CHAPTER XV.
THE CONSTITUTION OF GASES.
F late years the attention of those who study the mysteries of nature has specially tended in the direction of examining the very smallest particles into which the chemical elements can be divided. It is true that these particles or molecules, as we generally call them, are too minute to be appreciated by our senses; they cannot be detected even by the most potent microscope. Indeed, if we will but think of it, we could hardly expect our nerves to disclose the character of objects so minute as molecules. Like all the rest of matter, nerves are constituted of molecular particles, and the structure of the most sensitive fibre is far too coarse to transmit indications of the special characteristics of the molecules, of which matter in general is composed. The little objects about which we are to write are things which we can never see, which we can never feel severally. They require to be brought together in clustering myriads where individual peculiarities are merged in general properties before they can make any successful appeal to our organs of sense.
How then, it may well be asked, are we able to learn anything as to the nature of objects which so successfully elude giving any direct testimony appreciable to our senses? Seeing this difficulty, it can hardly be surprising if some should have doubted the accuracy of the results at which philosophers have arrived with regard to the ultimate constitution of matter. But there are methods of discovering truth which are in certain cases capable of more subtle work than the direct indication of our senses. It is these indirect processes which have taught us much regarding that invisible world which lies around. In certain respects we may contrast the subject about which we are now to be engaged with those great themes which more usually occupy the attention of astronomers. In the case of the heavenly bodies the mind is taxed by the effort to conceive distances so tremendous, masses so enormous, and periods so protracted that we often despair of obtaining adequate notions of magnitudes which altogether transcend our ordinary experience. We are now to make an appeal to the imagination in a precisely opposite direction. We are to speak of masses so minute, of distances so short, and of periods so infinitesimal, that it is utterly impossible for us to parallel them by the phenomena with which our senses make us directly acquainted.
At both extremes, however, we employ the same weapons for the study of the phenomena of nature. Mathematical investigation submits to no restriction either in the greatness of the space over which its command extends, or in the minuteness of the portions which must obey its laws. The principles of dynamics are equally applicable whether the periods of time which they contemplate shall be millions of years, as they often are in astronomy, or the millionth part of a second, as they often are in physics. Let me here endeavour to set forth some of the results at which natural philosophers have arrived with regard to the ultimate constitution of matter.
Take a lump of loaf sugar and crush it in a mortar, each of the fragments is, of course, a particle of sugar still. Let the operation of grinding be carried on until the entire lump has been reduced to powder of the utmost fineness, which any grinding apparatus is capable of effecting. Each of the minute particles is still, nevertheless, a fragment possessing the attributes and properties of sugar. It has the sweetness and the hardness, the solubility and the chemical composition of the original lump. There is a difference in dimensions, but no difference of any other kind. But now let us suppose that we were in possession of some pulverising apparatus which would permit the reduction of the sugar to be carried on to an extent far greater than that which could be obtained by the most perfect grinding-mill known to the mechanic. The sugar might be comminuted by such agency to so great an extent that the little particles into which it had become transformed could only be discerned as the smallest of specks under the most potent of microscopes. We have the best reasons for knowing that even these little specks, which are of such extreme minuteness that the original lump contained many millions of them, are still, neither more nor less than sugar.
Up to the present stage the reduction has not transformed, so to speak, the actual nature of the material submitted to the treatment. Though the particles have been crumbled to such an extent that after any further diminution they would cease to be visible, even in the microscope, yet we can, at all events, conceive that further disintegration could be carried on. In fact, the very smallest of these grains, only just visible under the microscope, might be crushed into a thousand parts, and still each little part would not yet have lost the attributes which belonged to sugar. We have now arrived at the conception of a magnitude too small to affect any of our senses, no matter how they may be fortified by the aid of instruments. But the trituration may be conceived to be carried on one step further, until, at last, the original lump has been reduced to particles of sugar so small as to admit of no further subdivision without a total transformation in character. This is an extremely important point. It may, in fact, be regarded as one of those cardinal doctrines which it has been the glory of modern science to teach. There was a time when it was believed that the subdivision of a particle of sugar might be carried on indefinitely. We now know that is not the case. We know there is a certain portion so small that it cannot be again divided. I do not mean that this particle is not in itself composed of separate objects, but what I do mean is, that if, when we have an ultimate particle of sugar, it were divided into two parts, as it might be by chemical processes, neither of those two parts would be sugar or anything like sugar. They would each be something which possessed neither the hardness, nor the colour, nor the sweetness, nor, indeed, any of the attributes characteristic of the original material.
This same argument may be applied to every other substance besides that which I have taken as a first illustration. The atmosphere, composed as it is of oxygen and nitrogen, with traces of other gases, must consist in ultimate analysis of myriads of gaseous molecules. There are molecules of oxygen, and molecules of nitrogen, as well as molecules of the other gases. No doubt the molecule may consist of parts; indeed we know, as a matter of fact, that it does consist of parts; it is therefore conceivable that the molecule could be subdivided, but these parts, whatever other properties they might have, would certainly not possess the characteristics of the original gas to which the molecule belonged.
It is something to have learned so much at all events with regard to the composition of the air we breathe. But we have been able to find out a great deal more, and to discover that the behaviour of these little molecules is of the most extraordinary and vivacious description. That air is eminently mobile is sufficiently obvious; but the air which fans our faces, or the wind which turns our windmills, or even the hurricane which devastates whole towns, gives only a very imperfect idea of the real mobility of air. The hurricane may move, perhaps, at a pace of a hundred miles an hour, but that is a velocity which might almost be described as sluggish in comparison with the molecular movements of the ultimate particles of gases. For our present purpose we may think of the air, not as it blows over the mountain tops, but as it lies in some secluded cavern where all seems absolutely still. No doubt to our ordinary methods of investigation the air and every particle of it may seem in such a case to be absolutely quiescent, but we have ascertained that the apparent quietness is really the result of the want of sufficient acumen in our organs of sense. Had our perceptive powers been endowed with the necessary subtlety, we should have perceived that the apparent calm had no real existence. On the contrary, it would have directly appeared that the ultimate molecules of the air were in a condition of exuberant liveliness.
No doubt the smallest particle of air which could be directly appreciable by any of our appliances for measurement, seems a homogeneous structure and perfectly quiescent in its several parts. When, however, we conduct the examination into its character by those refined methods of investigation which are now at our disposal, we find that the air is ultimately composed of myriads of separate particles. Each of these little particles, no matter how quiet the air as a whole may seem, is in a state of intensely rapid movement. Picture to yourself incalculable myriads of little objects, each dashing about with a speed as great as that of a rifle bullet, and often indeed far greater. The little particles are so minute that it would take about fifty millions of them, placed side by side, to extend over a single inch. The smallest object which we can discern with a microscope is perhaps one hundred-thousandth of an inch in length. The little gaseous molecule would therefore require to possess a diameter about five hundred times greater than that which it actually has, if it were to be large enough to admit of inspection by the utmost microscopic powers which we could bring to bear upon it. And yet, notwithstanding the fact that these particles are so extremely minute, we are able to reason about their existence, to discover many of their properties, and to ascertain the laws of their action in such a way as to throw light into many obscure places of nature. I do not, indeed, know any doctrine in modern science of a more instructive character than that which teaches us the composition of gases.
The movements of the gaseous molecules are, however, so wonderful that it is hardly surprising that those who are invited to believe these things should demand satisfactory evidence as to the existence of phenomena, which from the nature of the case seem to lie out of the reach of direct inspection by the senses. The methods by which our knowledge of the constitution of matter has been obtained, is by reasoning from the phenomena which our senses reveal to the more refined and supersensible conceptions of molecular physics. I could not undertake in a work of this description to give any complete account of the evidence by which these remarkable doctrines are sustained. I will therefore only indicate one of the main lines of argument, by which the necessity for the belief of an important part of the molecular doctrine of gases has been satisfactorily demonstrated.
There are no more fundamental properties possessed by a gas than those which are connected with the pressure which it exerts. If included within a closed chamber, a gas presses against the walls of that chamber. In this case there is a notable contrast between the behaviour of solids, of liquids, and of gases. Suppose, for instance, that a cubical box be fitted with a block of iron which fills it exactly. The metal presses, of course, on the bottom of the box, but not on all its sides. If the iron be removed and the cubical chamber be now filled with water, the liquid presses as before on the bottom with its entire weight, but in addition there will be a lateral pressure exerted by the liquid against the sides of the vessel. Even in this case, however, there is in general no pressure on the upper surface, and to this extent the behaviour of the water resembles that of the iron. Finally, suppose that the box be filled with gas or vapour, this substance will, like the solid or the liquid, press on the bottom of the box, with the entire weight of the gas, it will like the liquid exert a lateral pressure, but it will differ from both the other substances by its manifesting an upward pressure. It will generally, therefore, be necessary to provide a cover for the box, or if there be no cover to expose the upper surface of the gas to pressure in some other way, in order to retain it within the limits of the cube. No doubt under ordinary circumstances we may fill a vessel to the brim with carbonic acid gas, and the gas will remain much in the same manner as if the vessel had been filled with water. But the carbonic acid in such a case is kept down by the pressure of the superincumbent atmosphere. If that pressure were removed the gas would speedily expand and overflow, unless a cover were provided by which it was restrained, and then the gas would exert an outward pressure upon the cover, showing that it had the tendency to expand even though actual expansion was not permitted.
It will be seen that in this behaviour a gas is totally different from a solid or a liquid. No doubt evaporation is generally speaking taking place from the upper surface of a liquid, and the vapour thus produced acts as a gas, so that in this respect some slight qualification of the above statements might be necessary. But nothing can be more obvious than the fact that the upper pressure of the gas indicates some profound difference between its molecular structure and that of a solid or a liquid, We are so accustomed to this manifestation of gaseous pressure that its extraordinary character is apt to be overlooked on accounts of its familiarity. Let us, therefore, consider the matter carefully, and perhaps the simplest method of doing so will be to think of a vertical cylinder with a piston that fits closely, but can move freely. Beneath this piston gas is supposed to be present, and we may imagine the pressure to be so adjusted that the piston shall be ascending in consequence of the pressure exerted by the gas. The question to be examined relates to the force by which this upward movement of the piston is caused. At first it might be urged that the force is simply due to elasticity, and of course this is true, though it is far from providing the required explanation of the difficulty. Let us look a little closer into the matter and see if we cannot ascertain what may be the physical character of this so-called elasticity. We have seen that gas is composed of an innumerable host of molecules, and therefore it must be in some way owing to the action of the molecules that the piston is compelled to ascend in opposition to gravitation.
It is necessary to believe that what elevates the piston is nothing more or less than the hammering of the little gaseous molecules underneath. If the gas be compressed into half its volume then the distances of the molecules are lessened, and the number of blows that the piston receives in a given time is doubled, so that the force with which the piston is pushed upwards is also doubled. This accounts for that fundamental property of the gas which declares that when the temperature remains unaltered the pressure varies inversely with the volume. The effect of heat in increasing the pressure of a gas can be similarly explained. If the gas beneath the piston be heated the velocities with which the molecules are animated become increased. The energy with which they rap on the piston likewise becomes greater, in other words the effect of heating a given volume of gas is to increase its pressure. We thus see how the well-known properties of gases can be completely accounted for on the supposition that their constitution is precisely that which the molecular theory affirms.
As the gaseous molecules dart about they frequently come into collision. The effect of such a collision or encounter, as it is more properly called, is to deflect each of the molecules from the rectilinear path, which it had previously pursued, and to send it off in a new direction. These collisions take place with such frequency that in gas, at the ordinary temperature and pressure, each molecule experiences them at the rate of millions in a second. The path of each molecule thus consists of the free parts, during which it is practically uninfluenced by other molecules, and the disturbed parts during which it is acted upon by the molecules with which it has been fortuitously brought into collision. The frequency of these encounters depends, among other things, upon the density of the gas. In gas of the utmost rarity, such as that which is contained in the vessels employed by Mr. Crookes for his radiometers, the free path of the molecule may be as much as a quarter of an inch before it is turned aside in an encounter.
The actual parts of the molecule are themselves in a state of active vibration, and the nature of that vibration is often of a highly complex character. Notwithstanding the extreme minuteness of the vibrating particles, we are able in some degree to learn certain properties of the vibrations with which it pulsates. Let us take, for instance, the element hydrogen and see what can be ascertained with respect to the molecules of that gas and their vibration. For the purpose of the experiment hydrogen in a state of extreme rarification is put into a tube, and a current of electricity from the induction coil is passed through it. The gas begins to glow with luminosity, and when the light is transmitted through the slit of the spectroscope lines characteristic of hydrogen are displayed. The visible lines are now known to be only a small part of the total spectrum of this element. For when the radiation from glowing hydrogen, either as obtained from a terrestrial source or from some of the stars, is photographed after passing through the prism, several lines are indicated that do not consist of light visible to the eye though visible to the peculiar sensibility of the photographic plate.
This system of spectral lines, so characteristic of hydrogen, must arise in some way from the molecules of which we know the gas to be constituted. We shall, therefore, consider how such effects are produced. A bright line, such as one of those of which the hydrogen spectrum is composed, arises from vibrations in the ether of one definite refrangibility. The effect of transmitting light through a prism is to sort out the different rays in accordance with their several refrangibilities. When, therefore, the spectroscope shows that light from incandescent hydrogen resolved into a number of bright lines, it thereby demonstrates that the radiation emitted from the glowing gas consists of just so many rays of the particular refrangibilities to which those lines correspond. But the refrangibility of a ray of light depends upon its wave-length. Hence, then, we see that glowing hydrogen emits a number of rays possessing certain definite wave-lengths and no others. The rays of intermediate wave-length are entirely wanting. In this respect, of course, a fundamental contrast is presented between such a spectrum as that we are considering and the spectrum of an incandescent solid in which light of every wave-length between certain limits is manifested. Each wave-length corresponds, of course, to a certain system of undulation in the ether. We are hence assured that the radiation from hydrogen translates itself into a certain system of waves of ether, each with its own particular period.
We must, therefore, expect to find that the hydrogen gas possesses the means of imparting to quiescent ether those particular vibrations that the spectroscope reveals. It will be obvious that the movements of the molecule of hydrogen as a whole are not what will answer the purpose. Such movements are not in the nature of vibrations. It is indeed known that the speed with which a molecule of hydrogen is animated undergoes frequent changes. If the positions of the lines in the spectrum were directly dependent on the velocity of translation of the molecules, the spectrum could not be expected to exhibit the characters which we actually find it to possess. It is, therefore, impossible for the origin of the spectral lines to be attributed to any other source than those internal agitations which each molecule itself possesses. The oscillations of the several parts of the molecule impart vibrations to the surrounding ether which are from thence propagated as radiant light. The vibrations of an elastic body are isochronous, that is to say, performed in equal times, and to this extent the molecule behaves as an elastic body. The pulses which it imparts to the ether just possess the properties requisite for the production of light.
It is, however, necessary to suppose that the vibrations which the molecule communicates to the ether are not solely of one type. Were this the case only one set of waves would be propagated, and there would only be a single line in the spectrum. In the spectrum of hydrogen, however, there are, as we have seen, quite a number of lines. These seem to resemble harmonics of some fundamental note. It would, therefore, appear as if the molecule of hydrogen, in addition to its fundamental vibration in the note which properly belongs to it, possessed a number of subsidiary vibrations which might properly be regarded as harmonics. The molecule is thus acting in much the same way as a musical instrument, which, in addition to the primary note to which it mainly responds, disperses at the same time and in consequence of the same impulse a number of fainter notes which are harmonics of the fundamental one.
It is quite evident that the molecule of hydrogen must be of a much simpler character than the molecule of many other elements. For though the spectrum of hydrogen contains a large number of lines, most of them, if not indeed all, belong to a group of associated vibrations. In the case of other elementary bodies the complexity of the spectrum is such as to make us think that the vibrations of the molecule must be of a very complicated character. Thus in the case of iron, we find that when this element is brought to the gaseous state by heat, the light which it emits has a spectrum containing some thousands of lines. It may no doubt be true that groups of these correspond to harmonics of a smaller number of fundamental notes, but even with this admission the vibrations of the molecule of iron must necessarily be of a highly elaborate description.
The effect of heating a gas is to make its molecules move more rapidly. When this happens the collisions between the molecules take place with greater vehemence, and the internal agitations of the molecules arising from the shocks of their collision are all the more intense. Hence, when the gas becomes hot enough, the molecules vibrate sufficiently to produce undulations in the ether strong enough for the perception of light.
Much of what has been said with regard to light may be repeated with regard to heat. We know that radiant heat consists of ethereal undulations of the same character as the waves of light. Hence, we see that the heat or the light radiated from a glowing gas is mainly provided at the expense of the energy possessed by the molecules in virtue of their internal oscillations.
One of the most instructive applications of these principles is to afford an explanation of the means by which the sun sustains its heat, of which we have already spoken in a previous chapter. As the great luminary is a mass of glowing gas or vapour, it is of much interest to examine how far the doctrine of the molecular theory of gases can answer the great question of solar physics. It has of course been long known that the sun retained its power of radiating heat for so many ages in virtue of its contraction. Helmholtz had shown that the amount of potential energy due to gravitation in a mass of matter equal to that of the sun, and expanded over a volume a great as that which he occupies, would completely account for solar radiation. It was only necessary to suppose that this volume of matter contracted in consequence of the mutual attraction of its parts. As it diminished in hulk, the quantity of potential energy would be of course lessened. But as energy could not be lost, that disappearing potential energy must be manifested in some other form. This was accomplished by its transformation into heat, which kept the sun so far supplied as to maintain its radiation unabated for uncounted thousands of years. It was easily demonstrated that a shrinkage in the solar diameter too small to be appreciable by any measurements we could make, would, nevertheless, set free a quantity of heat sufficient to maintain the radiation for a period of two thousand years. The molecular theory of gases stands in a significant relation to this beautiful discovery of the great German philosopher. It is quite clear that the necessary energy is indeed afforded by the contraction, but it is not quite so easy to learn the precise character of the process by which the energy after disappearing from the potential form reappeared as heat. We want as it were to see the mechanism by which this is effected. This it is which the molecular theory of gases enables us to do; we can now follow the entire process of transformation which the energy undergoes.
Gravitation at the surface of the sun is of course very much greater than at the surface of the earth. It is easy to show that if two globes had the same mean density the gravitations at the surface of each would be simply proportional to its radius. As the radius of the sun is 109 times as great as the radius of the earth, it would follow that if the earth and the sun had the same mean density the gravitation on the large globe would be 109 times as great as that on the earth. It is, however, known that in consequence of the high temperature of the sun its materials are so much more expanded than are those of the earth, that the sun's mean density is only about one-quarter of that of the earth. In consequence of this we see that the gravitation of a body on the sun's surface must be one-fourth of what it would have been if the sun had a mean density equal to that of the earth. It thus appears that the gravitation at the surface of the sun must be about 27 times as great as the gravitation on the earth.
The effect of gravitation on our globe is well known to be able to impart to each body in the course of one second a velocity equal to 82 feet per second. It therefore follows that a body falling at the sun's surface receives in each second an increment of velocity to the extent of 864 feet per second. But the visible parts of the sun are composed of gaseous or vaporous materials. From the molecular spectrum of gases we have been taught to believe that the molecules of which the sun is composed are in incessant motion. Gravitation constantly tends to impart to each molecule an increase of velocity downwards. It is quite true that we cannot expect each molecule should actually acquire an additional velocity of 864 feet each second. Indeed, in our own atmosphere we have an illustration of the absurdity of such a notion.
The gravitation on the earth imparts to every falling body a speed of 32 feet per second. Of course if there were only a single molecule coming in from outside space it would doubtless hurry in towards the earth with a gradual augmentation of velocity at the rate we have named. Had our atmosphere been originally in a highly diffused state, gravitation would have drawn it in to the stable condition which it at present occupies. The condition of equilibrium in our atmosphere appears to be as follows. At the surface of the earth there is of course an unyielding surface so far as the air is concerned. We may regard the atmosphere as divided into a number of concentric shells around the solid sphere. Each shell has a density less than that of the shell above it, and greater than that of the shell below it. The upward pressure from the lower shell compensates for the effect of gravitation on the shell above, and thus the equilibrium is sustained. But in the case of the sun there seems to be no solid shell possible. The consequence is that there must be a general shrinkage of the entire mass; this being so the molecules on the whole get nearer to the sun's centre, and consequently, in virtue of the attractive power of the sun, work is done on them and they acquire enhanced velocity. Thus on the whole the velocities of the solar molecules in consequence of the solar attraction tend to increase.
On the other hand there is a distinct loss of energy to which the molecules are exposed. As the velocities increase the encounters between the different molecules become more severe. After each such encounter the molecule vibrates with increased energy, obtained at the expense of the velocity of translation. The molecules are thus rendered more competent to impart energy to the surrounding ether, that is to say, they acquire an increased power of radiation. Thus we see that the fact of the sun's contraction translates itself with a tendency to increased speed in the molecules. A portion of the energy thus arising is appropriated by the molecules and thus becomes fitted for the sustenance of the sun's heat.
So long as the sun shrinks in dimensions there will be an energy available towards the maintenance of its radiation. The termination of the supply will be reached when the sun has become so far solid that gravitation is no longer effective in reducing its volume at a sufficiently rapid rate.