GIFT OF SCIENCE FOR THE SCHOOL AND FAMILY. PART I. NATURAL PHILOSOPHY. BY WORTHINGTON HOOKER, M.D., PBOFKSSOB OF THE THEORY AND PRAOTIOE OF MEDICINE IN YALE COLLEGE, AUTHOR OF "CHILD'S HOOK OF NATURE," "FIUST BOOK- IN CHEMISTRY," "NATURAL HISTORY," "CHEMISTRY," ETC. Kllustrateti fc, Numerous Hnjjrabfnjjs. SECOND EDITION, REVISED AND ENLARGED. NEW YORK: HARPER & BROTHERS, PUBLISHERS FRANKLIN SQUARE. 1881. BY DR. WORTHINGTON HOOKER. THE CHILD'S BOOK OF NATURE. For the Use of Families and Schools; intended to aid Mothers and Teachers in training Children in the Observa- tion of Nature. In Three Parts. Illustrated by Engravings. The Three Parts complete in one volume. Small 4to, Cloth, $1 12 ; Separately, Cloth, Part I., 45 cents ; Parts II. and III., 48 cents each. PART I. PLANTS. PART II. ANIMALS. PART III. AIR, WATER, HEAT, LIGHT, &c. FIRST BOOK IN CHEMISTRY. For the Use of Schools and Families. Illus- trated by Engravings. Revised Edition. Square 4to, Cloth, 48 cents. NA TURA L HISTOR Y. For the Use of Schools and Families. Illustrated by nearly 300 Engravings. 12mo, Cloth, $1 00. SCIENCE FOR THE SCHOOL AND FAMILY. PART I. NATURAL PHILOSOPHY. Illustrated by numerous Engrav- ings. Second Edition, Revised and Enlarged. 12mo, Cloth, $1 00. PART II. CHEMISTRY. Illustrated by numerous Engravings. Second Edition, Revised and Enlarged. 12mo, Cloth, $1 00. PART III. MINERALOGY AND GEOLOGY. Illustrated by numerous Engravings. 12mo, Cloth, fl 00. Published by HARPER & BROTHERS, Franklin Square, N. Y. Any of the abpiz_ works seut by wail, postage prepaid, to any part of the United States upon receipt of the price. Entered according to Act of Congress, in the year 18T8, by HARPKR & BROTHERS, in the Office of the Librarian of Congress, at Washington. or. PREFACE. DANIEL WEBSTER, in his Autobiography, speaks thus of his entering upon the study of law: "I was put to study in the old way that is, the hardest books first and lost much time. I read Coke on Littleton through without understanding a quarter of it. Happening to take up Espinasse's Law of Nisi Prius, I found I could understand it ; and arguing that the object of reading was to understand what was written, I laid down the venerable Coke et alios similes reverendos, and kept company for a time with Mr. Espinasse and others, the most plain, easy, and intelligible writers. A boy of twenty, with no previous knowledge on such subjects, cannot understand Coke. It is folly to set him on such an author. There are propositions in Coke so abstract, and distinctions so nice, and doctrines embracing so many conditions and qualifications, that it requires an effort not only of a mature mind, but of a mind both strong and mature, to un- derstand him. Why disgust and discourage a boy by telling him that he ') nust break into his profession through such a wall as this ? I really often despaired. I thought that I never could make myself a lawyer, and was almost going back to the business of school-keeping. Mr. Espinasse, how- ever, helped me out of this in the way that I have mentioned, and I have always felt greatly obliged to him." Here is most graphically depicted a defect which is now, as it was then, very prominent in all departments of education. It is even more so in early education than in that of the college and the professional school. Even - in tender childhood pupils are put to studying books of which, as was true of Webster with his Coke on Littleton, they do not understand "a quarter part." If the rule is not "the hardest books first," there are many things 3G377'j viii PREFACE. in the books that it is not only hard but impossible for them to understand. And the hardest things are often prft first. For example, in a very popu- lar primary geography which lies before me the pupil is introduced to the world and its grand divisions at the outset, while he is taught about his own state and country only at the conclusion of the book. And this un- natural mode is the one very commonly pursued. Similar criticism can be passed upon most of the books used in teaching young children. Some of them are wholly useless. This is true of the grammars for primary schools. The formal statements, called the rules of grammar, are beyond the understanding of very young scholars, and therefore are useless bur- dens upon their memories. They are as useless to them as the three fourths of Coke which Webster could not understand was to him. If we follow education upward from the primary school we find the same defect throughout the whole course. In the books which are used in teach- ing natural science it is especially prominent. Even in the elementary books, or compendiums, so called, formal propositions and technical terms render the study uninviting, and to a great extent unintelligible. The pupil is apt to be disgusted and discouraged, as Webster was with Coke on Littleton, and for the same reason. Another defect intimately connected with that of which I have spoken is the very sparing and late introduction of the physical sciences. They are generally postponed to the latter part of the course of education, andrthen but little time is devoted to them. Generally, when a pupil designs to go through college, the study of these sciences is wholly neglected in his prep- aration, because a knowledge of them is not required for admission. Then in the college they are not attended to till the latter part of the course, and in the short time allotted to them there is so much to be learned that the teaching of them is a failure. Especially is this true of Chemistry and Geology. This defect is a radical one. A thorough change should be effected in this respect in the whole course of education. The natural sciences should be made prominent from the beginning to the end, not only because they are of practical value, but also because they are as useful in their way for mental discipline as the study of mathematics and of language. They can be taught to some little extent to the youngest pupils. There are facts PREFACE. ix about air, water, and the various objects that they see around them, which they can understand if they be presented in the right manner. And the busy inquiries which they make after the reasons of the facts, and their appreciation of them if stated simply and without technical terms, show the appropriateness of such teaching. Children are really very good phi- losophers in their way. They have great activity not only of their percep- tive but of their reasoning faculties also, to which due range should be given in their education. Beginning thus, not a year should pass during the whole course when the pupil shall not be engaged in studying some one of the physical sciences to some extent. This continued attention to such studies in a reason- able amount, so far from interfering with the due prosecution of the other studies deemed so essential, will so promote the pupil's advance in them as to more than make up for the time that is taken from them. It will do this not only by the genial influence which such studies exert upon the mind, but by the contributions which they make to the knowledge of language and mathematics ; for language is largely built up from natural objects and from the acquisitions of science, and there is an abundance of interesting appli- cations of portions of the mathematics in the facts which the physical sci- ences develop to us. I have said that the teaching of the natural sciences in our colleges is generally a failure, and it always will be so as long as the present plan is continued. In order to have it successful there must be the same gradation in teaching them that we have in teaching language and the mathematics. The college student needs to be prepared for the lectures which he hears on natural philosophy, chemistry, etc., and for his study of those branches, by previous familiarity with the simpler portions of them acquired in the school-room. There is another very important reason for the early introduction of the physical sciences into education. By far the larger portion of pupils in our schools stop short of the college, or even the academy and high-school. That they should go forth into the world with no knowledge of the princi- ples that lie at the basis of the arts in which so many of them are to engage is a shame and a wrong, if the communication of such knowledge be indeed practicable, as it undoubtedly is. Even those who are not to engage in X PREFACE. these arts will be greatly benefited by this knowledge, because in addition to its constant practical applications in the management of life, it will con- tribute to their mental power, and, what is no small consideration, to their enjoyment ; and it is, in fact, requisite to constitute them well-informed persons. If the views which I have presented be correct, there should be a series of books on the natural sciences carefully adapted to the different periods of the course of study. Those intended for the young beginner should be exceedingly simple, and should not attempt to present anything like a full view of the subjects treated. They should deal largely with familiar facts or phenomena. The terminology of science and formal statements of prin- ciples, such as we often see in so-called compendiums, should have no place in them, but should be gradually introduced as the series advances, and should be made complete only in the concluding books. It has been the object of the author to supply a part of such a series. The first book in. the series is the "Child's Book of Common Things," intended to teach the observation of familiar facts, or, in other words, the beginnings of philosophy, to children as soon as they have got well started in reading. Next comes the " Child's Book of Nature," which in its three parts (Part I., Plants; Part II., Animals; Part III., Air, Water, Light, Heat, etc.) extends considerably the knowledge of the philosophy of things which the child has obtained from the first book in the series. Then follows the "First Book in Chemistry." On a level with this is my "First Book in Physiology." The next step in the gradation brings us to three books under one title, "Science for the School and the Family;" Part I., Nat- ural Philosophy; Part II., Chemistry ; Part III., Mineralogy and Geology. On a level with these is another book, "Natural History," and on another still is to be written an "Introduction to Botany." The three books, of which the present is one, are intended for the older scholars in what are commonly called grammar-schools. At the same time they are suited to scholars who are advanced to a higher grade who have not gone through the previous books of the series. The preparation of books especially adapted to high-schools and colleges I have left to others, except in one branch of science, Physiology, on which I some years ago published a work entitled "Human Physiology." PREFACE. XI All of these books are from the press of Harper & Brothers except the two works on Physiology, published by Sheldon & Co., New York, and the " Child's Book of Common Things," published by Peck, White, & Peck, New Haven. The general plan and style of these books are very different from what we see in most of the books for schools on the same subjects. The order of the subjects and the mode of developing them differ from the stereotype plan which has so generally been adopted. One prominent feature is the free use of illustrations from familiar phenomena. This leads the pupil to reason or philosophize about common things, thus giving an eminently prac- tical character to his knowledge. At the same time it makes the books suitable for use in the family as well as the school, between which there should be more common ground than the present mode of education allows. The style which I have chosen for all the books I have written for use in teaching is what may be called the lecture style. There are three other kinds of style which are more commonly used in school-books. The most common is what I term the formal statement style. In this principles and rules are stated, and then illustrations are given. This makes a formal and uninviting book. The bare skeleton of the science is generally for the most part presented, and the young pupil is apt to learn the statements by rota without understanding them. It is a style fitted only for books intended for advanced scholars. Another style is the catechetical. This is an un- natural mode of communicating knowledge ; and, besides, it encourage* learning by rote as the formal statement style does. In the third style, th< dramatic, conversations are held between the teacher and some learners. The chief objection to this is that it undertakes to put in permanent shape what should be extemporized in the recitation.* What is needed in the book is simply clear and concise statement in an interesting style, and the living teacher and his scholars can best furnish the conversational element as the recitation goes on. In the" lecture style there may be and should be as much precision of statement as in the formal statement style, while it is more interesting, because it is the natural mode of communicating knowledge. In this style the facts are ordinarily so stated as to develop principles ; while in the other the order is reversed, the principles being first stated and the facts given X1L PREFACE. afterwards. One of the most successful books ever used in our colleges "Paley's Natural Theology" is in the lecture style, and it is a matter of surprise that this fact has had so little influence with those who have pre- pared books for instruction. Whatever may. be true of advanced scholars, in teaching the youny stu- dent in science bare, dry statement should be avoided, and the subjects should be presented in all their attractive features. I would not be under- stood as advocating the dressing up of science in adventitious charms. This is not necessary. Science possesses in itself an abundance of charms, which need only to be properly developed to attract the young mind ; and the lecture style furnishes the best vehicle for such a development. One grand essential for giving interest to any study is the presentation of the various points in the natural order in which they should enter the mind. They should be so presented that each portion of a look shall make the following portions more interesting and more easily understood. This principle, which is so commonly transgressed, I have endeavored to observe strictly in the preparation of these volumes. Questions are inserted for those teachers who desire to use them. There is also an Index. W. HOOKER. January, 18S8. PREFACE TO THE SECOND EDITION. IN revising this work, its essential features, as fully explained in the Author's Preface, have been carefully preserved; at the same time, many portions have been entirely rewritten and much new matter has been added. The chapter on Galvanism, omitted in the Second Edition of Part II., Chemistry, has been revised and inserted in the present volume. Many new wood-cuts have been introduced, taken chiefly from German sources. In the First Edition of this work the author makes frequent reference to Dr. Neil Arnott's Elements of Physics; the editor acknowledges his in- debtedness to the Seventh Edition of the same for many of the illustra- tions of physical phenomena, and for suggesting the arrangement of matter in certain parts of this revision. II. CARRINGTON BOLTON, Ph.D. TRINITY COLLEGE,) Nay, 1873. J A2 CONTENTS. CHAPTER FAGB I. MATTER 17 II. PROPERTIES OF MATTER 28 III. PROPERTIES OF MATTER (CONTINUED) 39 IV. ATTRACTIONS OF MATTER 51 V. ATTRACTIONS OF MATTER (CONTINUED) 67 VI. CENTRE OF GRAVITY 79 VII. MOTIONS OF MATTER 93 VIII. MOTIONS OF MATTER (CONTINUED) 112 IX. THE SIMPLE MACHINES 133 X. HYDROSTATICS 159 XI. SPECIFIC GRAVITY 181 XII. HYDRAULICS 196 XIII. PNEUMATICS 208 XIV. SOUND 235 XV. HEAT 252 XVI. HEAT (CONTINUED) 281 XVII. LIGHT 312 XVIII. ELECTRICITY 351 XIX. GALVANISM 375 XX. MAGNETISM 397 APPENDIX. THE METRIC SYSTEM 415 INDEX... .. 423 NATURAL PHILOSOPHY. CHAPTER I. MATTER. 1. Introduction. Since you are about to begin the study of the series of books embraced under the general title "Science for the School and Family," and of which this work on Natural Philosophy forms the first volume, it is necessary that you should clearly understand what is meant by Science. This word literally means knowledge; but in the sense in which it is commonly employed, science de- notes a systematic and orderly arrangement of knowledge. Superficial and incomplete information on any given topic, interwoven with fictions of the imagination, does not con- stitute science ; on the contrary, science implies a profound, penetrating, and comprehensive knowledge based on gen- eral truths and fundamental principles. Since the human mind is capable of apprehending the phenomena of the whole universe of nature and of thought, and can subject them to the action of both the reason and the imagination, it is evident that science in its fullest signification is well- nigh boundjess in its range and infinite in the variety of its material. To facilitate the study of so vast a subject as the sum of human knowledge, we naturally resort to sys- 18 "* -**" NAtUBA.L tematic divisions and methods of classification. To enter upon an examination of the various systems of classifying the arts and sciences proposed by different authorities is quite foreign to our object, and we shall adopt without argumentation the views of the late Dugald Stewart, for- merly Professor of Moral Philosophy in the University of Edinburgh. After carefully criticising the schemes of his predecessors, Professor Stewart concludes that the two most general heads on which to found an encyclopedical classification of science are MIND and MATTER. "No branch of human knowledge no work of human skill can be mentioned which does not obviously fall under the for- mer head or the latter." The sciences of mind and of matter are susceptible of subdivisions ; the former embraces Pure Mathematics, Met- aphysics, Mental and Moral Philosophy, Political Economy, Sociology, and other subjects upon which we do not dwell; the latter deals with the less abstract topics included in the sciences of Natural History, Astronomy, Chemistry, and Natural Philosophy or Physics. Natural History includes within its extended limits the sciences of minerals, or Mineralogy, and of rocks, or Geol- ogy; of plants, or Botany; of animals, or Zoology; and of man, or Anthropology. Under this head, too, may be placed Medical Science, Physiology, etc. Astronomy, as you know, teaches about the heavenly bodies, their motions, magnitudes, and periods of revolution ; Chemistry deals with the internal composition of substances and their mutual reactions ; and Natural Philosophy, or Physics, may be defined as that branch of science which treats of the properties and laws of matter. The term Natural Philoso- phy itself embraces a whole series of sciences,- as will ap- pear from an examination of the following chapters. 2. Effects of Matter on the Senses. The substance of MATTEE. 1 9 which material objects are made is called matter. Matter is often defined as anything perceptible by the senses a statement which demands closer consideration. Some forms of matter can be perceived by all the senses ; others can be perceived by only a part of them ; some by only one. Air you cannot see, nor smell, nor taste ; but you can feel it, and hear and see the effects of its motion. Sometimes mat- ter affects only the sense of smell, or that with the sense of taste. Sea-air smells of salt ; but the salt in the air is so finely divided we cannot see it. And yet it is the salt, entering the nostrils and coming in contact with the sen- sitive fibres of the nerves of smell, that produces the effect. Thus when we smell a flower, matter comes from it in par- ticles so minute that no microscope can detect them, but they produce sensation when they strike upon the nerve. Diflerent kinds of matter constitute the substances of which bodies are made. These bodies are subject to change of state, form, and mutual relation ; and a study of these phenomena is the province of Natural Philosophy. 3. Forms of Matter. Matter appears in three forms: solid, liquid, and gaseous or aeriform that is, like air. Sometimes matter is spoken of as having only two forms solid and fluid. In this case fluids are divided into two classes, the elastic and non-elastic. The air and the vari- ous gases and vapors are the elastic fluids; while those which are called liquids are the non-elastic fluids. A foot- ball bounds because the air in it is an elastic fluid. If it were filled with a non-elastic fluid, as water, it would not bound. When water takes the form of steam it becomes elastic. Though it was formerly very common to use the expression elastic fluids, the division of matter into three forms is the one now usually recognized, liquids having been found to be feebly elastic. Solids. In solid matter the particles cannot be moved 20 NATURAL PHILOSOPHY. about among each other; but each particle generally re- tains the same position in relation to those particles which are around it in other words, it does not change its neigh- borhood. This is more true of some solids than of others. It is absolutely true of such hard solids as granite and the diamond. In these the particles always maintain the same relative position. But it is not so with gold or lead. By hammering these you can change greatly the relative posi- tion of their particles. India-rubber is a solid, but the relative position of its particles can be much altered in various ways. Liquids. It is characteristic of a liquid that its particles change their relative position from the slightest causes. It is in strong contrast with solids in this respect. When you move any portion of a solid body you move all the other portions of it, and generally in the same direction. But a body of liquid cannot be moved altogether as one body except by confining it, as, for example, in the case of a water-pipe or a syringe. And then, the moment that the water can escape, the particles use their liberty of altering their relative position. Since wind and other agents act continually upon water, no particle stays for any length of time in the neighborhood of the same particles. "Unstable as water" is, then, an exceedingly significant expression. Water is never at rest. A particle of it may at one time be floating on the surface of the ocean, and at another be in depths beyond the reach of man. It flies on the wings of the wind, falls in the rain, runs in the stream, is exhaled from a leaf, trembles in the dew-drop, flows in the blood of an animal or in the sap of a plant, and is always hurrying along in its ever-changing course. Gases. The particles of gaseous or aeriform substances move among each other even more freely than those of a liquid. Air, therefore, is more unstable and restless than MATTER. 21 water. Even when the air seems to be perfectly still its particles are moving about among each other. You can see this to be true if you darken a room, leaving a single shutter a little open.* Where the light enters you will see motes flying about in every direction, which would not be the case if the air were really at rest. The particles of air have a greater range of travel than those of water; for the sea of atmosphere which envelopes the earth rises to the height of about fifty miles. How far water rises by evap- oration we know not ; but it is not at all probable that it rises to the uppermost regions of the atmosphere. f 4. Pilling of Spaces by Liquids and Gases. It is the free- ness with which the particles of liquids and gases move among each other that enables them to insinuate themselves into spaces everywhere. They are ever ready to enter into any substances which have interstices or pores of such size as will admit them. Mingled with the grains of the soil are not only water, but air and gases. These are present also in all living substances, both vegetable and animal. Water forms the chief part of sap and of blood, and water is always accompanied by air and other gases. Part of the air we inhale enters the blood in the lungs, and courses with it through the system. The fishes could not live in water if no air were mingled with it. This can be proved by experiment. If you put a fish into a close vessel it will soon die, because it uses up all the air held in solution by the water. In an open vessel the fish is kept alive by the con- stant accessions of fresh air to the water. Advantage is taken of this in the preservation of fish in large aquaria, where air is constantly pumped into the water contained in the tanks. Solution. When solid substances dissolve in* water or other liquids, the particles of the solids penetrate between the little particles of the liquid, and it is owing to the freedom with which the particles of water move about among each other that they are able to take in among them the minute particles of the solid. 12. 5. Relation of Heat to the Forms of Matter. Some kinds of matter are seen in all the three forms. Whether these shall assume one form or another depends on the amount of heat present. Thus when water is solid, ice, it is be- 22 NATURAL PHILOSOPHY. cause a part of its heat is gone. Apply heat, and it becomes a liquid, water. Increase the heat to the boiling point, and it becomes steam, or an aeriform substance. Alcohol has only two forms liquid and aeriform^ It has never been frozen. Iron is usually solid ; but in the foundry, by the application of great heat, it is liquefied. Mercury is liquid in all ordinary temperatures; but it often becomes solid in the extreme cold of arctic winters. A mercurial thermom- eter is of course useless under such circumstances, and the alcoholic thermometer is relied upon to denote the degree of cold. The difference between mercury, water, and iron in regard to the liquid state is this : Comparatively little heat is required to make mercury liquid, while more is re- quired for this condition in water, and much more in the case of iron. 6. The Nature of Matter Unknown. Let us now inquire, what do we know of the nature of matter ? Can we say that we know anything of it ? We may observe its phe- nomena and learn its properties ; but, with our most search- ing analyses, we can no more determine the nature of mat- ter than we can that of spirit. Newton supposed " that God in the beginning formed matter in solid, massy, hard, impenetrable particles." This he believed to be true of liquids, and even of gases, as well as of solids. In the gas these hard particles are much farther apart than in the solid. The supposition is a very probable one ; but if it be true, it does not teach us what matter is, for it leaves us in the dark as to the nature of the particles. Newton further supposed that these particles have always remained unaltered amid all the changes that are taking place ; these changes being occasioned by " the various separations and new associations and motions of these permanent particles." When, for example, anything is burned up, as it is ex- pressed, not one of the particles is destroyed; they merely MATTER. 23 assume new forms. Though most of the substance has flown off in the form of gas, the ultimate particles compos- ing the gas are the same as when they made a part of the solid substance ; and they may soon again become a part of some new solids. Such changes in the forms of matter are everywhere going on ; and when you study Chemistry, Part II. of this Series, you will become familiar with them. 7. The Constitution of Matter. The nature of the inter- nal structure of matter cannot be experimentally deter- mined, and we are again obliged to resort to hypotheses or suppositions. Two hypotheses of the internal constitu- tion of matter have been proposed ; according to the first matter is homogeneous throughout its mass, and pre- sents no interior void, or, in other words, is continuous. This is the supposition of Descartes, an eminent French philosopher of the seventeenth century, but possesses so small a degree of probability that the scientific world has abandoned it for the second hypothesis. According to this, bodies consist of an agglomeration of an immense number of excessively small particles called molecules / these small particles do not touch each other, but are held in their places by reciprocal attraction ; they are supposed to be continu- ally in motion, the amplitude of their oscillations varying .with the form of the body, solid, liquid, or gaseous. This hypothesis originated with ancient Greek philosophers about twenty-two centuries ago, but has been modified consider- ably in modern times. There are many reasons for accept- ing this view, some of which we will state briefly. In the first place, matter is divisible, as will be explained more fully in Chapter II, and it is difficult to comprehend its divisibility if it contains no void spaces. The solubility of solids is explained in 4 by a reference to this hypoth- esis. Secondly, the expansion of bodies by heat, and their contraction on cooling, is readily explained by the molecular 24 NATURAL PHILOSOPHY. hypothesis, for we may conceive that the spaces which separate the molecules become larger or smaller in conse- quence of the separation or approach of the latter. The fact that bodies assume three states, solid, liquid, and gase- ous, is explained in a somewhat similar manner. Thirdly, when two substances are brought together it often happens that they intimately interpenetrate, and, each losing its characteristic property, they acquire new properties com- mon to both. Chemical science affords us numerous exam- ples of such combinations. Sodium, for instance, is a white lustrous metallic substance, as soft as wax, fusible at a low temperature, lighter than water, tarnishing very readily, and decomposing water at ordinary temperatures ; chlorine, on the other hand, is a 'yellowish-green gas, heavier than air, of disagreeable odor, fatal to animals when breathed by them, possessing strong bleaching power, and soluble in water; and these two strangely dissimilar substances combine to form the white crystalline solid, common salt, so indispensable to man and animals. Such facts as these are comprehensible if we adopt the view that matter is composed of exceedingly small par- ticles, but it is impossible to explain them on the hypoth- esis of Descartes. Taking the example given, sodium and chlorine are each regarded as made up of minute particles having the properties named, and when combination takes place between individual particles they are associated in new forms and recognized as common salt. Fourthly, the various phenomena of light and of heat, and certain chemical laws which will be explained in Part II., combine with the foregoing proofs to form an argu- ment in favor of the molecular hypothesis not easily out- weighed. 8. Molecules. These particles of matter are so minute that they have never been seen by man ; the smallest par- MATTER. 25 ticle visible with the most perfect microscope is probably greater than ^oVo f a millimetre* in diameter, and it bus been calculated that to see these molecules we should re- quire a lens magnifying from 500 to 2000 times greater than any we now possess. We are about as far from see- ing the largest molecules as we should be from reading with the unaided eye the letters on a page of this book at the distance of one third of a mile. Eminent philosophers have. estimated the size of molecules, and have ob- tained remarkable coincidence of results from independent and widely different data ; from these calculations it may be concluded with a high degree of probability that in ordinary liquids or solids the diameter of the molecule is less than the ten-millionth and greater than the two-hundred- millionth of a millimetre. Molecules are believed to be continually in motion, and with very great velocity, estimated to average seventeen miles a minute. This motion is in all directions, and of an oscillatory character, the particles flying to and fro through excessively small paths, the diameter of which varies with the nature of the substance. Not only do molecules vary in size and velocity of mo- tion, but they also differ among themselves in weight; their weight depends on that of the atoms (see next para- graph) composing them, and can be determined in accord- ance with laws explained in Part II., Chemistry. Atoms. Molecules are believed to he composed of still smaller particles of matter called atoms. The number of atoms forming a molecule varies greatly; in certain cases a molecule contains but one atom, in others several hun- dred. If the atoms composing the molecule are of one and the same substance, the molecule is said to be simple or elementary ; if atoms of diverse kinds of matter unite to * See Appendix, Metric System of Weights and Measures. 26 NATURAL PHILOSOPHY. form a molecule, it is said to be compound. Thus the mole- cules of copper are made up of atoms of copper solely, and copper is consequently regarded as an elementary body ; on the other hand, molecules of sugar, of saltpetre, etc., are compound, the first named being made up of twelve atoms of carbon, twenty-two of hydrogen, and eleven of oxygen, and the second containing one atom of potassium, one atom of nitrogen, and three of oxygen. Atoms of different kinds of matter vary in weight, those of gold and lead, for example, being much heavier than those of hydrogen. By taking advantage of the extraordinary tinctorial power of certain aniline dyes, experiments have been made which show that an atom of hydrogen undoubtedly weighs less than 0.000,000,000,054 gramme ; ac- cording to another authority the weight of a hydrogen atom cannot be less than 0.000,000,000,000,000,000,000,000,0075 of a gramme. It is im- possible to conceive of such minute quantities, nor have these figures any practical value ; we give them chiefly as a subject of curiosity. The smallest particle of matter which can exist in a free state is the molecule ; atoms exist in combination only, and are sometimes defined as the smallest particle of matter which can enter into the composition of a molecule. The physical properties of bodies, hardness, transparency, elasticity, etc., depend mainly on their molecular relations; the chemical properties on their atomic relations. The study of the atomic composition of bodies, and of the laws governing their combination, is the province of chemistry, and will be fully explained in Part II. 9. Matter acted upon by Forces. The constant changes of form and mutual relations of bodies are caused by ex- ternal agents called forces. Gravitation, heat, light, and electricity are some of these forces. These physical forces were formerly regarded as exceedingly attenuated forms of matter, and, since they have no weight, were called ini- MATTER. 27 ponderable agents. At present, however, the opinion pre- vails that the phenomena caused by these forces result from the motions of the inappreciably minute particles of matter. It is believed also that there is in reality but one force in nature, and that heat, light, and electricity are different manifestations of this force. Just as a certain amount of matter was created, and continues to exist without diminu- tion in quantity, in like manner a definite amount of force was created, and this, too, is indestructible, though mani- festing itself in various ways to our senses. It will be shown farther on that the forces of heat, light, and electric- ity are mutually convertible and equivalent. They are all referred back to a common origin motion of the molecules of matter. The agency of the physical forces is of great importance and is very active, producing constant changes throughout nature ; they are also obviously and immediately essential to life. QUESTIONS.* [The numbers refer to the sections.] 1. What is meant by Science ? What is said about the classification of knowledge? Name some of the chief subdivisions. 2. What is said of ,he effects of matter on the senses ? 3. What are the forms of matter ? Illustrate the difference between elastic and non-elastic fluids. What is said of the union of the particles of a solid? Give the difference noted * Teachers differ much in their plans of conducting recitations. Some are very minute in their questions ; while others go to the other extreme, and merely name the topics, the pupils being expected to give in full what is eaid upon them. Nei- ther of these plans should be adopted exclusively, but the mode of recitation should be much varied from time to time. This variety is somewhat aimed at in the ques- tions which we have prepared, though in no case are the questions as minute as they should occasionally be made by the teacher. It would be well to have the pupils draw many of the figures upon the blackboard, and then recite from them. By drawing the simplest figures first sufficient skill may be acquired to enable the pupil to draw those which are quite difficult. 28 NATURAL PHILOSOPHY. between different solids. How does a liquid differ from a solid ? Give in detail what is said of water. What is said of the particles of gaseous sub- stances ? What of the atmosphere ? What of the vapor in it ?-^4. What is said of the entering of liquids and gases into interstices ? What of the mingling of gases with liquids ? Give the illustration in regard to fishes. What is said of the solution of solids in liquids ? What of the evaporation of water in the air ? 5. Illustrate the influence of heat on the forms of matter. What is said of the thermometer ? What of mercury, water, and iron in relation to the liquid state ? 6. What is said of our knowledge of matter ? What was the supposition of Newton about the composition of matter ? What is said of the changes of matter ? 7. What two supposi- tions have been made as to the internal structure of matter ? AVith whom did the more probable one originate? Name the principal reasons for adopting the molecular hypothesis ? Describe in full the chemical reasons. 8. What is said of molecules ? How near are we to seeing them ? How large are they believed to be ? What of their motions ? Of what are mole- cules composed? When are they elementary? Give examples. When are they said to be compound ? Give examples. What is said of the weight of atoms of hydrogen ? What properties of matter depend mainly on the molecular relations of bodies? 9. What forces act upon matter? What is said about the unity of force ? CHAPTER II. PROPERTIES OF MATTER. 10. Properties of Matter. All matter has properties or qualities ; these differ in the different kinds of matter as well as in substances of the same class. Some of these properties are common to all kinds and forms of matter, and are called universal properties ; others are peculiar to certain substances and are called specific properties. The properties of matter which we shall describe in this and the following chapters are : PROPERTIES OF MATTER. 29 Extension and Figure. Impenetrability. Indestructibility. Inertia. Universal Properties. ( _.. . ..... Divisibility. Porosity. Compressibility and Expansibility. L Elasticity. f Hardness. Flexibility and Brittleness. Specific Properties. . . 4 Tenacity. Malleability. I Ductility. Besides the specific properties named, there are others which do not here require detailed explanations, such as solidity and fluidity, transparency and opacity, color, etc. The universal properties are sometimes called essential properties ; that is, properties of which no kind or form of matter can be destitute. The distinction between the two groups named will be explained in the next section. 11. Extension and Figure. Extension is that property of matter by virtue of which a body occupies a limited portion of space and figure, the property by which it has some definite shape. You cannot conceive of any portion of matter, however small it may be, that does not occupy some space, and that has not shape or figure. This is, in fact, involved in the very idea of matter. A particle may be so small as to appear only as a point to the naked eye, but viewed through the microscope its shape becomes obvious. Even an atom must have length, breadth, and thickness, notwithstanding our inability to measure it or to see its shape with the most powerful microscope. The air is sometimes spoken of in common language as being shapeless. This is partly because it is invisible, and partly because no portion or body of air assumes any definite B 30 NATUKAL PHILOSOPHY. shape. But air is continually forced into definite shapes by confinement in rooms, boxes, etc. ; and then its extension in different directions can be measured as accurately as the extension of a solid. And, besides, the particles of which air is composed are undoubtedly solid, and we cannot con- ceive of their existence without attaching to them the idea of figure or extension. Extension is an essential or universal property of matter, since no por- tion of matter, hard or soft, can be destitute of extension ; on the other hand, hardness is not an essential property of matter, for some kinds of matter possess no hardness. 12. Impenetrability. In common language one substance is said to penetrate another when forced into it by pressure or by blows. Thus a needle penetrates cloth, a nail pene- trates wood, etc. But this .expression is not strictly cor- rect ; the needle does not enter the substance of the cloth, but goes between the fibres of it, pushing them to one side. And the nail goes between the fibres of the wood, and not into them ; it does not occupy the same room as the fibres at the same time. In like manner no atom of matter can penetrate or enter into any other matter, it can only push it out of the way, and then occupy its place. This property of matter where- by no two portions can simultaneously occupy the same place is called impenetrability. Impenetrability is usually accounted one of the universal properties of matter, but it is really a necessity of the existence -of matter and of its extension, as explained in 11. Illustrations. The property of impenetrability may be illustrated in many ways. If you hold a tumbler with its open end downward and press it into water, it will not fill with water, for the air in the tumbler prevents the water from rising; it cannot occupy the same space with the air. It fills indeed a portion of the tumbler, because the air is PROPERTIES OF MATTER. 31 compressible to a certain extent ( 17). If you introduce a glass funnel, a, Fig. 1, into a jar of water, , the water will not rise to fill it so long as you close the opening, c, with your finger. But if you remove your finger, the water will rise to the level of the water outside of the fun- nel, pushing out the air before it. The follow- ing neat experiment illustrates the same point. Float a lighted candle, a, Fig. 2, on a large flat cork (weighted with lead so as to support the candle) in a jar of water, and place over it an open jar or receiver, &, provided with a stop- cock, c. If you close the stopcock and press the receiver into the water, the candle will sink with it as represented in the figure, the air preventing the water from entering the jar. As soon as you open the stop- cock, however, the water will rush in, and the can- dle will appear to rise out of the water. Other Illustrations. The diving-bell, used for exploring the bottoms of rivers, lakes, etc., affords a good illustration of this property of matter. It consists of a metallic vessel, A, Fig. 3, shaped somewhat like a bell, and made suffi- ciently heavy to sink in water. It is lowered into deep water by means of a chain and cable, r m q. The water does not enter the bell any farther than the compressibility of the air allows. In order that the men in the bell may Fig. 2. 32 NATURAL PHILOSOPHY. remain under water for some time, fresh air is supplied by the tube I, being forced in by a pump, and the vitiated air is allowed to escape through valves provided for that purpose. The seats, s, s, are for the accommodation of the men who descend in the bell to work at the bottom of the sea or river. By this means treasures are often recovered which would otherwise be lost. You will observe some resemblance between the diving-bell and the ar- rangement shown in Fig. 2, the receiver representing the bell, and the lighted taper the men within. When a bullet is dropped into a glass of water it pushes the particles to one side, and occupies the room thus gained. If several bullets are thrown in, there is an evident rise of the water, and you may add enough to make it overflow. The same thing is true of the finest needle dropped into wa- ter ; it does not penetrate the water, but, like the bullet, displaces the par- ticles. When any substance, sugar or saltpetre for example, is dissolved in wa- ter, its particles do not penetrate those of the water, but they enter the spaces between the particles. In more concise language, solution results from inter-molecular penetration. In like manner when particles of odor- ous substances are diffused in the air, they are in fact between its particles. v 13. Indestructibility. We have alluded to the indestruc- tibility of matter in Chapter I, but it now requires ampli- fication. When substances waste away, or are burned up rapidly, the matter of which they are composed does not cease to exist it merely changes its form or condition. Gold may be melted, and even converted into vapor, but the form merely changes, and its substance is not lost. A candle* grows shorter and lighter as it burns, but by means of suitable apparatus it is possible to collect all the gases, smoke, etc., which invisibly rise, and it is found that there is no loss in weight. In short, we cannot create matter, and we cannot destroy it ; it is imperishable. The universe contains the same amount of matter as when first called into being by Omnipotence, and not the smallest particle will be put out of existence to the end of time. We occasionally hear of new elements, new kinds of matter, dis- covered by chemists ; but this signifies that the body discovered had pre- PEOPEETIES OF MATTER. 33 viously escaped observation, either on account of its great rarity, or by reason of the difficulty of distinguishing it from its associated substances having similar properties. New elements are discovered, not created, by chemists. The indestructibility of matter is forcibly brought to the mind of the chemist, who witnesses in his dealings with matter such marvellous transformations, disappearances, and reappearances. The changes which the various kinds of matter undergo belong to the province of Chemistry, and will be fully explained in Part II. 14. Inertia. Matter has no power to put itself in motion ; when it is moved, it is acted upon by some force outside of the matter, or communicated to it in some way. When your arm moves, it is not the matter in your arm that causes its motion ; it is the result of a force within you, exerted in obedience to the will. A book lying on a table has no power within itself of moving to another place ; and if you reach out your arm, pick it up, and throw it across the room, you communicate force to it from without, and thus set it in motion. When air moves, it is set in motion by some force acting upon it, as when you blow it from your lungs or move it with a fan. When the wind blows, the air is set in motion by heat and the attraction of the earth, as will be explained in another part of this book. Again, matter when set in motion has no power to stop itself. This inability of matter to move itself or to stop its motion is called inertia. If matter could stop itself, it would not be called inert. Owing to this inertness, matter once set in motion would keep moving forever were it not stopped by some force ; matter has no more tendency to stop moving when once put in motion than it has to begin motion when it is at rest. All motion would be perpetual if there were not forces opposing it. If there were only one body in the universe, and that were set in motion, it would move forever through empty space in a straight line ; for there would be no matter anywhere to resist its mo- tion or to attract it away from its onward course. 34 NATURAL PHILOSOPHY. When a stone falls to the ground, it stops simply because the earth ar- rests it. If the earth were not in the way, the stone would move straight on until it reached the centre of the earth ( 26). A stone thrown up in the air would keep on, and soon be out of sight, and never return to the earth, if it were not made to come down by forces acting upon it. One of these forces is the resistance of the air, which, from the moment the stone starts, is destroying its motion. Another force as constantly operat- ing to retard the stone is the attraction, or drawing force, exerted by the earth upon it. This powerful though unseen' force will be treated of fully in Chapter IV. Advantage is taken of inertia in matters of e very-day life. The massive fly-wheel of a stationary engine, once started on its course, continues to revolve by virtue of its inertia, and to give a steady regular motion to the machinery with which it is connected. The fly-wheel is made very heavy, because the heavier it is the greater resistance it offers to the friction which continually tends to stop its motion. When the locomotive of an incoming train is dis- connected and shoots swiftly ahead, the train, by virtue of its inertia, or inability to stop itself, follows after until its motion is spent or an application of the brakes brings it to rest. It is owing to the inertia of matter that leaping from a rapidly moving train is dangerous; a person on the cars partakes of their motion, and, on jumping off, his feet come suddenly to rest while his body continues to move forward, and he is thrown headlong to the ground. The inertia of matter may be illus- trated by a pleasing experiment. Bal- ance a card on the neck of a bottle, and place a small coin on the card directly over the opening ; by giving the card a quick, sharp blow with the finger, in a horizontal direction, the card will fly away and the coin will fall into the bot- Fig * 4 * tie. The coin does not move with the PROPERTIES OP MATTER. 35 card, because sufficient time does not elapse for the coin to partake of its motion. The law of inertia was first recognized by Galileo, an eminent Italian philosopher, about the close of the sixteenth century. A correct compre- hension of this important law was necessary before true explanations could be given of the laws governing the falling of bodies, of the vibrations of the pendulum, and of the motions of the planets in their orbits. 15. Divisibility of Matter. Any portion of matter, wheth- er solid or gaseous, may be divided into parts. Even if it be so small that it can be seen only with a powerful micro- scope, it could be still further subdivided, provided a suffi- ciently delicate instrument were available. A particle of matter the five-thousandth of a millimetre in diameter is no longer visible under a powerful microscope, and yet nothing but man's natural incapabilities prevents the divi- sion being carried yet finer. Whether or not there be a limit to the divisibility of matter is a question which has been discussed by philosophers in all ages. The theory prevailing at present is, that matter is not infinitely divis- ible, but is made up of definite ultimate parts called atoms, as explained in Chapter I. Of the actual divisibility of matter we have numerous examples, in which the division is carried far beyond that which can be effected by any cutting instrument. A gold-beater can hammer a grain (65 milligrammes) of gold into a leaf covering a space of fifty square inches (322.5 square centimetres). So thin is it that it would take 300,000 of such leaves, laid upon each other, to make the thickness of an inch. And yet so even and perfect is this thin layer of gold, that when laid upon any surface in gilding it has the appearance of solid gold. One fifty-millionth part of this grain of gold thus hammered out can be seen by the aid of a microscope which magnifies the diameter of an object ten times. 36 NATURAL PHILOSOPHY. Recently the divisibility of gold has been carried much farther. Mr. Outerbridge, of Philadelphia, has obtained (by electric deposition) films of gold so thin that one grain of the metal would cover nearly four square feet (0.37 square metre). This is ten thousand times thinner than ordinary writing-paper, and 2,798,000 such films would measure only one inch. Gold-leaf of this tenuity is trans- parent and transmits a green light. Further Illustrations. A soap-bubble is a beautiful example of tbe minute division of matter. That thin wall which encloses the air is composed of particles of the soap and of the water mingled together. It is supposed to be less than one millionth of an inch in thickness. The thread of the silk-worm is so minute that the finest sewing-silk is formed of many of these threads twisted together. But the spider spins much more finely than this. The thread by which he lets himself down from any height is made up of about 6000 threads or filaments, each coming from a separate hole in his spinning-machine. A quarter of an ounce (7.77 grammes) of the thread of a spider's web would extend 400 miles (643 kilometres). Platinum, which is usually regarded as the heaviest known metal, can be drawn out into wire still finer than the web of the spider ; 3000 feet (914.4 metres) of this wire weigh scarcely one grain (65 milligrammes), and a bundle of 140 of these wires would equal in thickness only a single silk- worm thread. See 22. Perhaps the most minute division of matter is exemplified in odors. A grain of musk will scent a room for years, and yet suffer no perceptible loss of weight. But during all this time the air is filled with fine particles coming from the musk. The microscope reveals to us many wonderful examples of the minute- ness of the particles of matter, both in the vegetable. and the animal world. If you press a common puff-ball a dust flies off like smoke. Examined with a microscope, each particle of this dust, which is the seed of the plant, is a perfectly round orange-colored ball. This ball is of course made up of very many particles, arranged in this regular form. Beautiful examples of various arrangements of the minute particles of matter are furnished by the pollen of different plants, as seen with the microscope. Each particle of the dust which adheres to yonr fingers as you catch a moth is a scale with fine lines upon it regularly arranged. And if you PROPERTIES OP MATTER. 37 look through the microscope at the wing of the moth, you will see, where the scales are rubbed off, the attachments by which they were held standing up from the surface of the wing, like nail-heads on a roof from which the shingles have been torn. The organization of exceedingly small animals, as re- vealed by the microscope, furnishes us with wonderful examples of the minute division of matter. A little of the dust of guano, examined through a powerful microscope, is seen to contain multitudes of shells of various shapes. These shells are the remains of animalcules that lived in the water, their destiny seeming to be in part to furnish food to other animals larger than themselves. In the chalk formations of the earth are seen multitudes of such shells. They have been discovered even in the glazing of a visiting- card ; for they are so small that the fine grinding-up of the chalk does not wholly destroy them. There are animals, both in the air and in the water, so small that it would take millions of them to equal in bulk a grain of sand, and a thousand of them could swim side by side through the eye of a common-sized needle. ISTow all these animals are furnished with organs, constructed of particles of matter, which are arranged in them with as much order and sym- metry as in the organs of our bodies. How minute, then, must these particles be ! How do such facts extend our views of the power of the Deity ! The same power that moulded the earth, sun, moon, and the whole " host of heaven," gave form and life and motion to the millions which sport in every sun- beam; the same eye that watches the immense heavenly bodies as they move on in their course looks upon one and all of these legions of animals in earth, air, and water, though unseen by human eyes, and provides that every particle shall take its right position, so that this part of creation may with all the rest be pronounced very good ; B 2 38 NATURAL PHILOSOPHY. and the same bountiful hand that dispenses the means of life and enjoyment to the millions of the human race for- gets not to minister to the brief life and enjoyment of each one of these myriads of animalcules, though they seem to be almost nothingness itself. QUESTIONS. 10. What is said of variety in the properties of matter ? Give the clas- sification. 11. What is meant by extension? What by figure? Has the air any extension or figure ? 12. Illustrate the meaning of impene- trability. Describe the experiment with the funnel and a jar of water. Also the experiment with the candle. State the arrangement of the div- ing-bell. Give the comparison between bullets and needles in relation to penetration. What is said of solution? 13. Explain what is meant by the indestructibility of matter. Can we create matter? What, then, is meant by new elements ? 14. What is inertia ? Give illustrations of it. Illustrate the fact that matter has no power to stop its own motion. What stops a body set in motion ? Illustrate by reference to a stone. What advantage is taken of inertia. Describe an experiment illustrating the inertia of matter. Who first recognized this law? 15. What is said of the divisibility of matter ? Give an example of the divisibility of matter by reference to gold-leaf. What is said of the soap-bubble? What of the thread of the silk-worm, and of the web of the spider? What of platinum wires? What of odors? What is said of the dust of the puff-ball ? What of pollen ? What of the dust rubbed from a moth's wing ? What of guano ? What of the glazing of visiting-cards ? What of the minuteness of some animals ? What is said of the Deity in re- lation to minute animals ? PROPERTIES OF MATTER. 39 CHAPTER III. PROPERTIES OF MATTER (CONTINUED). 16. Porosity. The particles composing bodies of every description are surrounded by empty spaces; those sub- stances which are called porous have quite large spaces in them. But even in those which are not commonly con- sidered porous the particles are by no means close to- gether. A celebrated experiment, tried at Florence in 1661, showed that the particles of even so dense a sub- stance as gold are separated by spaces sufficiently large to let water pass through them. A hollow golden globe con- taining water was subjected to great pressure, and its sur- face was bedewed with the water that came out through the pores of the gold. There are two kinds of pores sensible pores, which can be distinguished by the naked eye or by the aid of the microscope, and physical pores, or interstices among the molecules alluded to in Chapter I. Sensible pores are visi- ble in wood, sponge, pumice-stone, etc. ; physical pores are invisible, but their existence is shown by the fact that substances can be compressed into a smaller bulk than they usually occupy. Solids can be thus compressed; some more than others. But the most compressible substances are the gases and vapors. The amount of space between their particles must be very large to allow of so great com- pression. \Ve can form some idea of the great amount of space in a gaseous or aeriform substance by observing the difference between water in its liquid 40 NATURAL PHILOSOPHY. and in its aeriform state. A cubic cen- timetre of water, converted into steam, occupies 1696 times more room than be- fore. The difference in proportion is ex- hibited in Fig. 5, the inner circle repre- senting a volume of water, and the outer that of the steam into which it is con- verted. The water is not at all altered in its nature by being changed into steam. The particles are simply forced farther apart by the heat, and as soon as the Fig. 5. heat is withdrawn they come together again to form water, or, in other words, the steam is condensed into water. It is plain, therefore, that the space between the particles is 1696 times as great in steam as it is in the water from which the steam is made. When any substance, as sugar or salt, is dissolved in water, its particles are diffused through the intermolecu- lar spaces. In like manner, when water evaporates, the particles of water are diffused through the spaces between the particles of the air. Animal and vegetable bodies are the most porous, being constituted of an immense number of interlacing channels through which during life nourish- ing fluids circulate. This is evident on examination of bone and of wood which abound in cells and partitions. Density and Rarity. The density of a substance de- pends upon the quantity of matter it contains in a given space. The more dense, therefore, a substance is, the greater its weight. A piece of lead is forty times heavier than a piece of cork of the same size. Mercury is near- ly fourteen times heavier than an equal bulk of water. You see, then, that density must depend on the nearness of the molecules to each other. In so dense a substance as gold the molecules are all very close together ; in wood there are spaces, some of which are so large that you can see them ; and in air, steam, and the gases there PROPERTIES OF MATTER. 41 is a great deal of space among the particles, so that we speak of their rarity instead of their density. 17. Compressibility and Expansibility. Owing to poros- ity, matter may be compressed and expanded. Pressure applied to porous substances brings their particles nearer together, making them fill up in part their pores. You have a very familiar example of this in sponge. The greater the porosity of wood, the greater its compressi- bility. But even such dense substances as the metals can be compressed in some degree ; that is, the interstices be- tween their particles can be made smaller. Medals and coins have their figures and letters stamped upon them by pressure, just as impressions are made upon melted sealing-wax. The heavy and quick pressure required to do this actually compresses the whole piece of the hard metal, putting all the particles nearer together, so that it occupies less space than it did before it was stamped. It might be supposed from the freencss with which the particles of liquids move among each other, and from the spaces which exist among them, that these substances could be easily compressed. But it is not so. The heavi- est pressure is required to compress them even in a slight degree. Water can be compressed so very little that prac- tically it is regarded as incompressible. Although the interstices between the particles of -liquids cannot be varied by mechanical pressure, they can be by variations of temperature. Liquids are dilated or expanded by heat ; that is, their particles are put farther apart. They are contracted or compressed by cold ; that is, their particles are brought nearer together by the abstraction of heat. The most familiar example is the thermometer. The mercury rises in the tube when the heat increases the interstices between its particles, and it falls when the loss of heat allows the particles to come near together. Aeriform bodies are more compressible than any other substances, showing that in their ordinary condition there 42 NATURAL PHILOSOPHY. is a great deal of space among their particles. While they are thus unlike liquids in compressibility, they are affected by heat in the same way. 18. Elasticity. Closely allied to the compressibility of matter is its elasticity. We see this property strikingly exemplified in India-rubber. It occasions the rebounding of a ball of this substance when thrown against any immovable body the floor, for example. When the ball meets the resistance of the floor it is flattened, as rep- resented in Fig. 6. Then, as it assumes the round shape, shown in Fig. V, it Flg - 6 - Fig. 7. pushes downward upon the floor. . It is this sudden pushing downward that makes it rebound. It is as if there were a compressed spring be- tween the ball and floor. It may be likened also to jump- ing. When a person jumps he bends his limbs at the thigh and knee-joints, and then, in straightening himself up, gives a sudden push, like that given by the ball as it assumes its round shape, and so is thrown forward or upward, accord- ing to the direction of the pushing force. The same flat- tening occurs in an ivory ball, though to a far less de- gree. You can prove this by experiment. Let a marble slab be moistened, and drop the ball upon it. Quite a spot will be made dry by the blow of the ball, showing that it touched more of the marble than it does when merely placed upon it. When a stick or rod is bent, as soon as the bending force is withdrawn the stick becomes straight again from its elasticity. It is this elastic force of the bow, straightening it, that speeds the arrow. Observe in this case that while the particles on the concave side of the bent bow are brought nearer together, or compressed, those on the convex side are moved apart. This moving apart of the particles is often shown in India-rubber. You will see how very far apart particles in near neighborhood may be carried PROPERTIES OP MATTER. 43 if you stick two pins close together in a strip of India-rubber, and observe their movements when you stretch it. Some substances have so very little elasticity that practically they are considered as having none. Lead is one of these. A rod of lead when bent remains so, and a leaden ball does not rebound. While aeriform substances are the most compressible of all, they are also the most elastic. Compressed air returns to its usual condition the moment it is relieved from the pressure, and with a force proportioned to the amount of the pressure. So it is with steam and the gases. The varied results of this property of aeriform substances will claim our attention more par- ticularly in some other parts of this book. Glass is nearly perfectly elastic that is, it will retain no permanent bend ; but the limits of its elasticity are very small: it will not bend far without breaking. Hard bodies in general have a much smaller elastic limit than soft ones. This is evident on comparing the elasticity of steel, ivory, stone, glass, etc., with that of silk, catgut, India-rubber, and the like. Elasticity may be defined as that property of matter by which its particles, when brought nearer together or car- ried farther apart by any force, return to their usual con- dition when the force is withdrawn. Closely connected with elasticity is the property of flexibility, which will be explained in the next section. \ 19. Flexibility and Brittleness. If you bend a flexible body a piece of wood, for ex- ample it is obvious that the particles on the upper or con- vex side must be forced a lit- Fi s- 8 - tie farther apart, while those on the under or concave side are brought a little nearer together (Fig. 8). But the wood does not break, because the particles that are thus moved a little apart still retain their hold upon each oth- er. This is the explanation of what is called flexibility. On the other hand, the particles in a rod of glass cannot 44 NATURAL PHILOSOPHY. be put farther apart in this way. They are not actually in contact any more than are the particles of the wood, but they are in a fixed .relative position ; that is, a position which cannot be disturbed without & permanent separation of particles. If you attempt to bend the rod there is no slight separation of many particles, as in the bent wood, but a full and permanent separation in some one part of the rod. We call the property on which this result depends brittleness. Brittle substances are generally hard. Glass, while the most brittle of all substances, is hard enough to scratch iron. Steel. There are two kinds of steel, flexible and brittle. The steel of most cutting instruments* is brittle. The steel of a sword-blade is quite flexible, and that of a watch-spring is so much so that we can wind it up in a coil. This difference is owing to a difference in the mode of cooling the steel. If it be cooled suddenly, it is brittle ; if slowly, it is flexible. The process by which it is cooled slowly is called annealing. The expla- nation of all this is quite simple. The steel being expanded by heat that is, its particles being put farther apart than they usually are when they are suddenly brought together again they have not time to arrange their relative position properly. Brittleness is, therefore, the result. But, on the other hand, when the cooling is effected gradually, time is given for the arrangement. Steel suddenly hardened is too brittle for common use. A process called tempering is therefore resorted to for diminishing the brittleness. The steel is reheated after the hardening, and is then allowed to cool slowly. The degree in which the brittleness is lessened depends on the degree of heat to which the steel is subjected. It can be entirely removed by a red heat, for then the particles have a full opportunity to readjust themselves; and the more the heat comes short of this point the less thorough will be the adjustment, because the less perfectly are the particles released from their suddenly taken position. In lessening the brittleness we diminish hardness also, and therefore the tempering is varied in different cases ac- cording to the degree of hardness desired. Annealing of Glass. Glass for economical uses is always annealed. If this were not done our glass vessels and win- dow-panes would be exceedingly brittle, and be constantly PROPERTIES OF MATTER. 45 breaking. Articles made of glass are annealed by being passed very slowly through a long oven which is very hot at one end, the heat gradually lessening towards the other end. We have a striking example of brittleness induced by sudden cooling in what are called "Prince Rupert's Drops." These are made by dropping melted glass into cold water, and they usually have a shape resem- bling that of Fig. 9. If you break off ever so small a bit of the point of one of these drops, the whole will at once shiver to pieces. That is, the sudden arrangement of the particles is so slight and unnatural that the disturbance of the arrangement in a small part suffices to destroy the arrangement of the whole, very much as a row of bricks is thrown down by the fall of the first in the row. Faraday says that those drops were not, as is commonly supposed, invented by Prince Rupert, but were first brought to England by him in 1G60. They excited much curiosity at that time, and were considered "a kind of miracle in nature." But you see that this, like many other wonders, is capable of an easy explanation. The so-called "tempered glass," invented by a Frenchman named La Bastie, affords another example. La Bastie's process consists in heating the glass to a certain temperature, and passing it through oil or fatty ma- terials ; glass articles thus treated are rendered tough enough to stand rough usage, such as dropping on a wooden floor from a height of ten feet, and even hammering to a certain extent. And yet the glass is in a pe- culiar condition, and, when broken, is shivered into thousands of pieces, much as is the case with Prince llupert's Drops. 20. Hardness. This property seems to depend upon some 46 NATURAL PHILOSOPHY. peculiar arrangement of the particles of matter. We should suppose that the densest substances would be the hardest. But it is not so. Iron is the hardest of the metals, but its particles are not so close together as those of gold, which is quite a soft metal. And gold is about four times as heavy as the diamond, which is so hard as to cut glass easily. Common flint is hard enough to scratch glass, but will not cut it so well as the diamond. Advantage is taken of the different degrees of hardness possessed by minerals in determining their species. In the following table a number of minerals, whose degrees of hardness is very uniform, are arranged so as to form a con- venient scale, by reference to which the hardness of any substance can be determined. It is only necessary to secure specimens of the minerals named, and to ascertain which of these ten the body under trial will scratch. Since, how- ever, it is not always possible to obtain a complete set of these minerals, we have added remarks showing approxi- mately their hardness : SCALE OF HARDNESS. 1. Talc ; easily scratched by the finger-nail. 2. Gypsum ; not easily scratched by the nail ; does not scratch a copper coin. - < 3. Pure limestone (calcite) ; is scratched by a copper coin. 4. Fluor-spar ; not scratched by a copper coin. 5. Apatite ; scratches glass with difficulty, but is easily scratched by a knife. G. Feldspar ; scratches glass easily ; is scarcely scratched by a knife. 7. Quartz ; not scratched by a knife. 8. Topaz ; harder than quartz. 9. Corundum ; harder still. 10. Diamond ; is scratched by no other substance. The property of hardness depends on some circumstances not perfectly understood, for a- substance may be hard or soft according to the manner in which it is treated. That this is the case with steel has been mentioned PROPERTIES OP MATTER. 47 21. Tenacity. The power possessed by substances which causes them to resist being pulled asunder, termed tenac- ity, depends on the degree of attraction between the par- ticles. By attraction we mean a disposition in particles to come together, this disposition being manifested in op- position to any force tending to draw them apart. Tenac- ity does not exist at all in gaseous substances. The par- ticles of air and of steam, for example, show no disposition to cling together that is, have no tenacity. This property is weak in liquids; it is only strong enough in water to enable its particles to hang together in the shape of a drop. It is strong in solids, enabling their particles not only to hold together in large quantities, but also to hold up heavy weights suspended to them. It is strongest of all in steel. Various metals and other substances have been tested to ascertain their comparative tenacity. It was done in this way : Rods were made of the metals, etc., all of the same size, having, in fact, a cross-section of one square inch. Weights were suspended to them, and additions were made to the weights little by little till the rods broke. The table below was made by placing against each substance the greatest weight that its rod would sustain : TABLE SHOWING COMPARATIVE TENACITY OF MATERIALS. Cast steel 45 to 60 tons. Best wrought iron . 25 to 30 " Cast iron C to 13 " Copper 9to26 ' Platinum 8 Ash-wood 8 Silven 5 Beech-wood 5 Gold..... 4J- Zinc 2 tons. Tin about H to 2 " Lead.. 1 ton. 48 NATUKAL PHILOSOPHY. Some animal substances have great tenacity, as the thread of the silk -worm, hair, wool, and the ligaments and tendons of our bodies and of other animals. "The gradual discovery," says Dr. Arnott, " of substances possessed of strong tenacity, and which man could yet easily mould and apply to his purposes, has been of great importance to his progress in the arts of life. The place of the hempen cordage of European navies is still held in China by twisted canes and strips of bamboo ; and even the hempen cable of Europe, so great an improvement on former usage, is now rapidly giving way to the more complete and commodious security of the iron chain of which the material to our remote ancestors existed only as useless stone or earth. And what a magnificent spectacle it is, at the present day, to be- hold chains of tenacious iron stretched high across a channel of the ocean, as at the Menai Strait between Anglesea and England, and supporting an admirable bridge-road of safety, along which crowded processions may pour, regardless of the deep below or of the storm ; and beneath which ships, with sails full-spread, pursue their course unmolesting and unmolested." 22. Malleability and Ductility. Those metals which can be hammered into thin plates are called malleable. Gold furnishes us with the best illustration of this property. We have already mentioned ( 15), that a single grain of gold can be hammered out into a sheet the one 300,000th part of an inch in thickness. An alloy of 20 parts of gold and 22 of silver is equally malleable. Silver, copper, and tin are quite malleable; but the thinnest leaves of tin are the one 1600th part of an inch in thickness. Most of the other metals are very little so, and some of them are not at all, breaking at the first blow. A substance is said to be ductile when it can be drawn out into wire. The principal metals that have this quality are platinum, silver, iron, copper, and gold, and in the order named. The celebrated English chemist Dr.Wollaston obtained a platinum wire only the one 30,000th part of an inch in di- ameter by the following ingenious process. A small plat- inum wire was soldered within a cylinder of silver, and PEOPEETIES OF MATTEE. 49 the compound wire was drawn out in the usual way as fine as possible. The silver was then dissolved off by immersing the wire in nitric acid, and the platinum core remained about half the thickness of the thread of a spider's web. Melted glass is very ductile. It can be drawn out into a very fine thread ; and when this thread is cut and arranged in bunches, it resembles beautiful white hair. In hammering metals into plates, or drawing them into wire, there is a considerable change of relative posi- tion in the particles, similar to that which we have in fluids, though nothing like so free. In this change of position, those particles that remain in close neighbor- hood have a remarkable tenacity or attraction, preventing their separation. In welding two pieces of iron, which is done by the blacksmith by hammering them together when red-hot, there must be enough movement among the particles to permit those of one piece to mingle some- what with those of the other. 23. Usefulness of Variety in Properties of Matter. The vari- ous properties of matter brought to view in this and the preceding chap- ters are providential adaptations to the necessities of man. Each substance has those properties which best fit it for his use. Iron, for example, de- signed by the Creator to be both the strongest and most extensively useful servant of man among the metals, is therefore provided in great abundance, and has those strong, decided, and various qualities which fit it for the services it is to perform. Gold and silver, on the other hand, designed for services less extensive, and in a great measure ornamental, are provided in very much less quantity, and have properties admirably adapting them to the services for which they are so manifestly intended. The same can be substantially said of all other substances, and especially of those very abundant ones air and water. And it may be remarked also that the ingenuity of man is continually discovering new modes of bringing the various properties of matter into his service. We will give but a single il- lustrationthe tempering of steel. "This discovery," says Dr. Arnott, "is perhaps second in importance to few discoveries which man has made; for it has given him all the edge-tools and cutting instruments by which 50 , NATUllAL PHILOSOPHY. he now moulds every other substance to his wishes, and to which he owes all his modern mechanical improvements. A savage would work for twelve months with fire and sharpened flints to fell a great tree or carve a rough canoe, where a modern carpenter, with his tools of hard steel, could accomplish the same object better in a few days." QUESTIONS. 1C. What is meant by the porosity of matter? Show that gold is porous. Name the kinds of pores, and explain by illustrations. What proof is there that all substances have spaces in them ? What is said of the amount of space in gases and vapors? Give the statement in regard to steam. What is said of solutions of solids in fluids ? What of evapo- ration ? What of animal and vegetable bodies ? Upon what do density and rarity depend ? 17. What is said of compressibility ? Illustrate. What of the incompressibility of liquids ? How is the position of the particles of liquids affected by a change of temperature ? Which are the most compressible substances? 18. Explain elasticity by reference to a rubber-ball. Illustrate by reference to a bent stick. W T hat is said of the degrees of elasticity in different substances? Define elasticity. 10. Il- lustrate what is meant by flexibility. What of brittleness? Give ex- amples of flexible and brittle steel. Explain the actual difference be- tween them. Explain the tempering of steel. What is said of the an- nealing of glass ? What of Prince Rupert's Drops ? What of "tempered glass ?" 20. Upon what does the hardness of bodies depend ? What use is made of the different degrees of hardness in minerals? Name the typical minerals. 21. Define tenacity. What is said of the comparative tenacity of substances ? Which metal is the strongest ? Which the weakest? What is said of the value of tenacious bodies? 22. What is the difference between malleability and ductility ? Give examples. 23. What is said of the usefulness of the variety of properties in matter ? What of the importance of steel ? ATTRACTIONS OF MATTER. 51 CHAPTER IV. ATTRACTIONS OF MATTER. 24. Matter attracts Matter. We have already stated that matter is acted upon by forces, and we will now ex- plain this more fully. The minute particles of matter of which bodies are composed do not touch each other, but even in the densest substances are surrounded by void spaces, and these particles are held in their place by at- traction between them, each particle of matter attracting every other particle. This property invariably accom- panies matter of every form and under all circumstances. And since tangible masses are made up of small particles, what is true of the latter is equally true of the former. Every body in the universe attracts with greater or less force every other body, however near or distant they may be from each other. Sun, earth, moon, and stars attract each other; and this power binds them together as they roll through space. This force is generally called the attrac- tion of gravitation, a name given to it because we have such common examples of its influence in the fall of bodies jto the earth ; they are said to gravitate towards the earth. Whether the mysterious force which binds the minute particles of matter together to constitute masses is the same as that which controls the motions of celestial bodies is as yet unproved. That an attraction actually exists between small masses when they are brought ex- ceedingly close to each other is easily shown. Thus if two cork balls coated with varnish be placed on the sur- face of water near to each other, their attraction will soon 52 NATUJJAL PHILOSOPHY. bring them together. Thin globes of glass will exhibit the same attraction. So, also, floating pieces of wood are apt to be found together ; and when a ship is wrecked, the parts of the wreck collect in tangled masses here and there on the surface of the sea as soon as it becomes calm. The gravitation between particles and masses of matter may possibly be identical, and our appreciation of it depends upon their relative size and distance. For convenience of distinction, different names have been given to attrac- tion according to the distances at whiclrit acts. Gravitation is the attraction existing between matter at great or appreciable distances, as between the heavenly bodies, or between the earth and a stone thrown into the air. Cohesion is the attraction between molecules of the same kind of matter binding them together to form masses. Adhesion is the attraction between molecules of dis- similar matter, as exhibited in cements. A peculiar kind of adhesion is known as capillary attraction. Chemical attraction is the force which binds together the atoms of a molecule ( 8). Its study is the province of chemistry and will be fully treated in Part II. Explanations and illustrations of the phenomena result- ing from these attractions will occupy the remainder of this chapter and the succeeding one. 25. Gravitation. A stone falls to the ground for precisely the same reason that the two cork balls approach each other when floated on water ( 24). It falls owing to the attraction which the earth and the stone have for each other; in other words, the attraction is mutual. If you hold a stone in your hand and thus prevent its falling, you simply resist a power which is pulling it down. If it were possible to suspend the mutual attraction of the earth and the stone, you could release your hold of the stone, and it would remain suspended in the air until the attraction had ATTK ACTIONS OP MATTER. 53 been restored. The attraction of the earth and the stone is really mutual; but the earth is so immense in comparison with the stone that its motion towards the stone is exceed- ingly small, and may practically be considered as naught. This may be clearly illustrated by a comparison of the force of attraction with the force of muscular action. Suppose a man in a boat pulls on a rope which is made fast to a ship lying loose at the wharf, and in this way draws his boat towards it. He does not consider that he moves the ship at all ; but in reality he does, for if, instead of one, a hundred or more men in boats pull upon the ship, they will make the motion apparent. In the case of the single boat, the motion of the ship is as real as when a hundred boats are pulling it, but it is only tlie one-hundredth part as great. Now let the ship represent the earth, and the little boat some object, as a stone, at- tracted by it. The earth and the stone move towards each other, just as the ship and the boat do. And if, as we multiplied the number of boats, we should multiply the bulk of the stone till it is of an immense size, it would by its attraction have a perceptible influence upon the earth. Observe in regard to the illustration that it makes no difference whether the man pull in the boat or in the ship. In either case he exerts an equal force on the ship and the boat, making them to approach each other. So it is with the attraction between the earth and the stone. It is a force exerted equally upon both. Its effect on the earth is not manifest, because it is so much larger than the stone; just as the effect of the man's exertion is not manifest upon the ship, because it is so much larger than the boat. Proportion of the Mutual Motions of Attraction. Let us pursue the illustration a little farther. If a man stand in a boat, and pull a rope made fast to another boat of the same size and weight, both boats, in coming to- gether, will move over the same space. Just so rt is with the attraction between two bodies having the same quantities of matter or equal masses they attract each other equally, and therefore meet each other half-way. Suppose, however, that one boat is ten times as great and as heavy as the other. The small boat would move ten times as much as the large one when the man brings them together by pulling the rope. In like manner, if a body one tenth as large as the earth should approach it, they would attract each other, but in coming together the body would move ten times as far as the earth. In the case of falling bodies, even though they may be of great size, the earth moves so slightly to meet them that its motion is wholly imperceptible. It has been calculated that if a ball of earth the c NATURAL PHILOSOPHY. tenth of a mile in diameter were placed at the distance of a tenth part of a mile from the earth, and let fall, the motion of the earth would be only the one eighty-thousand-millionth (^o^^o'Vo^ ow) P art f an inch. 26. Attraction Towards the Earth's Centre. All bodies are attracted towards the centre of the earth. This is because the earth is spherical. Let the circle, Fig. 10, represent the earth, and a a body attracted by it. The lines drawn from the body to the earth represent the attractive force exerted by the earth upon the body. It is obvious from these that there is as much attraction on the one side of the line drawn from the body to the earth's centre as there is on the other. The attractive force, then, of the earth as a whole is ex- erted upon the body in the direction of this middle line. It tends to draw it, therefore, towards the centre. Consequently, a plumb-line points towards the centre of the earth, and it is evident that two weights sus- pended by two strings do not hang per- fectly parallel to each other. The dif- ference is so slight in an ordinary pair of scales that it cannot be perceived. But if it were possible to suspend in the heavens a beam so long as to stretch over a large extent of the earth's cir- cumference, as represented in Fig. 11, the scales attached to it would be very far from hanging parallel to each other. Substances suspended in different parts of the globe are hanging in different directions, and those which are hung Fig. 10. ATTRACTIONS OF MATTER. 55 up by our fellow-men on the opposite side of the earth are hanging directly towards us. Up and Down. All falling bodies fall towards the centre of the earth, and the remarks made in relation to suspend- ed weights are similarly applicable. Up and down are merely relative terms up being from the centre of the earth, and down towards it. As the earth moves round on its axis, the same line of direc- tion Avhich we call upward at one time is downward at an- other. This may be illustrated by Fig. 12. Let the circle rep- resent the circumference of the earth. In the daily revolution we pass over this whole circle. If we are at D at noon, we are at E at six o'clock, and at F at midnight. If, therefore, the ball A be dropped from some height at noon, the line in which it falls will be at right angles to a line in which it will fall if dropped from the same height at six o'clock; for this height will have moved in this same time from A to B. If it be dropped from- the same height at midnight, its line of direction will be directly opposite to the first ; for the place of the experiment will have moved in that time to C. It is not always true that falling bodies tend exactly towards the centre of the earth. The centre does not attract them, but it is the substance of the whole earth ; and since this is irregular in ijs density and form, the attrac- tion will be irregular also. Thus it is found by accurate experiments that a plumb-line suspended in the neighborhood of a mountain is attracted by it, and will not hang exactly parallel with another suspended at some dis- tance from the mountain. The difference is not, however, enough to have any practical bearing. 56 NATURAL PHILOSOPHY. 27. "Weight. That which we call weight is not a property of matter, but merely the resisted attraction of the earth. If two bodies fall to the earth, and one of them contain ten times as many particles of matter as the other, ten times as much force of gravity is required, and is actually exerted, to bring it to the ground. This will appear plain to you if you bear in mind that a body falls because it is drawn down by the force of attraction, and then com- pare this force to any other force, as, for example, that of muscular action. If you draw towards you two weights, one of which is twenty times as heavy as the other, or, in other words, has twenty times as great a quantity of mat- ter, you must exert twenty times as much strength on the former as you do on the latter. So it is with the force of attraction. The earth attracts a body having twenty times more matter than another with twenty times the amount of force. And the first body will have twenty times the weight of the other, for it will make twenty times the press- ure upon anything that resists the force with which the earth draws it. Weight, then, is the amount of resistance to the attraction existing beticeen the earth and the body weighed. If you place a substance in one side of a pair of scales, it goes down because of the attraction between it and the earth. By placing weights in the other side until the scales are balanced, you find how much is needed to coun- teract the resistance caused by the attraction of the sub- stance and the earth for each other ; or, in other words, you find out. how much it weighs. In doing this you use certain standard weights; that is, certain quantities of mat- ter which have been agreed upon by mankind, and are called by certain names, as ounces, pounds, grammes, kilo- grammes, etc. When a spring-balance is used, the spring has been tested by these standard weights, and its scale marked accordingly. ATTRACTIONS OF MATTER. 57 Weight not Fixed, but Variable. Weight does not depend alone upon the density of the body weighed, but also upon the density of the earth. For the attraction causing the resistance which we call weight is a mutual attraction, and is in proportion to the quantities of matter of both the body and the earth. If, therefore, the density of the earth were increased twice, three times, or four times, the weights of all bodies would be increased in the same proportion ; that is, the force with which the earth would attract them would be twice, three times, or four times as great as now. This would not be perceived by any effect on balances, for the weights and the articles weighed would be alike increased in weight. But it would be perceived in instruments that indicate the weights of bodies by their influence on a spring. These would disagree with scales and steelyards just in proportion to the increase of the earth's density. It would be perceived also in the application of muscular and other forces in raising and sustaining weights; every stone would require twice, three times, or four times the muscular effort to raise it. 28. Weight Varies with Distance. The nearer two bodies are to each other, the greater the mutual attrac- tion. The nearer a body is to the earth, the greater the attraction that draws it towards the earth in other words, the greater is its weight. The force of gravity, or Aveight, is greatest, therefore, just at the surface of the earth, and it diminishes as we go up from the earth. As we leave the surface of the earth, the force of gravity lessens in such a proportion that it is always inversely as the square of the distance from the centre of the earth. In other words, the force of gravity increases or decreases at the square of the rate that the distance decreases or in- creases. This requires still further explanation. If the distance from the centre of the earth to its surface, which is 4000 miles, be called 1, then 4000 miles from the earth would be called 2, or twice as far from the centre, and 8000 miles from the earth would be 3, 12,000 miles from the earth would be 4, and so on. The squares of these numbers are 1, 4, 9, 16, etc. Now, since weight decreases inversely as the square of the distance, any object weighing 58 NATURAL PHILOSOPHY. one pound on the surface of the earth would weigh but -J pound at the distance of 4000 miles, and only ^ pound at 8000 miles. An object weighs less on the summit of a high mountain than in the valley below, because it is farther removed from the great bulk of the earth, and is therefore not so strongly attracted. The difference, however, is but small ; a man weighing 250 pounds in the valley would weigh but half a pound less on the summit of a mountain four miles high. We have spoken of weight only in relation to the earth, but weight is an attribute of bodies everywhere, for wherever matter is found there must be attraction. The weight of the substances on the surface of the different heavenly bodies varies according to the quantity of matter in, or density of, those bodies. Since the moon is much smaller than the earth, a body which weighs a pound on the surface of the earth would weigh much less than a pound on the moon. And since the sun is much larger than the earth, the same body carried there would weigh much more than a pound. If we knew the exact densities of the sun and the moon and the earth, ns well as their size, we could estimate exactly the difference in the weights which any body would have in them; for the attraction which causes the resistance called weight is in direct proportion to the quantity of matter, and the quantity of matter depends on both density and size. 29. Cohesion. That form of attraction which binds to- gether the molecules of a body is called cohesion. Cohesion is stronger in some solids than in others. The mason with his trowel easily divides a brick; but he can- not do this with a piece of granite, for its particles have a greater attraction for each other than those of the brick. A blow which would break a glass dish would not in- jure a copper one of the same thickness. A weight that would hang securely from an iron wire would break a lead wire of the same size; that is, it would tear the particles apart, because they are not strongly attracted to each other. Cohesion has different modes of action in different ATTRACTIONS OP MATTER. 59 solids. It therefore fastens their particles together in dif- ferent ways, and thus occasions the physical properties which are so useful to us tenacity, elasticity, ductility, flexibility, etc. Cohesion is exerted only between molecules of the same kind; when two masses are made to cohere they must be of similar material and must be pressed very closely to- gether, because the attractive force is exerted only at in- appreciable distances. For this same reason also it is only the surface particles which influence the cohesion. Examples of cohesion of masses are numerous : two highly polished surfaces of glass may be made to stick together as if glued, and can only be separated by slid- ing one off the other. Before rubber tubing was a commercial article, it was made by a simple process based upon its cohesive property. A piece of sheet rubber of suitable length and width is wrapped around a glass or wooden rod, and a strip cut off, where the edges lap, with a pair of long scissors ; by press- ing together the freshly cut surfaces, they cohere firmly, making a perfect tube. The manufacture of various articles which are made by compressing powders until they form solids, as in the case of graphite for lead-pencils, sawdust for wooden ornaments, brick-dust for tiles, etc., are examples of practical applications of cohesion. If you cut two bullets so as to give to each a very smooth flat sur- face, you can make them cohere quite strongly by pressing them to- gether, especially if yon give a little turning motion at the same time that you press, for this will bring the particles on the surfaces in close con- tact. If the balls of lead are quite large and furnished with handles, as represented in Fig. 13, it will require considerable force to separate them when they have been thus pressed to- Fig. 13. gether. 30. Cohesion in Liquids. In liquids the attraction be- tween the particles is very feeble compared witli that in solids. The strength of the attraction of particles of steel is CO NATUKAL PHILOSOPHY. about three million times that of the particles of water. The estimate is made in this way: We find that a stool wire will sustain a weight equal to 39,000 feet (11.887 kilo- metres) of the wire. But a drop of water hanging to the end of a stick cannot be more than one sixth of an inch (42 millimetres) in length ; that is, water will hold together by the attraction of its particles only to this extent, which is a little less than the three-millionth part of the length of steel wire which could hang without breaking. The freedom with which the particles of a liquid move among one another is due to the comparative feebleness of cohesion, and to the fact that the molecules are more widely separated than in solids. This mobility of liquids varies considerably according to the intensity of the co- hesive power; in limpid liquids, such as ether, alcohol, naphtha, etc., the force of cohesion is very feeble, while viscid liquids, such as oil, molasses, glycerin, etc., are sluggish in their motions, being hampered by greater cohesion of their particles. For this reason, too, drops of viscous liquids are much larger than those of mobile ones poured from the same bottle ; sixty drops of water fill the same measure as one hundred of laudanum when poured from a lip of the same size. A knowledge of this and similar facts is of im- portance to physicians and druggists. 31. Globular Shape of Drops of Liquid. Since the parti- cles of a liquid move thus freely among each other, the attraction of cohesion disposes them to assume a globular or spherical shape. The reason of this can be made plain by Figs. 14 and 15. The outside of a perfect sphere is all at the same dis- tance from the centre ; and the circum- ference of a circle is equidistant from Fig. 14. the centre, as represented in Fig. 14. ATTRACTIONS OF MATTER. 61 * But this is not true of all parts of the surface of a cube or of a square : a, for example, is farther from the centre than b. Now in a drop of liquid all the particles are attracted towards the centre, for in that line from each particle lies the largest number of particles to attract it. This can be made obvious by taking some point in the drop, as repre- sented in Fig. 15, and drawing lines from it through the centre and in other directions. If a be the point in the drop, it is plain that the line from it through the centre is longer than a b or a c. Therefore a parti- cle, a, will be attracted towards the centre rather than in the direction Fig. i&. ab ov a c, because there are more particles in the direction of the centre, and the more particles there are the stronger is the attraction. But this is not all. The particles in the line a c, tending to make a go towards c, are balanced by the particles in the line a e, tending to make it go towards e. The two lines of particles, therefore, together tend to make it go in a middle line between them ; that is, to- wards the centre, just as two strings pulling equally, the one to c and the other to e, would make a body, a, move in a middle line between these two directions. The same can be shown of the two lines of particles a b and a d, and so of any other two alike in situation on each side of the line through the centre. The tendency of every par- ticle is, then, to move towards the centre, and a globular form results. 32. The Spherical Form in Different Liquids. The dis- position to form a sphere is seen more distinctly in mercury than in any other liquid. If you drop a little of it upon a plate it separates into globules, which roll about like shot. Why does water behave differently ? Why do the drops C2 G2 NATURAL PHILOSOPHY. of water hang upon the window-pane, showing only in an imperfect way their disposition to a globular arrange- ment ? It is because the particles of water have a greater attraction for other substances, and less attraction for each other, than the particles of quicksilver. Water sometimes exhibits its disposition to form spheroidal drops on the leaves of some plants, and rolls about in balls like mercury. This is because there is something on the surface of the leaf which repels rather than attracts the water. If you put your finger, however, on one of these drops, it will alter its shape, and your finger will be moistened, because there is an attraction between the particles of your skin and those of the water. Take another illustration of this dif- ference in attraction. If you drop a little oil upon the surface of water it will float about in round drops. This is because the water repels the oil. But when oil is spilled upon wood or cloth their particles have so strong an at- traction that they unite, instead of gathering into little round masses as they do on the surface of water. Manufacture of Shot. We have a good example of the tendency of fluids to form spherical drops in the manufacture of shot. Melted lead is poured into a large vessel, in the top of the shot-tower, having holes in its bottom, from which the metal falls in drops. Each drop, as it whirls round and round in its fall, takes the globular form. By the time that it reaches the end of its journey, about two hundred feet, it becomes so far cooled as to be solid, and as it is received in a reservoir of water, its glob- ular form is retained. Bullets cannot be made in this way, because a quantity of melted lead sufficient to make a bullet will not hold together in a globular form. 33. Spherical Form of the Earth and the Heavenly Bodies. It is supposed that the sun, moon, earth, and all the heav- enly bodies were once in a liquid state, and that they owe their spherical shape to this fact. As they whirled on in their course, the liquid mass gradually cooled, and at length they acquired their present state. How all the ATTRACTIONS OP MATTER. 63 mighty changes could be effected in our earth, converting it from a liquid into a body with a solid crust, having such a diversity of substances in it, and so variously arranged, with its depressions containing water, and the whole cov- ered with its robe of air fifty miles in thickness, we cannot fully understand. And yet there are some portions of the process which chemistry and geology have revealed to us, giving us some glimpses of the wonders which, during the lapse of ages, God wrought in our earth in preparing it for the habitation of man. 34. Crystallization. The attraction of cohesion is not in all cases uniformly strong in all directions around a mole- cule, and when the particles are free to move they often assume a more or less regular arrangement, becoming crys- talline. This happens most frequently when a substance passes from a liquid state to a solid one, and when it is de- posited from a solution. The process of crystallization is readily studied by slow- ly cooling saturated solutions of certain chemical sub- stances: alum, saltpeter, sulphate of copper, borax, and other substances. There is an immense variety of crys- talline forms, the study of which is pursued in connection with the science of mineralogy; we can here merely indicate a few of the forms which substances assume. Com- mon salt crystallizes in cubes, Fig. 16; alum in octahe- dra, or eight-sided figures, Fig. 17. Crystalline forms are also assumed by many minerals: the bright-red garnet crystallizes in the form shown in Fig. 18, and quartz takes the form of Fi. 19. All the 64 NATURAL PHILOSOPHY. Fig. 19. precious stones have a crys- talline structure, and even the common rocks under your feet exhibit the same crystal- line disposition in detail which you see in the mass. Pig. is. Water, when it changes into a solid, shows the same disposition, of which the crystals of the snow and the frost- work on our windows are familiar examples. When snow forms, the water of the clouds is suddenly crystallized by the cold air, the particles taking their regular places more readily and certainly than if they were guided by intelligence, because in obedience to an unerring law established by the Creator. Examples of this sudden crystallization of water are common. The water in a pitcher may remain fluid, although it is cooled down to the freezing-point, and even below it, if it be kept perfectly still. But on agitating the pitcher the water at once becomes filled with a net-work of ice-crystals. The stillness of the water prevented its particles from taking the crystalline arrangement needed for the formation of ice ; and the shaking of the particles assisted the motion necessary to the assumption of a crystalline form. 35. Frost and Snow. The frost-work on our windows is a wonderful exhibition of the variety of forms that crystal- lization can produce. It sometimes presents figures like leaves and flowers, such as are chased on vessels of silver, but much more delicate and beautiful. So varied and fan- tastic are the forms in which these water-crystals are ar- ranged, that it is very natural to ascribe them, as is done universally in the dialect of the nursery, to the ingenuity of a strange and fanciful spirit. Every snow-flake is a bundle of little crystals as regular and beautiful as the ATTRACTIONS OF MATTER. C5 crystals which you so much ad- mire in a inineralogical cabinet. And there is great variety in the grouping of these crystals. Figs. 20 and 21 show some of these forms as they appear under the microscope. It is a very quick operation by which the particles of water in the clouds thus mar- shal themselves, as if by magic, in these regular forms. But a quicker operation is that by which hail is formed so quick that the particles have not time to arrange themselves in crystalline forms, but are huddled together without order. The brilliant and glistening whiteness of the snow is owing to the reflec- tion of light from its minute crystals. In the arctic regions the beauty of the snow is often much greater than with us. "The snow crystals of last night," says Captain M'Clintock in his "Discovery of the Fate of Sir John Franklin," "were extremely beautiful. The largest kind is an inch in length ; its form exactly resembles the end of a pointed feather. Stellar crystals two tenths of an inch in diameter have also fallen ; these have six points, and are the most exquisite things when seen under a micro- scope. In the sun, or even in moonlight, all these crys- tals" glisten most brilliantly; and as our masts and rig- ging are abundantly covered with them, the Fox never was so gorgeously arrayed as she now appears." Order in Nature. We see in this gen- eral tendency to crys- tallization a striking 66 NATURAL PHILOSOPHY. illustration of the fact that the Almighty is a God of order. Disorderly arrangement is never seen except where there is an obvious necessity for it. And even when there is ap- parent disorder, a little examination generally shows that essentially there is order. The rocks that give so much variety to scenery seem to be piled up in confusion, yet or- der has evidently reigned in their construction. Pick up a common stone, and on breaking it you will see the crystal- line arrangement in its interior. Nay, more, much of the very soil is made up of separated and broken crystals. Amorphous Bodies. Substances which possess no regu- larity of structure are termed amorphous, that is, without crystalline form. Glue, soap, clay, chalk, and many min- erals are amorphous. Some substances may occur at one time in a crystalline state and at another without any trace of regularity of form. Carbonate of lime is one of these, being crystalline in limestone, Iceland spar, and various minerals, while in the form of chalk it is amorphous. Met- als, too, may occur both amorphous and crystalline. The attraction of cohesion, which produces crystalline forms, leads to peculiarities of structure which receive special names, as "hard," "brittle," etc., as already explained in Chapter III. QUESTIONS. 24. What is said of the attraction of matter ? What is the force gener- ally called, and why ? Show that attraction exists between small masses. Name and define the different kinds of attraction. 25. What is said of gravitation ? Illustrate the fact that attraction is mutual. Illustrate also the proportions of the mutual attractions. What is said of the motion of the earth? 20. Explain why bodies are attracted towards the earth's centre. How does this affect plumb-lines suspended at some distance from one another? Show that up and down are only relative terms. Why do falling bodies deviate from a line drawn exactly to the earth's centre? 27. What is weight? Give the comparison in regard to muscular force. What is said of scales and weights? What of using springs in weighing? ATTRACTIONS OF MATTER. 67 28. What would be the effect on weight if the density of the earth were increased ? In what ways would this be perceived ? 29. What is said of the variation of weight with distance? Explain the law. What is said of the difference of weight on mountains and in valleys ? What is said of the weight of bodies on the moon? 30. What is said of cohesion? Give examples of cohesion. Describe the experiment with two bullets. 31. What is said of cohesion in liquids? What of the mobility of liquids? What causes some liquids to be limpid and some viscid? Explain by reference to Figs. 14 and 15 the globular form of drops. 32. Give the difference between mercury and water in regard to the spherical form. What is said of drops of water on leaves ? What is said of oil in ref- erence to attraction? Describe and explain the manufacture of shot. 33. What is said of the spherical form of the earth and the heavenly bodies? 34. What is said of crystallization ? State the examples cited. What is said of the crystallization of water? Give and explain the ex- ample of sudden crystallization. 35. What is said of frost-work ? What of snow? What is stated in regard to the snow -crystals of the arctic regions? What is said of order in nature? What of amorphous bodies? CHAPTER V. ATTRACTIONS OF MATTER (CONTINUED). 36. Adhesion. Adhesion is the attraction between dif- ferent kinds of matter, as between solids and liquids, or between glue and wood. When a glass article is broken you cannot unite the pieces, however accurately you may bring them together, or however firmly they may be pressed. This is because the power of cohesion acts strong- ly only when the molecules are brought very near to- gether; and it is impossible to bring the particles on the two surfaces of a broken piece of glass as near together as they were before the fracture. If it were possible so to do, no crack would be visible. We are obliged therefore to resort to some kind of cement; this causes the two surfaces 68 NATUKAL PHILOSOPHY. to adhere because, while soft, it insinuates itself among the particles of glass, and on drying becomes a bond of union between the broken fragments. In adhesion as well as in cohesion only the surface layer of molecules exert any in- fluence, consequently a mere film over a surface suffices to alter its adhesive power, as when a glass is greasy. Examples of the adhesion of solids are familiar: silver and gold may be made to adhere to iron by a very great and sudden pressure. The iron must be made very smooth, and the silver or gold plate very thin. A powerful blow brings the particles of the thin plate into such nearness to those of the iron that union is affected, or, in other words, they attract each other sufficiently to be united. Similarly, a sheet of tin and one of lead can be made to adhere so as to form one sheet by the pressure of the rollers of a roll- ing-mill. 37. Adhesion of Solids and Liquids. The attraction which solids and liquids have for each other furnishes us with many interesting phenomena. The adhesion of drops of water to glass and other solids is a familiar example of this attraction. If you dip your hand into water, it is wet on taking it out, because your skin has sufficient attraction for the water to retain some of it. A towel will retain more of it for two reasons : owing to the interstices between its fibres it presents much more surface to the water (see 39, Capillary Attraction), and it has none of the oily substance which on your skin, though in small quantity, serves some- what to repel the water. If you clip your hand into mercury the latter will not adhere to it, and it would seem that the skin has an at- traction for water and none for mercury. This, however, is only apparent, for a small globule of mercury will adhere to the finger, though if it be brought in contact with a larger amount of mercury the globule leaves the finger and ATTRACTIONS OF MATTER. C9 loses itself in the liquid. This shows that liquids wet solids when the adhesion of the liquid to the solid is greater than the cohesion of the liquid. The attraction of solids and fluids for each other is shown very prettily in the experiment represented in Fig. 22. A plate of glass is attached by strings to one end of a bal- ance, and weights just sufficient to balance it are placed in r 4 U" " ' ! '" : '-'-'-' ' ''"" " '!"'!'!' ' y '~''~ ''\'-'i' - 1 "' 'Tv r "iM^:.,ar-a| Fig. 22. the opposite scale. When the glass is brought in contact with water, it will require additional weight in the scale to separate the glass from the water. This experiment, how- ever, does not measure the adhesion of the glass and water accurately, because we cannot detach the plate of glass clean and dry ; it merely measures the 'force necessary to overcome the cohesion of the liquid. Further Illustrations. When you see stems of plants rising above the surface of stagnant water you will observe that the water is considerably raised about them. This is from the attraction be- tween them and the water. For the same rea- son water rises higher at the sides of a tumbler Fig. 23 - than in the middle. If you immerse a piece of glass in water, the water will rise at its sides as represented in Fig. 23. If you immerse two NATURAL PHILOSOPHY. pieces together, as in Fig. 24, the water will rise higher between them than on the outside, because the particles between are attracted by two surfaces, while those outside are attracted by only one. It is for the same reason Fig. 24. Fig. -25. that two men can raise a weight higher than one of them can alone. And if the pieces of glass be brought quite near together, as in Fig. 25, the water will be raised higher still, because there is less to be raised by the two surfaces. Just as two men can raise a small weight higher than they can a large one. The same thing may be beautifully illus- trated in this way : Let two pieces of glass, as represented in Fig. 2G, be immersed in col- ored water, with two of their edges joined together, the op- posite edges being separated. The height to which the fluid rises will make a curved line, it being lowest at the edges which are separated, and highest at Fig. 26. the edges which are joined. 38. Rise of Liquids in Tubes. For the same reason that water rises higher between plates of glass than outside, it will rise higher within a tube than on the outside. The diagram in Fig. 27 will make this clear. It represents a transverse section of a tube, enlarged so that the demon- stration may be plain. Consider the case of one particle on the inside and another on the outside at equal distances from the glass. It is evident that the particle a is not so near to as many particles of the glass as is the particle b. ATTRACTIONS OF MATTER. The lines drawn show this. The longest lines extending from the particles a and b to the glass are equal in length ; that is, a e and a f are equal to b g and b h. It is clear, therefore, that all the glass between the lines at c and d is as near to the particle b as the glass between the lines at e and /'is to the particle a. But this is not all. The particle b is near enough to the whole inside of the tube to be attracted by it, while very little attraction is exerted upon a by any part of the glass beyond that which is included between e and /. The same difference can be shown with regard to all the particles on the inside of the tube compared with those outside. The former are nearer to more particles of the glass than the latter, and therefore are more strongly attracted. Again, the nearer the plates of glass, the higher the water rises between them ; so the smaller the tube, the higher will the water rise in it. You can try the experi- ment by immersing in water glass tubes of different diameters, as rep- resented in Fig. 28. It is obvious that the particle b (Fig. 27) would not be very strongly attracted by the part of the tube opposite if the tube were a large one ; but it would be if the tube were very small, for then it would be quite near to that part. Since glass is not wet by mer- cury, a tube plunged into this liquid causes a depression without and with- in. Figs. 29 and 30 show the contrast between water and mercury. Fi 72 NATURAL PHILOSOPHY. 39. Capillary Attraction. The term capillary (derived from the Latin word capilla^ hair) has been commonly ap- plied to the attraction exhibited under the circumstances just noticed, because it is most obvious and was first ob- served in tubes of very fine bore. The same term is used when the attraction is seen in the rising or spreading of a liquid in interstices as well as in tubes. Thus capillary attraction causes the rising of oil or burning-fluid in the wicks of lamps. The liquid ascends in the interstices, or spaces, between the fibres, as it does in the spaces of tubes. Other Examples. If you let one end of a towel lie in a bowl of water, the other end lying over upon the table, the whole towel will become wet from the spreading of the water among the fibres in obedience to capillary attraction. If you suspend a piece of sponge so that it merely touch the surface of some water, or if you lay it in a plate with water in it, the whole sponge will become wet. So, too, if you dip the end of a lump of sugar in your tea, and hold it there a little time, the whole lump will be moistened. In very damp weather the wood-work in our houses swells from the spreading of water in the pores of the wood in obedience to capillary attraction. Especially is this the case in basement rooms, where the water can ascend from, the ground in the pores of the walls, as well as from the damp air. In watering plants in pots, if the water be poured into the saucers, it .will pass through the earth by capillary attraction. For the same reason plants and trees near streams grow luxuriantly, being abundantly supplied with water, which rises to their roots through the pores of the soil. The disposition of the wood to imbibe moisture in its pores has sometimes been made use of very effectually in quarrying out millstones. First a large block of stone is hewn into a cylindrical shape. Then grooves are cut into it all around where a sepa- ration is desired, and wooden wedges are driven tightly into them. These are then moistened with water, and eventually swell so much as to split the stone in the direction of the grooves. Blotting-paper furnishes an illustration of capillary attraction, the ink being taken up among the fibres of the paper. Ordinary writing-paper will not answer as a blotter, because the sizing fills up the interstices between the fibres. As already stated ( 38), whenever a body is wet by a liquid, a rise of its surface ensues ; but when otherwise, ATTRACTIONS OF MATTER. a depression takes place. Thus a sewing-needle washed with alcohol is easily wet by water when placed on its surface, and sinks immediately ; when, however, the same needle is somewhat greasy, so that it can make a depres- sion, it will float. Some insects which skip about on the Fig. 31. surface of the water are protected from being wet by it. The feathers of water-fowl are always slightly oily, and thus they remain quite dry even when swimming in the water. 40. Opposition between the Modes of Attraction. Al- though adhesion and gravitation are essentially the same thing, we see them continually acting in opposition to each other. Abundant illustrations might be given, but we will cite only a few. If you pour water out of a tumbler, there is a struggle between the attraction of adhesion and gravitation for the mastery the attraction of adhesion tending to make the water adhere to the tumbler, and run down its side, as in Fig. 32, and gravita- tion tending to make it fall straight down. But when water is poured out of a pitch- er, as in Fig. 33, the ( lip of the pitcher acts in favor of the at- Fig. 32. Fig. 74 NATURAL PHILOSOPHY. traction of gravity; for the water would have to turn a very sharp corner to run down the outside of the pitcher iu obedience to adhesion. In pouring water from a tum- bler, we can often, by a quick movement, throw the water, as we may say, into the hands of gravity before the attrac- tion of adhesion can get a chance to turn it down the tumbler's side. If you can only make the water begin to run from the tumbler without going down its side there will be no difficulty; for there is an attraction of cohesion between the particles of the water, tending to make them keep together, which in this case acts against the adhesion between the water and the glass, and there- fore acts in favor of gravitation. It is adhesion together with cohesion that forms the drop on the lip of a bottle as we drop medicine cohesion between the particles of the liquid, and adhesion between the latter particles and those of the glass. It is gravitation, on the other hand, that makes the drop fall, it becoming so large that the force of gravity overcomes the adhesion between the drop and the bottle. Size of Drops Influenced by Gravitation. Were it not for the attraction of gravitation, there would be no limit to the size of drops of any liquid. When the drop reaches a certain size, it falls because it is so heavy ; or, in other words, because with its slight adhesion the attraction of the earth brings it down. Now if this attraction could be suspended, and the at- traction of adhesion left to act alone, particles of water might be added to the drop to any extent, and they would cling there. You can see the struggle between adhesion and gravitation very prettily illustrated if you watch the drops of rain on a window-pane. If two drops happen to be quite near together, they unite by attraction, and then, being too large to allow of its being retained there by adhesion in opposition to gravitation, the united drop runs down. If it meet with no other drop, it soon stops, because by adhesion some portion of it clings to the glass all along its track, and thus becomes small enough to again admit of suspension. It is owing to the influence of the attraction of gravitation that the drops of different liquids differ in size, the heavier yielding small, and the lighter ATTRACTIONS OF MATTER. large ones. You have another illustration of a similar character in the adhesion of chalk to a black-board or any surface. The chalk crayon itself cannot adhere, for the attraction of the earth does not permit it. But small quantities of it can adhere for the same reason that water ad- heres to surfaces in small quantities. Dust also clings to the vertical sides of furniture, though a lump of earth would not. 41. Size of Solid Bodies Limited by Gravitation. We can illustrate the limitation of size in solid masses by Figs. 34 and 35. Suppose that a and &, Fig. 34, are two pieces of timber projecting from a post, b being twice as large as a. It is evident that b cannot support twice as much weight as , for gravitation is dragging it downward from its connection with the upright post with twice the force that it does a. The case is still Fig. 34. when, as represented in Fig. 35, the larger timber is twice as long as the smaller. Here d has four A A times the bulk of c. But it can- not support four times as much weight at its end, not only be- cause its own weight presses it downward, but because half of its weight is at a greater distance from the place of attachment than the smaller beam is. Gravitation here operates in opposition to cohesion in such a way that the projecting timber, if carried to a certain size, will fall by its own weight, either breaking in two or tearing away from its attachment. This tendency is very commonly resisted in buildings and other structures by 76 NATUKAL PHILOSOPHY. braces, as represented in Fig. 36. Here the weight of the horizontal timber at some distance on each side of a is made to press upon the upright post instead of directly downward. The above Principles Transgressed by Man. Man often transgresses these principles in his struct- ures. For example, a building settles because the foundation is not strong enough to bear the super- incumbent weight. In other words, the force of gravitation is not suffi- ciently taken into account. When a very tall building is erected, the lower portions ought to be made of very cohesive substances. Firm granite is therefore an appropriate material for the lower story of tall brick buildings. At least the walls of the lower stories of such buildings should be made thicker than usual, to resist properly the force of gravita- tion in the weight above. Stores intended to bear much weight on their floors are often built without due regard to the cohesive force required to sustain the weight. Long timbers are sometimes supported only at the ends, when their own weight, to say nothing of what may be brought to press upon them, requires that they should be supported at other points. While in modern buildings the timbers are often too small, in some old buildings the upper timbers are so heavy as to lessen rather than increase the strength of the structure. Especially is this true of the unsightly beams which in some very old houses we see extending along the ceilings. Many other examples could be given, but these will suffice. 42. Adhesion, Cohesion, and Gravitation the Same. We again refer to the statement made in 24, that cohesion, adhesion, and gravitation are only different modes of action of the same power, viz., the attraction which mat- ter everywhere has for matter. At first thought it would appear that there is something peculiar in the attraction of particles when they are brought together so as to ad- here. For if we take any substance a piece of glass, for example its particles seem to be held together by an attraction vastly stronger than that attraction which in- clines different bodies to move towards each other. If ATTRACTIONS OP MATTER. 77 you break the glass, however closely you may press the two pieces together, they will not unite again. It would seem, at first view, that there must be some peculiar ar- rangement of the particles which is destroyed by breaking the glass. But we can readily account for the facts in another way. The attraction between bodies of matter is greater the nearer we bring them together. The nearer, for example, the moon is to any portion of the earth, the greater the attraction which it exerts, as seen in the tides ; and if it were much nearer to the earth than it is, our tides would prove very destructive. What is true of masses is also true of the particles of which they are composed. Though their attraction is comparatively feeble when at a distance from each other, it increases not in the arith- metical, but the geometrical ratio as they approach; so that when they are exceedingly near together the attrac- tion is very powerful. It must be remembered in regard to the pieces of broken glass that you cannot bring the particles on their surfaces as near as they were before the glass was broken ; and the attraction being inversely as the square of the distance, a little distance must make a great difference. The particles of some substances you can bring so near together as to cause adhesion, as in the case of the two bullets ( 30). That their adhesion depends merely upon their particles being brought near to each other appears from the fact that the smoother you make the surfaces, the more strongly will they adhere. And the reason that liquids and semi-liquids adhere so readily to solid substances is that their particles, moving freely among each other, have thus the power of arranging themselves very near to the particles of the solid. Thus, when a drop of water hangs to glass, all the particles of water in that part of the drop next to the glass touch, or rather are exceedingly near to, the particles of the glass. D 78 NATURAL PHILOSOPHY. 43. Chemical Attraction. The kinds of attraction hith- erto explained in this work belong to the study of Natu- ral Philosophy, but another kind, known as interatomic or chemical attraction, is capable of producing the most won- derful effects. The former produce chiefly mechanical ef- fects, while chemical attraction goes farther and affects the composition of substances. Eor example, the attraction be- tween the two gases oxygen and hydrogen, which makes them combine to form water, belongs to Chemistry; while that which makes the particles of water cohere is in the province of Natural Philosophy. You will learn more about chemical attraction in Part II. of this series. Variety in the Results of Attraction. It is one and the same force, then, which binds the particles of a pebble together, and makes it fall to the ground which " moulds the tear" and "bids it trickle from its source" which gives the earth and all the heavenly bodies their globular shape, and makes them revolve in their orbits. How sublime the thought that one simple principle which gives form to a drop extends its influence through the immensity of space, and so marshals "the host of heaven" that, with- out the least interruption or discord, they all hold on their course from year to year and from age to age ! Thus Om- nipotence makes the simplest means produce the grandest and most multiform results. / QUESTIONS. 36. What is adhesion ? Why can you not make the surfaces of broken glass adhere? Explain the cementing of glass. How may silver and gold be made to adhere to iron ? What is said of the adhesion of tin and lead ? 37. What is said of the adhesion of liquids to solids ? What of the ac- tion of mercury ? Describe an experiment showing the adhesion of solids and liquids. What is said of stems in stagnant water? Explain Figs. 23, 24, and 25. Explain Fig. 27. 38. Explain the rise of fluids in tubes by CENTRE OP GRAVITY. 79 Fig. 28. How does mercury act with respect to tubes plunged into it ? 39. What is meant by capillary attraction? Give familiar examples of the rising of liquids in interstices. Describe and explain the process of getting out millstones. How does a blotter differ from writing-paper? Describe the experiment with a sewing-needle. What is said of certain water insects ? 40. What is said of the various results of attraction? Ex- plain fully why you can pour water from a pitcher easier than from a tum- bler. Explain the operation of the quick movement by which you prevent water from running down the side of a tumbler in pouring it out. What is said of dropping from a vial ? How is the size of drops limited ? What is said of the movements of drops on window-panes ? Why do the drops of different liquids vary in size? Give the illustration about chalk. Give that about dust. 41. Illustrate the limitation of size in solid masses. Show how these principles are transgressed by man. 42. Give the sum- mary referring to the connection between the different ways in which at- traction is exerted. 43. Wherein does chemical attraction differ from the other kinds ? What is said of the variety in the results of attraction? CHAPTER VI. CENTRE OF GRAVITY. 44. Centre of Gravity Illustrated. If you support a ruler on your finger as in Fig. 37, it balances when there is just as much weight on one side as on the other. Now just over your finger, in the middle of the ruler, there is a point called the centre of gravity; or, in other words, the centre of the weight of the ruler. This point is indicated in the figure. There is as much of the weight of the ruler on the one side of 80 NATURAL PHILOSOPHY. this point as on the other, and also as much above it as be- low it. If your finger should be a little to the one side or the other of this point, the ruler would not be balanced, and would fall. When balanced, it does not fall, simply because this central point is supported by being directly over the end of the finger. The whole weight of the ruler, then, may be considered as practically concentrated at that point, for all the downward pressure of the ruler is there exert- ed. When the ruler is balanced on the finger as repre- sented in Fig. 38, it will maintain its position so long as its centre of gravity is directly over the point of the finger. If it be to the one side or the other, as in Fig. 39, it is not supported, and the ruler therefore falls. You see, then, that when a body is balanced, the cen- tre of gravity lies directly over the point of support. If, on the other hand, a body is suspended, the cen- tre of gravity is directly under the point of support. If a plumb-line from the centre of gravity of any body could be prolonged into the earth, it would go directly to its centre. The body may be considered as making all its pressure from its centre of gravity towards the centre of the earth, in obedience to the attraction of gravitation. The best definition, then, that we can give of the centre of grav- ity is, that point in a body from which proceeds its pressure as a whole toicards the centre of the earth. It is that point, therefore, the support of which insures the Fig. 33. Fig. 39. CENTRE OF GRAVITY. 81 Fig. 40. support of the whole body. And in speaking of the weight of a body, or its downward pressure, we may con- sider all the matter composing it as collected or concen- trated in that point. The body, therefore, can be balanced in any position in which this point is supported, as shown in Figs. 37 and 38. When a body is suspended, it is at rest only when the centre of gravity is directly under the point of support. Thus, if you have a circu- lar plate suspended at E, Fig. 40, it will not be at rest when moved to the one side or the other, as represented by the dotted lines, but only when the centre of gravity, c, is directly under the point E. 45. How to Find the Centre of Gravity of a Body. If you take a piece of board, and suspend it at a, Fig. 41, and hang a plumb-line from the same point, the centre must be somewhere in that line. But exactly at what point it is you do not know. How will you ascertain this? Mark the line a c on the board, and suspend the board by another point, as in Fig. 41. Yig. 42. Since the centre of gravity must be somewhere in the plumb-line as it now hangs, of course it is where the two lines ac and bd cross, and the board suspended by a cord attached at this point will remain evenly balanced. Scales and Steelyards. When two bodies are connected by a rod or bar, the centre of gravity of the whole is somewhere in the connecting rod. If the two bodies be equal in weight, as in Fig. 43, the centre of gravity is 82 NATURAL PHILOSOPHY. exactly in the middle of the rod, as marked. But if the bodies are un- equal, as in Fig. 44, the centre of gravity is nearer to the larger body than e Fig. 43. Fig. 44. to the smaller. In weighing a body in one pan of a balance by means of weights placed in the other, we have a case parallel to that of Fig. 43. The centre of gravity of the body weighed, the weights and the pans, as a whole, is midway between the scales, at the point of support. In the steelyard the heavy body to be weighed is nearer the centre of gravity than the small weight on the long arm, and so the case is similar to that of Fig. 44. 46. The Centre of Gravity of a Body not Always in the Body itself. The centre of gravity of a hollow ball of uniform thickness is not in the substance of the ball, but it is in the centre of the space within the ball, for the line of the ball's downward pressure is situated at that point. If the ball had a framework in it, as represented in Fig. 45, the centre of gravity would obvious- ly be at A, the centre of this frame- work. But if there were no frame- work, and perpendicular lines were supposed to be drawn from different points of suspension, C, B, D, and E, these w T ould intersect at the point A, showing that this is the centre of gravity, according to the rule for finding it given in 45. In like manner, the centre of gravity of an empty box, or of an empty ship, is an imag- inary point in the space inside. In a hoop it is the centre of the hoop's circle. 47. The Centre of Gravity Seeks the Lowest Point. The centre of gravity always assumes the lowest place which the support of the body will allow. In a hanging body, therefore, it is always directly under the point of suspension. To reach one side or the other of this posi- CENTRE OF GRAVITY. 83 tion, it must rise. This the attraction of gravitation forbids, and if by any force it is made to rise, this attraction at once brings / it back. This is manifest in the case of a / suspended ball, Fig. 46. If the ball be moved to b, it will, on being let go, return ( ^ to its first position, simply because its -," centre of gravity, in obedience to the earth's ^^ attraction, seeks the lowest place, possible. From inertia ( 14), it moves beyond this point, and con- tinues to vibrate back and forth for some time ; but when its motion is stopped, it hangs perpendicularly ; that is, in such a way that its centre of gravity shall have the lowest possible position. Many illustrations of this point might be mentioned. When a rocking-horse is at rest, its centre of gravity is directly over the point at which it touches the floor, for in that position the centre of grav- ity is as low as possible. If it be rocked, the centre of gravity is moved to a higher point, and for this reason it rocks back again. The same is seen in the swing, the cradle, the rocking-chair, etc. Most interesting illustra- tions are found in the Loggan Stones, as they are called, several of which are seen on the rugged parts of the British coast. An immense rock, loosened by some of the forces of nature, rests with a slightly rounded base on another rock which is flat, and it is so nicely balanced that one person alone has sufficient strength to set it rocking. Similarly balanced "rocking-stones" are found near Salem, Massachusetts, in Great Barring- ton, Massachusetts, and in many other localities. 48. Further Illustrations. An egg lies upon its side be- cause the centre of gravity seeks the lowest position. When on its side, the centre of gravity is at its lowest point, as is manifest by a comparison of Fig. 47 with Fig. 48. Children have a toy, called a witch, which illustrates the same thing in another way. It is constructed of some light substance, as pith, with a shot or bullet fastened in one end. It always stands up on its loaded end, and can- 84 NATURAL PHILOSOPHY. Fig. 47. Fiff. 48. not be made to lie down on its side, because the centre of gravity would not then b6 at the lowest point. The figure of a fat old woman, Fig. 49, loaded with lead at the bottom, is another form of this toy. If the figure be thrust over to one side, as shown by the dotted lines, the centre of gravity is raised, and the upright position is at . so. once resumed. Fig. 49. If the toy were not loaded, it would lie in the position represented in Fig. 50, just as the egg lies on its side. Certain curious cases which at first sight appear to be exceptions to this law are really interesting proofs of it. If a light wooden cylinder loaded with lead on one side be placed upon an inclined plane with the lead in the po- sition e (Fig. 51), the lead, in fall- ing to o, will cause the cylinder to roll up the incline. What is ap- \ ^/ .& parently a rolling up-hill is really a falling of the centre of gravity. Fig. 51. For the same reason a billiard-ball placed on the smaller ends of two billiard-cues laid on a table with their points CENTRE OF GRAVITY. 85 in contact and their larger ends slightly separated, will roll towards the large ends, apparently rolling up-hill; actually, however, the cen- tre of gravity falls as the ball rolls alonec the cues. Fig. 52. But if you place another stick as a brace, in Curious Experiments. You can- not hang a pail of water on a stick laid upon a table as represented in Fig. 52, for the centre of grav- ity is not supported. the manner represented in Fig. 53, so as to push the pail under the table, it will hang securely, because the centre of gravity will be brought under the point of suspension. In an entirely similar manner a needle passed through a cork into which a fork is thrust (as shown in Fig. 54), may be suspended on the edge of a table. We have Fig. 53. another illustra- tion in the common toy represented in Fig. 55. The horse, made of very light material, stands securely, because the centre of grav- ity of the whole is in the heavy ball, which is under the point of suspension. If the horse be made to rock back and forth, the centre of gravity in the ball moves in a curved line, as in the case of a ball suspended by a string (Fig. 46). It is at its lowest place only when the horse is at rest. The hanging of a cane with a hook-shaped handle on the edge of a table is to be explained in the same way. D2 Fig. 54. Fig. 55. 86 NATURAL PHILOSOPHY. - 49. Stability of Bodies. The firmness with which a body stands depends upon two circumstances the height of its centre of gravity and the extent of its base. The lower the centre of gravity, and the broader the base, the firmer the body stands. A cube, represented in Fig. 56, is more stable that is, less easily turned over than a body shaped like that in Fig. 57, because it has a larger base. The contrast is still greater between Figs. 56 and 58. The reason of the stability of a body with a broad base is found in the fact that in turning it over the centre of gravity must be raised more than in turning over one of a narrower base. The curved lines indicate the paths of the centres of grav- Fig. 56. Fig. 57. Fig. 58. ity as the bodies are turned over. In the case of a per- fectly round ball, the base is a mere point, and therefore the least touch turns it over. Its centre of gravity does not rise at all, but moves in a horizontal line, as shown in Fig. 59. The pyramid is the firmest possible structure, be- CENTRE OF GRAVITY. 87 cause it possesses in the highest degree the two elements a broad base and a low position of the centre of gravity. On both these accounts the centre of gravity must ascend considerably when the body is turned over, as shown in Fig. 60. 50. Unstable Bodies. When a body does not stand upright, its stability is diminished because only a portion of the base is concerned in its support. In Fig. 61 the base is broad, but the body is so far from being upright that / the centre of gravity bears upon the - very extremity of the base on one side, as indicated by the perpendicular line. A small force will turn it over, because the centre of gravity need not as- cend the least when this is done. You see, then, that the less upright a body is, the less of the base is of service in its support. The famous tower of Pisa, Fig. 62, one hundred and thirty feet high, overhangs its base fifteen feet. Wheth- er it was built intention- ally in this way to excite wonder and surprise, or whether it settled on one side after its completion, has long been discussed ; we are inclined to the former theory, for what would otherwise have been a very unsafe structure is rendered sta- ble and safe by the arrangement of its materials. Its NATURAL PHILOSOPHY. lower portion is built of very dense rock, the middle of brick, and the upper of a very light porous stone. In this way the centre of gravity of the whole structure is made to have a very low position. Familiar Illustrations. You are now prepared to understand a fact which common experience teaches every one, that the taller a body, and the narrower its base, the more easily is it overturned. This is exemplified in the twq loads, Fig. 63. The base is the space included by the wheels. The centre of gravity is so high in the tall load that a perpendicular line drawn from it falls outside of the base if the cart reaches a considerable lateral in- . C3. clrnation of the road. But the small- er load, under the same circumstances, is perfectly secure. A high car- riage is more easily overturned than a low one, for the same reason. A stage, if overloaded on its top, is very unsafe on a rough road. Sta- bility is given to articles of furniture by making their bases broad and heavy, as shown in tables supported by a central pillar, candlesticks, lamps, etc. The tall chairs in which children sit at table would be very insecure if the legs were not widely separated at the bottom, thus widening the base of support. 51. Support of the Centre of Gravity in Animals. The base of support which quadrupeds have, viz., the space in- cluded between their four feet, is quite large ; and this is one reason why they are able to walk while yet very young. A child does well who can walk at the end often or twelve months, for the supporting base is quite small compared with that of a quadruped. It requires skill, therefore, in the child to manage the centre of gravity in standing and walk- ing, and this is gradually acquired. It is on account of the smallness of the base furnished by the feet that the statue of a man is always made with a large base or pedestal. Although we exert considerable skill in walking, it is by no means so great as that which the Chinese ladies require CENTEE OF GRAVITY. 89 with their painfully small feet. Still more skill is exercised by one who has two wooden, legs, or one who walks on stilts. The base made by the feet can be varied much by their position. If the toes be turned out and the heels brought near to each other, the base will not be so large as when the feet are straight forward and far apart, as is manifest in Fi^s. 64 and 65. It is for Fig. 64. 05. this reason that the child, in his first attempts at standing and walking, instinctively manages his feet as in Fig. 64. 52. Motions of the Centre of Gravity in Walking. In walking, the centre of gravity is alternately brought over one foot and the other, and so moves in a waving line. This is very manifest as you see people before you going down the aisle out of a church. When two are walking together, if they keep step the two waving lines of their centres of gravity run parallel, as in Fig. 66, and they walk easily ; Fig. 60. but if they do not keep step these lines run as in Fig. 6V, and the movement is both awkward and embarrassing. This line of movement of the centre of gravity is always slightly waving upward also, as seen in Fig. 68. In the Fig. 63. NATURAL PHILOSOPHY. case of a man with wooden legs, the line would not be gently waving, but somewhat angular, as represented in Fig. 69. 53. The Centre of Gravity and Attitudes. The object of various attitudes assumed under different circumstances is to keep the centre of gravity over the base of support. A man with a load on his back would not stand straight, but would assume the position of Fig. 70, so that the centre of gravity of his load may be directly over his feet. A man carrying a pail of water in his left hand leans to the right, and raises his right hand in order to bring the centre of gravity over his feet (Fig. 71). In ascending a hill a man appears to lean forward, and in descending to lean Fiir. 70. Fig. Tl. backward ; but in fact he is in both cases upright in refer- ence to the plain on which the hill stands. A perpendicu- lar line drawn from his centre of gravity strikes the ground midway between his feet, that is, in the middle of the base, and if prolonged would go straight to the centre of the earth. When one rises from a chair he draws his feet back- ward, and then bends his body forward to bring the centre CENTRE OF GEAVITY. 91 of gravity over the feet. Unless this is done, it is impos- sible to rise, at least deliberately, as you will find by trying the experiment. A man standing with his heels close to a wall cannot stoop forward and pick up anything, for the Avail prevents him from moving any part of his body back- ward, and therefore when he stoops forward, the centre of gravity being brought in advance of the base, he loses his balance and falls. A man who did not understand this undertook to stoop in this way to pick up a purse contain- ing twenty guineas, which he was to win if he succeeded, the forfeiture in case of failure being ten guineas. Of course his lack of knowledge as to the principles of the centre of gravity made him lose his wager. Great skill is exhibited by the rope-dancer in supporting the centre of gravity. He carries a long pole in his hands, loaded at each end, and when he inclines to one side he throws it a little towards the other side, that the reaction may restore his balance. Similar skill is seen in feats of bal- ancing, as, for example, in balancing a long stick upright on the finger. In these cases the centre of gravity is very little of the time directly over the point of support. It is kept in constant motion nearly but not quite over this point this unstable equilibrium, as it is called, being vastly less difficult to maintain than stable equilibrium ; that is, keeping the balance in one unvarying position. It is the motion of the top that makes it stand upright upon its point a very beautiful example of unstable equilibrium. The centre of gravity revolves around a perpendicular line, at exceedingly little distance from it at first, but greater and greater as its motion be- comes less rapid, till at length the centre of gravity gets so far from this line that the top falls. For a similar reason an intoxicated man may not be able to keep himself up if he undertakes to sjand still, and yet may do so if he keep moving. 54. Centre of Gravity in Floating Bodies. The same prin- ciples w r hich apply to the centre of gravity in bodies stand- ing on a firm basis apply also to floating bodies. That the centre of gravity may be low in a loaded vessel the heavy part of the cargo is put underneath, and generally ballast of stone or iron is necessary for the same purpose. In large 92 NATURAL PHILOSOPHY. flat-boats, the base of support being extensive, there is not the same need of taking care that the centre of gravity be low. If a ship be laden in part with an article which will dissolve in water, there is much danger, if the ship should leak, lest this portion of the cargo be dissolved and pumped out with the bilge -water; this would alter the trim of the vessel by removing the centre of gravity from over the middle line, and bringing it too far forward or carry- ing it too far back, making the ship wholly unmanageable. Four large English ships, in part loaded with saltpetre, were supposed to have been lost from this cause in 1809 oif the Isle of France. The immense ice-islands, or icebergs, which float about in summer in the polar regions, by melting ir- regularly often change the place of their centre of gravity, and in turning over present one of the most sublime spec- tacles in nature. A mountain of ice, extending high in the air and deep in the sea, suddenly turns over, and produces a rolling of the ocean which is often felt at the distance of many leagues. QUESTIONS. 44. Show what we mean by the centre of gravity by Figs. 37, 38, and 39. Give the definition of centre of gravity, and explain it. What is shown by Fig. 40 ? 45. How can we find the centre of gravity of a body ? What is said of scales and steelyards ? 4G. State what is represented by Fig. 45. 47. Illustrate the fact that the centre of gravity seeks always the lowest point. Give the illustrations of the rocking-horse, the swing, etc. What is said of the Laggan Stones ? 48. Why does an egg lie on its side? Give the illustrations from toys. Explain how a ball may be made to roll up an incline. Describe the experiment with a pail. And that with a toy horse. 49. Upon what two things does the stability of a body depend ? What is said of the stability of bodies whose shapes are repre- sented in Figs. 56, 57, and 58 ? W T hat of that of a round ball ? Why is the pyramid the firmest of all structures ? 50. What is the relation of upright position to stability ? What is stated of the tower of Pisa ? Give some familiar illustrations. 51. What is said of the support of the centre of MOTIONS OF MATTER. 93 gravity in animals ? What is said of the skill exercised in walking ? What of the mode of walking in a child ? 52. What of the motions of the centre of gravity in walking ? What is said of the walking of a man with wooden legs ? 53. Illustrate the management of the centre of gravity in different attitudes. Describe and explain the way in which one rises from a chair. State and explain the wager case. What is said of unstable equilibrium ? Give the illustrations. 54. What of the centre of gravity in floating bodies? What is said of icebergs ? CHAPTER VII. K MOTIONS OF MATTER. 55. Matter, Motion, Force. When a ball is rolled over the floor a superficial observer sees but little occasion for scientific discussion, but a philosophical mind finds therein a symbolic illustration of certain phenomena of nature ever present with us, and a comprehension of which is of the highest importance. Were the sentence, "A ball rolls," critically analyzed by a student of grammar, he would tell us of the three parts of speech represented, and of their relation to each other; in like manner the stu- dent of the laws of nature, analyzing the same sentence, would tell us that it embodies three facts, and that their mutual relations, intelligently studied, cover the whole groundwork of Natural Philosophy. We will endeavor to explain our meaning by dissecting the sentence. " A ball rolls " leads us, in the first place, to consider the ball itself; the phrase being indefinite, we have no informa- tion as to the material of which the ball is made, whether of wood, iron, or rubber; whatever the substance may be, it is called matter, as explained in Chapter I. The ball, then, abstractly considered, is merely an indefinite quantity 94 NATURAL PHILOSOPHY. of matter having a spherical form, the latter idea being as- sociated with the term ball itself. In the second place, this sentence leads us to regard the ball as changing its place with reference to some other body not mentioned. The ball "rolls," i.e., is in motion, or moves from one place to another in a particular manner known as rolling. Motion, then, in the abstract, is a change of place, and is so defined. Now we have already learned that matter is of itself inert ( 14), and cannot put itself in motion, hence there must be some external cause for the rolling of the ball; and this leads us to the third point, viz., the idea of force. That which causes motion in matter is called force : the force of the explosion of gunpowder sets the bullet (matter) in motion; \\\Q force of a violent wind uprooting a tree also sets matter in inotion. A clear un- derstanding of these three phenomena, and of their mutual relations as governed by laws, is essential to the study of Natural Philosophy, and their discussion will occupy us throughout this Chapter. Force. We have already stated that force is that which tends to move matter. When a body begins to move, changes the style of motion it acquired, or ceases to move, it is the result of one or more forces acting upon it from without. Force is not an attribute of matter like divisi- bility or hardness (Chapter II.), but merely a tendency to put it in motion ; we say a tendency, because force may exist where there is no actual motion. Thus a huge rock may rest quietly for years on the sloping hill-side, prevent- ed from moving by a small quantity of earth in front of it, but let this obstacle be removed by shovelling, or by a sud- den flood of water, and the rock will roll down the hill with immense force, crushing everything in its path. The mag- net, about which you will learn more in Chapter XX., af- fords another illustration of the correct idea conveyed by the MOTIONS OF MATTEK. 95 word force. A magnet has the power of attracting to itself pieces of iron ; if the magnet lies on the table, and no iron objects are near it, the fact of its possessing this peculiar force is not apparent the force is sleeping as we may say; but bring near to the magnet some iron nails or some steel filings, and this sleeping force is aroused, and manifests itself by drawing the iron articles towards the magnet. 56. Motion Universal. The material universe is in cease- less motion. The rising and setting of the sun, the changes of the seasons, the falling of the rain, the running of rivers into the ocean, the ascent of water into the air by evaporation, the wind moving in silence or rushing on in its might, are familiar examples of motion constant and everywhere present. But with all this motion, sometimes in conflict and often variable, order and regularity reign. The forces causing motion, though various in their opera- tion, are kept by the Creator from producing confusion and disorganization by a few simple laws, which regulate the movements both of atoms and of worlds. The principal of these causes of motion are the forces mentioned in Chapter IV. ; we will briefly recapitulate them. Attraction is the most universal of the causes of motion in the universe. While it binds atom to atom, it also binds system to system throughout the immensity of space ; and while it makes the stone fall to the ground, it moves the countless orbs forever onward in their courses. It is this which causes the tides to flow and the rivers to run down their slopes to the ocean, and thus by keeping up the never-ending motion of water all 'over the earth in seas, lakes, rivers, and the millions of little streamlets, diffuses life and beHuty over the vegetable world, and gives to man the vast resources which we see developed in the numberless applications of water-power and naviga- tion. Heat is everywhere uniting its influence with the other forces to cause motion. It is heat that produces all the motions of the air, termed winds. It is heat that causes the rise of the water all over the earth in evaporation, so that it may be collected in clouds, again to descend to moisten the earth 96 NATURAL PHILOSOPHY. and keep the ever-flowing rivers full. Heat applied to water gives to man one of his best means of producing motion in machinery. Light and electricity are also manifestations of this universal force, as will be shown in Chapters XVII. and XVIII. ; these are, to a certain ex- tent, productive of motion. The agencies which Chemistry reveals to us are ever at work causing motion among the particles of matter ; and though they generally work in silence, they sometimes show themselves in tremendous explosions, and in convulsions of nature. Busy life is everywhere producing motion, more especially in the animal world. It gives to the myriads of animals, great and small, that swarm the earth not only the power of moving themselves, but also the power, to some extent, of moving the material world around them. 57. Varieties of Motion. The different kinds of motion have received distinguishing names; the following list em- braces the principal varieties, with examples taken from familiar sources : Varieties of Motion. Examples. Slow The sun's shadow. Swift Lightning. Straight A stone dropped into a well. Curved The path of a stone in the air. Uniform The hands of a clock. Variable Winds, animal motions, etc. Accelerated Gradually increasing motion. Retarded Gradually diminishing motion. Whether motion is slow or swift is altogether a relative matter; a boy may run very swiftly, yet he moves slowly compared with a race-horse, and the horse in turn cannot compete with the locomotive, while the speed of the latter is as nothing compared with the inconceivably rapid mo- tion of electricity. The rate of motion is called velocity, and it is measured by the space traversed in a given time. Ve- locities are compared by reference to the distance travelled in one second, taken as a standard of time, very swift ve- MOTIONS OF MATTER. 97 locities being expressed in miles per second, and slower ones in feet per second ; this will be understood by exam- ining the following table : TABLE OF COMPARATIVE VELOCITIES.* Miles ill one second. Light 1 92,500 Electricity not less than 200,000 Electric currents in telegraph wires 1 2,000 Feet in one second. Relative motion of the sun in space 205,920 Mean rate of the earth's centre in its path around the sun. . . 101,061 Sound traversing solid bodies 11 ,286 A 24-pound cannon-ball (maximum) 2,450 lline-ball (maximum) 1,600 A point at the surface of the earth under the equator 1 ,525 Volcanic stones projected from Etna 1,250 A point at the earth's surface, latitude of London 950 The most violent hurricane 146 Flight of a swallow 134 A hurricane 117 Locomotive running 65 miles per hour 95 An ordinary race-horse 42 Flight of a crow 37 A brisk wind 8G The fastest sailing vessel 15 A carriage travelling six miles an hour nearly 9 A man walking 6 Straight motion is one which does not change its direc- tion at any point ; curved motion, on the other hand, is con- tinually changing its direction. These require no special explanations, but to the latter we shall refer again. When a moving body passes over equal distances in each second of time, it is said to have a uniform motion. Our standard of uniform motion, with which we compare and * Condensed from Arnott's "Elements of Physics," Seventh Edition. 98 NATURAL PHILOSOPHY. measure all other motions, is that of the earth round its own axis. "Here we have a huge spinning-top, which, not for hours or days, but for unknown ages, has kept up its orig- inal speed practically undirninished. All our notions of time are based on the regularity with which the earth turns round." Watches and clocks are contrivances for obtaining a uni- form motion which can be compared with that of the earth, and for marking off smaller intervals than can be conven- iently observed in the revolution of the earth. There are very few cases of uniform motion in the world, other forces than that which started the uniform motion constantly re- tarding or otherwise modifying it. Motion which is not uniform or regular is said to be variable. In determining the velocity of a body having a variable motion, we must observe the rate of motion at various equal intervals of time, and average them. The distance traversed by a sail- ing vessel or steamer is ascertained by frequently " throw- ing the log," by means of which the speed at definite times is obtained, and calculating the average velocity. When a moving body passes over gradually diminishing distances in equal intervals of time, its motion is said to be retarded. Examples of uniformly retarded motion are fa- miliar: a ball rolled along the ground moves more and more slowly under the influence of gravitation and the resistance offered by the air until it finally comes to rest. A train detached from a locomotive has its motion uniformly re- tarded owing to the same causes ; should brakes be applied and then suddenly released, its motion would also be re- tarded, but not uniformly. Opposed to retarded motion is accelerated motion, in which the velocity of a body contin- ually increases until external forces bring it to rest; as, for example, when a stone is dropped from a height, it falls 1G feet in the first second, 04 feet in the next second, 144 feet MOTIONS OF MATTER. 99 in the third second, and so on, the motion being uniformly \ accelerated, owing to the action of gravity. \ 58. Motion and Rest. Though we use the term rest in >\ opposition to motion, it is obvious from some of the illus- trations given that rest is only a relative term, for not a particle of matter in the universe is at rest. When we are sitting still we call ourselves at rest, though we are moving every hour, by the revolution of the earth on its axis, 1000 miles eastward, and 68,000 miles in our annual journey round the sun. Why, then, are we so insensible to these rapid motions ? It is partly because the motions are so uniform, but chiefly because all things around us, our houses, trees, and even the atmosphere, are moving along with us. If we were moving along alone, even at a slow rate, while all these objects were standing still, we should be conscious of our motion, as when we ride along in a carriage objects at the roadside do not appear to move along with us. This can be made more clear and impressive bj a familiar comparison. A man on board of a steamboat, by confining his attention to things within the boat, may, after a while, be almost unconscious of the boat's moving, if the water be smooth, though the boat may be going at the rate of fifteen miles an hour. If he be reading in the cabin, he will think as little of his motion as he would were he reading in his parlor at home. Should he be blindfolded, and turned around a few times, it would be impossible for him to tell the direction in which the boat is going. Now the case is similar with a man on the earth he is unconscious of the motion of the earth for the same reason that the man in the boat is unconscious of the boat's mo- tion. All objects around him are moving along with him, as the objects around the man in the cabin of the boat are moving along with him. We can carry the parallel farther. While the man sits in the cabin he knows not how fast the boat moves, nor even whether it moves at all. He must look out to decide this, and even then he may not be able to tell whether the boat moves, or whether he merely sees the water running by it. We are often actually deceived in this respect. A steamboat struggling against wind and wave may appear to those on board to be advancing when it is really stationary, or even when it is losing ground. So when we look at 100 NATURAL PHILOSOPHY. the sun, we know not whether it is the sun or the earth that is moving. Mere vision, without reasoning on the subject, leads one to think that it is the sun that moves. 59. Absolute and Relative Motion, The motion of a body is said to be absolute when it is considered without relation to the position of any other body. Its motion is said to be relative when it is moving with respect to some other body. Absolute rest is unknown, for no spot in the universe is known to be without motion. But a body may be relatively at rest, that is, in a fixed relative position to other bodies. Every body is in a state of abso- lute motion, and yet it may be in a state of relative rest. All objects that appear to us to be at rest have a very rapid absolute motion. They appear to be at rest merely because they have the same rapidity and direction of abso- lute motion that we have ourselves. And all the motions which are apparent to the eye are only slight differences in the common absolute motions, of which, though they are so exceedingly rapid, we are entirely unconscious. Thus, if you stand still, and another at your side walk at the rate of three miles an hour eastward, you both have a com- mon absolute motion of 1000 miles in every hour, and he merely adds three miles to his thousand you move 1000 miles, and he 1003. So if you sit still in your parlor, and your friend travel eastward at the rate of 20 miles an hour, you move every hour 1000 miles, and he 1020. And if he travel westward at this rate he really travels more slowly than you do he has* an absolute motion eastward of 980 miles, while you move 1000. At the same time you are both whirling on in the annual journey around the sun at the rate of 68,000 miles an hour. 60. Compound Motion. From what has been shown in the preceding section, it is evident that a body may partake of two motions at one and the same time, and these motions MOTIONS '0V M$iWBi J '*' 5% * 101 may be in the same direction or in different directions. If a man travelling on a steamboat walk towards the bow, he will move forward with the boat at the same time; sup- pose the steamboat moves at seven miles an hour, and he walks at the rate of three miles an hour, during the time that he passes from the stern to the bow of the boat his total velocity will be ten miles per hour ; if, on the other hand, he turn about and walk back to the stern at the same rate, his velocity will be only four miles an hour. That is, if we refer his motion to the banks of the river on which the steamboat moves ; but if we refer his motion to the steamboat only, his velocity will be three miles an hour, no matter in what direction he walks. This is an example of simultaneous motions in the same direction ; we will now give one of simultaneous motions in different directions. If a man attempt to row a boat straight across a swift- ly running river, he will reach a point not directly opposite to that from which he started, but below. Two forces act upon the boat: the current tending to carry it straight down the stream, and his rowing tending to carry it straight across. The boat will go in neither of these directions, but in a line between them. Let A B, Fig. 72, represent the bank of the river, from which he starts at A, with the bow of the boat pointing to C, on the opposite bank. Suppose, now, Flg - 72> that in the time that it takes him to royr across the cur- rent would carry him down to B if he did not row at all. He will in this time, by the two forces together, reach the point D, opposite to B, his course being the line A D. If the wind blow upon a vessel in such a way as to carry it eastward, and a current be pushing it southward, the vessel will run in a middle line, viz., southeast. For the same reason, if a boy kick a foot-ball already in motion, it E 102 PHILOSOPHY. will not be carried in the direction in which he kicks it, but in a line between that direction and the direction in which its former motion was carrying it. In swimming, flying, rowing, etc., we have examples of compound mo- tion, the middle line between the directions of the forces always being taken by the body moved. If we take Fig. 72, illustrating the movement of the boat, c, ,,D and draw two lines, one from A to C and the other from B to D, we shall have the parallelogram A C D B, Fig. 73, in which B the line A C represents the force of the Fig. 73. rowing, A B the force of the current, and A D the path of the boat. You see, then, that if we wish to find in what direction and how far in a given time a body acted upon by two forces will move, we are to draw two lines in the direction of these forces, and of a length proportionate to the distances to which they would move it in that time ; then by drawing two lines parallel to these we shall have a parallelogram, and the diagonal of this will represent the distance and the course of the moving body. If a body be acted upon by two equal forces and at right angles to each other, the figure described will be a square, as you see in Fig. 74. If they vary from a right angle, the figure will vary in the same proportion from the square figure, as seen in Figs. 75 Fig. 74. and 76. In the three figures, A B and A D represent the two forces and A C the resulting motion. You observe by these diagrams that the nearer the two forces are c to the same direction, the farther will they move the body. This Fig. 75. MOTIONS OF MATTER. 103 is shown by the different leno-ths of the diagonals in O O Fig. 74 and Fig. 76. The more nearly, therefore, the Avind coincides with the current, the more rapidly will a vessel be carried along before the wind. When, on the other hand, the angle at which two forces act upon a body is much greater than a right angle, they will propel it but a small distance. Thus, if two forces act on a body at D in the directions D A and D 0, Fig. 77, they will move it only the distance represented by the diagonal D B. This diagram represents the motion of a vessel sailing almost directly against a current by a wind the force of which is equal to that of the current, while Fig. 76 represents the motion of a vessel where wind and current, being of equal force, very nearly coincide. In the above diagrams we have supposed the forces to be equal-; but the same truth can be shown in regard to unequal forces. 61. Momentum. The momentum of a body is its quan- tity of motion. In estimating the momentum of any body two things must be considered its velocity, and its quan- tity of matter or weight. * A bullet fired from a gun has a vastly greater force, or power of overcoming obstacles, than one thrown by the hand, owing to its greater velocity. Now, suppose the weight or quantity of matter to be in- creased ten times, and that it moves with the same velocity as before; it will have ten times as much force as before, and will overcome ten times as great an obstacle. For this reason, a small stone dropping upon a man's head may do 104 NATURAL PHILOSOPHY. but little harm, while one ten times as large, falling from the same height, may stun and perhaps kill him. But if the large stone could fall with only one tenth of the velocity of the small one, the effect of both would be the same. The rule for calculating the momentum of a moving body is to multiply its weight by its velocity. Using the above illustration for an example, suppose the weight of the small stone be 1 ounce, and that of the large one 10 ounces. If they fall from a height of 16 feet, the force with which thu large one will strike will be expressed by 160 (16 x 10), that of the small one by 16 (1 x 16). Suppose, however, that by some force in addition to gravity the small one could be made to move ten times as fast as the large one, the force with which it would strike would be equal to that of the large one, and would be expressed by the number 160. We will illustrate this in another way. Let a and , Fig. 78, be two balls of clay of equal size hanging over a graduated arc. Now if b be let fall from the top of the arc 6, on striking against a it gives half of its motion to a, and they both move on together. But how far will they go ? To 3 on the other side of the arc. Why? Let the quan- tity of matter in each ball be called 1, and the motion of b 6. The momentum will, therefore, be 6. Now the momentum of the two together will be the same after the blow as that of b was before it. But the quantity of matter is twice as great, and must be called 2. Therefore the motion must be represented as 3, to make the momentum 6 (2 x 3). But suppose that b is twice as large as a. Falling from 6, its momentum would be represented by 12 (2 x6). After it has struck , the momentum of the two together would be the same as that of b before the stroke ; MOTIONS OF MATTER. 105 but the quantity being 3, the motion would be represented by 4. They would, therefore, move to 4 on the arc. Examines. A few examples illustrating momentum, as dependent upon weight and velocity, will suffice. If a musket-ball of an ounce weight were so far spent as to move with a velocity of only a foot in a second, its force would be so small that if it hit any one it would do little harm. But a cannon-ball weighing a thousand ounces moving at this slow rate would have a very great force equal, in fact, to the momentum of an ounce ball moving 1000 feet in a second. If a plank push a man's foot against a wharf, he will scarcely feel it ; but if the plank, instead of being alone, is one of a thousand planks fastened together in a raft, and the whole move with the same velocity, the force will be increased a thousand-fold, and the plank will crush the foot. And if the one plank, when alone, should move a thousand times as fast as the whole raft, the same result would follow. So soft a substance as a candle can be fired through a board from the mo- mentum given to it by an immense velocity. Perhaps there is no better example of the great force given to a substance by an enormous velocity than we have in the wind. So light a thing is air that people think of it as almost nothing. But let it be set in rapid motion, and the velocity gives to it a force, a momentum, which will drive ships upon the shore, throw over buildings, and tear up trees by the roots. In this last example we see beautifully illustrated the meaning of the expression quantity of mo- tion. In the moving air each particle does its share of the work in the de- structive effects mentioned. Each particle, therefore, may be considered as a reservoir of motion, and the quantity of motion in any case depends upon the quantity which each particle has and the number of the particles. 62. Relation of Force to Velocity. It would seem, at first thought, that the motion produced in any body must be in exact proportion to the force producing it; that is, that twice the force which produces a giv-en velocity would double that velocity, and three times would treble it, etc. This is true where there is no resistance to motion, as in the case of the heavenly bodies moving in their orbits. But in all motions here upon the earth there is resistance ; and the greater the velocity, the greater the resistance. If, therefore, you increase the velocity of any body, you not only have to communicate more motion to it, but you must 106 NATURAL PHILOSOPHY. overcome also the increased resistance. The rate of in- crease of force for increased velocities has been very accu- rately ascertained. A boat moving from B to A, Fig. 79, we will suppose, displaces a quantity of water represented Fig. 79. by the space between the two lines extending from B to A. Now if it move from B to C, it displaces twice the bulk of water B C ; and as it is displaced in the same time that B A was, each particle is displaced with twice the velocity. Double the force is required to displace a double portion of water, and to do this with double the velocity the force must be doubled again. So if the boat be made to move three times as far in the same time that is, from B to D three times the quantity of water is displaced, and each of these three portions, B A, A C, and C D, is displaced with three times the velocity. The force required, then, to do this is nine times that required to carry the boat from B to A in the same time. It is plain, therefore, that with veloc- ities represented by 'the numbers 1, 2, 3, 4, etc., the forces requisite to produce these velocities must be as the squares of these numbers; viz., 1, 4, 9, 16, etc. This law is a very important one, in a practical point of view. For example, it shows us how much larger a quantity of coal is required to produce in steamboats a high velocity than a moderate one. Its application, too, to the science of gunnery is im- portant. When the weight of a moving body is multiplied by its velocity, we obtain ( 61) its momentum; when the weight is multiplied by the square of the velocity, we obtain the force with which a body strikes a resisting substance. This is directly deduced from the explanation just given. 63. Accelerated Force. You have learned in 57 some- MOTIONS OP MATTER. 107 thing of the varieties of motion: these are obviously the re- sult of the action of corresponding forces on matter. Thus we have uniform, accelerated, and retarded forces. If the momentum remain the same, independently of time, the force is uniform; if the momentum increase, the force is. ac- celerated ; and if diminished, the force is retarded. Were there no obstacles to motion, such as resistance of the air, etc., we might have uniform forces; but since we do not meet with absolutely isolated or free matter, all moving forces are more or less variable. Even in the production of very rapid motions the force is seldom instantaneously applied, but is rather gradual in its action ; the motion is not the result of a single impulse, but a succession of im- pulses is required to accumulate sufficient momentum to overcome the resistance opposed. The action of gunpow- der upon a bullet issuing from a gun is apparently an in- stantaneous and single impulse, but it is not really so. The great velocity given to the bullet is due to the continued impulse of the expansive force of gases produced from the powder, and it therefore depends much on the length of the barrel. If this be short, the force of the powder is not con- fined long enough to the bullet to give it a great velocity. It is on the same principle of continued action that a man lifts his ham- mer high when he wishes to inflict a heavy blow. In this case both grav- itation and the muscular power of the arm exert their force on the hammer through the whole space. A horse in kicking does the same thing, and by the great length of the leg the velocity given to the foot by this continued action of the muscles is very great. An arrow is not shot by a single mo- mentary impulse of the bowstring, but the string, by following it through a considerable space, gives it a continued impulse. One of the best examples of accelerated force is the attraction of gravity. You know that the greater the elevation from which a body falls, the greater is its velocity, and, therefore, the greater the force with which it strikes. Why is this ? If it fell because of a single impulse drawing it towards the earth, this would not be the case ; and if there were no air 108 NATURAL PHILOSOPHY. in the way, the velocity would be uniform. But the resistance of the air would retard the velocity ; so that if a number of bodies should receive the same impulse at different elevations, the one farthest off would be most retarded, and, therefore, come down slower than all the rest. In this case, the higher the elevation from which a man should fall, the less would be the injury. But a body does not come to the ground by a single im- pulse, but by a succession of impulses, or, rather, a continued impulse. Ev- ery moment that the body is coming down it is drawn upon by the attrac- tion of the earth, and this continued action causes an increase in the rapid- ity of motion. Expressing this in somewhat different language, we may say that gravity is an accelerating force. Of this examples are innumerable: "A person may leap from a chair with impunity; if from a table, he receives a harder shock; if from a high window, a topmast of a ship, or the parapet of a high bridge, he will probably fracture bones; and if he fall from a balloon at a great height, his body will be lit- erally dashed to pieces." Water falling from a height acquires a power proportion- al to the elevation. The same is true of meteoric stones, which approach the earth with such immensely accelerated velocity that they become heated in their passage through the atmosphere, and bury themselves deep in the earth when they strike its surface. 64. Gravity a Uniformly Accelerating Force. An acceler- ating force may be uniform or variable; gravity is not only an accelerating force, but it is uniform in its rate of increase. A stone dropped from a height falls through a distance of 16 feet in one second, 64 feet in two seconds, 144 feet in three seconds, and so on. Now, after the stone has passed through the 16 feet that is to say, at the end of the first second of time, its velocity is 32 feet per second ; at the end of two seconds, 64 feet per second ; at the end of three sec- onds, 96 feet per second, and so on. Thus the velocity at the end of 2, 3, 4 seconds is double, triple, quadruple, etc., MOTIONS OF MATTER. 109 that at the end of one second ; that is, its rate of increase is uniform, viz., 32 feet per second. This law holds good for all bodies, no matter whether they are heavy or light. At first sight it seems very par- adoxical that a ball weighing one pound dropped from a height will reach the ground just as quickly as one weigh- ing ten times or one thousand times as much. And yet such is the case ; gravity causes all unimpeded bodies to fall with equal rapidity, without reference to their weight. Any one who throws a feather and a bullet into the air, however, observes tl^at the bullet falls to the ground long before the feather, and will be disposed to dispute the statement just made. Such a one must remember that the resistance of the air must be taken into account, as we will now proceed to show. When a stone is thrown into the air, its upward motion is gradually destroyed by the attraction of the earth and the re- sistance of the air. Observe, now, why it descends. It is from the action of one of the causes which arrested its upward flight the attraction of the earth. In its descent it is re- tarded by the resistance of the air, as it was in its ascent. This retardation is very obvious in the case of substances which present a large surface to the air, as a feather. A small piece of lead will outweigh many feathers, and, therefore, since its quantity of matter is so much greater in proportion to its surface than that of a feather, it will fall to the ground much more quickly. That this is owing wholly to the resist- ance of the air can be proved with the air-pump. Suppose that you have a tall receiver, Fig. 80, on the air-pump, and a piece of lead and a feather are placed at its upper part in such a way that they can be made to fall at the same instant. Ex- haust the air, and then let them fall. They will go down side by side, as represented by the figure, and reach the bottom of the receiver at the same time, because there is no air to resist the progress of the feather. The toy called the water-hammer illustrates the same thing. When water falls through the air, the resistance of the air tends E2 110 NATUEAL PHILOSOPHY. to separate its particles, as we see in the falling of water thrown up by a fountain. In the water-hammer, which is a closed tube containing a little water and no air, when the water is made to fall from one end to the other, as there is no air to divide it, it falls as one mass, and gives a sharp sound like the blow of a hammer. An instrument essentially like this can be made with a thin glass flask. Put a little water into it, and, after heating it to boiling over a spirit-lamp, cork the flask tightly, and then leave the water to cool. As all the space above the water was filled with steam when the flask was corked, it is a vacuum now that the steam is condensed. 65. Retarded Force. We have seen ( 63) that force is never instantaneously communicated, and that a succession of impulses are required to communicate motion. In like manner, no force can be instantaneously arrested, and a gradual resistance to motion is necessary to make it dis- appear. Examples showing the gradual nature of the re- tardation of force are numerous. It is by the gradual or continued resistance of the air that the motion of a cannon- ball is destroyed. Now if, instead of this gradual resist- ance, any hard substance, as a block of granite, were op- posed to the progress of the ball, it would be at once broken asunder. We see, then, the reason that a hard sub- stance of moderate thickness does not offer so effectual a resistance to a body moving very rapidly as some sub- stance of a more yielding kind and of greater bulk. For example, a bale of cotton will arrest a ball which would pass through a plank, for the cotton, yielding easily, permits the force of the ball to be felt and resisted by a larger bulk, while the wood, not yielding, opposes but a small portion of its whole bulk to the force of the ball, and therefore does not arrest it ; in other words, the momentum of the ball is communicated to a much larger quantity of matter in the cotton than in the wood. These principles afford a ready explanation of a feat which is sometimes performed. A man lies upon his back, and, having an anvil carefully placed upon his chest, allows some one to MOTIONS OF MATTER. Ill strike a heavy blow with a hammer upon the anvil, and no injury is received. Why? Because the momentum, or force, of the hammer is diffused throughout the bulk of the anvil, and then again throughout the bulk of the yielding chest. The man takes good care to have his lungs well filled with air at the moment of the blow, for this increases the bulk and elasticity of the chest, and thus promotes the diffusion of the momentum. If the blow of the hammer were received directly upon the chest, great injury would be done, for the force would then be spent upon one small spot alone. The principles above elucidated are applied by men instinctively in their common labors and efforts. Watch a man catching bricks that are tossed to him. As he receives the bricks in his hands he lets his hands and the bricks move together a little way, so that he may gradually arrest the mo- tion of the bricks. To do it suddenly would give him a painful lesson on momentum. So when a man jumps from a height he does not come to the ground in a straight position. This would cause a sudden and therefore a painful arrest of the motion of the whole body. To avoid this he comes to his feet with all the great joints of his body bent, so that the different portions approach the ground successively, his head having its motion arrested last. QUESTIONS. 55. Explain the relations of matter, motion, and force as seen in the rolling of a ball. Define motion. Define force. Show that force may exist without motion. Give the illustration of the magnet. 56. What is said of the universality of motion ? What are the principal causes of motion? How does attraction act? Explain the* influence of heat and of other forces. 57. Name the varieties of motion, and give examples of each. How is velocity measured ? How compared ? Name the rate of motion of light. Of electricity. Of sound. Of a violent hurricane. Of a man walking. Illustrate uniform motion. Illustrate variable motion. Give examples of uniformly retarded motion. Of accelerated motion. 58. Show that motion and rest are relative terms. Give the comparison of the steamboat. 59. What is the difference between absolute and rel- ative motion? What is said of absolute rest ? GO. What is said of com- 112 NATURAL PHILOSOPHY. pound motion. Give the example of a man walking the deck of a moving steamboat. Illustrate simultaneous motions in different directions. Ex- plain the principles illustrated by the parallelograms, Figs. 73, 74, and 75. Gl. What is the momentum of a body? Give the rule for calculating momentum, and give an example. Give the illustration of two balls of clay. Also of the cannon-ball. And of the plank. What is said of the wind as a reservoir of motion ? 62. What is said of the relation of force to velocity ? 63. What is said of accelerated force ? Show that rapid motions are usually caused by a succession of impulses. Give the illustra- tions of the hammer, of the horse, and of the arrow. Show that gravity is an accelerating force. Give illustrations. 64. Show that gravity is uni- formly accelerating. State the law. Explain why bodies of different weights fall with equal rapidity. Describe the experiment in a vacuum. Give the illustration of the water-hammer. 65. What is said of retarded force? Give examples. Explain the anvil trick. Mention illustrations taken from every-day life. CHAPTER VIII. MOTIONS OF MATTER (CONTINUED). 66. Course of Bodies Thrown into the Air. When any body a stone, for example is thrown straight upward into the air, it does not, in reality, go up or come down vertically. If it did, it would come down at a great distance from us. Suppose it takes two seconds for it to go up and to reach the ground. If we stand at the equator, in that two sec- onds we move from the point where we threw up the stone nearly 3000 feet eastward ; and, therefore, if the stone rose and fell vertically, it would fall 3000 feet westward of us. Why, instead of this, does it fall at our feet? Because when thrown into the air it not only has the upward mo- tion given by the hand, but also the forward motion of the earth. It is a case similar to that of a man on board of a steamboat, who, though the vessel move fifteen miles an MOTIONS OP MATTEK. 113 hour, tosses up his ball or orange and catches it as well as if he were on land. This he could not do if both he and the orange did not have the same forward motion as the boat. If a man fall from a mast-head, he reaches the deck at the foot of the mast when the vessel is sailing rapidly, just as if it were lying still at the wharf. If he did not by inertia ( 14) retain the forward motion which he had in common with the vessel, he would fall at some distance behind the mast. The Earth and the Atmosphere. The air being held to the earth by at- traction, it has a motion in common with the earth. It revolves with the earth just as the tire of a wheel revolves with the wheel. This being so, our winds are nothing but slight variations of this constant rapid whirl of the aerial coating of the earth. If the atmosphere were suddenly to stop whirling round with the earth, we should move through it with a velocity of 1500 feet a second; and the destructive effect upon us would be the same as if the earth were standing still while the air moved over its surface with this fearful velocity. A thoughtless man, not reflecting that the atmosphere moved with the earth, proposed rising in a balloon, and waiting till the country to which he wished to go should pass under him, and then to descend to the earth. 67. Path of Projectiles. If we consider the connection between the motion of the earth and the course of a body thrown into the air, and ascertain its actual path, we find that it forms a peculiar curve. Anything thrown into the air is called a projectile / and the path which it follows is that of & parabola. Suppose a stone be thrown by a man standing at A, Fig. 81, in the direction A C E G, it will de- viate from a straight line on account of the attraction of gravity, and actually de- scribe the parabolic curve 114 NATURAL PHILOSOPHY. A D F B. If the stone, having reached the point C, has fallen towards the earth a certain distance, represented by C D, when it reaches the point E, twice as far from A, it will fall a distance not twice, "but, four times as great as C D, viz., E F, and so on, thus forming the curve. Of course, it is understood that, besides the propelling force of the arm and the attraction of gravity, a third force acts upon the stone, viz., the resistance of the air; but this being in direct opposition to the first, it only retards the motion, and does not tend to turn it from its straight course. If the stone be thrown horizontally, it also describes a parabola. If the propulsive force be very great, as in the case of a bullet discharged from a gun, the path will appear to be straight; but this is not so. The force of gravity pulls the bullet towards the ground from the in- stant that it leaves the gun. This deviation is very slight, however, and for short distances the bullet may be con- sidered as moving in a straight line. When, however, a marksman shoots at long range, he must make allowance for this bending-down of the motion. Accordingly, for the sake of precision, a double sight is provided in modern guns, as shown at A and B, Fig. 82. This arrangement secures Fig. 82. the pointing of the gun a little above the level of the object aimed at, that level being indicated by the dotted line. Let us further study the path of a projectile impelled MOTIONS OF MATTER. 115 horizontally. In the case of the musket-ball just men- tioned, we have seen that two forces act upon it, viz., the projectile force given by the powder and the force of gravi- tation. The force of gravity being always the same, the shape of the curve which the projected body describes must depend on the force with which it is projected. This is very strikingly exemplified in the curves described by the different streams of water in Chapter XII. But whether the projectile force be great or small, the moving body thrown horizontally will, in every case, reach the ground in the same time. Thus, if two cannons stand side by side on a height, one of which will send a ball a mile and the other half a mile, the two balls, if fired together, will reach the ground at the same instant, though at first thought it would seem that the ball which travels twice as far as the other would take a longer time to accomplish it. This is because the horizontal force of the ball does not oppose in the least the downward force of gravity. If it were thrown upward instead of horizontally, the projectile force w r ould be opposed to gravity, and in proportion as the direction came near to being vertical. As horizontal force does not interfere with the action of the force of gravity, it follows that, if a ball be dropped at the instant at which another is fired, both will reach the ground at the same instant. This can be made clear by Fig. 83. Suppose it takes three seconds for a ball to fall from the top of a tower to its foot. In the first second it falls to a. The ball projected horizontally from the cannon, being operated upon by the same force of gravity, will fall just as far, and will be on a level with it at b. Both balls fall farther and farther each second, both being accelerated in the same de- gree because it is done by the same force. The projected ball will reach d when the falling ball is at c, and the plane at / when the falling ball is at 6, the foot of the tower. 116 NATURAL PHILOSOPHY. D The same holds true in all cases. A bullet dropped from a level with the barrel of a gun, paradoxical as it may seem, will fall to the ground no sooner than one which is shot from the gun. 68. All Falling Bodies really Projected. When a body falls from any height, it does not, as you have already seen in 66, fall in a straight line, as it appears to do. It falls in a curved line, for, like all projectiles, it is acted upon by a horizontal force as well as the force of gravity. But what is this horizontal force ? It is the motion which the body has in common with the earth in its rotation on its axis. In this rotation the height from which the body falls goes to the eastward 1500 feet in a second. If, therefore, the body did not partake of the motion of the earth, and de- scended in a straight line in a second, it would reach the ground 1500 feet westward from the foot of the height whence it fell. But it does partake of the earth's motion, A -^-44^ o and, moving eastward as fast as the height, it describes the curved line of a projectile. Suppose a ball falls from Fig. 84. - a height, A, Fig. 84. and in a second of MOTIONS OF MATTER. 117 time that height passes to C. The forward or projectile force would tend to carry the ball to C, and the force of gravity would tend to carry it to B. But both forces acting together, it pursues a middle path, and this path is a curved line, because one of the forces is a continued force. (See 63.) For the same reason, if a ball be dropped from a railway car in motion, and it take a sec- ond to fall, at the end of that second it will strike the floor just under that part of the car from which it fell. Although the car may have moved a considerable distance, the dropped ball, partaking of its motion, goes along with it in its fall. For the same reason, a ball dropped from a masthead when a ship is in motion, partakes of the mo- tion of the ship. The ball in each of these cases describes in its fall a curved line. s . G9. Motion in Orbits. Why is it, let us ask, that a cannon-ball shot horizontally from some great height will not revolve around the earth like the moon. It has the same two forces acting upon it as the moon has viz., a projectile force and the attraction of the earth and both ball and moon describe a curve in their motion. But the curve of the ball bends to the earth, while that of the moon ever sweeps around the earth. Why is this? In the first place, the resistance of the air continually re- tards the velocity of the ball. But, secondly, even if the ball could be projected from an elevation sufficiently high to be outside of the atmos- phere, the force of the projection would not be great enough. We know, from the rate of progress of the heavenly bodies in their orbits, that it would require an immense velocity to keep the ball from being brought to the earth by its attraction. The Creator of these worlds, when he launched them into their orbits, gave them precisely that impulse which is needed to balance the centripetal force ( 73) of attraction, and so they pursue a middle course between the two directions in which these two forces tend to carry them. And as their velocities have never been retarded by the resistance of air or any other substance, they have been ever the same from the beginning. 70. Newton's Laws of Motion. By investigating the 118 NATURAL PHILOSOPHY. principles of motion, Sir Isaac Newton arrived at throe laws, which have been in some measure anticipated in the preceding sections. These laws may be briefly stated as follows : I. A body free from the interference of external matter or force will, if at rest, remain at rest, and if in motion, will move uniformly in a straight line. II. A given force always produces the same effect, wheth- er the body on which it acts be in motion or at rest, and whether it be acted upon by one or more forces simulta- neously. III. Action and reaction are equal and opposite. These laws are far more comprehensive than they at first sight appear, and require some explanation. The first part of the first law follows from inertia, 14; a body at rest will remain at rest until some external force causes its motion ; and a body has no power in itself to change the rate or direction of its motion. Hence in the communication of motion a certain amount of time elapses before its effects are made evident. Of this we have many examples, some of which are given in the following sec- tions. 71. Inertia Shown in the Communication of Motion. When the sails of a vessel are first spread to the wind, the vessel does not move swiftly at once, for some time is re- quired for the force applied to overcome the inertia of so large a mass, and to put it in rapid motion. Horses make a greater effort to start a load than they do to keep it in motion after it is started. If a person stand up in a car- riage, and the horses start off suddenly, he falls backward, because his body, from its inertia, does not readily and at once partake of the motion of the carriage. If a person start forward quickly with a waiter, filled with glasses, in his hands, the glasses will slide backward. MOTIONS OP MATTER. 119 The foregoing illustrations show that it requires some time to communi- cate motion to any body. We .will give some illustrations of this fact of a more striking character. If a ball be thrown against an open door, it will move the whole door, and perhaps shut it ; but the same ball fired frorr a rifle will pass through the door without moving it perceptibly. In tht latter case its velocity is so great that there is not time enough to com- municate motion to the whole door, and it moves only that part of it with which it comes in contact. A bullet thrown with but little force against a window will crack a whole pane of glass ; but if shot from a pistol, it mere- ly makes a round hole. A cannon-ball having a great velocity may pass through the side of a ship, doing perhaps comparatively little damage, while one moving with much less velocity may do vastly more damage by splintering the wood to a considerable extent. For the same reason a rapid ball hitting a person may occasion less suffering and do less harm than a slow ball ; for a rapid ball kills merely the parts which it touches, leaving the flesh around in a sound state, while the slow ball bruises over a large space. If a large pitcher filled with some heavy liquid be quickly taken up, the handle will break, leaving the pitcher behind. Large dishes are some- times broken in this way when heavily loaded. 72. Inertia Shown in the Disposition of Motion to Con- tinue. As in the case of the ship, in the first illustration in 71, it takes time to communicate motion to the whole ship, or, in other words, to overcome its inertia, so, when the ship is once in rapid motion, it does not stop suddenly when the sails are taken down, but its inertia tending to keep it moving is gradually overcome by the resistance of the water. If a person stand up in a carriage in motion, and the horses suddenly stop, he will be thrown forward, for his body has a motion in common with the carriage, and from inertia is disposed to go on when the carriage stops. When you strike your foot against anything to get the snow off, you give the foot and the snow a common motion together, then arresting the motion of the foot, the snow through inertia passes on. The same thing is illus- trated in 'striking two books together to remove the dust. If a ship strike upon a rock, everything on board which is loose 120 NATURAL PHILOSOPHY. is dashed forward. The earth, as it revolves on its axis, has a velocity at the equator of about 1000 miles an hour. If this revolution should be suddenly arrested, everything loose on its surface, having acquired the motion of the earth, would be at once thrown eastward, just as the fur- niture, etc., on board ship are dashed forward when the vessel is stopped by running against a rock. All the houses, monuments, and structures of every kind would fall prostrate eastward. An Equestrian Feat, In the feat of jumping over a cord from the back of a galloping horse, represented in Fig. 85, the only exertion made by the rider is to raise himself sufficiently to pass over the cord. He comes down again upon the horse's back, simply because of the motion which he has in com- mon with the horse, his feet going in the path represent- ed by the dotted line. If he should attempt to throw himself forward, as in leaping from the ground, he would go too far, and perhaps strike upon the horse's neck in- stead of his back. Skill in jumping from a moving car- riage consists in making the proper allowance for the forward motion which is had in common with the car- riage. Most persons are apt to overdo the matter, and so come to the ground prostrate, and with unnecessary violence. A Case in Court. A dashing young man driving a light phaeton ran against a heavy carriage. His father was induced by his son's represen- tations to prosecute the driver of the carriage for driving too fast. A knowledge of motal inertia very readily decided the case. The son and his servant both declared in the witness-stand that the shock of the car- MOTIONS OF MATTEK. 121 riage against the phaeton was so great that they were thrown over the horses' heads. They thus proved themselves guilty of the fast driving, for it was their own rapid motion that threw them out when the phaeton was stopped by running against the carriage. The following case is a parallel one : If two boats the one, of large size, sailing slowly up stream ; the other, a small one, sailing rapidly down run against each other, a man standing in the bow of the one going down will be thrown much farther forward than one standing in the bow of the other. 73. Centrifugal Force. The second part of the first law states that if a body in motion be not interfered with, it will move uniformly in a straight line. This disposition of mo- tion to be straight is well illustrated by a consideration of centrifugal force ; but, before explaining it, we will briefly mention the nature of curved motion. We have shown in 60 that when two or more forces act upon a body simultaneously, the motion resulting is in a straight line. If, however, you have understood the ex- planation of the parabolic path of a projectile ( 67), you have observed that two forces may also produce curved motion, provided one of them communicate a single im- pulse and the other a succession of impulses. Of this we have a familiar example in a ball whirled around at the end of a string. You can give it an impulse, and then, holding it in your hand, let it whirl. Here the impulse given the ball is one force, and the tension of the string is the other, the latter acting continuously. Your hand holding the end of the string is the centre about which the motion revolves; the impulse. which you have given the ball tends to make it fly away from the centre in a straight line, and hence is called the centrifugal force ; the tension of the string keeps it from thus flying off, and is called the centripetal force. This will appear clearer by examining the diagram, Fig. 86. If the hand holding the string be at A, the impulse given the ball B will tend to move it in the direction B C, 122 NATURAL PHILOSOPHY. Fig. 86. but the string A B pulls it towards the centre; and when the ball reaches any other point, as D, it is prevented E from pursuing the straight path D E by the same cause ; consequently, the ball revolves in a circle. That the ball would take the direction B C but for the resistance of the string can easily be shown by experiment : in place of a ball fastened to a string we may use a stone in a sling, and the instant the stone is set at liberty it will dart off as straight as an arrow (Fig. 87). When the earth, at the creation, was put in motion, it would have moved in a perfectly straight line were it not constantly drawn towards the sun by attraction, the continuous action of this latter force being the same as the tension of the string in the case of the whirling ball. The force of attraction, then, is the centripetal force of the earth, and the impulse which was given to it by the Creator in the beginning is its centrifugal force; and, balanced between these two forces, the earth and all the heavenly bodies move uniformly onward in their orbits. The centrifugal force in these illustrations is simply the tendency of motion to a straight line, which is constantly counteracted by the centripetal force. < 74: Illustrations of Centrifugal Force. When a wet mop is whirled, the water flies off in every direction by its centrifugal force. On the same principle a dog, coming out of the water, shakes off the water by a semi- rotary motion. When a suspended bucket of water is revolved swiftly, the water rises high on its sides, and leaves a hollow in the middle. It is the tendency to fly away from the centre of motion that causes this. If the Fig. 87. MOTIONS OF MATTEK. 123 bucket be held firmly by the cord and swung swiftly around the hand as a centre, the cen- trifugal force of the water against the bottom and sides will prevent its escaping, even when the bucket is upside down, as shown in Fig. 88. Large wheels, revolving with great velocity, have been broken by the centrifugal force of their particles, and hence the necessity of having such wheels made very strong. The immense grindstones used in gun-factories have some- times been broken, through in the middle, or have burst into pieces with destructive vio- lence from the same cause. A man riding horseback on turning a sharp corner inclines his body towards the corner, to avoid being thrown off by the centrifugal force. So, in the feats of the circus, a man standing on a horse running at full speed around the ring inclines his body strongly inwards, as shown in Fig. 89. The horse also instinctively in- clines in the same direction for the same rea- son. If the rider find himself in danger of falling, by making the horse go a little faster, thus adding to the centrifugal force, the difficulty is relieved. The centrifugal force is made use of in milling. The grain is admitted be- tween two circular stones by a hole in the centre of the upper one, and as Fior.89. ^ ne stone revolves Fig. 88. 124 NATURAL PHILOSOPHY. it constantly moves towards the circumference, and there escapes as flour. Bends in Rivers. We see the operation of centrifugal force in the bends of rivers. When a bend has once commenced in a river, it is apt to increase, for as the water sweeps along the outer bank of the bend it presses strongly against it, just as the water in the whirled bucket presses against its sides, by its centrifugal tendency, or, in other words, its ten- dency to assume a straight motion. Of course, the result is a wearing-awny of this outer bank, and in propor- tion to the looseness of the mate- rial of which it is composed and the velocity of the river's current. And when one bend is formed, an- Fig. 90. other is apt to form below, but on the opposite bank. The water, by sweeping along the bend a, Fig. 90, is directed by it towards the opposite bank at b, and makes a bend there also. It is in this way that a river, running through a loose soil the Mississippi, for example acquires a very serpentine course. As the water in the whirled bucket rises around the sides, so in the river the water will be higher against the bank a than on the opposite side. Eddies and whirlpools are produced on the same principles, when water is obliged to turn quickly around some pro- jecting point. If a current were moving swiftly along the shore a towards the point 6, Fig. 91, it would be directed outwards by the resistance of this projection, and so a depression would be left at c, just behind it, and this depression would be surrounded by a revolving body of water. Fig. 91. 75. Application of Centrifugal Force in the Arts. Much use is made of centrifugal force in the arts, and we will mention a few examples. In the art of pottery the clay is made to revolve on a whirling table, the workman at the same time giving the clay such shape as he chooses with his hands and various instruments. In doing this he constantly pays attention to the centrifugal force, giving the table a velocity proportioned to the amount of this force which is needed in each stage of the operation. One MOTIONS OF MATTER. 125 of the most beautiful applications of this force is in the manufacture of common window-glass as formerly conduct- ed. The glass-blower gathered up on the end of his iron tube a quantity of the melted glass, and blew it out into a large globe. When it was of sufficient size and thinness, he placed it on a rest, as shown in Fig. 92. A second man then came with a rod having some melted glass on the end, and attached this to the globe at a point opposite to that where the tube of the first man joins it. Then a boy gave this tube a quick blow and severed its connection with the globe, leaving a hole in the globe where the glass breaks out. The second man, having the globe attached to his rod, carried it to a blazing furnace,*and, resting the rod on a bar at its mouth, put the globe directly into the flame. The glass being soon softened, he whirled the globe continually around. The hole in the globe enlarged by the centrifugal force, and at length by this force the globe was changed into a flat, circular disk, from which were cut panes of glass. In sugar-refineries the crystallized sugar is freed from P 126 NATURAL PHILOSOPHY. the viscid molasses by being placed in a box revolving with great speed; the liquid is thrown off by the centrifugal force, and collected in a suitable manner. This method of drying substances by means of centrifugal motion is fre- quently adopted in the arts ; perhaps the most curious ap- plication is to the honey-comb. It has been observed that honey-bees provided with a clean comb will at once proceed to fill it with honey ; accordingly, filled combs are carefully shaved to remove the caps on the cells, and placed in a cen- trifugal machine. When the machine is set in motion, the honey is thrown out of the cells quite perfectly, and the emptied comb is replaced in the beehive. By this means the valuable time of the busy bees is economized, and they are spared the trouble of making fresh wax and new combs. Steam- Governor. The operation of centrifugal force is beautifully exemplified in this regulator of the steam-en- gine. It consists of two heavy balls, Fig. 93, sus- pended by bars from a vertical axis, the bars being connected to the axis by hinges. The bars have also a hinged con- nection at their lower ends with two smaller bars, and these latter have a similar connec- tion with a collar that slides up and down on the axis. Now the fast- Fig - 93> er the axis turns, the far- ther the balls fly out from it, from the centrifugal force, and the higher the collar slides up on the axis. From the collar extends a lever. This is connected with a valve in MOTIONS OF MATTER. 127 the steam-pipe, and so regulates the amount of steam that enters the working part of the engine. The object of this ingenious contrivance is to make the engine regulate its own velocity. When it is not working too fast, the valve in the steam-pipe is wide open. But the moment that the engine begins to move too rapidly, the balls extend out far from the axis, so that the collar rises, and by the lever partly closes the valve. Less steam, therefore, can come to the engine ; and the engine working, in consequence, less rapidly, the balls fall again, opening the valve. You see, then, that the regulation of this valve by the governor effectually prevents the engine from running at a danger- ously high speed. 76. Shape of the Earth Influenced by Centrifugal Force. If the potter should make a ball of soft clay revolve rap- idly around on a stick run through it, the ball would bulge out at the middle, where the centrifugal force is greatest, and would be flattened at the ends where the stick runs through it. This is precisely what has happened to the earth. At the equator, where the centrifugal force is great- est, it has bulged out about thir- teen miles, while it is -flattened at the poles. This shape was of course assumed before the earth became solid. Fig. 94 represents E the shape of the earth, N S being the polar diameter, and E E' the equatorial diameter. The depres- sion at the poles is much exag- gerated in the figure in order to make the shape manifest. The tendency to take this shape from the centrifugal force may be illustrated by the in- strument represented in Fig. 95. It consists of two circu- lar hoops of brass connected with an axis, b a. The hoops 128 NATUKAL PHILOSOPHY. Fig. 95. are fastened to the axis at , but are left free at b. By some simple machinery at the top the hoops can be made to revolve rapidly; and bulging out at the sides by the centrif- ugal force, they slide down on the axis at b. / 7Y. Uniformity of Motion. A third point in the first law refers to the uniformity of mo- tion in the absence of any in- terfering cause. This uniformity is true both of the direc- tion and of the velocity. Suppose a body to be set in motion, and to meet with no opposition from friction, or the resistance of air, or at- traction, it would move on forever, and with the same ve- locity with which it began. Now precisely these circum- stances exist in the motion of the heavenly bodies in their orbits. They are, it is true, under the influence of attraction, but in such a way, as you will soon see, as not to interfere with the uniformity of their motion. Were it not for this uniformity, we should have no regularity of times and seasons. It is only by the uniform motion of the earth round the sun, and round its own axis, that we can calculate for to-morrow, or next week, or next year. If these motions were irregular, it would throw confusion into all our calculations for the future and all our recollections of the past. We can measure time by nothing else than reg- ular motion ; and were there no regular motion, we should have merely the very inaccurate measure furnished by our sensations. To measure time with accuracy, we take some great and extensive uniform motion as our standard. Thus, the revolution of the earth around the sun we take as one MOTIONS OF MATTER. 129 division of time, and call it a year. We observe that dur- ing this time it whirls around on its own axis 365 times, and the time occupied by each of these revolutions we call a day. The impossibility of producing on the earth's surface a condition of things similar to that in the empty space through which the heavenly bodies move is an argument against the attainment of perpetual motion. It is evidently impossible to annihilate external forces, such as gravity, the re- sulting friction, etc., and consequently the motion of any object will not be uniform, but continually retarded. Perpetual motion (the dream of vision- ary philosophers of many centuries) is, then, a mechanical impossibility. 78. The Second Law of Motion. The second la\v of mo- tion states that a given force always produces the same effect, whether the body on which it acts be in motion or at rest, and whether it be acted upon by one or more forces simultaneously. This is in reality an expansion of the first law, and its principles have been anticipated in speaking of compound motions ( 60) and of projectiles ( 67). Thus, whatever the number of forces acting upon a body, each force may be regarded as producing independently its own change of motion. When a ball is thrown horizontally, the deviation from a straight line leads to the inference that it is affected by another and vertical force that of gravity. 79. The Third Law of Motion. The third law of motion states that action and reaction are equal that is to say, when any of the causes of motion act, the" action is met by an opposite and equal reaction. If, for example, a blow be given, an equal blow is received in return. For this reason, if one in running hit his head against the head of another, both are equally hurt. When a child knocks his head against a table, there is sound philosophy in the com- mon saying that he has given the table as good a blow as he has received, though it may afford him no comfort. 130 NATURAL PHILOSOPHY. Many very interesting illustrations of this law of motion suggest themselves, of which we will give a few. A swimmer, pressing the water downward and backward with his hands and feet, is carried along forward and up- ward by the reaction of the water. And in this case, as in every other, the greater the action, the greater is the reac- tion ; in other words, the more strongly he presses with his hands and feet, the more rapidly is he borne along by the reaction of the water against the pressure. A boat ad- vances in proportion to the force with which the oars press against the water. So the rapidity of a steamboat depends on the force with which the paddles drive the water astern. Birds rise in the air by the reaction of the air against their wings as they are pressed downward. A sky-rocket pur- sues its rapid flight because a large quantity of gaseous matter issues from its lower end, and, being resisted by the air, its pressure throws the rocket upward. If a ship fire guns from the stern, its advance will be accelerated ; but if from the bow, it will be retarded. When a broadside is fired, the ship inclines to the other side. Further Illustrations. If a spring be compressed between two equal bodies, it will throw them off with equal velocities. If they are un- equal, the velocity of the smaller body will be greater than that of the larger, and in proportion to its smallness. For this reason, when a ball issues from a cannon, though the cannon and the ball are equally acted upon by the elastic or expansive force of the gases set free by burning the powder, the gun is moved but very little, because the force is diffused through so large a mass ; while the ball, being so much smaller, moves with great velocity. When a volcano throws stones from its crater, the earth may be compared to the cannon, the stones to the ball, and the explosive materials throwing the stones to the exploding powder projecting the ball. Since the cannon is moved as much as the ball, the earth also is moved as much as the stones, the only reason that it does not move so far and so rapidly being that the force is diffused through so large a bulk. These examples illustrate very well the relation of action and re- action ; for whenever there is an action of one body upon another, it is as if MOTIONS OF MATTER. 131 a spring were between the two bodies, acting equally upon both. When a man jumps from the ground, it is as if a spring were compressed between him and the earth, and this expanding moves the earth exactly as much as it does the man. He really kicks the earth away from him. The motion of the earth is not obvious because it is diffused through so large a mass. The case is parallel to that of the ball and cannon. The same force is exerted upon the man and the earth ; but the man, like the ball, moves the most, and in proportion to his small size. So when a bird hops from, the ground, the earth moves as really as the bird. If the bird hop from a twig,' you perceive that the twig is moved by the pressing-down of the bird as it rises. When it starts from the ground, it exerts the same downward pressure, and moves the earth as really as in the other case it did the twig. Of course, many of these motions are far too small to be perceptible, and too insignificant to take into account under ordinary circumstances. 80. Communication of Motion in Elastic Bodies. Addi- tional proof of the truth of this law is shown in the communication of motion in elastic bodies. Momentum is transferred from one body to another very differently in elastic and non-elastic bodies. As shown in 61, when one non- elastic body strikes upon another, the momen- tum is divided between them, and both move on to- gether. Now, if a and b, Fig. 96, were elastic bodies, as ivory balls, and b should be let fall against a, it would give all its momentum to a. Therefore b would stop, and a would move on to the same height O from which b came. The reason is, that the velocity lost by b and re- ceived by a is just double what it would be if the balls were non -elastic, reason, if a and #, being elastic, meet each other from equal heights on the arc, they will both rebound, and re- turn to the same heights from which they came. But if non-elastic, they simply destroy each other's momentum and stop. The effect produced in the former case is just Fig. 96. For the same 132 NATURAL PHILOSOPHY. twice as great as in the latter, as you may see by reckon- ing on the arc. For the same reason, too, if you have a row of elastic balls, as in Fig. 97, and let a fall from the point i upon by it will stop there ; and O communicating all its momentum to b, this momentum will pass from b to c, and so on through all the row of balls to e, the last one, which will fly off to the point A, at the same height with i, the point from which a fell. If b be held still, and a be let fall upon it, a will rebound to the height from which it fell, for then the compressed elastic spring of each ball, b being immovable, communicates all the motion to a. It is for this reason that an elastic ball, on being thrown against anything fixed, rebounds. If it be thrown against a perfectly elastic body, it rebounds with a force equal to that with which it is thrown. The transmission of sound by the air takes place in a somewhat similar manner, as will be shown in Chapter XIV. QUESTIONS. 06. What is said of the course of bodies thrown into the air ? Give the comparison of a man on a steamboat. Why does the atmosphere move with the earth? 67. Explain the parabolic path of projectiles. What three forces act upon a stone thrown into the air ? What is the path of a body projected horizontally? Show that the shape of the curve is modified by the force exerted. Show why a ball dropped from the mouth of a can- non will fall to the ground in the same time as one fired from it. 68. By what two forces is a falling body acted upon ? Explain Fig. 84. What is the course of a ball dropped from a railway car or from a mast-head ? 60. Give the comparison between the cannon-ball and the moon. What is said of the velocities of the heavenly bodies ? 70. What are Newton's laws of motion? From what principle does the first law follow? 71. Illustrate the fact that inertia is shown in the communication of motion. 72. Give THE SIMPLE MACHINES. 133 illustrations of inertia as shown in the disposition of motion to continue. Describe and explain the equestrian feat mentioned. What is said of skill in jumping from a moving carriage ? Relate the case in court. 73. What is stated in the second part of Newton's first law ? What is said of curved motion ? Explain the diagram (Fig. 86). What are centrifugal and cen- tripetal forces ? What forces correspond to these in the revolution of the earth around the sun ? 74. Give illustrations of the various operations of centrifugal force. What is said of the formation of bends in rivers ? Show how eddies and whirlpools are formed. 75. How is centrifugal force used in the art of pottery. How in making window-glass ? How in sugar- refineries ? W T hat is said of the honey-comb ? Describe and explain the operation of the steam-governor. 7G. What is said of the agency of cen- trifugal force in shaping the earth? Explain the operation of the ap- paratus mentioned. 77. What is said of uniformity of motion ? What of its uniformity in velocity ? State by what means we calculate time. What is said of perpetual motion ? 78. What is stated in the second law of motion ? 79. What is stated in the third law of motion ? Illustrate the law. Give the illustration of the spring. Of the cannon-ball. Of the volcano. What is said of the jumping of a man from the ground ? What of the reaction in the case of a hopping bird ? 80. Explain the additional proof of the law shown in the communication of motion in elastic bodies. CHAPTER IX. THE SIMPLE MACHINES. 81. Machines not Sources of Power. As shown in 56, the forces of nature at our command are few in number, and under many circumstances only one gravitation is available. Nature seldom provides forces in a form direct- ly suited to the accomplishment of work, and we therefore resort to contrivances called machines, by which one form or degree offeree is transformed into another, and rendered serviceable. From an erroneous idea of the principles in- volved, six simple machines, named respectively the Lever, the Wheel and Axle, the Inclined Plane, the Wedge, the F2 134 NA.TUKAL PHILOSOPHY. Screw, and the Pulley, were formerly spoken of as the Mechanical Powers. These machines, however, are in no sense powers, but merely means of applying power to advantage, and are not in themselves sources of power. No instrument or machine can create power, and the only use of all the variety of tools and machinery is to enable us to apply power in such a manner, with such a velocity, and in such a direction as to effect the objects which we have in view. Excepting old usage, there is no reason why the term mechanical powers should have been confined to the six contrivances above named. Any arrangement of solid or rigid parts, moving with different velocities whereby one manifestation offeree is converted into another, equal- ly deserves the appellation mechanical power. Before proceeding to a consideration of the six simple machines, we will explain a few of the terms employed. Power is the force by which a machine or instrument is moved. Weight is the resistance to be overcome. If the resistance be in some other form than that of weight, it is TO i called technically by this name. So what is called power may be in the form of weight. The fulcrum is the point on which the instrument or machine is supported while it is in motion. * 82. Lever of the First Kind. A beam or rod of wood, iron, or any other material, resting at one part on a prop, or fulcrum, about which the beam can move is called a lever, the name being derived from a Latin word mean- ing to lift. The lever is the most simple of all simple machines, and is therefore in universal use. Though the savage makes use of few tools in comparison with the civilized man, he uses the lever almost constantly in some form. The wedge is the only one of the other simple ma- chines that he uses to any great extent. Levers are of three kinds, commonly called the first, second, and third THE SIMPLE MACHINES. 135 kinds, the difference depending on the relative position of the power, the weight, and the fulcrum. In the lever of the first kind the fulcrum, or prop, is be- tween the weight and the power. The common crow-bar, or hand-spike, is a fa- miliar example, as seen in Fig. 98 the stone, S, or other heavy body to be moved being the weight, the stone or block of wood, F, on which the bar rests being the fulcrum, and the pressure of the hand, H, the power. The nearer the fulcrum to the weight, or the farther the power from the fulcrum, the greater is the force of the lever. This may be illustrated in Fig. 99. Here the short arm of the lever, as it is called, C W, is one eighth of the length of the long arm, A C. If the weight hanging at the end of the short arm be 72 pounds, a weight of 9 pounds, or the force of a hand equivalent to this, will bal- ance it at the end of the long arm. But if the power should be applied at only four times the distance from the fulcrum at which the weight is, then.it would require a force of 18 pounds to balance the 72 pounds on the short arm. Similar variations can be made by altering the length of the short arm. The power and the weight bal- ance each other when the weight multiplied by the length of the short arm, and the power multiplied by the length of the long arm, give equal products. Steelyards and the Balance. Examples of levers of this Fig. 99. 136 NATUEAL PHILOSOPHY. Fig. 100. kind are very common. In an ordinary balance, Fig. 100, we have a lever the two arms of which are equal, and therefore equal weights suspended at the ends balance. If they be not exactly equal, a heavier weight will be necessary on the shorter arm. The inequality will injure the buyer if the prop be too near the pan in which the weights are placed, and the seller if it be too near that which holds the article to be sold. Any difference can be easily detected by changing the places of the article and the weights. Whenever cheating is practised by the " false balance," it is of course done in a small way, to avoid any observation by the eye of the inequality of the two arms of the scale- beam, and the weight of the pan hanging from the shorter arm is made a little greater than that of the other, so that they may balance. Balances may be rendered very accu- rate by making the fulcrum or pivot of hardened steel, and of a wedge shape, with a sharp edge, in order to avoid fric- tion as much as possible. The steelyard, Fig. 101, differs from the balance-beam in having the arms of different lengths. The principles on which this instrument is constructed were developed in ex- plaining Fig. 99. With either the balance or the steelyard, when two weights balance each other, the centre of the weights and the apparatus taken together is just over the fulcrum. Hence the necessity for placing the prop near the large weight when we wish to balance it by a small one. THE SIMPLE MACHINES. 137 Fig. 101. Iii Fig. 101 C is the ful- crum, P the weight to be determined, and Q the power applied in the form of a hanging weight. Other Examples. Scissors are double levers of the first kind. The fulcrum is the rivet, the weight or the resistance to be overcome is the article to be cut, and the power is applied to the long arms of the levers by the fingers. With large shears hard substances can be cut. Even plates of iron are cut like paper by shears worked by a steam-engine. Pincers are double levers. The hinge, or rivet, is the fulcrum. The common hammer, as used in drawing nails, is a good example of the power of this kind of lever. Though crooked, it acts in the same way with a straight lever. The fulcrum is the point on the board where the hammer rests, and this is between the resistance to be moved, the nail, and the power, that is, the hand which grasps the handle. 83. No Gain of Power in this Lever. We will now illus- trate the truth that there is no gain or saving of power in this lever, as might at first thought seem to be the case. Let a b, Fig. 102, represent a lever, and e its fulcrum. Let the arm a e be twice as long as e b. A pound, then, suspended from a will balance two pounds at b.> If now, when the weights are suspended, the long arm be raised so that the lever oc- cupy the position represented by the line c d, and then let go, the one pound at c, balancing the two Fig. 102. pounds at c7, will bring the lever again to the position a b. It will be perceived that the end of the long arm of the 138 NATURAL PHILOSOPHY. lever moves through the space a c, which is larger than b d, through which the end of the short arm moves, in the same time. The one-pound weight, in fact, falls two feet in raising the two-pound weight one foot, and it moves twice as far as a one-pound weight suspended at i would do. If a one-pound weight could raise a two-pound weight without thus moving through twice as much space, an actual gain of power in the lever would indeed result. But it evidently makes no difference whether one pound moves through two feet or two pounds through one foot ; the force is the same in both cases. For the momentum or force of a moving body is in proportion to its weight and velocity ( 61) ; and therefore the pound weight moving through two feet has as much momentum as the two-pound weight moving through one foot in the same time. The small weight does the same amount of work that the larger one would by moving twice as far in the same time, just as a boy who carries a load half as large as a man will do as much work as the man if he carry it twice as fast. The Seesaw. The same thing is illustrated in the see- saw, Fig. 103. The man, being much heavier than the boy, is nearer the prop ; and as they move up and down the boy passes over a much larger space than the man, describing an arc in a much larger circle. Archimedes's Lever. Archi- medes, a distinguished mathema- tician and philosopher who lived about 250 years before the Chris- tian era, said that if he could have a lever long enough and a prop strong enough, he could move the world by his own weight. But he did not think how fur he himself would have to move to do this, owing to THE SIMPLE MACHINES. 139 the vast difference between the weight of his body and that of the earth. "He would have required," says Dr. Arnott, "to move with the velocity of a cannon-ball for millions of years to alter the position of the earth by a small part of an inch." Somewhat analogous to this is the case of the Hydrostatic Bellows and of Bramah's Press, as will be explained in Chap- ter X. In all these cases great effects are produced by small power, which itself has to accomplish extensive motion. 84. Lever of the Second Kind. In the second kind of lever the weight is between the fulcrum and the power, as shown in Fig. 104. The same rule of equilibrium applies here as in the case of the lever of the first kind. The 72 pounds of weight can be sustained by 8 pounds of power, because the Fig. 104. power acts on the lever at 9 times the distance from the fulcrum that the weight does, for 1 x 72 = 9x8. The com- mon wheelbarrow, Fig. 105, is an example of this kind of lever. The point at which the wheel presses on the ground is the ful- crum, and the weight is the load, its downward pressure from its centre - 105. of gravity being indicated at M. Of course, the nearer the load is to the fulcrum, the easier it is, on starting, to raise the handles. The common hand-barrow furnishes another illustration (see Fig. 106). If the load be placed in the centre, each of the men carries half, for the pole becomes a lever, of which each porter is a fulcrum as regards the other; if the load be shifted towards one of the men, he will have to carry a larger 140 NATURAL PHILOSOPHY. share than the other. The crow-bar can be used as a lever of the second kind when its point is placed be- yond the weight to be raised. The chip- ping-knife, Fig. 107, Fig. loo. is another example. The end attached to the board is the fulcrum, the press- ure on the handle the power, -and the resistance of the substance to be cut is the weight. Nut- crackers operate in a sim- ilar manner. In shutting a door, by pushing it near its edge we move a lever of this kind. The hinge is the fulcrum, and the weight is between this and the hand. We see, then, the reason that the slight push of a hand shutting the door may even crush a finger when Fig. 108. where the hinges are. the fulcrum that the power moving through a great space acts upon it with immense force. The same explanation applies to the severe bite of the finger when it is caught in the hinge of a pair of tongs. The oar of a boat is a lever of this kind, the weight to be moved being the boat, and the fulcrum, singularly enough, being the unstable water. 85. Lever of the Third Kind. In the third kind of lever caught in it at the side The finger is a resistance so near THE SIMPLE MACHINES. 141 the power is between the fulcrum and the weight, as seen in Fig. 109. In the first two kinds of lever the power may be less than the weight, but in this the power must always be greater than the weight. The advantage of this lever consists in the great extent of motion obtained. Applying the same rule here as in the other levers, let us calculate the result. If the weight, as in Fig. 109, be 9 times as far from the fulcrum as the pow- er, it will require a power equal to a weight of 648 pounds to sustain a weight of 72 pounds, for 9 x V2 = l x 648. Examples. When a man puts his foot against the end of a ladder, and raises it by taking hold of one of the rounds, the ladder is a lever of this kind. It is evident that he spends his force upon it at a great mechanical disadvantage, for the power is applied much nearer to the fulcrum than is the weight of the ladder, taken as a whole. If you push a door to by plac- ing your hand very near the hinges, you do not shut it as easily as when you take hold of it at its edge. In the first case it is a lever of the third kind, and the hand moves through a small space, and therefore must exert a considerable force ; while in the latter case the door is a lever of the sec- ond kind, and the hand, moving through a greater space, puts forth less force. When we use a pair of tongs, we use a pair of levers of the third kind. They are an instrument in which convenience rather than power is needed. We cannot grasp anything very firmly with them because the power is so much nearer to the fulcrum than the weight to be lifted. For this reason, a pinch with the ends of the tongs is of small moment com- pared with one in the hinge. The anatomical structure of animals fur- nishes a most beautiful example of this lever. Take, for example, the principal muscle which bends the elbow, as represented in Fig. 110. This comes down from the shoulder in front of the bone of the arm, and is in- serted just below the elbow-joint into one of the bones of the forearm. It pulls upon the forearm very near the fulcrum, which is the elbow-joint, and so acts at a great mechanical disadvantage. The object of this arrange- ment is to secure quickness of movement, which is here, as in almost all muscular motions, of more importance than great strength. When great 142 NATURAL PHILOSOPHY. 110. weights are lifted, the fact that the muscles act at such mechanical disad- vantage makes the exhibition of power wonderful. 86. Compound Levers. When several levers are con- nected together, we call the whole apparatus a compound lever. Let each of c Fig. 111. the levers in Fig. Ill be 3 inches long, the long arms being 2 inches, and the short ones 1 inch. One pound at A will, according to the rule, balance 2 at B, and 2 at B will balance 4 at C, and 4 at C will balance 8 at D. Therefore 1 pound at A will balance 8 pounds at D. Hence it is evident that an equilibrium is effected when the power is to the weight as the product of all the short arms is to the product of all the long arms. The compound lever is used in weighing heavy loads as hay, coal, etc. Fig. 112 shows a represen- tation of the ar- rangement. The load, W, stands on a platform, A B, which rests upon two levers, E D and E C. The long arms of Fiff.ll-2. THE SIMPLE MACHINES. 143 these levers are E G and E F, and the short arms are G D and F C. The ends of the long arms press upon the fulcrum of the lever, H I. The pressure is transmitted from the end of the long arm by the rod, I K, to a small lever, K L, where a small weight or power, P, balances the weight of the heavy load, W. The two objects secured by this arrangement are accuracy and the occupation of a small space. 87. Wheel and Axle. The next of the simple machines is the wheel and axle. The most familiar applications of this power are seen in drawing water and in raising heavy articles in stores. The principle of this power is the same as that of the lever, as may be shown in Fig. 113, which represents a section of the wheel arid axle. The power, P, hangs by a cord which goes round the wheel, and the weight, W, by a cord around the axle. We may consider the power as pulling on a lever represented by A B, the long arm of which is A C, and the short arm B C. You see that the wheel and axle, then, may be viewed as a constant succession of levers, and it is therefore some- times called the perpetual lever. And the same rule of equilibri- um applies here as in the simple lever. In the com- mon windlass Fig. 114. the power is ap- Fig. 113. 144 NATURAL PHILOSOPHY. plied to a winch or crank, C F, Fig. 114, instead of a wheel. In estimating the power of this arrangement, F C must be considered the long arm of the lever, and half the diameter of the axle, B B, as its short arm. The Capstan. In the capstan, represented in Figs. 115 and 116, the axle is in a vertical position. The top of it is pierced with holes, into which levers are introduced. Fig. 115 shows the instrument as commonly used in moving buildings. Some- times horse -power is applied at the ends of the levers. Great power is ex- erted by this in- strument; but we have the same fact here as in all other cases where a small force produces a great effect the effect is slow, and the force passes over a great space in producing it. The moving of a building a foot requires many circuits of the horse around the axle. The capstan, as constructed for use on ships, Fig. 116, has a circular head, with many holes for levers, so that many men can work together in raising a heavy anchor. The cable, being wound around the capstan several times, is prevented from slipping by friction; and, as one end of the cable unwinds, the other is wound up. Fig. no. Fusee of a Watch. In the fusee of a watch we have a wheel and axle of a peculiar construction. When we wind up a watch, the chain is wound around the spiral pathway on the fusee, B, Fig. 117, and, at the same time, Fig. 115. \ THE SIMPLE MACHINES. 145 Fig. 111. the spring is coiled up tightly in the round box, A. The spring, in gradually uncoiling itself, turns this round box around, and thus pulls upon the chain, c, making the fusee to revolve, and thus give motion to other parts of the machinery. Now the spring, in its effort to uncoil, acts strongest at first; and, therefore, if the fusee were of uniform size, the watch would go fastest when first wound up, and go gradually slower as it ran down. This diffi- culty is obviated by giving the power a small wheel to pull on at first, and gradually enlarging the wheel as the spring uncoils. Because, in order to produce a certain effect on a given weight, the less the power, the longer must be the arm of the lever on which the power acts. 8'8. Pulleys. Another simple machine is the pulley, by which masses moving with different velocities may be con- nected, and thus forces of different degrees of intensity balanced. Pulleys are of two kinds, fixed and movable. Fig. 118 represents a tixed pulley ; the wheel, A B, has a groove in its circumference which prevents the rope from slipping. Its action may be conceived of as that of successive levers of equal arms, and, therefore, equilibrium requires equality of power Fig. us. and we igjj t< Fixed pulleys are used to change the direction of forces, as in hoisting sails on board ship. By a combination of two fixed pulleys a hori- zontal force may be used to raise weights vertically, as shown in Fig. 119. Fte. liu. Movable Pulleys. Fig. 120. 146 NATURAL PHILOSOPHY. Fig. 120 represents a movable pulley. In this case it is evident that the force exerted by the weight is equally di- vided between the ropes S 2 and Sj. A movable pulley is sometimes called a " runner," and a fixed pulley is often connected with it in order to give the desired direction to the force. Pulleys are often connected in complicated Fig. 122. Fig. 123. THE SIMPLE MACHINES. 147 Fig. 121 shows a system of fixed and movable pulleys; the weight, q, is evidently upheld by six cords, which divide the weight equally among them. If q weigh six pounds, equilibrium will be obtained by mak- ing the weight of p equal to one pound ; at the same time, it must be remembered that p will move six feet while q moves only one. Other arrangements of pulleys are shown in Figs. 122 and 123. The combination of pul- leys in one block having a single axle (Fig. 122) is in com- mon use. 89. The Inclined Plane. This, being a very simple con- trivance, is much used, especially when heavy bodies are to be raised to only a small height, as in moving large boxes and hogsheads into stores. The advantage of the inclined plane may be illustrated by Fig. 124. The line A c represents an in- clined plane. If a weight be drawn up this plane, it is raised only the height I> c. A smaller power is requisite to draw the weight up the plane than to raise it perpendicularly ; and the power necessary will be the less the longer the plane. A pow- er which would balance a weight on an inclined pi, -me would be to the weight as the height of the piano to its length. Thus, if A c be twice as long as B c, a weight of four pounds on the plane may be balanced by a two -pound weight suspended by a cord passing from the weight over the summit of the plane. A flight of stairs is constructed on the principle of an inclined plane, the projections in it being for the purpose of affording a sure footing in ascending or descending. In like man- ner hogsheads are let down the steps of a cellar-way by ropes, and it makes no difference in the principle 148 NATURAL PHILOSOPHY. of the operation whether planks be laid on the steps or not. It is supposed that the immense stones in the pyramids and other massive Egyptian structures were put into their position by means of inclined planes. Roads, when not level, are inclined planes ; and the steeper the inclination, the more power is required to draw a load up the road. Great mistakes were formerly made in carrying loads straight over high hills. Besides failing to take advantage of the principles of the in- clined plane, in many cases the horse, in going over a hill, passes over quite as much space as he would if the road were made to go round the base of the hill, and sometimes even more. If the hill were a perfect hemisphere, a road over it would be just equal in length to a road around its base to the opposite point. ; 90. The Wedge. This simple device may be considered as two inclined planes placed with their bases together, as seen in Fig. 125. Indeed, sometimes the wedge has one side only inclined, it being but half of the ordinary wedge. The difference between the inclined plane and the wedge in op- eration is that in the first the inclined plane is fixed, and the weight is made to move up along its surface ; while in the latter the weight that is, the resistance is stationary, and the surface of the plane is made to move along upon it. The power of the wedge is estimated just like that of the inclined plane; that is, by comparing the thickness of the wedge with the length of its side. The less the thickness of the wedge compared with its length, obviously the more powerful is the wedge as a penetrating instru- ment. The wedge is used for splitting blocks of wood and stone, for producing great pressures, for raising heavy bod- ies, etc. All cutting and piercing instruments knives, ra- zors, axes, needles, pins, nails, etc. act on the principle of the wedge. THE SIMPLE MACHINES. 149 Knives, planes, chisels, etc., are often used somewhat in the manner of a saw, by drawing their edges against the object to be cut, at the same time that the pressure ap- plied exerts the influence of a wedge. The edge of a sharp knife examined under a microscope proves to be serrated. The sharpest razor, it is said, may be pressed directly against the hand with considerable force without cutting the skin, while if drawn ever so little lengthwise it will inflict a wound. 91. The Screw. This is another of the simple machines. Its principle is essentially that of the inclined plane. The "thread" running around the screw is an inclined plane which is spiral instead of .straight; and the corresponding part in the nut is an inclined plane running in the opposite direction. In the common screw the nut is fixed, and the screw is made to play up and down in it; but sometimes the screw is fixed, and the nut is made to play around it. The screw acts like a wedge, and has the same relation to a straight wedge that a road winding up a hill has to a straight road of the same length and rise. Especially does the comparison hold when the screw is forced into wood ; the wedge goes straight into the wood, but the edge of the screw's thread enters the wood spirally. To estimate the force of the screw, we compare the length of one turn of the thread around it with the height to which the thread rises in going round. Let a 6, Fig. 126, represent one turn of the thread, b c the height to which it goes. It is clear from the figure that the principle which ap- plies to the inclined plane and to the wedge applies here also. Since the less the height of the plane, the easier it is for a weight to be drawn up it ; and since the less the depth of the wedge, the less is it resisted; therefore, the less the height of the turn of the screw's thread, the easier is it to move the screw, and the greater the force which it exerts. Hence the G 150 NATURAL PHILOSOPHY. Fig. 127. prodigious power of a screw with a thread which rises very slowly in its spiral turns. Screws are much used when great pressure is required, as in pressing oils and juices from vege- table substances, in compressing cot- ton into bales, in bringing together with firm grasp the jaws of the vice, etc. In turning the screw a bar is used, so that we have in this instru- ment the combined advantages of the screw and the lever (Fig. 127). That you may have some idea of the power of these two instruments acting to- gether, we will state an imaginary case. Suppose it is desired to raise by the screw a weight of 10,000 pounds. Let a turn of the screw be ten inches long, and the rise be but one inch. Then, so far as the screw is concerned, the power requisite to raise the 10,000 pounds will be 1000 the ratio of the height of the thread's turn to its length. But the power of the lever is yet to be estimated. Let the length of the lever, passed through the head of the screw so that it is equal on each side, be thirty inches. The diameter of the screw is about three inches, or one tenth of the diam- eter of the circle described by the end of the lever. It will take but a power of 100 pounds to raise the weight, the ratio of the radius of the screw to half the length of the lever. 92. Other Simple Machines. When the old idea prevail- ed that the simple machines were but six in number, it was shown that these could be reduced practically to three, for the wedge and the screw are modifications of the inclined plane, and the wheel and axle is a modification of the lever. As already mentioned, however, there is no neces- sity for limiting to so small a number the simple machines, provided we regard them as simply modifiers of motive power. The toggle-joint is a simple machine, in which the connected parts are arranged so as to move with different velocities. It is used to raise carriage -tops, and, when THE SIMPLE MACHINES. 151 made of immense strength, to exert great pressure through a small space, as in shearing and punch- ing iron. Fig. 128 represents, in skeleton form, a toggle-joint. Machines which change the direc- tion of the force applied are very numerous, but a study of them belongs properly to higher me- chanics. We see their applications in compli- cated machines' in common use the printing- press, sewing-machine, steam-engines, locomo- Jj'ig. tives, and many others. 93. The Pendulum. Certain mechanical contrivances are designed for the modification of mere motion, without any reference to the transmission of forces : such are watches, clocks, and timepieces of every description. These instru- ments have for their object the production of a perfectly uniform motion with a view to the measurement of time. The motion-regulator by which clocks are controlled the pendulum demands a somewhat extended notice. Various modes of measuring time have been adopted by mankind. At first, time was inaccurately divided by mere- ly observing the sun. But after a while man resorted to various contrivances to measure short periods of time with accuracy. All of these depend upon the uniformity of mo- tion alone. The sundial measures time by the uniform movement of the shadow on its face, caused by the uni- form movement of the earth in relation to the sun. The hour-glass measures time by the uniform fall of sand pro- duced by the attraction of gravitation. The best measure- ment of time is by the comparatively modern invention of clocks and watches, in which time is divided into very minute periods by the uniform motion of the pendulum or the balance-wheel. The pendulum furnishes an interesting example of motion sustained by the influence of gravity. It was not till the time of Galileo, less than three centuries 152 NATURAL PHILOSOPHY. ago, that its operation was understood and appropriated to the measurement of time. He observed that a chandelier hanging from the lofty ceiling of a cathedral in Pisa vi- brated very long and uniformly when accidentally agi- tated, and the thought of the philosopher evolved from this phenomenon the most important results. Though it had been before men's eyes in some shape or other since the creation, it was reserved for Galileo to observe its significance, and to pave the way which has led to tluj use of the pendulum as man's time-keeper over the whole earth. Explanation of its Operation. A pendulum commonly consists of a ball or weight at the end of a rod suspend- (i ed so as to vibrate with little s friction at the point of the sus- \ pension. Let a b, Fig. 129, rep- \ resent such a pendulum. When \ it is at rest, it makes a plumb- line hanging towards the centre of the earth. If it be raised to dr*\ ly/fr c and be left to foil, the force of Fig - 129 - gravity will not only carry it to &, but, by the accumulated momentum acquired in its de- scent, gravity will carry it to d. The same would be true of its return from d. And it would vibrate forever in this way if it could be entirely freed from the resistance of the air and from friction. But, as it is, the pendulum, left to itself, gradually loses its motion from these obstacles. In the common clock, the office of the weight ,is to counteract the influence of these obstacles and keep the pendulum vi- brating. In the watch, the mainspring performs the same office to the balance-whgel. The times of the vibrations of a pendulum are nearly equal, whether the arc it describes be great or small; for THE SIMPLE MACHINES. 153 when the vibration is a large one, the velocity which the pendulum acquires in falling is greater than when the vibration is of small extent. The reason is, that the higher it rises, the steeper the beginning of its de- scent. Thus a c, Fig. 130, is steeper than c b. The longer a pendulum, the longer time does its vibration occupy. It requires a pendulum of the length of a little over thirty-nine inches (39.13") to vibrate once every second. Cold weather, by contracting the pendulum, makes it vibrate quicker than in summer, and so makes the clock go faster. Various contrivances have been resorted to in order to counteract the variation of length in pendulums by heat and cold, one of which we will describe in the chapter on heat ( 167). The popular idea that a heavy body falls quicker than a light one is dispelled by the fact that pendulums vibrate equally fast or slow, no matter of what material they are constructed. Similar pendulums of lead, glass, iron, or wood, or even a hollow ball, vibrate at the same rate. 94. Friction. Friction is the resistance offered to a body by the surface on which it moves. It seems to arise from adhesive attraction between the touching substances and from the roughness of their surfaces. The rougher the surfaces brought in contact, the greater the friction, the little cavities and projections fitting into each other and necessitating a certain force to raise the projections on one surface from the cavities in the other. Substances which appear quite smooth to the naked eye, as polished steel, nevertheless exhibit inequalities of surface when examined under the microscope. Friction acts as an obstacle to motion. When we roll \ 154 NATURAL PHILOSOPHY. a ball, the rougher the surface on which it is rolled, the greater the friction and the sooner the ball stops. Ma- chinery, no matter how carefully constructed, suffers a waste of power through friction, even to the extent of a third or a half of the force applied. Hence various expe- dients are resorted to for the purpose of diminishing fric- tion, such as polishing the rubbing surfaces, and oiling or otherwise lubricating them. Using wheels, as on car- riages, effects the same end. A heavy load, which the most powerful horse could not move if placed on a " stone- boat," is readily drawn along in a wheeled vehicle. Cast- ers attached to household furniture prevent the friction arising from dragging it over carpets. The very fact that rapidity of motion is lessened by fric- tion is in some cases of the greatest importance to us. " But for friction, men walking on the ground or pavement would always be as if walking on ice ; and our rivers that now flow so calmly would all be rapid torrents. It is fric- tion which retains all loose objects on earth in the situa- tions in which, for convenience, men choose to place them the furniture of a house, the contents of libraries, museums, etc. Friction, therefore, is essential to our existence." Fig. 131 illustrates a simple method of taking advantage of friction. The weight, P, can be lowered gradually, and with compara- tive ease, by wrapping the rope about the cyl- inder, A C B ; whereas, without the friction of the rope, the force of gravity would be be- yond the control of the power, Q. In this way heavy casks which are otherwise unman- ageable are lowered into cellars. Fig. 132 shows us at once the advantages of friction, and a means of overcoming its disadvantages. The block of stone, Q, is supported by roll- Fig. 131. THE SIMPLE MACHINES. 155 Fig. 132. ers, in order to overcome the friction of its surface on the ground ; and by means of the friction between the rope, B, and the axle, O C, the rope is prevented from slipping when power for moving the block, Q, is ap- plied to the lever, A. The friction of the driving-wheels of a locomotive upon the rails pre- vents them from slipping. In this case the wheel pushes backward on the rail at each successive point of contact. To make this clear, suppose a common wheel be deprived of its rim and be made to revolve on the ends of its spokes. The end of each spoke gives a backward push as it strikes the ground. Now the rim of a wheel makes the same pushes, but they arc more numerous they are continuous, being made by all the successive points in the rim. Sometimes the rails of a railroad are too smooth, from frost or some other cause, and then sand is thrown upon them to enable the locomotive to start. The sand serves to prevent the wheels from sliding by enabling them to get some hold upon the rails in their backward pushes. 95. The Real Advantages of Machinery. If there is, then, no saving, but a loss, of power in tools and machinery, what, let us inquire, are their advantages? If one man can do alone by the aid of some instrument that which would otherwise require the exertion of many men, although slow in accomplishing.it, yet it is a great advantage. Thus, one man with a lever can move a stone which it would require perhaps thirty men to move with- out it; and though it take him thirty times as long, it saves him the trouble of getting a company of men to help him. So if a man can raise his goods by a wheel and axle to the upper loft of his store, though he raise them more slowly than several men would lift them directly by ropes, 156 NATURAL PHILOSOPHY. it is an advantage to him, since it saves the hiring of a number of laborers. It must, however, be remembered that what is gained in amount of work is lost in time, and what is gained in time by using any machine is lost in the amount of work. Another advantage is that, in applying the force, inter- vals of rest may be secured without any loss. This is obvious in the case of the pulley, but still more so in the case of the screw. It is friction in both these cases which enables the workman to rest. It saves to him all that he has gained by opposing any tendency to slip back. The same thing is true of the wedge. When this is driven into Avood, it remains fixed because prevented from returning by the friction of the wood against its sides. It is the same cause which holds a nail in its place, and opposes any effort to draw it out. In driving the wedge, the workman can have as long intervals as he pleases between his blows, because friction saves all that is gained. This effect is very well exemplified in the capstan, Fig. 115. It requires but little exertion of the man who sits there to hold the rope, because the few turns of it around the axle prevent its slipping easily. A third advantage which often attends the use of tools and machines is that force may be made to produce motion at various distances, in various directions, and in various degrees of velocity. Thus, as to distance, a man standing on the ground can raise a weight to the top of a house by a pulley. A water-wheel may by the connections of ma- chinery produce motion at considerable distances from it. Then, as to direction, horizontal motion may be converted into vertical, rotary into straight, etc. The velocity of motion is generally varied by cog-wheels. Thus, a wheel of 60 cogs, revolving once in a minute, playing on a wheel of 10 cogs, will make it revolve once in 6 seconds. THE SIMPLE MACHINES. 157 Another advantage of tools and machines is that they secure a better mode of applying power than we otherwise could have. Thus, when sev- eral men are pulling on a rope, much power is lost by their pulling irregu- larly, a difficulty which is removed by the pulley. The same can be said of applying pressure by the screw. One man presses more steadily, and therefore more effectually, than fifty men would without the screw. The arrangements of tools and machines are so made as to provide convenient ways of applying our strength. An instrument, for example, for moving a weight by hand is so shaped as to hold the weight well, and also to afford a good handle for the hand to grasp. The common claw-hammer is a very good illustration. We grasp the nail by an iron claw ; with the handle we can apply not merely the force of the hand, but that of the whole arm, and then we have the immense lever power of the instrument. We have a good illustration of convenience in an instrument in what is called a Lewis, rep- resented in Fig. 133. It is used for raising blocks of stone in building. It has three parts, ABC. It is used in this way : A hole of the same shape as the instrument is made in the Fi - 133> upper part of the block of stone to be raised ; then A and C arc inserted, and B is pushed in between them. With the ring, D, bolted through the instrument, the stone is raised to its place by the ordinary machinery. The principle of the instrument, you see, is that of the wedge. 96. Man a Tool-making Animal. Though there is no ac- tual saving of power in the tools and machines which man uses, yet so great are the advantages which he reaps from them that, more than two thousand years ago, a philos- opher thought that man could not be better distinguished from brutes than by calling him a tool -making animal. If the distinction was so striking in the time of Aristotle, when tools and machines were so few "in number and so rudely contrived, and so few of the sources of power were appropriated by man to his use, how much more striking is it now, with all the variety and perfection of instruments and machinery, and with the ever-extending appropriation of the sources of power furnished by the elements ! The power which air and water and gravitation supply is ap- plied constantly with more and more variety and effect ; G 2 158 NATUKAL PHILOSOPHY. and the appropriation of that mighty source of power, Bteam, is wholly a modern invention. QUESTIONS. 81. What is said of the forces of nature and of machines? Name the six simple machines. Why is the term mechanical powers, formerly ap- plied to them, erroneous ? Explain the terms power, weight, and fulcrum. 82. How are levers classified? What is the lever of the first kind? Illustrate its uses. What is said of steelyards and the balance? Give other examples of this kind of lever. 83. Show that there is no gain of power in this lever. What is said of the seesaw ? What boast did Ar- chimedes make ? 84. What is a lever of the second kind ? Give examples of its use. 85. What is a lever of the third kind ? Give examples. 80. What constitutes a compound lever? Explain its use in platform scales. 87. Explain the action of the wheel and axle. What is said of the windlass ? What of the capstan ? Explain the construction of the fusee of a watch. 88. What is the advantage of the pulley ? Describe the fixed pulley and illustrate its uses. Describe a movable pulley. Explain some of the arrangements of pulleys. 89. Illustrate the mechanical advantage of the inclined plane. What is said of railways ? 90. What is a wedge ? Give examples of its uses. 91. Upon what principle does the screw work? How is its force estimated? Give an example. 92. Describe some other simple machines. 93. What is said of the pendulum? Who first made use of it for the measurement of time? Explain its operation. 94. What is meant by friction ? What is its effect in machinery ? How may it be overcome? Illustrate the uses made of friction. 95. What is the first advantage of the simple machines which is mentioned ? Give the illustra- tions. What is the second advantage ? Give the illustrations. What is the third advantage ? Give examples. How is the velocity of motion in machinery usually varied ? What is the fourth advantage ? Mention ex- amples. Describe the instrument called a Lewis. 9G. What is said of the title by which Aristotle distinguished man from other animals ? HYDROSTATICS. 159 CHAPTER X. HYDROSTATICS. 97. What Hydrostatics Teaches. A single substance may, as we have seen, exist in three forms solid, liquid, and gaseous and these forms are distinguished one from another by the difference in the mobility, or flow, of the par- ticles composing the substance. In a solid the particles are comparatively rigid, the force of cohesion being strong ; in a liquid or a gas they are not in such close contact, and are freer to move about each other. A body in either the liquid or the gaseous state is called a fluid, on account of ilwflow of the particles. A very important branch of Nat- ural Philosophy relates to the pressure, motion, and other phenomena of fluids, which for convenience is considered under three heads, viz. : Hydrostatics, which treats of the pressure of liquids ; Hydraulics, which treats of their mo- tion ; and Pneumatics, which treats of the same phenomena in air and gases. In order to understand the phenomena of Hydrostatics, you must bear in mind that they result from the influence of the attraction of the earth upon liquids, and that they depend upon the two great characteristics of liquids, their mobility and incompressibility ( 17). 98. Level Surface of Liquids. Owing to the perfect mo- bility of the particles among each other, and their being equally attracted towards the centre of the earth, liquids at rest assume a level surface. The particles forming the surface may be regarded as the tops of so many columns of particles supported by a uniform resistance or pressure 160 NATURAL PHILOSOPHY. below; for no particle below can be at rest unless urged equally in all directions, and therefore all the particles, at any one level, which, by equally urging one another, keep themselves at rest, must be bearing the weight of equal columns. Thus, a higher column, however produced, must sink and a lower one must rise until just balanced by those around ; that is, until all become alike. The particles of water may be compared to shot ; if you place shot in a box and heap them up in any portion of the surface, on shaking the box those that are highest will roll down, and a level surface will result. They would do this without agitation if they were as free to move among themselves as are the particles of water. If a microscope could be made strong enough to distinguish the shape of the parti- cles of water, the surface might possibly appear like the level surface of shot in a vessel. But the particles of water are so exceedingly minute that the surface of water, when entirely free from agitation, is so smooth as to constitute a perfect mirror, often feasting our eyes with another world of beauty as we look down into its quiet depths. Strictly speaking, the surface of a liquid is not level or horizontal ; being parallel to the surface of the earth, it forms a curve, but this curved surface is of so great a radius. that it cannot be perceived unless we take into view a very large surface, as the ocean. Here it is very manifest ; for whenever a ship sails out of port, the topmost sail is the last thing seen from the shore, the rest of the ship being concealed by the water rounded up between it and the observer. This is illustrated in Fig. 134. ML HYDROSTATICS. 161 If the earth had no elevations of land, or if there were water enough to cover them, the water would make a perfectly globular covering for the earth, being held to it by the force of attraction. The reason for this is precisely the same as was given in 31 for the disposition of a drop of liquid to take the globular form. As in that case, so in this, it can be de- monstrated that each particle is attracted towards a common centre, and that this will produce in the freely moving particles a uniformly rounded surface. What could thus be shown to be true if the earth were wholly covered with water is true of the portions of water which now fill up the depressions in the earth's crust. Spirit-Level. What is commonly called a perfectly level surface is, then, one in which every point is equally distant from the centre of the earth, and is therefore really a spher- ical surface. But the sphere is so large that any very small portion of it may be considered, for all practical purposes, a perfect plane. A hoop surrounding the earth would bend about four inches in every mile. In cutting a canal, there- fore, there is a variation in this proportion from a straight level line. Since the variation is but an inch in a fourth of a mile, it is of no account in taking the level for buildings. Levels are ascertained by what is called a spirit-level. This consists of a closed glass tube, g Fig. 135, nearly filled with alco- hoi. This liquid is used in pref- Fig. 135. erence to water because it never freezes and is more mo- bile. The space .not filled with alcohol is occupied by air. The tube is placed in a wooden box for convenience and security, there being an opening in the box at a. Now, when the box with its glass tube is perfectly level, the bubble of air will be seen in the middle at a\ but if one end be higher than the other, the bubble will be at or towards that end. This simple instrument is used by masons and carpenters for the purpose of levelling walls or floors of buildings, by engineers in surveying, and by others. 99. Flow of Rivers. If a trough be exactly level, the 162 NATURAL PHILOSOPHY. water will be of the same depth at one end as at the other, for the surface of the water at both ends will be at the same distance from the centre of the earth. But if one end be raised, the water will become deeper at the other end. If it were not so, the surface at the two ends would not be at the same distance from the centre of the earth. Now, if water run in at the tipper end of an inclined trough and out at the lower, we have an illustration of what takes place in all rivers the water is in constant motion. A very slight incline gives a flow to water, for the particles are so mobile that, in obedience to the force of gravitation, they descend the inclined plane to seek a level. Three inches per mile in a smooth straight channel gives a veloc- ity of about three miles an hour. The Ganges, which gath- ers the waters of the lofty Himalaya Mountains, in running 1800 miles falls only 800 feet; and to fall gradually these 800 feet in its long course, the water takes nearly a month. The gigantic Rio de la Plata has so gentle a descent to the ocean that, in Paraguay, 1500 miles from its mouth, large ships arrive which have sailed against the current all the way by the force of the wind alone. 100. How some Rivers have been Made. Changes are con- stantly 'produced in the earth by the disposition of water to seek- a level. In doing this the water carries solid substances of various kinds from ele- vated places into depressed ones, tending to fill up the latter. New chan- nels are also sometimes made by the water. The boy who makes a little pond with his mud-dam, and lets the water overflow from it into another pond on a lower level, as he sees a channel worked by the water between the two ponds becoming larger and larger, witnesses a fair representation on a small scale of some extensive changes which have, in ages past, taken place in some parts of the earth. It is supposed, and with good reason, that many rivers had their origin in the way above indicated. For exam- ple, where the Danube runs its long course there was once a chain of lakes. These becoming connected together by their overflow, the channels cut be- tween them by the water continually became larger, until at length there was one long, deep, and broad channel, the river ; while the lakes became HYDROSTATICS. 163 dry, and constituted the fertile valley through which that noble river runs to empty into the Black Sea. It is said that a similar process is mani- festly going on in the Lake of Geneva, the outlet of it becoming continu- ally broader, while the washing from the neighboring hills and mountains is filling up the lake. Towns that a century ago lay directly upon the bor- ders of the lake now have gardens and fields between them and the shore ; and Dr. Arnott says, "If the town of Geneva last long enough, its in- habitants will have to speak of the river threading the neighboring valley, instead of the picturesque lake which now fills it." 101. Canals. The management of the locks of a canal is in conformity with the disposition of water to seek a level. A ground view of one lock and a part of two adjacent locks is given in Fig. 136. The lock C has two pairs of flood- gates, D D and E E. The water in A is higher than in C, but the level is the same in C and B, because the gates, E E, are open. Suppose there is a boat in the lock B that you wish to get into the lock A. It must be floated into the lock C, and the gates E E must be closed. The water may now be made to flow from *the higher level, A, into C, till the level is the same in both A and C. But this cannot be done by opening the gates D D, for the pressure of such a height of water in the lock A would make it difficult, perhaps impossible, to do this; and, be- sides, if it could be done, the rapid rush of water into C would flood the boat lying there. The discharge is there- fore effected by openings in the lower part of the gates 164 NATURAL PHILOSOPHY. D D. These openings are covered by sliding shutters, which are raised by racks and pinions, as represented in Fijj. 137. When the water has become of the same level Fig. 13T. in A and C, the gates D D can be easily opened, and the boat may be floated from C into A. If a boat is to pass downward in the locks, the process described must be re- versed. Canals are also extensively used for supplying water by side openings to turn water-wheels for the working of machinery. The water turns the wheel by the force which gravitation gives it as it descends from the level of the canal to the level of the river. One of the grandest canals in the world is that cutting through the Isthmus of Suez, constructed in 18(54-69 under the direction of a French engineer, M. I)e Lesseps. It is about one hun- dred miles in length, and connects the waters of the Mediterranean with those of the Red Sea. The importance of canals as a means of transporta- tion of heavy goods is evident from the fact that a horse which can draw but one ton on our best roads can draw thirty with the same speed in a canal-boat. 102. Other Illustrations. We see the tendency of liquids to rise to the same level in other ways. In a coffee-pot HYDROSTATICS. 165 the liquid has the same level in the spout as in the vessel itself, whatever may be its position, as seen in Fig. 138. If it be turned up so far that the level of the fluid in the vessel is higher than the outlet of the spout, the fluid runs out. If two reservoirs of water be connected, the water will stand at the same height in both, whatever the dis- tance between them may be. In the aqueduct pipes that extend from a reservoir, the water will rise as high as the surface of the water in the reservoir itself. If the outlets of the pipes be lower than this level, the water will run from them, as in the case with the coifee. The cause of these and similar facts is the same as that of the level surface in vessels and reservoirs the action of gravi- tation. This may be made plain by Fig. 139. Let the figure rep- resent the section of a vessel with divisions of different de- grees of thickness, these divi- sions, however, not extending to the bottom of the vessel. Water in this will stand at the same level in the different com- partments, just as it would if the vessel had no such divi- sions. This is simply because the attraction of the earth acts upon the water in the same way with the divisions as 166 NATURAL PHILOSOPHY. Fig. 140. without them. And you can see that it will make no dif- ference whether these divisions be thick or thin, or whether the apartments be near together or far apart, as in the case when branch pipes extend from a reservoir. A branch pipe may be considered as having the same relation to the reservoir as one of the narrow compartments in the figure has to the rest of the vessel. The result is not at all affected by either the size or form of the tubes that may be connected with a common reservoir: a fluid will stand at the same height in all. Thus we have, in Fig. 140, tubes of various size and shape, A, B, C, connected by the pipe, m ?i, with a reservoir, D ; and if water be poured into the latter, it will rise to the same height in all, just as in the different compartments of the vessel represented in Fig. 139. A man once thought that he had solved the chimerical problem, per- petual motion, by means of a vessel constructed as in Fig. 141. He rea- soned in this way : If the vessel contain a pound of water and the tube only an ounce, since an ounce cannot balance a pound, the water in the vessel must be constantly forcing that in the tube upward. It therefore must constantly run out of the outlet of the tube, and as it flows into the vessel the circulation must go on, the only hin- drance to perpetual circulation being the evap- oration of the water. He was confounded when he discovered, on pouring water into the vessel, that it stood at precisely the same level in the vessel and in the tube. He forgot that a common teapot is nearly such a vessel, and yet does not overflow. A glass tube on the outside of a cistern or a boiler, and connected with it at the bottom, shows at once the level of the water within. Another illustration of the fact that water is alwavs seeking its level is found in the water-pipes which HYDROSTATICS. 167 distribute water to the inhabitants of large cities : the water pumped into a reservoir situated on an elevation rises by the action of gravity and its perfect mobility to the height of every cistern not above the level of the reservoir, no matter ho\v much lo\ver may be the depression crossed by the pipes. We are not to suppose that it was ignorance of this law of liquids that led the ancients to build aqueducts of stone at immense expense, in some cases spanning valleys at great heights ; but this enormous labor was necessitated by the lack of a suitable material such as iron. 103. Springs and Artesian Wells. The principles devel- oped in the previous paragraphs will explain the phenom- ena of springs, common wells, and Artesian wells. The crust of the earth is largely made up of layers of different materials, as clay, sand, gravel, limestone, etc. When these were formed they were undoubtedly horizontal, but they have been thrown up by convulsions of nature in such a way that they present every variety of arrangement. Since some of these layers are much more pervious to water than others, the rain which falls and sinks into the ground often makes its way through one layer lying be- tween two others which are impervious to water, and so may make its appearance at a great distance from the place of its entrance, and at a very different height. How this explains the phenomena of springs, common wells, and Artesian wells is made clear by Fig. 142. A A and EBB are designed to represent porous layers of earth lying between other layers which are impervious to water. Fig. 142. The water in A A will flow out at C, making what is com- monly called a spring. If we dig a well at F, going down to the porous layer, B B B, the water will rise to G, be- 168 NATURAL PHILOSOPHY. cause this is on a level with the surface of the ground, II. 3 / / where the supply of water enters. From this point it may be raised by a pump. If the well be dug at D, the water will rise not only to the surface, but to E, because this is on a level with II. Water is sometimes obtained under such circumstances from very great depths. In this case the porous stratum containing the water is reached by boring, and then we have what is termed an Artesian well. The name comes from the province of Artois, in France, where this operation was first executed. There is a cele- brated well of this sort at Grenelle, a suburb of Paris, where the water rises from a depth of nearly 1800 feet below the surface, and is further carried to a height of a hundred feet above it, furnishing a supply of beautifully clear water at the rate of 800,000 gallons a day. 104. Pressure of Liquids is in Proportion to Depth. The pressure of a fluid is in exact proportion to its depth. For, all the particles being under the influence of gravity, the upper layer of them must be supported by the second, and these two layers together by the third, and every layer must bear the weight of all the layers above it. This pressure, being occasioned by the weight acting vertically downward, is not dependent on the amount of the sur- rounding liquid, nor on the shape or size of the containing vessel. In a vessel having the shape A, Fig. 143, it is evi- Pig. 143. H YDKOSTATICS. 169 dent that the pressure of the liquid within upon the bottom b depends upon the height of the column a ; in the ves- sel B, which widens at its mouth, the pressure on' the bot- tom/is equal to that of the weight of the column e f, for the rest of the liquid exerts pressure upon the sides cf,df 9 and balances the column e f on all sides round about. In the case of a vessel tapering at its mouth, C, let us suppose the bottom g h divided into a number of portions of the same size as the mouth L and that there are ei a known weight of it is weighed in oil or some liquid which does not dis- solve it, and the specific gravity of the oil having been determined by some one of the methods explained in 118, the specific gravity of the substance is calculated by means of the following formula : If the weight of the substance in air=W and " " " inoil=W Sp. gr. of the oil =A Sp. gr. of water being = 1 then W W'=W"=the liquid displaced ; and A:1=W":W" W Whence sp. gr. of substance T^rrr (III.) To determine the specific gravity of a body lighter than water and insoluble in it, weigh it first in the air, then attach to it a piece of lead sufficiently heavy to sink it, and weigh the two together in water ; lastly, weigh the lead alone in water, then calculate from this formula : Weight of cork in air = W " lead in water =W Weight of lead and cork in water -W" Then, Sp-gr. ==^77^ W'-W"+W SPECIFIC GRAVITY. 191 (IV.) The fourth case, that of substances lighter than water and soluble in it, is of comparatively rare occurrence ; examples are found, however, in the case of the alkaline metals, sodium, potassium, etc. Weigh the body in the air, then in some liquid of low specific gravity in which the body is not soluble naphtha, for example and calculate as below : Weight of body in air = W " " naphtha=W \v-w'=w" Sp. gr. of naphtha = A " water =1 A: W"::l : W'" Before proceeding to the determination of the specific gravity of liquids, we will give one more formula which enables us to find the weight of each of two substances when combined in one mass. Some such formula must have been used by Archimedes in ascertaining the proportion by weight of the gold and silver forming the alloy of which Hiero's crown was made ( H6). Sp. gr. of the alloy =Sp. gr. Weight " alloy =W Sp. gr. of one constituent s' Sp. gr. of second " = s" Weight of one " =w' Weight of second " - w" Then, (s -s ) sp. gr. And w // =w _ w ,* To insure accuracy, all determinations of specific gravity should be made at one and the same standard temperature. This fixed temperature is 4 C. that at which water has its greatest density. 118. Determination of the Specific Gravity of Liquids. Several methods may be employed for ascertaining the * For proofs of this formula see " Galloway's First Step in Chemistry," p. 74. 192 NATURAL PHILOSOPHY. specific gravities of different liquids. We will describe three of them: I. By the flask; II. By weighing a sub- stance in it ; III. By the hydrometer. I. The method by the flask is exceedingly simple. Hav- ing selected a specific-gravity flask, determine its weight, fill it with water, and weigh again. Then empty it, dry it carefully, and, filling it with the liquid of which the specific gravity is desired, weigh again. Let weight of flask =F " " " and water =W " " " " liquid=W W' F Then, Sp. gr. of liquid TTT r; II. Take a body of known specific gravity, and insoluble in the liquid to be examined ; weigh the body in air, and then in the liquid ; if Weight of body = W " in liquid =W Sp. gr. of body ==A W:(W-WO::A:Sp. gr. *,*&$& III. The most expeditious method of ascertaining the specific gravity of liquids is by means of an instrument called a hydrometer. This instrument consists of a glass tube widened into a large and a small bulb at one end, the smaller bulb containing a few shot or a little mercury to cause the centre of gravity of the instrument to fall in the lower part; the narrow portion of the tube, called the stem, is furnished with a scale for reading the depth to which the instrument sinks when plunged in any liquid. The lighter the liquid to be tested, the deeper will the hydrometer sink in it. The manner of using a hydrometer is obvious: it is simply floated in the liquid to be tested, SPECIFIC GEAVITY. 193 and the figure on the scale at the point where it touches the upper surface of the liquid is accurate- ly noted. The graduation of the hydrometer varies for each liquid ; or, if the scale indicates specific gravity, and not arbitrary degrees, the relation between specific gravity and the strength of the liquid examined is ascertained by reference to ta- bles printed for the purpose. Hydrometers receive different names according to the liquids for which they are constructed: that for testing alcohol is called an alcoholometer / for solutions of sugar, sac- charometer ; for milk, a lactometer. Both in Europe and America the lactometer is used to test the quality of milk. In large cities the adulteration of milk with water has become so common a fraud that the police (in some instances) are authorized to collect samples of suspected milk for examination with the lactometer. In New York City the Board of Health has recommended a cer- tain lactometer as a standard. Besides the forms of hydrometer mentioned, there are many others; p . 1M as, for example, the salimeter (for salt solutions), the vinometer (for wines), the acidometer (for acids), etc. In determining the specific gravity of liquids, attention must be paid to the temperature at which the observa- tion is made, for bodies increase in volume with a rise of temperature, and this increase is not uniform for all substances. 119. Tables of Specific Gravity. Use is made of a knowl- edge of the specific gravity of certain substances to identify them ; especially is this the case with precious stones and minerals. We give below two tables one of the specific gravity of solids, and the other of liquids. Observe that the specific gravity of living men being 0.89, or lighter 194 KATUEAL PHILOSOPHY. than water, they should float if the precautions mentioned in 114 were properly taken. TABLES OF SPECIFIC GRAVITY. Solids. Cork 0.24 Oak-wood 0.84 Living men 0.89 Starch 1.50 Alum 1.70 Charcoal 1.85 Roll sulphur 2.00 Saltpetre 2.10 Quartz 2.G5 Marble 2.83 Glass (flint) 3.33 Diamond 3.52 Iron pyrites 5.00 Tin 7.29 Iron (malleable) 7. 84 Copper (cast) 8. 78 Silver (fused) 10.50 Lead 11.34 Gold 19.50 Platinum.. . 21.50 Liquids. Gasoline 0.66 "B." Naphtha 0.72 Ether 0.72 Kerosene oil 0. 80 Alcohol (absolute). . . 0. 80 Oil of turpentine 0. 86 Ammonia (solution) . 0.87 Olive-oil 0.92 Distilled water 1.00 Sea water 1.02 Milk (cow) 1.03 Human blood 1.06 Water of Dead Sea.. 1.16 Glycerin 1.27 Chloroform 1.49 Nitric acid 1.51 Sulphuric acid 1.84 Bromine 2.98 Thallium ethylate. . . 3.55 Mercury 13. 59 Specific Gravity of Gases. The specific gravity of gases is determined by a process much like that for liquids, men- tioned in 118. Air (sometimes hydrogen) is assumed as the standard. A large glass globe filled with air is weighed, then exhausted by an air-pump, and weighed again, the access of air being prevented by a stop -cock. The difference between the weights gives the weight, A, of a certain volume of air; the globe is then filled with the gas under examination, and weighed a third time ; by subtracting the weight of the empty globe the weight, T> B, of the gas is obtained. And , or the weight of the A gas divided by the weight of an equal volume of air, SPECIFIC GKAVITY. 195 gives the specific gravity of the gas. Corrections must of course be made for temperature. QUESTIONS. 112. Explain what is meant by specific gravity. What are the stand- ards of comparison for the three forms of matter? 113. Explain the sink- ing of heavy substances in water. Explain diagrams Figs. 159 and 160. Give the illustrations : lifting a stone ; raising a bucket ; raising the arm in a bath. Relate the anecdote of Archimedes. What is said of iron boats ? 114. What is said of the specific gravity of birds? Of insects? Of fishes ? What of the specific gravity of the human body ? 115. State the principal avoidable causes of drowning. What is narrated about children in China? Why is wading in deep rivers sometimes dangerous? 116. What four cases may arise in determining the specific gravity of sub- stances ? Explain the manner in which the specific gravity of a solid is obtained. Describe the experiment of weighing water. What is stated of Archimedes and the crown? 117. Give a condensed rule for finding the specific gravity of a body heavier than water. Illustrate by an ex- ample. Give what is known as the method by the flask. How is the spe- cific gravity of a substance soluble in water determined ? How that of a body lighter than water and insoluble in it? How that of substances lighter than water and soluble in it? How can you find the weight of two metals .in an alloy ? At what temperature should accurate determi- nations be made? 118. Describe the first method for determining the specific gravity of a liquid. The second method. What is a hydrom- eter ? How is it used? Name some of the varieties of hydrometers. For what is the lactometer used? 119. What is said of tables of specific grav- ity? Give a few examples from the table of solids. Give examples from the table of liquids. What is said of the process for determining the spe- cific gravity of gases ? 1 . 196 NATURAL PHILOSOPHY. CHAPTER XII. HYDRAULICS. 120. Hydraulics. Hydraulics teaches about liquids in motion, whether issuing from vessels or moving in chan- nels, of the employment of water as a source of work-power, and of machines used for raising water to a height. If an opening be made in the bottom or side of a tank filled with water, the liquid will flow through the orifice in obedience to gravitation, the particles of liquid near the orifice being pushed out by the pressure of those around and above them. Let us examine more carefully some of the phenomena connected with this flow of liquids through an opening. Let A, Fig. 165, represent a ves- sel of water having three open- ings, B, C, and D, C being equi- distant from B and D. Sup- pose B and D are closed and water flows from C; it is plain that the rapidity with which it issues must depend upon the pressure, and consequently upon the height of the liquid above the opening ; and since this level continually falls, the pressure of the liquid and the velocity of the flow diminish also. If the level be not maintained by replenishing a vessel, it takes twice as long to empty it as it otherwise would do. Again, suppose the orifice B is one foot below the stir- Fig. 166. HYDKAULICS. 197 face of the water, and that the pressure there causes a cer- tain quantity, say a litre, to flow out in one minute ; if we want the water to issue twice as fast, say two litres a min- ute, we must make the pressure four times as great ; or, what is the same thing, another opening, C, of the same size must be made four feet below the level of the water. For the discharge of three litres a minute the pressure must be nine times as great ; for a flow of four litres a minute the force must be sixteen times as great, and so forth, in the proportion of squares. The reason for this is that to move double the number of water particles would require double the force if they moved with only the same veloc- ity ; but because twice as many have to press through the same-sized opening in the same time, each must move with double speed, and hence the force must again be doubled ; but two doublings are equivalent to a fourfold increase. When a liquid descends from an opening in the side of a vessel, it follows the path of a projectile ( 67). In Fig. 165 the water is represented as spouting farthest horizon- tally from the orifice C, in accordance with the law that a stream will spout to the greatest distance from an opening half-way between the surface and the bottom of the liquid. If B and D are equidistant from C, the water issuing from them will strike the ground at the same distance from the foot of the vessel, A. The amount of the water dis- charged depends upon the size of the orifice and the velocity of the stream. For any given time the rule for finding the quantity discharged is as fol- lows: Multiply the area of the 'orifice by the velocity per sec- ond, and this product by th'e 198 NATURAL PHILOSOPHY. number of seconds. The shape of the aperture through which the water flows has also a marked influence on the volume discharged. A funnel-shaped tube having a circu- lar section, Fig. 166, discharges more liquid in a given time than an opening of any other shape. 121. Water-Clocks. The ancients took advantage of this regular flow of water through openings to measure time before the invention of clocks and watches. The water-clocks, or clepsydra, as they were called, were analogous in principle to the common sand-glass. Ctesibus, a cele- brated Greek philosopher of Alexandria, about 250 B.C., contrived a most ingenious form of this instrument. Water flowed as tears from the eyes of a statuette which seemed to be deploring the passage of time ; the tears gradually filled a reservoir, and raised a floating figure which pointed to the hours marked on a scale. This reservoir emptied itself by means of a siphon arranged, as in the cup of Tantalus ( 143), once every twenty- four hours, and the discharge of the water worked mechanism which indi- cated the day and the month. 122. Flow of Liquids through Tubes. The flow of liquids through long tubes and pipes is considerably affected by friction. An inch tube 200 feet long, connected horizontal- ly with a reservoir, will discharge water only one quarter as fast as an inch orifice in the side of the reservoir. Sudden turns in a pipe should be avoided, because they oc- casion so much friction against the sides of the pipe and among the particles of water by disturbing the regularity of the current. In the entrance of the arteries into the brain, in order to prevent the blood from flowing too rap- idly into this organ, there are sudden turns in the arteries to retard the blood ; and in grazing animals, since there is special danger that the blood will flow too freely to the brain as the head is held down in eating, there is a special provision to prevent this in a net-work of arteries. If the arteries of the brain in such animals were straight tubes, they would continually be dying of congestion of the brain or of apoplexy. HYDRAULICS. 199 Friction of liquids in a small pipe is greater in proportion to its size than in a large pipe. In a pipe an inch in diam- eter water moves only one fifth as fast as in a tube two inches in diameter. This may be made clear by Fig. 167, which represents the area of a small tube inside of the area of a tube hav- ing twice its diameter. Suppose the eifect of the friction in the large tube to extend in to a. In the small one it will extend in as far that is, to b. But e a is about five times as long as e 5, so that there is fully five times Fig.i6T. more water uninfluenced by friction in the large tube than in the smaller one. Friction in Streams. The retarding effect of friction is very obvious in brooks and rivers. The water in the middle of a stream runs much more rapidly than it does near its banks. When a river is very shallow at its sides, the water there scarcely moves, though in the middle the water may be running at a rapid rate. A tide, therefore, flowing up a river, moves more freely near its banks than it does in the middle of the stream, because it there meets with less resistance from the downward current. Water moves less rapidly at the bottom of a river than at the surface. For this reason, if a stick be so loaded at one end as to stand upright in water, in the cur- rent of a river its upper end will be carried along faster than its lower end, and therefore it will incline forward, as in Fig. 1 68. As the sea rolls in over a beach, each wave at length pours over its crest and breaks, because the lower part of the wave is retarded by friction on the beach. Were it not for the constant retardation of friction at the sides and bottom of rivers, and at their bends, those rivers which have their rise at a considerable height above the level of the sea would ac- quire an immense velocity. Thus the Rhone, drawing its waters from 1000 feet above the level of the ocean, would pour them forth with the velocity of water which had fallen perpendicularly the same height that is, at the rate of 170 miles an hour did not friction continually diminish the velucit v. \ 200 NATURAL PHILOSOPHY. 123. "Waves. Waves are generally formed by the fric- tion of air upon water. As soon as any portion of water is raised above the general surface, it tends by gravity to fall to a level with the water around it, and in so doing the portion next to it is forced upward, forming another wave ; thus one wave produces another, each one being smaller than the preceding, till at length the motion is wholly lost. This is always the process when the cause of the motion is a single impulse, as when a stone is dropped into the wa- ter. But when the waves are produced by a succession of impulses, as by the wind, they are mostly of the same size. It is quite a common notion that the water moves forward as rapidly as the waves appear to do; but the water really remains nearly stationary, rising and falling, while merely the form of the wave advances. The same wave is made up continually of a succession of different portions of water, or rather it is a succession of different waves. This is very well illustrated by the waving of a rope or carpet. In an open sea a wave slopes regularly on either side ; but when it comes near the shore, for the reason given in 122, it grows more and more nearly perpendicular on the side tow- ard the shore, till at length it falls over; and if it be very large, the roar thus caused by its breaking is heard to a great distance. Height of Waves. "So awful," says Dr. Avnott, "is the spectacle of a storm at sea that it is generally viewed through a medium which biases the judgment; and, lofty as waves really are, imagination pictures them loftier still. Few waves rise more than fifteen feet above the ordinary sea- level, which, with the fifteen feet that its surface afterwards descends below this, gives thirty feet for the whole height from the bottom of any water- valley to an adjoining summit. This proposition is easily verified by ob- serving at what height on a ship's mast the horizon remains always in sight over the top of the near waves at the time when she reaches the bottom of the hollow between two waves. Allowance must of course be made for accidental inclinations of the vessel, and for her sinking in the water to HYDRAULICS. 201 much below her water-line. The spray of the sea, driven along by the violence of the wind, is of course much higher than the summit of the liquid wave ; and a wave coming against an obstacle may dash to an eleva- tion much greater still. At the Eddystone Light-house, reared on a soli- tary rock ten miles from the land, a wave which has been growing from far across the Atlantic often dashes above the lantern at the summit, which is about ninety feet high." 124. The Tides. The rise and fall of the water of the ocean, called tide, result from the attraction of the moon. The inoon actually lifts the water towards itself. The attraction of the sun sometimes increases and sometimes diminishes the tides, according to its position in relation to the moon and the earth. If the land were as movable as the water, or, in other words, if its particles were held together by no stronger attraction than those of water, there would be the same motion over the surface of the earth, when in its revolution successive portions of it pre- sent themselves towards the moon. When the flood-tide returning from the sea meets the out- ward current of a river flowing into a gradually narrow- ing arm of the sea, the immensely powerful mass of the ocean moves inland, like an almost vertical wall, with irre- sistible force. Such a heaping-up of the waters where the two currents meet is called the bore. This phenomenon is seen to a remarkable degree in the branches of the Ganges; its roaring is heard long before its arrival, and all small vessels seek positions of safety on shore, while even large ships are occasionally damaged by its resistless sweep. At Calcutta the w r ater sometimes rises five feet instanta- neously, and the huge wave rolls on at the rate of fifteen miles an hour. The effects of a strong tide are also seen in certain places where the configuration of the coast com- pels the incoming water to rise to great heights. In the Bay of Fundy the returning tide advances with such ra- 202 NATURAL PHILOSOPHY. pidity that a person on horseback who incautiously ven- tures too near can scarce escape being overwhelmed. 125. Relation of Bulk to the Resistance of Liquids and Gases. You have already seen, in 64, that the greater the surface of a body in proportion to its weight, the greater the resistance of the air to its motion. This truth, which applies to liquids as well as to gaseous substances, explains the. fact that small bodies meet with proportion- ately more resistance than large ones. The body B, Fig. 169, is made up of eight cubes of the size of the cube a, that is, it has eight times the quantity of matter. Now, if B were moving through air or Fig. 169. water, any one of its sides pushing the water before it would meet with only four times as much resistance as a would, for its surface is only four times as large, although the body is eight times as large as a. And the greater the difference of size, the greater is the differ- ence of resistance. If B were a cube twenty-seven times as large as a, it would meet with only nine times as much resistance. This explains why shells and cannon-balls can be thrown much farther than bullets and small shot. The sportsman does not throw away his shot by foolishly aim- ing at birds at great distances, and yet shells and large cannon-balls can be thrown a distance of several miles. The difference is not in the degree of velocity which the powder produces, but in the resistance of the air. For the same reason rain falls with greater rapidity than driz- zling mist. Since liquids and aeriform substances resist solids in motion in propor- tion to the amount of surface which the solids present to them, when they strike against solids they cause motion in them in proportion to the amount of surface acted upon. Thus a violent wind which could not move a lump of tin could, nevertheless, raise a sheet of it, or tear up a HYDRAULICS. 203 roofing of it if permitted to get beneath. Clouds of sand are raised into the air in the deserts of Africa, although the particles are of the same ma- terial as stones, and therefore have the same specific gravity. For the same reason dust, feathers, the down and pollen of flowers, etc., are blown about, although they are heavier than the air. A pebble is moved more easily by a current of water than a stone, because it has a larger surface, in proportion to its weight, to be acted upon by the water. For the same reason sand is moved more easily than pebbles, and fine mud than sand, though stones, pebbles, sand, and mud may all be of the same material. This explains why you find mud where the current is slow, sand where it is faster, pebbles and stones where it is still faster, and where the current is exceedingly rapid you will find nothing but large rocks sand, pebbles, and stones not being able to resist its force. For the same reason, in the process of winnowing, the chaff is carried away by the wind; while the grain, presenting less surface in proportion to its weight to be acted upon by the air, falls to the floor. Influence of Shape on Resistance of Liquids to Solids. The resistance of air or water to a flat surface is greater than to a convex one, because the latter readily turns the particles aside. Thus, a concave surface is resisted much more than a flat one, because the particles of the air or water cannot so easily escape sideways. Fishes are of a spindle-like and slender shape, that they may offer as little resistance as possible to the water. It is for this reason that a fish has no neck, otherwise the upper por- tion of its body would, from the resistance of the water striking against it, prove a serious impediment to rapid- ity of motion. Mankind has in some. measure imitated the shape of fishes in their boats and ships. Boats which are intended to bear light burdens and go swiftly are made very long and narrow. The webbed feet of water-fowls, when they are moved forward, are folded up so as to meet with as little resistance as possible; but when they are moved backward they are spread out so as to press against the water a broad concave surface. For the same reason the wings of a bird are made convex upward 204 NATURAL PHILOSOPHY. and concave downward ; and when it moves its wing up- ward it cuts the air somewhat edgewise, but in moving it downward it presses directly with the whole concave surface. I 126. Machines for Raising Water. A great variety of contrivances for raising water from a lower to a higher level have been devised, some of which are based on a simple application of one or more of the six simple ma- chines described in Chapter VI. Such are the well-sweep, acting on the principle of the lever, and the rope and bucket suspended from a wheel and axle. An old system of raising water is by means of a succession of buckets attached to an endless rope passing over two wheels, so that the buckets fill as they are carried over the lower wheel and discharge as they pass over the top wheel. The chain pump, used in many parts of this country, is somewhat similar ; but the buckets are replaced by flat disks of metal, which are drawn up through a long tube or barrel, like loose-fitting pistons, and raise an abundant stream of water. The celebrated philosopher Archimedes invented a simple machine, known as Archimedes's screw, by means of which water may be readily raised to a mod- erate elevation. It consists of a tube open at both ends, wound spirally around an inclined cylinder as represented in Fig. 170. The low- er end of the tube dips below the water ; on revolving the cylinder the open end scoops up Fig. 1TO. water, and when it has turned half-way around, the point D is lower than the end C, and, in obedience to gravitation, the water descends to D. On continuing to revolve the screw, the water rises to the top, B, as if drawn up an inclined plane. Archimedean HYDEAULICS. 205 screws are still used in Holland for draining, and are gen- e rally driven by windmills. The various kinds of pumps used for raising water, being dependent upon the principles of pneumatics, will be de- scribed in the chapter treating of that topic. 12V. Water-wheels. Water flowing in streams having considerable descent affords motive power of first impor- tance. It can be made to perform work through the agency of water-wheels. These wheels are of three princi- pal kinds the Undershot wheel, the Overshot wheel, and the Turbine. The undershot wheel consists of a wheel re- volving on an axle, and having a number of float-boards attached to its circumference, Fig. 171. These float-boards Fig. 171. dip into the water, which, by its momentum, drives the wheel around, the velocity depending upon the height of the fall of water. In overshot wheels the float-boards are shut in by flat sides, so as to form buckets round the wheel into which the water is allowed to fall at the top of the wheel, Fig. 172. In this wheel the water acts almost solely by its weight ; as the wheel revolves, the buckets, filled at the top, descend, and discharge the water, so that by the 12 206 NATUEAL PHILOSOPHY. Fig. 1T2. time they begin to rise on the opposite side they are empty. When the water is received half-way up the wheel, or higher, the arrangement is called a Breast Wheel. The Turbine pre- sents a very differ- ent appearance : it consists of a hori- zontal wheel divided into compartments by curved lines, as shown in that portion of the cut (Fig. 173) without the heavy circle. Within this is fitted a fixed cylinder, also divided into compartments similar to those in the wheel, but running in the opposite direction. Water, from a height, enters a tube con- nected with this cylinder, and, following the course given by the curved lines, strikes against the partitions of the wheel, causing it to revolve about a vertical axis. Owing to the pressure of the water within the tube, and to its striking the parti- tions nearly at right angles, turbines turn to account a larger proportion of the motive power (four fifths) than any other wheel. Fig. 173. HYDRAULICS. 207 Somewhat similar in principle is the so-called Barker's Mill ; it consists of a vertical cylinder ar- ranged in a frame in such a way that it can revolve upon the point upon which it rests. Water running i I into the cylinder escapes by two arms having holes on the alternate sides; by this arrangement the re- action upon the issuing water makes the cylinder revolve rapidly, causing the ends of the arms to revolve as represented in the figure (Fig. 174). QUESTIONS. 120. Of what does Hydraulics teach? Describe some of the phenom- ena connected with the flow of liquids through an opening. What is the path of a liquid issuing from a lateral opening ? Upon what depends the amount of water discharged? 121. What is said of water-clocks ? 122. How does friction affect the flow of liquids through long tuhes ? What is said of the effect of friction in brooks and rivers? In what part of a stream does the water move most rapidly ? Explain the formation and breaking of the crest of waves rolling over a beach. What is said of the velocity of rivers'as affected by friction ? 123. Explain the formation of waves. What is it that really advances in the forward movement of a wave? Give the comparison mentioned. What is said of the height of waves? 124. What causes tides? What is a bore? Mention some places where its effects are noteworthy. 125. Illustrate the relation of bulk to the motion of solids produced by moving gases and liquids. What is said of the opposition of gravitation to water and air in moving solids ? What difference does the presence of obstacles make in the relation of force to velocity ? What is said of the relation of shape to velocity ? What is said of the shape of fishes ? What is said of the shape of boats ? What of 208 NATURAL PHILOSOPHY. the management of the webbed feet of water-fowls ? What of the wings of birds? 126. What is said of machines for raising water? Describe Archimedes's screw. 127. Name the principal kinds of water-wheels. Describe the undershot wheel, and explain its action. Also the other forms. The turbine. Describe Barker's Mill. CHAPTER XIII. PNEUMATICS. 128. What Pneumatics Teaches. Hydrostatics, as yon have learned in the preceding chapters, treats of the press- ure and equilibrium of liquids, and Hydraulics of the laws governing their motion. Pneumatics is that branch of phys- ics which treats of the same phenomena in air and other aeriform bodies. The name is derived from a Greek word signifying breath or air, just as the term hydrostatics comes from the Greek for icater. In explaining the laws of" liquid level," " equal pressure in all directions," and of " pressure varying with the depth," we have studied the phenomena with reference only to water as the most convenient liquid ; but these laws hold good with all other liquids. In like manner, the laws which we are about to teach concerning common air are equally applicable in the case of all other gases under similar circumstances. Air Material and has Weight. That air is a material substance has been shown in 12, where its impenetrabil- ity was demonstrated. It is much less dense than water by reason of a greater separation and repulsion of its par- ticles; but analogous phenomena are observed with both these fluids. For example, if you fill an India-rubber bag with water and tie its mouth, you cannot flatten it by pressure; and PNEUMATICS. 209 if you blow into it until it is distended and again fasten its moutl}, it remains bulky, forming what is known as an air-cushion. Life-preservers and foot-balls are examples of such air-cushions. Then, again, the resistance offered by air to motion, as in fanning, the power possessed by currents of air to move light as well as heavy objects, and the flight of birds in the air, all prove the material nature of air. That air has weight can be proved by weighing it as you would any other substance. Let a hol- low globe, A, Fig. 175, having a neck with a stop-cock, B, be emptied of air and weighed. When you open the stop-cock, and let in the air, the other beam of the scale will rise, be- Jb lg. 175. cause the globe is heavier than it was before. The additional weight required to make the scales balance will indicate the weight of the air which the globe contains. It is about one eight-hundredth (y^) of the weight of the same volume of water. How the globe can be emptied of the air will be shown in another part of this chapter (see 134). 129. Air Attracted by the Earth. The weight of the air is simply the result of the attraction of the earth ( 27). Air is attracted by the earth in the same manner as water ; and the water takes its place below air because it is attract- ed more strongly than the air. If you put into a bottle mercury, water, and oil, the mercury will lie at the bottom, because it is more strongly attracted by the earth than the other fluids. The water will be next, then the oil, and lastly, over all, the air, that being less attracted than any of the other substances. This attraction of the air by 210 NATURAL PHILOSOPHY. the earth is the origin of the chief phenomena of Pneu- matics. Why Some Things Fall and Others Rise in Air. Most substances fall in air for the same reason that very heavy substances sink in water. They fall because the earth attracts them more strongly than it does the air. The reason that some substances rise in air is precisely the same as that given in 113 for the rising of substances in water. The air, being attract- ed more strongly, pushes them up to get below them, as cork or wood is pushed up by water. Thus a balloon filled with hydrogen gas rises in air for the same reason that a bladder filled with air rises in water. 130. Thickness of the Earth's Air - Covering. -The air makes a covering for the earth about fifty miles deep. If the earth were represented by a globe a foot in diameter, the air might be represented by a covering a tenth of an inch in thickness. The line #, Fig. 176, shows the curve of Fig. 1T6. the surface of such a globe, and the space between a and b represents the comparative thickness of the covering of air. This is ascertained by calculation from the press- ure of the air upon the earth in the same manner as the depth of water is calculated from the pressure which i.ti exerts. The earth flies on in its yearly journey around the sun $t the rate of 11 CO miles per minute, and yet it holds on to this loose airy robe by its attrac- tive force, so that not a particle of it escapes into the, surrounding ether. Of itself it is disposed to escape ; and it would do so, and be diffused through space, if the attraction of the earth for it wejre suspended. 131. Compressibility of Air. In considering the influence of gravitation upon air, it must be remembered that air is very compressible, while water is very nearly incompressi- ble ( 1 7). While, therefore, in a body of water the particles PNEUMATICS. 211 arc very little nearer together at the bottom than at the surface, the particles of the air are much nearer together at the surface of the earth than at a distance from it. All the particles of the air being attracted or drawn towards the earth, those below are pressed together by the weight of those above. The air therefore becomes more rarefied as we leave the surface of the earth, and in the outer regions of the sea of air it is too rare to support life. Even at the tops of very high mountains, or the heights sometimes reached by balloons, disagreeable effects are often experienced from the rarity of the air. The air has been compared, in regard to its varying density at different heights, to a heap of some loose compressible substance ; as, for example, cotton-wool, which is quite light at the top, but is pressed more and more compactly as you go towards the bottom. Hydro- gen gas is only one fifteenth as heavy as air at the sur- face of the earth ; and therefore the hydrogen balloon rises till it reaches a height where the air is so rare that the balloon is of the same weight with an equal bulk of air, and there it stops. 132. Similarity of Aeriform Substances and Liquids. You have learned in 17 in what the air and gases differ from liquids. But in one very important respect they are alike viz., the mobility of their particles. Hence pressure in air, as well as in water, is equal in all directions, so that in the experiment with the bladdeiyin 107, it makes no difference in the result whether it be filled with water or air. For the same reason, pressure is in proportion to the depth in aeriform substances as well as in liquids, and the laws of specific gravity apply to the one as well as to the other. You are now prepared to understand the results of the action of gravitation upon air and the gases or, in other words, the principal phenomenon of Pneumatics. 212 NATUKAL PHILOSOPHY. 133. Pressure of the Atmosphere. The amount of the pressure of the atmosphere is very readily estimated, by a process which we will explain in another part of this chap- ter. It has been ascertained that the atmosphere presses with a weight of fifteen pounds on every square inch. When you extend your outspread hand horizontally in the air, you feel no pressure upon it, notwithstanding it sustains a pressure of some two or three hundred pounds. If your hand be five inches long and three broad, it presents a sur- face of fifteen square inches, on every one of which the at- mosphere is pressing with the weight of fifteen pounds ; that is, there is a pressure on the upper surface of your hand of a column of air weighing 225 pounds, and on the lid of a box only thirty inches square there is a pressure of 13,500 pounds. The whole pressure on the body of a man of com- mon size is about fifteen tons. But why is it that the lid of the box is not broken in, your hand not borne down, and your body not crushed ? It is simply from the fact, shown in the previous chapter in regard to liquids, and in this one as to aeriform substances, that the pressure is equal in all directions. The lid and the outspread hand are there- fore balanced by' an upward pressure equal to the down- ward, and the body sustains an equal pressure on all sides. If the air could be removed from within the box, the lid would be crushed in ; if from under the hand, that would be borne down ; and if from one side of the body, the body would be forced violently in that direction till it met with an opposing pressure. But besides this equal pressure of the air on all sides, air exists within the pores and interstices of all bodies that are not very dense, and its particles are subject to the same laws as are those on the outside. All this can be made clear to you by experiments with the air-pump. PNEUMATICS. 213 Fi 134. Air-pump. Fig. 177 represents an air-pump as com- monly arranged. A, B, are two pump -barrels, the pistons in which are worked by means of the handles, G and M. These pumps are very nicely made, and the frame-work to which they are attached is very strong and firm, so that the pumps may work evenly. J is a bell-shaped glass vessel, called a receiver, closed at the top, but open at the bottom, the edge of which is ground very true, so that it may fit exactly on the large, smooth metallic plate. In the mid- dle of the plate is an opening which leads to the pump- barrels, and it is through this that the air is pumped out of the glass receiver, J. If we wish to let the air in after 214 NATURAL PHILOSOPHY. Fig. 178. we have pumped it out, we loosen the screw at K, for there is a passage from this opening to that in the mid- dle of the plate. The operation of the air-pump can be made clear by reference to Fig. 178. But one pump- barrel, a, is represented, with a piston, c, work- ing in it. In the pis- ton there is a valve, i, opening upward, and also one at b, at the end of the tube leading to the centre of the plate on which is the receiver, d. The working of the instrument is as follows : If the piston, c, be forced down, the air under it, being compressed, will close the valve at 6, and will rush upward through the valve i in the piston. Let the piston now be raised ; the resistance of the air above it will close the valve t, while the valve b will be opened by the air rushing from the receiver, d, through the passage, e, to fill the space between the piston and b. You see, then, that every time the piston is drawn up air passes out of the receiver through the valve b into the space between this valve and the piston. None of this air which has passed out can return ; for the moment you press upon it by forcing downward the pis- ton, the valve 6 closes and the air escapes through the valve i. Each time, therefore, that you work the piston up and down, you pump some of the air out of the receiver ; and after some time exceedingly little air will be left in it, and that, of course, will be diffused throughout the receiver. It will be rarefied like that in the upper regions of the atmosphere. With the double-barrelled air-pump, shown in Fig. 177, the operation is similar but more rapid, because when one piston is raised the other is lowered, and the action is continuous. L is a gauge to indicate the completeness of the ex- haustion, which acts on the principle of the barometer. 135. Experiments. When the receiver J (Fig. 177) is full of air, it can be moved about on the plate easily, and can be PNEUMATICS. 215 lifted from it. But if you work the pumps a few strokes, the receiver will be firmly fastened to the plate, since the air within, being rarefied, presses with little force com- pared with the air outside. If the pumps be worked for some time, it will be very difficult to release the receiver from the pressure without breaking it. But turn the screw, K, admitting the air, and the equality of the pressure within and without is at once restored. Remove this large re- ceiver, and place a small glass jar, open at both ends, on the plate, with the hand covering the upper opening, as represented in Fig. 179. On exhausting the air, the hand is so firmly pressed into the glass that it requires consid- erable force to disengage it from the pressure. If we tie a piece of bladder or India- rubber over this jar, as in Fig. 180, and then pump out the air, the bladder is at first pressed in ; and if we continue to pump, it at length bursts inward with a loud report. It would make no difference in the result of the experiment if the jar were shaped as in Fig. 181, for the pressure is the same in all directions. The resemblance be- tween air and liquids in this respect may be . isi. illustrated thus : Suppose that a flat fish rests against the tube of a pump so as to cover the end with one of his sides. He feels no uncomfortable pressure, because the water in the pump and that below it press equally upon him. If, however, the pressure of the water in the pump be sud- denly removed by the piston, the fish would be pressed up- ward into the tube, just as the bladder is pressed upward in Fig. 181, or downward in Fig. 180. The so-called "Mag- deburg Hemispheres," Fig. 182, illustrate very strikingly 216 NATURAL PHILOSOPHY. the pressure of the atmosphere. They consist of two hollow half- globes of metal whose edges fit very accurately upon each other. The air being exhausted through the stem and a handle screwed on, great force must be exerted to pull the hemispheres apart. The force required depends upon the extent of their surface. In the famous experiment at Magdeburg, in 1654, by Otto von Guericke, Flg - 182 ' the inventor of the air-pump, two strong hemispheres of brass three feet in diameter were employed ; and when he exhausted them on the occasion of a public exhibition, it is said that twenty coach-horses of the emperor were unable to pull them asunder ! In the so-called "Mercury Shower," we have another example of the immense pressure of the atmosphere. Fig. 183 represents a receiver with an opening at the top. mented in this opening is a wooden cup, a, ter- minating in a cylindrical piece, b. If mercury be poured into the cup and the air within the receiver be exhausted, the mercury will be forced through the pores of the wood by the external air, and will fall in a silver shower. A tall jar, c, is placed there to receive it, to prevent any of it from entering the opening in the metallic plate. The boy's sucker illustrates the pressure of the air. It is simply a circular piece of leather with a string fastened to its centre, as shown in Fig. 184. When the leather is moistened and pressed upon a smooth stone, it adheres by its edges to the stone, just as the receiver adheres to the plate of the air-pump when the air is pumped out. Many animals have contrivances Fig. 184. PNEUMATICS. 217 of a similar character to enable them to walk in all positions, to seize their prey, etc. The gecko and the cuttle-fish furnish interesting examples, as noticed in Hooker's Natural History. Snails, limpets, etc., adhere to rocks by a like arrangement. Some fishes do the same ; one, called the remora, attaches itself by suckers to the side of some large fish or a ship, and thus enjoys a fine ride through the water without any exertion on his part. In all such cases it is water instead of air that makes the pressure, but the principle is the same. Flies and some other insects can walk up a smooth pane of glass, or along the ceiling, because their feet have contriv- ances similar in principle to the boy's sudker. The hind-feet of the wal- rus are constructed somewhat like the feet of the fly, enabling this huge animal to climb smooth walls of ice. 136. Density of the Air Dependent upon Pressure. The fact that the degree of the density of the air is dependent on pressure has been already shown in 131. The same thing can be shown in various ways by experiments with an air-pump. If a small bladder partly filled with air, Fig. 185, and loaded with a weight so as to sink in water, be placed in a jar of water, and the whole be set under the receiver of the air-pump, on ex- hausting the air the bladder will swell out, owing to the expansion of the air, and will rise. The reason is, that the pressure being removed from the surface of the water, the bladder bears only the pressure of the water, and not that of the air plus the water ; hence the air within expands and becomes less dense. If an In- dia-rubber bag be partly filled with air, Fig. 186, and put under the receiver, when the air is exhausted the bag is relieved of pressure, and the air in it becomes ex- panded that is, rarefied. For the same reason, if a vessel with soap-bubbles in it be placed under the receiver, on pumping out the air the bubbles will become much enlarged. A very pretty ex- Fig. i9c. periment illustrates the same principle. Let an Fig. 185. 218 NATURAL PHILOSOPHY. egg with a hole in its small end be suspend- ed in a receiver, as represented in Fig. 187, a wine-glass being placed beneath it. On exhausting the air, the egg will run out of the shell into the wine-glass, and then, on admitting the air, the larger part of it will run back again into the shell. This may be explained^as follows: The large end of the Fig. 137. e gg contains air. As soon as the pressure of air is removed from the egg, the air in the egg expands, forcing out the contents; but when the air is admitted into the receiver, the air in the egg is at once condensed to its former small bulk by the surrounding pressure. Hydrostatic Balloon. The philosophical toy represented iu Fig. 188 illustrates very beautifully the influence of pressure upon the density of the air. The balloon in the jar of water is constructed of glass, having a small orifice at its lower part. Water is intro- duced into the balloon, care being taken to put in just enough to make the balloon of a little less specific gravity than water. In that case it will rise to the top of the jar, with a very little of its top above the surface of the water. Now tie a piece of India-rubber cloth over the top of the jar, and the apparatus is complete. On pressing upon the India-rubber the balloon will descend in the jar, and on removing the pressure it will rise. The explanation is as follows: The pressure upon the India-rubber is felt through the whole body of the water in the jar, and forces a little more water into the orifice of the balloon, condensing the air within it. The balloon conse- quently becomes heavier, and, having a greater specific gravity than water, sinks. But when the pressure is re- moved, the condensed air in the balloon, by its elasticity, Fig. 188. PNEUMATICS. 219 returns to its former bulk, expelling the surplus water just introduced; and the balloon, becoming therefore as light as before, rises. 137. Pores of Substances Contain Air. We have said that the pores and interstices of wood, flesh, and a great variety of substances contain air. In all these cases the presence of the air can be made manifest by removing the pressure of the surrounding air, and thus allowing the air in these substances to ex- pand. If an egg be placed in a jar of water, Fig. 189, under the receiver of an air-pump, on exhaus- tion being made, air-bubbles will constantly rise in Fig. is*, the water from the egg. In like manner, the surface of a glass of ale, Fig. 190, will be covered with foam, the carbonic-acid gas in it escaping freely when the pressure of the air upon it is re- moved. The same thing may be seen to some extent even in water, for it always contains some Fig. 190. air. For a similar reason a shrivelled apple will become plump and fair when the pressure of the external air is removed, but will shrink at once to its shrivelled state when the air is admitted into the receiver. 138. Elasticity of the Air. All the phenomena men- tioned in 136 and 137 exhibit the elasticity of the air. Owing to this property it is always disposed to expand when pressure is removed from it. This is, most strikingly exhibited when the air is much condensed by pressure; the greater the condensation, the stronger the expansive or elas- tic force. Fig. 191, page 220, represents an instrument called the condenser. In the cylinder, A B, moves the piston, P. Air is admitted to the cylinder at F, and into the receiver, V, at G. The valve at F prevents any air from escaping from the cylinder, and the valve at G prevents it from escap- ing from the receiver. The instrument operates thus : If the 220 NATUKAL PHILOSOPHY. Fig. 191, piston be pressed downward, the compress- ed air in the cylinder shuts the valve F and opens G, and so enters the receiver, V. If the piston be raised, air rushes in at F to fill the space in the cylinder. It cannot come from V, because the valve G is shut by the pressure of the air within. By work- ing the piston for some time, you can force a quantity of air into V of very great density. It is evident that this instrument is the very opposite of the air-pump. The receiver, V, contains condensed air, while the receiver of the air-pump contains rarefied air. If you compare the two instruments, you will see that the opposite results are owing to a different arrangement of the valves. Until quite recently air had never been condensed to the liquid state. This was accomplished by Messrs. Pictet and Cailletet, who subjected it to enormous pressure and a very low temperature. The term permanent gas formerly applied to air must now be abandoned. The elasticity of the air and other gases results from an incessant commotion of their particles. We must picture to our minds the molecules of a gas as moving in all direc- tions, constantly striking against each other, and thus pro- ducing pressure on the sides of an enclosing vessel. We have already referred to this motion of the molecules of a gas in 8. The force with which the molecules strike against the confining walls will be greater the smaller the space through which they are allowed to move, a consider- ation which explains the fundamental principle known as Marriotte's law viz., the pressure of any quantity of gas is inversely proportional to its volume. That is to say, the greater the pressure to which a gas is subjected, the less PNEUMATICS. 221 space it occupies. Thus a body of air which under a cer- tain pressure occupies six cubic feet will be condensed to three cubic feet by twice the pressure, and to two cubic feet by three times the pressure, etc. Illustrations. Air-guns and pop-guns illustrate the elasticity of con- densed air. The air-gun is constructed in this way : A receiver like V, Fig. 191, is so made that you can screw it on and off the instrument. After being charged with condensed air, it is screwed upon the gun, its stem communicating with the barrel. In order to discharge the gun there is a contrivance connected with the trigger for raising the valve, G, so that some of the condensed air may enter the barrel. On doing so, its sudden expansion rapidly forces out the contents. The principle on which the common pop-gun operates is similar. Air is confined be- tween the two corks, P and P', Fig. 192. As the rod, S, is pushed quickly Fig. 192. in, the cork P' is carried nearer to P, so that the air between them is condensed. With the condensation the expansive force is increased ; and when it becomes so great that the cork P can no longer resist it, it throws the cork out, and so quickly as to occasion the popping sound. The explosion of powder furnishes a good illustration of the expansive force of condensed air or gases. These gases are produced so suddenly from the powder that at the instant they are in n very condensed state, and therefore expand powerfully. The power of steam is in proportion to its condensation. When formed under the confinement of a boiler, on being allowed to escape it expands with great force. The application of the expansive power of steam will be treated of particularly in 182. 139. Pressure of the Air on Liquids. If you plunge a tumbler into a vessel of water, and, turning it over, hold it so that its open part is just under the surface, it will re- main full. This is because the weight of the air pressing upon the surface of the water in the vessel prevents the water in the tumbler from passing downward. Now, K 222 NATURAL PHILOSOPHY. Fig. 193. if you introduce a bent tube under the tumbler, as shown in Fig. 1 93, and blow through it, the air forced up into the tumbler presses the water down, taking its place. That is, the press- ure of the air within the tumbler acts in opposition to the pressure of the air upon the surface of the water. If instead of a tum- bler you take a tall jar, as represented in Fig. 194, and, filling-it with water, invert it upon a small shelf placed beneath the surface of the water, you will have a representation of the pneumatic trough used by the chemist in collecting gases. To fill the jar a with gas he puts be- neath it the mouth of the retort from which the gas issues, and the gas pass- Fig. 194. ing upward expels the water. In Fig. 195 is represented an experiment which shows not only that the press- ure of the air sustains the column of water in the cases cited above, but also that it makes no difference in what direction this pressure is exert- ed. Take a glass, fill it even full with water, and, placing a piece of writing- paper over its mouth, carefully invert it, as shown in the figure. The paper will remain, and the water will not Fi-^.195. run out. It is the pressure of the air PNEUMATICS. 223 that sustains the water, and the paper only serves to main- tain the surface of the water unbroken. If the paper were not there the particles of the air would insinuate them- selves among those of the water, and pass upward in the glass. This explains why a liquid will not run from a barrel when it is tapped, if there be no vent-hole above, unless so large an opening be made as to let the air work its way in bubbles among portions of the liquid. It is this entrance of the air that causes the gurgling sound heard in pouring a liquid from a bottle. 140. Amount of Atmospheric Pressure. If, instead of the glass jar in Fig. 194, you use a tube thirty-four feet long, and closed at the top, it will remain full of water. If the tube be longer, the water will stand only at thirty-four feet, leav- ing an empty space, or vacuum, above it. It makes no dif- ference what the size of the tube is ; the result will be the same in all cases.* That is, a column of water thirty-four feet high can be sustained by the pressure of the atmos- phere. It is easy, therefore, to estimate the weight or press- ure of the air. The pressure of the column of water is found to be fifteen pounds to the square inch of its base, and this, of course, is the amount of pressure or weight of the atmos- phere which it balances. Mercury is thirteen and a half times as heavy as water, and therefore the air will sustain a column of it only about thirty inches in height (76 cm.). 141. Barometer. The weight of the atmosphere varies to some extent at different times, and the barometer is an instrument for measuring these variations. It is con- structed on the principles developed in the previous para- graphs. Fig. 196, on the following page, represents a very simple form of the instrument. A glass tube about 35 inches * This is true except when the tube is so small that capillary attraction exerts considerable influence. 224 NATURAL PHILOSOPHY. (88.8 centimetres) long, closed at one end, is fill- ed with mercury, and then inverted in a cup of the same liquid, n n. The vacuum produced by the falling of the mer- cury is called the Torricellian vacu- um, from Torricelli, an Italian, who first developed the principles of the instrument in 1642. Fig. 197 shows another form of the instru- ment, with a scale attached. The mercury generally stands at the height of about 30 inches. But it varies with the weather. When the weather is bright and clear, the air is heavier, and, pressing upon the mercury in the vessel, forces it up higher in the tube. But when a storm approaches, the air is apt to be lighter, and there- fore, pressing less strongly on the mercury in the vessel, the mercury in the tube falls. The barometer is of great service, espe- cially at sea, in affording the sailor warning of an approaching storm. An incident is related by Dr. Arnott which strikingly illus- Fig. 196. Fig.l9T trates its value in this respect. He was at sea in a southern latitude. As the sun set after a beautiful afternoon the captain foresaw danger, although the weather was perfectly calm, for the mercury in the barom- eter had suddenly fallen to a remarkable degree. He gave hurried or- ders to the wondering sailors to prepare the ship for a storm. Scarcely had the preparations been made when a tremendous hurricane burst upon the ship, tearing the furled sails to tatters, and disabling the masts and yards. If the barometer had not been observed, the ship would have been wholly unprepared, and shipwreck, with the loss of all on board, would in all probability have resulted. PNEUMATICS. 225- A water-barometer could be made, but it would be very unwieldy, for the tube must needs be more than 34 feet long. Besides, it would not answer in very cold weather, for the water would freeze. So short a column of the heavy fluid mercury balances the weight of the atmosphere that a barometer made with this is of very convenient size ; and then there is no danger of the mercury's freezing, except in the extreme cold of the arctic regions. The Barometer a Measurer of Heights. The atmosphere, as stated in 131, diminishes regularly in density as we go upward. The rate of this diminution has been accurately ascertained, and therefore we can estimate heights by the amount of pressure on the mercury in the barometer. At a height of 500 feet the barometer will be half an inch lower than in the valley below. At the summit of Mont Blanc it stands but half as high as at its foot, indicating a height of 15,000 feet. Du Luc, in his famous balloon ascen- sion from Paris, saw the barometer at one time standing at about twelve inches, showing an elevation of 21,000 feet. The Aneroid Barometer. The inconvenience of travel- ling in mountainous regions with a long tube filled with mercury is very great, and has led to the invention of another form of barometer which is called an Aneroid. The principle involved in its construction may be ex- plained by reference to Fig. 198. The curved tube a , when exhausted of air and hermetically closed, is sen- sitive to the variations in the pressure of the atmos- phere, the ends of the tube Fig. 19s. 226 NATURAL PHILOSOPHY. approaching with increased pressure, and receding with re duced pressure. Kow, if a similar tube be inserted in a case, and the curved ends be connected by means of a mechanical contriv- ance with a hand like that of a watch, we will have the simplest possi- ble form of the aneroid barometer. The hand points to figures around the dial-plate of the in- strument corresponding to the height of the mer- curial barometer. The general appearance of such an instrument is that of a watch, and it is but little larger (Fig. 199). 142. Relation of the Air's Pressure to the Boiling-point. Water heated to 212 degrees Fahrenheit (100 Centi- grade) boils that is, it becomes vapor. If water bo heated on the summit of a high mountain, it boils be- fore it reaches this temperature. On the top of Mont Blanc it boils at 180 degrees (82.2 C. ) that is, 32 degrees (17.8 C. ) below the boiling-point of water at the foot of the mountain. This is because the pressure of the air acts in opposition to the change of water into vapor ; and the less the pressure, the less heat will be re- quired to vaporize the water. We may illustrate this in- fluence of the pressure of air upon boiling by the follow- ing experiment. Let a cup of ether, which boils at 95 degrees (35 C.), be placed under the receiver of an air- pump. On rarefying the air by the pump, the ether will Fig. 199. PNEUMATICS. 227 boil. The general - effect of pressure upon boiling may be prettily illustrat- ed by another ex- periment. Boil some water in a thin flask over a spirit-lamp. While the steam is still issuing cork the flask tightly, invert it, and let the boiling cease. If, now, you pour some cold wa- ter over the flask, the boiling will com- mence again with considerable energy. Why? Because you condense the steam above the water by the application of cold, and thus remove the pressure. Then, again, if you pour hot water over the flask while the water is boiling, the boiling ceases, because the heat favors the accumulation of steam, and therefore renews the press- ure on the surface of the water. It is evident from what has been stated that most liquids have that form owing to the pressure of the atmosphere upon* them. If there were no atmosphere, ether, alcohol, the volatile oils, and even water, would fly off in vapor ; and the earth would be enveloped in a gaseous robe, for the particles of the vapors would be held to the earth by attraction, just as the particles of the air now are. 143. Siphon. The pressure of air upon fluids is beauti- fully exemplified in the operation of the siphon. This in- strument is simply a bent tube having one branch longer Fig. 200. 228 NATUKAL PHILOSOPHY. Fig. 201. than the other. Its operation is shown in Fig. 201. The tube having been first filled with the liquid, its shorter branch is placed in the liquid of the ves- sel A, which is to be emptied, and beneath the other is held the vessel B, which is to receive the liquid. As shown here, the opening of the long branch is below the surface of the liquid in B. It is manifest, therefore, that the air presses equally upon the surfaces in both vessels, tending to support the fluid in the tube, just as the water is supported in the jar in Fig. 194. But, not- withstanding these equal pressures, the liquid runs up the tube from A, and down its longer branch into B. Why is this? Since the pressure of a column of fluid is in pro- portion to its height, there is greater pressure or weight in the longer branch than in the other; and it is this difference in w r eight that causes the flow from A into B through the siphon. The difference in the columns in the two branches is not the difference in length of these branches, but the distance between the levels of the fluid in A and B that is, the distance from a to b. The operation, then, of the instrument is this : there is a constant tendency to a vacuum at C, the bend of the tube, from the influence of gravitation on the excess of fluid in the long branch over that in the short one. This tendency is constantly counteracted by the rise of fluid in the short branch, it being forced up by the pressure of the air upon the surface of the fluid in A. If the siphon were so placed that the surface of the liquid in A were precisely on a level with that in B, as repre- PNEUMATICS. 229 sented in Fig. 202, the liquid would remain at rest, for, since pressure is in propor- tion to the height, and the pressures on the two sur- faces are equal, there would be an exact balance. But Fig. 202. let the surface in B be ever so little lower than in A, and the flow will begin. And the greater the distance between the two levels, the more rapid will be the flow, for the greater will be the influence of gravitation in the long branch. Again, if the end of the long branch of the siphon be free, as in Fig. 203, the siphon will operate in the same way, for the air, pressing in all directions equally, tends to support the column of fluid in the long branch by a direct upward pressure, but is prevented from do- ing so by the excess of fluid in it above that in the shorter one. The operation of the siphon is commonly represented in this way; but we have given first the ar- rangement in Fig. 202, in order that you might more clearly see the principle of the instrument. Uses of the Sip/ton. The siphon is used chiefly for discharging liquids from one barrel or vessel into another. For convenience, it is often constructed after the plan of Fig. 204. To the long branch, B C, is attached the tube E D. It is used in this way : The end of the short branch, A, being intro- duced into the liquid to be drawn off, you close the K2 Fig. 204. 230 NATURAL PHILOSOPHY. run end C with a cork or your finger; and after filling the siphon by suction at E, you remove the finger and let the liquid run. The siphon has sometimes been used to drain pits and mines. It of course can never be used where the . elevation over which the tube is to bend is over 34 feet from the surface of the water to be discharged, for then the air would not press the water up to the bend of the siphon. The so-called cup of Tantalus is a pretty toy ; it consists simply of a goblet contain- ing a siphon which is concealed by a human figure. In Fig. 205 the figure is omitted to show the position of the siphon. On pour- ing water into the cup, it will remain there until you pour in enough to cover the bend of the siphon ; as soon as this is done, the siphon fills, and the water flows out through the long branch which passes through the bottom of the cup. The lips of the human Fig. 205. figure being on a level with the bend of the siphon, it is apparently prevented from drinking in a tan- talizing way. 144. Intermitting Springs. The operation of an intermit- ting spring is essentially the same with that of the cup of Tantalus. Fig. 206 represents such a spring. There is a cavity in a hill, sup- plied with water from a source above. There is also a passage from the cavity which takes a bend upward like a siphon. Now, when the water in the cavity is low, it will not run out from the siphon - like channel ; but when the cavity becomes filled above the level of the bend, the water will at once flow out, just as it does PNEUMATICS. 231 from the cup of Tantalus as soon as the bend of its siphon is covered. 145. Pumps. The accompanying cut represents a com- mon form of pump. A tube extends down into the well, B. Above this is the barrel of the pump, a 5, in which the piston works up and down. There is a valve in the piston, and anoth- er at the bottom of the barrel. Both of them open upward. We will suppose that the pump is entirely empty of wa- ter. If the piston de- scend, the piston valve shuts down, and the low- er valve opens, letting the air between pass up- ward. When the piston rises, the air above the piston cannot get below, for its pressure will shut the valve in the pis- ton. But there will be a tendency to a vacuum below the piston as it rises, and the air will pass up through the valve in the barrel to fill up the space. But why does the air rise? Fi s- 20L Because of the pressure of the air upon the surface of the water in the well. This forces up in the pump the water 232 NATURAL PHILOSOPHY. and the air above it, just in proportion as the downward pressure in the pump is lessened. If the pumping be con- tinued, all the air will soon be expelled, the water follow- ing it and flowing out at the opening, r. It is obvious that the pump will be useless if the valve in the barrel be over 34 feet above the surface of the water in the well, be- cause the pressure of the atmosphere will not sustain a higher column of water. In common language, the operation of the pump is attributed to what is called a principle of suction, as if there were a drawing-up of the water. But that water, you see, is not drawn, but forced up. So it is with all operations of a similar character. When we apply the mouth to suck up a fluid through a tube, the fluid is forced up because the pressure downward in the tube is removed. But how is it removed ? It is done by a move- ment of the tongue downward from the roof of the mouth ; thus removing the pressure of the air, in the same manner as the upward movement of the piston in the pump. To fill the space made by the movement of the tongue, the air is forced up the tube, the liquid following ; and, as in the case of the pump when the air is all expelled, the liquid will begin to dis- charge into tke mouth. Forcing-Pump. The forcing-pump is constructed differ- ently from the common pump. Its plan F is given in Fig. 208. It has a pipe, C D, and a barrel, A B, like the common pump. It has also the valve E at the bottom of the barrel. But it has no valve in the piston. Connected with the barrel is another pipe, F G, from which the water issues. This has a valve, H, opening upward. The opera-, tion of the pump is obvious. As the piston is drawn up, E opens and H shuts; and when it is forced down, E shuts and H opens. 146. Fire-Engine. The fire-engine has commonly two PNEUMATICS. 233 forcing- pumps, with a contrivance for making the water issue in a uniform stream. This contrivance can be ex- plained by reference to Fig. 209. The discharging -pipe, /* #, extends down into a large vessel, a, which is filled with air. The uniformity of the stream depends upon the elastic force of compressed air, as will appear from an ex- planation of the operation of the machine. When the wa- Fig. 209. ter is forced through the openings c b, it compresses the air in , for the tube h g is too small to allow all the water to escape that comes from the larger tubes, b b. Now, the moment that the piston is raised it ceases to force the wa- ter through c, and the elastic force of the compressed air operates, shutting down the valve c and forcing the water up h g. The result is a continuous rise of the water in this tube, and therefore a uniform stream. The valves d d permit the water in the reservoir surrounding the cylin- ders to enter when the pressure in e is relieved. By hav- ing two cylinders and pistons communicating wfth one air- 234 NATURAL PHILOSOPHY. chamber, , as in the figure, the continuity of the stream of water is doubly insured. QUESTIONS. 128. What does pneumatics teach? How can you show that air is ma- terial ? How that it has weight ? Describe the experiment. What is its weight compared with that of water? 129. What is said of the attrac- tion of the air by the earth ? Explain why some things rise and others fall in air. 130. How thick is the earth's air -covering? How is the height of the atmosphere ascertained ? At what rate does the earth move round the sun? 131. State the influence which gravitation has upon the density of the air at different heights. Give the comparison of air to wool. What is said of hydrogen and balloons? 132. In what are gases and liq- uids alike, and what are the results of the similarity? 133. What is the amount of pressure of the atmosphere on each square inch of surface ? Give the calculations in regard to this pressure. Show why the great pressure of the air does not produce injurious effects. 1 34. Describe the air-pump. Explain by Fig. 178 the plan and working of the air-pump. 135. State some of the experiments with the air-pump. How can you prove that air, like water, presses equally in all directions ? State the com- parison about the fish. What is said of the Magdeburg hemispheres ? Give the experiment with mercury. Explain the operation of the boy's sucker. Give the statements about sucker-like arrangements in animals. 136. State the experiment of the bladder and weight. Give the experiment with the India-rubber bag. State the experiment with the egg. Explain the opera- tion of the hydrostatic balloon. 137. What is said of the presence of air in various substances ? 138. What is said of the elasticity of air ? Describe and explain the condenser. What is meant by a permanent gas ? To what is the elasticity of the air due ? What is Mnrriotte's law ? Show how the air-gun operates. Explain the pop-gun. Explain the operation of gun- powder. Explain that of steam. 139. Describe and explain what is rep- resented in Fig. 193. Explain the collection of gases in the pneumatic trough. Explain the experiment represented in Fig. 194. What is said of tapping a barrel ? What causes the gurgling sound when a liquid is poured from a bottle? 140. How high a column of water will the press- ure of the atmosphere sustain ? How do you find from this the pressure of the air on every square inch of surface? How high a column of mer- cury will the atmosphere sustain? 141. Explain the barometer. Relate SOUND. 235 the incident given by Dr. Arnott. Why would not a water -barometer answer ? What is said of the barometer as a measurer of heights ? De- scribe the aneroid barometer. 142. How is the boiling-point influenced by the amount of the air's pressure? Give the experiment with ether. State the experiment with the flask. What would happen to liquids if the atmosphere were removed from the earth? 143. Explain the oper- ation of the siphon. Explain what happens if the siphon be placed as shown in Fig. 203. Explain the uses of the siphon. Explain the opera- tion of the cup of Tantalus. 144. How are intermitting springs account- ed for ? 145. Explain the operation of the common pump. Why does the water rise in the pump? How is sucking done? Explain the forcing- pump. 146. Explain the working of a fire-engine. CHAPTER XIV. SOUND. 147. That branch of natural philosophy, or physics, which treats of the phenomena of sound is called Acoustics, the name being derived from a Greek word meaning " I hear." Acoustics deals mainly with the produc- tion, transmission, and comparison of sounds, leav- ing the question of the pleasurable feelings they may arouse to the science of music. Sound may be defined as a sensation excited in the organs of hear- ing resulting from the vibratory motion of bodies, which motion is usually transmitted by the air. Bodies which emit clear and regular sounds are said to be sonorous. That the production of sound is due to their vibrations may be made manifest to the senses in many ways. If we place the hand upon a large bell that has been struck, we can feel the vibration. If we strike one of the ends of a tuning-fork upon some hard body, we can see the vibration, as represented in Fig. 210 by the dotted Fig. 210. 236 NATURAL PHILOGOPIIY. lines. If we examine the strings of a piano while it is played, the vibration of the larger strings is very notice- able. If we rub the edge of a drinking-glass with a moist- ened finger so as to produce a musical sound, the water within it will be thrown into waves by the vibration of the glass. In wind instruments, as the flute, horn, etc., the sound is caused by the vibration of the body of air within the instrument. In the common tin whistle or bird-call, Fig. 211, the sound is produced by the vibration imparted to the contained air by the impulse of the breath through the Fi - 211 - orifice, B. 148. An Analogy. The vibration of a sonorous body is much like that of a pendulum. The end of the tuning-fork, Fig. 210, on being struck passes to #, and in returning pass- es by the point of rest, A, just as a pendulum does, and reaches a. So, also, if a string, tightly stretched between two points, A B, Fig. 212, be drawn aside to D, as it flies back to C it will by its in- n ertia pass on to E, and will A