IN MEMORIAM FLOR1AN CAJORI tttoerriae Science Aeries NUMBER II. THE PHYSICAL PROPERTIES OF GASES BY ARTHUR L. KIMBALL cience THE PHYSICAL PROPERTIES OF GASES BY ARTHUR L. KIMBALL BOSTON AND NEW YORK HOUGHTON, MIFFLIN AND COMPANY <&ty fttoewibe prejstf, Cambridge 1890 Copyright, 1890, BY ARTHUR L. KIMBALL. All rights reserved. The Riverside Press, Cambridge, Mass., U. S. A. Electrotyped and Printed by H. 0. Houghton & Company, PREFACE. IN the following pages it is sought to give a general view of the physical properties of gases, developing as fully as the circumstances admit the reasoning by which physicists have been led, from the properties of gases as they are discov- ered by experiment, to the present conception of their nature. It is thus hoped to meet the wants of many who, lacking the time for a more thor- ough study of the subject, wish to know some- thing of modern views and the basis on which they rest. The general arrangement that has been adopted is to treat first the properties which belong to gases considered as fluid masses, and then to take up those which depend on their molecular structure, reviewing finally the evi- dence for the kinetic theory. The first few chapters, relating to the equilibrium and pressure of fluids, will be in the main familiar to those iv PREFACE. who have studied the subject in elementary text- books, but they are necessary to give complete- ness to the treatment. It has not been thought necessary to cite au- thorities, as any one wishing to make a more thorough study will turn at once to the standard works on physics, and will there be guided to the special papers relating to the subject. It is hoped that this little volume may con- tribute something towards the intelligent appre- ciation of some of those more hidden wonders of the universe which are only revealed through patient and earnest investigation. A. L. K. JOHNS HOPKINS UNIVERSITY, April 23, 1889. CONTENTS. CHAPTER PAGE I. INTRODUCTION . 1 II. PRESSURE AND BUOYANCY .... 23 III. ELASTICITY AND EXPANSION WITH HEAT 46 IV. GASES AND VAPORS ...... 78 V. AIR-PUMPS AND HIGH VACUA . . . .110 VI. DIFFUSION AND OCCLUSION . . 129 VII. THE THERMODYNAMICS OF GASES . . .149 VIII. AVOGADRO'S LAW AND THE KlNETIC THEORY 168 IX. GEISSLER-TUBES AND RADIANT MATTER . 199 X. CONCLUSION ... .... 221 LIST OF ILLUSTRATIONS. FIG. PAGE 1. PRESSURE OF GAS .27 2. TORRICELLI'S EXPERIMENT 30 3. FORTIN'S BAROMETER 35 4. BALANCE IN VACUO 42 5. BOYLE'S EXPERIMENT 47 6. MODIFICATION OF BOYLE'S EXPERIMENT . . 49 7. COMPRESSION OF GASES 51 8 a. CLOSED MANOMETER 59 8 b. CLOSED MANOMETER . . . ... .59 9. BOURDON GAUGE 60 10. JOLLY'S AIR THERMOMETER 70 11. PRESSURE OF SATURATED VAPOR .... 82 12. FARADAY'S EXPERIMENT 91 13. CAILLETET'S APPARATUS FOR LIQUEFACTION OF GASES 96 14. DIAGRAM OF PICTET'S APPARATUS ... 98 15. DIAGRAM OF CARBONIC ACID GAS .... 102 16. ISOTHERMALS OF A PERFECT GAS . . . 103 17. VON GUERICKE'S AIR-PUMP 110 18. TWO-CYLINDER Am-PuMp 112 19. AIR-PUMP 113 20. CYLINDER 114 21. MODIFIED GEISSLER PUMP 120 22. SPRENGEL'S AIR-PUMP 125 23. DIFFUSION .132 24. DIFFUSION OF GASES 133 25. MAXWELL'S VICOSIMETER 138 26. WORK DONE BY EXPANDING GAS .... 154 27. JOULE'S EXPERIMENT .... 157 viii LIST OF ILLUSTRATIONS. 28. HEATING AND COOLING ACTION OF A JET OF Am 163 29. VOLUMES OF GASES FOKMING WATER VAPOR . .178 30. DIAGRAM TO ILLUSTRATE THE DISTRIBUTION OF MOLECULES IN AIR ...... 198 31. RADIOMETER 202 32. GEISSLER-TUBE 212 33. CROOKES' TUBES .214 34. CROOKES' TUBES . . . . . . .216 35. CROOKES' TUBES 217 36. CROOKES' TUBES 218 37. FORMATION OF SPECTRUM 223 38. SPECTRUM OF CARBON BAND 225 39. CARBON BAND ANALYZED 226 A number of these cuts are reproduced from Ganot's Physics. THE PHYSICAL PROPERTIES OF GASES. CHAPTER I. INTRODUCTION. THE word " gas " is from a similar word in German which was first used by the alchemist Van Helmont, and was probably suggested by the German word geist, a spirit. 1 The atmos- phere is the most familiar type of gas, and ac- cordingly Cavendish, in the last century, speaks of other gases as " fictitious airs ; " " marine air " was the style given one of them, and in the ex- pression " dephlogisticated air " we are reminded of the time when a hypothetical substance, phlo- giston, played a most important part in chemi- cal theories, and was made to account for most chemical actions. 1 Van Helmont lived near the close of the fifteenth century, and was the most distinguished alchemist and physician of his time. He was the discoverer of carbonic acid gas, and found that it was produced when charcoal was burned. He was also able to identify it with the gas given off during the fer- mentation of wine and of yeast. This was the first gas to be distinguished from atmospheric air. 2 THE PHYSICAL PROPERTIES OF GASES. But before proceeding to the study of their physical properties it may be well to mention a few of the best known gases, with a brief state- ment of some of their chemical properties and relations, that it may be seen that the class of bodies which is to be considered is by no means a small or unimportant one. Hydrogen, originally known as " combustible air," is named from two Greek words, hudor, water, and gen-, to produce, because when it burns in air water is produced. It was the ear- liest known of all the simple gases ; is perfectly colorless and odorless, and a jet of it escaping into the air will burn with a pale blue flame. An animal breathing only hydrogen soon dies, not because the gas is poisonous, but from suffo- cation, because the hydrogen cannot supply what is necessary to sustain life ; but if a small quan- tity of this gas were mixed with the air which the animal breathes, no injury would result. Nitrogen, named from the Greek words nitron, niter, and gen-^ to produce, because it is a con- stituent of that substance, is also a colorless gas like hydrogen, but is distinguished from the lat- ter by not burning in air. It is like hydrogen in being unable to sustain life, and yet it is not poisonous, but constitutes four fifths of the air we breathe ; but in an atmosphere consisting ex- clusively of nitrogen, animals soon die. INTRODUCTION. 6 Oxygen was discovered by Priestley in 1774, two years after the discovery of nitrogen. Its name signifies the acid-former, since it was sup- posed at first to be an essential part of every acid. This is now known not to be the case, but the name still reminds us of the early days of chemical theory. Oxygen is a colorless and odorless gas, like hydrogen and nitrogen ; but unlike these, it is the element in the atmosphere which is necessary for the life of animals, and it is also due to its presence that ordinary combus- tibles burn in air. In an atmosphere of pure oxygen, not only will those substances which burn quietly in air be kindled into a more intense flame when once ignited, but a smoulder- ing candle will be relighted ; phosphorus will burn with sunlike brilliancy ; and a steel watch- spring will be consumed like a thread, throwing out dazzling scintillations. In the atmosphere oxygen is diluted by the presence of nitrogen, for every pound of oxygen there being four pounds of nitrogen present. Another well-known gas is chlorine, which was discovered by Scheele in 1774, the same year in which oxygen was first obtained. It was named >dephlogisticated marine air by Scheele, but in 1810 Davy recognized it as an element, and gave it its present name from chloros, the Greek word for green. It is a heavy greenish colored gas, 4 THE PHYSICAL PROPERTIES OF GASES. with a pungent, suffocating smell ; it rapidly de- stroys animal tissues, and is therefore dangerous to breathe. Many substances will burn in chlo- rine : powdered antimony takes fire sponta- neously when dropped into a vessel of this gas, and copper also will readily burn in it. The gases that have just been mentioned are all known as elements ; that is, chemists have been unable to resolve them into any other sim- pler substances. Besides these, there are many other gases which are compounds formed by the chemical union of two or more elements. Thus ammonia, which, when dissolved in water, is sold under the name of hartshorn, is a chemical compound of hydrogen and nitrogen, and is a colorless gas with its well-known intensely pun- gent odor, although neither of its components, hydrogen nor nitrogen, have any perceptible smell. Carbonic acid gas, or carbon dioxide as chem- ists now prefer to call it, is a compound of the two elements carbon and oxygen, and is the gas with which mineral waters are aerated ; it is produced when substances such as coal or wood or oil, which contain carbon, burn in the air. It is also a product of respiration in the higher animals, air before inhalation being rich in oxy- gen ; but after it is exhaled, the oxygen is found to be largely replaced by carbonic acid gas. INTRODUCTION. 5 Ordinary illuminating gas is a compound, or rather a group of compounds, of carbon and hydrogen. Equal volumes of hydrogen and chlorine, when mixed, will unite explosively if exposed to sunlight, and form a compound known as hydrochloric acid gas. Other well- known gases are nitrous oxide, or laughing gas, which has come so extensively into use as an anesthetic, and is a compound of nitrogen and oxygen ; sulphurous acid gas, which makes its presence known by its suffocating odor when sulphur is burned in the air ; and carbon mon- oxide, which is the poisonous gas that escapes from badly constructed stoves and furnaces. These substances are a few of the group of gases, and although very different in their chem- ical properties, as shown by the ways in which they combine with each other and with other substances, and by the compounds which are thus formed, are still so much alike in their physical characters that they are treated by physicists as a class by themselves. Material bodies are naturally divided into solids, liquids, and gases, the two latter classes being frequently included under the common name of fluids. The characteristic property of a solid is that it does not change its shape or size. Of course this requires to be qualified somewhat when it is recollected that all solids 6 THE PHYSICAL PROPERTIES OF GASES. are subject to change with changes of tempera- ture, most substances expanding with rising tem- perature ; while some, as certain crystals, expand more in one direction than in another, so that there is a change of shape as well as of size. Then, too, many solids change their form and size, owing to variations in the amount of mois- ture that they have absorbed. Wood swells with increased absorption of water, and it swells more across the grain than lengthwise. So also, when bodies are examined carefully, it is seen that all are subject to strains when forces are applied to them. However stiff and inflexible a body may seem to be, when it is moved or sup- ported differently, a close examination always shows that it has bent or sagged, or been sub- ject to some other strain. There is, therefore, no such thing known as a perfectly rigid body, though many may be treated as such for all ordinary purposes. But in solids each particle of the substance preserves its position relative to the remaining particles of the body, unless torn or pushed away by the exercise of consider- able force : there are reasons for thinking that the ultimate particles are not at rest, but in a state of active vibration ; but they always exe- cute their motions in very circumscribed regions, and are not free to travel from one part of the body to another. Liquid masses, on the other INTRODUCTION. 7 hand, change their forms on the application of the slightest forces, but remain constant in size or volume. This remark must be qualified, as in the case of solids ; for liquids also expand and contract with changes of temperature, and are slightly compressed when subjected to high pressures. But these changes in size are very insignificant, compared with the wonderful free- dom with which they adapt their shapes to the containing vessels, and flow from one point to another on the slightest disturbance of the level. In a liquid the particles of the substance are free to move over each other from one place to another, so that there may be currents set up by almost imperceptible differences in temperature. But this freedom of movement in the particles of a liquid is shown still more strikingly in the facts of diffusion. If, for example, into a ves- sel of pure water there is introduced carefully at the bottom by a pipette a strong solution of blue vitriol or copper sulphate, taking care not to set up disturbing currents, the blue sulphate solution, being heavier than the water, will form a layer at the bottom of the vessel, and the water will float upon it. If it is now allowed to stand, the lower part of the water will be seen to become gradually tinged with blue, which will deepen and creep upwards until in time the whole mass will assume a uniform appearance. It may 8 THE PHYSICAL PROPERTIES OF GASES. be shown that finally every part of the solution will be equally strong, the lower parts contain- ing no more of the sulphate than the upper parts. The particles of copper sulphate, as it were, elbow each other farther and farther apart until they are uniformly distributed through the whole region within which they are free to move. Nothing can show the freedom of motion of the particles in a liquid mass more conclusively than such an experiment, for the action goes on en- tirely irrespective of currents, and indeed, in all studies of diffusion, currents must be carefully avoided. In both of these classes of bodies there is no very noticeable change in the size of the mass when the pressure is altered. Liquid or solid masses may be therefore said to have definite volumes. A quart of water remains practically a quart, whether it is under a pressure of one pound to the square inch or five hundred. But in the case of gases, a class of bodies, is met in which neither the size nor shape is permanent. Gases expand and completely fill the vessels in which they may be placed, conforming to those vessels both in size and shape, and that, too, however large the vessels may be. Here, then, not only do the particles have all the freedom of movement that is seen in liquids, as the facts of diffusion are even more striking in the case of INTRODUCTION. 9 gases, but there is an additiona^freedom in that the range of motion of the particles is limited only by the surrounding solid or liquid bound- aries, and the volume of the mass of gas is not constrained to be constant, or even nearly so. To form a clearer conception of these pecul- iarities, it is important to glance briefly at what is known as the molecular theory of matter. More than nineteen hundred years ago Lucre- tius wrote : " There really exist bodies that are of a solid and eternal corporeal substance ; which bodies we prove to be the seeds and primary particles of things, of which the whole generated universe now consists. . . . And though the primary particles of matter are perfectly solid, yet all things which are formed of them may be ren- dered soft and yielding, as air, water, earth, and fire ; . . . but this happens because there is vacant space intermingled with the substance of things." And the Latin poet received his atomic philos- ophy from the Greek philosophers, Leucippus and Democritus, so that an atomic theory can- not be regarded as of modern suggestion. But the modern atomic theory dates from the begin- ning of this century, when John Dalton, an English chemist, who may well be called the founder of modern chemistry, placed upon a 10 THE PHYSICAL PROPERTIES OF GASES. scientific basis the theory thus vaguely antici- pated by poet and philosopher. There are two ways in which a mass of ap- parently homogeneous substance, such as water, may be thought of as constituted. It may be conceived to be perfectly continuous and struc- tureless, completely filling the space it occupies, each minutest part being exactly like every other part, and that, however small a portion is taken, it may still be divided into smaller parts, each exactly alike in properties. Or, on the other hand, it may be thought of as possessing a definite structure, and made up of certain parts, which are exactly alike, and are the smallest particles of the substance that can have an independent existence : if these units are themselves divided by any means, the parts will generally differ from each other, as well as from the original substance in their properties. With reference to the first theory, it is dif- ficult to form a conception of how a structure- less, continuous substance can be compressible, and all known substances can be compressed more or less. Yet it is true that we have no right to dispute the truth of this way of regard- ing matter, merely on the ground that compressi- bility is inconceivable in such a case ; for our power of forming conceptions of this nature de- pends on our experience, and to say that such a INTRODUCTION. 11 supposition is inconceivable is only to assert that our experience has not been such as to enable us to conceive of it. But there is abundant evi- dence, as will be shown later, that matter is not homogeneous beyond a certain point ; that is, there is a limit to the smallness of the parts into which any given kind of matter can be divided, and still retain its characteristic properties. If it is asked whether these smallest particles are to be regarded as in contact with each other in a mass of water, for instance, it may be replied that all that we know of contact is that, when one solid body is brought up to another, there is a certain point when there suddenly appears a force resisting any further approach, and beyond that point the exertion of very great force only brings them slightly nearer together. The bodies are then said to be in contact. In this sense the water particles are in contact, for only a slight compression can be effected by very great pressure. But if by contact it is meant that two particles are so close that they cannot be nearer, then the water particles cannot be said to be in contact ; and more than this, we have absolutely no evidence that any particles can ever be brought into such contact, or that there is any reality corresponding to this con- ception. It is important to be on our guard against 12 THE PHYSICAL PROPERTIES OF GASES. being misled, in speculations on the structure of matter, by the rough-and-ready terms which serve so well in practical life. It may be that the ultimate particles of matter are hard and absolutely incompressible, as Lu- cretius imagined, but there is no evidence either that they are or that they are not, and it is a question beyond the range of physical science. We can deal with matter, and investigate its properties, but what it is is a question which it is impossible even to ask in intelligible terms. Since we do not regard matter as infinitely homogeneous, and there is a limit to the small- ness of the particles into which any substance may be resolved and still retain the character- istic properties of the substance, the number of these ultimate particles or molecules in a given mass of substance is perfectly definite, though it may not be possible to determine it ; and so, when the average distance between the centres of two adjoining molecules is spoken of, the con- ception is perfectly definite, and this distance could be at once determined if we knew the number of molecules in a mass of known size. But when the size of a molecule is spoken of, there may be considerable doubt as to what is meant. If the molecules are supposed to be in contact in a liquid, then the average distance between the centres of adjoining molecules is INT ROD UCTION. 1 3 the measure of their diameters. This distance evidently becomes less as the pressure is in- creased and the substance is condensed, and, on the other hand, it increases as the substance ex- pands ; but if the substance were to be vapor- ized, and allowed to expand until the molecules were on an average three inches apart, would it be proper to speak of the molecules themselves as having expanded to this size? There are strong reasons for not doing this, and when a substance is so far expanded that the mole- cules are not hampered or interfered with in their internal vibrations by their nearness to others, we shall consider that they are no longer in contact; just as when two tuning-forks are sounding independently, however close they may be, we say they do not touch, until a discordant jangle announces that one is interfering with the other. According to the molecular theory, a sub- stance is conceived as made up of particles or molecules, the distances between their centres depending on the degree of compression of the substance. Each molecule is the smallest por- tion of that kind of matter that can exist by itself ; if the molecule be broken up or divided, then the chemical nature and properties of the substance are changed. It is not asserted that the molecule cannot be separated into simpler 14 THE PHYSICAL PROPERTIES OF GASES. elements, but that, if it is so separated, the com- ponent parts possess properties different from the original substance. Thus chemistry shows how to break up water into the two gases, hydro- gen and oxygen; and when it is thus decom- posed, there is always found twice as much hydrogen as oxygen, measured by volumes. The theory, then, is that each water molecule, when broken up, gives one volume of oxygen and two of hydrogen, and reasoning from chemical exper- iments indicates that the oxygen which enters into the water molecule is the smallest quantity that can exist in any known combination ; and since it has never been found possible to resolve oxygen into any simpler substances, this smallest particle of oxygen is known as an atom, from a Greek word signifying that which cannot be divided or cut. Similar reasoning, based on many chemical experiments, indicates that the smallest amount of hydrogen which ever en- ters into combination is one half that contained in the water molecule ; hence the latter is said to contain two atoms of hydrogen. To get a clear view of this theory, let us take an example, such as water, and, beginning with the atom, pro- ceed from the simpler to more complex struc- tures, trying to picture the relation of each to the others. First, then, we have the atom of hydro- gen and the atom of oxygen, each being the Iff TR OD UCTION. 15 smallest portion of those substances that is ever found to enter into combination with others. All the atoms of hydrogen are conceived to be exactly alike, and in a constant state of vibra- tion ; and just as a number of tuning-forks made exactly alike will all have the same period of vibration, and, when struck, will all give out sounds of the same pitch, so each of the hydro- gen atoms makes the same number of vibrations in a second as every other, and each atom may further have many different modes of vibrating, just as a flute may give different sounds when differently blown. When oxygen and hydrogen gases are not merely mixed, but are made to chemically combine, which may be brought about by igniting the mixture, or by passing an elec- tric spark through it, each atom of oxygen seizes upon two of the hydrogen atoms, and the three form a system or association which is the water molecule. It is not to be supposed that the atoms are actually in contact in the molecule, nor so closely connected as to prevent them from vibrating, though their natural modes of vibra- tion may be somewhat interfered with ; there is good evidence that they continue to vibrate in the new combination. Now in the molecule not only are its parts or atoms vibrating, but it is, as a whole, in rapid motion. All molecules of the same kind of substance are alike, and are 16 THE PHYSICAL PROPERTIES OF GASES the smallest particles of the substance that can have separate existence. In accordance with this theory, solids are bod- ies in which the molecules cannot pass from one part of the substance to another, but are so close together, and in some way so firmly held by their mutual attraction, that each molecule can vibrate only in a very restricted region, and about a mean position which it cannot leave, though in that position it is free to vibrate and spin round in a variety of ways. In a liquid the molecules are free to move from place to place, and are constantly rolling and slipping over each other, and moving from one part of the mass to another, held by their mutual attraction, it may be supposed, from going farther apart, but remaining at a sufficient dis- tance from each other to admit of considerable freedom. Thus they appear to be in a state of balance or equilibrium under two forces, one urging them closer together and keeping them from flying apart, and the other a repulsive force keeping them at a distance from each other. The nature of these forces is unknown, though it will appear later, when we come to take up more particularly the kinetic theory of gases, that in the gaseous state the repulsion may very likely be due to the motions of the molecules themselves, bounding to and fro in INTRODUCTION. 17 every direction, and striking against their neigh- bors. In gases the molecules are thought to be at such distances from each other, and vibrating with such energy, that when one strikes against another it rebounds, and, instead of being re- tained by their attraction, it flies off so as to soon be beyond its range, and continues moving in a straight line until it strikes against another particle, when it rebounds or glances off and con- tinues its course till a third particle is met, and so on. Evidently, if we conceive of a mass of such particles liberated in a large vessel, those molecules on the outside which are moving out- wards will continue till they meet the walls of the vessel, when they will rebound. Such a system of particles would soon distribute itself uniformly throughout the whole inclosed region, just as a gas does, and the continuous battering of innu- merable particles against the walls may be shown to produce a pressure obeying the same laws as gaseous pressure. Professor Clifford illustrates this theory most vividly in the following manner. A bell has certain natural periods of vibration, as shown by its always giving out the same tones when struck in one particular manner. Now imagine a num- ber of bells of different sizes fixed on the ends of elastic rods which all project from the same 18 THE PHYSICAL PROPERTIES OF GASES. centre. These bells have each their own proper periods of vibration ; each one can also swing to and fro as a whole on its elastic stem, and finally each may be supposed to be capable of spinning around on the end of its stem. This somewhat complex structure may represent for us a mole- cule. The bells may even be taken to represent the constituent atoms, each having its own proper periods of vibration, and each capable of spin- ning round and vibrating as a whole in the mole- cule. When we come to consider the relations between molecules, each may be thought of as surrounded by an elastic shell or framework, within which it vibrates, which represents the repulsive action by which molecules are kept apart. Of course it is not intended to suggest that there is anything of the shape of a bell in a molecule, or any long elastic stems ; the model is merely an illustration to embody the conceptions that we have of the varied capacity for vibration which it possesses. That molecules are capable of vibrating in many ways, cannot be doubted. To illustrate the state of the molecules in a solid, the model that has just been described may be conceived as held in position by elastic bands, so that when displaced it will vibrate to and fro, and perhaps rotate, but will never leave far its mean position. In a liquid the molecules are thought of as rolling over each other, kept apart INTRODUCTION. 19 by the elastic frame ; while in a gas they are fly- ing about in every direction, rebounding when- ever they come in contact either with the walls or with each other. The above brief sketch of the molecular theory has been given at this point as we shall often have occasion to refer to it, and the various phe- nomena of gases will be better understood as they are studied in their relation to the theory. The evidence on which the theory rests, and the reasoning by which it has been developed, will be discussed farther on in their appropriate connections. It is now held, with some variations in the details, by almost all scientific men ; and although when it is asserted that the ultimate particles of a body such as a block of iron, ordi- narily thought of as fixed and solid, are in a state of the most intense activity, making mil- lions of vibrations in a second, evidence will be demanded of the most convincing character, yet so many and so different are the facts that con- spire to point in this direction, that it seems nec- essary to conclude that what is thus conceived to be the structure of material bodies must in its principal features be very near the truth. As to the size of molecules, estimates have been made by Sir William Thomson by four entirely different methods, based on the distance of mo- lecular action, inferred from entirely different 20 THE PHYSICAL PROPERTIES OF GASES. physical facts, and the results have agreed in showing that the distance between two molecules of a drop of water is such that there are between five hundred millions and five thousand millions of them in a cubic inch. He expresses this re- sult in the following rather striking way, that, if a drop of water were to be magnified to the size of the earth, then the coarseness of grain that it would show, owing to its molecular structure, would be somewhere between that of a mass of cricket-balls and one of small-shot. This would be entirely beyond the range of vision of the most powerful microscopes ; and indeed as the high- est magnifying power of the best microscopes is about 6,000 to 8,000 diameters, it would be nec- essary to have an instrument that would magnify this result as much again, in order to render barely visible the molecular structure of water. Professor James Clerk Maxwell, who has him- self made most important contributions to the development of the molecular theory, makes the following very interesting remark in this connec- tion. On the basis of the above conclusion, " we may assume that the smallest organized particle visible under the microscope contains about two million molecules of organic matter. At least half of every living organism consists of water, so that the smallest living being visible under the microscope does not contain more than about INTR OD UCTJON. 21 a million organic molecules. Some exceedingly simple organisms may be supposed to be built up of not more than a million similar molecules. It is impossible, however, to conceive so small a number sufficient to form a being with a whole system of specialized organs. Thus molecular science sets us face to face with physiological theories. It forbids the physiologist from imag- ining that structural details of infinitely small dimensions can furnish an explanation of the in- finite variety which exists in the properties and functions of the most minute organisms." It is in the study of gases more than of any other class of bodies that light has been thrown on the structure of material masses. For the laws that relate to gases have a simplicity not found in dealing with other bodies ; and yet all are so closely connected that many conclusions arrived at from their study may be extended, with slight modifications, to the case also of liq- uids and solids. For it is now known that a gas, by suitable changes of temperature and pressure, may be made to become a liquid ; but so gradual is the change that there is no point during the passage from the one condition to the other that one can with certainty point out and say just here the change took place. So, too, a series of substances might be arranged, starting with pitch in its hard, brittle condition, and passing down 22 THE PHYSICAL PROPERTIES OF GASES. through various mixtures of it with tar or tur- pentine, ending finally in turpentine, which would at once make it obvious that there is every con- ceivable gradation between a solid and an un- doubted liquid. Gases have, therefore, a peculiar interest to the physicist, and have received a great deal of study, and it is to present the most important and interesting results of this study that the present volume has been prepared. CHAPTER II. PRESSURE AND BUOYANCY. THE principal laws of fluid pressure were dis- covered by Archimedes 250 years before the Christian era, and were set forth in a " Treatise on Floating Bodies ; " but it is remarkable that after him not a single step forward was taken for two thousand years, until the latter part of the sixteenth century, when Stevin, and a little later Galileo, laid anew the foundations of accurate knowledge on this subject. Not only had no ad- vance been made in the intervening centuries, but at the end of that period, when, in the revival of learning, modern science was just coming into existence, the propositions that had long before been established by Archimedes were very im- perfectly grasped. It was at this time that the fact, that the total pressure on the bottom of a vessel could be greater than the weight of the liquid which it contained, came to be known as the hydrostatic paradox, though it is per- fectly easily explained on Archimedes' principles. From the time of Galileo and Stevin of Bruges, however, there was steady progress. 24 THE PHYSICAL PROPERTIES OF GASES. We must now consider the principal laws of fluid pressure. When a mass of gas is inclosed in a vessel it expands and fills it, and being restrained from further expansion it exerts a pressure against the walls of the vessel. This pressure is the same on equal amounts of surface, so that, if a square inch of surface is pressed outwards with a force of ten pounds at one point of the vessel, then every square inch of the surface of the vessel will be pressed against with that same force, and this pressure is always exerted to push the sur- face directly outwards. If the perfect freedom of motion of the particles of a gas is borne in mind, it will be seen that this is exactly what should have been anticipated. When gas is being forced into a vessel, the pressure while the operation is actually going on will be slightly greater at the place where the gas is entering than at any other point ; but the instant it comes to rest, the pressure is found to be the same at every point. This property gases share with liq- uids, since it results from the perfect mobility of these substances. In solids this law evidently does not hold, for a pillar may support a pres- sure of many thousand pounds in one direction, while in the direction at right angles to this it is merely pressed against by the surrounding at- mosphere. If it were attempted to impose a like PRESSURE AND BUOYANCY. 25 pressure on the ends of a column of water, it would be found necessary to inclose it in a cyl- inder to prevent its flowing out sideways, and the pressure on every square foot of the cylinder surrrounding it would be exactly the same as that on each square foot of the ends of the col- umn. Another law of fluid pressure closely re- lated to that just mentioned is, that at any point in a fluid mass the pressure is the same in every direction ; for it must not be imagined that pres- sure is only exerted against the sides of the inclosing vessel, but every part of the fluid is in what is known as a state of stress, that is, every part is being pressed upon by the surrounding fluid, and reacting or pressing back by the same amount, these equal and opposite pressures bal- ancing each other, so that the particle remains at rest. And since the parts are free to move, there must be as much pressure urging any particle upwards as downwards, and the forces acting to push it to the right must be balanced by an equal force in the opposite direction ; otherwise the fluid would move, and there would be cur- rents. If, therefore, the open end of a tube con- nected with a pressure gauge is brought to some point in a mass of gas, the gauge will register the pressure at that point ; and it is entirely im- material whether the open end points upwards or downwards or sideways, since the pressure is the 26 THE PHYSICAL PROPERTIES OF GASES. same in every direction. A good example of fluid pressure is found in the ordinary steam- boiler. Suppose it is required to find how thick the iron must be in a cylindrical boiler to stand a pressure of eighty pounds to the square inch. There are two ways of thinking of this question : first, imagine the boiler to be cut in two parts by taking a slice across it, just as when a pipe is cut in two. How much force will be required to hold these two parts together when the steam has the above-mentioned pressure? If we im- agine a circular sheet of paper just the size of the section of the boiler put between the two parts when they are held together, it is evident that the pressure of the steam on one side of it will exactly balance the pressure on the other ; and so, if the pressure on every square inch is multiplied by the number of square inches in the cross section, the force with which the steam on one side of the paper is pushing against that on the other will be found, and this is exactly the force that is required to hold the two parts of the boiler together. If the boiler were two feet in diameter, its cross section would be 452 square inches ; and if the pressure were eighty pounds to the square inch, the force pushing the two parts apart would be more than 36,000 pounds, or eighteen tons. This force has to be supported by the iron shell of the boiler, which PRESSURE AND BUOYANCY. 27 is a little more than six feet in circumference. It must therefore be made of iron so thick that there would be no danger of pulling apart a strip of it six feet wide by a force of eighteen tons. The second way of looking at the problem is to imag- ine the boiler split by a cut running lengthwise through its centre. Then, just as before, to find the force which is necessary to hold these two halves together, the pressure must be multiplied by the number of square inches in this longitudi- nal section, and this force has to be borne by the strip of iron that was imagined to be cut through. This illustration has been given as it brings out very clearly that every part of the gas or fluid is under the same pressure, and also that that pressure is equal in all directions. In the cases that have just been discussed, the fact that all fluids have weight has been neglected. In consequence of this weight it is not exactly true to say that the pressure at any point in a mass of fluid is the same as at every other point. Take, for example, the case of a mass of gas inclosed in a cyl- inder, having a piston at the top (see Fig. 1). The upper layer of the gas is pressed upon simply by the force Fig. 1. with which the piston is pressed down ; but the bottom layer of gas is pressed upon, not only by 28 THE PHYSICAL PROPERTIES OF GASES. the pressure of the piston, but in addition by the weight of the gas lying above it, so that the pres- sure will steadily increase from the top to the bottom of the cylinder. The statement, there- fore, that in a fluid mass the pressure is the same at every point, is only true when the fluid has no weight. In small vessels containing gases the increase of pressure due to weight may be neg- lected, since all gases are very light ; but where liquids are concerned, the increase in pressure due to their weight must always be taken into account. The difference between the languid way in which water flows from an opening in the side of a vessel near the surface, and the ve- locity with which it spurts out of an opening at a greater depth below the surface, is entirely due to the increased pressure at the lower level due to the weight of the water above it. If in such a vessel, however, the pressure were to be in- creased, for example, if in the case repre- sented in Fig. 1 the piston were to be pushed down with greater force, then the pressure at every point in the cylinder would be increased by exactly the same amount. In a steam-boiler the pressure is chiefly due to the elastic force of the steam. The difference between the pressure at the top of a boiler and at its bottom, due to the weight of the steam and water, would scarcely be more than one or two pounds to the square inch. PRESSURE AND BUOYANCY. 29 The difference in pressure between two levels, measured in pounds, per square inch, will be the weight in pounds of a column of the fluid one inch square, extending from the upper level vertically downwards to the lower one. If the pressure per square foot is sought, the column of fluid whose weight is taken must be one square foot in cross section. Thus, at a depth of one hundred feet in water, the pressure will be greater than it is at the surface by the weight of a column of water one hundred feet high and one square foot in cross section ; and since one cubic foot of water weighs about sixty-two pounds, the pressure will be greater than at the surface by about 6,200 pounds per square foot, or forty-five pounds to the square inch. The diminution in pressure of the atmosphere from the earth's surface upwards was the first well-recognized evidence that the air has weight. The ancients understood that water would rise in a tube when the air was sucked out (the force-pump was known as early as 120 B. c., and was invented by Ctesibius of Alexandria), and the commonly accepted explanation of this fact which was given by the Aristotelian philos- ophers was that " nature abhorred a vacuum ; " but Galileo, about the beginning of the seven- teenth century, found that water could not be drawn up by a suction-pump to a greater height 30 THE PHYSICAL PROPERTIES OF GASES. than about thirty-four feet. It at once became a question why nature's abhorrence of a vacuum should cease at that point. Torricelli, a pupil of Galileo and his successor in the chair of math- ematics at Flor- ence, experimented on this point by using other liquids than water, and found that heavier liquids could not be raised as high as lighter ones, mercury, for exam- ple, which is thir- teen times as heavy as water, could only be drawn up one thirteenth the dis- tance that water could be raised. To repeat Torricel- li's most celebrated experiment, which was first performed in 1643, take a glass tube rather more than thirty inches long, and sealed up at one end, and after filling it with mercury cover the Fig. 2. Torricelli's Experiment. PRESSURE AND BUOYANCY. 31 open end with the finger, and, inverting the tube, introduce its open end below the surface of the mercury contained in a small trough, and remove the finger. No air has been allowed to enter if the experiment is carefully performed, and yet the mercury at once sinks in the tube until it stands about thirty inches above the level of the mercury in the trough. In this case, nature's abhorrence of a vacuum evidently ceases at the height of thirty inches, or thereabouts. Torri- celli, observing that the weight of a column of mercury thirty inches high was the same as that of a column of water thirty-four feet high, hav- ing the same cross section, and therefore that the pressure that would be required to support such a column of mercury would be also capable of raising water to the observed height, came to the conclusion that the effects were due to the pressure of the atmosphere, which, acting on the surface of the mercury in the open vessel, forced it to rise in the tube until the pressure of the mercury column exactly balanced that of the air without. As soon as air is admitted to the tube, the mercury sinks to the same level as in the vessel outside, since the atmospheric pressure is now the same within and without the tube. Pascal, wishing to test the truth of Torricelli's conclusion, requested one of his relatives to re- peat the experiment on the summit of the Puy de 32 THE PHYSICAL PROPERTIES OF GASES. Dome, a mountain in Auvergne ; reasoning that if the mercury is supported by the pressure of the atmosphere, and if that pressure is due to the weight of the air, then it should diminish as we ascend in the atmosphere. The result entirely confirmed his sagacity ; the column was found to stand three inches lower at the top than at the bottom of the mountain, showing that the pressure of the air was less, and could therefore be balanced by a shorter column of mercury. The amount of the pressure of the air can be measured with great accuracy by Torricelli's mercury column, for if the tube have a cross section of one square inch, the weight of the column of mercury, supported by the atmos- pheric pressure, will be about fifteen pounds, since a cubic inch of mercury weighs half a pound ; the pressure of the air is therefore about fifteen pounds to the square inch at the sea level. The pressure of the air may be shown by many experiments. If by means of an air-pump the air is pumped out of a strong, wide-mouthed jar, across the opening of which a bladder or other membrane is firmly tied, as the air is ex- hausted from the jar and the pressure dimin- ishes on the inside, the membrane is strained inwards until a point is at last reached when it is no longer able to keep back the atmosphere pressing upon it, and bursts with a loud report. PRESSURE AND BUOYANCY. 33 Otto von Guericke, a citizen of Magdeburg, after the experiments of Torricelli and Pascal had demonstrated the weight and pressure of the air, set himself to work to obtain a vacuum. He first took a stout barrel and filled it with water, and then tried to pump the water out, but as fast as the water was removed the air leaked in through the cracks and pores of the wood and took its place. He then constructed a hollow globe of copper, and was astonished to find that by means of his pump the air could be removed as readily as water could, and when the globe had been exhausted, on opening the stop- cock the air would rush in with a whistling noise. This was the first use of the air-pump, and took place in 1650. The pressure of the air was shown in a most striking way by this ingen- ious experimenter. Two large hemispheres of copper were constructed so that they fitted to- gether with great exactness, forming a spherical box. The edges being greased where they fitted together, the air was exhausted from the vessel through a stopcock in one of the hemispheres. And now the pressure of the air held the two parts so firmly together that it was found impos- sible to separate them, though when the stopcock was opened and the air entered they fell apart by their own weight. In 1651 this celebrated experiment was performed by Von Guericke be- 34 THE PHYSICAL PROPERTIES OF GASES. fore the Emperor Ferdinand III. at an imperial diet at Ratisbon ; two hemispheres of copper nearly two feet in diameter were used, and it is recorded that twenty-four horses, twelve on each side, were unable to pull them asunder, and that the whole court was filled with amazement at the sight. The barometer is an instrument for measuring the pressure of the air, and the mercury column of Torricelli is still the model of the most accu- rate of these instruments. The word barome- ter means instrument for measuring weight; it indicates merely the pressure of the air at the point where it is placed. All weather forecasts based on barometric observation are simply in- ferences, more or less probable, drawn from the observed changes in pressure and based on pre- vious experience. There are two kinds of barometers in common use, the mercurial barometer and the aneroid. The former, as its name implies, is simply the mercurial column of Torricelli, so arranged as to be portable and convenient for observation. When the tube of a good mercurial barometer is being filled, the mercury is heated and made to boil in the tube so as to remove every trace of air and moisture from inside the glass. The vacuum above the column of mercury is so good that, if the instrument is inclined so that the PRESSURE AND BUOYANCY. 35 mercury rises to the top of the tube, it will come against it with a sharp metallic click, as if struck with a steel hammer, owing to the lack of the cushion of air above it ; and if care is not used, the tube will be broken. To prevent an instrument of this sort from being broken in this way during transportation, the mercury is first made to completely fill the tube, which is then inverted, the instrument being so constructed that the reservoir at the bot- tom can be inverted with the tube with- out the escape of mercury. The figure represents a very conven- ient barometer of this form. The glass tube is surrounded by a protecting sheath of metal, through which a slit is cut, so that the height of the column may be observed. A scale is marked upon this sheath, so that the height of the column above the surface of the mercury in the reservoir may be easily read. It is evi- dent that when the pressure is small, the column will stand low, and mercury will have passed out of the tube into the reservoir, so that the level in the latter Yig. 3. will be somewhat raised ; but in measur- Fortin's ing the pressure, the height of the col- * umn must always be taken from the sur- 36 THE PHYSICAL PROPERTIES OF GASES. face of the mercury in the reservoir or trough ; and as the scale for reading the height of the column is fixed in this form of instrument, it always measures from the same fixed point, and therefore some device must be made use of to bring the surface of the mercury in the reservoir always to the same level before reading. This is attained by making the bottom of the reservoir of a flexible piece of leather which is raised or lowered by means of a screw until a certain little ivory index that is fixed so as to point down into the reservoir just touches the surface of the mer- cury ; the scale gives the height of the column above the tip of the ivory index. It is evident that this instrument must be hung or supported in a perfectly vertical posi- tion, since it is the vertical height of the column that measures the pressure. The aneroid barometer, as its name signifies, is constructed without any liquid. It is essen- tially a flat metal box, in shape something like a blacking-box. The sides and back are made of stout metal, while the top is made thin and flexi- ble. The air is exhausted from this box, which is then hermetically sealed, and the pressure of the atmosphere causes the thin elastic top to spring inwards ; by means of delicate levers, a pointer is made to move over a dial on the slightest motion of this thin metal plate; and as the PRESSURE AND BUOYANCY. 37 pressure fluctuates, every change is indicated by the pointer as it moves right or left over the dial. The indications of such an instrument must be compared with the mercurial barometer to determine the pressure corresponding to each reading. This form is often made as portable as a watch, and is very useful to travelers and explorers, as the mercurial instrument, though more reliable, is subject to accident. If a barometer were to be taken down into the ocean, the pressure would be noticed to rise regularly as we went down, at such a rate that the mercury column would stand one foot higher for every thirteen and a quarter feet increase in depth ; and this is true no matter to what depth we might go, for water is so incompressible that even at a depth of a mile a cubic foot of water will weigh only about half a pound more than at the surface, out of a total weight of sixty- three pounds, making the increase in weight only one pound in every one hundred and thirty, although the pressure reaches the enormous amount of one and one fifth tons to the square inch. The measurement of depths in water by means of a barometer would therefore be a very simple matter, if we only had one capable of reg- istering the great pressures to which it is sub- jected. In the atmosphere, on the other hand, although the pressure does diminish continuously 38 THE PHYSICAL PROPERTIES OF GASES. as we go upwards from the earth's surface, and this diminution of pressure is easily observed with the barometer, yet it is by no means even approximately true that a difference of ten feet in height near the earth's surface is accompa- nied with the same change in pressure as would have been observed for that same difference in height a few hundred feet above the earth's sur- face. The upper layers of the atmosphere rest on the lower, and therefore the lower layers are under greater pressure than the upper ; and since gases unlike liquids are very compressible, the density of the air near the earth's surface is very much greater than in the higher regions. At a height of about three and a half miles above the sea level, the weight of a cubic foot of air is only half what it is at the surface of the earth, and at seven miles only one fourth as much, and so on. The weight of the air might be found by tak- ing readings of a barometer at two points, one vertically above the other; the difference be- tween the readings gives the height of a mercury column one inch square that would be required to balance the column of air of the same cross section, reaching from the lower point up to the upper one. If the barometer were to be taken up ninety-two feet above the earth's surface, the fall in the mercury would be about one tenth of PRESSURE AND BUOYANCY. 39 an inch, so that a column of air ninety-two feet high weighs only as much as a column of mer- cury one tenth of an inch high, that is, mercury is a little more than eleven thousand times as heavy as the same volume of air at the earth's surface. A mercurial barometer will readily show a difference in pressure between one floor and an- other in an ordinary dwelling-house, while some aneroids are so sensitive that a difference in reading can be detected when the instrument is raised from the floor to a table or shelf. Two hundred and fifty years before the Chris- tian era a most important principle was discov- ered by Archimedes, the distinguished philos- opher of Sicily. It is related that a goldsmith, to whom a mass of gold had been committed by Hiero of Syracuse to be wrought into a crown, was suspected of cheating his royal patron, and of having alloyed the gold with silver. The weight was as it should have been, and no way of solving the question without injuring the crown was known. It is said that the method of solving the difficulty occurred to Archime- des as he was entering the bath, and noticed the rise in the level of the water as his body became submerged, and that in the eagerness and joy of discovery he sprang from the bath, and ran to his house, exclaiming, " Eureka ! " (I 40 THE PHYSICAL PROPERTIES OF GASES. have found it.) Taking a vessel filled with water to the very brim, he immersed in it a lump of silver of exactly the same weight as the crown, and caught the water that ran over ; this gave the amount of water equal in volume to the sil- ver. Then, after filling the vessel again, a lump of gold of the same weight was immersed, and the equivalent quantity of water obtained in this case also, and it was found to be less than when the silver was employed. Finally the crown itself was put into the vessel, and the displaced water caught and measured, and found to be less than that displaced by the silver, but more than was displaced by the gold. From these three measurements the gold that had been re- placed by silver was readily determined, and the goldsmith was no doubt sufficiently pun- ished. This investigation led to the discovery that when a body is immersed in a liquid it is buoyed up by a force which is exactly equal to the weight of the displaced liquid. Suppose, for example, a piece of iron weighs 73 pounds in air ; now, if it is hung so that it is entirely immersed in water while being weighed, it will be found to weigh only about 63 pounds, and the principle of Archimedes asserts that this difference of ten pounds is the weight of the water displaced by the iron, or, what is the same PRESSURE AND BUOYANCY. 41 thing, is the weight of a mass of water of the same volume as the iron. The weight of a body is the force with which it is drawn to the earth by the attraction between them. This force is opposed, when the body is immersed in a liquid, by the upward pressure or buoyant force of the liquid. A little consideration will make evident the truth of the principle that has been stated. For in a mass of liquid at rest, think of a certain portion as separated from the remainder by an imaginary wall around it. This portion of liquid is attracted by the earth, as all other masses are, and therefore has weight ; but instead of sinking downwards it remains in equilibrium, for the surrounding liquid has weight also, and buoys up the part that we have selected. Since this portion is at rest, it is therefore buoyed up by a force which exactly balances its weight. Now suppose a piece of iron of exactly the shape of the selected portion of liquid should be put in its place, it is surrounded and pressed upon and therefore buoyed up exactly as was the mass of liquid. But the force by which the liquid mass was buoyed up was exactly equal to its weight ; therefore the iron, being supported by the same force, is buoyed up by a force equal to the weight of the liquid that it replaces. This important fact is true not only of liquids 42 THE PHYSICAL PROPERTIES OF GASES. but of gases also, and so we find that all objects are buoyed up to some extent by the air sur- rounding them. A familiar experiment is to take a pair of scales in which a light, bulky ob- ject, such as a hollow globe, is exactly balanced by weights that are solid and made of brass or platinum, or some dense sub- stance, and, put- ting the whole ar- rangement under the receiver of the air pump, exhaust the air. There is no longer a balance, as the air pres- sure is removed; but the scale beam tips, showing the globe to be heavier than it appeared to be when weighed in air. Evidently the globe when sur- rounded by air was buoyed up by it, and so also were the weights by which it was balanced. But the buoyant force is equal to the weight of the air that is displaced, so that the body having the largest volume is buoyed up most. In the case that has been taken, the globe displaced more air than did the weights, and therefore was PRESSURE AND BUOYANCY. 43 more buoyed up, so that the weights that were sufficient to balance it in air when aided by this buoyant force were not able to support it when the air was exhausted. In all exact determinations of weight it is therefore necessary to take the supporting effect of the air into account. It would be of course exceedingly inconvenient to actually make weighings in a vacuum, but by an ingenious method of conducting delicate weighings this difficulty is overcome, and all the accuracy ob- tained that is desired. This method is to make the volume of the bodies in one pan of the bal- ance the same as the volume of those in the other. Both sides are then buoyed up by the same force, since they displace equal weights of air. A very good example of this practice is found in the experiment made by the celebrated French physicist Regnault to determine the density of air and other gases. A delicate balance was employed, and from each pan was suspended a large glass globe. One of these was full of air and kept closed. The other was provided with a stopcock, so that the air could be pumped out of it ; both were nearly of the same size, so that they would be equally supported by the sur- rounding air, and of almost the same weight, so that only a few small weights would be required 44 THE PHYSICAL PROPERTIES OF GASES. to make them exactly balance. The globe with the stopcock was then exhausted, and weights added until there was an exact balance. The stopcock was then opened, and, after dry air at a known temperature and pressure had been al- lowed to flow in and fill it, weights were added until equilibrium was again obtained. The amount of these additional weights required to bring about a balance, after the air had flowed in, was the weight of that quantity of air. In both cases the buoyant effect of the outer air was balanced by having the two equal globes ; the weights themselves also displaced a certain amount of air, but this could easily be allowed for ; and since this correction would be a very small part of the whole weight of the air, no se- rious error would be introduced even if it were not known with very great exactness. So a chemist, in making an exact weighing of a very small quantity of substance, will put in one balance-pan the vessel containing the sub- stance to be weighed, and in the other pan the weights, together with another vessel as near as possible like the first ; the weights added repre- sent the actual weight of the substance, together with whatever small difference there may be in the weights of the two vessels, and the buoyant effect of the air is largely neutralized. It may seem that this supporting power of the PRESSURE AND BUOYANCY. 45 air is so small as to be entirely insignificant, but a globe a foot in diameter will weigh less in air than in vacuum by considerably more than half an ounce ; while the air displaced by the body of a large man will weigh nearly a quarter of a pound, under the ordinary conditions of temper- ature and pressure found at the surface of the earth. By this principle the lifting power of balloons is easily explained, for a balloon is merely a con- trivance by which a very light body displaces a large amount of air. To find the lifting power of a balloon it is only necessary, then, to estimate the weight of the air that is displaced, which is the measure of the buoyant force that is called into play: from this must be subtracted the weight of the balloon itself, with its car and ap- pendages, and also the weight of the gas that fills it, and the difference is the measure of the addi- tional weight necessary to just keep it from ris- ing. CHAPTER III. ELASTICITY AND EXPANSION WITH HEAT. SOON after the time when the discoveries of Galileo had given such an impetus to the scien- tific study of nature, and the discovery of the weight of the air, followed by Torricelli's demon- stration of its pressure and Pascal's conclusive experiments in the same direction, had especially roused interest in the properties of gases, a com- pany of learned Englishmen interested in the study of science arranged to hold occasional meetings, where, unmindful of the political ex- citement and disorder of the times, they might report on their various investigations, and dis- cuss them together for mutual instruction and profit. This company was incorporated in 1662, and became the celebrated Royal Society of London ; and one of these original members was Robert Boyle, whose name is now most commonly recalled in connection with his careful investiga- tion of the elastic properties of the air. When Boyle took up this work, although it was known that air could be compressed and expanded, no experiments had been made to find ELASTICITY AND EXPANSION WITH HEAT. 47 the relation between its change of volume and the force applied to produce the compression. The apparatus employed by him was as simple as it was effective. A glass tube was taken, and bent in the shape indicated in Fig. 5. The short arm was only a few inches long, and sealed at the upper end ; the other arm was more than six feet in length, and open at the top, so that mercury could be readily poured in. The tube was carefully supported with both arms vertical. A little mercury was now poured in, which lying in the bend of the tube sep- arated the air in the short arm from the outer air. At first, when the mercury just filled the bend of the tube, it stood at the same level in both arms, since the air inclosed was at the same pressure as the outer air ; g ' but as more mercury was added, the level rose in both arms of the tube, Boyle's Experi- ment. 48 THE PHYSICAL PROPERTIES OF GASES. but more rapidly in the long arm, so that by the time the air in the short arm had been com- pressed to one half its original volume the mer- cury stood twenty-nine inches higher in the long arm than in the other. But, on observing the barometer at the same time, it was found that the mercury stood at a height of twenty-nine inches, showing that the pressure of the atmos- phere was capable of just supporting such a col- umn of mercury. Now the air inclosed in the short arm was compressed by the weight of the column of mercury twenty-nine inches high, and also by the pressure of the atmosphere on the top of that mercury column. It was, therefore, under a pressure twice as great as that of the atmosphere ; but its volume had become reduced to one half of what it was at first. Continu- ing the experiment, on adding mercury until the height of the column was fifty-eight inches, or sufficient to produce a pressure twice as great as that of the atmosphere, the inclosed air, which was under a pressure of three atmospheres, due to the mercury column and the pressure of the external air on its surface, was found to be com- pressed to one third its original volume. Con- tinuing these experiments through the whole range of pressures possible with the tubes at his command, Boyle arrived at this law as express- ing the behavior of gases when compressed with- ELASTICITY AND EXPANSION WITH HEAT. 49 out change of temperature : The volume of a gas diminishes in the same ratio as the pressure upon it is increased. Boyle's apparatus that has been described was, however, only suitable for studying gases with pressures greater than one atmosphere. Later he devised a modifi- cation of the experi- ment, by which he was able also to examine the changes of volume when the pressures were less than one atmosphere. A long, straight tube was ta- ken, sealed at one end, and nearly filled with mercury, and the air filling the remaining space was entrapped by inverting the tube in a deep trough of mercury made by tak- ing a second tube rath- er larger than the first, closed at the bottom, and long enough so that the first could be almost Fig. 6. 50 TEE PHYSICAL PROPERTIES OF GASES. entirely submerged in the mercury with which the second was filled. The first tube was then thrust down into the bath until the mercury stood at the same level within the tube as without, indicating that the inclosed air was at the same pressure as the outer air, and the volume of the air within the tube observed. The tube was then raised, so that it stood higher above the surface of the mercury in the bath ; and the mercury within the tube was also observed to rise, though not as much as the tube, so that the space occupied by the air was greater than before. When the tube had been raised so far that the air-space was double that which it had been at the atmospheric pres- sure, it was observed that the mercury had risen in the tube to just one half the height of the barometric column. The mercury then just bal- anced one half of the atmospheric pressure, so the air above the mercury had to resist only the remaining half ; its volume was, therefore, doub- led when the pressure was reduced to one half of what it had been. When the tube was raised still more, the mercury within rose higher as the volume of the air increased ; and when the mer- cury had risen to two thirds of the height of the mercury in the barometer, the air had in- creased to three times its original volume, for the mercury balanced two thirds of the atmos- pheric pressure, and the inclosed air was only ELASTICITY AND EXPANSION WITH HEAT. 51 subject to the remaining one third. The law which had been established for pressures greater than one atmosphere was by these experiments shown to be true also for smaller pressures. This property of the air, that its volume in- creases in the same ratio as the pressure dimin- ishes, is by similar experiments found to be very nearly true for all gases, and is ordinarily known in this country as Boyle's Law. 1 The following ex- periment gives a striking illustration of the similar be- havior of different kinds of gases un- der pressure : Take a strong vessel with a number of open- ings in the top, in which several glass tubes can be firmly screwed. The up- per ends of these tubes are closed, and the lower ends project below the surface of mercury contained 1 On the continent of Europe it is more commonly styled Mariotte's Law, from a French investigator who traversed the same ground fourteen yeai-s after Boyle's results had been communicated to the Royal Society. Fig. 7. 52 THE PHYSICAL PROPERTIES OF GASES. in the vessel. Suppose that, in putting the ap- paratus together, one tube is filled with oxygen, one with hydrogen, one with carbonic acid gas, one with nitrogen, and one with dry air. If now by means of a pump more mercury is forced into the vessel, these gases will be compressed, and the mercury will rise in the tubes. If the tubes are carefully examined, each volume of gas will be found to have been compressed by very nearly the same proportional amount. This is obvious if the tubes are all of the same length, as in that case the mercury will rise to the same height in all the tubes. If, however, the pres- sure is raised to more than two or three atmos- pheres, the various gases are observed to behave differently. The mercury is seen to rise higher in the tube containing carbonic acid gas than in the others, showing that at high pressures Boyle's law cannot be true for all these gases. We shall have to consider this fact more in detail in the next chapter. 1 For the present it is sufficient to remember that in case of dry air at ordinary temperatures, Boyle's law is a very close state- ment of what takes place between the lowest pressures we can produce and pressures of about 1 In the figure two of the tubes are represented as contain- ing gases such as ammonia and sulphurous acid gas, which con- dense at comparatively low pressures, and so only the two right hand tubes show even approximately equal volumes, though the pressure is only about four atmospheres. ELASTICITY AND EXPANSION WITH HEAT. 53 160 atmospheres, or 2,400 pounds to the square inch. Air compressed by a pressure of seventy- five atmospheres would have a volume about two per cent, less than that computed from Boyle's law, but this is the greatest divergence that would be found below 160 atmospheres' pres- sure. The remarkable simplicity of this law of the compression of gases distinguishes them from all other classes of bodies, and indicates a sim- plicity of structure that no other bodies possess, and consequently gives to their study a profound interest. It has been already seen that the lower layers of the atmosphere near the earth's surface are under pressure from the weight of the atmos- phere above, and that, if we climb a mountain and carry with us a barometer, the pressure will be observed to steadily fall as we approach the summit. By means of Boyle's law we are now able to compare the density of the air on the mountain with that below. For if the barometer stood at thirty inches at the foot of the mountain and at twenty-seven at its summit, then the pres- sure has diminished by one tenth; and so by Boyle's law a mass of air, which at the foot of the mountain occupies a volume of one cubic foot, will at the top have expanded so as to occupy one foot and one tenth. The air is, therefore, one 54 THE PHYSICAL PROPERTIES OF GASES. tenth less dense at the top of the mountain than at its base, provided it is at the same tempera- ture. Since the density of the air diminishes from the surface of the earth upwards, the pressure indicated by the barometer will obviously not diminish as rapidly at great heights as near the surface. The fall in the mercury column, in going from the base to half the height of the mountain, will be much greater than that during the remainder of the ascent. This complicates somewhat the determination of heights by means of the barometer, yet by making use of Boyle's law the relation between the height and pressure may always be determined. The law according to which the pressure di- minishes may be best understood by an exam- ple. Suppose one has ascended a mile above the surface of the earth, and finds that the pres- sure has diminished to four fifths of what it was at the surface ; then, if he continues to rise, at a height of two miles the pressure will be found to be four fifths of what it was at one mile above the surface, and consequently sixteen twenty-fifths of its value at the earth's surface. In the same way, at a height of three miles the pressure will be four fifths of what it was when two miles high ; and so an ascent of one mile, whether near the surface or at a great height, ELASTICITY AND EXPANSION WITH HEAT. 55 will always be accompanied by the same propor- tional diminution in pressure. A similar law holds, also, whatever may be the intervals which are taken. The fall in pressure in a rise of one thousand feet will evidently be very different from that in a rise of one mile ; but during the ascent of one thousand feet, starting at any point, the pressure will diminish to a certain proportional part of the pressure at the starting place, and that proportional decrease in pressure will be the same whether we start from the surface or any height above it. A compact way of expressing this law is, that, as heights measured above the earth's surface increase in arithmetical ratio, the pressures di- mmish in geometrical ratio. In the case of our atmosphere this diminution is such that at about three and a half miles above the earth the pressure is one half what it is at the surface. At seven miles it will therefore be only one fourth, and at ten and a half miles one eighth as much. At this rate it is easy to reckon that at thirty-five miles above the earth the pressure and density of the atmosphere must be one one-thousandth part of what it is at the sea-level, and at seventy miles only one mil- lionth part of that amount. It must be borne in mind, however, that these results hold only in case of uniform tempera- f 56 THE PHYSICAL PROPERTIES OF GASES. ture; on account of the coldness of the upper air the pressure at a great height would be even less than in the case considered. From what has been observed in the case of meteors, which are small masses moving with im- mense velocities, and which are heated, on com- ing into our atmosphere, to brilliant incandes- cence, simply from the heat developed by the friction of the air against them as they rush through it, some have believed that the atmos- phere extends to a height of 100 or 200 miles above the earth's surface, though in a condition of extreme tenuity. And this greater height is favored by observations on the extent of the twi- light made at Kio Janeiro, which indicate so strong a reflected light from the atmosphere fifty or sixty miles above the earth's surface, as to make it improbable that the atmosphere at that height is of the high degree of rarefaction indicated by Boyle's law. In connection with the law of the expansion of gases, there are some points of great interest in the ordinary gas-balloon. A most absurd proposition has recently been made to construct balloons of a thin, rigid shell of steel, and then to exhaust the air from the interior, and thus get rid of the weight of the gas with which or- dinary balloons are filled. A slight calculation ELASTICITY AND EXPANSION WITH HEAT. 57 of the weight of a steel shell, sufficiently strong to withstand the enormous crushing force to which it would be subjected by the atmosphere, will convince any one that a silk bag filled with hydrogen possesses substantial advantages. But let us for a moment suppose that we possess such a balloon, and that it displaces a weight of air which at the start is fifty pounds greater than the total weight of the balloon. This ex- cess of the buoyant force over its weight will cause it to rapidly ascend, but as it rises it comes into regions where the air is more rarefied ; and since its own size remains unchanged, the weight of the air which it displaces will become less and less, until at a certain height the buoy- ant force exactly balances its weight and it can- not rise farther, but floats at a constant height above the earth. In case of the ordinary gas-balloon, the case is quite different. The silken bag is never en- tirely filled with the light gas, but room is left for it to expand. If it is desired to ascend to a height of three or four miles above the surface, the balloon must not be more than half filled with gas at the start ; for as it rises and the pres- sure of the atmosphere diminishes, the inclosed gas expands, and unless the balloon gives room for free expansion the pressure on the inside may soon become sufficient to cause it to burst. 58 THE PHYSICAL PROPERTIES OF GASES. It is interesting to observe that, since all gases have been found to expand by very nearly the same amount for equal changes in pressure, the expansion and consequent rarefaction of the gas within the balloon, as long as it is free to expand, will keep pace with that of the air without, so that if the excess of the buoyant force over the weight of the balloon is ten pounds at the earth's surface, as it rises into more rarefied regions that excess will remain the same ; for though the balloon floats in a less dense atmosphere, its vol- ume is increased just enough, by the expansion of the contained gas, to make it displace the same weight of air as at the earth's surface. The height, therefore, to which it can rise is lim- ited only by the capacity of the balloon, which of course prevents unlimited expansion, and when the point is reached where the gas has completely filled its envelope, then, on further rise, it must be allowed to escape by the safety valve, or the pressure may become dangerously great. But since the buoyant force diminishes far more rapidly than the weight of the balloon due to any such escape of gas, it will soon come to a point beyond which it cannot rise, and where it floats at a constant level. The reason that the buoyant force diminishes as the gas escapes, while the balloon is rising into rarer regions, is that the volume of the bal- ELASTICITY AND EXPANSION WITH HEAT. 59 loon being supposed now to be constant, it being completely inflated, while the inclosed gas has expanded so that one cubic foot has es- caped, the air with- out has expanded at the same rate, so that the buoyant force is diminished by the weight of a cubic foot of air, while the weight of the balloon is less by the weight of the cubic foot of gas that escaped. The buoy- ancy or force causing the balloon to rise is therefore dimin- ished by the differ- Fig. 8 a. ence between the weight of the gas that escapes and the weight of the same volume of air under the same pressure. The compressibility of gases has been made use of in the construction of pressure gauges. Such a gauge is represented in the figure. It consists of a strong glass tube, closed at the top, filled with air at the ordinary pressure of the at- mosphere, and screwed firmly into an iron reser- 60 THE PHYSICAL PROPERTIES OF GASES. voir containing mercury. When pressure is transmitted to the surface of the mercury through a small tube communicating with the reservoir, the mercury is forced up into the tube, and the air is compressed. The amount of the compression of the air gives at once, by Boyle's law, the pressure to which it is subjected ; the pressure in the mercury reservoir is, then, equal to the pressure of the compressed air, together with that due to the column of mercury that stands in the tube above the level in the reser- voir. The chief defects in this form of gauge for measuring high pressures are, that it is very sensitive to changes of temperature, and when the pressures are great, and the'air is compressed into small compass at the top of the tube, a great change in pressure will only be indicated by a very small change in the volume of the compressed air ; the pressures cannot, therefore, be read accu- rately.- The ordinary instru- ment employed for meas- uring high pressures is based on another princi- ple, and is the invention of a Frenchman, M. ELASTICITY AND EXPANSION WITH HEAT. 61 Bourdon. It will perhaps not be out of place to give here a brief description of the Bourdon spring gauge. A piece of round brass tube three quarters of an inch in diameter and about ten inches long, flattened so as to have an ellipti- cal or oval cross section, is closed at each end with a brass plate, and bent into the form of a nearly closed ring three or four inches in diameter, so that the breadth of the ring is somewhat greater than its thickness, this being also the way in which the tube is most easily bent. If now, through an opening in one end, air or water is forced into the flattened tube, it will spring a little and become more nearly circular in cross section, and in so doing will slightly unbend, as if to straighten out. This ring-shaped metallic box of oval cross section is the Bourdon spring ; and when one end is rigidly fixed, and provided with a tube through which the liquid or gas un- der pressure is admitted, the other end will move as the spring bends or unbends under the fluctu- ations of pressure. This motion is communi- cated by means of a delicate chain or lever to the index, by which it is greatly amplified, so that a slight motion of the spring gives rise to a large movement of the index. This form of gauge is the one in most common use for indi- cating steam pressures. One other interesting application of Boyle's 62 THE PHYSICAL PROPERTIES OF GASES. law should be mentioned. A great source of difficulty in taking soundings at sea from a steamer in motion is that the sounding-line does not go vertically down, but in a slanting direc- tion. Sir William Thomson has devised a form of sounding apparatus in which the depth is in- dicated by the pressure at the bottom. A glass tube two feet long, having a bore of perhaps an eighth of an inch in diameter, and sealed at one end, is coated on the inside with a substance which changes its color on coming in contact with sea-water. This tube, with its open end downwards, is fixed in an iron tube and lowered to the bottom by a wire. When it is drawn up, the discoloration of the inner coating shows how far the sea-water, under the pressure due to the depth, has been forced up into the tube, compress- ing the air which it contained. From the com- pression of the air, the .pressure is at once known by Boyle's law, and therefore the depth of the water. And this result, it will be seen, is entirely independent of whether the tube was lowered to the bottom in a straight line or in a slanting direction ; it is only necessary to know that the tube actually went to the bottom, and then the discoloration seen when it is drawn up tells all that is necessary to determine the depth. Boyle's investigation showed clearly how gases behaved under changes of pressure when the ELASTICITY AND EXPANSION WITH HEAT. 63 temperature was unchanged. It is important to inquire in what way a rise in temperature affects a gas. Do gases show any greater simplicity of behavior in this respect than other classes of bodies? To make the investigation as simple as possible, the pressure may be kept constant, so that the changes in volume that are observed may be wholly due to change in temperature. Gay-Lussac, a French physicist, made a study of this subject about the year 1801, and em- ployed the following method. A glass bulb with a long tubular neck was taken and filled with dry air, which was separated from the external air by a short column of mercury in the tube. The whole was placed in a horizontal position in a bath, where it could be cooled to the freezing point by packing it with melting ice, or warmed by heating the water to any desired tempera- ture. As the air was heated and expanded, the mercury column was pushed farther along the tube, and by noting its position for each temper- ture, and determining the volume of the bulb and the size of its stem, the increase in volume of the air corresponding to each position of the mer- cury thread could be easily determined. It will be noticed that the inclosed air was subject to the pressure of the atmosphere, since the freely moving column of mercury was all that sepa- rated the two. The pressure of the air was 64 THE PHYSICAL PROPERTIES OF GASES. very nearly constant, and could be observed by means of a barometer, and a correction made to the result in case it had changed. Of course, this early experiment is open to many criti- cisms. The mercury thread cannot be supposed to move perfectly freely and without trace of friction, and the glass itself of which the bulb is made expands with the rise in temperature, and this causes the inclosed air to appear to expand less than it really does, but the main results ob- tained by this means are interesting and impor- tant. Gay-Lussac found that a mass of air, when raised from the freezing to the boiling point of water and kept at constant pressure, in- creased in volume by about J^jf of its volume at the colder temperature. Similar experiments were made when the bulb was filled with other gases, such as hydrogen, nitrogen, carbonic mon- oxide, carbonic acid gas, nitrous oxide, cyano- gen, and sulphurous acid gas, and, singularly enough, these all showed almost exactly the same rate of expansion. Some idea of the amount of this expansion may be obtained by considering that the volume is increased more than one third as much again on heating from the freezing to the boiling point. If the expan- sion of metals such as iron were as great as this, a pail that would contain three quarts of ice- water would expand enough to hold four quarts ELASTICITY AND EXPANSION WITH BEAT. 65 when filled with boiling water ; but the expan- sion of metals is one hundred times less, and beside they differ very greatly among them- selves. If Boyle's law be now taken into consideration, it will appear that gases must have the same rate of expansion, whatever may be the pressure, for consider a mass of gas at the freezing tem- perature and atmospheric pressure. If the pres- sure is doubled, the volume will be reduced one half. The same would be true if it had been at the temperature of boiling water. Its volume at the lower temperature will be to that at the higher in the same ratio at the high pressure as at the ordinary atmospheric pressure ; so also for any other pressure whatever. Another way of studying the effect of temper- ature on gases is to keep the volume of the gas constant, and observe the increase in pressure which it exerts against the walls of the vessel as it rises in temperature. This is often the most convenient mode of studying the effect of heat on a gas. If Boyle's law were exactly true for any gas, the proportional increase in pressure for that gas, kept at constant volume and raised in tem- perature, would be the same as the proportional increase in its volume, when the pressure is kept constant during the same rise in temperature. 66 THE PHYSICAL PROPERTIES OF GASES. This will be evident if we first think of the gas rising in temperature at constant pressure, and increasing in volume. Suppose it to be heated enough to make its volume just double what it was at first. Now keep it at the new tempera- ture and compress it to its original volume, and by Boyle's law the pressure will become double what it was at first ; but now the gas is in exactly the condition it would have been if we had simply kept it at constant volume and raised its temperature as before. In the one case, the vol- ume is doubled, in the other case the pressure is doubled. The statement that all gases, when raised from the temperature of melting ice to that of boiling water, increase in volume |^ of their volume at the lower temperature, is known as the law of Gay-Lussac, or sometimes as the law of Charles, since the latter made the discovery a few years before Gay-Lussac, though he did not publish his result, and his work would very likely have remained unknown but for Gay-Lussac's notice of it. Later and more perfect experiments, devised and carried out by the great experimental skill of Kegnault, show that the above results, though close approximations to the truth, are not rigor- ously exact. Regnault found that there are dif- ferences in the rates of expansion of the differ- ELASTICITY AND EXPANSION WITH HEAT. 67 ent gases, which are, however, exceedingly small in the more perfect gases, such as air, hydrogen, nitrogen, oxygen, and carbon monoxide ; and also very careful experiments showed that, when the gases were kept at constant pressure and al- lowed to expand, slightly different results were obtained from those found when they were kept at constant volume, and the increase in pressure measured. The following table exhibits Regnault's re- sults in the case of some well-known gases. In the first column the increase in volume is shown under constant pressure when the temperature is raised from the freezing to the boiling point of water. In the second is shown the increase in pressure when the volume is kept constant through the same range of temperature. Increase in volume, pressure constant. Volume at 32 Fahr. = 1.0. Increase in pressure, volume constant. Pressure at 32 Fahr. = 1.0. Hvdrosren 3661 03667 Atmospheric air . . Nitrogen 0.3670 0.3665 0.3668 Carbonic oxide . Carbonic acid . . . Sulphurous acid . . 0.3669 0.3710 0.3903 0.3667 0.3688 0.3845 It will be noticed that the agreement is re- markably close among the first four gases. These gases, as will be seen later, are all con- 68 THE PHYSICAL PROPERTIES OF GASES. densed with extreme difficulty, while the last two mentioned may be liquefied with compara- tive ease. The indications seem to be that the more a gas is expanded and removed from the point of condensation, the more nearly do its temperature coefficients agree with those of the more permanent gases, as those first mentioned are sometimes called. The fact that all gases expand in the same way when heated is utilized in the measurement of temperatures. The ordinary scales of temper- ature that are in use depend on the expansion of some substance, usually mercury or quick- silver, contained in a glass tube. This choice of substance is perfectly arbitrary, and dictated only by convenience ; no other reason could be given why we should not rather measure temper- atures by the expansion of a rod of copper or iron. Suppose two thermometers are taken, and so made that each stands at 32 when put in melting ice, and at 212 when in boiling water. Then, if the tubes of the thermometers are of uniform bore, and each is divided into the same number of equal degrees between these two fixed points, we should expect them to agree at all other temperatures ; but on making trial it may be found that they do not exactly agree, and half way between 32 and 212 this discrepancy may amount to as much as half a degree ; and we find ELASTICITY AND EXPANSION WITH HEAT. 69 on examination that the two are not made of the same kind of glass, one having perhaps been made in Germany and one in England. If, in- stead of two mercury thermometers, one had been a spirit thermometer, the difference might have been still more serious. While, for the purpose of regulating 'the tem- peratures of our dwellings, such an uncertainty would not signify anything, it would be in the highest degree perplexing if we were engaged in a series of experiments on the properties of steam, for instance. Which thermometer is right ? Each behaves according to the properties of the substances of which it is made, and one is as much entitled to respect as the other. But some one must be chosen, to avoid uncertainty ; and now, if temper- atures observed in one place are to be compared with those observed in another, there is nothing to be done but compare the one thermometer throughout its entire range with the other which is taken as standard. But we have just seen that there is a large class of bodies, the gases, that expand in almost exactly the same way as each other. Would it not be well to make the expansion of some of these substances the basis of a system of thermometry ? A gas, in addition, possesses the advantage of expanding so much more than other substances 70 THE PHYSICAL PROPERTIES OF GASES. that the expansion of the glass bulb in which it is contained is small enough in comparison to be easily allowed for. If temperatures should be measured with such a thermometer as this, and if the expansion of the glass bulb was allowed for, so that simply the expansion of the gas itself was taken into account, then there would be no uncertainty whatever ; for if an experimenter in Germany wishes to compare his results with those obtained else- where, he has simply to compare his thermometer with such a gas thermometer, since dry air, or hydrogen, or whatever the gas may be, expands in the same way in Germany as in any other part of the globe, and the expansion of the glass, which is the disturb- ing element, comes in only as a small amount, and is corrected for. In the figure there is repre- sented a form of air thermom- eter as constructed by Professor Jolly of Munich. It employs Fig- 10. Jolly's the method of keepillg the vo i. Air ihermometer. . . ume 01 the inclosed air constant, and observing the rise in pressure. It consists of a glass bulb filled with dry air, which is con- ELASTICITY AND EXPANSION WITH HEAT. 71 nected by a very fine tube with a vertical glass tube about half an inch in diameter. This tube is connected by means of a flexible rubber tube with another vertical glass tube of the same internal diameter as the first. Enough mer- cury is contained in these tubes to completely fill the flexible one, and to extend some dis- tance up into the glass tubes. The right hand tube may be raised or lowered, by which means the level of the mercury in the left hand tube may be adjusted so as to come exactly to a fixed mark near the end of the small tube con- necting with the bulb. The difference in height between the two ends of the mercury column, together with the pressure of the external air, as indicated by a barometer, is the pressure to which the air in the bulb is subjected. If the temperature of the bulb is now raised, the air expands and forces the mercury down in the left hand tube. The right hand tube must, there- fore, be raised until the pressure of the column of mercury is great enough to cause the mercury again to rise in the left hand tube to the original mark, and thus compress the air to its former volume. The increase in pressure indicated by the greater difference of level between the mer- cury in the two tubes is the measure of the in- crease of temperature. Of course this instrument has not the port- 72 THE PHYSICAL PROPERTIES OF GASES. ability and convenience for rapid use of the ordinary mercurial thermometer ; so in practice it is used only to standardize the ordinary ther- mometers. Beside this, its use requires the ut- most care and skill to obtain reliable results. Before leaving this subject, it is important to say a few words concerning what is called the absolute scale of the air thermometer. If we take such an air thermometer as has been de- scribed, the pressure, when the bulb is placed in boiling water, is J^jj- greater than when it is placed in melting ice. The pressure at the tem- perature of melting ice is, therefore, to that at the higher temperature, in the ratio of 273 to 373. If, therefore, a scale of temperatures, were to be adopted in which the freezing temperature were to be called 273, and the boiling point 373, it would be one such that the pressure of any gas, whose volume was constant, would always be very nearly proportional to its temperature meas- ured on that scale, and the size of the degrees would be such that there would be 100 degrees between the freezing and boiling points of water. Now there is a scale in general use on the conti- nent of Europe and among scientific men every- where, the centigrade scale, in which the freez- ing point is marked 0, and the boiling point 100. It is only necessary to add 273 to tem- peratures measured on the centigrade scale to ELASTICITY AND EXPANSION WITH HEAT. 73 obtain their values on the above-mentioned scale, which may be called the absolute centigrade scale. In the same way an absolute scale may be constructed based on the Fahrenheit scale. In this case the size of the degrees must be such that there shall be 180 of them between the freezing and boiling points, as in the ordinary Fahrenheit scale. Then, if temperatures are taken as proportional to pressures in the air thermometer, the freezing point will be 492, and the boiling point 672, since the pressures at these points are as 273 to 373, or, what is the same thing, as 492 is to 672. The pressure of any gas kept at constant volume would be very nearly proportional to its temperature measured on such a scale, and the size of the degrees would be the same as in the regular Fahrenheit scale. Temperatures measured on the ordinary Fahrenheit scale may, therefore, be changed to the above, which may be known as the absolute Fahrenheit scale, by merely adding 460 to the observed readings. This scale is, therefore, simply the ordinary Fahrenheit scale, in which the zero point is made 460 below the ordinary zero. Since, when the pressure is maintained con- stant, the volume of a gas changes under changes of temperature almost exactly as the pressure 74 THE PHYSICAL PROPERTIES OF GASES. changes when the volume is kept constant, it fol- lows that, when a mass of gas is kept at constant pressure, its volume will be directly proportional to the absolute temperature ; that is, its volume at 400 is to its volume at 500 as 4 to 5. But 400 would be 60 below zero Fahrenheit, as we usually reckon, and 500 would be 40 Fahren- heit. It will be seen that this system of meas- uring temperatures is exceedingly convenient in all cases where we have to do with gases and vapors. But it may be objected that, if the tempera- ture measured in this way is proportional to the volume of the mass of gas, then the zero of temperature will be that temperature at which the gas has no volume at all ! But it is not asserted that it is possible to reach the zero of this scale, even if the greatest possible cold could be obtained, though there are reasons for thinking that the volume of the gas at the coldest possible temperature would be so small that the air thermometer would indicate not as much as one degree above the absolute zero. The absolute scale of the air thermometer in the way in which we have treated it is a very convenient one, for it applies to a large and important class of substances ; but if this were all, it would have little more claim to respect ELASTICITY AND EXPANSION WITH HEAT. 75 than a scale based on the expansion of a bar of copper, and so devised that the length of the bar should be proportional to the temperature on that scale. But there is another and really scientific reason for styling it the absolute scale. A system of measuring temperature has been proposed by Sir William Thomson, based on the law of the conservation of energy and the prop- erties of engines that derive their power from heat, which does not depend on the expansion of any arbitrarily chosen substance. It is well known that a theoretically perfect steam-engine, which does not waste any of the energy that it receives from the steam, cannot possibly convert all that energy into useful work, but must give some of it up in the exhaust steam that goes to the condenser. It may also be shown that, if the engine is what is called a perfect one, and loses no heat by conduction, that the relation between the amount of heat taken in from the boiler and that given out to the condenser depends only on their temperatures, and has nothing to do with the substance that is used, whether it is steam or the vapor of oil or ether. Sir William Thom- son has, therefore, proposed a scale of tempera- tures on which the temperature of the boiler will be proportional to the heat given to the engine, and that of the condenser to the heat 76 THE PHYSICAL PROPERTIES OF GASES. received from it. Thus, if the boiler were at the ordinary boiling temperature and the condenser at the freezing temperature of water, it is found that the heats given to the engine by the boiler, and received by the condenser, are as 373 to 273 : these would be, therefore, the temperatures on such a scale in which the boiling and freezing points of water are 100 degrees apart. This is called the centigrade thermodynamic scale of temperatures. If the temperature of the condenser were zero of this scale, then the perfect engine would do an amount of work equal to the energy which it received, and consequently the exhaust steam would have no heat energy whatever. It may be shown that there is no lower degree of tempera- ture possible than this absolute zero of the ther- modynamic scale : it is therefore a scale that has great scientific interest. Now the absolute scale of the air thermometer derives its importance especially from this fact, that, throughout a range of temperatures extend- ing from the highest attainable to those so low as to be only obtained by the most refined pro- cesses at the command of the physicist, it corre- sponds almost exactly with the thermodynamic scale. So that the point which has been taken as the absolute zero of the air thermometer, namely, 460 below zero Fahrenheit, is justly en- ELASTICITY AND EXPANSION WITH HEAT. 77 titled to be known as the absolute zero, since the lowest possible temperature may be shown to be 460 below zero Fahrenheit on the thermody- namic scale. It is surely a remarkable fact, that all gases not only expand and contract in the same way under changes of temperature, but that their volumes are proportional to temperatures meas- ured on this absolute thermodynamic scale. CHAPTER IV. GASES AND VAPOKS. SCARCELY any fact in physics is more famil- iar than evaporation. Every one has watched water boiling away, and passing off in vapor into the surrounding air. The cloud of condensed steam that rises from boiling water is often mis- taken for water vapor. It is really fine drops of water that result from the condensing of the steam as it rises into the cooler air. But if we watch the cloud of steam, it will be seen not merely to spread and diffuse itself through the air, but it will actually vanish : the fine water particles that were formed at the place where the air was saturated with moisture evaporate and disappear as they pass into drier regions. True water vapor is invisible, the air is charged with it at all times, particularly in summer. It escapes into the air from every water surface, whether hot or cold, though it is given off more rapidly from hot water, and only stops when the water is dried up, or when the air is so fully charged that it can contain no more. Vapor may even be given off from solids : ice and snow GASES AND VAPORS. 79 are constantly giving off vapor. When the air is dry and cold, snow will gradually vanish with- out melting. All have seen the " steaming " of ice in very cold weather. So, also, a piece of cam- phor will soon vanish, passing directly from the solid state to the form of vapor, if exposed in the open air ; but when it is kept in a stoppered bottle, the inclosed air is soon fully charged or saturated with the vapor of the camphor, and then the evaporation ceases. What is the difference, if any, between a vapor and a gas ? Vapors seem to mix with gases and resemble them. Is it possible that what we are accustomed to call gases are really vapors ? Before attempting to answer this question, the properties of vapors should be more closely ex- amined. Let us imagine that we have a room, measuring ten feet every way, completely devoid of air, or any other gas or vapor. If now a small vessel of water is placed in that room, it will boil violently, and pass off as vapor into the room, and soon will have entirely vanished. If it is summer weather, and the temperature is about 80 Fahrenheit, nearly a pint and a half of water will evaporate in this way before the limit is reached. The space will appear as transparent as before, the walls will be dry, there will be no sign of moisture. But when about a pint and a half of water has been evaporated in this way, 80 THE PHYSICAL PROPERTIES OF GASES. the process will stop, and no more vapor will be given off, however much water may be intro- duced. The space is then said to contain a sat- urated vapor. If a barometer is now introduced into the room, it will be seen that the vapor exerts a pressure that will support a mercury col- umn one inch high, or about one thirtieth the amount of the atmospheric pressure. If one of the walls of the room is made so that it can be pushed in, and if we diminish the size of the room in this way, a proportional amount of the vapor will condense and return to the liquid form. If the room is reduced to half its original volume, then half the vapor will return to the form of water; but what is left will continue to exert exactly the same pressure as at first, as may be seen by the barometer, in which the mer- cury obstinately stands at one inch in height. And so, also, no change in pressure would be pro- duced, as long as any room was left for the vapor. If the operation is reversed, and the room is made larger and larger, the pressure will be seen to re- main constant until all the water is evaporated. But when it is still further enlarged, the pressure will fall in such a way that, when the volume of the room becomes twice as great as at the instant the last drop of water disappeared in vapor, the pressure will have been reduced to about one half an inch of mercury. When the volume GASES AND VAPORS. 81 is three times as great as at the saturation point, the pressure will be reduced to nearly one third of an inch of mercury, and so on. This behavior after passing the saturation point is evidently according to Boyle's law for gases. But now let us return to the case where the vapor is satu- rated, that is, where any diminution in the vol- ume of the room containing it will cause conden- sation. It has been seen that the pressure of the saturated vapor is constant, and does not de- pend on the size of the vessel that contains it ; but it does depend on the temperature, for if the temperature is lowered, some of the vapor will condense and the pressure will be diminished. If the vessel is so large that the vapor is not nearly saturated, then, on cooling, there will be a diminution of pressure without condensation, unless the cooling is great enough to bring it to the condition of saturation. The diminution of pressure, as long as the vapor is not saturated, is according to the same law that holds for gases : the pressure is proportional to the abso- lute temperature. To sum up, then, a vapor that is not near the saturation point behaves like a gas under changes of temperature and pressure ; but if it is sufficiently compressed or cooled, it reaches a point where it begins to condense : it then no longer obeys the same laws as a gas, but its 82 THE PHYSICAL PROPERTIES OF GASES. pressure cannot be increased by diminishing the size of the vessel containing it, but remains constant, except when the temperature is changed. These properties are beautifully illustrated by the following simple ex- periment. Take a tube closed at the top, and after filling it with mer- cury invert it, and intro- duce its open end into a deep bath of mercury, allowing no air to enter. If the tube projects more than thirty inches above the surface of the mercury bath, we shall have the vacuum above the mercury column, as in Torricelli's experiment. If a drop of ether is now passed into the lower end of the tube, it will rise to the top, in- stantly vaporize, and the mercury column will be seen to stand lower than it did before. The amount that it falls measures the Fi g- pressure of the ether vapor in the tube, since the GASES AND VAPOJIS. 83 air pressure without is balanced by the pressure of the mercury column, together with that of the ether vapor. If another drop is introduced, the column will stand still lower, showing an in- crease in pressure ; and if the process is contin- ued, the pressure will fall till the mercury col- umn stands about ten inches high, when no further increase in pressure will be observed, though considerably more ether may be intro- duced : it will rise and float as liquid ether on top of the mercury column. The vapor is now saturated, and the pressure will remain the same as long as the temperature is constant. If now the tube is raised as far as possible without re- moving its lower end from the mercury bath, the space above the mercury column will be increased vas the tube is raised ; the ether will evaporate rapidly, to fill the larger space with saturated vapor ; and the mercury will remain at exactly the same height, for the change does not affect the pressure of the vapor which de- termines the height of the mercury column. But if the ether is all evaporated at any point before the tube is drawn up as high as possible, then as the tube is raised beyond that point the vapor ceases to be saturated, and its pressure accordingly diminishes as the volume increases, and so the mercury column is seen to rise in the tube. 84 THE PHYSICAL PROPERTIES OF GASES. Suppose, in the case of the experimental room which we imagined to be entirely devoid of air before the water was introduced, the conditions are changed, and the room is supposed to be full of air, but perfectly dry, or free from water vapor. Then, if water is introduced as before, it will be evaporated and the vapor will fill the room, permeating everywhere through the air of the room ; and though this will take place much more slowly than when the water vapor alone filled the room, yet exactly the same amount of vapor will be given off from the water, before the saturation point is reached, as was found in the former case. The water vapor seems to distrib- ute itself in the same way in the room, whether air is present or not, and whatever the pressure of the air may happen to be. It is very interesting to inquire what causes this cessation of the evaporation when the vapor pressure reaches a certain point. It might at first glance be thought to be simply due to the pres- sure on the surface of the liquid becoming so great as to stop all further evaporation ; and we might suppose that if at the start enough air were introduced to make the pressure on the in- side equal to one inch of mercury, then, on intro- ducing water, it would find its surface pressed upon by a pressure equal to that of its saturated vapor, and would consequently be prevented GASES AND VAPORS. 85 from giving off any more vapor, but nothing of the sort takes place: it immediately gives off vapor, and continues to do so until its vapor pressure becomes equal to an inch of mercury, and no sort of regard is paid to the pressure to which it is already subjected by the inclosed air, the only effect of the latter being to delay the action. The same is true if any other gas than air presses on the surface of the liquid. If the sur- face of the liquid is covered with any solid or liquid through which it does not readily pass, that will of course stop its evaporation ; for ex- ample, a layer of oil over the surface of water will prevent the evaporation of the latter : but the only gas that can prevent a liquid evaporat- ing seems to be its own vapor. An ingenious theory has been proposed to explain this curious fact : it is that the mole- cules or smallest particles of the liquid are in a state of constant activity, flying about with considerable velocities. At the surface of the liquid, some of these molecules are continually escaping beyond the range of the attraction of the liquid. These free molecules constitute the vapor ; but as they bound to and fro they occa- sionally come within range of the liquid's attrac- tion, and again become entangled as it were, and make part of the liquid. .While there is but 86 THE PHYSICAL PROPERTIES OF GASES. little vapor, far more molecules escape than are returned to the liquid. This is while what we call evaporation goes on ; but after a time the region above the liquid contains so many of these flying molecules that, on an average, as many are entrapped by the liquid in every second, and so return to it, as there are that escape. When this point is reached, no more evaporation appears to take place. The molecules are not to be supposed as an- imate in any sense, because they have been spoken of as " flying " to and fro ; they are to be thought of as bounding and rebounding, as a billiard ball does. It will be seen that the above way of looking at the relation between a liquid and its vapor affords a perfectly rational explanation of the behavior that has been described. It is evident, in the light of this explanation, that the cessation of the evaporation must depend only on the den- sity of its vapor, and not at all on the pressure of any other gas on the liquid surface. In this connection a very interesting and im- portant way of stating the law of gaseous pres- sures, which is due to Dalton, should be given. It is that every portion of a mass of gas inclosed in a vessel contributes to the pressure against the sides of the vessel the same amount that it would have exerted by itself had no other gas GASES AND VAPORS. 87 been present. For instance, a grain of air in- troduced into a vessel having one cubic foot ca- pacity will produce a certain pressure. If now another grain of air be introduced, the pressure will become twice what it was at first ; if a third is added, it will become three times the original pressure, and so on. It will be seen that this is really merely a new way of stating Boyle's law ; for the density has been increased three times, and the pressure is found to be three times as great, or pressure is proportional to the density of a gas. But the particular interest in this mode of looking at the question is seen in the mixture of various gases and vapors. The law holds here, also, in all cases where the gases and vapors that are mixed are chemically inactive towards each other. Thus, if a certain quantity of hydrogen when put in a given flask will exert a pressure of one pound to the square inch against the sides of the flask, and if another quantity of ni- trogen if put by itself in that same flask would exert a pressure of four pounds to the square inch, and if a certain mass of water vapor would in the same vessel cause a pressure of one half a pound, then when they are all put in the flask together the total pressure will be five and a half pounds to the square inch. But how is it, if liquids give off vapors that 88 THE PHYSICAL PROPERTIES OF GASES. have decided pressures of their own, and these pressures are to be added to the pressure of the air already present, that the stoppers are not blown out of the bottles that contain such vola- tile substances as ether or carbon disulphide? To this it may be said that, if the air above the liquid surface in a bottle of ether were at the atmospheric pressure, then this air together with the ether vapor would exert a pressure on the inside of the bottle that would be greater than that of the outside atmosphere by about five pounds to the square inch, or the amount of the pressure due to the ether vapor alone, and this would surely blow out the stopper ; but in fact, while the ether is being poured into the bottle, it is giving off vapor which is filling the air around it, and this mass of air at the ordinary pressure, together with the ether vapor, exerts on the surrounding air this greater pressure: but the surrounding air, being simply at the ordinary atmospheric pressure, yields before the combined pressure of the air and the ether vapor with which it is charged, and allows the whole mass to expand until a balance is effected, which will be when the air charged with ether vapor has so far expanded that its pressure, together with that of the ether vapor it contains, is exactly equal to the atmospheric pressure. It results, therefore, from this expansion, that GASES AND VAPORS. 89 the air inclosed in a bottle of ether is not at the atmospheric pressure, but so much has been driven out by the expansion that only as much remains as will, together with the ether vapor, have a pressure equal to that of the atmosphere. The same explanation answers the difficulty that many persons feel in the statement that air charged with water vapor is lighter than dry air, which is made to explain the fact that when the air is charged with moisture the barometer sinks, showing the pressure to be less. Water vapor is lighter than dry air at the same temperature and pressure. When the air is charged with water vapor, it must be remem- bered that the water vapor exerts a pressure of its own, so that the mass of air thus charged with moisture expands and presses back the sur- rounding air, so that, if a cubic foot of the mix- ture be taken, it will be found to contain less air than a cubic foot of dry air at the same tem- perature and pressure, part of the air having been supplanted by the water vapor ; but the water vapor is lighter than air of the same tem- perature and pressure, which must be the case of the displaced air. Therefore the mixture is seen to be lighter than dry air, because water vapor is not simply added to the dry air, but displaces an amount that would produce the same pressure as the vapor does. 90 THE PHYSICAL PROPERTIES OF GASES. But now we turn to some remarkable experi- ments that have settled the question as to the identity of gases and vapors. In the year 1823 Michael Faraday, following out a suggestion made by Sir Humphry Davy, took some crystals of hydrate of chlorine, which Davy had shown to be a compound of chlorine with water, and, sealing them up in a strong glass tube, heated them. A clear liquid was observed to form at the bottom covered with a layer of a lighter greenish liquid, which Faraday suspected was chlorine in a liquefied condition. To examine this still further, and separate, if possible, the two liquids from each other, he em- ployed a bent tube of the form represented in the figure. Into the longer arm of this tube some crystals of the hydrate were introduced, and the tube was hermetically sealed, and then the crystals were heated. The clear liquid was observed to remain in the longer arm of the tube, while the greenish liquid distilled over, and was condensed in the shorter arm, which was kept cooled. On breaking the tube at the bend, the two parts sprang apart with a force that showed 'there was considerable pressure in the tube, and the greenish liquid was immediately vaporized, the vapor showing by its odor and color that it was chlorine gas, while the clear liquid proved to be, on examination, water containing some chlorine dissolved in it. GASES AND VAPORS. 91 This experiment was but the prelude to a great many in which a number of gases were condensed to liquid form. A bent glass tube, similar to that used in the experiment just described, was taken, and into the longer leg, which was closed, was introduced some sub- stances which would evolve gas when heated. Fig 12 Faraday , 8 Experi . The shorter leg was men t, then sealed up, and cooled by being placed in a freezing mixture. When now heat was applied to the longer arm of the tube, as the gas was given off the pres- sure increased rapidly, and in many cases the gas thus obtained was found condensed in liquid form in the shorter arm. Thus carbonic acid gas was readily liquefied by heating sodium bicar- bonate in such a tube. Cyanogen was produced and liquefied when cyanide of mercury was the substance employed ; and liquid ammonia also was obtained by taking advantage of the fact that chloride of silver absorbs about two hun- dred times its volume of that gas. A mass of the silver chloride was taken fully charged with ammonia gas, and then introduced into the 92 THE PHYSICAL PROPERTIES OF GASES. longer arm of the experimental tube and gently heated. The ammonia was rapidly given off ; and as the pressure rose, it condensed in the shorter arm of the tube as a liquid. The glass tubes employed in these experiments need to be very strong, as they may be subjected to pres- sures of two hundred or three hundred pounds to the square inch. The pressures at which the condensation took place were observed by intro- ducing into the experimental tube a little tube sealed at one end, and inclosing air which was separated from the gas in the outer tube by a drop of mercury. The amount of the compres- sion of the air in this tube indicated the pres- sure. By this means it was observed that the pressure steadily increased up to the point where condensation began, and then remained constant as long as the temperature of the liquid gas was kept the same. This agrees exactly with what has been noted as to the pressure of vapors. The inference is, therefore, clearly that these gases are simply the vapors of the liquids into which they condense ; but under ordinary tem- peratures and pressures they are very far re- moved from the saturation point. In Faraday's experiments, however, under the combined influ- ence of pressure and cold, they were brought to the saturation point ; and then, as more gas was given off, condensation took place. GASES AND VAPORS. 93 Faraday was the first to condense into the liquid form many of the gases. A very inter- esting extension of knowledge in this direction was made by Thilorier, who first devised an ap- paratus by which the liquid carbonic acid could be obtained in considerable quantities. His ap- paratus consisted of two strong iron vessels, each provided with a stopcock, and connected by a strong iron tube. Into one of these vessels bi- carbonate of soda and sulphuric acid were intro- duced, by whose chemical action the gas was evolved ; as the pressure rose, it was condensed in the other vessel, which was surrounded by a freezing mixture of ice and salt. Thus consid- erable quantities of the liquid carbonic acid were collected. If this liquid gas, when thor- oughly cooled by being packed in ice and salt, is allowed to escape freely through a fine jet, it rushes out with a hissing sound, and the sudden expansion of the escaping gas lowers its temper- ature so much that part of it falls to the ground frozen into fine snow. If a small woolen bag or pouch be put over the jet, this solid carbonic acid may be caught in considerable quantities. It may be handled and examined under ordinary atmospheric pressure, as it only gradually disap- pears by passing directly into the gaseous condi- tion, since it requires to receive heat from sur- rounding bodies before it can return to the 94 THE PHYSICAL PROPERTIES OF GASES. gaseous state, and so great are its demands in this respect that they can be only gradually met ; but while this is going on, heat is taken from all the bodies about it, so that, if it be roughly han- dled and pinched, it will take heat so rapidly from the skin as to cauterize it as though with -a hot iron. If a fragment of the solid be allowed simply to rest on the hand without pressure, it does not burn the skin, because the gas is escap- ing from its surface so rapidly, particularly from the surface next the warm hand, that it makes a little cushion by which the solid is prevented from actually coming in contact with the hand. When solid carbonic acid is mixed with ether, a freezing mixture results, which is capable of giving a temperature of 140 below zero Fahren- heit, and will freeze solid four times its weight of mercury. The frozen mercury may be cut with the knife, and shows very much the same toughness and malleability as a piece of lead would have at ordinary temperatures. Later experimenters improved the apparatus employed for the condensing of gases. Natterer arranged a force-pump in connection with a strong reservoir, so that all could be kept at a low temperature. But although many attempts were made to liquefy oxygen, hydrogen, and nitrogen, they were without avail. Faraday cooled a tube con- GASES AND VAPORS. 95 taining compressed oxygen, in a mixture of solid carbonic acid and ether, and, to increase the cool- ing effect, exhausted the air from above the freezing mixture, lowering the pressure to only about one twenty-fifth of one atmosphere, and thus greatly increasing the evaporation of the freezing mixture, and in consequence its cooling effect. By this means he obtained a temperature of 148 below zero Fahrenheit, according to his alcohol thermometer; and though the pressure of the oxygen was 27 atmospheres, there was no sign of condensation observed. Nor was he able to produce condensation of nitrogen by 50 atmospheres' pressure, nor of carbon monoxide by 40 atmospheres. Natterer even subjected these gases to the enormous pressure of nearly twenty tons to the square inch. Colladon em- ployed a pressure of 400 atmospheres, and at the same time cooled the gases to 22 below zero of Fahrenheit's scale by means of a freezing mixture, but no evidence of condensation was obtained. These gases were, therefore, some- times called permanent gases, in distinction from those that could be condensed. But after an interval of nearly twenty years, in which nothing further had been attempted, on the 24th of December, 1877, at the same meeting of the French Academy, it was an- nounced that Cailletet of Paris and Pictet of 96 THE PHYSICAL PROPERTIES OF GASES. Geneva had actually achieved the condensation of these gases working entirely independently, and reaching the goal of their wishes almost simultaneously. In Cailletet's apparatus, the gas to be com- pressed was contained in a glass bulb terminat- Fig. 13. Cailletet's Apparatus for Liquefaction of Gases. ing in a narrow glass tube about a foot long, sealed at the top, and of great strength. The bulb was inclosed in a strong iron cylinder, the narrow tube alone projecting through a collar into which it was firmly cemented. Mercury GASES AND VAPORS. 97 was then forced into the iron cylinder by means of a pump, and, entering the bulb by an opening in the bottom, compressed the contained gas and forced it up into the projecting narrow tube. This tube was surrounded by liguid sulphurous Jicid, and cooled to about 22 below zero Fahren- heit, the whole being surrounded by a vessel in which the air was carefully dried, so that the deposition of frost on the chilled tube might not interfere with seeing what took place in the inner tube. When the contained gas was com- pressed in this tube to about 300 atmospheres, or 4,500 pounds to the square inch, and was thoroughly cooled, it was suddenly allowed to expand by opening a valve and relieving the pressure. This expansion caused an extreme chilling of the gas, the temperature being re- duced in this way to more than 300 Fahrenheit below zero, and a white cloud of vapor in the tube showed the condensation of the gas. There were formed distinct drops of nitrogen on the sides of the tube, and it was even frozen as a \vhite frost, showing clearly the solid state. Oxygen was thus condensed, and hydrogen, though less obviously than the others, still showed a faint cloudiness which proved condensation beyond question. Pictet obtained the condensed gases on a much larger scale. The peculiarity of his method was 98 THE PHYSICAL PROPERTIES OF GASES. that he laid the greatest stress on obtaining as low a temperature as possible. The apparatus which he employed was therefore mainly con- Fig. 14. Diagram of Pictet's Apparatus. structed with this in view. It was very elabo- rate, and cost about fifty thousand francs. The principle of the apparatus will be readily understood from the diagram. Sulphurous acid gas, which can be readily condensed at compara- tively low pressures, is contained in the vessel B in liquid form. The pressure in this vessel is diminished by a pump which causes the liquid GASES AND VAPORS. 99 to boil, the escaping gas being pumped out, com- pressed again into the liquid state, and forced into the receiver A, where it is cooled by a stream of cold water, and is then returned again to the vessel B. The same mass of gas is thus caused to circulate by the pump in such a way that it is constantly vaporizing in the vessel B, and there producing an intense cold. The heat which it abstracts from B is carried back with it through the pump, where its temperature is raised so much by the compression that the stream of cold water can remove the extra heat that it took from the vessel B, although the water is at a much higher temperature than B. In this way the ves- sel B is brought to a steady temperature of about 90 below zero Fahrenheit. In the vessel B there is a tube through which liquid carbonic acid gas is pumped into the vessel D, whergit vaporizes, just as the sulphurous acid vaporized in the ves- sel B, and is then pumped out and again com- pressed to the liquid state and cooled by being passed through the tube through B, and returns thus cooled to again vaporize in D. The vessel B thus plays the same part in this operation as the vessel A did in the first case. In this way a steady temperature of about 200 below zero Fahrenheit is maintained in the vessel D, a de- gree of cold such that the carbonic acid is in part frozen solid in that vessel. Oxygen is de- 100 THE PHYSICAL PROPERTIES OF GASES. veloped in the vessel E, and is condensed in the tube passing through the vessel D by the com- bined action of cold and its own pressure. When a sufficient quantity is accumulated, the stop- cock at F is opened and the stream of liquid oxygen escapes. Pictet observed that in the ~^~ff escaping jet there was a central portion, a few inches long, the white color of which indicated the liquid or solid condition, while the outer por- tion was transparent and of a bluish tinge where the oxygen had returned to the gaseous state. When the escaping jet was illuminated by the electric light, the reflected light was found to be polarized, indicating the presence of solid par- ticles. When hydrogen was sought to be condensed, nitrous oxide, or laughing gas, was used instead of the carbonic acid gas, as in that way a greater degree of cold could be obtained. The stream of escaping hydrogen was steel-blue in color, and appeared to be opaque for a distance of about four inches. On closing the stop-cock F after allowing some of the hydrogen to rush out, the pressure in the tube was observed to continue to diminish from 370 to 215 atmospheres, evidently due to the freezing of part of the hydrogen re- maining in the tube from the cold resulting from the sudden expansion. When the stop-cock F was now again opened, the escaping stream was interrupted and foamy white. GASES AND VAPORS. 101 To understand fully the cause of the failure of so many attempts to liquefy oxygen, hydrogen, and nitrogen, it will be well to examine the re- sults of a very careful investigation of the prop- erties of carbonic acid gas which was made by Dr. Andrews of Belfast, and published in the Philosophical Transactions of the Royal Society of London for the year 1869. These results are* best expressed in the dia- gram on page 102. In this diagram each point represents a certain state of a pound of the car- bonic acid gas. Such a point, for example, as the upper end of the line marked 32. 5 signifies that the pound of gas, at 32.5 centigrade, occu- pies a yolume which is represented by the dis- tance of that point from the vertical line on the left, when it is under a pressure of about 85 at- mospheres, as indicated by the scale at the side. The pressures are given in atmospheres, while the scale of volumes is such that the width of the diagram indicates a volume of 12.5 thou- sandths of the volume of the gas at zero degrees centigrade and one atmosphere pressure. It will be observed that the lowest pressure shown is about 46 atmospheres. This is merely for con- venience, as the part of the diagram in which we are interested lies above that pressure. The true base line is the line corresponding to zero pressure, and does not appear in this diagram. Fig. 15. Diagram of Carbonic Acid Gas. GASES AND VAPORS. 103 All points on the line marked 35.5 indicate conditions of pressure and volume in which the gas is at a temperature of 35. 5 C. If a pound of carbonic acid is, then, at a temperature of 35. 5, its pressure and volume will be related to each other in a way represented by some point on this line. Every such line is known as an isothermal, or line of equal temperature. Six such isothermals are represented in the diagram. If the diagram represented the case of a gas that was very far from being condensed into the liquid state, so that it closely followed Boyle's law, then the isothermals could be drawn as in Fig. 16, where A, B, C are points on the same isothermal line. Since by Boyle's law the vol- umes must diminish in the same propor- tion as the pressures increase, the isother- mal line must be such a curve that if any two points, A and B, are taken, then o v, p which represent the volume in the state A, must be as much greater than o v', which is the volume in the con- dition B, as the pressure in the first condition, which is represented by o p, is less than o p f , the 104 THE PHYSICAL PROPERTIES OF GASES. pressure in the state B. The curve that satis- fies that condition is known by mathematicians as an hyperbola, and is similar to the curve drawn in the figure. The three different lines are three different isothermals of the same gas, and all indicate that it obeys Boyle's law. The isothermals on the left correspond to lower tem- peratures than those to the right, since, when the pressure is kept constant, a gas increases in vol- ume as its temperature rises. The straight line p B, D, E represents the series of states of a gas, when the pressure is kept constant, and as D is a state of greater volume than E at the same pres- sure, it must correspond to a higher temperature. But to return to the diagram of page 102, it will be seen that this diagram represents three distinct states of the substance. If the isother- mal of 13.l is followed up, beginning with its right-hand end, it shows that at the first state represented in the diagram the volume was 13.5 thousandths of the volume at zero centi- grade and one atmosphere pressure, and the pressure 47 atmospheres, and that as the pres- sure increased the volume diminished ; but it will be seen that the diminution is not according to Boyle's law, for in the corner of the diagram some lines are drawn showing how the isotherms are inclined in the case of a gas satisfying Boyle's law. The carbonic acid isotherms are GASES AND VAPORS. 105 seen to be much less steep, indicating that the gas diminishes more rapidly in volume as the pressure increases than it would if Boyle's law were satisfied by it. When the volume is re- duced to 12.5 thousandths, the isotherm is seen to take suddenly a horizontal direction at a pressure of about 48 atmospheres. At this point the substance is just brought by the compres- sion to the state of a saturated vapor. Further compression produces only condensation of part of the vapor but no change in pressure. The isotherm therefore continues horizontal until a volume of about 2. thousandths of the standard volume is reached, when it rises suddenly and steeply, showing that enormous increase in pres- sure produces but slight change in volume. The point where the isothermal suddenly rises indi- cates that the volume has been so far diminished that the vapor is all condensed to the liquid state, in which it is extremely incompressible. If we now follow similarly the next isotherm for 21.5 C., it shows the same main features ; but the volume 8.9 thousandths is somewhat smaller before condensation begins, and the vol- ume of the condensed liquid, about 2.7 thou- sandths, is rather greater than for the lower temperature. The line connecting those points which represent the condition of saturated va- por at the various temperatures may be called 106 THE PHYSICAL PROPERTIES OF GASES. the line of saturated vapor, and is seen to slope upwards towards the left, showing that the higher the temperature the denser the vapor has to be before it will begin to condense. The region to the right of this line represents only gaseous conditions of the substance. The line connecting the various points that indicate that the substance has just been com- pletely condensed to the liquid form may be known as the liquid line, and only liquid condi- tionsrof "the' substance are denoted by points to the left of this line. The liquid line slopes up to the right, showing that the condensed liquid is more expanded and less dense at high temper- atures than at low ones. The region between the liquid line and the line of saturated vapor indicates states of the substance in which it is partly condensed liquid and partly saturated vapor. As the temperatures are taken higher and higher, it is found that the difference between the volume of the vapor when just at the point of condensing and the volume of the condensed liquid becomes less and less, until finally the line of saturated vapor and the liquid line meet at what may be called the critical point. The isotherm of 31. 1 C. passes through this point, and therefore does not have the horizontal part that indicates points where condensation is tak- ing place ; but it becomes just horizontal as it GASES AND VAPORS. 107 reaches the critical point and then bends up again, showing that the gas, when compressed at that temperature, becomes more compressible up to the critical point, when it begins to be less easily compressed and behave more like a liquid ; but there is nothing like condensation taking place, no separation into two parts, one of con- densed liquid and one of vapor. The isother- mals for temperatures higher than the critical one still show an increase in compressibility as the critical volume is approached, followed by a decrease after it is passed, but this is by no means as marked as at the critical temperature. At temperatures lower than the critical temper- ature if the gas is sufficiently compressed, it will condense into a liquid. At higher temperatures no amount of pressure will cause condensation. The following table exhibits the critical tem- peratures and pressures of some of the more familiar gases : Name of Gas. Critical Temperatures. Degrees Fahr. ! Critical Pressures. Atmospheres. c? Chlorine, 286 83.9 Oxygen, -171 - 3 50.0 Nitrogen, 230 - IV r 35.0 Marsh Gas, 148 50.0 Nitrous Oxide, 96 75.0 Carbonic Acid, 89 I0f] 77. Ammonia, 266 115. Hydrogen, 280 prob. 73 99. 108 THE PHYSICAL PROPERTIES OF GASES. When we notice the critical temperatures of oxygen, hydrogen, and nitrogen, the reason of the difficulty experienced in condensing them is at once evident. It was Faraday who first sug- gested the idea of there being a critical temper- ature above which no amount of pressure could produce condensation in a gas. Do the vapors of ordinary liquids, such as water, alcohol, or ether, show anything like a critical temperature? Let us turn for answer to some experiments made by Caigniard de la Tour in the year 1822. This experimenter filled a strong glass tube four fifths full of ether, and after sealing it heated it in a bath of oil to a high temperature, and observed that as the tem- perature rose the vapor appeared to become more dense, while the liquid ether decreased in density until, at 36 9. 5 Fahrenheit, the surface separating the two suddenly vanished, and the ether in the tube appeared perfectly uniform throughout, but on allowing it to cool a little be- low that temperature the surface separating the liquid from its vapor suddenly appeared. The pressure at which this took place was 37.5 at- mospheres. Evidently the ether was near its critical point. In the same way the critical tem- perature of alcohol was observed, and it was at- tempted also to determine that for water, but in the last case great difficulty was experienced, as GASES AND VAPORS. 109 temperatures were so high and the pressure so great that the water actually began to dissolve the glass tubes in which it was confined. These experiments require great caution on account of the liability to accident by explosion. The fol- lowing are very near the true values of the crit- ical temperatures and pressures of these sub- stances : Temperature. Pressure in Fahr. Atmospheres. Ether 369.5 37.5 Alcohol 497.5 119.0 Water . .... . 773.0 It appears, therefore, that those substances which are gases under ordinary circumstances, and can only be condensed with difficulty, have critical temperatures that are very low, while those which are commonly known in the liquid form have very high critical temperatures, and there is no distinction between gases and vapors far removed from the saturated state. CHAPTER V. AIR-PUMPS AND HIGH VACUA. THE air-pump was first used by Otto von Guericke of Magdeburg in 1650. It has already been mentioned that his first attempt to pro- duce a vacuum by pumping water from a barrel proved futile. He then constructed a successful Fig. 17. pump on the plan shown in the figure. A brass cylinder was connected with the copper vessel to be exhausted by a short curved neck, so that the pump could be conveniently worked while the receiver was inverted. This was important, be- cause it was Yon Guericke's plan to fill the ves- sel to be exhausted with water, and then pump AIR-PUMPS AND HIGH VACUA. Ill that out. The piston was a plain one without valves. To prevent the air from returning to the receiver after a stroke had been taken, Von Guericke invented the stopcock substantially in the same form as it is made to-day. There was also a small plug or stopper fitted to a hole in the connecting tube ; and after the piston had been drawn out and the stopcock closed, the stopper was removed, and the air contained in the cylin- der was expelled by pushing the piston down. The stopper was then replaced and another stroke taken. As the exhaustion proceeded it required the united strength of two strong men to pull out the piston against the pressure of the out- side air. It was this apparatus that Von Guericke employed in performing his celebrated experiment with the Magdeburg hemispheres. Important improvements were soon made on this crude apparatus. The piston was operated by a rack and pinion, thus giving greater power. Dionysius Papinus, about 1675, added the plate and bell jar, which greatly facilitated experi- ments with vacua ; he also introduced the use of valves in the piston and in the tube leading to the receiver ; while Hawksbee in 1709 em- ployed two cylinders, having* their piston-rods geared to the same pinion, so that one was driven in when the other was drawn out, by which ar- rangement the pressure of the outer air upon 112 THE PHYSICAL PROPERTIES OF GASES. one piston was balanced by that upon the other, making the pump easy to operate. Fig. 18. Two-Cylinder Air-Pump. But a radical defect in Hawksbee's pump is, that throughout the entire stroke the full pres- sure of the atmosphere is on one side of the pis- ton, while on the other side it is nearly a vacuum. A slight leakage in the piston would under these circumstances prevent any very high exhaustion AIR-PUMPS AND HIGH VACUA. 113 being obtained, for a very little air leaking in under full atmospheric pressure would, on enter- ing the exhausted space, expand sufficiently to make a whole cylinderful of rarefied air, so that the leakage would wholly make up for the Fig. 19. Air-Pump. air removed by the pump, and the rarefaction would stop. In air-pumps as now constructed the cylinder 114 THE PHYSICAL PROPERTIES OF GASES. is only put in communication with the external air at one point in the stroke, when the air that has been withdrawn from the receiver is forced out. A simple and good form of pump is that represented in Fig. 19. The principal parts of an air-pump, as shown in Fig. 18, are R, the usual glass receiver or bell jar, which rests on the flat metal plate V. The lower edge of the bell jar is carefully ground flat, so that it fits the plate, and the joint is made air-tight by a little tallow put on the edge of the jar be- fore putting it upon the plate. The stopcock S admits of cutting off con- nection with the pump when the exhaustion is carried as far as desired. At E is shown a gauge which indicates the degree of exhaustion that has been attained. The details of a good air- pump cylinder are shown in the adjoining fig- ure. The upper part of the cylinder is closed, the piston-rod passing through a stuffing-box that is kept well supplied with oil, but in the Fig. 20. Cylinder. AIR-PUMPS AND HIGH VACUA. 115 upper cylinder-head there is a valve consisting of a group of fine holes, over which lies a flap of closely woven oiled silk. There is also a valve in the piston itself, besides the valve at the bottom of the cylinder closing the tube that leads to the receiver. This last valve is made so as to be opened and closed automatically by the motion of the piston ; otherwise its opening or closing would be left to the pressure of the air, which, as the exhaustion proceeds, soon becomes too small to operate the valve, so that in those pumps in which this valve is not moved automat- ically the exhaustion cannot go beyond that pres- sure which is just necessary to lift the valve. The usual device for operating this valve is simple and effective : it is attached to the end of a rod which is slightly shorter than the inside length of the cylinder ; this rod passes through the piston-head, fitting so closely that when the piston is raised the rod is raised with it until the upper end of the rod meets the end of a lever let into the upper cylinder-head, which stops its further rise, while the piston slips over it in rising to the top of the cylinder. The rod is thus kept raised, and the valve open while the piston is rising, until just as the piston reaches the top the rod is pushed down and the valve closed by the action of the lever, thus preventing air from returning to the receiver when the valve in the 116 THE PHYSICAL PROPERTIES OF GASES. piston is opened. On descending, the piston again slides over the rod, keeping the valve closed until the bottom of the cylinder is reached. The valve is by this means kept shut while the piston is descending, and open while the piston is rising. The valve in the piston itself is so made that it is closed during the rise of the pis- ton, and open during its descent, that the air may have free access to the upper part of the cylinder. Suppose such a pump to be operated : as the piston rises the valve at the bottom of the cyl- inder is kept open, and the air in the receiver expands so as to fill both the receiver and cyl- inder ; as the piston reaches the top, the valve connecting with the receiver is closed, while, as soon as the piston begins to descend, the piston valve is opened, allowing the air to pass freely into the upper part of the cylinder. As the pis- ton now rises a second time, the air in the upper part of the cylinder is prevented from returning by the closure of the valve in the piston ; and as the latter rises, it is compressed until its pressure is equal to the atmosphere, when it opens the valve in the top of the cylinder and escapes into the open air. At the same time a second cyl- inderful of air is drawn from the receiver into the lower part of the cylinder. It will be seen that only at the end of the AIR-PUMPS AND HIGH VACUA. 117 stroke, while the air above the piston is escaping into the outer air is the full atmospheric pressure felt on one side of the piston. This form of ma- chine is usually operated by a crank, and the end of the stroke is exactly the position in which the mechanical advantage of the crank is great- est, so that, after the first few strokes, the ma- chine can be easily operated in spite of the great force pressing on the piston at the upper end of the stroke. Suppose this machine is perfect in construc- tion so that there is no leakage, is there anything that limits the degree of exhaustion that can be obtained by its means ? A moment's considera- tion shows that it is limited by the fact that the air which is in the upper part of the cylinder cannot escape into the outer air until it reaches a pressure slightly greater than that of the at- mosphere, so as to be able to lift the valve in the top of the cylinder. Now there must al- ways be a small space or clearance between the piston and the top of the cylinder when the pis- ton is at its highest point. Suppose the piston comes within a sixteenth of an inch of the top of the cylinder, the whole length of the stroke be- ing eight inches, then if the whole cylinderful of air is compressed into this space it will only be compressed 128 times, so that the air above the piston in this case cannot be rarefied to 118 THE PHYSICAL PROPERTIES OF GASES. more than the 128th part of an atmosphere, and the highest exhaustion that would be attainable in the receiver would be the 128th part of that above the piston. It is therefore desirable to make the clearance small. But perfection cannot be attained, and the best of workmanship will not secure a piston that will not leak, and the difficulty still remains that, at one point in the stroke at least, the full atmospheric pressure is on one side of the piston. To meet this difficulty, a form of air-pump has been constructed which is provided with a sec- ondary cylinder for pumping the air out of the main cylinder into the outer air. By this ar- rangement air at atmospheric pressure is entirely excluded from the main cylinder, and on one side of the piston the pressure is only slightly greater than on the other, so that a slight leakage of the piston would cause very little trouble. By such a pump as this, with automatic valves, exhaustion should easily be carried to less than a thou- sandth part of the atmospheric pressure. If it were not for the practical defects that necessarily enter into this form of air-pump, the pressure after a certain number of strokes could readily be calculated in the following way : The air that is originally in the receiver expands, and fills both the receiver and cylinder during the first stroke of the pump. If the volume of AIR-PUMPS AND HIGH VACUA. 119 air that the cylinder will hold is one tenth the capacity of the cylinder and receiver together, then in the first stroke one tenth of the air orig- inally in the receiver will be removed, and the pressure will accordingly be reduced one tenth. In the second stroke one tenth of what is left is removed, and so on, so that it may readily be cal- culated that after ten strokes the pressure will be reduced to nearly one fourth of what it was at first, and after one hundred strokes it will only be one forty thousandth of that amount. In the same way the calculation could be made for any other relation between the capacity of the cyl- inder and that of the receiver. It is evident that it would require an infinite number of strokes to produce perfect exhaustion, even were the pump perfect. But in practice there is no difficulty on this score, for the exhaustion, that a comparatively small number of strokes would give, were there no leakage, is far beyond the limitation of the best pumps. After a very short time the leakage in an ordinary pump bal- ances the removal by pumping. For producing what are ordinarily known as high vacua, other means must be employed. And among the most important of these is the mercury lift-pump, or Geissler pump as it is or- dinarily called. The construction of this pump may easily be understood from Fig. 21. The 120 THE PHYSICAL PROPERTIES OF GASES. vessels A and B are glass reservoirs to contain mercury. D is an overflow pipe leading from B and having its lower end so shaped as to form a trap to exclude the air. C is the receiver or vessel to be exhausted. In the diagram it is represented as a glass bell jar, closed at the bottom by fitting air-tight over a flat brass or ground glass plate, through which opens the tube leading to the vessel B. The tube connections may all be made of glass, except part of the tube connecting A and B, which must be of flexible india- rubber tubing. To oper- ate the pump, the vessel A must be nearly filled with mercury. It is then raised until it is slightly Fig. 21. Modified Geissler higher than the vessel B, so that the mercury flows into B, filling it, and driving the air out through the tube D. As soon as B is completely filled with mercury, so that a little has run over and filled the tube D, the vessel A is lowered so as AIR-PUMPS AND HIGH VACUA. 121 to be more than thirty inches below the bottom of B. The atmospheric pressure cannot sustain a column of mercury greater than thirty inches in height, and consequently it flows back out of the vessel B into A, and also the mercury in the tube D sinks until it stands about thirty inches above the lower end of the tube. The system now resembles a double barometer, there being a column of mercury in the tube between A and B supported by the pressures of the at- mosphere, and another in the tube D, while the space B between these two is a Torricellian vac- uum. But as A is lowered, the mercury sinks low enough to uncover the tube connecting with the receiver C and the air in C at once expands and fills also the vessel B. This influx of air into B causes the mercury in the tube D to sink considerably, since the difference between the height of the mercury in D and the barometric height is the measure of the pressure of the air in the vessel B. The operation is now repeated by raising A, and allowing the mercury again to flow into B and drive out the air it contains through the overflow pipe D. This air bubbles up through the mercury in the cup and escapes, and again the mercury is lowered and air flows from C into B. In this way an amount of air equal to the volume of the vessel B is driven out at every operation, and the apparatus is really a 122 THE PHYSICAL PROPERTIES OF GASES. pump with automatic valves and a mercury pis- ton that cannot leak, working up and down in B as a cylinder. At E is shown a stopcock through which air may be allowed to enter, or by which any other gas with which it is desired to fill the receiver may be introduced. A gauge is seen at F which indicates the pressure of the air in the receiver. It consists only of a U tube, half full of mercury and closed at one end while the other connects with the receiver. At ordinary pressures the mercury completely fills the closed arm of the tube, but as the pressure in the receiver di- minishes, the mercury in the two arms becomes more nearly at the same level ; and since there is a Torricellian vacuum above the mercury in the closed branch of the tube, the two sides will not come to the same level until the pressure in the receiver has been diminished to the same amount. The difference in level, then, of the mercury in the two branches of the tube, measures the pres- sure of the air in the receiver. But suppose the exhaustion is being carried to the utmost extent possible, and it is desired to form an idea of the pressure in the receiver, it is obvious that there would be great uncertainty in measuring such pressures as one ten-thousandth that of the at- mosphere, since such a pressure would corre- spond to a difference in height between the two sides of the gauge of only about one three-hun- AIR-PUMPS AND HIGH VACUA. 123 dredth part of an inch, a quantity which it would be impossible to accurately observe. There is, however, a device called a McLeod gauge, employed in measuring very small pres- sures, in which a quantity of the rarefied air is compressed a certain known amount, perhaps a thousand times, before its pressure is measured, and the pressure before compression is then ea- sily calculated. The pump that we have just described affords a very good illustration of this mode of measuring pressures. For suppose the tube D is of so small a bore that the volume of the vessel B is ten thousand times as great as that of a portion of the tube D one inch in length ; if then it is desired to know the pressure in the receiver, it is only necessary to observe the way in which the air in B becomes compressed in being forced out through the tube D. If, when the air has been pushed out of B and down D so far that there is only a column of mercury fifteen inches high separating it from the outer air it should form a bubble only two inches in length, we should conclude that its pressure was one ten - thousandth of an atmosphere before compression. For according to the supposition made above it occupies one five-thousandth part of the volume of the vessel B, and its pressure as measured by the height of the mercury col- umn in D is one half an atmosphere. It would 124 THE PHYSICAL PROPERTIES OF GASES. therefore have to be compressed twice as much to have a pressure of one atmosphere. In this way exceedingly small pressures may be meas- ured with ease and certainty. The above form of air-pump is one of the most useful that physicists possess for obtaining high exhaustions. Its action is certain and quite rapid, and it is therefore either this form or the following that is commonly used in exhausting the glass globes of incandescent electric lamps. Where, however, it is desired to obtain the very highest possible degree of exhaustion, the Geiss- ler pump yields to another form of mercury pump devised by Sprengel. In this air-pump the principle is entirely dif- ferent : mercury flows from a reservoir and es- capes by drops into a long vertical tube with a bore, rather smaller than the lead of a lead-pencil, and air is entrapped between the drops and car- ried out in this way. Fig. 22 is a diagram of such a pump. The mercury is introduced into the reservoir A, and escapes by drops at B into the long vertical tube, its flow being regulated by a stopcock at S. The tube leading to K, the vessel to be exhausted, is connected at B, and a pressure gauge also is usually added. At first the vertical tube is full of drops of mercury, sep- arated from each other by little columns of air that are thus caught and carried out. As the AIR-PUMPS AND HIGH VACUA. 125 exhaustion proceeds, these become fewer, and the mercury column in the long tube stands at a a height of nearly thirty inches above the point where it escapes. The tube is made more than forty inches long, so that the drops of mercury as they enter it have a dis- tance of ten or twelve inches to drop through, and each as it falls in compresses the column of air under it like a spring, until finally enough is caught in this way to make a bubble that can be forced out. When the exhaustion is well ad- vanced, each drop, owing to the absence of the cush- ion of air, gives a sharp metallic click as it strikes against the top of the mer- i i, i TM. Fi - 22. Sprengel's Air- cury column below. Ihe rump. mercury that escapes at the bottom of the pump is caught and returned to the receiver A, and is used over again. In the tube connecting with the receiver is a larger piece of tubing, C, filled with gold-leaf, or con- 126 THE PHYSICAL PROPERTIES OF GASES. taining sulphur, to absorb the vapor of the mer- cury. This pump is exceedingly slow in its ac- tion, and so it is often used in combination with the Geissler pump, the latter being used as long as it is of any advantage, and then the Sprengel is employed to complete the exhaustion. By the use of this pump, taking extraordinary precautions to secure freedom from moisture and the vapor of mercury, Crookes has been able to obtain exhaustions higher than one fifty-mil- lionth of an atmosphere, but to attain this de- gree of rarefaction the pump requires to be in action for many hours, and even days, in ex- hausting vessels of only a few cubic inches capa- city, and all the parts to be exhausted require to be repeatedly heated to drive off the gases con- densed on the surface of the glass. But in obtaining the highest vacua, chemical means also are usually employed. Sir Humphry Davy first employed this method : Having put into the vessel to be exhausted some caustic pot- ash, and then filled it with carbonic acid gas, he pumped out the gas as far as possible, and hav- ing sealed the vessel, left the residual gas to be absorbed by the caustic potash, and thus ob- tained a very good vacuum. This plan is now often used, and also advantage is taken of the great absorbing power of freshly prepared cocoa- nut-shell charcoal. AIR-PUMPS AND HIGH VACUA. 127 These high exhaustions are called by courtesy vacua, as they are the nearest approaches that physicists have been able to make to an absolute vacuum by the most refined methods known to science ; and yet we should hardly call that space a vacuum in every cubic inch of which there are 350 million million molecules of the gas, and, according to the latest conclusions of the molec- ular theory, that is about the number in a cubic inch of air when it is reduced to one millionth of the atmospheric pressure. To form some conception of the vastness of this number, we may consider that if, through the side of a little glass bulb of one cubic inch capacity that had been exhausted to this extreme degree, a hole were to be made through which a million mole- cules could enter in every second, it would take ten years for the pressure inside the bulb to be doubled, that is, for as many more molecules to pass through as those already contained in the bulb. These considerations show how very far from anything like an absolute vacuum are the high- est exhaustions in the power of the physicist. The difficulty of making high vacua is further enhanced by the way in which gases condense on the surface of glass. To form a true conception of the state of the case, we must picture to our- selves the interior of the glass tubes and bulbs 128 THE PHYSICAL PROPERTIES OF GASES. that are being exhausted as covered with a film of air or gas in a highly condensed state, which escapes in part as the exhaustion proceeds, and serves to keep up the air pressure in the vessel, so that it is very probable that Boyle's law may fail at very low pressures partly on this account. CHAPTER VI. DIFFUSION AND OCCLUSION. IF a jar filled with hydrogen is inverted over a jar of carbonic acid gas, the two jars being fitted together mouth to mouth, it might be ex- pected that the hydrogen would remain in the upper vessel and the carbonic acid gas in the lower one, since the latter gas is about twenty- two times as heavy as the former, but this is not the case. If left for a comparatively short time, the hydrogen will be found to be mingled with carbonic acid gas in the same proportion in every part of the inclosing vessel. If the lower jar had been a vacuum instead of being filled with the heavier gas, the hydrogen would instantly have expanded and filled the whole space. In the same way the carbonic acid gas would have expanded into the upper jar if it had been empty. But when both jars are full, as in the first case, exactly the same thing takes place, but more slowly, for the hydrogen really expands and dis- tributes itself uniformly throughout both jars, just as if the other gas had not been present, and the carbonic acid gas also does the same 130 THE PHYSICAL PROPERTIES OF GASES. thing, and the result is that there is a uniform mixture filling the whole vessel. If the hydro- gen had been in the lower vessel, the same thing would have taken place, but more rapidly. This curious property of gases, that each, in distrib- uting itself, pays no more attention to any other gas present than if it were not there, suggests the somewhat similar way in which each portion of gas or vapor present in a mixture exerts the same amount of pressure on the walls of the vessel that contains it that it would if the other components of the mixture had not been present. All gases show this power of mixture, or of dif- fusion, as it is usually called. It may be ob- served taking place if, for example, flasks con- taining hydrogen and chlorine are connected by a long tube. The color of f the chlorine enables the progress of the diffusion to be watched. If the gases in these experiments are sepa- rated by a porous diaphragm of some sort, such as a plug of dry plaster-of-paris, or of porous earthenware, the action proceeds in the same way, and in the end the diffusion is just as per- fect as before ; but in this case, while the process is going on there may be a change in pressure in the vessels, that in one increasing, while it decreases in the other, both, however, finally coming again to the same pressure. To see clearly the meaning of this fact, it will be well DIFFUSION AND OCCLUSION. 131 to examine a very simple case, that of the escape of a gas under pressure through a fine opening. By the establishment of the principle of the conservation of energy, it becomes possible in many cases to predict results that might other- wise only have been discovered by experiment. By this principle it may be shown that the ve- locity with which a gas under pressure will escape into a vacuum will be inversely propor- tional to the square root of its density, that is, oxygen, which is sixteen times as heavy as hy- drogen, would, under exactly the same circum- stances, escape through an opening only one fourth as fast as the latter gas. This result is abundantly established by exper- iment, and is made the basis of an instrument in common use for testing the density of illu- minating gas. The gas to be tested is introduced into a gas-holder where it can be kept at constant pressure ; it is then allowed to escape into the air through a metal plate having a fine hole pierced in it ; the gas flows through a meter by which the quantity that escapes in a given time is measured. By the above law, the relative den- sities of two samples can in this way be readily determined. A porous diaphragm or membrane that does not act on the gas, or in which it is not dissolved, acts in the same way as the small aperture, for 132 THE PHYSICAL PROPERTIES OF GASES. such a diaphragm, for instance, as a plug of plaster-of-paris presents a great many fine open- ings through which the gas may escape. Suppose a tube, open at one end and closed at the top with a dry plug of plaster-of-paris, is filled with hydrogen, and placed with its open end in a trough of water. The at- mosphere without contains no hydrogen ; the inclosed gas therefore diffuses through the plug as it would into a vacuum, until it has entirely escaped. But at the same time air from outside dif- fuses through the plug until the air pressure is the same on the inside as without. But hydrogen passes out of the tube in this way more rapidly than air enters it, for two rea- sons : it is more than 14 times lighter than air, and will therefore diffuse 3.8 times as fast as air under the same circumstances, and, besides this, it is diffusing into a region where there is prac- tically no hydrogen, and so keeps passing out- wards at a constant rate, while the air diffuses inwards more and more slowly as the air pres- sure on the inside increases. The result is that the pressure in the tube Fig. 23. DIFFUSION AND OCCLUSION. 133 diminishes on account of the rapid escape of hydrogen. This is shown by the rise of the water in the tube ; soon a stationary point is reached, and then, as the air pressure on the in- side becomes greater, the column of water sinks till it finally comes to the same level as that in the trough. Another experiment that illustrates very well the difference between the rates of diffusion of different gases is as follows : Take a wide- mouthed jar full of carbonic acid gas, and tie over its mouth a bladder, and place the whole Fig. 24. Diffusion of Gases. under a bell jar filled with hydrogen. The blad- der will become strongly distended from the dif- fusion inwards of the hydrogen being more rapid than the outward diffusion of the carbonic acid. If the jar be filled with hydrogen and inclosed in a bell jar full of the heavier gas, then the bladder will be distended inwards on account of 134 THE PHYSICAL PROPERTIES OF GASES. the rapid escape of the hydrogen gas ; but in either case, if left long enough, the pressure within will become the same as that without the jar. The difference in pressure is then merely a temporary inequality due to the hydrogen dis- tributing itself uniformly within and without the jar more rapidly than the carbonic acid gas. Where the diaphragm, through which diffu- sion is taking place, consists of a membrane, such as a bladder, or sheet of india rubber, the action is not exactty the same as when it is of porous earthenware, or plaster-of-paris. In the latter case the diaphragm is inert; it merely presents many fine holes through which the gas may pass, and the law of diffusion is the same as for a single fine opening. In case of the diaphragm being a membrane, an animal tissue or india rubber, the rate of diffusion is found to be different from that for a single fine open- ing. It is believed in this case that there is a kind of solution taking place, the gas being dis- solved by the membrane on one side, and escap- ing by a sort of evaporation on the other side, as the membrane becomes saturated with it. In support of this view is the fact that the more readily a gas is absorbed by a membrane the more rapid is the diffusion of that gas through the membrane. In this case the rate of diffusion depends not only on the density of the DIFFUSION AND OCCLUSION. 135 gas, but on its relation to the substance of which the diaphragm is made. The subject of diffu- sion was first carefully studied by Graham, and it is to his investigations that we are indebted for most of our knowledge of this subject. One other of Graham's experiments is of such importance that it deserves especial men- tion. A mass of hydrogen was allowed to dif- fuse through a porous partition, and the portion of gas that diffused through first was separated from that diffusing through later, and caused to diffuse again through the partition; again the part coming through first was selected and sub- jected to another diffusion, and so on many times, with the idea that perhaps, in this way, a mass of hydrogen might be obtained that would dif- fuse more rapidly than ordinary hydrogen, but no difference could be discovered. This experiment furnishes most important evi- dence that all particles or molecules of hydro- gen have very nearly, if not exactly, equal masses. There is an important case of the escape of gas through a small opening that should be considered, as it leads to results of great signifi- cance which we shall have occasion to recur to in a later chapter. If a gas under pressure escape through a long fine tube, such, for example, as are produced when glass tubes are heated and 136 THE PHYSICAL PROPERTIES OF GASES. drawn out to the fineness of hairs, and are, therefore, known as capillary tubes, it does not obey the same laws as when simply escaping through a fine hole in a thin plate. When escaping through a thin plate into vacuum, the velocity of efflux is proportional to the square root of the pressure ; that is, a four- fold increase of pressure will only double the velocity of the escaping gas. Then, as the tem- perature rises, the gas becomes less dense, and so for the same pressure the velocity of efflux will be greater. But when the escape is through a capillary tube, it is found that the velocity de- pends directly on the pressure, so that twice the pressure will produce twice the velocity ; also the longer the tube, the less the velocity of the escaping gas, other things being equal; and when the gas is warm, it escapes less rapidly than when cold. These results might be thought to be due to something like friction between the gas and the sides of the tube through which it escapes. But it is further found that the mate- rial of which the tube is made has scarcely any effect one way or the other. It is, therefore, believed that the tube is coated on the inside with a layer of gas which is nearly, if not quite, at rest, and that the stream of escaping gas has its greatest velocity along the centre or axis of the tube, while nearer the sides of the tube the DIFFUSION AND OCCLUSION. 137 gas flows more slowly. Each layer of gas will thus be moving more rapidly than the layer just outside of it, and less rapidly than the one in- side it, and nearer the axis of the tube ; and so, unless each layer slips with perfect freedom over the other, there will be retardation due to this sort of friction which takes place in the mass of gas itself, and not where it comes in contact with the surrounding tube. In addition to this, there is the friction between the outer layer of gas and the sides of the tube. No substances are perfectly fluid ; all exhibit to a greater or less degree that internal friction of one part against another which is so charac- teristic of tar and molasses. It is a character- istic of this sort of friction that it may oppose great resistance to rapid motions, as is expe- rienced if one tries to stir thick molasses or tar rapidly, but that the substance yields to the very slightest forces which act steadily upon it. Thus, no matter how thick tar may be, it will settle to the bottom of the vessel that contains it, and its upper surface will become as level as water, if only time enough is given it. This property of fluids is known as viscosity, and these experi- ments with the capillary tubes show that gases also possess viscosity ; otherwise they would flow from a long tube with the same velocity as from a short one, or hole in a plate. 138 THE PHYSICAL PROPERTIES OF GASES. But more than this, a French investigator, Poiseulle, having measured the diameters and lengths of the tubes used and the quantity of gas flowing through in a certain time, was able to calculate exactly the amount of this viscosity in different gases. Professor Clerk Maxwell also investigated the viscosity of gases in the year 1866 by an en- tirely different method. Three parallel flat discs or circular plates of metal were suspended in a horizontal position by a fine wire, so that, when the combination was started rotat- ing, it would spin now around in one way and now in the opposite way, as the suspending wire twisted and untwisted. Four oth- er plates of metal were fixed, one above the oscillating system, one between each of the pairs of discs, and one below them, so that each disc oscillated between two fixed p i ates fa e suspension wire . A ,11. i passing through holes in the cen- tres of the fixed plates. This whole apparatus was placed in a closed vessel, so that the air could be exhausted, or other gases substituted. The mode of experiment was to set the discs vibrating, and observe the rate at which the vibrations died out. If it is remem- Fig. 25. Max- well's Visco- simeter. DIFFUSION AND OCCLUSION. 139 bered that the layer of air in contact with a disc must oscillate with it while the layers next the fixed plates will remain at rest, it will be evident that between the discs and the plates the air will be in a state of motion, which will be greatest near the discs. It is possible, by tak- ing into account the size of the discs and the dis- tance between them and the plates, and the rate at which the oscillations die out, and correcting for the viscosity of the wire by which they are suspended, to calculate the viscosity of the gas filling the vessel. These experiments of Maxwell's confirmed and extended the results obtained by Poiseulle, giving the viscosity of various gases under dif- ferent pressures. The most remarkable result of these investigations was to show that the vis- cosity of a gas was very nearly independent of the pressure, being the same at the ordinary at- mospheric pressure as it is at one sixtieth of that amount. It was also found by Maxwell that the viscosity increased with the temperature in such a way as to be proportional to the absolute tem- perature. But other investigators have found that the viscosity does not increase so rapidly with the rise in temperature as Maxwell's result would indicate, though all find that the viscosity increases as the temperature rises. In the case of liquids exactly the reverse is true : the viscos- 140 THE PHYSICAL PROPERTIES OF GASES. ity diminishes as the temperature rises. This result explains why it is that the escape of a gas through a capillary tube is slower at high than at low temperatures. It is interesting to notice here that each of these results had been anticipated by Maxwell, reasoning from the kinetic theory of gases. He was, therefpre, led to make the investigation as a test of the truth of this theory; and these two results, which might otherwise perhaps be regarded as insignificant, at once appear impor- tant in their relation to this remarkable theory. The viscosity of gases is exceedingly small, compared with that of ordinary liquids, air being eighty times less viscous than water. But small as this quantity is, it is this that enables the air to support clouds of small water particles and fine dust. Water in its liquid state and the substances of which dust is made are much more dense than air, and cannot be said truly to float in the air as a balloon does. A fine drop of water will undoubtedly sink downwards in the air ; but, owing to the viscos- ity of the air, this motion may be so slow that for all ordinary purposes it may be regarded as actually floating. Professor Stokes has inves- tigated the resistance which a spherical body would meet in moving through a viscous fluid, and from this it appears that a drop of water DIFFUSION AND OCCLUSION. 141 one one-thousandth of an inch in diameter would sink through the air at the rate of about eight tenths of an inch per second if the air were one thousand times less dense than the drop itself, which would be very nearly the case at the ordi- nary height of a cloud; while, if its diameter were only one ten - thousandth of an inch, it would fall one hundred times as slowly, or about half an inch in a minute. The same is true of dust particles : they are really slowly sinking through the air, as shot will sink down through a mass of tar if left long enough ; but in the mean time they are carried hither and thither with the mass of air through which they are thus slowly and laboriously fall- ing. A mass of gas thus charged with dust or water particles may be in this way made heavier than the surrounding air, and sink as a whole mass, the heavier particles dragging the air mass with them. It is in this way that muddy water is heavier than clear. Were it not for viscosity, the particles of clay would sink at once to the bottom ; but, as it is, they drag the water with them, giving the whole mass a downward tend- ency. Many gases are readily absorbed by water. Other liquids also possess this power in a greater or less degree. Water will, for example, absorb its own volume of carbonic acid gas, four hun- 142 THE PHYSICAL PROPERTIES OF GASES. dred and thirty times its volume of ammonia, two and a third times its volume of chlorine, and only about one twentieth of its volume of oxygen. The absorption of a gas by water is readily shown by collecting a jarful of chlorine gas, and then, after covering its open mouth with a card, invert it, placing its mouth below the sur- face of a trough of cold water, and withdraw the card. As the gas is absorbed the water will rise and fill the jar. Gases, unlike solids, are dissolved more freely in cold water than in warm. This does not seem strange when it is recollected that by heating solids they are melted and brought to the liquid state, while when it is desired to condense a gas it is cooled. According to the dynamical or kinetic theory of gases, the molecules of the gas at a high temperature are moving with greater velocities than at low temperatures, and are therefore less apt to be caught and held within the range of attraction of the liquid particles, just exactly as at a high temperature the pres- sure of a vapor before it begins to condense is greater than at a low. The laws of the solution of gases in liquids have been carefully investigated by Bunsen, who finds that the weight of gas that is absorbed by a given volume of liquid is proportional to the DIFFUSION AND OCCLUSION. 143 pressure. But as the volume of a mass of gas is less as the pressure is greater, it follows that the volume which a given amount of liquid can ab- sorb at a certain temperature will be constant, whatever the pressure. Water, for example, can absorb its own volume of carbonic acid gas at at- mospheric pressure ; it will also dissolve its own volume if the pressure is twice as great, but in that case the gas will be twice as dense, and con- sequently twice the weight of gas is dissolved. This is sometimes known as Henry's law, from the name of the Englishman who discovered it about the year 1803. There is no probability that it is true for high pressures when the gas is near condensing. We again find evidence of the peculiar gase- ous indifference that has been already noted, in the fact that the amount of any gas that a liquid can dissolve has no reference to the amounts of any other gases that it may already hold in solu- tion. If a mass of water contain no oxygen, it will absorb just as much of that gas, and no more and no less, when the water is perfectly pure as it will when saturated with other gases. But if it holds any oxygen in solution it will be capable of absorbing just so much less of that gas than it otherwise would. Gases are condensed in a greater or less de- gree on the surface of all solids. In some cases 144 TEE PHYSICAL PROPERTIES OF GASES. this amount is enormous. Bunsen lately found in some of his experiments that a third of a cubic inch of carbonic acid gas was condensed on the surface of some fine threads of glass to less than one one -hundredth part of its original volume. The threads were left in the gas for about three years. Their total surface was very great, amounting to more than fifteen hundred square inches. When lines or figures are drawn with a stick upon a sheet of glass, which is then breathed upon, the markings are distintly seen. So, also, if a coin or signet be laid for a time on a clean, freshly polished metal plate, on breathing on the plate the figure of the coin or the outline of the signet will be distinctly seen. If a polished silver plate is used, which, after the coin has rested on its surface, is exposed to the vapor of mercury, the figure of the coin dis- tinctly appears. And these curious results may be obtained even when the objects are only placed very near the plate, and not in immediate contact. This action was explained by Waidele as due to the layer of gas condensed on the surface of the plate of metal, glass, or wood ; his idea being that a clean plate was quickly coated with a layer of gas, and that the objects placed upon it inter- fered more or less with this action, or caused DIFFUSION AND OCCLUSION. 145 the layer condensed at one point to differ from another. Among other experiments by which he tested this theory was the following : The coin was exposed in an atmosphere of carbonic acid gas, and then laid on the clean silver plate ; when exposed to the mercury vapor the conden- sation took place over the rest of the plate, leav- ing the figure of the coin marked by its absence. The plate was then exposed so as to become coated with gas, after which a clean coin was laid upon it. On now exposing to the mercury vapor, it was condensed on the spot where the coin had rested. Porous bodies present an immense surface on which condensation may take place, and thus absorb in some cases enormous quantities of gas. One cubic inch of boxwood charcoal, at ordinary temperatures, will absorb 90 cubic inches of am- monia, 35 cubic inches of carbonic acid gas, and 9 cubic inches of oxygen. This is a reason why charcoal is so useful as a deodorizing agent. The metal platinum may be prepared in the form of a light porous mass known as plati- num sponge, and this has very great absorptive power. It is said to absorb 250 times its vol- ume of oxygen gas ; and if such a sponge is placed in a fine jet of hydrogen, the heat gener- ated by the rapid condensation of the gas is suffi- cient to set fire to the jet. 146 THE PHYSICAL PROPERTIES OF GASES. At high temperatures both iron and platinum absorb considerable amounts of hydrogen, which seems to penetrate into the interior mass of these substances, and not be simply held on the sur- face. It is almost like a combination of the gas with the metal. Graham, who made a careful study of this property of certain metals, called it occlusion. He found that on heating plati- num red-hot, and then allowing it to cool while immersed in hydrogen gas, it would absorb four times its volume. Iron possessed the same prop- erty to a much less degree. Silver also absorbed seven times its volume of oxygen, and one vol- ume of hydrogen. But the most remarkable instance of occlusion is found in the case of the metal palladium, which will absorb hydrogen when cold. This is seen in particular when water is decomposed into its constituents, ox- ygen and hydrogen, by a current of electricity. If the electrode where the hydrogen is set free is made of palladium, it will absorb 980 times its volume of gas. The gas, being just set free from one combination, is in what is called the nascent condition, and is in a state favorable to forming new relations. The volume of the palladium, after thus ab- sorbing nearly one thousand times its volume of gas, is slightly increased ; it becomes nearly one tenth greater than before. To compress by sim- DIFFUSION AND OCCLUSION. 147 pie mechanical means such a volume of hydro- gen into a volume equal to that of the palladium would require a pressure of fourteen thousand pounds to the square inch. It seems probable that an alloy is actually formed between the hy- drogen and palladium. In all these cases of occlusion the gas may be driven out of the metal by heating it, just as gases dissolved in liquids may be driven out by heat. This curious property of occlusion seems to explain another observation of Graham's, that hydrogen gas will pass through iron and plati- num when those metals are hot. The gas seems to be absorbed on one side or dissolved in the metal, and then, after the metal becomes satu- rated, is given off from the other side in a kind of evaporation. This transmission takes place through red-hot iron or platinum even more rap- idly than through a sheet of india rubber of the same thickness. By reason of its infusibility, platinum might have been chosen as a material suitable for the bulb of an air thermometer to be used in meas- uring high temperatures ; but on account of the readiness with which it transmits gases at high temperatures it is evidently unfit for such a use. Cast-iron, when very hot, will allow carbonic monoxide to pass quite freely through it by a 148 THE PHYSICAL PROPERTIES OF GASES. similar process. This gas is the poisonous coal gas that is produced in stoves and furnaces by imperfect combustion. It appears, then, that the physicist must re- member constantly that all the materials and apparatus that he makes use of are not only im- mersed in a sea of gas, the atmosphere, but that, even when taken out of the air and put in any of our so-called vacua, their surfaces are wet, so to speak, with a layer of gas that it is extremely difficult to get rid of ; and if it is necessary to remove entirely any particular gas, almost the only way in which it can be satisfac- torily done is to substitute some other gas. If it is sought to remove the last trace of oxygen from a vessel, it is filled with some gas, such as carbonic acid gas or hydrogen, and exhausted, and then filled again and left for some time, that the film of air may be replaced as far as possi- ble by the other gas, after which it is again ex- hausted. By repeating this process a number of times the oxygen may be very completely removed. CHAPTER VII. THE THERMODYNAMICS OF GASES. THE principle of the conservation of energy has come to be perhaps the best established, as it has been by far the most fruitful, generaliza- tion of modern physics. Every phenomenon in nature, every experiment, every application of physical principles in the arts, becomes, when investigated, at once a test and a confirmation of its truth. It is fruitful because it gives the physicist immense power in dealing with new problems. It is so far-reaching that there is no department of physical science into which it does not enter as an essential element, for every- where is found energy in a constant state of transformation, so that the physicist in his pur- suit of it needs to be constantly on the alert, lest it elude him in some of its protean forms. But whenever it can be traced in its transformations, and submitted to measurement, the confirmation comes that no energy is ever destroyed, but is changed from one form to another. When this great principle is stated in the form in which it particularly applies to the subject of heat, it 150 THE PHYSICAL PROPERTIES OF GASES. asserts that, whenever work is transformed into heat by friction or otherwise, or whenever, on the other hand, heat is used up in doing work, the quantity of heat is always in a constant ratio to the work done, and this constant amount of work which is equivalent to unit quantity of heat is called the mechanical equivalent of heat. This particular statement of the principle is the first form in which it was recognized, and it was for its establishment that Dr. Joule of Manches- ter began, about the year 1843, a long series of experiments, which he carried on with the great- est ingenuity and scientific accuracy during many years of his life. These investigations were un- dertaken especially to determine the exact rela- tion between heat and work ; but as experiment after experiment led to the same result, whether the heat was produced by stirring water with paddles, or by rubbing two iron plates together, or by the heat developed in the flow of an electric current, the idea took larger proportions. For it was always found that the same amount of heat was produced, when the work was spent in turning the paddles or in overcoming the fric- tion of the iron plates, as when it was spent in driving the dynamo-electric machine that gave the electric current; and it was seen that the work done, whether made to develop heat di- rectly or made to produce electrical energy, which THE THERMODYNAMICS OF GASES. 151 was afterwards converted into heat, was always exactly the same for the same amount of heat produced. It was thus established that 772 foot- pounds of work, or the work required to raise a weight of 772 pounds a distance of one foot, must be expended in order to develop the heat required to raise the temperature of a pound of water one degree Fahrenheit. This is known as the mechanical equivalent of heat, or Joule's equivalent, from its distinguished investigator. But these experiments went farther, and estab- lished the fact that, to produce an electrical cur- rent of a certain strength in a given conductor, the expenditure of the same amount of work is always required, whether as ordinary mechani- cal work or in some other form, as heat or chem- ical energy ; thus leading to the wider conception of the conservation of energy, which was due to these experiments of Joule's rather than to any other one cause. It is proposed to discuss in this chapter some important properties of gases considered in the light of the mechanical equivalence of heat and work. It has already been noticed that there are two principal ways of observing the effects of heat on gases ; one when the gas is kept in a vessel of constant volume while it is heated, and the other where it is allowed to expand during the heat- 152 THE PHYSICAL PROPERTIES OF GASES. ing, so that the pressure is always the same. In the former case its pressure increases; in the second its volume becomes greater. Careful experiments show that it requires more heat to raise the temperature of the gas by any given amount, as ten degrees, when the pressure is kept constant, than is required for the same rise in temperature when the volume is unchanged. Dr. Julius Mayer, of Heilbroun, first ex- plained the reason for this difference in the year 1842. With singular clearness for his time, he grasped the idea of the equivalence of heat and work, and found in this relation the reason for the greater amount of heat required in the one case than in the other. Let us follow his reasoning, changing it some- what to conform to modern modes of expression. When a mass of gas is confined so that it can- not expand, whatever heat is added to it goes simply to increase its temperature and pressure. But as the walls of the vessel that contain it do not yield to this pressure, and so receive no motion from this pressure, there is no work done, for work is done only when force brings about the motion of the body on which it acts. Thus work, in the sense in which it is used by the physicist, is not done when a pillar supports a roof, for there is no motion. The downward pressure of the roof on the pillar is exactly THE THERMODYNAMICS OF GASES. 153 balanced by the upward reaction of the pillar against the roof. But when the materials con- stituting the roof were raised into position, work was done, for the resistance due to their weight was overcome through the distance they were raised. The amount of this work is measured by the product of the weight that is raised by the distance through which it is lifted, or, stated in more general terms, the amount of work done in any case is the product of the force which is acting, by the distance through which the body on which it acts moves in the direction of that force. It is obvious, then, that the gas that is heated, while its volume remains constant, does no work outside of itself. The energy of the heat goes to the gas, and increases its stock of energy, and raises its temperature and pressure, but without other effect. It is very different, however, in the case of the gas that is allowed to expand so as to remain at constant pressure. In expand- ing, the outer air is pressed back, and work is done outside the gas itself. The amount of this work may readily be estimated in the following way : Suppose the mass of gas has, in the first place, a volume of one cubic foot at the atmos- pheric pressure, and that it is kept at that pres- sure as the temperature rises. Let it be sup- posed to be contained in a cylinder of exactly 154 THE PHYSICAL PROPERTIES OF GASES. one square foot cross section, and separated from the outer air by a piston that is just counter- poised, so that the only pressure to which the gas is subject is that of the atmosphere on the piston. If the temperature of the air is now raised, say 100 degrees, the air will expand, and the piston will move up- wards. The external work that will have been done is then found by multiplying the distance through which the piston has been moved by the total pressure upon the piston, which is of course the force that is overcome. The force on the piston will be about 2,116 pounds, since it is one foot square, and the air pressure is 14.7 pounds to the square inch. If in the expansion the piston had been moved through one third of a foot, then the work done would be 705.3 foot-pounds. The heat, then, which is supplied to the gas in the second case, has not only to raise its tem- perature, but also to supply the energy necessary for doing the work of expansion. The conclusion was, therefore, that the differ- ence between the amounts of heat required in Fig. 26. THE THERMODYNAMICS OF GASES. 155 the two cases was solely because in the one case external work was done, while it was not done in the other, and that the amount of this work done in the expansion was the mechanical equivalent of the excess of heat that was required when the expansion took place over that required when the gas was not allowed to expand. On this basis, from measurements that had been made of the amounts of heat required for raising the temperature of gases in the two cases mentioned, Mayer calculated the value of the mechanical equivalent of heat, and reached a result that was only astray by reason of the imperfection of the data that he employed. But, looking more closely at the above reason- ing, its conclusiveness may well be questioned ; for there appears to be one serious break in the argument. It has been assumed that the differ- ence in the amounts of heat required in the two cases was wholly due to the work done in ex- panding. But in the one case, as the result of the heating, we have an unchanged volume of gas at a higher temperature, while in the other we have a larger volume of gas at a higher tem- perature, together with some external work that has been done. In order, then, to prove that the excess of heat in the second case is mechanically equiv- alent to the work of expansion, it must be 156 THE PHYSICAL PROPERTIES OF GASES. shown that if there were no external work done, there would be no more heat required in the sec- ond case than in the first. Mayer saw this, and chose gases, because an experiment which Gay- Lussac had performed some years before had seemed to show that the temperature of a gas was not changed by expansion when no external work was done. If Mayer had chosen such a substance as water, for example, his conclusions would have been entirely wrong. In the year 1845 Joule carried out with great care a series of experiments to test this property of gases more accurately than Gay-Lussac's ex- periment had done, and established in the case of gases that, when no external work is done, no more heat is required to raise the tempera- ture of the gas a certain amount when it is kept at a constant volume than when it is allowed to expand. Or, stated in another may, the total energy of a gas depends only on its temperature, and not at all on whether it is expanded or compressed. The expanded gas has, therefore, the same energy as the gas that was not allowed to ex- pand, when their temperatures are the same; and therefore, since more heat energy must be supplied in raising the temperature of a gas when it is allowed to expand at constant pres- sure than when its volume is kept constant, the THE THERMODYNAMICS OF GASES. 157 excess must be equivalent to the external work done, and have disappeared in that way. Joule's experimental proof of this property of gases is interesting. He took two strong re- ceivers connected by a short tube having a stopcock, and from one of these vessels the air was exhausted, while in the other it was com- pressed to the amount of 20 atmospheres, or 300 pounds to the square inch. This whole apparatus Fig. 27. Joule's Experiment. was put into a vessel of water, so that its temperature could be accu- rately determined. After the water was thor- oughly stirred, and the whole had been left stand- ing long enough for the air inside to come to the same temperature as the water, the tempera- ture was carefully taken ; the stopcock was then opened, and the gas allowed to rush into the second vessel. After stirring the water, the temperature was not found to have changed enough to be detected, although the gas had now expanded and filled both vessels instead of one. An interesting modification of this exper- 158 THE PHYSICAL PROPERTIES OF GASES. iment was made by putting the two receivers into separate vessels of water, so that the change in temperature of each receiver could be sep- arately observed. In this case, when the stop- cock was opened, the water surrounding the vessel in which the air had been compressed showed a fall in temperature, while that around the vessel into which the escaping air rushed was raised in temperature by exactly the same amount. The second experiment explained the first. There was no change of temperature in the first case, because the cooling effect of the expansion of the air in the one vessel was equal to the heating effect due to the in-rush of air into the other vessel. In this experiment, then, the air can do no external work ; it is constantly inclosed in the two connecting vessels, and there is no pushing back of the outside air in its expansion. The temperature of the gas, after it has expanded and fills both vessels, is the same as when it was compressed into only one. There has no energy been given to it, or taken from it. This experi- ment of Joule's established the fact that the intrinsic energy of a mass of gas depended only on its temperature, and was not affected by the volume it occupied. Later Dr. Joule and Sir William Thomson THE THERMODYNAMICS OF GASES. 159 carried on a series of experiments that were much better adapted to test this property of gases, and it was found that the law just stated is very nearly true, but that with no gas is it per- fectly so. The variations from it were found to be small in every case, but greatest in those gases that showed the strongest divergence from Boyle's law. Thus, when air was expanded in such a way that no external work was done, it was found to be slightly cooled. Hydrogen gas differed from all other gases in being slightly heated; but the change in temperature was so small as to be scarcely recognizable with cer- tainty. It was found that a mass of air, taken at two atmospheres' pressure, and allowed to ex- pand to double its volume, thus reducing the pressure to one atmosphere without doing exter- nal work, was cooled less than five tenths of one degree Fahrenheit. In carbonic acid gas, which is much more easily condensed than the others just mentioned, the cooling is five times as great as in the case of air. A gas that perfectly obeyed Boyle's law, and conformed also to this law of Joule, if it had no viscosity, would be known as a perfect gas. It is needless to say that this is merely an ideal which does not exist in nature, and to which known gases conform more or less closely. Those gases that most nearly resemble a perfect 160 THE PHYSICAL PROPERTIES OF GASES. gas in their properties are the ones that are con- densed with the greatest difficulty, and are usu- ally regarded as typical gases. It will be instructive to examine closely the second experiment of Joule's, in which the two receivers were put in separate vessels of water, so that their changes of temperature could be observed independently. It will be recollected that the one in which the air had been condensed was found to be cooled as the gas escaped, while the one that had been exhausted was heated as the air rushed into it from the other receiver. As the stopcock was opened between the two vessels, the compressed gas expanded, and part of it was forced out with a rush into the other vessel. In thus expanding, it did work which was spent on the gas that was forced out, just as the gas developed in a cannon by the explosion of the powder does work as it expands in giving motion to the projectile. This work can only be done by the compressed gas at the expense of its energy ; it therefore loses an amount of en- ergy equivalent to the work done in expansion, and this loss of energy is shown by its fall in temperature. On the other hand, the gas that is forced out into the other vessel has this work done upon it. It receives energy from the ex- panding gas by which it has been expelled. The energy that it has thus received is chiefly in the THE THERMODYNAMICS OF GASES. 161 form of energy of motion as it enters the sec- ond vessel, just as the work done on the cannon- ball exists principally as energy of motion : but when the cannon ball strikes the target, then the energy is converted into other forms, perhaps sound and light are produced, a great deal of heat is developed, and pieces of the target go flying off with energy of motion which they get from the ball ; but in the end the pieces fall to the ground and come to rest, the sound and light die out or are absorbed, and all the energy becomes finally heat. So, also, the energy of the gas rushing into the second vessel, though at first chiefly energy of motion, soon becomes con- verted to heat, as the gas cannot escape, and comes to rest when the pressure in the two ves- sels becomes equal. The energy expended by the expanding gas is, therefore, found in the form of heat in the vessel into which the gas rushed. There has been no work done in the operation outside the closed vessels, and the energy that disappears in the one must appear in the other. The result is, therefore, that the temperature of the second vessel rises as much as that of the first is lowered. Professor Tyndall has illustrated this matter very beautifully by allowing a jet of gas escap- ing from a vessel in which it had been com- pressed to rush by a delicate thermometer or 162 THE PHYSICAL PROPERTIES OF GASES. thermopile. There is at once shown a decided cooling effect. If now air is forced through the same jet by a bellows or syringe, the thermom- eter instantly rises, showing that it is heated. Literally, we thus " blow hot and cold from the same mouth." In the first case the energy that causes the jet comes from the expanding gas itself, and so the jet, as it escapes, is chilled, the chilling being greatest just at the point where the gas escapes with greatest velocity ; for it has itself lost heat energy by expansion, and what- ever it has received by being forced out by the other gas is still in the form of energy of motion, and is only converted into heat energy as it comes to rest. But in the case of the jet from a bellows the energy is supplied by the per- son working the bellows, and thus the gas does not expend energy in causing the jet, but ac- tually receives it from outside ; it is, therefore, heated. Sir William Thomson has shown that a ther- mometer may be placed in a jet escaping from a cylinder of condensed gas in two ways, in one of which it will be cooled, and in the other it will be heated. If the gas escapes under pres- sure through a small hole not more than a twen- tieth of an inch in diameter in a thin metal plate, and if the bulb of the thermometer is brought as close to the opening as possible without touching THE THERMODYNAMICS OF GASES. 163 Ill the metal plate, a cooling effect will be noticed, owing to the expansion of the escaping air. But if the thermome- ter is placed half Cooled. Heated, an inch from the opening, and sur- rounded with a tube of hard rub- ber, leaving only a narrow space for the air to slip through, the air striking the bulb will largely lose its energy of motion in the narrow in- terval between the bulb and the sur- rounding tube, and the thermometer Fig. 28. will be heated. These properties of gases are very important in the case of air-compressors, and of certain kinds of refrigerating machines. In the use of compressed air for the transmis- sion of power, the heating which results when air is compressed is a source of considerable in- convenience. When air is compressed, all the work which is done in the compression is con- Compressed Air. 164 THE PHYSICAL PROPERTIES OF GASES. verted into heat, and shows itself in the rise in temperature of the compressed gas. As the gas becomes hotter it is compressed with more diffi- culty ; so in practice many devices are employed to carry off the heat as fast as it is developed, and keep the temperature down. But it is not possible in any way to totally remove this diffi- culty. But it may be objected, if all the work done in compression is converted into heat, and if this heat is then gotten rid of as soon as possible, then the work must be virtually thrown away, and the compressed air can have no more energy than it had before compression. It is true that the compressed gas has no more en- ergy than the gas had before compression, if its temperature is no higher, but the advantage of the compression lies in bringing its energy into more available form. The total energy of the compressed and uncompressed gas is the same at the same temperature, but the available energy is much greater in the former case. The rise in temperature due to compression is so great that if a mass of air at the freezing temperature of water is compressed to one fourth its original volume, its temperature will be raised three hundred and seventy-six degrees Fahren- heit, if no heat is allowed to escape. When the compressed air is used in driving a rock drill, or any other piece of machinery, it THE THERMODYNAMICS OF GASES. 165 gives up energy equal in amount to the work it does, and its temperature is accordingly greatly reduced. In the refrigerating machines that are now so commonly used in breweries, the required low temperature is obtained by the chilling of a gas on expansion. Ammonia gas is commonly used because it is easily condensed, for it may be re- duced to the liquid state by a pressure of ninety- eight pounds to the square inch, at a tempera- ture of fifty degrees Fahrenheit. An engine is employed which compresses the gas into receiv- ers, which are kept cooled by a stream of water. The heat due to compression is removed in this way, and now if the gas is allowed to expand its temperature will be greatly reduced; it is ac- cordingly permitted to escape slowly into pipes leading through the rooms to be chilled, and is exhausted from these pipes and compressed again into the receivers by means of the pump. There is no loss of gas except by leakage, and when the vaults are once brought to the required low tem- perature there will not be required a great sup- ply of water to cool the compressed gas. For the rate at which heat is removed from it will necessarily be the same as the rate at which heat must be removed from the vaults to keep them at the required steady low temperature ; and if the vaults are well protected, heat will be able to flow into them but slowly. 166 THE PHYSICAL PROPERTIES OF GASES. Sir William Thomson first pointed out that this property of gases explains the general dis- tribution of temperature in the atmosphere. In a medium like the atmosphere, which is a poor conductor of heat, the principal changes of tem- perature will be due to the transfer of great masses of air that have been heated or cooled by contact with hot or cold districts of the earth. A mass of air rising from the surface of the earth into the higher regions will expand as the pressure diminishes, but as it expands it cools ; and as all its neighboring masses of air have ex- panded in coming to that height above the sur- face, all will be cooled ; and so where there is a rapid circulation in a medium that is a bad con- ductor, the average temperature at any height will be as much lower than the temperature of the air at the surface as would be caused by the expansion of a mass of air in rising to that height. To give some idea of the amount of this cooling, it may be instanced that, supposing the average surface temperature to be 50, at 16,000 feet, or about the height of Mont Blanc, it would be 36 below zero, and at a height of ten miles it would be 230 below zero ! But the temperatures of the upper air, as actually ob- served in balloon ascents, show no such extremely low temperatures. In one of Mr. Glaisher's most celebrated ascents, he reached a height of THE THERMODYNAMICS OF GASES. 167 nearly seven miles, and the thermometer indi- cated about zero Fahrenheit at that height. It is evident, then, that other causes determine the temperature of the upper air besides the cooling effect due to expansion. These are the effect of water vapor in the air, which, as it condenses, gives up heat to the air, the absorption of direct radiation from the sun and of radiation reflected from the earth. CHAPTER VIII. AVOGADRO'S LAW AND THE KINETIC THEORY. UP to this point, with the exception of a short sketch of the molecular theory in the introductory chapter, we have simply described the behavior of gases under various conditions, without any assumption as to the constitution of this class of bodies. We now come to the discussion of a most important law, which in its very statement assumes that gases are made up of separate par- ticles or molecules. It is hardly possible in this place to go adequately into the reasons that led chemists to adopt the atomic theory of the con- stitution of matter ; but some of the most impor- tant experimental results on which this theory is based may be mentioned. Dalton, the founder of the atomic theory of modern chemistry, stated the results of experi- ment in the following four laws : First, that the elements entering into the for- mation of any compound substance are always found in that substance in the same proportion by weight. Thus, in water the oxygen weighs eight times as much as the hydrogen, and that, AVOGADRO'S LAW. 169 too, no matter how much or how little may be taken, or what may be the source of the water. The two elements always enter in exactly this fixed proportion by weight. The same is true of all other chemical compounds. The second law of Dalton is, that the propor- tions in which two elements unite with a third have a simple relation to the proportions in which they unite with each other. Thus oxygen and hydrogen unite in the proportion 8 to 1, and form water. Carbon and hydrogen unite in the proportion by weight of 6 to 1, and form ole- fiant gas, and oxygen unites with carbon in the proportion 8 to 6, and forms carbon monoxide gas. Oxygen also may unite with carbon in the ratio of 8 to 3 or 16 to 6, and form carbonic acid gas. Each of these ratios bears evidently a very simple relation to the first two. The third law states that when one substance combines with another in more ways than one, the higher proportions are simple multiples of the first or lowest. This is illustrated by the two compounds of oxygen and carbon just mentioned. But a more remarkable illustration is found in the various compounds of oxygen aud nitrogen. In nitrous oxide or laughing gas the weight of nitrogen is to that of oxygen in the ratio 14 to 8 ; there are also well-known compounds of these gases, in 170 TEE PHYSICAL PROPERTIES OF GASES. which the ratios are 14 to 16, 14 to 24, 14 to 32, 14 to 40. Here 16, 24, 32, and 40 are all mul- tiples of 8, and no compounds of oxygen and nitrogen are known to exist that do not conform to this law. The fourth and last law is, that the combining proportion of a compound substance is the sum of the combining proportions of its constituents. Thus carbonic acid gas is a compound of 16 parts of oxygen and 6 parts of carbon, while lime is made up of 20 parts of the substance calcium and 8 parts of oxygen. When carbonic acid gas and lime unite, they form common lime- stone or marble, and they always unite in the proportion 16 + 6 to 20 + 8, or 22 to 28. These remarkable laws rest on experiment, and every exact chemical analysis that is made gives additional confirmation of their truth. The atomic theory, as we now know it, had its origin in the attempt to form a conception of matter such that the above laws should not only be in harmony with it, but should naturally re- sult from it. This theory supposes that all substances are made up of molecules which are exceedingly small particles of the substance, and all of which for any given substance are alike. These mole- cules are the smallest portions of the given sub- stance that exist in a separate state, and the con- AVOGADRO'S LAW. 171 stituent parts of the molecule are called atoms. The term " atom " is usually restricted to denote the smallest particle of one of the so-called ele- ments that ever enters into combination with other atoms. All the atoms of any one sub- stance are supposed exactly alike. All mole- cules of any compound body are made up of sim- ilar combinations of atoms. When compound bodies are decomposed by chemical processes, the molecules are thought of as broken up into their constituent atoms, or separated into new molecules or groups of atoms. It is readily seen that this mode of regarding matter adapts itself beautifully to the known laws of combination. For instance, if an atom of oxygen weighs sixteen times as much as an atom of hydrogen, and if it is supposed that each molecule of water consists of one atom of oxygen and two of hydrogen, then evidently in every molecule of water there must be eight times as much oxygen by weight as hydro- gen ; and since water can only be decomposed by whole molecules, it follows that whenever water is either formed or decomposed, the oxy- gen and hydrogen must be in the proportion 8tol. The hydrogen atom is the lightest known, and the number of times any atom is heavier than the hydrogen atom is called its atomic weight. 172 THE PHYSICAL PROPERTIES OF GASES. Thus the atomic weight of oxygen is 16, and that of carbon is 12, meaning that these atoms are respectively 16 and 12 times as heavy as an atom of hydrogen. Since whenever a compound is formed of any substances, a whole number of atoms of each of the components must be contained in the new molecule, it follows that the proportion in which the substances enter must be simple multiples of their atomic weights, and this at once satisfies Dalton's second and third laws of combination. The fourth law, also, is seen to result directly from the theory. For when two compound sub- stances unite, all the atoms in a molecule of one must unite with those in a molecule of the other. The molecular weight of each substance will be the sum of the weights of the atoms that are contained in its molecule. If, therefore, one substance unites as a whole with another, then the combining weights will be proportional to the molecular weights of these two substances. It may be asked why, in the case of water, for example, it should be said that the molecule con- sists of one atom of oxygen and two of hydro- gen, calling the atomic weight of oxygen 16 and hydrogen 1, instead of saying that the molecule consists of one atom of each, the atomic weight of oxygen being 8. Either way of looking at it would agree with the experimental result that AVOGADXO'S LAW. 173 the weights of oxygen and hydrogen in water are in the ratio of 8 to 1. Indeed, the latter mode of regarding its composition was very gen- erally adopted even as late as 1860, but is now entirely abandoned. It would be out of place here to attempt to go fully into the reasons in favor of the first view rather than the second. But it may be said that, in general, those values are taken as atomic weights which express the observed facts in the simplest way, and also that other prop- erties of the substance, such as its specific heat and vapor density, have to be taken into account in coming to a decision. One evidence in favor of the new view is that whenever substances are changed by the removal of part of their oxygen, or by giving to them more oxygen, it is almost invariably found that their molecular weights are increased or diminished by some multiple of 16. So that, if the atomic weight of oxygen is taken as 8, it must be supposed that in almost every case two atoms of oxygen, or some multi- ple of two, are added or taken away, and there can be given no sufficient reason why the change should always be in this way rather than by sin- gle atoms. But if the atomic weight of oxygen is 16, then no difficulty exists, for a change of one atom of oxygen would then make a change of 16 in the molecular weight, and no less change 174 THE PHYSICAL PROPERTIES OF GASES. could take place. In the series of compounds of nitrogen and oxygen that have already been re- ferred to, there is no difficulty, for the ratios 14 to 8, 14 to 16, etc., may be each doubled, and become 28 to 16, 28 to 32, etc. ; and since other relations indicate that 14 is the atomic weight of nitrogen, the first of this series would have a molecule consisting of two atoms of nitro- gen and one of oxygen, the next, two of nitro- gen and two of oxygen, and so on through the series. Reasoning such as the above has led to the universal acceptance of the atomic theory by chemists as the best working hypothesis that has been suggested ; and whether it shall be finally established or not, it has been of incalculable service to chemical science in systematizing the course of investigation. But the molecular theory has a physical as- pect that is not less important than its chemical relations, and, indeed, perhaps it is on the phys- ical side that the evidence for the molecular structure of matter is most conclusive. In the year 1804, Gay-Lussac and Biot made a famous balloon ascension under the auspices of the Institute of France, in which samples of air were collected at different altitudes, and were afterwards subjected to the most careful anal- yses by Gay-Lussac and Humboldt, whose joint AVOGADRO'S LAW. 175 report was presented to the Academy of Sciences in 1804. In this memoir we meet the first an- nouncement of the fact that when oxygen and hydrogen combine to form water, the volume of the hydrogen that enters is exactly double that of the oxygen when the two are under the same conditions of temperature and pressure. A few years later, Gay-Lussac, as the result of careful investigations, was able to announce further that, whenever two gases united to form a chemical compound, their volumes bore very simple ratios to each other. This remarkable conclusion at- tracted great attention, and, though disputed by so able a chemist as Dalton, was finally estab- lished as a fact. Among the important observa- tions made in this connection by Gay-Lussac, none is more far-reaching than the conclusion that the densities of gases and vapors are sim- ply proportional to their atomic weights. Take the case of water again as an example. The weight of oxygen in water is eight times the weight of hydrogen, but it was shown that the volume of the hydrogen was twice that of the oxygen before they combined. It follows, there- fore, that if equal volumes of oxygen and hydro- gen are taken, the oxygen will weigh sixteen times as much as the hydrogen, but its atomic weight, as compared with hydrogen, is sixteen. In a similar way, by the consideration of other 176 THE PHYSICAL PROPERTIES OF GASES. cases, the general result was reached that the density of any gas or vapor, as compared with hydrogen, was either equal to its molecular weight or was a simple multiple of that quantity. In the year 1811, Amadeo Avogadro, a distin- guished Italian chemist, working along the line of Gay-Lussac's investigations, gave a statement of this law, which is so simple and conveys so clear a conception that it is usual to state the above results in the form which is known as Avogadro's Law, which asserts that equal vol- umes of all gases, under the, same conditions of temperature and pressure, contain the same number of molecules. A given vessel, when full of oxygen gas at the atmospheric pressure, will contain the same num- ber of molecules of that gas as it would contain of hydrogen if it were filled with the latter sub- stance at the same temperature and pressure as in the case of the oxj^gen. It evidently results from this that the densities of gases must be proportional to their molecular weights. It will be at once seen that such a relation is of the utmost importance to chemists in enabling them to determine the molecular weight of a substance. In the case of many of the carbon compounds, analysis can readily determine the relative proportions of carbon, hydrogen, and oxygen in the substance In alcohol, for exam- AVOGADRO'S LAW. 177 pie, it is found that there are twenty-four parts by weight of carbon for every six of hydrogen and sixteen of oxygen. This is the relation that would hold if a molecule of alcohol contained two atoms of carbon, six of hydrogen, and one of oxygen. But it would also equally be satisfied if the alcohol molecule contained any multiple of these numbers, such, for instance, as four atoms of carbon, twelve of hydrogen, and two of oxy- gen. To decide what is the true number of atoms in the molecule by purely analytic meth- ods is often extremely difficult, but if the sub- stance can be vaporized and the density of its vapor determined, the constitution of the mole- cule of the vapor becomes at once known. In the case of alcohol, the vapor is found to have a density twenty-three times as great as that of hydrogen ; and since the weight of the molecule of hydrogen is 2, that of the alcohol vapor mole- cule must be 46, which indicates that it consists of two atoms of carbon, six of hydrogen, and one of oxygen. It has been assumed above that the hydro- gen molecule consists of two hydrogen atoms, and therefore has 2 as its molecular weight. The law of Avogadro leads to the conclusion that in most elementary gases the molecule is made up of two atoms, the vapor of mercury, however, being a notable exception, as it ap- 178 THE PHYSICAL PROPERTIES OF GASES. Water Vapor. Oxygen. pears to be monatomic. It will be interesting and instructive to consider the reasoning in the case of oxygen and hydrogen that leads to the belief that the molecules are diatomic, or made up of two atoms. It is found by experiment that when a certain volume of hydrogen Hydrogen. combines with one half its volume of oxygen, there is pro- duced an amount of water vapor which will occupy the same volume as that which was occupied by the hydrogen gas when at the same temperature and pressure. Thus the relative volumes of hydrogen, oxygen, and water vapor are as shown in the figure, all being taken at the same temperature and pressure. According to the law of Avogadro, there will be the same number of molecules of water vapor as there are of hydrogen, since both occupy the same volume, while there will only be half as many molecules of oxygen ; each molecule of water vapor must therefore consist of one mole- cule of hydrogen gas in composition with one half a molecule of oxygen. If the molecule of water vapor consists of two atoms of hydrogen Fig. 29. AVOGADRO'S LAW. 179 and one of oxygen, as the weight of evidence indicates, then it follows that each molecule of hydrogen is made up of two atoms of hydrogen, and that each oxygen molecule consists of two atoms of oxygen. If the molecules of oxygen and hydrogen were monatomic, there could only be found as many molecules of water vapor as there were of oxygen, and the volume of the water vapor would be only equal to that of the oxygen instead of the hydrogen gas ; but it is established by experiment that the volume of the vapor of water is really equal to that of the hy- drogen gas that enters into its composition. Thus far, in considering the internal structure of gases, we have been led largely by chemical evidence to the atomic conception of matter, and then, by consideration of the volumes and den- sities of vapors, combined with what chemistry has to say as to their molecular structure, a law, remarkable both for simplicity and for the ex- tent of its application, has been deduced which reveals the relation between the numbers of molecules in two masses of gas. Let us turn now to the more purely physical evidence in favor of the molecular structure of gases. As long ago as 1738 Daniel Bernoulli, one of a family that were leaders in the movement from which grew the modern developments in 180 THE PHYSICAL PROPERTIES OF GASES. mechanics and mathematics, suggested that a gas might be regarded as made up of an immense number of small particles or molecules which are continually bounding and rebounding against each other and the walls of the containing ves- sel. The motions were thought of as taking place in every conceivable direction, and the pres- sure of the gas against the sides of the contain- ing vessel was conceived as due to the incessant bombardment to which each minutest portion of the surface was subjected by the molecules strik- ing against it. This conception in its simplest form was made the subject of calculations, and the pressure was estimated according to the or- dinary mechanical principles that apply to the case of perfectly elastic particles rebounding from a fixed wall. In this way Bernoulli was able to show that Boyle's law was a direct con- sequence of this hypothesis; for when the gas was compressed so as to occupy one half the original volume, there would be twice as many molecules in every cubic inch, and consequently there would be twice as many to strike against any portion of the surface in every second of time, and the pressure produced would be twice as great. But no important further progress was made in this theory of gases till 1857, when it was taken up and developed by Clausius, and later AVOGADRO'S LAW. 181 by Maxwell and others. In Bernoulli's simple treatment of the case, the molecules were sup- posed to be indefinitely small, and no account / was taken of the vibrations that were set up in 1 the molecule itself. But if we consider the case \ of two billiard balls striking against each other, it is evident that they not only rebound from each other, but vibrations are set up in each one by the impact, just as a bell is set vibrating by the blow of the hammer. The later investigators, however, have taken account of these internal vibrations, and of the fact that the molecules cannot be infinitely small, but must have some action upon each other when they come within a certain distance of one another ; and the molecules are no longer sup- posed to be all moving with equal velocities, but with velocities varying through a considerable range. The whole treatment has to be by the method of averages, which, while it would not do for the treatment of the motions of a system consisting of only a few particles, is eminently suitable in such a case as this, where millions of millions of particles are concerned. In the throw of a pair of dice, for example, the chances are even that double aces will be thrown once in every thirty- six times ; but it by no means follows that in seventy-two throws there will be two throws of 182 THE PHYSICAL PROPERTIES OF GASES. double aces and only two, but in a million throws the number of double aces will be found to agree very exactly with the probable number. Any one may readily convince himself of the signif- icance of probabilities when applied to a large number of cases by throwing a single die fifty or one hundred times, and adding the amounts thus thrown. It will be found, if the die is well made, that the sum will average twenty-one points for every six throws. Thus, in the kinetic theory of gases, taking account of the manner in which the molecules must rebound from each other and the effect of these collisions on their velocities, the most prob- able distribution of velocities among the mole- cules is calculated, as it will be after an incon- ceivably great number of collisions, and then the average velocity can be calculated. In this way the theory of probabilities indicates that by far the most of the molecules have velocities that differ but little from the average velocity ; but there will be a few whose velocities will be far greater, and a few whose velocities will be very much less, than the average. These calculations are so complicated that only a sketch of some of the most important conclusions can here be given. It will be borne in mind that when work is done in compressing a gas, it acquires energy and is heated. When a gas expands and does AVOGADR&S LAW. 183 work, it expends energy and is cooled. It is natural to push the inquiry further, and ask, in what way does the energy exist in the gas? When force is exerted to set a body in motion, work is done, and the body acquires energy which shows itself in the velocity which it has acquired. The amount of this energy may be shown to be measured by the mass of the mov- ing body multiplied by the square of its veloc- ity, so that if of two equally heavy cannon-balls one has twice the velocity of the other, the first will have four times the energy of the second, and will be able to penetrate four times as far into a bank of earth. Now the effect of pushing in a piston and compressing a mass of gas, if the pressure is caused as the kinetic theory supposes, will be to cause each molecule, as it strikes against the piston, to bound back with greater velocity than if the piston had been at rest, and the work that is done in pushing in the piston against the pressure of the gas will go to in- crease the energy of motion of the molecules ; but the energy of motion of a molecule is meas- ured, just as in the case of the cannon-ball, by the product of its mass by the square of its velocity. The effect of compressing a gas is, therefore, to increase the average value of the squares of the velocities of the molecules. But 184 THE PHYSICAL PROPERTIES OF GASES. experiment shows that the rise in temperature of a mass of gas, measured on the air thermom- eter, is directly proportional to the amount of energy which is given to it ; and since the mole- cules of the gas will have no energy of motion when it is at the absolute zero of temperature, it follows that the kinetic energy, or energy of motion of the molecules of the gas, is propor- tional to the temperature of the gas as measured from the absolute zero. It was shown by Maxwell, by reasoning based on the well-established principles of mechanics, that if two kinds of molecules are put in the same vessel, one kind being, it may be, much heavier than the other, and moving with very different velocities, that they will act and react on each other, and the velocities will change till the average energy of motion of the mole- cules of one kind is equal to the average energy of motion of those of the other kind. When this state of things has come about, there is no longer any tendency for the average velocities to change. This is a very interesting result, and gives further evidence, if it were needed, that the energy of motion of the molecules of a gas is the quantity that determines its temper- ature. For when two masses of gas are mixed, they come to the same temperature; and now from the kinetic theory we learn that the aver- AVOGADRO'S LAW. 185 age kinetic energy of their molecules becomes equal, a conclusion which certainly indicates that the average kinetic energy of the molecules of a gas is the measure of its temperature. Still another way of looking at this subject is important. The experiments of Joule have demonstrated that heat is a form of energy. When two bodies of different temperatures are brought in contact, heat flows from the hotter to the colder body till both come to the same temperature. This flow of heat by conduction is really the passage of a certain amount of energy out of the one body and its diffusion into the other one. If two masses of gas are so related to each other that there is no tendency for energy to pass from one to the other when they are brought in contact or mixed, they are at the same temperature ; but by Maxwell's law, when the average kinetic energy of the mole- cules of the one gas is equal to that of those of the other, then there is no tendency for any change in these average energies when the two are mixed : therefore two masses of gas are at the same temperature when the average kinetic energies of their molecules are equal. For ex- ample, in the case of oxygen and hydrogen, the oxygen molecule being sixteen times as heavy as that of hydrogen, the average value of the square of its velocity can only be one sixteenth 186 THE PHYSICAL PROPERTIES OF GASES. that of the hydrogen molecule at the same tem- perature, so that on an average the oxygen molecule has only one fourth the velocity of the hydrogen molecule at the same temperature. For simplicity, let us consider the case of a mass of gas inclosed in a vessel having a ca- pacity of one cubic foot. The kinetic theory shows that the pressure will depend only on the number of molecules contained in the vessel and their average energy of motion. This re- sult is stated exactly by symbols in this ex- pression, where P is the pressure, N is the number of molecules in the vessel, and ^ MV 2 or E is the average energy of motion of the molecules, the energy of each molecule being found by mul- tiplying one half its mass by the square of its velocity. Evidently, if two such vessels are taken con- taining different gases, and if the pressure is the same, and the average molecular energy of each the same, then the number of molecules in each must also be equal. But the average ki- netic energies will be equal when the two masses of gas are at the same temperature ; therefore two equal volumes of gas at the same temper- ature and pressure contain equal numbers of molecules, which is Avogadro's law arrived at AVOGADRO'S LAW. 187 in this case from reasoning based simply on the kinetic theory. Again, if the two masses of gas that we have just considered are raised to some higher tem- perature, the average energy of motion of their molecules will be increased by the same amount in each case, since they start at the same lower temperature, and are each raised in temperature by the same amount. But as the vessels are supposed to be closed, so that the number of molecules in each must remain unchanged, it follows that the pressure will be increased ex- actly as much in the one case as in the other, since it depends only on the number of mole- cules in the vessel and their average kinetic energy. But this result is the same as the law discovered by Gay-Lussac and Charles, that all gases expand by the same proportional amount when raised from 32 to 212 Fahrenheit, or, if not allowed to expand, that their pressures will increase in the same proportion. About the year 1819 two French physicists, working together, remarked that the quantity of heat required to raise a pound of a substance one degree in temperature was greater in pro- portion as the molecular weight of the substance was smaller, so that by multiplying the molec- ular weight by the specific heat of a substance, a quantity was found which was nearly the same 188 THE PHYSICAL PROPERTIES OF GASES. for all simple substances. This law is known from its discoverers, as that of Dulong and Petit. In the following table the quantities are given in case of a few gases. The second column gives the amount of heat required to raise a pound of gas one degree in temperature, as com- pared with the amount required by a pound of water. Gas. Specific Heat. Molecular Weight. Molecular Heat. Oxygen . . . 0.2175 32 6.9600 Hydrogen . . . Nitrogen . 3.4090 0.2438 2 28 6.8180 6.8264 Carbon monoxide 0.2479 28 6.9412 In the above table the last column gives the product of the corresponding numbers in the second and third, and the agreement is very striking. If gases that are more easily con- densed into the liquid condition had been taken, or some of those having more complex mole- cules, it would be seen that they in all cases give rather larger values. The following are some well-known gases that show this deviation : Chlorine 0.1210 71 8.59 Carbonic acid gas . . . . 0.2169 44 9.54 Sulphurous acid gas . . . 0.1544 64 9.88 Water vapor 0.4803 18 8.64 The agreement, it will be observed, though AVOGADRO'S LAW. 189 sufficient to attract notice and to indicate an important relation between the two quantities, yet is by no means exact, and the variations even in case of the more perfect gases are greater than could be accounted for by errors in the ex- periments by which they are determined. It cannot be said, therefore, that the product of specific heat by molecular weight is a con- stant quantity, though it is nearly so in the case of gases. If we look at this subject from the point of view of the kinetic theory, it at once becomes more intelligible. The rise in temperature of a gas is measured by the increase in the average kinetic energy of its molecules. If, therefore, we have two different gases, and raise both from a lower temperature to a certain higher one, the increase in kinetic energy per molecule is the same in both. But in a pound of the gas that has heavy molecules, there will be fewer mole- cules than in a pound of the gas which has light ones. Therefore, since the increase in energy per molecule is the same in both, the total amount of energy that each mass of gas must receive will be directly proportional to the num- ber of molecules it contains, and so the gas hav- ing the lighter molecule will receive the most energy, or, in other words, has the greater spe- cific heat. Two pounds of hydrogen which has 190 THE PHYSICAL PROPERTIES OF GASE8. molecular weight 2 will contain the same num- ber of molecules as 32 pounds of oxygen whose molecular weight is 32. If, therefore, each mole- cule of oxygen requires the same increase in energy as a molecule of hydrogen for the same rise in temperature, then the total heat required for the two pounds of hydrogen will be the same as for 32 pounds of oxygen, and it is this quan- tity of heat that is called the molecular heat in the above table, because the numbers so found are proportional to the quantity of heat required per molecule of the substance to raise its tem- perature one degree. It will be remembered that by Avogadro's law equal volumes of all gases under the same conditions of temperature and pressure contain the same number of molecules. All gases should, therefore, be expected to have the same specific heat when equal volumes are taken instead of equal weights ; or, in other words, if a cubic foot of gas is taken at some standard temper- ature and pressure, the quantity of heat required to raise its temperature one degree will be the same whatever the gas that may be taken. This is evidently only another way of stating the law of Dulong and Petit. But the above table has shown that this is not exactly true, and therefore it must be concluded that the molecules of some gases require a greater AVOGADRO'S LAW. 191 increase in energy for a rise in temperature of one degree than others. To understand why this should be so, it must be remembered that the molecule is by no means a simple thing, and that part of the energy com- municated to it goes to increase its internal energy, perhaps to set it vibrating like a bell or a tuning-fork while it is also bounding to and fro as a whole. All energy expended in this way will not count directly towards the increase in temperature of the gas, though it of course always accompanies rise in temperature. For the law of equilibrium of temperature accord- ing to the kinetic theory shows that only that increase in energy which causes the molecule to move as a whole with greater velocity is directly concerned in rise of temperature. So that, when two gases are at the same temperature, the ki- netic theory asserts that the average energy of motion of the molecule as a whole is the same in both gases ; but it by no means follows that the internal vibrations of a molecule of the one gas have the same energy as those in a molecule of the other. Indeed, the variation from the law of Dulong and Petit that has been referred to indicates that there are probably great differ- ences in this respect in different gases. It is quite in accord with this view that, in gases hav- ing complex molecules made up of many atoms, 192 THE PHYSICAL PROPERTIES OF GASES. the departure from the law of Dulong and Petit should be on the side of greater molecular heat ; for in this case the greater complexity of the molecule affords opportunity for a greater vari- ety of internal vibrations. Clausius has sup- posed that when energy is communicated to a molecule, a certain proportion goes to increase its internal energy, and this proportion is always the same for molecules of the same gas. The viscosity of a gas, its power of conduct- ing heat, and its diffusibility or rate of diffusion might readily seem to have very little connec- tion with each other, and it would scarcely occur to one to study the viscosity of a gas in order to discover its conductivity, or to experiment on its power of conducting heat in order to find its rate of diffusion ; yet the kinetic theory in the hands of Professor Clerk Maxwell has revealed a close relationship between these three quan- tities. What explanation has the kinetic theory to offer of the viscosity of a gas ? It is perhaps difficult to see at first how a theory that supposes such perfect freedom of motion in the case of every individual molecule should be able to ex- plain how it is that it requires the exertion of a force to cause one layer of gas to move over an- other, so that it is as if there were actually fric- tion between the different layers of gas. It is AVOGADRO'S LAW. 193 evident that there is gaseous friction ; every minute drop of water that floats away in a cloud of steam is evidence of it, for water is denser than air, and would drop at once to the ground but for the viscosity of the air. Maxwell has shown that the viscosity of a gas may be readily explained by the kinetic theory ; for, if one layer of gas is made to move over another layer, in the course of their inces- sant bounding and rebounding from each other, molecules will be constantly passing from the first layer into the second, and from the second layer into the first : but as the first layer is mov- ing over the second, its molecules will have on this account an average momentum which will be different from that of the molecules in the second layer, and every molecule that passes from one layer into the other carries with it the momentum that it had in the layer from which it came, and imparts it to the other, so that from this cause there is a constant equalization of the average momenta of the two layers, and they tend to move in the same way, and the effect is that one layer of gas tends to drag the next layer along with it, and it is this that con- stitutes the viscosity of the gas. A good idea of this process may be obtained by thinking of two very long canal-boats, one at rest and the other moving along beside it ; the mere passing 194 THE PHYSICAL PROPERTIES OF GASES. of one beside the other would not set the second in motion, but let us imagine both to be crowded with men who are not only jostling against each other, but continually leaping across from one boat to the other. It as evident that every one who jumps from the moving boat carries with him some forward momentum which is imparted to the other boat ; and, on the other hand, each person who springs from the stationary boat to the moving one retards its motion, since his for- ward momentum is less than the average for- ward momentum of the men among whom he has come ; and it will finally result, if the opera- tion is kept up long enough, that both boats will acquire the same velocity, unless some other forces come in to prevent. By a careful mathematical investigation of the viscosity of gases, taking various conditions into account, Maxwell was able to show that, according to the kinetic theory, the viscosity of a gas should increase with the rise in its tem- | perature, and that the viscosity is the same for all densities. This second result is rather 1 startling, and yet experiment has confirmed the \ truth of both, the viscosity of air at one sixtieth of the ordinary pressure being found the same as at the pressure of one atmosphere, and it is also found to increase as the temperature of the gas increases. AVOGADRO'S LAW. 195 It is seen from the above that the viscosity of a gas depends on the rate at which momentum is communicated from one layer to an adjoining one. In the case of heat conduction, it is not momentum but energy that is communicated ; and as we have seen that the energy of motion of a molecule depends on its mass and on the square of its velocity, while the momentum of a molecule depends on its mass and velocity, there is evidently a very close connection be- tween the two. Again, the diffusibility of a gas depends on the rate at which its molecules pass from one layer to another ; and evidently this also is closely allied to the viscosity and conduc- tivity, for it is by the passing of the molecules from one layer to another that momentum and energy are communicated. These three quantities (diffusibility, viscosity, and conductivity) in gases, representing the rates of diffusion of mass, of momentum, and of en- ergy, are thus seen to be very nearly related, so closely, indeed, that Maxwell was able to calcu- late the numerical relations that they hold to each other. The experiments by which these quantities are measured are difficult, particularly in the case of the heat conductivity of gases ; but the most accurate data that have been obtained serve to establish the accuracy of Maxwell's conclusion, 196 THE PHYSICAL PROPERTIES OF GASES. thus affording a most striking confirmation of the kinetic theory. The following table exhibits the conductivity of certain gases for heat on a scale such that the heat conductivity of copper would be about 1.10. The values in the first column are calcu- lated from the coefficients of viscosity ; those in the second are determined by direct experiment. The agreement is as good as could be expected, considering the difficulty of the investigation : Heat Conductivity. Calculated. Observed. Air 0000492 .0000480 Hydrogen 0003497 .0003324 Nitrogen 0000491 .0000524 In closing this chapter it may be well to give some of the numerical results which have been obtained in accordance with this theory in the case of nitrogen, that gas being chosen because it makes up four fifths of the air, and the same numbers will also not be very wide of the truth in case of oxygen, which makes the remaining one fifth of the atmosphere. In the case, then, of nitrogen at the ordinary atmospheric pressure and at the temperature of melting ice, the molecules are found to have an average velocity of 1,485 feet per second, which is greater than the velocity of sound, and about that of a pistol-shot. This is given first because AVOGADRO'S LAW. 197 it is the most easily obtained of any of the numer- ical data, and was first calculated by Dr. Joule from the expression for the pressure of a gas which is given on page 186. The mean free path of the molecule, or the distance which it goes on an average before colliding with another mole- cule, is determined by experiments on the viscos- ity of the gas. In nitrogen it is found to be 39 ten-millionths of an inch. The number of colli- sions that a single molecule undergoes in a sec- ond is, on the average, about 4,760 millions. The number of molecules in a cubic inch, as we have already seen, is the same whatever the gas, under the same conditions of temperature and pressure, and is probably not very far from 350 million million million ; and, remember- ing that the weight of a cubic inch of nitrogen is about one fourth of a grain, the weight of a single molecule is evidently such that about 1,400 million million million are required to weigh a grain. The average distance apart of the molecules of all gases must be about the same under the same conditions of temperature and pressure, and is probably from 12 to 16 hundred-millionths of an inch. Some idea of these figures may perhaps be obtained by im- agining a cubic inch of gas at the ordinary pres- sure of the atmosphere to be taken and made to expand until it has become a cube measuring 16 198 THE PHYSICAL PROPERTIES OF GASES. miles along each edge. The distribution of the molecules will then be somewhat nearly repre- sented by the dots in the figure (Fig. 30). So .... that the number of parti- . * '. \ ' , ' . cles required to fill a cube *,*.**" measuring 16 miles each * \ " * \ * " ." way, when distributed ." * \ . * ' " . throughout that entire re- ;* .* . .**.'. gion so as to be about as *"//'.' far apart as the dots in the Fi 30 diagram, is about the num- ber of molecules in a cubic inch of the air we breathe. CHAPTER IX. GEISSLER-TUBES AND RADIANT MATTER. IN the year 1873 Professor Crookes, of Lon- don, discovered certain properties possessed by gas in a highly rarefied condition, that were so singular and unexpected as to arrest the att^en- tion of the scientific world, and to lead Professor Crookes to call it a fourth state of matter, or the radiant condition, to distinguish it from the ordinary gaseous state. In the course of an elaborate investigation of the atomic weight of thallium, an element which had recently l>een discovered by the aid of the spectroscope, Crookes thought best to perform the delicate weighings that were necessary in a vacuum, in order to avoid the disturbance due to the buoyancy of the air. The balance was accordingly placed in a metallic box from which the air was exhausted. But during the course of the experiments, when heated bodies were weighed in this way, the balance showed irregu- larities in its action that were difficult to explain by the currents of air resulting from the differ- ences of temperature, and Crookes therefore un- 200 THE PHYSICAL PROPERTIES OF GASES. dertook a thorough investigation of the phenom- enon. As early as 1825 Fresnel had observed that when a hot body was brought near a light movable one, there was an apparent repulsion between the two. Many later observers had made similar observations, and the action was generally attributed to air currents. In Crookes' earlier experiment a light balance was made, consisting of a piece of straw a few inches long, with a pith-ball on each end, and having a short piece of needle, sharpened at both ends, thrust through its middle. This little bal- ance was slipped into a tube just large enough to freely admit the steel crosspiece. When in position, the points of the needle, resting against the side of the tube, made a delicate support, allowing the balance to turn with the slight est force. The tube was now connected with a Sprengel air-pump, arranged so that the ex- haustion could be pushed to any desired de- gree. In this investigation it was found that there was a certain critical pressure at which there was no appreciable effect when a warm body was brought near the balance. When the pressure of the air or other inclosed gas was greater than this amount, there was an apparent attraction, probably due to currents of air. At pressures less than the critical one there was an opposite GEISSLER-TUBES AND RADIANT MATTER. 201 effect, a repulsion instead of an attraction, which became more evident as the exhaustion increased, until a pressure of about four mil- lionths of an atmosphere was reached, after which the action became less and less as the vacuum became more complete. The critical pressure that marked the point below which there was attraction, and above which there was repulsion, was not a fixed quan- tity for any given gas, but depended on the na- ture and surface of the object that was repelled. When a light section of pith formed the end of the balance, the critical pressure was decidedly greater than when a piece of platinum was used having considerably greater mass in comparison with its surface. It appeared, therefore, that there were two actions going on, one due to currents most marked at greater pressures, and one due to some unknown cause that produced its greatest effect at a very low pressure, somewhere about four millionths of that of the atmosphere. These two opposed each other, and the absence of action at the critical pressure was due to the one counteracting the other. Later experiments conducted to investigate the cause of the repulsion at very low pressures led to the construction of the instrument known as the radiometer, in which a light flier or wheel 202 THE PHYSICAL PROPERTIES OF GASES. with four vertical vanes made of very thin slips of mica, each coated on one side only with lamp- black, is delicately poised on a steel point, so that it can easily rotate. The lampblacked faces of the vanes are all turned the same way, and the whole is in- closed in a glass bulb some two or three inches in di- ameter, from which the air has been very completely exhausted. When this instrument is put in the sunlight, it at once begins to rotate in such a way that the mica faces are directed forwards, and the lampblacked surfaces back- wards. To cause it to rotate, it is not necessary that it should Fig. 31. Radiometer. . J be in the light ; a vessel or hot water brought near it, or the warm hands put upon the bulb, will at once cause the mo- tion. When surrounded by ice, or when a stream of cold water flows over the bulb, it will rotate in the opposite direction. Many explanations of this remarkable behav- GEISSLER-TUBES AND RADIANT MATTER. 203 ior have been offered, but none can be said to be satisfactory except that based on the kinetic theory of gases. To understand this explanation, a few words will be necessary as to radiation. There are two principal ways in which heat is communicated between bodies : by conduction and by radiation. The flow of heat by conduction is a slow pro- cess, and requires that the bodies between which it flows shall be in close contact ; it consists in the communication of the energy of motion of the molecules from one directly to another, the energy thus gradually spreading from the hotter to the colder parts of the body. It is in this way that heat is communicated from one part to another of a metal bar. In this case the flow always takes place from a hotter to a colder part. But there is another way in which all bodies are giving out energy which does not depend on the temperature of the bodies that receive it, namely, by radiation. It is a familiar fact that when a body is heated enough it gives out light and heat ; if somewhat cooler, it gives out heat, but not light, as in the case of a closed iron stove that is not hot enough to glow. But careful inquiry does not stop here ; it examines whether bodies at ordinary temperatures may not also be giving out what may be called rays of heat, and it is not only 204 THE PHYSICAL PROPERTIES OF GASES. found that this is true at ordinary temperatures, but Professor Langley has been able to detect and measure the heat rays coming from a block of ice. It is, therefore, believed that not only what we call hot bodies, but substances at all temperatures give out heat rays. But experi- ment shows that the rays that produce heat have the same properties as those that give light. Both are propagated with a velocity of 186,330 miles per second; both are reflected and re- fracted in the same way ; both are polarized by the same means. There is, therefore, no reason that can be given why it is not right to say that light and heat are simply two different effects of the same thing, just as, when a hammer strikes a blow, the noise, the heat developed, and the motion of the nail, are all effects of the one action, and the energy of motion of the hammer is absorbed in producing them. Near the beginning of the present century, the theory that light was communicated from one body to another by waves that were given off by the glowing body became firmly established. But there cannot be waves without a medium, and these light -waves were, then, waves of what ? Clearly not of air, for the velocity of a wave depends on the medium, and air-waves, as seen in the case of sound, travel with a velocity of only 1,100 feet a second, instead of 186,330 GEISSLER-TUBES AND RADIANT MATTER. 205 miles, and, further, light will pass with greater velocity through the highest vacuum than through air. There is no way of accounting for these waves of light except on the supposition that there is a medium filling all space out to the remotest visible stars, and pervading all trans- parent bodies. This medium is called the ether ; it cannot be detected by our senses, and cannot be weighed. It has very lately been shown that certain electrical effects are communicated by waves that move with the same velocity as waves of light. This is another evidence of the exist- ence of the ether, and goes to confirm what has long been suspected, that light-waves are waves of electric disturbance. The wave theory of light has steadily gained ground from the first, on account of the beauti- ful explanation it affords of very complicated effects, such as those of polarization and inter- ference, and because it has led to important dis- coveries, and to-day the evidence for its truth is overwhelmingly strong. No other theory has been proposed that can account for the varied effects of light in crystals as well as interference effects, so that the wave theory is not only the accepted theory, but there is no other that has been proposed that can stand for a moment. The effect of these waves of the ether in ex- citing sensation through the retina of the eye is 206 THE PHYSICAL PROPERTIES OF GASES. what we know as light. But these waves have energy, and, when absorbed, that energy appears as heat in the absorbing body. Every ether- wave possesses energy, and therefore produces heat when absorbed, but only waves of certain special periods of vibration or wave-length can affect the eye as light, just as, in the case of the vibrations which solid bodies give to the air, only those whose frequencies are between 30 a second and 40,000 a second affect the ear as sound : slower vibrations, and those which are quicker than these limits, are unheard. Yet both slower and quicker vibrations possess energy, and though unheard may even have more than those that impress the ear as loud sounds. Light and heat are to be regarded as the effects of the ether-waves ; and we shall therefore now, instead of speaking of a luminous body as giving out light rays and heat rays, say that it is giving out ether-waves, or that it is radiating, the term " radiation " being employed to mean the ether- waves that are sent out by a hot body. All bodies are then to be thought of as radi- ating, and the radiation from all bodies, when absorbed, produces heat. Those bodies that send out radiation of suitable intensity and wave- length to affect the eye give light, and are said to shine or be luminous. The radiations by which we see bodies must be of this nature, but GEISSLER-TVBES AND RADIANT MATTER. 207 generally the radiations by which bodies are seen are those that come from the sun, and are simply reflected to the eye from the object. Thus a piece of white paper sends out, its own proper radiations, whether it is in the dark or not ; but we do not see it in the dark, for the ra- diations by which it is seen are not those proper to itself, but those coming from the sun or other intense source of radiation, which it reflects in addition to its own. But it may be objected, if cold bodies send out radiation, and radiation, when absorbed, pro- duces- heat, why may we not warm our hands by holding them near a block of ice, or, at least, why should they not grow slightly warmer ? It is true that the hands do receive heat from a block of ice when held near it, but it must be remembered that the hands themselves are bodies which are radiating, and every wave of radiation which they give off takes a certain amount of energy ; and as they are warmer than the ice they are radiating faster, and hence giv- ing up their energy more rapidly than they are receiving it from the ice, so that, on the whole, they are cooling, not because the ice takes heat away from the hands, but because it stands in the way of the abundant radiation coming to- wards them from other warmer objects, and sub- stitutes its own feeble stream of radiation instead. 208 THE PHYSICAL PROPERTIES OF GASES. We are now prepared to consider the reason for the motion of the vanes in the radiometer. Lampblack is one of the best absorbers of ra- diation that is known, and nearly all the ether- waves coming from a hot body, and falling on the lampblacked sides of the vanes, will be absorbed, while most of the radiation that falls on the bare mica will be reflected or transmitted to the lampblack on the other side. The result is that the lampblacked sides of the vanes be- come hotter than the other sides. To understand the effect of this difference in temperature between the two sides in causing motion of the flier, let the globe be first sup- posed full of air at the ordinary atmospheric pressure. We have seen that pressure in a gas is, according to the kinetic theory, caused by the impacts of the innumerable molecules against each other and the walls of the vessel. At first, when the air and the vanes are all at one tem- perature, there is no communication of energy from one to the other. The molecules strike against the walls of the vessel or against the vanes and rebound with the same velocity which they had before impact. The pressure is the same against each side of a vane, so that there is no tendency to move. If now the system is exposed to radiation from a hotter body, the lampblacked sides become hotter than the oth- GEISSLER-TUBES AND RADIANT MATTER 209 ers, and the temperature of the gas is but slightly affected, as it is a poor absorber. There is scarcely any change in the relation of the gas to the mica sides of the vanes, and the molecules that impact against them rebound with about the same speed with which they struck against them. It is different, however, with those mole- cules that meet the lampblacked surface. They find a surface hotter than the gas, or, in other words, the energy of motion of the molecules of the lampblack is greater than that of the gase- ous molecules, and when they strike against each other energy will be communicated to the gaseous molecules, and they will rebound with greater velocity than they had before striking the surface of the vane. But whenever the ve- locity of a molecule is increased in this way, the lampblacked surface experiences an equal and opposite reaction which amounts to an in- crease in pressure due to that molecule ; and if there were no change in the number of mole- cules that struck against it in every second, the total pressure on that side would be greater than before, and would overbalance the pressure on the other side of the vane, and it would rotate. Now when the gas is at the atmospheric pres- sure, the mean free path of the molecules is about 39 ten-million ths of an inch, so that the molecules, rebounding with increased velocity 210 THE PHYSICAL PROPERTIES OF GASES. from the hot surface, would, on the average, strike against other molecules in about that distance from the surface, but, coming with greater velocities, they will drive back the other molecules by their impacts more powerfully than they would have done before meeting the hot surface ; the result is that the remainder of the gas is compressed, and some is thus pressed around towards the cold side of the vane, in- creasing the pressure against that side, while the number of molecules striking against the hot side is diminished, and the result is that the pressure becomes slightly increased on both sides, and the vane does not move. But when the gas is highly rarefied the mean free path of the mole- cule may be as long as from the vanes to the sides of the globe, and in this case the action will be quite different. The molecules rebounding from the lampblacked surfaces, for the most part, will riot collide with other molecules of gas before striking against the walls of the inclosing globe. The gas will not then be beaten back by the more energetically moving molecules that re- bound from the hotter side of the vane, and accordingly there will be no diminution in the number of molecules that strike against the hot sides of the vanes, and no crowding of the mole- cules around towards the cold sides ; but, since the molecules rebounding from the hot surfaces GEISSLER-TUBES AND RADIANT MATTER. 211 have a greater velocity after impact than those rebounding from the colder surfaces, the reac- tion or pressure against the hotter sides will be greater than against the colder, and the flier therefore turns so that the lampblacked surfaces always look backwards, unless the source of ra- diation is a body colder than the vanes them- selves, in which case the lampblacked surfaces become the colder, and the motion is reversed. It is found, also, that the action is greater when the exhausted globe containing the flier is small than when it is large, and this agrees with the above explanation. When the bulb contain- ing the radiometer is floated in water it turns slowly in the opposite direction to that in which the vanes are moving. This should be expected, however, in any case, and simply shows that the vanes are made to move by the action of the in- closed gas, in some way, and not by the direct action of the radiation falling upon it. Professor Crookes has also discovered that the character of the electric discharge through gases at these very high exhaustions exhibits certain remarkable peculiarities which it will be interesting to consider briefly. At the atmospheric pressure, the discharge from an electrical machine or induction coil passes through the air in a series of sparks which leap from one pole to the other, following irreg- 212 THE PHYSICAL PROPERTIES OF GASES. ular paths, like miniature flashes of lightning, as they are, anji accompanied by more or less noise. As the air is more rarefied the discharge be- comes less intermittent in character, but still exhibits a certain streakiness like a loose bundle of irregular threads of light, gathered together at the ends ; as the exhaustion proceeds, this character entirely disappears, and the whole tube through which the discharge takes place becomes filled with a pale blue light. At still higher exhaustions a stratified appearance, such as is shown iii Fig. 32, is observed. Even a careless Fig. 32. Geissler-Tube. observer could hardly help remarking a decided difference between the discharge as seen at the two poles. The negative pole is surrounded with pale bluish light, the negative glow, as it is called, and this is separated from the stratified light that seems to proceed from the positive pole by a perfectly dark region, called the nega- tive dark space. The above effects are seen when the pressure of the gas is reduced to be GE1SSLER-TUBES AND RADIANT MATTER. 213 about one ten-thousandth part of that of the at- mosphere. It was discovered by Crookes that when the pressure is still further decreased, so as to be about one millionth that of the atmosphere, the whole character of the discharge is changed. The faint negative glow has extended and filled the tube, and seems to proceed out from the negative pole in nearly straight lines, without any regard to the position of the positive pole ; and wherever it meets the sides of the tubes a strong fluorescence is excited in the glass, caus- ing it to glow with pale greenish yellow light with some kinds of glass, and with blue fluores- cence in others. This peculiarity of the discharge at high ex- haustions is well shown by the glass bulbs repre- sented in Fig. 33. In both bulbs the negative terminal of the induction coil or electrical ma- chine is represented as connected with the right- hand electrodes which consist of slightly concave discs of aluminium. The positive pole may be connected to either of the remaining electrodes. In the left-hand tube rarefaction is supposed to be about that in ordinary so-called " vacuum tubes," and the discharge takes place, with its ac- companying stratifications, between the negative electrode and the one which is connected with the positive pole, the luminous stream bending 214 THE PHYSICAL PROPERTIES OF GASES. up or down or across, in the manner shown in the figure. But in the right-hand tube the ex- haustion has been pushed so far that the gas is in the peculiar Crookes state, and then the discharge from the negative pole takes place directly at right angles with the surface of the Fig. 33. Crookes' Tubes. electrode ; and since it is made slightly concave, the discharge is concentrated, as light is by a concave mirror, on the opposite part of the bulb, without any reference to the point where the GEI8SLER-TUBE8 AND RADIANT MATTER. 215 positive pole is connected, whether at the top, bottom, or side. There seems to be taking place in this case an actual bombardment of the bulb opposite the negative electrode by the molecules of gas, the electrode being a miniature battery concentrating its fire on one point. This is shown by the fact that a powerful fluorescence is excited, and the gas speedily becomes hot at that point. If the positive pole is connected with this electrode, and the negative with one of the others, there will be no such action pro- duced by the positive pole ; around the negative terminal, however, the strong fluorescence of the glass shows that the discharge is taking place. A striking illustration of the way in which the discharge is always given off nearly at right an- gles to the surface of the negative electrode is afforded by a tube of the form shown in Fig. 34, in which the negative pole is connected with the lower electrode, and the positive pole with the top of the left-hand branch. The negative elec- trode is made to face the right-hand branch, and accordingly the right-hand branch fluoresces un- der the Crookes discharge, while the current is transmitted through the left arm of the tube. In one of Crookes' experiments, the negative elec- trode was made in the form of a concave surface of aluminium, in the focus of which was placed a slip of platinum foil. The discharge being con- 216 THE PHYSICAL PROPERTIES OF GASES. centrated on the foil, it was heated to a glow- ing white heat and finally fused. To show that the discharge takes place in Fig. 34. straight lines from the negative electrode, the tube shown in Fig. 35 was used, in which a screen in the form of a Maltese cross was placed in the path of the discharge from the negative electrode. The screen is hinged at the bottom, so that it can by a slight jar be thrown down, so GEISSLER-TUBES AND RADIANT MATTER. 217 as to lie flat upon the bottom of the tube. When the screen is in position a sharply denned shadow is thrown on the end of the tube, the parts ex- posed to the discharge fluorescing, perhaps, with beautiful green light, while the part screened re- mains dark. When the screen is thrown down, Fig. 35. Crookes' Tubes : Maltese Cross. the glass formerly protected is now exposed to the action of the discharge, and fluoresces more strongly than the surrounding parts, which show a sort of fatigue, and do not fluoresce as strongly as at first, so that a bright green cross is now seen on a darker ground. In still another experiment of extreme beauty, the mechanical action of the discharge is shown by the arrangement shown in the figure, in which the discharge from the negative electrode is di- 218 THE PHYSICAL PROPERTIES OF GASES. rected against the light mica vanes of a little paddle-wheel, made so as to roll with the least possible friction on two level guides. By revers- ing the discharge, the wheel may be made to roll first in one way and then in the other, always rolling away from the negative electrode. These experiments appear to show that in this extremely rarefied state the molecules of the gas Fig. 36. fly off in nearly straight lines from the negative electrode, and with considerable energy, as is evi- denced by the heating of the piece of platinum when exposed to the battering of the molecules, and by the motion of the paddle-wheel against which the discharge is directed. It is on this account that Crookes has proposed to call this the radiant condition of matter ; and the essen- tial characteristic of this condition, in which it differs from the gaseous state, appears to be that at these high exhaustions the molecules may fly GEISSLER-TUBES AND RADIANT MATTER. 219 through very considerable distances, even from one side of the vessel to the other, without striking against each other. The radiant condition is ap- parently, then, that state of a gas in which the average free path of the molecule is about three or four inches in length, instead of a few mil- lionths of an inch, as at the ordinary pressures of the atmosphere. In the discharge of electricity through gases it is also noticed that the discharge will take place more freely as the air is more rarefied ; that is, an electrical machine that would only give a spark one inch long in the open air, will discharge through a length of many inches when the air is rarefied. This diminution of the air resistance increases as the exhaustion proceeds up to a certain point, depending, among other things, on the distance between the electrodes, after which, as the exhaustion increases, the re- sistance also increases, until in the most perfect vacua it is found that the electricity will more readily spring several inches between the elec- trodes outside the tube than pass across a dis- tance of one tenth of an inch in the vacuum. The kinetic theory of gases explains this ac- tion by the assumption that the electric dis- charge in gases is convective, that is, electricity is carried from one electrode to the other by the molecules of the gas which become charged at 220 THE PHYSICAL PROPERTIES Of GASES. one pole, and then fly across and are discharged at the other. In such a case, as the exhaustion proceeds, and the mean free path becomes longer, the discharge takes place more freely ; but when the exhaustion has gone so far that most of the molecules can fly backwards and forwards, from one pole to the other, without encountering oth- ers that interfere with them, then any further exhaustion will not aid the discharge, for the molecules have already all the freedom of motion they require, and further rarefaction only takes away some of the carriers, and thus reduces the ease of transfer. In this way is explained the fact that, when the pressure is lowered beyond a certain amount, the discharge diminishes instead of increasing. These experiments on the discharge of elec- tricity through rarefied gases, and the phenom- ena of the radiant condition of matter as devel- oped by Crookes, furnish, perhaps, the strongest experimental evidence of the truth of the kinetic theory of gases in its essential features. Other facts lead by a more or less indirect route to this conclusion, and only when these are care- fully considered is the strength of the argument in favor of the theory appreciated ; but the be- havior of the radiometer and the phenomena of the electric discharge in Crookes' vacua furnish evidence of the most convincing character in favor of the kinetic theory. CHAPTER X. CONCLUSION. IN the introductory chapter a sketch was given of the molecular theory of the constitution of bodies, and the development that this theory has received in the case of gases has been indicated in the chapter which discusses the kinetic the- ory ; but before concluding this sketch it will be well to place in compact form the main fea- tures of the argument leading to this view of the structure of gases, and to give an account of some of the modes of estimating atomic distances and dimensions. And first, the evidence for the statement, that the ultimate parts or particles of which a gas is constituted are all alike, depends chiefly on the chemical properties of gases, and on their radiating and absorbing powers. No matter how small a portion of gas is se- lected, its chemical properties and affinities are exactly the same as those of any other portion of the gas. If it is found possible to decompose it, or dissociate it, or break it up into other component gases, the same treatment will bring 222 THE PHYSICAL PROPERTIES OF GASES. about the same result in any portion of the gas, however minute it may be. But the most convincing proof of this asser- tion is to be found in spectrum analysis. When a beam of light from a piece of white-hot iron is allowed to pass through a prism, it*is spread out into a band of colored light, the spectrum, in which there is a regular gradation of color, beginning with red at one end, and passing through orange, yellow, green, and blue down to violet, and so fading out. Physicists have found that the various colors correspond to waves of light having different wave-lengths, the longest waves that are visible producing the sensation of red light, while the shortest waves give rise to the sensation of violet light ; there are others that are longer than the waves of red light, and some that are shorter than any visible violet waves, but these are only made known to us by their heating effects and photographic action, as they are entirely invisible. In the formation of the spectrum by the prism the light first falls upon a screen with a narrow opening or slit in it, and when the light from the slit meets the prism all waves are bent out of their original direction by an amount that de- pends on their wave-length. Those that have the longest wave-lengths are bent least, so that the direction of the red, yellow, blue, and violet CONCL US I ON. 223 Fig. 37. Formation of Spectrum. rays, after passing through the prism, will be somewhat as shown in the diagram. But all the red light of the same wave-length will be bent in the same way, will form a red picture or im- age of the slit atR. The yel- low light will form an image of the slit at Y, the blue light at B, and the vio- let at V. If there were only these four special wave-lengths in the light, the spectrum would consist of four narrow bands of light, one each of red, yellow, blue, and violet. If the slit were very wide and the prism did not separate the light very much, these bands might touch each other, or even overlap so that the spectrum might appear continuous, although really containing only four different kinds of wave-lengths; but if the slit were made very narrow, the bands would become narrow lines of light sharply sep- arated from each other. In light from a mass of white-hot iron waves of every length are present, and so it gives as its spectrum the brilliantly colored band per- fectly continuous from the red to the violet, and gradually fading out at each end. No matter 224 THE PHYSICAL PROPERTIES OF GASES. how narrow the slit is made, or how much the spectrum may be spread out, there is no sign of any discontinuity. But if any wave-lengths were lacking, there would at once be seen dark lines at those points in the spectrum corresponding to the absent wave-lengths. When the light from a gas glowing with in- tense heat, or made luminous by the electric discharge, is thus analyzed in the spectroscope, there is seen, not a continuous spectrum, but one consisting of separate bright lines, in many cases grouped in a most wonderful manner ; and these lines are extremely characteristic, no two gases giving the same spectrum, but the same gas, under the same conditions of excitement, always giving the same lines, so that gases may be at once identified by their spectra. Therefore gases do not give out all wave-lengths of light, but only certain particular ones. To give an idea of the complexity yet regu- larity that holds in many of these spectra, there is represented in Fig. 38 a group of lines in the spectrum of carbon, as obtained from the incandescent vapor that exists between the car- bons in an electric arc light. It is a beautiful group, the lines being a brilliant blue in a dark ground, but its most noticeable feature, at the first glance, is the arrangement of the lines at the left. There seems to be a sharply defined CONCLUSION. 225 starting-point, called the head of the group, where the lines are massed so closely together as not to be separately distinguishable ; but as we pass to the right the distances between the Fig. 38. Spectrum of Carbon Band. lines are seen to increase in a manner so regular that the law can be easily determined, and the lines belonging to this series can be picked out of the apparently irregularly distributed lines to the right. A second series of lines has its head a little to the right of the first, and is distin- guished frgm it by a somewhat different law of arrangement. Still farther to the right will be seen the head or starting-point of a third series of lines, in which also the distances between the lines regularly increase as we go towards the right ; and finally a fourth series will also be seen, and it is now evident that the irregular distribution to the right is merely due to the superposition of these separate groups of lines. In Fig. 39 each series of lines is represented separately, and the wonderful regularity is at once seen. As many as one hundred lines have been identified as belonging to one series in one of the carbon groups. Besides this more obvi- 226 TEE PHYSICAL PROPERTIES OF GASES. ous structure, careful examination shows that every line is double, consisting of two fine lines close together ; so that this band of the carbon spectrum is full of wonders. But this is only a Fig. 39. Carbon Band analyzed. part of the whole spectrum of carbon, which contains several such bands, each with its char- acteristic peculiarities. Each line in this spectrum signifies that light of that particular wave-length is being given out by the glowing gas, so that the gas is sending out energy in waves of the luminiferous ether, with regular vibrations, and having a particular component vibration corresponding to every line in its spectrum. But this property does not be- long to the gas only in bulk ; it does not depend on the shape or size of the vessel containing it, but is common to every particle of the gas. But it is certainly inconceivable that such a complex system of vibrations should arise in a simple, CONCLUSION. 227 continuous, structureless portion of matter, just as we should say, on hearing the complex harmo- nies and varied tones of the organ, that in that instrument there must be many and varied parts and complicated connections. The conclusion is then inevitable, that each portion of the gas is a more or less complex structure ; and, since all portions of the same gas give the same spectrum under the same conditions, it is judged that these parts are all alike. Any differences among the particles of a gas that would cause some to give out slightly different vibrations from others would cause the lines of the spectrum to appear blurred and broadened, unless the number of particles that differed in their modes of vibra- tion were so few in comparison with the others as to produce no perceptible effect. But not only are gases to be regarded as made up of distinct elementary parts of a more or less complex structure, which we call molecules, it also seems clear that these molecules must be quite separate from each, other. Again, the evi- dence must rest largely on what spectrum anal- ysis has to tell us. It is found that the spectrum of a gas is subject to scarcely any change when the gas is rarefied, although the change in den- sity may be very great. Following the analogy of sound, it is hard to see how this can be if the molecules are closely in contact ; for consider a 228 THE PHYSICAL PROPERTIES OF GASES. number of tuning-forks all vibrating and giving out the same tone. We may think of a region, such as a room, filled with such tuning-forks, and if they were supported so as not to touch each other each would give out its tone clearly and un- disturbed ; but if they were to be crowded to- gether so as to touch, there would only be a confused jangle of sounds. But it is not necessary to resort to analogical reasoning. Experiment shows that, as a gas is greatly condensed, the lines in its spectrum be- come broader and less sharply defined, indicating that the periods of vibration of the molecules are being affected by their proximity ; and if, instead of a gas, a glowing liquid or solid is taken, it is found that, whatever the substance may be, the spectrum is perfectly continuous from one end to the other, indicating the pres- ence of waves of light of all lengths. Thus a continuous spectrum is obtained from a white- hot piece of iron ; but if it be vaporized in the intense heat of the electric arc, its vapor or gas gives a spectrum of bright lines that is entirely characteristic of iron. In the condition of vapor or gas, the molecules of iron are so far removed from each other that there is no clashing, no in- terference with each other, and each vibrates in its natural manner; but in the liquid or solid states the molecules are so close together that CONCLUSION. 229 they cannot vibrate without disturbance, and the confused and irregular vibrations give rise to waves of all wave-lengths, and the characteristic spectrum of the substance is no longer seen. The conclusion, therefore, seems unavoidable, that the molecules of a gas are so far apart, so entirely separate from each other, that there is no mutual action between the molecules which constrains in any way their free modes of vibra- tion. In this respect gases are in marked con- trast to liquids and solids. One further evidence of the similarity of all the molecules of a gas has been already adduced, in the fact that it is found impossible by means of any process such as diffusion, to sift a gas in such a way as to obtain two parts, in one of which the average weight of the molecules is less than in the other. If it is now granted that a gas is made up of separate molecules which must be very closely if not exactly alike, how can it be shown that the pressure of a gas is due to the battering of these particles against the walls of the contain- ing vessel, and not to a repulsive force of some kind existing between the molecules themselves, and causing them simply to get as far apart as possible, the force depending in some way on the distance between them ? The supposition of a repulsive force depend- 1 230 THE PHYSICAL PROPERTIES OF GASES. ing on the distance between the molecules may be shown to be inconsistent with Boyle's law, and therefore cannot be accepted. For let us take a cubical vessel measuring one foot in each direction, and fill it with some gas until the pressure is eight pounds on each square foot. If the vessel is now made to enlarge without allowing any gas to enter or escape until it meas- ures two feet in each direction, its volume* will become eight times its original volume, and the pressure of the gas will be, according to Boyle's law, one eighth of what it was at first ; that is, it will be one pound on each square foot of sur- face. But each side of the vessel has now a surface of four square feet, and the total force against each side is therefore four pounds, which is just one half of what it was at first, but the mole- cules of gas are just twice as far apart in the ex- panded state as at first. It follows, therefore, that if the pressure is due to repulsion of the particles, in order to satisfy Boyle's law, the repulsion be- tween two molecules must diminish in the same proportion as the distance between them in- creases, so that when the molecules are twice as far apart the repulsion is one half as great, when three times as far apart the repulsion is one third as great, and so on. But this law of repulsion cannot be accepted as true : for New- ton has shown that when such a law holds, the CONCLUSION. 231 action of the more distant parts of a mass of particles on any one of them is greater than that of the nearer ones, if this law held in the case of gases, the pressure would depend on the shape of the vessel containing the gas as well as upon its size, but this is contrary to all experience. It is, therefore, concluded that the pressure of a gas cannot be due to a repulsion between the molecules depending upon the distance between them. The impact theory of gaseous pressure seems to be the only resort left, and the more thor- oughly it is developed, the more clearly it is seen that it explains the facts in a remarkable way. For not only does it lead directly to the known laws of gaseous pressure and expansion, but it gives at once Avogadro's law that equal volumes of different gases at the same temperature and pressure contain the same number of molecules, besides leading to conclusions as to the heat conductivity and viscosity of gases that have since been verified by experiment. When these results of the kinetic theory are considered, and when it is remembered that the experiments on the electric discharge in rarefied, gases and Crookes' experiments all point strongly in the same direction, one can hardly doubt the es- sential correctness of this view of the gaseous state. 232 THE PHYSICAL PROPERTIES OF GASES. In a previous chapter we have given, for the case of nitrogen, the estimated average velocities of the molecules, the mean free path, and their number and mass. The figures for the velocity of the molecule, something like that of a rifle- ball, are at first startling, especially when it is considered how comparatively long a time it takes one gas to diffuse thoroughly through an- other. Graham concluded from his experiments on diffusion that in still air the hydrogen mole- cule would work its way at the rate of about one foot per minute, while particles of air will travel the same distance in four or five minutes. Clau- sius has, however, shown completely that there is no inconsistency, owing to the great numbers of the molecules and the frequency of impacts. The molecular velocity is obtained directly from the pressure and density of the gas, and is the first of these numerical results to be ob- tained, and is probably the most accurately known of any of them. The mean free path, or the average distance that a molecule traverses between successive collisions, is obtained directly from experiments on the viscosity of the gas. These experiments are somewhat difficult, but there is very good agreement among the results of different observers, so that the mean free path may be regarded as a pretty well deter- mined quantity. The determination of the num- CONCLUSION. 233 ber of molecules, however, depends not only on the mean free path, but on the estimated size of the molecules, and here there is considerable un- certainty. One method of finding the size of the molecules makes use of the assumption that when a mass of gas is condensed, its volume in the liquid state may be taken as the sum of the volumes of all the molecules of which it is made up. -But it seems to be evident that this volume is rather greater than the sum of the molecular volumes, and so this method should lead to re- sults which are rather too large. Another much more trustworthy method is based on the observed deviations of gases from Boyle's law. The kinetic theory shows that the relation between the pressure and volume of a gas, when the temperature is kept constant, de- pends to some extent on the size of the mole- cules, so that it is only in case the molecules have no size at all, or are mere points, that the simple expression given on p. 186 is exactly true. If the molecules have any size, the density will not be exactly proportional to the pressure. In all the more important gases the relation between the pressure and density has been carefully in- vestigated, and the departure from Boyle's law determined. This gives, therefore, the basis on which a calculation of the sizes of the molecules may be made. These two methods lead to re- 234 THE PHYSICAL PROPERTIES OF GASES. suits which are of the same order of magnitude, but the first leads to greater values than the sec- ond, as was to have been expected ; for example, the molecule of carbonic acid gas is found to have a diameter of forty-five thousand millionths of an inch by the first method, and seven thou- sand millionths of an inch by the second method. The second value is believed to be more nearly correct. These results are of course approx- imate, but there is reason to believe that they are of the right order of magnitude; that is, they are probably not ten times too large nor too small. It must be constantly borne in mind that molecules are not to be thought of as little round hard bodies, nor are the atoms themselves to be so regarded. When we consider the com- plexity of the spectrum of iron vapor, for in- stance, or of carbon, some peculiarities of whose spectrum have already been mentioned, it is quite impossible to regard the molecules giving out such complicated vibrations as being other than complex in structure themselves. Many chemists to-day hold that the elements, as we now know them, are not really simple, but are compound bodies built up from some more fundamental substances, but so closely bound to- gether as to resist the ordinary methods of anal- ysis, and that more powerful methods may in CONCLUSION. 235 the future reveal their composition and relation- ships. When, therefore, the size of a molecule is spoken of, it is simply meant that the molecules cannot come closer together than little, round bodies of that size can come. It is not said nor implied what keeps them apart, whether it is a repulsive force which is exerted like gravitation in some entirely unknown way, or whether it is due to the actual substance of the molecule filling the space, and thus effecting the separa- tion by actual contact of the masses in a way we are apt to think we know something about. When one billiard ball rebounds from another, we should certainly say that there was contact, and not what is ordinarily called action at a dis- tance ; but if it is considered carefully, it will be evident that all that can be said is that the particles at the surfaces of the balls came so close together that the resistance to further approach was sufficient to cause the rebound. When, on putting the hand down towards a table, the force opposing the motion becomes so great that we cannot move it farther, we are said to be touching the table. If this force rises suddenly to its full value, the object is said to be hard ; if it increases more gradually, the object is softer. It appears, then, that all that is known of the size and shape of any object, 236 THE PHYSICAL PROPERTIES OF GASES. large or small, is that, when other bodies are brought up to it, they are opposed at certain dis- tances by forces that prevent their further ap- proach ; the two are then said to be in contact, and the surface over which contact takes place is called the surface of the body. It is then perfectly correct to say that the size of a molecule is determined by the closeness with which other molecules may be brought up to it. What may be the nature of the repulsive forces, and how two molecules can act on each other, is neither an easier nor a more difficult question than how one billiard ball acts on an- other. Both are insoluble. They are questions which deal with the fundamental postulates of physics, matter and force, and are therefore be- yond the ken of the physicist. Every explana- tion that can be given in physical science is but a reducing of a complex problem to the simpler elements of which it is made up. The manifold motions of the heavenly bodies are shown to be deducible as consequences of certain habitual relations between matter and force, which are known as the laws of mechanics ; these are few, so that the problem is now reduced to the ex- planation of a few underlying phenomena from which all the other more complicated cases re- sult. In each case, however, the explanation CONCLUSION. 237 must be made in terms of ideas that arise out of our experience. In thinking, we can only make use of those ideas that experience has given us, combining them into new forms it may be, but never originating. So every theory that at- tempts to explain gravitation merely substitutes one force for another, the force due to the im- pact of small particles, or the force due to the pressure of a fluid, in each case assuming a force between particles near at hand, instead of at a greater distance. And the most brilliant hypoth- esis as to the nature of ordinary material atoms is that due to Sir William Thomson, in which the atoms are assumed to be vortex rings in a continuous frictionless fluid which fills all space, thus taking a continuous structureless matter as the basis of ordinary matter. Beyond force and matter, therefore, the physi- cist cannot go ; experiment can teach him noth- ing of this realm ; he can form no conceptions more fundamental than these; he has reached the ultima thule of physical research. This sketch of the properties of gases cannot be more suitably closed than by a quotation from Professor James Clerk Maxwell, one of the most distinguished physicists of recent years, and one of the founders of the modern kinetic theory of gases. After commenting on the im- possibility of any theory of evolution accounting 238 THE PHYSICAL PROPERTIES OF GASES. for the various kinds of molecules, since each individual is permanent and there is no genera- tion or variation of them, and all the molecules of any one substance are alike, and quite differ- ent from those of any other substance, and since there cannot be found any intermediate kinds forming a continuous gradation from those of one kind to those of another, Maxwell goes on to say : " But if we suppose the molecules to be made at all, or if we suppose them to consist of some- thing previously made, why should we expect any irregularity to exist among them ? If they are, as we believe, the only material things which still remain in the precise condition in which they first began to exist, why should we not rather look for some indication of that spirit of order, our scientific confidence in which is never shaken by the difficulty which we experience in tracing it in the complex arrangements of visible things, and of which our moral estimation is shown in all our attempts to think and speak the truth, and to ascertain the exact principles of distributive justice?" THE Detente Aeries. A COLLECTION OF BOOKS SETTING FORTH THE A CHIE VEMENTS OF SCIENTIFIC AND MECHANICAL SKILL AT THE PRESENT DAY. In uniform volumes, each, i6mo, $1.25. Now READY. 1. A CENTURY OF ELECTRICITY. By Prof. T. C. MendenhalL 2. PHYSICAL PROPERTIES OF GASES. By A . L. Kimball, of Johns Hopkins University. IN PREPARATION. 3. HEAT. By R. H. Thurston, of Cornell Uni- versity. 4. LIGHT. By Charles S. Hastings, of the Shef- field Scientific School, Yale University. Messrs. 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