72 



The Bearing of Rotation on Relativity. 



line of the Earth's disk, — which would bring him into the 

 meridian of Greenwich. If we suppose that there is a definite 

 moment of occurrence of the geometric phenomenon, each 

 observer would get it late by the same amount, about l s *3, 

 being the time of transmission of light; but on repeated 

 observations each would have exactly the same time-intervals 

 of what may be called a lunar day at his service for common 

 standardization of time. 



In conclusion, I would add a few sentences on the general 

 bearing of these remarks. I take it there is no useful 

 knowledge apart from repetition, including its opposite, 

 contrast. An isolated event, with no indication of its 

 history or relation, is meaningless — like an inscription without 

 a clue. Consequently we find that in the field of mechanics, 

 the cases that involve perpetual repetition are those reduced 

 to the best order — as the rotation of the Earth, the revolution 

 of the planets, and periodical mechanical motions of every 

 kind. Therefore, in spite of the apparently greater simplicity 

 of pure translational motion, I submit that it is in the simplest 

 cases of circular motion that we should naturally look for 

 light upon the question of how far we are able to perceive 

 our own drift through the aether. It is not tolerable to erect 

 a new theory, of completely general scope, and leave on one 

 side these familiar natural events, the best analysed that we 

 possess. Properly regarded, the paradoxes to which a 

 theory leads are its most promising features, for they indicate 

 points where something can be learnt by pressing the 

 examination. Some of the numerous paradoxes to which 

 the Theory of Relativity has given rise may prove to be 

 merely verbal or otherwise unessential; those exposed above 

 suggest, I submit, something more than this — namely, that 

 the theory for rectilinear motion is a degenerate case, which 

 leads to untrue results if we attempt to embrace circular 

 motions ; admirably compact as its mathematical form may be, 

 it owes this coherence to a reduction that shuts off the best 

 known fields of Nature. 



Yet no one can doubt that w r e must have a theory of 

 relativity, limiting, and probably limiting very much, what 

 it is possible to know. It is the theory of the interdependence 

 of our senses of intensity or measurement in their various 

 fields — space, time, and if you like, others. It is the work 

 of pure mathematicians to give us one. Owing to the difficulty 

 of his task, the mathematician must be allowed to make any 

 abstraction which he finds workable. The interest thereafter 

 is to see how far his construction may be taken as depicting 

 Nature, in the way that we know Nature to work. 



