therefore it is not from this point of view that the solution can at present be improved; nor can we well form an idea of the nature of the modification which the results of the approximate method would undergo. But the idea which I have just mentioned with reference to tidal friction, which has not yet been taken account of in the solution of these planetary problems, shows at once that so long as the parts of any moving integral portion of the system are capable of being displaced relatively to one another, and so moving relatively with friction, so long must there be a cause tending constantly to the degradation of the rates of motion in the system, and therefore that stability of the planetary system is impossible under present conditions. Remember that it was in the imagined interests of religion that the earth's motion was denied. History repeats itself here. An ill-informed Teleologist, however good his intentions, is far more dangerous to the cause he has at heart than the bitterest of its declared enemies.

Then let us take the question of the heat developed by compressing a gas. You all know that a piece of tinder can be set on fire when it is enclosed in a cylinder in which the air is suddenly compressed by pushing in a tight-fitting piston. Great credit has recently been claimed for two speculators, Séguin and Mayer, who independently propounded the hypothesis that the heat developed in such a case is the equivalent of the work spent in compressing the air; or its converse, that the heat lost in expansion is the equivalent of the work done by the expanding material. To make such hypotheses without preliminary experimental measurements, is simply to fall into the fatal error to which I have already adverted, the à priori assertion of physical principles.

To see that it is so, we have only to consider that a gas might (for all we can tell without experiment) have the properties of a spiral spring. Suppose, in fact, instead of air, the cylinder above spoken of to be filled with a number of spiral springs so adjusted as not to interfere with each other's motions. In compressing such a set of springs, exactly the same amount of work may be spent as in compressing air, and yet we may find no trace whatever of heat generated. It therefore appears obvious that until we know for certain the ultimate nature of a gas, the only way (independent of mere guessing) to discover the relation between the heat developed by compression and the work spent in producing it, is to experiment; and that without experiment it is impossible to lay down any general relation between them. The modern view of the constitution of a gas, in which its particles are supposed to be flying about with great velocity in all directions, and constantly impinging upon one another and upon the sides of the vessel, leads us almost directly to many valuable conclusions, among which I will refer for the moment only to the result known as Boyle's law, where we contemplate the compression of a gas whose temperature is kept constant. Suppose, for instance, the particles to be moving with a certain velocity in every direction, we find that if the piston could be moved half way down the cylinder, and the velocity of the particles not thereby increased,1 the number of impacts per second upon the ends of the cylinder must become twice as great as it was before, because the length of the cylinder is only half as great.

1 This would be a violation of the principle of Dissipation of Energy, as will be seen by the reader of Lecture VI. But that does not invalidate its usefulness as an illustration of the present argument.

Also, the number of impacts per second per square inch upon the curved sides of the cylinder must likewise be doubled, simply because there is the same number of particles as before, impinging with the same velocities, but upon only one half of the surface. If we could manage to advance the whole piston by infinitesimally small stages, so as at each such advance to take advantage of the absence of all molecular pressure upon the piston, or to advance at every instant those parts of the piston upon which for the moment no impact was impending, we should produce this diminution of bulk without altering in any respect the velocities of the particles of gas; and therefore, according to Boyle's law, and according to the analysis just given, we should have the case of a gas doubled in pressure, and occupying exactly one half the bulk which it occupied at first, but without increase of temperature. Here then is another mode of contemplating the compression of a gas without any production of heat. This question is one of great importance, and I intend to treat it pretty fully in the course of these lectures.

The only other fallacy which I shall mention for the present, is that of basing physical results upon the old dog-Latin dogma, causa æquat effectum. It is difficult to decide whether the Latinity or the (semi-obscure) sense is in this dogma the more incorrect. The fact is, that we have not yet quite cast off that tendency to so-called metaphysics which has often completely blasted the already promising career of a physical inquirer. I say 'so-called' metaphysics, because there is a science of metaphysics; but from the very nature of the case, the professed metaphysicians will never attain to it. In fact, if we once begin to argue upon such a dogma as the

above, the next step may very naturally be to inquire whether cause and effect are simultaneous or successive and then we shall have become so mystified. about the meaning of the word Cause that we may well be ready to inquire (as many have already done) what is the necessarily ever acting cause of the uniform motion of a body upon which no forces act!

The originator of true experimental science seems to have been Gilbert of Colchester, whose deservedly celebrated treatise De Magnete was published 300 years ago. After him came Galileo and Newton, each making gigantic strides in the true direction, and by them this, the ONLY way of attaining to a discovery of physical laws, was permanently established. The proof of this is, that the last two centuries and a half have achieved, in purely physical science, million-fold what had been accomplished before them. And it is not that we are now more able, nor that we have more leisure-certainly not :

... for Romans now

Have thewes and limbs like to their ancestors'.'

It is rather that whenever the direction, given to inquiry is a proper one, the men come forward. This direction was good in Britain at certain memorable times, as when Newton and Hooke were contemporaries; in the days. of Maclaurin and Cotes, and in those of Cavendish and Watt. At intervals it broke down entirely as regards mathematical physics, partly as regards experimental physics, and once again it has become good; and consequently, since the ever-memorable days of Young and Davy, we have had Green and Hamilton, Faraday and Graham, and we can still rejoice in the possession of Stokes and Thomson, Adams and Clerk-Maxwell, Joule

and Andrews. This list is as good as either of the others, and might be considerably increased. Other countries have had their similar fluctuations, all I believe traceable to similar causes. Little more than half a century ago, France had such mighty names as Ampère, Laplace, Lagrange, Poisson, Fresnel, Fourier, Carnot, Cauchy, etc. I name them just as they occur to me. We cannot do much in the way of classifying men like these. Germany now has Helmholtz, Weber, Kirchhoff, and has but recently lost Gauss, Jacobi, Dirichlet, Plücker, Riemann, and Magnus.

The sad fate of Newton's successors ought ever to \ be a warning to us. Trusting to what he had done, they allowed mathematical science almost to die out in this country, at least as compared with its immense progress in Germany and France. It required the united exertions of the late Sir J. Herschel and many others to render possible in these islands a Boole and a Hamilton. If the successors of Davy and Faraday pause to ponder even on their achievements, we shall soon be again in the same state of ignominious inferiority. Who will then step in to save us?

Even as it is, though we have among us many names quite as justly great as any that our rivals can produce, we have also (even in our educated classes) such an immense amount of ignorance and consequent credulity, that it seems matter for surprise that true science is able to exist. Spiritualists, Circle-squarers, Perpetual-motionists, Believers that the earth is flat and that the moon has no rotation, swarm about us. They certainly multiply much faster than do genuine men of science. This is characteristic of all inferior races, but it is consolatory to remember that in spite of