fixed stars there would still be relative motion between it and other things. It is true that these other relative motions would not be connected with the depression of the water by the same simple laws which connect that depression with the rotation of the pail relative to the fixed stars. But the depression would be connected with these other relative motions by laws which are mathematical transformations of these simpler ones. In that sense it would be true to say that the annihilation of the fixed stars would not necessarily make any difference to the phenomena. On the other hand, we can still admit with Mach that it would not be safe to assume that laws which have been discovered and verified in the presence of the fixed stars would necessarily continue to hold when such a large and important part of the material universe as the fixed stars had been annihilated. The difference between our answer and Mach's comes to this: Mach accepts it as a necessary consequence of the Relational Theory that the existence of the fixed stars is an essential condition of the phenomena under discussion; he then devotes himself to showing that we ought not to be surprised at the disappearance of these phenomena in the absence of the fixed stars, and therefore that this consequence of the Relational Theory is no objection to it. We argue that this is not a necessary consequence of the theory, but add that we too should not be surprised if laws which had been ascertained in the presence of the fixed stars should be found to break down after so huge a change as the annihilation of those bodies.

The upshot of the discussion seems to me to be that there is no conclusive objection to the view that all motion is relative, and that all arguments which have been produced to show that we must recognise, and can indirectly measure, absolute motion, are fallacious. This being so, I think there are strong reasons for rejecting the Absolute Theory. After all, the laws of motion are empirical laws, discovered by observing and

reflecting upon the actual movements of actual bodies. Now, all that we can observe in the way of motion is the change in position of one body with respect to others. It were strange indeed if such observations could lead to laws about something which is, from its very nature, unobservable, and stranger still if such laws enabled us to control and predict the movements of bodies in nature. Absolute Space, Time, and Motion have all the appearance of being mathematical devices, and not substantial constituents of nature, and a theory is to be preferred which reduces such mathematical scaffolding to a minimum, provided of course that it is adequate to all the facts with which it professes to deal. I think that mathematicians and writers on dynamics have been justified in rejecting the Relational Theory in the forms under which it has been commonly presented in the past; but I think that this is because it has been badly and inadequately stated, and not because it is impossible to make it fit all the facts.

This is about as far as we can go when we confine the discussion to ordinary mechanical phenomena. But the whole question arose again in recent years over electro-dynamics, and it has been found that reflection on the facts of this region of phenomena necessitates a still more radical overhauling of the traditional concepts of kinematics. This leads to the Theory of Relativity, which I shall deal with in the next chapter.

The following additional works may be consulted with advantage:

LEIBNIZ, Correspondence with Clarke.

E. MACH, Science of Mechanics, Chap. II., § vi., Appendix XX.
and XXII.

B. A. W. RUSSELL, Principles of Mathematics, vol. i., Chap.
LVIII.

A. MÜLLER, Das Problem des absoluten Raumes. (Vieweg.
Braunschweig., 1911.)

P. PAINLEVÉ, Les Axiomes de la Mécanique. (Gauthier-
Villars, Paris, 1922.)

H. POINCARE, Science et Hypothèse, Chap. VII. (Flammanon,
Paris.)

H. POINCARÉ, Science et Méthode, Part II., Chap. I.

"

CHAPTER IV

Ah! that accounts for it," said the Hatter. "He won't stand beating. Now, if you only kept on good terms with Time, he'd do almost anything you liked with the clock. You could keep it to half-past one as long as you liked."

(LEWIS CARROLL, Alice's Adventures in Wonderland.)

Modification of the Traditional Kinematics in the Region of Physics (continued). (2) The Special Theory of Relativity

THE older controversies between Absolutists and Relationists, which we have discussed in the last chapter, took place wholly within the region of dynamics, i.e. they dealt with the movements of bodies and with the changes of shape, such as flattening and depression, which some of these movements produce. It is clear, however, that the same kind of question could be raised over anything whatever that moves, and over any kind of effects which movement may seem to produce. Now there is good evidence-some of which will be mentioned in a later chapter- for the view that light travels out from its sources with a very great but finite velocity; and this velocity has been measured. Again, the motions of charged bodies produce magnetic effects which vary with the velocities of the bodies.

Thus in theory the whole question between the Absolute and the Relational views of Motion might be argued out again in the regions of light and electromagnetics. A wave of light might be expected to have all sorts of different relative velocities, and the question might be raised: Which, if any of these, is what the physicist means by the velocity of light? The Absolutist

might here step in and say that by the velocity of light we must mean, not any of its relative velocities, but its absolute velocity, in the sense discussed in the last chapter. Similarly, we might ask: Which, if any, of the numerous different relative velocities of any charged piece of matter produces magnetic effects? And the Absolutist might say that no relative velocity has this effect, but only the absolute velocity of the charged body. I do not think that these additional facts really make any difference in principle to the conclusions which we reached about the Absolute and the Relational Theories in the last chapter. I will try to justify this statement before going on to discuss what modifications the new facts do make in the traditional kinematics.

The subject is a little confused at the outset through the introduction of a new friend-the Luminiferous Ether-which did not enter into the purely dynamical arguments. Thus we get an apparently intermediate view, put forward by physicists who reject Absolute Space, Time, and Motion with righteous horror as metaphysical figments, and tell us that what is important in light and electro-magnetics is motion, not with respect to this or that body, but with respect to the Luminiferous Ether. It seems to me that for the present purpose there is no important difference between the Ether and Absolute Space. A distinction was originally drawn, because various physical properties, such as elasticity and density, used to be ascribed to the ether, and because it was supposed to produce various effects on ordinary matter. This is inconsistent with the traditional view that Space does nothing, has no physical properties, and is thus distinguished from Matter. But there are two circumstances which make the distinction between the Ether of the modern physicist and the Absolute Space of the older Mechanics so slight as not to be worth keeping. Absolutist has really no right Space does nothing to matter.

On the one hand, the to say that Absolute For it is of the essence

of his view that absolute motion produces flattening and other mechanical effects on matter; and, since Absolute Space is involved in Absolute Motion, it is clear that he ought to hold that it is an essential factor in the production of these effects. On the other hand, as we shall see, the Ether has proved to be a more and more retiring entity, until it is difficult to discover that it plays any part in physics except that which Absolute Space played in the older Mechanics. Thus I do not regard the two views that the velocity of light means its absolute velocity and that it means its velocity relative to the Ether as genuine alternatives. The Ether just is Absolute Space plus some hypothesis as

our present purpose.

Having cleared this complication out of the way, we can see fairly easily that the facts about light and electro-magnetism make no difference in principle to the question of Absolute versus purely Relative Motion. When the velocity of light was measured, and when the fundamental equations of the electro-magnetic field were laid down, writers did not as a rule state very clearly what frames of reference they were assuming. But it is certain that they were, in fact, assuming the familiar frame of reference with respect to which Newton's laws of motion hold. If this be Absolute Space, then they were talking about Absolute Motion, and if it be the fixed stars, then they were talking about motions with respect to the fixed stars. Every reason that there is for taking the latter alternative as regards ordinary dynamics exists for doing the same with regard to light and electro-magnetics. The velocity of light is something that has been experimentally measured, and what has been measured must have been the time that a wave of light took to get from one body to another (or rather from one body to a second and then back again to the first). Clearly it was the velocity of light relative to these bodies that was measured, and not the time