velocity between the two trains-since only when their velocities are equal can there be no alteration of velocity by shifting a part transversely from one train to the other.

This illustration, of course, is a perfectly easily conceived one; but it will help us to understand what has until very lately been an extremely obscure subject,— viz., how it is that there can be such a thing as friction between portions of air; how it is that streams consisting each of detached particles flying about among themselves, can act as if they were solid bodies rubbing against one another. It enables us, I say, to explain upon what depends friction in fluids; in gaseous fluids at all events,—if it does not quite enable us to explain friction in liquids. Of course the explanation of friction in solids must depend on totally different principles. I shall, in my remaining lectures, explain the molecular motions due to heat in gases, and must therefore recur in part to our present inquiry.

LECTURE XII.

STRUCTURE OF MATTER.

Limits of Divisibility of Matter. In physics the terms great and small are merely relative. Various hypotheses as to structure of bodies-Hard Atom-Centres of Force-Continuous but Heterogeneous StructureVortex-atoms-[Digression on Vortex-Motion.] Lesage's Ultramundane Corpuscles. Proofs that matter has a grained structure. Approximation to its dimensions from the Dispersion of Light :-from the phenomena of Contact Electricity.

As I promised in my last lecture, I intend to take up to-day the consideration of recent results as to the ultimate nature and constitution of matter. This is a problem which has exercised the intellects of philosophers from the very oldest times. I have no doubt you are all acquainted with some of the speculations which, whether their own or not, Lucretius and others have given forth upon the subject. These, in many cases, possess even now some interest; but in comparatively modern times such inquiries have usually led to what may rather be called metaphysical than physical disquisitions. It became, in fact, the question of 'Yes' or 'No' for infinite ultimate divisibility of matter. Now that is a problem which, however simple it may appear to the metaphysicians, is at present quite as far from us physicists as it was in the time of Lucretius. We have made certain steps towards the knowledge of

the nature of particles or molecules of matter; but as to the question of atoms,-that is to say, whether in going on dividing and dividing, if we could carry the process far enough, we should finally arrive at portions of matter which are incapable of further division, -that is a question, I say, whose solution seems to recede from our grasp as fast, at least, as we attempt to approach it.

There is a preliminary to all inquiries of this kind which, though obvious to every one worthy of the name of mathematician, is by no means obvious to an intellect (however naturally acute) which has no mathematical training. It is this:-that there is no such thing as absolute size, there is relative greatness and smallness— nothing more. To human beings things appear small which are just visible to the naked eye-very small when they require a powerful microscope to render them visible. The distance of a fixed star from us is enormous compared with that of the sun :-but there is absolutely nothing to show that even a portion of matter which in our most powerful microscopes appears as hopelessly minute as the most distant star appears in our telescopes, may not be as astoundingly complex in its structure as is that star itself, even if it far exceed our own sun in magnitude.

Nothing is more preposterously unscientific than to assert (as is constantly done by the quasi-scientific writers of the present day) that with the utmost strides attempted by science we should necessarily be sensibly nearer to a conception of the ultimate nature of matter. Only sheer ignorance could assert that there is any limit to the amount of information which human beings may in time acquire of the constitution of matter.

However far we may manage to go, there will still appear before us something further to be assailed. The small separate particles of a gas are each, no doubt, less complex in structure than the whole visible universe; but the comparison is a comparison of two infinites. Think of this and eschew popular science, whose dicta are pernicious just in proportion as they are the outcome of presumptuous ignorance.

I shall commence by briefly sketching one or two of the more plausible or justifiable opinions which have been enuntiated by various philosophers as to the socalled ultimate constitution of matter. The firstthat which I have just referred to-is the notion of the perfectly hard atom. You meet with it, not only long before the time of Lucretius, but also in all subsequent time, even in the works of Newton himself. We find Newton speculating on this subject in his unsuccessful attempt to account for the extraordinary fact that the velocity of sound, as calculated by him by strictly accurate mathematical processes, was found to be something like one-ninth too little. We find Newton suggesting that possibly the particles of air may be little, hard, spherical bodies, which, at the ordinary pressure of the atmosphere, are at a distance from one another of somewhere about nine times the diameter of each; and, he says, sound then may be propagated instantaneously through these hard atoms, or particles of air, while it is propagated with the mathematically calculated velocity through the space between each pair. This is no doubt a very ingenious suggestion, and it enables him to get rid of the outstanding difficulty, because it virtually reduces the space through which the sound has to travel to ths of what it other

T

wise would have been; and therefore it enables him to add th to the calculated velocity of sound. In fact, it virtually makes sound pass over 3th more space in a given time than the mathematical investigation showed it should do. But, unfortunately for this explanation, it implies that sound should move faster in dense than in rare air at the same temperature. This is inconsistent with the results of direct measurement.

The true explanation, however, why the velocity of sound is different from that given by Newton's mathematical calculation, was furnished by Laplace, who showed that during the passage of a sound-wave through the air, the alternate compressions and dilatations take place so suddenly that the air has not time to part with the heat generated by the compression, or to supply the loss of temperature produced by the expansion, and therefore its pressure increases more when it is compressed, and diminishes more when it is dilated, than it would do if it were kept constantly at the same temperature. [In the language of Lecture V., above, the compressions and dilatations by which sound is propagated take place adiabatically.] And it is found by experiment that the amount of heat developed by compression of air, or the amount of heat absorbed in its expansion, is completely and exactly sufficient to account for the ninth which Newton found wanting; so that, although we have in this way Newton's authority for the supposition that there may exist ultimate hard particles through which sound or any motion may be transmitted instantaneously, the ground upon which he introduced them has now been found not to warrant that introduction, and therefore we are left as much in difficulty as before.