ESSAYS 479 



physical reality, the ether, which formed the requisite framework of reference, 

 although, perhaps, too dimly outlined in his mind to enable him to crystallise the 

 concept into a statement which would have carried conviction to the minds of his 

 contemporaries. 



Poincare argued, in the work previously referred to, that the inhabitants of a 

 planet, so veiled in clouds that no external bodies would be perceptible, could 

 not infer with certainty that the planet was rotating, but only that such an assump- 

 tion would provide the simplest basis possible for a system of mechanics. But he 

 so far qualified his contention in a later work, La Valeur de la Science, as to admit 

 that the assumption would make it possible to establish so much wider a correlation 

 amongst physical phenomena that it might be considered as of the same order of 

 probability as the reality of the external world. That is to say, he admitted that 

 practical, though not theoretical, certainty of the rotation would be attainable by 

 the inhabitants. And theoretical certainty must certainly be regarded as unattain- 

 able in any conclusions derived from experience. 



Bertrand Russell has shown, in his Principles of Mathematics, that strictly 

 demonstrable mathematical concepts of absolute time, and of absolute position and 

 direction in space, are attainable, and he upholds Newton's actual verbal expressions 

 from this point of view. But in his references to absolute motion, Newton was 

 not dealing with the purely mathematical concepts of rational dynamics, but with 

 the physical concepts of practical dynamics — quite another matter. 



In order to investigate even so simple a case of motion in space as the path of 

 a raindrop relatively to a fixed point O on the earth's surface, we must choose 

 some framework of reference, and as simple a one as any would be to imagine three 

 straight lines of lengths sufficient to extend to the limits of the field of motion, one 

 east and west— the X axis, say, one north and south— the Faxis, and one vertically 

 up and down — the Z axis. Then the position of any point P, relatively to O, can 

 be specified by the lengths of three straight lines, x,y,z, representing the distances 

 from the planes YZ, ZX, XY, to P, and therefore parallel, respectively, to OX, OY t 

 OZ, reckoned positive if drawn eastward, northward, or upward, and negative if 

 drawn westward, southward, or downward. Then x, y, z are called the co-ordinates 

 of the moving drop, or, strictly speaking, of the centre of the drop, at the time /, 

 reckoned from a moment selected as the starting-point in time. Since we know 

 with great accuracy the motions of the earth relatively to the centre of the sun, 

 we could then determine the motion of the raindrop relatively to the sun's centre. 

 We should simply imagine a similar set of axes with its origin at the sun's centre 

 and parallel to X, Y, Z, respectively at the time l = o, the starting-point in time. 

 We could then determine at any time t the co-ordinates of the point relatively to 

 the sun's centre and the angles between the corresponding axes, and hence the 

 co-ordinates of the point P relative to the sun's centre. Similarly, if we knew 

 the earth's motion through the ether we could find the co-ordinates of P relatively 

 to a set of axes fixed in the ether, the terrestrial axes and the etherial ones being 

 coincident at the time t = o. But without knowing the earth's motion through the 

 ether, we can picture it without difficulty. For the ether of present-day physics 

 must be considered as a substance of great density filling all space and allowing 

 material bodies to pass through it very much as a piece of wire gauze can be 

 drawn through mercury, but with the difference that the ether offers no resistance to 

 such motion, and that it remains fixed in position like a solid, its smallest portions 

 being capable only of making minute vibrations about their permanent positions, 

 instead of wandering freely from place to place, like the particles of a liquid. 



By adopting Riemann's most fruitful suggestion of regarding space as a 



