besides all these relative spaces, these spatial things moved within a space containing stars, sun, and earth, and so far unmoved by any of the motions of the various bodies contained by it. Relative spaces and motions of bodies are always included in a containing space. We may add that their relative times are also included in a containing time. We may also propose a new definition of motion within containing space and during containing time. Motion is a change of anything spatial, from place to place within a containing space from moment to moment during a containing time.

Professor Einstein has neglected containing space which itself unmoved contains the motions of relative spaces. But, it will be said, a containing space is only relatively immovable; for example, the containing space between Weymouth and Oxford, though unmoved by bodies between these places, moves with the earth and its relative space round the sun. True; but containing space has no limit, because one containing space is contained in another; and, as it becomes more and more extended, becomes unmoved on a larger and larger scale. The earth, all other planets, and the sun itself are and perform all their movements in the one containing space of the solar system. The solar system and all other stars are in the one containing space of the stellar system; and finally, the stellar system and the ether which occupies the intervals between all ponderable bodies and their corpuscles are included within the containing and pervading space, which includes all bodies whatever, and their relative spaces, and is in fact no other than the extended universe. It is this all-embracing space of the extended universe, which Giordano Bruno said is infinite, and Newton called absolute space, not only unmoved but immovable; for if there could be any space beyond this space, this space would not be all containing and infinite

space. Hence the following passage in Newton's Scholium:

'Now no other places are immovable but those that from 'infinity to infinity do all retain the same given position to one another, and on this account must ever remain un'moved, and do thereby constitute what I call immovable space."

Sir, I feel confident that, if the learned men of our day will condescend to study the geometry of the Greeks, adopted and improved by Sir Isaac Newton, they will conclude that space is the all-containing extension of the spatial universe; that Professor Albert Einstein's theory of space is deficient because he has neglected the fact that all motion is from place to place in containing space; that his prediction and the observations of the total eclipse of May 29 have corrected Newton in an important detail concerning the deflection of light; but that neither Einstein nor anybody else has destroyed Newton's theory of space. On the contrary, his distinction between absolute and relative space is one of the achievements which have raised him to the eminence which he has long deserved in the history of science. Weymouth, November 17, 1919.

II. ABSOLUTE SPACE AND TIME

FROM The Times, APRIL 5, 1921.

The correspondence initiated by your Scientific Correspondent on March 29, and continued by Professors Fleming and Wildon Carr, seems to evince a somewhat hesitating confidence in the theory of relativity. As then on Nov. 22, 1919, at the outset of the discussion on this subject, you kindly published a letter from me to the effect that Sir Isaac Newton was right in contending that space and time are not only relative, but also absolute, perhaps, now that The Theory of Relativity has been published by Professor Einstein, and in an authorized translation by Dr.

Lawson, I may be allowed to make some critical remarks on the subject, and to defend my belief that space is the extension and time the duration of the

universe.

In Chapter III, on Space and Time in Classical Mechanics, Professor Einstein asks what is meant by motion in space, and this is his answer:

'We entirely shun the vague word space, of which we must ' acknowledge we cannot form the slightest conception, and 'we replace it by motion relative to a rigid body of reference.' He takes as an example the motion of a stone thrown out of the window as relative to a railway carriage moving and to an embankment at rest. Hence your Scientific Correspondent says by way of approval that space is only a relation between pieces of matter. He might have gone farther back to Leibniz, who, having defined space as a relation of coexistence and time as a relation of succession, may claim to be the chief founder of the theory of relativity.

The objection to this treatment of space and time is that, so far as it is true, it is not the whole truth. What is true is that all finite bodies, resting or moving, are related as either coexistent or successive, as well as otherwise. What is false is that space and time can be defined in this way of Leibniz, or that space can be dismissed in the way of Einstein from the definition of motion. A stone, a carriage, and an embankment, in order to be coexistent with each other must each be extended, and in order to succeed one another must each be enduring as well as extended. Now what is extended is space, and what is enduring is time. It follows, therefore, that every finite body, being extended and enduring, must have space and time of its own, in order that it may coexist with, or be successive to, any other finite body. Moreover, as space is essentially extension and time essentially duration, while extension

and duration, though both essential attributes of body, are not relations, it follows that space and time are not relations. Finally, the truth about space and time is that in themselves they are essentially extension and duration, and are also conditions of extended and enduring finite bodies being related to one another as coexistent and successive.

Having dispensed with 'motion in space', as he does, Professor Einstein can hardly be expected to define motion, which, however, through the whole history of mechanics, from Aristotle to Galileo and Newton, and from them to the text-books on the kinematics of the present day, has been defined as a change of a finite body through space during time, and reduced to the equations for velocity (v), space (s), and time (t); namely, v = s/t .. s = vt .. t =s/v. Professor Einstein is of course well aware of these primary equations, and applies them in Chapter VIII to the velocity of the propagation of light as being c = 300,000 kilometres a second, where c is a special symbol for the velocity of light. On the other hand, he does not surrender his former preference for 'motion relative to a practically rigid body of reference'. But the truth is that velocity is essentially a change through the extension of space during the duration of time, though involving, but only as a consequence, a change in the relative position of bodies. As a method the use of these relative positions is a useful measure of velocity; but it is not the only method, and it does not afford a definition of the velocity of motion at all.

When we say with confidence that the earth moves in its orbit round the sun with the velocity of about 30 kilometres a second, that a ray of light moves from the sun to the earth with a velocity of 300,000 kilometres a second in about 8 minutes, that the illustration on page 127 of Professor Einstein's book represents a ray of light first issuing far away from

a fixed star, then being deflected into a curve by the sun, and finally reaching the earth, and when we reflect that the whole starry heaven displays one vast illumination, what space, and of what body do we mean? It cannot be the space of the finite body moving, nor of any body perceptible. It may seem to be the space of ether, well defended by Professor Fleming on March 31, in The Times, but even that is not sufficient for all motion through space, because there is no proof that ether, when it comes into contact with dark bodies such as the earth, is the only vehicle of the motions of all bodies through the earth, and a fortiori through the multitudes of bodies, which have never been proved to consist entirely of ether. What then? Sursum corda. Space and time are both continuous, and as such not a mere continual series, even when so measured, but absolutely continuous extension and duration from infinity to infinity, as the ancient geometers saw and Newton saw after them. The bodies again which are near us consist of corpuscles and are again themselves corpuscles in larger and larger bodies, until at last they are all united in one body of the universe containing all bodies as its parts, and containing their extensions and durations and motions, as well as all their other attributes. I believe then that space is the infinite extension, and time the infinite duration, of the infinite and absolute body of the universe. Professor Einstein is right in recognizing bodies, but he has omitted the all-containing body. April 3, 1921.

III. IS SPACE PHYSICAL?

FROM The Times, DECEMBER 3, 1921.

In a letter which you published on November 25, Sir Oliver Lodge quoted with approval a statement of Professor Einstein that according to the general

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