JSote on Gravitation. 139 



refer to those experiments which are still uncompleted. As 

 their subject-matter forms the whole basis of gravitational 

 relativity, their importance is obvious apart from the line of 

 attack here considered, and they will be dealt with separately 

 on completion. 



One direction in which we might expect to find effects of 

 the kind here contemplated is in the displacement of the 

 spectral lines as between different isotopes. There is of 

 course such a displacement to be expected on Bohr's theory 

 on account of the dynamical effect of the changed mass of 

 the nucleus. There might, however, be an additional effect 

 due to the modification of the field of force arising from the 

 nuclear charge owing to the change in the mass associated 

 with it. As a matter of fact, Aronberg * and Merton f both 

 find a small displacement for a given line as between uranium 

 lead — ordinary lead — thorium lead. For example, Merton 

 for \ = 4058A.U. finds 



X (Ur. lead) -A, (ord. lead) = 0'0050 A±0'0007 A 

 \(ord.lead)-\(Th. lead) =00022 A + 0-0008 A. 



Whilst these displacements are small they are nevertheless 

 many times larger than the Bohr shift calculated from the 

 dynamical effect of the change in the mass of the nucleus. 

 Merton also finds a displacement as between thallium from 

 pitchblende and ordinary thallium. On the other hand, 

 ordinary lithium (atomic weight 6" 94), which has been 

 claimed to be a mixture of isotopes (atomic weight 7 with 

 a small proportion of 6), shows no evidence of the expected 

 duplicity in its spectral lines. However, there is no evidence 

 of the Bohr shift, which should be large in this case ; so that 

 the lithium observation does not seem very helpful in this 

 connexion. 



There are, of course, other possible causes for the displace- 

 ment of the spectral lines of isotopes such as, for example, a 

 small variation in the electrostatic field of the nucleus arising 

 from a difference in the configuration of its electronic con- 

 stituents ; but if, for the sake of argument, we assume it 

 arises from a modification of the law of force of the more 

 fundamental kind now under consideration, the connexion 

 between such modification and the change of wave-length 

 may be calculated as follows ; — 



Using the notation of ' Electron Theory of Matter,' 2nd 

 edn. p. 616, let capital letters denote positive and small 



* Astrophys. Journ. vol. xlvii. p. 96 (1918). 

 t Roy. Soc. Proc. A, vol. xcvi. p. 388 (1920). 



