336 Sir Joseph Lannor 



whicli a priori was well worth looking for, would seem to await 

 explanation on other lines. 



Again would there be an observable change of periods of 

 spectral lines according as the vibrating source was at the Sun or 

 at the Earth? The underlying absolute periods of radiating 

 hydrogen molecules would be always and everywhere the same: 

 thus the apparent period in the gravitational world would vary 

 inversely as the local scale of time, and be longer at the Sun. 

 But this is a local apparent period. The waves sent out from the 

 solar molecule are observed at the earth: we have seen that their 

 length changes as they progress, being inversely as the local scale 

 of length, and their speed changes also, so that their period changes 

 inversely as the local scale of time. Thus when they have reached 

 the Earth their period conforms to the local scale and would agree 

 with that of the radiation of a similar terrestrial molecule. In fact 

 if complete correspondence is established*, element for element, 

 as above, all periods or intervals of time measured at any element 

 are changed in the same ratio depending on the locality alone. 

 Any other conclusion would make the pulsating rays into signals 

 establishing absolute time throughout the apparent universe, 

 which could hardly be a result of a theory of relativity. 



The condition 8ct = prescribes a definite ray- velocity for each 

 element of arc, the same forwards as backwards, only when Scr^ 

 involves St'^ but no products of St with other differentials: in 

 other cases it gives two velocities, not equal and opposite, and 

 this spacial scheme of rays seems to fail. If rays are to be pro- 

 perties of the space a very severe restriction is thus imposed on 

 the form of 8cr^, but one which seems to be satisfied for the slight 

 modifications that would be involved in the actual gravitation of 

 experience. 



In the modifications of the expression for 8cr^ which absorb 

 gravitation the coefficients do not involve the time explicitly: 

 therefore the ray-paths are fixed in the space, and it almost looks 

 as if they were guides imposed by the nature of the space alone, 

 as thus modified, for the alternating energies of radiation to run 

 along. 



Any inference that because a ray is fixed in space, as many 

 waves must run in at one end as run out at another, would be at 

 variance with the very notion of relativity, by providing a scale 

 of absolute time throughout the universe. Such an argument 

 seems to amount in more general form essentially to this: when 

 the expression for 8a^ does not contain t explicitly it will make no 



* As has been estabKshed for the more general case in a beautiful analysis by 

 Prof. Th. de Bonder, of Brussels, Comjptes Rendus, July 6, 1914, Archives du 

 Musee Teyler, Haarlem, vol. iii, 1917, pp. 80-180. [It is merely continuity with 

 non-gravitational fields, and not correspondence, that is established.] 



