theory of relativity space is endowed with physical qualities'. How far is this statement true?

Space is one of the many attributes of body, and to that extent Professor Einstein's statement is true. But it does not follow that space is a physical attribute of body; on the contrary, it is without the most essential physical attributes of body. It is not impenetrable, since all finite bodies, resting or moving, penetrate space during time. It offers no resistance. It is neither passive as matter nor active as force. Therefore, though one attribute of body, space is not 'endowed with physical qualities'.

Space is a quantitative not a qualitative attribute, but that of being extended long, broad, and deep; and only one quantitative attribute, while another quantitative attribute closely connected with, but different from, space is time, which is the attribute of being enduring, past, present, and future. A third quantitative attribute is number, different from both; but it is not true that any of these three quantitative attributes of body is endowed with physical qualities', though the body itself as a whole is so endowed.

Professor Einstein's theory of space is the Achilles' heel of his system. If he had said that the same body is quantitative, qualitative, and relative, all might have been well, except that relativity would have sunk into a subordinate and proper position in the analysis of body. But his ignorance of the fact that space is body only so far as triply extended has concealed from him the consequence that space so limited is the object of the pure geometry of the Greeks. In the very first section of his popular book on Relativity, translated by Dr. Lawson, Professor Einstein begins by declaring that pure Euclidean geometry deals with ideas, and therefore is not true about things. He then flies off to the contrary extreme that, in order to become true about things,

the Euclidean propositions resolve themselves into propositions on the possible relative positions of practically rigid bodies, and adds that geometry supplemented in this way is to be treated as a branch of physics. But the truth lies in the middle: pure Euclidean geometry deals neither with mere ideas nor with rigid bodies, but with space, which is body so far as triply extended long, broad, and deep, and therefore a real thing but not a physical thing.

Pure geometry and physics are closely connected, but not the same. The former is a mathematical science, the latter a natural science. Pure geometry has to define and divide space into its segments, and to discover and demonstrate their universal laws: physics has to discover particular facts and causes and to account for them by geometrical as applied to physical laws. Thus the Greek mathematician, Apollonius, in the third century B. C., laid down the purely geometrical major premiss that a curve in which the ordinate squared varies with the abscissa is a parabola. After a gap of some eighteen centuries the Italian physicist, Galileo, added the mechanical minor premiss that the motion of a projectile tends to be such a curve; and by combining these two different premisses, one geometrical and the other physical, he deduced the mechanical conclusion that the motion of a projectile tends to be a parabola. This combination of pure geometry and physics, the one supplying the principles of space and the other applying these principles to the facts of nature, is necessary to the progress of physics. But Professor Einstein would spoil this order of two different sciences by confounding them together.

The cause of his error is his oblivion of the fact that one and the same body is on the one hand mathematical as continuous extended space and enduring time, and on the other hand physical and discrete as consisting of finite bodies, from the

smallest corpuscles to ourselves, thence to the earth and other planets, thence to the sun and other stars, up to the permeating and illuminating ether, which is apparently the greatest finite body; while every one of these finite bodies, small and great, is on the one hand spatially extended and temporarily enduring, and on the other hand physically impenetrable, resistant, passive matter and active force. Professor Einstein, however, obliterates the distinction contained in this analysis of body into its mathematical and its physical being; and that too, not only in the passage quoted by Sir Oliver Lodge, but also in the very last section of his book on Relativity, translated by Dr. Lawson. He begins the section as follows:

According to the general theory of relativity the geometrical properties of space are not independent but determined by ' matter.'

He ends the section as follows:

Since in reality the detailed distribution of matter is not uniform, the real universe will deviate in individual parts 'from the spherical-id est, the universe will be quasi'spherical.'

But is the universe spherical, or does it only appear to be spherical to any man at any place looking round him? The truth is that the geometry of Einstein is a false relapse to primitive mensuration by hands and feet, rods and plumb-lines, and, what is still worse, to the illusion of the blue sky and the spherical firmament of antiquity.

Corpus Christi College, Oxford, Dec. 3, 1921.

IV. THE INFINITE BODY OF THE UNIVERSE

SPACE DURING TIME

FROM The Times, DECEMBER 24, 1921.

I concluded in my letter of December 3, with an analysis which I hope you will allow me to develop.

The body of the universe is a substance or whole thing, which is on the one hand continuous as extended space and enduring time, and on the other hand discontinuous, as consisting of all finite bodies, which are its discrete parts, descending from the ether, apparently the greatest part, to the corpuscles, which are the smallest known particles. This analysis shows, that the space, which is the body of the universe as triply extended, and is the object of pure geometry, is not the physical space to which Professor Einstein would reduce it, nor an object of physical science, and in consequence not a tensor. As Einstein himself says in The Meaning of Relativity, p. 60 (English translation), the density of matter and of energy has the character of a symmetrical tensor': this being so, a tensor is not pure space, but is a body exercising stresses in pure space.

The body of the universe involves a further subdivision. Each finite body is on the one hand spatially extended and temporally enduring, and on the other hand physically resistant, passive matter and active force. Hence Aristotle divided space into common space in which all bodies are, and private space in which an individual body primarily exists. This private space is the local space of Professor Einstein, and he rightly holds that it changes with each finite body; but he wrongly omits common space in which all finite bodies are and all bodies change or rest.

It was a difficult task to prove that a finite body suffers a contraction of its private space in the direction of its motion; yet in spite of the negative result of the Michelson-Morley experiment, FitzGerald's suggestion of this contraction has been calculated by Lorentz. It was a still more difficult task when Professor Einstein predicted that the sun would turn out to have a somewhat greater power of deflecting rays of light than could be completely

explained by Newton's law of gravitation. May not these two examples of contraction and deflection be brought under the mechanical law that the private spaces of finite bodies are lessened by impressed forces, but tend to recover according to their different degrees of elasticity?

It is a pity that Professor Einstein did not rest content with the conclusion that the sun is the force which directly deflects the light. But he has somewhat marred his discovery by supposing that the sun first deflects the space between it and the light, and that then the supposed geometrical curvature of space deflects the light. As this warping of space would not be the private space either of the sun or of the deflected light but only that of the common space of the body of the universe, it follows that the sun could not cause this immovable space to change from a straight line to a curve; if it could, it would warp the continuous space of the whole body of the universe; and, if it could perform that miracle, even then the deflected space between the sun and the light could not deflect this light, because space is not a force. This paradox of warping space shows that Professor Einstein understands the private spaces of finite bodies better than the common space of the infinite body of the universe, which contains all private spaces of all finite bodies, but is itself immovable. To deflect light is one thing, to deflect its containing space quite another.

The general analysis of the body of the universe involves yet another subdivision; and here again Aristotle helps us by his constant opposition of the continuous and the discrete. The body of the universe is not only continuous extended space, but as continuous space is also potentially divisible to infinity into extended segments of space, which are not physical discrete parts; nor are they geometrical points, because a point is a substance as placed but