340 . Sir Joseph Larmor 



now expelled general metric ideas of position. Would it be entirely 

 wrong to assert that local or sectional relativity has been retained 

 for nature, so far as this order of ideas extends, by transferring the 

 laws of nature into a space-time frame which itself no longer 

 possesses that quality? 



The distinction has thus been made between an ultimate idea 

 of space as mere threefold continuity, marked but uncharted, and 

 the metric that may be imposed on it by which it becomes a frame 

 fit for the purposes of description of nature. There is only one 

 space: but its practical aspect, whether Euclidean or elliptic or 

 merely heterogeneous, depends on the metric that we choose to 

 assign to it. The metric would thus appear to pertain more closely 

 to the order of nature for which it is to form the most convenient 

 frame for description, than to space itself. For space is primarily 

 bare threefold continuity; though a set of descriptive coordinates 

 jp, q, ... is unavoidable as a foundation of thought, any set is as 

 valid as any other. For ultimately, the count or census of the points 

 or marks that pervade the continuity and render it descriptively 

 given to us, is the same count however it be made. May we say 

 that the insistent, originally uncritical, notion of relativity reduces 

 itself ultimately into this postulate, that as nature is presented to 

 us, it is such that in mental operations we need attend only to 

 one portion of the spacial continuity at a time? This makes the 

 onefold time, or rather mere temporal succession as representable 

 by the 8a of Minkowski, the fundamental feature*, which however 

 diverges spacially into a manifold: according to Hamilton long 

 ago, algebra was the science of pure time. 



In the above, space is given by a manifold array of points, of 

 which the coordinates p, q, ... express one of the varieties of 

 numerical census. Is then space-time absolute, or is it continually 

 being constructed by physical science as it ranges over the void, 

 for its own purposes, just to the extent that it may be required? 

 May we say that the formless manifold is the fundamental feature, 

 that the array of points and their census do not need to be 

 definite in any respect a priori, and that the metric which is 

 imposed on it and makes it into a definite working type of space 

 is related to the physical world and so is to be regarded as evolved 

 in connexion with our organic description or mapping of nature, 

 and to be just as permanent? 



What remains of the original notion of relativity after this 

 sifting of ideas would then coincide with the principle of Newton, 

 Faraday and Maxwell, originated by Descartes, that the operations 

 of nature are elaborated in fourfold extension according to a scheme 

 purely differential, that is by transmission from element to element 



* The spacial sign here attached to 8(r^ is an accident of the order of exposition. 



J 



