about NATURAL PHILOSOPHY. 159 in a curious manner, and finally arranges itself in straight lines and curves upon the plate. The sand gathers where there is least vibration, and shows that the plate vibrates in segments (p. 104) . The plate in the cut shows eight segments. Now, each of these vibrating parts starts an undulation in the air, and consequently there are eight different sounds combined in the one shrill tone which is heard. Overtones. Whenever a piano- wire or the cord of a harp is struck, it vibrates as a whole and in segments at the same time. Its vibration as a whole j'ields its fundamental tone. Its vibrations in segments yield higher tones, called OVER- TONES, or sometimes HARMONICS. The fundamental with its overtones are combined in the sound which is heard whenever the wire or cord is struck. Helmholtz' Theory. The quality of a sound depends on the number and prominence of the different undulations which are combined to produce it. Each different set of undulations produces a resultant wave of a different/orm, and x'/\ these waves of differ- / / \ ent form affect the ear *\ as sounds of different quality. 65. The Phonograph is an instrument for recording and reprodu- cing sounds. It acts on the principle that waves of the same rate, am- plitude, and form are exactly the same sound. Pi g . 71. The Phonograph. The construction of Edison's phono- graph or " talking-machine " is shown in Figs. 71 and 72. 160 NATURAL PHILOSOPHY. A spiral groove is cut around a cylinder of metal, A, which may be turned with a crank. On one end of its axle a screw-thread is cut, so that when the cylinder is turned it is at the same time moved forward. In front of this cylinder is a mouthpiece, B, with a thin disk of metal, C, which the voice will vibrate, and between the disk and the cylinder is a needle-point p which vibrates with the disk. To record the Voice. A sheet of tinfoil is wrapped smoothty around the cj'linder, and the mouthpiece is then adjusted so that the needle-point will press lightly against its surface just over the spiral groove. The speaker then talks loudly into the mouthpiece while the C3'linder is turned. The air- waves of the voice vibrate the disk ; and the vibrat- ing disk drives the needle-point against the tinfoil, and presses it to greater and less depths into the groove. This tracing of the needle is a record of the voice. The closeness of the depressions represents the pitch. The depth of the depressions represents the loudness. The form of the depressions represents the quality. To reproduce the Voice. Move the mouthpiece so that the point no longer touches the tinfoil, and turn the cyl- inder back to the place it was in when the record be- gan. Then again bring the point in contact with . 72. the tinfoil and turn the cylinder forward exactly as at first. The needle- point will follow the tracing which it made before, and in going over the prominences and into the depressions will com- pel the disk to repeat the same vibrations which it made be- fore under the influence of the voice. These vibrations of the disk reproduce the air-waves which the voice threw against it* NATURAL PHILOSOPHY. 161 and if the ear be placed near the mouthpiece, or, better still, if a large cone, shown by dotted lines in Fig. 71, be used, the utterances of the speaker will be repeated by the phonograph. 66. 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. Stringed Instruments. 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 sim- ple vibration of a cord is not able to produce sound of suffi- cient intensit}^ ; 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. Pitch varied by using Strings of 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. Illustration. Suppose we wish to know the lengths of eight strings of the same weight and tension, which will give the eight notes of the scale. We have learned that the number of vibrations per second is inversely as the length of the cord, and we have learned also that the relative num- bers of vibrations for the eight notes are expressed by the series 1, f, j, f , f , f, -^-, 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, f, f, f, f, f, ^, J. Knowing the length of the string to give the fundamental, 162 NATUKAL PHILOSOPHY. 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 f x 18 ; the third must be ^x 18 ; the fourth must be |x!8 ; and so on until the eighth, which must be 1x18. Pitch is varied by using String's of different Tension. According to the second law of vibrating strings, the num- ber of vibrations made in a second increases when the ten- sion increases. Hence the pitch of sound made by the string will be higher when the tension is made greater. Pitch is varied by using Strings of different Weights. According to the third law of vibrating strings, the num- ber of vibrations made in one second varies inversely as the square root of the weight of the strings. Hence the pitch of the sound will be higher, when the string which makes it is lighter. II. WIND-INSTRUMENTS. Wind-instruments. 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 T}^ndall on Sound.) In the clarionet the sounds are always made by air-vibrations aided by a reed. Organ-Pipes. The pitch of sounds in pipes depends upon the lengths of the pipes. A pipe, to produce the lowest note used in music, must be thirty-two feet in length, and the pitch of tones from other pipes will vary inversely as the lengths of the pipes. Organ-pipes are sometimes open at the top, and sometimes closed. An open organ-pipe } T ields 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 sixteen feet in length. NATURAL PHILOSOPHY. 163 SECTION III. ON MUSICAL AND SENSITIVE FLAMES. 67. When a gas-flame burns within a glass tube, a musical sound is produced. The pitch of the tone depends on the length of the tube and the size of the flame. A silent flame may be made to sing by sound- ing near it the note of the tube. Naked flames are also sensitive to the action of neighboring sounds. (G. 281.) The Musical Flame. Let a flame of common coal-gas, placed under the end of a glass tube T (Fig. 73), be slowly raised into it ; when a particular height is reached, the flame, if small enough, will burst forth into a loud and continuous sound. This sound is often harsh, sometimes melodious. Fig. 73. At the beginning it is sometimes low and smooth, like the whistle of a very distant locomotive ; but, as the experiment goes on, the intensity of the sound rapidly increases until, like the long monotonous screech of the engine at hand, it becomes almost unbearable. 164 NATURAL PHILOSOPHY. In tubes of tin and pasteboard, sounds of different quality are obtained. "Explanation. That a gas-flame flutters when exposed to a gentle breeze, is a fact sufficiently familiar. Now, this fluttering flame, like a vibrating tongue or reed, must cause A r ibrations in the air around it. This is the key to the ex- planation of musical flames. The air in the tube is heated by the flame ; it rises, and an upward current through the tube is thus produced. The flame flutters in this current, and causes a system of waves, whose rapidity and amplitude give pitch and intensity to the note produced. If we inquire further about the cause of the fluttering, we are told that experiments by Faraday proved that gas issues from a burner in an unsteady stream, due to the friction against the sides of the tube, and that in burn- ing it makes a series of inaudible explosions. A current of air heightens both of these effects, and makes them sensible. Evidence that the Flame is intermittent. That a musical flame is thus intermittent, is shown by the following beautiful experiment. The tube T (Fig. 74) is blackened so as to keep the light from falling on the screen placed behind it at S. A concave mirror M, in front of the flame, forms an inverted image of it on the screen. If the mirror is turned horizontally, while the flame is silent and steady, the image will move, and if the motion of the mirror is swift, an unbroken band of light will be seen on the screen. But if, when the flame is singing, the mirror is swiftly turned, a series of distinct images will appear. The Pitch of the Note. In these tubes, as in organ- pipes, the pitch of the sound depends upon the length of the tube. But, while the pitch depends chiefly upon the length of the tube, it is partly governed b} 7 the size of the flame. If one tube is just twice the length of another, its funda- mental note is an octave below ; but, when placed over a flame whose size fits it to sing in the shorter tube, the note NATURAL PHILOSOPHY. 165 of the shorter tube will be produced. Then let the flame be gradually emarged, and in a little time the low funda- mental note of the tube suddenly bursts forth. By varying Fig. 74. the size of the flame it is possible to obtain the fundamental note, its octave, and its four harmonics, from the same tube. Sensitive Flames. The name ' ' sensitive flames ' ' is given to those which, without being inclosed in tubes, are 166 NATURAL PHILOSOPHY. affected by sounds. Certain sounds in an instrumental con- cert often cause curious motions of the gas-flames in the room. This observation was first published in 1858. The motions referred to consist of a u jumping " of the flame to considerable height, or a thrusting forth of tongues of flame from its upper edge. (See Tyndall on Sound.) An effect just opposite this, the shortening of tall flames, was first noticed by Mr. Barrett of London, in 1865. He says ("Chemical News, American Reprint," July, 1868), "A jet of gas issuing from a V-shaped orifice was found to be quite insensible to sound until the flame reached a height of ten or twelve inches (see Fig. 75) ; and then, at the sound of certain high tones, the flame shortened, and spread out into a fan-shape." Another flame he thus describes: "So sensitive is this flame, that even a chirp made at the far end of the room brings it down more than a foot. Like a living be- ing, the flame trembles and cowers down at a hiss ; it crouches and shiv- ers as if in agony at the crisping of this metal foil, though the sound is so faint as scarcely to be heard ; it dances in tune to the waltz played by this musical box ; and, finally, it beats time to the ticking of my watch." Mr. Barrett also suggests that these flames may yet be turned 'to some use, and, to illustrate, suggests an arrange- ment shown in Fig. 75. Near the tall sensitive flame a, stand two vertical brass rods, b c. Projecting from these rods are two metallic rib- bons, made of layers of silver, gold, and platinum welded together. The ends of the ribbons are about half an inch apart. By heat the different metals expand unequally, and, Fig. 75. NATURAL PHILOSOPHY. 167 bending the ribbons, bring their ends together. The brass rods are connected by wires with an electric bell at a distance. Now, as long as the tall flame is not disturbed, the metallic ribbons are not in contact: the circuit is broken, and the bell is silent ; but at the sound of a whistle the flame jumps down, warms the ribbons, completes the electric circuit, and rings the distant bell. SECTION IV. REVIEW. I. SUMMARY OF PRINCIPLES. Undulations with rates between 16 per second and 38,000 per second will affect the ear as sound. Such undulations can traverse all kinds of elastic bodies, but not with the same velocity. The velocity in a denser medium is less than in a rarer one. In a more elastic medium it is greater than in one less elastic. The laws are expressed by the formula : V = When sound-waves flow against an obstacle, they are thrown back, or reflected. The angle of reflection equals the angle of incidence. Any sound repeated with great regularity and rapidity becomes a musical tone. Tones differ in pitch, in intensity, and in quality, or, as the French call it, timbre. The pitch depends upon the rate of the waves. The intensity depends upon the amplitude of the waves. The quality depends upon the form of the waves. Waves of the same rate, amplitude, and form will be recognized as the same sound, in whatever way they may be produced. 168 NATURAL PHILOSOPHY. II. SUMMARY OF TOPICS. 61. Sound-waves. Traverse elastic bodies. With different velocfty. The first law. The second law. Velocity uniform in the same medium. Application. The formula. Effect of temperature. 62. Reflection of sound. The law. Explanation of the echo. Multiple echo. 63. Musical sound. Continuous tone by rapidly repeated impulses. The siren. Description of the siren. Ex- planation of its action. 64. Pitch depends on rate. Intervals. The diatonic scale. English and French standards of pitch. Relative rates for the eight notes. Absolute rates. Intensity. Quality defined. Compound tones. Illustration. Over- tones. Helmholtz' theory of quality. . 65. The phonograph. To record the voice. To repro- duce the voice. 66. Stringed instruments. Pitch varied b} T strings of different lengths. Different tensions. Different weights. Wind-instruments. 67. The musical flame. Pitch of the tone. The sensi- tive flame. NATURAL PHILOSOPHY. 169 CHAPTER VII. ON RADIANT ENERGY: LIGHT. SECTION I. ON TRANSMISSION. 68. 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. The art of Photometry depends upon this second law. (G. 489, 491-493, 495 ; A. 795, 803.) Wave-Front. When a pebble falls into quiet water, a wave advances outward like the rim of an expanding wheel. The outside of this circular wave is the wave-front. When a gas-jet is lighted, a wave darts outward, advancing in ever} 7 direction like the surface of an expanding sphere. The outside of this spherical wave is the wave-front. The outside of an advancing wave of any kind is called the WAVE-FRONT. Kays of Light. A single line of light, or, more accu- rately, the path of a single point in the wave-front, is called a RAY of light. But a ray of light is quite too delicate a thing to be seen. The smallest portion of light which can be separated by experiment consists of many rays. A col- lection of parallel rays is called a BEAM of light. A collec- 170 NATURAL PHILOSOPHY. tion of ra} T s which diverge from a point, or which converge toward a point, is called a PENCIL of light. Kays of Liglit are transmitted. Some substances per- mit 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 ex- amined, can be seen to transmit light. All substances are doubtless able to transmit light in some degree. Liglit moves in straight Lines. That light moves in straight lines, is shown by numerous familiar facts. We can not see through a crooked tube, simpl}' 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, and the paths of the sunbeams are seen streaking the air with bars of light. With uniform Velocity. Light travels through space with a uniform velocity of about 186,000 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 accu- rac} T . 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. The re- sult is about 186,000 miles a second. For all distances on NATURAL PHILOSOPHY. 171 Fig. 76. the surface of the earth, the passage of light may be con- sidered instantaneous. It would go around the world almost seven times in a single second. The Second Law. That the intensity of light varies inversely as the square of the distance, may be easily proved by experiment. A square piece of stiff cardboard, A (Fig. 76), 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 will be larger as the small card is moved nearer to the flame ; it will be small- er as it is moved the other way. The figure is intended to show the small card to be just one-fourth as far from the flame as the large one. In this case the shadow will be found to be exactly sixteen times as large as the card in front 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. But, if the same amount of light is spread over sixteen times as much surface in one case as in another, it can be only one-sixteenth as intense. At four times the distance from the luminous bod}', in this case, the intensity of the light is one-sixteenth as great. At three times the distance, the light would, in the same way, be found to be one-ninth as intense. In other words : the in- tensity of light varies inversely as the square of the distance from the luminous body. Photometry. It is often desirable to compare the illu- minating powers of different flames. , The art of doing this is called PHOTOMETRY. The simplest method is to place the two flames at such distances from a screen, that the intensi- 172 NATURAL PHILOSOPHY. ties of the light they shed upon it shall be equal ; the illu- minating powers of the flames must then be as the squares of these distances. Suppose, for example, that we wish to know how many times more light one candle will give than another of inferior quality. Let a slender rod B (Fig. 77) be put just in front of a white screen A, and then move the flames to such distances that the two shadows of the rod, falling side by side Fig. 77. upon the screen, shall appear to be of equal 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 the} T 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. SECTION II. ON REFLECTION. 69. When light in passing through one medium comes against the surface of another, only a part will enter ; another part will be reflected, obeying the following law : The angles of incidence and reflection must be equal, and in the same plane. (G. 497; A. 881, 882.) Reflection. The reflection of light is in all respects like the reflection of sound. The same terms are used to describe it ; the same figure may be reproduced to illustrate it. Thus in NATURAL PHILOSOPHY. 173 Fig. 78, the line I A ma}' represent a beam of light passing through air, and striking upon the surface of a plate of glass at A. One part of the 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 R. The beam I A is the incident beam. The beam A R is the reflected beam. The point A is the point of incidence. The Law of Reflection. The reflection of light is also governed by the same law as the reflection of sound. The angle I A P (Fig. 78) is the angle of incidence. The angle P A R is the angle of reflection. These two angles must be equal. Illustrations. How various and beautiful are the phe- nomena which this principle of reflection explains ! The sky, with all its floating clouds or shining stars, is painted in ever}' 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. 70. 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 ; While a convex mirror always separates the rays which it reflects. (G. 506.) 174 NATURAL PHILOSOPHY. Mirrors. 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. The effect of Plane Mirrors. The rays of light which fall upon a mirror may be parallel, or converging, or diver- ging, but can have no other relation. Now, let the mirror be represented by the straight line A B (Fig. 79), and sup- pose, 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 eg will be the angle of incidence. Then draw the line c/, so as to make the angle of reflection, g c f, equal to the angle of incidence, and cf 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/and d e, will be parallel. Suppose, second, that two ra}*s, a c and 6 d (Fig. 80), are converging, and strike the mirror at the points c and d. By making the angles of incidence and reflection equal, ex- actly as it was done in the preceding case, we find that the reflected rays will take the directions c e and d e ? converging to the ppint e. NATURAL PHILOSOPHY. 175 Fig. 81. Suppose, third, that the ra} r s are diverging. Represent them by lines a c and a d (Fig. 81). Erect the perpendicu- lars, and construct the angles of incidence and reflection equal, and the directions of the reflected rays will be ce and d /, diverging from each other. In each of these three cases, the reflected rays have the same relation as the incident rays. The effect of Concave Mirrors. We will notice only those concave mirrors whose surfaces are spherical. If we know the direction of the incident ra3"s, 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 mir- ror, erect a perpendicular to the concave surface at the point of incidence ; and all difficulty disap- pears when we remember that a perpendicular to any spherical surface is the radius of the sphere. In Fig. 82, MN repre- sents a section of a con- cave 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 inci- dent rays, and we wish to find the direction they take after reflection, we may draw the radii C A and C B, making the angles of incidence E A C and D B C, and then draw the "EM o* 176 NATURAL PHILOSOPHY. lines A F and B F, so as to make the angles of reflection equal to these. B}' so doing, we find that the reflected rajs converge, and cross each other at the point F. In Fig. 83, the lines E A and D B represent converging rays. By construct- ing the angles of in- cidence and reflec- tion in the same wa} T as before, we find that the reflected ra} T s cross each other at the point F, con- verging faster after reflection than be- fore. In the same figure, F A and F B may represent diverging rays, striking the mir- ror at the points A and B. By constructing the angles* of incidence and reflection equal, we find the reflected rays tak- ing the directions A E and B D, diverging less after reflec- tion than before. Now, since parallel rays are made converging, and con- verging rays are made more converging, while diverging rays are made to diverge less, we may sa}' that the general effect of a concave mirror is to collect rays of light. Foci. A focus is any point where rays of light cross, or appear to cross, after reflection. The points F, in Figs. 82 and 83, are foci. The axis of a mirror is a straight line drawn through the center of curvature and the middle point of the mirror. In Fig. 84, the line C A is the axis of the mirror M 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. 84) are near and parallel to the axis C A, they will, after reflection, cross each other at the point NATURAL PHILOSOPHY. 177 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 mir- ror. The effect of Con- vex Mirrors. In Fig. 85, a convex mirror is represented by M 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 construct the angles of incidence, we must erect per- pendiculars to the surface at these points. The perpendic- ulars are the radii, C A and C B, extended beyond the convex Fig. 84. Fig. 85. 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 H. We notice that parallel rays are rendered diverging. 178 NATURAL PHILOSOPHY. So we might show that diverging rays would be made more diverging, and that converging ra}'s would be made to con- verge less. We say, therefore, that the general effect of a convex mirror is to separate rays of light. 71. When the light reflected from a mirror enters the eye, we see an image of the object from which the light proceeds. The image of an} r point will always be found where the rays of light which go from that point either meet, or appear to meet, after reflection. The image formed by a plane mirror is always as far be- hind the mirror as the object is in front of it ; the same size as the object, and erect. (G. 501-503 ; A. 883-885.) Images by Reflection. When an object, a lighted candle for example, stands before a looking-glass (Fig. 86), numberless ra}'s of light from every point of it fall upon the mir- ror. These rays are reflected, and man}' of them are thrown into the e} r e. Those w r hich enter the eye cause us to see the image in the glass. The Image of a point. Now, if the rays of light, which form the image in the glass, were visible, the person would be able to trace them back from the eye, converging toward the points on the glass from which they are reflected, and they would appear as if they came from points in the image behind the glass. This will be better understood by means of Fig. 87. Let M N represent a plane mirror. From the point A, number- Fig. 86. NATUBAL PHILOSOPHY. 179 Fig. 87. less rays fall upon the mirror, some of which, after reflection, will enter the e}'e supposed to be at O. Two of these ra}*s are represented in the figure. The e}'e will receive these rays as if they came from the point 132 ' of tourmaline, it will be found to be polarized. Or if another plate of black glass, N, is placed parallel to the first, the beam will be reflected as the figure shows it ; brt let the plate be turned 90, as shown by the dotted lines, and the beam will be wholly cut off. Turn it 90 farther, and the reflected beam appears again ; another 90, and it is again cut off. At an}*- other angle of incidence than 54^, the light will be only partly polarized : 54l is the polarizing angle for glass. Polarizing Instruments. The instruments, called po- lariscopes, by which to study polarized light, consist essen- tially of two parts, one to polarize the light, the other to examine it after it has been polarized. The first is called the POLARIZER, the second the ANALYZER. One of the simplest forms of the instrument is shown in the figure (Fig. 133). The polarizer, P, is a plate of glass, covered on the back of it with black varnish. The analyzer, A, is a plate NATUKAL PHILOSOPHY. 219 of tourmaline set into a movable tube. Objects to be examined by polarized light are supported in a movable ring O. Theory of Polarization. To explain the phenom- na of polarization, we must remember that light consists Fig. 133. of undulations, and add to this the assumption that the vibrations of the ether-particles take place in all possible directions at right angles to the direction in which the ray it- self is going. Let us for a moment suppose that we could see the ether, and that we look squarely at the end of a beam of light. We may fancy that we should see a circular outline, with the particles of ether moving swiftly in the directions of all its diameters. Let A (Fig. 134) represent this view. Now, the theory assumes that by refraction or Fig. 134. reflection, all these vibrations are changed into two sets, one in a horizontal plane, B (Fig. 134), and the other in a vertical plane, C (Fig. 134). This change is what is called POLARIZATION. The tourmaline plate, or the plate of glass, will let one of these sets of vibrations pass through it only when in certain positions, owing to some peculiar arrange* 220 NATURAL PHILOSOPHY. ment of its molecules, but when in position to cut off one set it allows the other to pass freely. Effects of Polarization. When a thin plate of mica, or other doubly refracting medium, is put at O, in the polari- scope (Fig. 133), the two beams emerging, ~by interfering, produce most beautiful colors. When seen in certain direc- tions, colored rings of surprising beauty, with a black cross, appear. The form and arrangement of these rings differ in different crystals a fact of much interest to the mineralo- gist. Some substances have the power to change the position of the plane of vibration, in a ray of polarized light. Thus if the analyzer (Fig. 133) is turned so that the polarized light is turned off, a thin plate of quartz at O will cause the ra}~ to re-appear. In this case suppose the vibrations to be in the vertical plane, and that the anatyzer is turned to the right just 10 ; the quartz must bend the plane of vibra- tion 10 to the right also, in order that the ray may pass. This is called ROTARY polarization. A great number of liquids have this power. Some of them turn the plane to the right ; such is a solution of cane- sugar : others turn the plane to the left ; such is a solution of grape-sugar. This fact is of great interest to the chem- ist, and it assists the physician at times to determine the healthy or diseased condition of the fluids of the human s}*stem. SECTION VII. REVIEW. I. SUMMARY OP PRINCIPLES. The undulations of the ether, expending their energy upon the e}'e and the sense of touch, are recognized as light and heat. These undulations are transmitted through all bodies with greater or less facility. NATURAL PHILOSOPHY. 221 Bui when they strike the surface of a second medium only a part of them enters : another part is thrown back, or re- flected, making the angle of reflection equal to the angle of incidence. All effects of mirrors are explained by this principle of reflection. The waves which enter the second medium are partly transmitted and partly absorbed. Those which are transmitted are bent, or refracted, mak- ing the index of refraction always the same for the same media, but different for different media. The effects of lenses are explained by this principle of refraction. Those waves which are absorbed in their passage through a body are transformed into heat or actinism, expending their energy in warming the body or in causing some chemi- cal change. In the sunbeam there are a multitude of waves of different rates. The prism is able to separate them, and when sep- arated the} T affect the eye as different colors. Color, there- fore, depends on the rate of the undulation, and is analogous to the pitch of sound. The intensity of light depends on the amplitude of the undulations ; it is analogous to the loud ness of sound. All the phenomena of color are explained on this principle of decomposition of light. The relation between wave-length, velocit}' in space, and y rate of the undulation, is shown by the formula L = - For light, the value of V is found by observations on the eclipses of one of Jupiter's satellites, and also by experiment. The value of L is found by experiment with Newton's rings and in other ways. The value of R may then be found by the formula. Velocity of light=186,000 miles a second. Wave-length, for red=. 0000266, and for violet =,00001 6 7 inch. 222 NATURAL PHILOSOPHY. Rate for red=392 millions of millions, and for violet=754 millions of millions a second. Undulations whose rates are less than that of the red are recognized only as heat, and those with rates above that of the violet are recognized only by chemical effects. Light and radiant heat may be polarized, but sound can not. This difference between light and sound is explained by supposing that the vibrations in the wave of light or heat are transverse, while in the wave of sound they are longitudinal. II. SUMMARY OF TOPICS. 68. Wave-front. Rays of light. Are transmitted. Light moves in straight lines. With uniform velocity. The law of intensit} 7 . Photometry. 69. Reflection. The law. Illustrations. Vision. 70. Mirrors. Effect of plane mirrors. Of concave mirrors. Foci. Effect of convex mirrors. 71. Images by reflection. Image of a point. Image by a plane mirror. 72. Images formed by a concave mirror. Images of points. Of an object beyond the center. Of an object between the center and focus. Of an object between the focus and the mirror. 73. Images by a convex mirror. 74. Reflection from rough surfaces. 75. Experiment showing refraction. Definition. The first law. The second law. Illustrations of refraction. 76. The index of refraction. The law. Index varies with the media. 77. Lenses. Effect of convex lenses. Foci. Effect of concave lenses. 78. Images are formed by lenses. Explanation. 79. Image of an object twice the focal distance. Of the object farther away. Of the object at less distance. Of Mie object between the focus and the lens. NATUKAL PHILOSOPHY. 223 80. Image by concave lens. 81. Prisms. Refract light. Also decompose light. Recombination of the colors. 82. A pure spectrum. The spectroscope. Fraunhofer's lines. The bright lines. Spectrum analysis. Invisible parts of the spectrum, heat. Another experiment, chem- ism. The energy of the sunbeam. 83. The equal diffusion of heat. Transmission of heat. Depends on temperature. Nature. Condition of surface. 84. The primary rainbow. Red on the outside. Colors in form of an arch. The secondary bow. 85. The color of bodies. The color of the sky. The color of the clouds. 86. Sound and light alike. Interference of sound. Of light. The conditions. Wave-lengths of light. The measurement. Color depends on rapidity of vibration. Diffraction. Explanation. Illustrations. 87. The microscope. Compound. The telescope, Gal- ileo's. The astronomical. The terrestrial. Reflectors. The Herschellian. The magic-lantern. The camera- obscura. The e3~e. 88. Double refraction. Both beams are polarized. Polarizing by reflection. Polariscopes. Theory of polari- zation. Effects. 224 NATURAL PHILOSOPHY. CHAPTER VIII. ON ELECTRICAL ENERGY. SECTION I. ON FRICTIONAL ELECTRICITY. 89. Electricity ma}' be produced by friction. The elec- trical machine is an apparatus for this purpose. It ma}' be detected by instruments called electroscopes, showing its action in two ways, by attraction and repulsion. Its intensity may be measured by instruments called electrome- ters. 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. (G. 704, 711, 714; A. 928-931.) Electricity produced by Friction. If a well-dried glass tube be thoroughly rubbed with a flannel cloth, it will be found to have new and curious properties. Hold 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 deli- cate bits of loose cotton, and the}' will rush toward it (see Fig. 135), 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. NATURAL PHILOSOPHY. 225 The Electrical Machine. The electrical machine is an apparatus for producing electricity by friction. It is rep- resented in Fig. 136. Its principal parts are, 1st, a body Fig. 135. upon whose surface electricity is to be evolved ; 2d, the rubber b} 7 the friction of which electricity is produced ; and, 3d, the conductor on which the electricity may be accumu- lated. 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. The rubber R is made of leather, covered with an amalgam made of mercury, tin, 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 upon a glass pillar. The conductor, or as usually called the prime con- ductor, C, is a brass ball, or a cylinder with rounded ends, mounted on a glass support. Connected with the prime conductor, is a brass fork F, one prong of which is on each side of the plate, with man}' sharp projecting points reaching toward the glass. 226 NATURAL PHILOSOPHY. Its Action. 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 arcund to the fork, and the prime conductor is thrown into the same electrical condition. We shall soon see how this action is explained on the principle of induction. The glass support prevents the electricity 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. When a machine of this kind, of medium size, is in suc- cessful operation, the effects of the glass tube are experi- Fig. 136. enced 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 fry to its surface ; and, if the knuckle or a brass ball be brought near, bright and zigzag sparks may NATURAL 227 be drawn through a distance of from one to two inches, the light being accompanied by a sharp report. Electricity detected by Electroscopes. When the electricity is feeble, there should be some more convenient way of showing its presence. Any instrument for this purpose is called an ELECTROSCOPE. The simplest form is called the pith-ball electroscope. It consists (see Fig. 137) of a ball of pith from the corn-stalk, or elder, hung by Fig. 137. a slender silk thread from a glass support. This little ball will instantly announce the presence of electricity by moving toward the body which contains it, and after a moment leaping away again. Two Opposite Actions. In this experiment the elec- tricity shows its presence both b} r attraction and repulsion. If the pith-ball of the electroscope be brought near to the prime conductor of the electrical machine, it will fly toward 228 KATtJfcAL PHILOSOPHY. 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 at- tracted. Notice, that the pith-ball is repelled by the elec- tricity of glass, and attracted by the electricity of sealing-wax. It is thus seen that the electricities of glass and sealing-wax 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 condi- tions without the other also. The positive always appears on one of the bodies rubbed together, and the negative upon the other. The 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. Thor- oughly rub the glass tube ; bring it in contact with the balls ; the}' both receive positive electricity from the tube, and it will be found that the}' will no longer remain in contact. We learn" from this experiment that two bodies with the same kind of electricity repel each other. Again : let the sealing-wax be thoroughly rubbed and brought near to the two pith-balls while the}' are repelling each other, and they will both fly toward it. We learn from this experiment that bodies with different kinds of electricity attract each other. . Bodies in the same electrical condition repel one another; in opposite conditions they attract. Application. This law furnishes an easy test by which to find out which kind of electric force is, in any case, pro- duced. Is the prune conductor of the electrical machine NATtTfcAL PHILOSOPHY. positive or negative? To decide the .question, rub the glass tube ; bring it in contact with the pith-ball of the electro- scope ; the electricity of the ball is thus known to be posi- tive. 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, be- cause, if the chain be removed, and the electrified pith-ball be brought near the brass mounting of the rubber, it will be attracted. 90. A charged or electrified bod}', acting through a non- conductor upon an insulated conductor, polarizes it. This action is called induction. (G. 722-726, 728.) A charged. Body. Whenever by friction, electricity is developed upon the surface of a body, the body is said to be electrified ; and if, by bringing another bod}' 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 be- comes charged. A Non-Conductor. rSome bodies allow electricity to pass freely over their surfaces ; such bodies are called CON- DUCTORS : 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 accumulat- ing. The brass allows the electricity to pass into the per- son ; 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. Potential. The electric condition of the earth is the standard with which to compare the electrfc conditions of other bodies. In the earth we suppose the -f- and electri- 2SO NATtTRAL PHILOSOFHt. cities to be just balanced : the electric power is zero. The term potential is used in comparing electric conditions. When the condition is the same as that of the earth, the potential is zero. High and Low Potential. When the electricity at any place is greatly in excess of that in the earth, it is described as a high potential. A less and less excess is spoken of as a lower and lower potential. And, when the electricity falls below that of the earth, the potential is negative. The potential of a bod}' is the difference between its electric power and that of the earth in its neighborhood. Electro-Motive Force. Now remember that electricity always passes from a place of high to one of lower poten- tial, as surely as water will run from a high to a lower level. And just as we speak of the force of gravity as the cause of the flow of water, so we speak of electro-motive force as that which urges electricity along over a conductor. Electro-motive force may be also described as the differ- ence in the potentials of two places. An insulated Body. Whenever a bod} T is quite sur- rounded 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. A charged Body polarizes an insulated Conductor. A bod}* 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 ma- chine, and let a small insulated con- ductor be placed near it (see Fig. 138). When the ball is charged, the motion of the pith-balls fastened to the small conductor shows that it is also electrified, and, if its electricity be tested, it will be found to be positive at one NATURAL PHILOSOPHY. 231 end and negative at the other. Both electricities are devel- oped upon its surface at the same time, and the body is said to be polarized. The action of the ball, by which this body is polarized, is called INDUCTION. 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 is positive electricity. This is always true : when a body is electrified by induction, the end or side nearest the charged body is al- ways in a condition opposite to that which develops it. The insulated conductor is electrified only when near to the ball. Let it be moved away, and the pith-balls drop. To charge it. But if, when the conductor is polarized, we touch it with the finger, the electricity which is like that of the charged bod}' will pass off, and the entire surface will remain charged with the opposite kind. It will remain charged, even when taken beyond the influence of the body which polarized it. 91. A series of insulated conductors, placed end to end, near each other, ma}' be all polarized by bringing a charged body near to one of them. Faraday's theory explains in- duction by supposing the molecules of a body to be polar- ized, one by another, in the same way. (G. 724, 726, 729.) A Series of Conductors may be polarized. Let a number of small insulated conductors be placed end to end, near together, with one end of the first one near to a brass ball connected with the prime conductor of the machine (see Fig. 139). The motion of the Fig> 139 ' pith-balls will show that they are all polarized. The effect will be greater if another brass ball, connected with the rub- ber of the machine, is placed at the other end of the series. The positive and negative electricities are on opposite ends 232 NATURAL PHILOSOPHY. of each conductor. All the ends toward the positive ball are negative ; all the ends in the other direction are positive. Faraday's Theory of Induction. 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 electrici- ties on its opposite sides. Difference between Conductors and Non-Conductors. The theory goes further, and supposes that the molecules of conductors discharge their electricity 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 conductors, as fast as they are polarized, give their electricit}' to their neighbors. The positive electricity given from one to another, in one direction, accumulates at one end of the conductor ; the negative, given from one to another in the other direction, accumulates at the other end. Polarization precedes Elec- trical Attraction. The first ac- tion of an electrified body is to polarize every other in its neighbor- hood. The attraction of pith-balls or cotton (Figs. 137 and 135) by the excited glass takes place after they have been polarized. Illustration. Fig. 140 shows a chime of bells, which are to be rung by electricny. The two out- Pig. 140. side be | ls are f astene( j b meta j chains to a rod of metal which hangs from the end of the, NATURAL PHILOSOPHY. 238 prime conductor of an electrical machine. The middle bell is hung by a silk thread, and has a chain passing from it to the floor. Finalh r , notice two little balls of metal between the bells ; these balls are hung by silk threads also. When the machine is in operation, these little balls will fly back and forth and ring the bells merrily. Now when the outside bells are -f, they polarize the balls. The sides of the balls nearest the bells are , and hence bells and balls attract. The balls then strike the bells, become -f- b}' contact, and balls and bells repel. The middle bell is polarized : the + balls strike it, and discharge their electricit}', which passes off into the earth by the chain. This series of actions is repeated over and over again. Polarization, attraction, charge, repulsion, discharge, follow repeated!}' in regular order. Iii the Electrical Machine. We are now prepared to see how the prime conductor of the electrical machine be- comes charged. The glass plate near the fork is electrified with -f electricity. It polarizes the prime conductor near it. The electricity which accumulates in the adjacent end is discharged from the points of the fork upon the surface of the glass, and this leaves the conductor charged with + electricity. 92. The Holtz machine is an in- strument with which to develop electricity by the continuous induc- tive action of an electrified body. (G. 736.) Description. Fi - 141 - One form of the Holtz machine is shown in Fig. 141. Two thin glass plates are insulated, as near together as 234 NATURAL PHILOSOPHY. possible without touching. The larger plate is stationary, while the smaller one may be rotated very swiftly by a wheel and pulley. Two windows are cut in the stationary plate, and two paper sectors, called armatures, are ce- mented against the back side of it, on opposite sides of the windows. From the edge of each sector a set of points project into the window. Opposite these points, and sep- arated from them by the revolving plate, are two brass combs. These combs are also connected each with a brass ball in front of the machine, and these balls are on sliding rods so that the distance between them may be changed at will. Each comb and ball are in connection with the in- side of a Leyden-jar, which we shall very soon describe, while the outsides of the jars are joined by a chain. Its Action. To put the machine in action, one of the ai-matures is first electrified by bringing an electrified piece of vulcanite against it, and then turning the wheel. In a few seconds the difference of potential in the two jars be- comes so great that they discharge in a series of vivid sparks leaping between the balls in front. Explanation. The -f- armature polarizes the comb in front of it, and attracts the electricity which is projected from its points upon the surface of the revolving plate, leav- ing the comb charged with + electricity. The other arma- ture is , and by a similar induction causes a charge in the other comb. These + and charges accumulate in the Ley- den-jars until they discharge between the balls. Such, in a general way, is the theoiy of the Holtz, but the details of its action are complex and puzzling. For a full explana- tion the student may consult a larger work on physics. 93. The Leyden-jar is an apparatus for accumulating elec- tricity 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 mak- ing a conducting communication between its two coatings. HATURAL PHILOSOPHY. 235 Pig. 142. The Leyden battery consists of several Leyden-jars con- nected. (G. 743, 757, 758 ; A. 945.) The Leyden- Jar. The Ley den-jar consists of a glass jar, coated both inside 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 conducting sur- faces, separated from each other by a non- conductor. Various Forms. This idea may be em- bodied in a variety of forms, any one of which will act on the principle of the Leyden- jar. 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, illus- trates the same idea : the glass, a non-conductor, separates two conducting surfaces the water on the inside, and the hand upon the outside. It may be charged. By bringing the ball of the Ley- den-jar in contact with the prime conductor of the machine, positive electricit}' passes into the inside coating. This posi- tive electricity polarizes the glass and 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 thus leave the outside coating permanently charged with negative electricity. When by this action the two coatings have opposite elec- tricities, the jar is said to be charged. It may be removed from the prime conductor, and remain charged, because the two electricities attract each other without a chance for dis- 236 NATURAL PHILOSOPHY. charge through the glass. The jar may be handled without danger, if care be taken not to touch the ball and the out- side at the same time. The jar is charged with positive electricity when the in- side is positive : it is charged with negative electricity when the inside is negative. It may be discharged. The difference of potential between the inside and outside is very great, and, when a con- ducting communication is made between the two coatings of the jar, the electricity passes until equilibrium is restored, and the jar is said to be discharged. The conducting com- munication may be made in many waj's. 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, ma}* 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 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. The Leyden 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 sur- faces are all connected by conductors reaching from knob to NATUKAL PHILOSOPHY. 237 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 same extent of surface. 94. The electricity of the atmosphere is of the same nature as that produced by friction. Lightning is the dis- charge of oppositely charged clouds, illustrating, on a grand scale, the action of a Leyden-jar. 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 electro- scope will usually indicate positive electricity, its intensity increasing as the air from which it 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 thunderstorm these changes follow each other, at times, with remarkable swiftness. It is of the same Nature as frictional Electricity The bright flash and loud report which announce the dis- charge 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 which he employed. 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 238 NATURAL PHILOSOPHY.. 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 b}' 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 an}* sign of electricnVy. He was about to give up in despair, when he caught sight of some loose fibers of the hempen cord bristling up as if re- pelled. He immediately presented his knuckle to the ke} r , and received an electric spark. The string of 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 electricit}'. Lightning 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-con- ductor 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. Consider- ing the large extent of cloud surfaces discharged, we need not be surprised at the magnitude of the spark, nor at the deep intensit} r of the sound. When the discharge is not hidden by clouds, we can trace the whole length of the spark, and we witness chain-light- ning : but at other times the spark is behind the clouds ; we see only the light of the discharge spread over the surface of the clouds, and this gives rise to what is called sheet- lightning. At times the earth and a cloud are the two charged sur- faces, 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 NATURAL PHILOSOPHY. 239 in its passage. In going from a cloud to the earth it takes these bodies in its way ; animals are often killed, trees shat- tered, and buildings torn to pieces or set on fire. 95. A bod}* having points projecting from its surface can not be charged even when insulated. Or, if a pointed con- ductor be held toward its surface, it will prevent a charge from accumulating. Upon this principle, buildings are pro- tected from the effects of lightning by lightning-rods. The effect of Points. It is found to be impossible to charge a conductor when there are sharp points on its surface, or held near to it. 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 from 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 mole- cules become polarized, and are first attracted to the point and then repelled. On coming in contact with the point, the} 7 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 the point on the prime con- ductor, it will be blown away from it, and may even be extinguished. Lightning-Rods. We have seen that because build- ings are better conductors of electricity than air, they are liable to injury from strokes of lightning. But, since pointed conductors silently discharge the force from a charged body, 240 NATUBAL PHILOSOPHY. why not disarm the cloud of its lightning by the use of pointed metallic rods? This question was no sooner sug- gested 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 lightning-rods. The} r should be made of metallic rods, pointed at the upper end, reaching several feet above the highest part of the building which the}' are designed to protect, and downward, without interruption, into the ground below its foundation, far enough to be always in moist earth. 96. The effects of frictional electricity are mechanical, chemical, and physiological. (G. 760-762, 770; A. 949, 951.) Mechanical Effects. We have already had abundant illustrations of motions caused by electricit}'. Poor con- ductors 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 cardboard ; the card will be pierced with a burned or ragged perforation. This effect is produced on a large scale by the lightning-stroke ; even rocks are sometimes shattered, while trees are often splin- tered from top to root, and their fragments scattered far and near in all directions. Chemical Effects. The chemical effects of electricity are shown through the agency of the heat which it de- velops. To illustrate by experiment : wrap the ball of a Le}'den-jar with loose cotton, and sprinkle upon this, very finely powdered resin. This done, charge the jar power- fully, 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. Physiological Effects. The effect of electricity upon NATURAL PHILOSOPHY. 241 the human system is peculiar and startling. No descrip- tion 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 Lej'den-jar, and with the other hand touch its knob. He will find that he 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 all at once experience these effects. SECTION II. ON MAGNETIC ELECTRICITY. 97. Magnets are either natural or artificial, and may be made in different forms ; but in any form the magnetism is stronger at the ends than in the middle. The ends are called poles. (A. 967, 974; G. 670, 895.) Magnets. Bodies that attract iron in preference to other metals are called MAGNETS. Fragments of an ore of iron are sometimes found, which have the properties of a magnet. Such a fragment is a NATURAL MAGNET or LODE STONE. If a bar of iron or steel be rubbed against a magnet, it will become magnetic ; it will then be an artificial magnet. Soft iron or steel will lose its magnetic properties quick!}' ; hardened iron or steel will retain them. 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 (see Fig. 143) ; its ends are thus brought near together. A piece of soft iron acro3s the ends, N S, is tailed the armature. 242 NATURAL PHILOSOPHY. Experiment. To illustrate their peculiar preference for iron, let some iron-filings be mixed with some filings of brass ; bring one end of the magnet among the filings, and on removing it great numbers of the iron parti- cles will be seen clinging to it, while the brass particles are all left behind. 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 cling- ing to its ends, their numbers get- ting less toward the middle of the bar, where very few, if an}', will be held. (Fig. 144.) By this experi- ment we learn that the magnetism is not equally distributed over the sur- faces of magnets, but, on the con- trary, that it is 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. Magnetism shows itself both ig. 143. ky a tt rac ti on an( j repulsion, obe}'ing the following law : Poles of like names repel each other ; those of different names attract. Attraction and Repulsion. Iron which is not mag- netized will be attracted equally by both poles of a magnet ; it is not so when two magnets act upon each other. By pre- senting the south pole of a magnet to the north pole of another, it will show an at- traction for it, while the north pole, being presented to the north pole, will repel it. Thus magnetism, like electricity by friction, shows itself by both attraction and repulsion. NATURAL PHILOSOPHY. 248 It is also evident from these experiments that poles of the fame name repel, while those of opposite names attract. 99. A magnet, like a charged body, will polarize a bar of iron brought near to one of its poles, always inducing mag- netism 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 eveiy 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. (G. 669.) A Magnet will polarize a Bar of Iron. If a bar of iron n s, and a magnet N S (Fig. 145), be placed end to end, the iron itself becomes a magnet. That it is a magnet, may be shown by its power to attract or repel the poles of another magnet. Both kinds of magnetism are developed in it, and hence we call it polarized. Each pole of a magnet will always induce the op- posite kind of magnetism in that end of the bar which is nearest to it. Unlike frictional electricit3 r , there is no discharge of magnetism when opposite kinds are brought to- gether : the polarization takes place even when the lg * 14 ' bar is in contact with the magnet, and, if the bar be made of steel, the polaritj^ remains after the magnet is removed. Several Bars may be polarized. A second bar may be placed with one end near to the first, and it will 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 by experiment : from the north pole of a strong bar magnet hang a key ; from the lower end of this one a smaller key ma}' be hung ; a third still smaller, or a nail, will be held by this^, and a tack will cling to the lower end of the last. The series of keys and 244 NATURAL PHILOSOPHY. nails has become a series of magnets, each with its north and south pole, their north poles all directed downward. (See Fig. 146.) All the Molecules of a Magnet 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 trans- fer 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 bod}~ charged with electricity, may polarize an- other, but it can not, like the charged body, become neutral by giving up its force. then, is the middle of a magnet neutral, F- 14( * while only toward its ends do the forces show them- selves ? Not because the force of one kind leaves the mole- cules of one end and goes to the other, but because 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 freely 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. (G. 679.) If a Bar Magnet be supported. A magnet may be supported in three ways so as to have free motion. It ma}' be balanced upon a pivot. (See Fig. 147.) It may be hung from a fixed support \>y a fine thread tied about its middle point (Fig. 148). Or it may be, for purposes of simple experiment, fastened to a cork, and laid upon water. NATURAL PHILOSOPHY. 245 It will point North and South. The magnet sup- ported 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 magnetic pole of the earth toward which it points. 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 this purpose it is placed J over a card upon which the "points of com- pass,' ' north, south, n \ & east, west, and others, are marked ; and, for protection, put into a 147 ' box supported by pivots, vis ' 148 ' so that it will keep the needle in a horizontal position amid all the rolling or plunging motions of the ship. Such an arrangement is called the MARINER'S COMPASS. Its Variation. While it is true that the needle points in a direction which ma} r be described as north and south, we must not understand that this description is exact. In- deed, 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 VARIATION. The Line of no Variation. If those places on the earth's surface at which the needle points due north and south be joined by a line, this line is called the LINE OF NO VARIATION. This line goes quite around the globe in a north and south direction. It is, however, an irregular line, bend- ing now to the eastward and then to the westward. We 246 NATUBAL PHILOSOPHY. may trace its general course through North America, by remembering that it strikes the continent near Cape Look- out, on the coast of North Carolina, passes through Staunton in Virginia, a little east of Cleveland in Ohio, across Lake Erie, and thence onward to Hudson Bay. At places east of this line the variation is toward the west ; at places west of it the variation is toward the east. The Annual Variation. The variation of the needle at any place is continually changing. For example : the variation at Washington, D.C., was 36' west in the year 1800, but in 1860 it had increased to 2 54'. Such a change is going on }'ear by year at all places. The variation in- creases for several years, and then again diminishes. So the needle vibrates, first westward, then eastward, and back again, taking man} 7 years to make a single vibration. The Daily Variation. Besides this annual variation, the needle has a daily variation, much greater in summer than in winter amounting to about 15' in the former, and only about 10' in the latter. At about 8 A.M., the^orth pole begins to swing westward, and this motion continues until about 1 P.M. Soon after this time it slowly moves back toward the east until, at about 10 P.M., it has reached its starting point. It then moves west again until about 3 A.M., after which it swings back to the eastward until 8 A.M. It completes these two full vibrations every twenty- four hours. 101. If a magnetic needle be allowed to move freely up and down, it will seldom rest in a horizontal position. Its inch' nation is called the dip of the needle. In the northern hemisphere the north pole of the needle dips ; in the southern hemisphere the south pole dips. The Dip of the Needle. If a slender steel needle be balanced upon a horizontal axis so that it may freely move up and down, and be then magnetized, it will be no NATURAL PHILOSOPHY. 247 longer balanced : the north pole will sink until the needle takes a position very much inclined (Fig. 149). The amount of this inclination is called the DIP OF THE NEEDLE. In the southern hemisphere the needle also takes an in- clined position, but it is the south pole that points downward. As the dipping needle is carried farther north, the dip increases until a point is reached where the needle stands in a vertical position. Of course this point must be the north magnetic pole of the earth : it is a curious fact, that it is not the same as the geographical north pole. It is in latitude 70 5' N. and longitude 96 45' W., a little north and west of Hudson Ba year 1832. Then, traveling southward in the southern hemisphere, the south pole of the needle dips more and more, and there is evidently a south magnetic pole of the earth. This point has never yet been found. Fig. 149. It was found by Capt. Ross, in the X SECTION III. ON DYNAMICAL ELECTRICITY. 102. A current of electricity may be obtained by chemical action in a simple voltaic cell, or better in a Grove, a Bunsen, or other form of battery. (G. 772-774, 783.) 248 NATURAL PHILOSOPHY. Different Names used. Frictional electricity shows itself by a single discharge, or, in the case of the sparks of a Holtz machine, in a series of discharges which follow at intervals ; but in DYNAMIC electricity there is a continuous action like the steady flow of a stream, and hence it is ver}* properly called CURRENT electricit}*. Because it was discov- ered by Galvani it has been called GALVANIC electricity ; and, because of Volta's valuable researches, it is also known as VOLTAIC electricity. Chemical Action. Put some bits of common zinc into a goblet, and pour upon them some weak sulphuric acid. The fluid \fdll soon begin to boil violently, and bubbles of Ivydrogen gas will be given off, so that often, if a lighted match is held near, the gas will take fire. This will give the curious appearance of water on fire. After a while the action will stop, but not until much and perhaps all the zinc has been used up. In this case both the zinc and the acid are changed into other substances, and on this account the action is called a CHEMICAL ACTION. None with Pure Zinc. Common zinc is impure, and if the pure metal be used for the ex- periment almost no chemical action will occur. Or let the zinc be amal- gamated, that is, covered with a coat- ing of mercury, and there will be very little chemical action. No bubbles of gas form where cop- per is used instead of zinc. The Simple Cell. The simple cell is represented in Fig. 150. Into a glass vessel is put a quantity of water, mixed with a little sulphuric acid. A strip of copper and another of amalgamated zinc are inserted in this liquid, and from the upper ends of these strips two metal- NATURAL PHILOSOPHY. 249 lie wires project. Now, when these two wires are brought together, a multitude of little bubbles of gas rising alongside of the copper strip show that there is chemical action ; and, if the ends of the wires be brought together and then carefully separated in the dark, a very delicate spark may be seen between them, showing that electricity is produced. The Chemical Action. The zinc takes the place of Irydrogen in the acid, and forms zinc sulphate. This re- mains dissolved in the fluid while the hydrogen is forced along from molecule to molecule through the acid until it reaches the copper plate where it escapes in bubbles. This chemical action is believed to be the chief source of the electricity in the circuit. The electric Conditions in the Cell. The zinc in. the acid is positive, the copper negative. In other words, the surface of the zinc has a high potential, the surface of the copper a low potential, and hence electricity passes from zinc through the liquid to copper to restore the equilibrium. But the chemical action again quickly renews the difference of potential, and another discharge follows. A very rapid charge and discharge throughout the circuit so rapid as to seem continuous is what is called the ELECTRIC CUR- RENT. The Direction of the Current. From the -f- or gen- erating plate (which is always the metal acted upon by the fluid) the + electricity passes through the liquid to the plate, then through the wires back to the -f- plate. The Poles. The ends of the two wires are called the POLES or the ELECTRODES of the circuit : that from the cop- per strip is the positive pole ; the one from the zinc strip is the negative pole. Enfeeblement of the Current. The current in this simple cell rapidly grows weaker. There are three principal reasons for this ; viz. : First, The acid is being neutralized by the zinc. The chemical action diminishes on this account. This difficulty 250 NATURAL PHILOSOPHY. can only be remedied by renewing the acid from time to time. Second, There is local action, that is, an action between the impurities and the particles of the generating plate, by which a multitude of little circuits are made, so that the energy of the plate is not thrown into the general current. This difficulty can be remedied by amalgamating the zinc, which is done by immersing the clean zinc in mercury. No chemical action then occurs until the wires are brought together, or the circuit is closed. Third, There is the " polarization " of the negative plate. A layer of hydrogen gradually fixes itself upon the surface of the copper, and we have a surface of Irydrogen instead of copper. The plate, in this way, gradually becomes + instead of , and the difference of potential disappears. This difficulty can be remedied only by managing to use up the hydrogen in some way, so that it shall not come in contact with the plate. This may be accomph'shed by using a second fluid. In Grove's Cell. In Grove's cell two metals, zinc and platinum, and two liquids, dilute sulphuric acid and nitric acid, are used. The peculiar mode of putting these together may be understood by an attentive stud} T of Fig. 151. A glass vessel, V, is partly filled with dilute sulphuric acid. Into this fluid is placed a zinc cylinder, Z, with a slit from top to bot- 151. tom ^ to a u ow foe fluid to circulate, both inside and outside of it, freely. Inside of the zinc cylinder is put a porous earthenware cup. Into this cup is poured strong nitric acid, and a strip of platinum is inserted in this fluid. One wire is fastened to the zinc, and another to the platinum. These may be brought together to close the circuit. The platinum pole is positive; the zinc pole is negative. What becomes of the Hydrogen ? There is the same chemical action as in the zinc-copper or simple cell, but the NATURAL PHILOSOPHY. 251 hydrogen, on its way to the platinum, must enter the nitric acid. The nitric acid is decomposed by the hydrogen which takes oxygen from it, and the two remain in the harmless form of water. Bunsen's Cell. Bunsen's cell (Fig. 152) differs from the one just described, by having a carbon cylinder, or rod, Fig. 152. fn place of the strip of platinum. This does not greatly diminish its action, while it makes it much cheaper, plati- num being a very costly metal. Other Forms. There are man}" varieties of voltaic cell in market. They are made by ingeniously varying the materials and shape to fulfil the condition for a current. This is the Condition. There shall be two metals and a liquid so related that the liquid shall act chemically upon one more than upon the other. 252 NATURAL PHILOSOPHY. 103. Ohm's law states that the strength of the current is equal to the electro-motive force divided by the resistance. Definitions. "The force by which electricity is set in motion in the circuit is called the ELECTRO-MOTIVE FORCE." It is commonly regarded as the difference of potentials main- tained by the cell. " The quantity of electricity which, in a unit of time, flows through a section of the circuit, is called the STRENGTH OF CURRENT." It is also called INTENSITY. No substance is a perfect conductor of electricity, and some substances forbid its passage altogether. This opposi- tion to the passage of the current is called RESISTANCE. The resistance which a wire offers to the action of elec- tricity through it depends upon the material of which it is made, and upon its size. The metals are the best con- ductors, silver standing at the head of the list, copper next, and lead being among the poorest. The larger and the shorter the wire, the less resistance it offers. The Formula. The relation of these values as stated above in Ohm's law may be simply expressed in the formula, -p (7= -^; in which C stands for strength of current, E for the H electro-motive force, and R for the resistance. 104. The resistance in a circuit is partly in the cell, internal, and partly in the conductors outside, external. The best effect is obtained in the use of a battery when the internal and external resistances are equal. If the resistance to be overcome is small, we need a battery of low resistance ; but, if it is great, a battery of high resistance. A Battery of Low Resistance. The resistance in the cell depends chiefly on the fluid, because the Conductivity of the metals is so vastly greater than that of the fluid. Now, we have seen that the resistance of a conductor NATURAL PHILOSOPHY. 253 depends on the area of its cross section. If we enlarge the plates in the cell we make the area of the conducting liquid between them larger, and so diminish its resistance. This is most conveniently done by taking several common cells, and joining all their zincs together by a wire outside, and all their coppers by another wire. This forms a battery of low resistance. It is sometimes called a battery for quantity. Its Electro-Motive Force. In the zincs, all joined together, there is the same potential as if there were only one alone. There is no greater difference of potential in zincs and coppers than if there were a single cell ; that is, the electro-motive force is not increased. Its Strength of Current. By linking cells in this way, the internal resistance is diminished, while the electro-motive force remains the same. If there were no external resistance, E then R in the formula G = -= would be less and less as the H TF number of cells increases, and hence -= would be greater ; that is, the strength of current, C, would be greater in pro- portion to the number of cells. Hence, when in using electricity, there is little external resistance, a loio-resistance battery should be used. A Battery of High Resistance. We may link the cells together in another way. Let the zinc of one be joined to the copper of the next, and its zinc with the copper of the next throughout the series, and finally close the circuit by joining the first copper with the last zinc. This forms a battery of high resistance. It is sometimes called a batteiy for intensity. Its Electro-Motive Force. In this case each zinc acts separately, and the electro-motive force of the battery is the sum of the electro-motive forces of the separate cells. For n cells of the same kind it would be n E. The Resistance, The internal resistance is also in- 254 NATUKAL PHILOSOPHY. creased in the same ratio, for a dozen cells yield a dozen times as much resistance as one cell. But the external re- sistance is not at all affected by changing the number of cells ; and if we suppose it to be very, very much greater than the internal resistance of one cell, it would also be much greater than the resistance of a dozen cells, and the total resist- ance may be very little greater with n cells than with one. The Strength of Current. Then in the formula C = -. R' with n cells the numerator is increased to n E. while the denominator remains almost unchanged. Hence C is in- creased almost n times. That is : The strength of current increases almost in proportion to the number of cells. Hence, when in using electricity, there is great external resistance, a high-resistance batter}* should be used. Quantity and Intensity. Large surfaces of elements in the battery yield large quantities of electricity : a large number of cells in series yields electricity of great intensity. The greatest difference between current electricity and frictional electricity is this : current electricity is remarkable for its great quantity but feeble intensity, while frictional electricity is equally remarkable for its great intensity but small quantity. 105. Current electricity produces : Heat whenever it is resisted in its action. Light whenever its intensity enables it to leap through air, or to render a poor conductor incandescent. Magnetism whenever its conductor encircles a bar of iron. Chemical action whenever it goes through an electrolyte. (G. 809-813, 816-820, 854, 856.) Heat. Electricity, when resisted in i x s action, shows itself as heat. When it acts through a fine wire, the wire may be made red-hot, and in man}' cases melted, by the Jieat produced. Several inches of fine iron wire may be thus NATURAL PHILOSOPH t. 255 melted by a batteiy of twelve or fifteen cells. This power of electricit} 7 is applied to the exploding of gunpowder, for blasting rocks. For this purpose, a cartridge is made by filling a tin tube with gunpowder, and corking its ends tightly. Through one of the corks two copper wires pass, joined in the powder by a fine steel wire soldered to their ends. The copper wires are then connected with the poles of a distant battery. The instant that the circuit is made, the fine wire in the gunpowder becomes intensely hot, and its heat explodes the gunpowder. Light. When the wires which lead from the poles of a powerful battery are tipped with charcoal points, if these points are brought in contact and then separated for a short distance, the space between them will be bridged over by an arc of blinding light. On examination, this light is found to be due to the intense whiteness of the carbon tips, chiefly, but not to their combustion, since in a vacuum, where com- bustion can not occur, the light is of equal intensit}'. The heat of this arc of light is wonderfully intense. Platinum, more difficult to melt than other metals, melts in this heat like wax in the flame of a taper. Even quartz, and other bodies equally difficult to melt, are fused by it readily. The electric light is produced not only by the "electric arc," but also by "incandescence." If a platinum wire, or a small rod of carbon, is placed in the circuit of a battery of high resistance, it will be heated intensely, and glow with a fine white light. Electric lamps arc of these two classes : some are con- structed to yield the light by the arc, others to 3*ield it by incandescence. Mag-iietism. Bars of soft iron inclosed in coils of wire are called ELECTRO-MAGNETS. The coil is generally called a HELIX. If the two ends of the coil be fastened to the poles of a battery, the electricity darts instantly through the coil, ancl the iron becomes a magnet. The bar of iron may 256 NATURAL PHILOSOPHY. be of an}' form ; when in the shape of the horseshoe mag- net, the coil is made in two parts, one encircling each arm of the iron. A horseshoe electro-magnet, A B, is seen in Fig. 153. The strength of electro-magnets is something surprising. One belonging to Yale College, weighing 59 pounds, lifted a weight of 2,500 pounds. This wonderful power is developed only when an armature, c d (Fig. 153), is in contact with the poles. Without this, the magnet will not lift a tenth part of what it could otherwise sustain. The iron is magnetic only while the electricity acts around it. Let the circuit be in an}' wa}" broken, and the grasp of the giant is at once loosed ; the load falls. On again making the cir- cuit, the magnet is instantly as strong as before. The rapidity with which an iron bar will thus receive and part with its magnetism, as the circuit is made and broken, is truly astonishing. B}- the electric register for vibrations, the author has caused an electro-magnet to un- dergo this change at the rate of 8,400 times a minute. Yx' The Electric Telegraph acts on this Principle. It is upon this principle that the electric telegraph has ena- bled man to send his thoughts, with lightning-speed, across continents and under oceans, to his most distant fellow- men. Having found that a bar of iron will become magnetic as NATURAL PHILOSOPHY. 257 often as electricity is sent round it, and cease to be so on the instant the circuit is opened, let us next notice that the wires conveying the force may be of any length, even miles, and hence the battery may be in one city, while the magnet may be in another, and still an armature will be drawn against its poles ever}* time the circuit is made. Now, if the motion of an armature to and from the poles can be made to write, then can messages be sent from one city to another. The apparatus consists of three parts : the key, the line, and the register. The Key is an instrument by which the circuit can be made and broken at will. It is in the office from which the message is to be sent. A brass lever, L (Fig. 154), moves on an axis, A. Two projections, n and m, from its lower side, are just above two others, one of which, a, is joined by a wire with the battery, while from the axis, A, another wire reaches to the distant sta- tion. By pressing the fin- ger on the end of this lever, the point is brought in contact with the battery- wire at a, and the electricity can then act through the lever, from the battery-wire to the wire from the axis. Let the finger be lifted, and the lever will rise by the action of a spring, s, and the circuit is broken. The Line consists of a wire, L, reaching from the key over the country to distant places. At first two wires were used, one from the positive pole, the other from the nega- tive pole, of the battery ; but it was soon found that the earth may take the place of one of these wires. The Register is shown in Fig. 155. One of the screw- cups at the end of the instrument is connected with the line wire, L, which reaches from the key of the distant station, while the other, M, is connected with the earth. When tho 258 NATURAL PHILOSOPHY. circuit is made, the electric force darts around the electro- magnet, and draws the armature down against its poles : this raises the long arm of the lever, and presses the steel point, I, against a strip of paper, which is pulled along from the spool, E, by clock-work. When the circuit is broken, the armature is released from the poles of the electro-magnet ; the long arm of the lever falls by its own weight, or by the force of a spring, and the point is removed from the paper. If the point press the paper for an instant only, a dot will Fig. 155. be made, but, if it be held against it for a longer time, a dash will be left upon it. Now, the letters of the alphabet are represented by dots and dashes. Two operators who know this alphabet can communicate with each other ; one by pressing the key causes a series of dots and dashes to be marked upon the paper of the register at a distant place, while the other can read this written language. A skillful operator knows the letters by the sound of the clicks of the instrument. He uses a " sounder " instead of a writer. Such is an outline of the essential parts of the electric NATURAL PHILOSOPHY. 259 telegraph. A larger work, or, better, a visit to the tele- graph-office, will make one full}- acquainted with the many details of its operation. The steam-engine and the electric telegraph may be re- garded as the body and the spirit of modern civilization, the first distributing matter, the second thought; both laboring toward a more general diffusion of comfort and knowledge and s} r mpathy among men. Chemical Action. Acidulated water will be decomposed by the current when the electrodes of a battery of two or mdre cells in series are immersed in it. The electrodes of the battery (Fig. 156) pass up through the bottom of a vase into the very dilute acid, and two tubes filled with the liquid are inverted over them. The moment the circuit is closed, a multitude of gas-bubbles break from the electrodes, and are caught in the tubes above. These gases prove to be hydrogen and oxygen, the constituents of water. Various other liquids may be decomposed by the current ; all such are called ELECTROLYTES. 260 NATURAL PHILOSOPHY. Fig. 157. 106. The current swaj's a magnetic needle near which it flows. The galvanometer detects and measures the current on this principle. Effect on the Needle. Let a magnetic needle be placed in a rectangle of wire provided with pole-cups as shown in Fig. 157. It will be found that whenever the current flows through the wire, the needle will turn. The current tends to put the needle at right angles to its own direction. If the current pass from south to north, above the needle, the north pole will turn to the west; if from north to south, the north pole will turn to the east. If the current pass below the needle, the north pole turns in direc- tions opposite those just mentioned. The motion of the needle declares the presence of a cur- rent ; the direction of the motion tells the direction of the current ; and the distance the pole moves measures the strength of the current. The Astatic Needle. This consists of two needles fastened together with the north pole of one opposite the south pole of the other. The ends of this needle are equally attracted and repelled by the earth's magnet- ism. But the north pole is usually left a little stronger than its com panion, so that the earth's magnet- ism is not quite neutralized, and the needle will be ' ' true to the pole," although with a ver} T feeble force. The Galvanometer. A sen- sitive form of this instrument is shown in Fig. 158. Fig. 158. NATURAL PHILOSOPHY. The astatic galvanometer consists of a coil of very fine silk-covered copper wire wound on a flat wooden bobbin ; an astatic needle, the upper half near the upper plane-sur- face of the helix, the under one in the middle section of the helix ; the needle is suspended by a silk fiber ; a graduated circle is placed under the upper needle ; the coil rests on a mahogany base with leveling screws, and is covered by a glass shade. (Ritchie.) 107. Induced or secondary currents are developed in a conductor : 1st, B}- the approach or departure of a batter} 7 current. This principle is embodied in the Ruhmkorff coil. 2d, By the approach or departure of a magnet. This principle is embodied in magneto-electric machines and the telephone. (G. 874-876, 883, 886, 889.) I. INDUCTION BY A CURRENT. Description of Apparatus. Two coils, one containing a few feet of stout copper wire, and called the primary coil, and another containing a very great length of fine copper wire, and called the secondary coil, are so made that the primaiy may be placed inside the secondary or taken out at pleasure (Fig. 159). The primary is connected with a battery, and the secondary with a galvanometer. Results of Experiment. While the primary is passing into the secondary coil, the galvanometer needle swings, show- ing a current in the secondary moving in a direction opposite to that of the battery current. It is called an inverse cur- rent. While the primary is being withdrawn, the needle swings the other way, showing a current in the secondary coil moving in the same direction as the battery current. It is a direct current. But the current may be introduced into the secondary coil, and withdrawn in another way. We may leave the primary 232 NATURAL PHILOSOPHY. coil inside the secondary, and then simply close and open the battery circuit. On closing the circuit the current darts through the primary coil, and on opening it the current ceases. Now we find that on dosing the primary circuit, the motion of the galvanometer declares an inverse current in the secondary coil. On opening the primary circuit, the motion of the galvanometer shows a direct current in the secondary coil. Fig. 159. Induction Coils. It is upon this principle of induction that the Ruhmkorff coils are constructed. In these impor- tant instruments there is first a primary coil of large copper wire, inside of which is put a bundle of iron wires. Outside of this is placed the secondary coil, which is made of fine copper wire many thousands of feet in length. The two coils are insulated from each other with the utmost care. The ends of the primary coil are attached to the battery, while from the ends of the secondary coil the electricity is taken in experiments. Ritchie's Induction Coil. The induction coil, as con- structed by Ritchie, is represented in Fig. 160. The primary consists of about 200 feet of stout copper wire. The sec- NATURAL PHILOSOPHY. 263 onclary contains about 68,000 feet of fine copper wire. The two are separated by a thick glass bell whose knob is seen at the top. The primary circuit is opened and closed by a toothed wheel, b. The ends of the secondary are fastened to sliding rods on glass supports. When the poles of a battery are placed in the bind- ing-posts s and c, let the circuit be opened and closed by turn- ing the toothed wheel 6, and electric sparks in rapid suc- cession will leap through the air be- tween the ends of the insulated rods. The length of the ~~Fig7i0o. spark depends upon the size and insulation of the coils, and the strength of the 6atteiy. The instrument just described is able to yield a spark nine inches in length. II. ^-INDUCTION BY A MAGNET. Results of Experiment. It is found that if a magnet be used instead of the primary coil in Fig. 159, the same effects are produced. Hence the motion of a magnetic pole induces a secondary current, in one direction as it enters, in the other as it emerges. If a bar of soft iron be placed in the secondarj^, and then a pole of a magnet be moved toward and from it (Fig. 1G1), the same effects will be produced. The soft iron becomes a magnet by the approach of the pole, and loses its magnetism when the pole departs. This is, in effect, onh' another way to introduce and withdra-w the magnet. 264 NATURAL PHILOSOPHY. Finally, insert a permanent magnet in the secondan* coil, and move a bar or disk of soft iron toward and from its pole : currents in the coil are induced by this motion. The soft iron becomes magnetic by induction, and then affects the magnet in the coil, strengthening it b}* approach and weakening it by departure. Hence an}* change in the strength of a magnet will induce an electric current in a coil which surrounds it. Fig. 161. Magneto-Electricity. Electricity induced by a magnet is called MAGNETO-ELECTRICITY. Man}' forms of apparatus have been devised with which to generate magneto-electricity, and the currents of enormous power, needed for electric lighting and other applications of electricity in the arts and industries, are produced b}' late and powerful forms of these " dynamo-electric machines." A Simple Form In this instrument (Fig. 162), two coils of wire, W, inclose the two arms of a bar of soft iron, having the form of a horseshoe magnet, which by a band and wheel, M, can be put in rapid motion in front of a ven r pow- erful compound magnet, S. The soft iron becorrtes magnetic NATURAL PHILOSOPHY. 265 whenever its ends are in front of the poles of the permanent magnet, and hence its two branches are being alternately magnetized in opposite states at every turn. The effect of Fig. 162. this is to produce two opposite currents in the coils at every revolution. These currents are taken by the wires, e, and thence under the instrument to the screw-cups, K and P.-'//^ The Telephone. Any instrument for transmitting sound to a distance is a TELEPHONE. Two general classes of the instrument are in use, magneto telephones, in which a mag- net is used, and electro-chemical telephones, in which a bat- tery is employed. The Bell Telephone. The Bell telephone belongs to the first class. Fig. 163 shows the inside structure, and Fig. 164 the external appearance, of the instrument. B is a magnet, and A a coil of wire around one of its poles. C is a thin disk of sheet-iron, called the diaphragm, very near but not touching the pole of the magnet. F F are wires leading from the coil to the end of the handle, where one is joined to the line and the other to the earth. At the other end of the line is a second instrument of just the same kind. Its Action. A speaker puts his lips to the mouth of the 266 NATURAL PHILOSOPHY. cone of one instrument, and speaks, while a listener puts his ear to the mouth of the other, and hears what is spoken. The air-waves of the voice vibrate the diaphragm C. Its motions toward and from the pole of the magnet strengthen and weaken the magnetism, and thus send electric pulses through the wire to the distant station. The electric pulses from the transmitting telephone act through the coil of the receiving telephone at the other end of the line, and alternately strengthen and weaken its mag- net. The diaphragm in front of this magnet is attracted by Fig. 163. it, and, as the strength of the magnet varies, the thin disk springs back and forth. This vibration of the disk produces air-waves which enter the ear of the listener. Now, two sets of air-waves which are exactly alike will affect the ear in exacth' the same way, no matter how they are produced, and hence, all that is needed to make any thing speak is to cause it to move so as to produce just such air- waves as the voice makes. The air- waves of the voice of the speaker vibrate the iron plate in the transmitter: the iron plate in the receiver vibrates in exactly the same way, and hence the air-waves which enter the ear of the hearer are faithful copies of those which leave the lips of the speaker, and are heard as the same sound. NATTJKAL PHILOSOPHY. 267 Hence, by the telephone, sound-waves are converted into electric pulses in the transmitter, and these electric pulses reaching the receiver are converted back again into sound- waves. Edison's Carbon Transmitter. In the Bell telephone we notice that the transmitter and receiver are exactly alike. But an Edison transmitter is often coupled with a Bell re- ceiver. The telephone then becomes electro-chemical instead of magnetic. The electric resistance of carbon varies with the pressure Fig. 164. upon it, doubtless, because heavier pressure secures a better contact of conductors. This is the principle used in the Edison transmitter. Pure lampblack is formed into a compact button, and placed in a battery-circuit which also includes a Bell instru- ment at the distant station. A diaphragm is fixed so that its center presses gently against this button. When the diaphragm is at rest a steady current from the battery flows through the distant telephone. But, when the voice of the speaker vibrates the diaphragm, it exerts a varying pressure/ on the button, and this varying pressure transforms the steady current into an undulatory one. The diaphragm of the receiver is compelled to vibrate in unison with these un- dulations, and emit the sound. 268 NATURAL PHILOSOPHY. Fig. 165. The Microphone. In the microphone the transmitter consists simply of a rod of carbon, A (Fig. 165), supported between two small blocks, C C, of the same material, its pointed ends resting loosely in shallow cups in the blocks. The whole is fixed to an upright thin board fastened to a solid base, D. This transmitter is put into circuit by joining one block to a battery by a wire Y, and the other b}* a wire X to the line lead- ing to the dis- tant receiver. The ticking of a watch be- fore this in- strument is distinctly heard in the telephone, and even the steps of a fly over the board are heard by the distant listener. 108. Electricity may be developed by heat: it is then called THERMO-ELECTRICITY. (G. 900, 904.) Thermo-Electricity. We have seen that electricity will produce heat ; we are now to notice that heat will produce electricity. When two pieces of different metals are sol- dered together, and their junction heated or cooled, a current of electricity is produced. The metals antimony and bis- muth are best suited to this purpose, but any others, or, indeed, two pieces of the same metal, will, in some degree, produce the same effect. Nor is it quite necessary that metals should be used at all : other solids, and even fluids, give rise to this kind of electricity. Two pieces of metal soldered together, with wires at- tached to their other ends, through which the electricity NATURAL PHILOSOPHY. 269 ' act, is called a THERMO-ELECTRIC PAIR. When stronger currents are desired, a combination of pairs, the two metals alternating throughout, is used. Such a combination is called a THERMO-ELECTRIC PILE. Metals which differ most in conducting power and crys- talline texture, are best suited to produce thermo-electric currents. The force of the electricity is in proportion to the difference of temperature at the two ends of the pile, pro- vided the difference does not exceed 80 or 90 F. It is in all cases very feeble; yet the galvanometer (Fig. 158) responds to so delicate a current that the slightest change of temperature in the pile can be detected by the electricity it produces. Indeed, the thermo-electric pile and galvanom- eter (Melloni's apparatus), is the most delicate thermometer known. SECTION IV. REVIEW. I. SUMMARY OF PRINCIPLES. The electricity produced by friction shows its presence by attracting and repelling light bodies. Two bodies charged with the same kind, either positive or negative, repel, but, when charged with different kinds, attract. A charged body polarizes every other body in its neigh- borhood, inducing the same kind of electricity in all sides toward itself, and the opposite kind in all sides away from itself. Electricity resides only upon the surface of a charged body. Upon the surface of a sphere, electricity is uniformly dis- tributed : if the I ody is not a sphere, the electricity will be most intense at the ends. The potential of a body is the excess or defect of its 270 NATURAL PHILOSOPHY. electric charge above or below that of the earth in its neighborhood. The electro-motive force is that which urges electricity along over a conductor. The poorer the conductor, the greater the electro-motive force needed to carry electricity through it. In frictional electricity the electro-motive force is very great, as shown by its passage through air, which is among the very poorest conductors. Two magnetic poles of the same name repel, but if of different names the}* attract, each other. A pole of either name can not exist alone ; but both are always found at once in the same piece of metal. The mag- netic condition is always a polarized condition. There is no conduction of magnetism. Current electricity is generated by chemical action in a galvanic cell, which may consist of any two different metals in a liquid which can act chemically on one more than on the other. Current electricity differs from frictional electricity in its electro-motive force and quantity. Its electro-motive force is vastly less, its quantity vastly greater. The + pole of a battery is always that one which is con- nected with the metal acted on least by the liquid. Hydrogen is evolved by the chemical action, and clinging to the plate " polarizes " it. The current on this account soon becomes weak. A ' ' constant battery ' ' is one in which the hydrogen is prevented from reaching the plate by means, usual!}*, of a second liquid which changes the hydrogen into water. The three most important elements of a current are its strength, C, its electro-motive force, E, and its resistance, pi R. Ohm's law is expressed in the formula C = H Each of these elements can be measured in terms of ap- propriate units. The unit of R is called the OHM. A piece of No. 16 NATURAL PHILOSOPHY. 271 copper, wire (about T ^- inch diameter) 60 feet long has a resistance of about one ohm. The resistance of ten times this length of the same wire is about ten ohms. (G. 908, 909.) The resistance of the Atlantic cable is eight thou- sand ohms. The unit of E is called a VOLT. A single cell of Daniel's battery yields an electro-motive force of about one volt. A Grove or Bunsen cell is more powerful : its electro-motive force is about 1.8 volts. The unit of C is called an AMPERE. A current of one Ampere strength will decompose .0000945 gramme of water in a second. Electrical measurements are of the utmost importance in telegraphy and in other practical applications of electricity. When great resistance is to be overcome, the cells of a batter}' should be joined " in series." When the resistance is small, the best effect is obtained by joining all plates of the same kind together. The energy of the current may be converted into heat or light or magnetism or actinism. Momentary currents are induced in a conductor by the making and breaking of a current in a conductor near it, or by the approach or departure of a magnet. An undulatory current is induced in a conductor by the alternate strengthening and weakening of a primaiy current near it, or by the alternate strengthening and weakening of a magnet around which it is coiled. II. SUMMARY OF TOPICS. 89. Electricity by friction. The electrical machine. Its action. Electroscopes. Positive and negative. The law. Application of the law. 90. A charged body. A non-conductor. Potential. High and low potential. Electro-motive force. Insulated body. Polarization. A charge b} T polarization. 91. Polarization in series. Faraday's theory. Differ- 272 NATURAL PHILOSOPHY. ence between conductors and non-conductors. Polarization before attraction. Illustration. 92. Description of the Holtz machine. Its action. The explanation. 93. The Leyden-jar. Various forms. May be charged. May be discharged. Battery. 94. Electricity of the atmosphere. Same as fractional electricity. Lightning. 95. Effect of points. Lightning-rods. 96. Mechanical effects of electricity. Chemical. Phys- iological. 97. Magnets. Experiment. Poles. 98. Attraction and repulsion. 99. Magnetic polarization. In series. Among the molecules. 100. A bar-magnet supported. Points north and south. Its variation. Annual and daily changes. 101. Dip of the needle. 102. Different names for current electricit}*. Chemical action. With pure zinc. The simple cell. Chemical action in simple cell. Electric conditions of the cell. Direction of the current. Enfeeblement of the current. Remedied in Grove's cell. What becomes of the hydrogen? The Bunsen cell. Other forms. 103. Statement of Ohm's law. Definitions. The formula. Units of C, E, and R (see Review Summary). 104. Battery of low resistance. Its electro-motive force. Strength of current. Batten* of high resistance. Its electro-motive force. The resistance. Strength of cur- rent. Quantity and intensit} T . 105. Electricity produces heat. And light. And mag- netism. The electric telegraph. The key. The line. The register. Electricity produces chemical action. 106. The current deflects a magnetic needle. The astatic needle. The galvanometer. 107. Description of apparatus for induction by a current. NATURAL PHILOSOPHY. 273 Results of experiment. Induction coils. Ritchie's. Experiment with a magnet. Magneto electricit}'. Simple form of machine. The telephone. The Bell telephone. Its action. Edison's carbon transmitter. The micro- phone. 108. Thermo-electricity. 274 NATUKAL PHILOSOPHY. CHAPTER IX. ON MACHINERY. SECTION I. ON THE SIMPLE MACHINES, 109. THE principle of work, applied to any one of the simple machines, will determine its law of equilibrium. The Principle of Work. We remember that work is the overcoming of resistance, and that it is measured by the product of the weight by the vertical height through which it is lifted. The principle of work states briefly that two forces^ acting in opposite directions upon the same body, will be in equilibrium when they do equal amounts of work. Let us illustrate a single case by means of Fig. 166. Suppose two bodies, M and N, hang from the ends of a bar, A B, which rests upon the point C, about which it may -g freely turn. If it does turn, and M goes up, N will go down, and if the distance B C is twice the distance A C, then N will go M "" twice as far as M. In all cases, Pig< 166< the vertical heights through which the two bodies will move have the same ratio as their distances, A C and B C, from the center of motion. These lines may then be used instead of the vertical heights in calculating work. Then the work which may be done by M will be M x A C, and that of N will be N x B C. Now, if these works are equal, then the two bodies will be exert- NATURAL PHILOSOPHY. 275 ing equal forces upon the bar A B, and, if once brought to rest, they will just balance each other. Machines. Machines are instruments by which forces ma}* 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 work done by the two forces must be equal. The resistance to be overcome is alwaj^s called the WEIGHT : the force which overcomes it is called the POWER. Simple Machines. There are six simple forms of ma- chines, 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. The Law of Equilibrium. By the term, law of equi- librium, 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. 110. Levers are of three classes. The principle of mo- mentum, applied to the lever, shows that the power and weight will be in equilibrium when they are to each other inversely as the 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. F A Levers. A lever is an inflexible bar, able to turn Fig . 167t freely upon one point. Thus, if the line A B (Fig. 167) represents an inflexible bar, resting upon some support at F, upon which it has 276 NATURAL PHILOSOPHY. free motion, it represents a lever. The point F, about which the lever turns, is called the FULCRUM. Three Classes of Levers. That point of a lever to which the power is applied is called the POINT OF APPLICA- TION. That on which the weight acts is called the WORKING POINT. Now, the ^ ^L. B lever takes different ^ names according to the relative positions JL w|j| f the point of ap- Fig. 168. plication, the work- ing point, and the fulcrum. In the lever represented in Fig. 168, whose ful- crum is at F, a power, P, acts upon one end of the lever, A, while a weight, W, acts upon the other, B. The fulcrum is between the point of application and the working point. This is called a lever of ihe first class. In the lever (Fig. 169), the working point, B, is between the point of application, A, and the fulcrum, E. This is a lever of the second class. In the lever (Fig. 170), the point of ap- plication, A, is between . the working point, B, ^ and the fulcrum, F. This is a lever of the . w third class. All levers belong to Fig ' 169 ' these three classes. They need not, however, be made in the simple straight form shown by the figures. In Fig. 171. the line A F B represents a lever whose arms make a right angle at the fulcrum, F. It is a lever of the first class ; so also is that shown in Fig. 172 by the curved line A F B. Application of the Principle of Work. Now, if we NATURAL PHILOSOPHY. 277 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, if in motion, they would do equal amounts of work. w F w; Fig. 170. Fig. 171. The lines B F and A F have the same ratio as the vertical heights through which they move if motion occurs. The work of the power is therefore P x A F ; that of the weight is W x B F. If equilibrium takes place only when the amounts of work are equal, then PxAF = WxBF; hence, P : W :: B F : A F. 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. 172. 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 that the force of the power, acting obliquely at B, is not all expended to lower the lever, but that if it were acting upon the point N, perpendicularly, it would exert all its forces to move the arm N F. So the effect of the weight 278 NATURAL PHILOSOPHY. acting obliquely upon A will be the same as if it were acting perpendicularly upon an arm, M F. Hence P X N F may be taken as the work of the power, and W x M F as the work of the weight. Putting these equal, PxNF = WxMF; hence, P: W :: M F : N F. Law of Equilibrium. This proportion teaches that the power and weight will be in equilibrium, when the power and weight are in- versely as the per- pendicular dis- tances from the fulcrum to the di- rections in which they act. This principle is called the LAW OF EQUILIBRIUM Fig. 172. for the lever. It will apply to all possible forms. The 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. 173 shows a compound lever made up of two simple levers having their fulcrums at F and F'. In this case the work of the power will be equal to P X C F X B F', and that of the weight will be equal to W x D F' x A F. If these products are put D t P |F J 4 Fig. 173. 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 product of all the arms on its side of the fulcrum is NATURAL PHILOSOPHY. 279 equal to the weight multiplied by the product of all the arms on its side. The compound lever is used when it is not convenient to have a very long lever, and }*et a small force is required to sustain a very large weight. If the long arms of the two simple levers be six and eight feet, and each short arm is one foot, then one pound power at C w r ill balance 48 pounds at D ; while if a simple lever had been used whose long arm was as long as those two long ones together, 6 + 814 feet, and whose short arm was one foot, then one pound at C would only be enough to balance 14 pounds at D. Applications of the Lever Of levers of the first kind man}' familiar examples might be named. The hand-spike and crow-bar are levers of this class. Shears and pincers are _ - 4t - pairs of levers, also of the first (*imiE^^ class ; their fulcrums being at / \ ^ A their joints. / \ / \ The balance is one of the / \ <3Lzmh> most useful applications of the lever. Fig. 174 represents a very simple form of this instrument. The beam a b is a lever poised at its center, the pivot or fulcrum c being a little above its center of gravity. 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 to balance it. Balances are of continual use in commerce ; the}* are indispensa- ble in the laboratory of the chem- ist, for whose use they are made with so great skill that a weight equal to the y^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. 175, to be weighed, is hung \ 280 NATURAL PHILOSOPHY. from the short arm of 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 W, 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 W, balanced by P, when at these points. Levers of the second class are not so common ; the wheel- barrow, however, is an example sufficiently familiar. 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, singular!}* enough, the unstable water ^?1 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 be- tween the fulcrum and the weight. Ill 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. The Wheel and Axle. One form of the wheel and axle is shown in Fig. 176. 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 circumference of the wheel, and the weight, "W, acts upon the axle by means of a rope winding around it in the opposite direction. NATURAL PHILOSOPHY. 281 It acts on the Principle of the Lever. If we have an end view of the machine, it will be seen, as shown in Fig. 177, where the 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 acts on the wheel, 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 Fig. 176. Fig. 177. points A and B, it will pass through the center, and repre- sent a lever, whose fulcrum is at C. It is upon the ends of such a lever that the power and weight are constantly acting. Application of the Principle of Work. The work of the power is represented by P x AC; that of the weight by W x B C. If the two forces are able to balance each other, these products are equal. Hence, P x A C = W X B C ; or, P : W :: B C : A C. But, in the figure, we notice that A C is the radius of the wheel, and that B C is the radius of the axle. Then the proportion teaches us that the power and iveight will be in equilibrium when the power is to the weight as the radius of the axle is to the radius of the wheel. If the radius of the axle is one foot, and that of the wheel three feet, then one pound upon the wheel will balance three pounds upon the axle. 282 NATURAL PHILOSOPHY. Fig. 178. The Compound Wheel and Axle. When more thati one wheel and axle are connected, so that the axle of each may act on the wheel of the next, the machine is a com- pound wheel and axle. Such an arrangement is shown in Fig. 178. We may get the law of equilibrium in the same way as in the compound lever. The work of the power will be P, multiplied by the several radii of the wheels ; that of the weight will be W, multiplied by the several radii of the axles. If the two forces are able to balance each other, these values must be 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 much larger weight than it could by acting upon a simple wheel and axle, unless the wheel should be so large as to be unwield}'. One Wheel may turn another by means of Cogs. In Fig. 178, there may be seen projecting teeth on the circumferences of the axles, b and c, which fit into equal notches on the circumferences of the wheels. Neither 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 illus- trate this mode of communicating motion. By Friction. When the circumferences of the wheels and the axles are made smooth, the}' may be pressed so snugly together, that neither can turn without turning the other at the same time, in the opposite direction. In this NATURAL PHILOSOPHY. 283 case, the motion is communicated by the friction of the parts against each other. 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 b;y 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 threshing-machine, also, motion is given to the C} T linder by means of a belt. Applications 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. 176. 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 a wheel ; the stone itself is the axle. The power is the force of the hand, while the weight is the resistance offered b} r the tool pressing on 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 CAP- STAN, 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. 178. 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 one foot, and of each wheel ten feet, then 284 NATURAL PHILOSOPHY. 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. In this way, a great power ma} T 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 re-appears, multiplied a thousand-fold, in the buzzing saw. 112. The pulley may be either fixed or movable. In the fixed pulle}* the power and weight will be in equilibrium when they are equal. In the movable pulley, with a single rope, the power and weight will be in equilibrium when the power is equal to the weight, divided b}* 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 two raised to a power shown by the number of pulleys. The applications of the pulley are common and important. The 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. 179. The grooved 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. Is either Fixed or Movable. If the axis of the pull- ey is stationary (see Fig. 179), the pulley is called a FIXED PULLEY. One whose axis moves with the weight is called a MOVABLE PULLEY. This will be understood by means of Fig. 180. The wheel, E, is a movable pulle} r . 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. NATURAL PHILOSOPHY. 285 The Principle of Work applied to the Fixed Pulley. The fixed pulle}' is shown in Fig. 179, to which we again refer. It is clear that, when motion occurs, the power, P. will go down exactly as far as the weight, W, goes up. To do equal work when the distances are equal, the bodies must have equal weights. Hence, in the fixed pulley the power and weight can balance each other only when they are- equal. pQ W Fig. 179. Fig. 180. The Principle of Work applied to the Movable Pulley with a single Rope. In the movable pulley with a single rope (see Fig. 180), the weight rests upon two branches of the rope, H and E ; and, when it rises, both branches must be equally shortened. But the rope, F P, will lengthen just as much as both the branches shorten. It is clear that the power, P, must move down just twice as far as the weight, W, goes up. Let V represent the vertical height through which the power moves, then ^ will represent the vertical height through which the weight is lifted. The work of P will be represented by P x V, and that of W by W X ^, and the two forces will balance each other when P X V = W X |, or when P = f . 286 NATURAL PHILOSOPHY. Now let us take another case. Suppose there are two movable pulleys, C and D (Fig. 181), 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 distance of P downward must be four times as great as that of W upward. Then, if V is the vertical height for P, J will be the vertical height for W ; and, if they do equal work, P X V - W x |, or P = f . In like manner, if three movable pullej's are used, we shall find that, to be in equilibrium, Pig. 181. p __ w 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, we have this general principle : in movable pulleys, with a single rope, the power and weight will be in equilibrium when the power equals the weight divided by the number of branches which support it. The Movable Pulley with separate Ropes. When each pulley has a separate rope, the law is very different. Fig. 182 shows such a s} T stem. The three ropes, d fh, are fastened to the beam. The first, after passing around the pulley, b d, is fastened to the axis of the one above : so the rope /, after going around the pulley e/, is fastened to the axis of g h; but the rope 7i, after going under the pulley g 7i, passes over a fixed pulle}', and receives the power at the other end. The Principle of Work applied to the Movable Pulley with separate Ropes. This system is only a NATURAL PHILOSOPHY. 287 combination of movable pulleys with a single rope. Suppose the pulleys b d and ef were taken away, the weight being hung from the axis of g li. There would be left an arrange- ment exactly like that shown in Fig. 180. g h is a movable pulley, with a single rope, to lift the pulley e f, which is likewise a movable pulley, with a single rope, to lift the pulley b d; while b d is itself a movable pulley, with a single rope, to lift the weight, W. The effect of the power, P, will be doubled by each pulley thus : - With 1 pulley, P = 5 = 5 ; " 2 pulleys, P = f = f, ; " 3 pulleys, P = f = 5,. If we notice that the denominator, in each of these values of P, is a power of two, whose index is the num- ber of pulleys, we infer that, in a sj's- tem of movable pulleys with separate ropes, the power and tveight will be in equilibrium when the poiver equals the weight divided by a poiver of two, whose index is the number of pulleys. For example, with a system of five pullej^s, how much weight will a power of ten pounds balance ? P = w . or 10 = ,w . hence w = 320 pounds. Applications of the Pulley. No mechanical advan- tage is gained by the use of the fixed pulley, because the weight must move just as fast as the power, }~et it is of great value in the arts, for changing the direction of forces. A sailor standing upon the deck of his ship ma}', by the use of a fixed pulle}*, 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. 183), will lift them as effectually as though he were able to climb the perpendicular wall with the same rapidity. 288 NATURAL PHILOSOPHY. The Movable Pulleys with single rope are in common use for moving heavy weights through considerable distances. Merchandise may be lifted by means of them, from the hold of a ship to the wharf, or to the upper stories of store- houses ; or, by a different arrange- ment 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 made compact. In all pull's 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 stiff- ness of the ropes used ; so that the weight, actually overcome by a given power, is always less than Fig. 183. the laws of equilibrium would afford. 113. The principle of work applied to the inclined plane shows : 1st, 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, when 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. The Inclined Plane. Any plane, hard surface, placed in an oblique position, may be used as an inclined plane. In NATURAL PHILOSOPHY. 289 Fig. 184, A B represents an inclined plane. The distance B C is the height of the plane, and A C is its base. The weight, W, may be urged up the plane by a force acting par- allel to A B, or parallel to A C, or at any angle to these. We are to notice the first two cases only. If the Power acts parallel 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. ^^ ^^S Now, a force which will urge the weight from A to B is lifting ^ it only through the vertical height, C B. Fig ' 184 ' 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 work of the power is, therefore, represented by P X A B ; that of the weight, by W x C B. When these products are equal, the two forces will be able to balance each other. Thus : PxAB = WxCB; or P : W :: CB : A B. This proportion teaches us that, when in equilibrium, the power is to the weight as the height of the plane is to its length. If, for example, the height C B is four feet, and the length of the plane, A B, is sixteen feet, a power of one pound will balance a weight of four pounds. For 1 Ib. : 4 Ibs. :: 4 ft. : 16 ft. If the Power acts parallel to the Base of the Plane. Let A B (Fig. 185) represent a plane whose height is C B, and whose base is A C. The power acts upon the weight by means of a cord passing over the pulley 290 NATURAL PHILOSOPHY. Fig. 185. 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 pulle}*, 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 pull- e}', will let the power down a distance equal to A C. The work of the power is, there- fore, represented by P X A C, and that of the weight, by W x C B. If now these products are equal, the power and weight will just balance each other. Hence PxAC = WxBC; or P : W :: BC : AC. From this proportion we learn that, when the power acts parallel to the base of the plane, the power and iveight will be in equilibrium ivhen the power is to the weight as the height of the plane is to its base. Thus, if the height of the plane is two feet, and the base is ten feet, a power of one pound will balance a weight of five pounds. For 1 Ib. : 5 Ibs. :: 2 ft. : 10 ft. Applications of the Inclined Plane. This machine is used to lift heavy weights through short distances. Many familiar examples might be named. If a barrel of mer- chandise is to be placed upon a wagon, it is often rolled up on a plank, one end of which rests on the ground, the other on the wagon. A hogshead which a dozen men could not lift may thus be raised by the strength of one or two. Our common stairs are, in principle, inclined planes, the NATURAL PHILOSOPHY. arrangement of steps only giving a firm footing. If the dis- tance between the floors be three-fourths the length of the stairs, then, besides the ordinary effort of walking, the per- son must continually, while going up, labor to lift three- fourths of the weight of his body. 114. 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. The Wedge. This instrument is shown in use b}' Fig. 186. A B is called the back of the wedge: A c and B c are its sides, and c is its edge. It is generally used in cleaving timber, and sometimes for raising heavy weights through very short distances. For these purposes its edge is put into a crevice made for it, and it is then driven by blows Pi g . with a sledge. Since we can not calculate the force of a blow, no attempt is here made to establish a law of equilibrium for the wedge. 115. This principle 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 con- tiguous threads is to the circumference of the circle in which the power moves. The screw is used extensively to produce great pressure. It is also often used to measure delicate distances. The Screw. The screw consists of a cylinder of wood or metal, with a spiral groove winding around its circumfer- ence. This grooved cylinder (C, Fig. 187) 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 nut. The raised part between the grooves of the cylinder is called the thread. 292 NATURAL PHILOSOPHY. Suppose the nut to be stationary : then, n the screw is turned by a power acting upon the lever at B, it must ad- vance downward at every revolution, and the pressure of the advancing screw will be ex- erted upon an} T object placed under the press-board, E F, against which the end of the screw presses. Application of the Principle of Work. By one turn of the screw, it will advance downward a distance just equal to the distance between two con- tiguous threads. The press- board, E F, which may be regarded as the weight, will be moved along through an equal distance, a 6, by every turn. The power act- ing at B will, in the same time, move through the circumference of the circle whose radius is B C. Hence the work of the power will be repre- sented by P x circumference of the circle whose radius is B C, and that of the weight by W X a b. If these products are equal, the two forces, when at rest, will be in equilibrium. Hence : P x circ. B C = W x a 6; or P: W ::ab : circ. B C. This proportion teaches that the power and weight will be in equilibrium ivhen 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. Thus, if the distance between the threads is \ inch, and the circumference traveled by the power is 5 feet, or 60 inches, what weight on the nut would one pound power at B balance? Pig. 187. NATURAL PHILOSOPHY. 293 1 Ih. : W :: 1 in. : 60 in. W = 120 Ibs. Applications of the Screw. The screw is used when great weights are to be lifted short distances, or when heav}* 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 . Micrometers. 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, and called MICROMETERS, are used for this purpose. Suppose a screw with a hundred threads in one inch of its length ; then, at every turn its end would advance just jfa of an inch, and, if it carry a steel marker, spaces of that length may be marked off on any body alongside of which it moves. Now, let the power move in a circle ten inches 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 the screw will go forward only ^^ of an inch. If the power goes ^ inch, then the marker will advance only Tffj- *- /I ,/, X, n? f j-t r- 1 \ / rr r^ RECElvl-U MAY 2 70 -ft KM ; ----- C? 5 ^ LD 21A-50m-12,'60 (B6221slO)476B General Library University of California Berkeley R44393 1 THE UNIVERSITY OF CALIFORNIA LIBRARY