396 On the Einstein Spectral Shift. 



proceeds to elements o£ higher atomic number. The relation- 

 ship is exhibited graphically in curve B of fig. 1, in which 

 the values of log b are plotted against log N. The points 

 fall accurately oh a straight line, whose equation is log 6 = 

 2-09 log N — -44 and therefore b = '36 N 209 . The constant of 

 proportionality is of no significance, being merely determined 

 by our arbitrary choice of the centimetre as the unit of 

 length. Provided one does not extrapolate over too great a 

 range of atomic numbers, Schmidt's results agree with the 

 idea that the atomic scattering coefficient is proportional to 

 the square of the atomic number. 



This result is predicted by Sir Ernest Rutherford's theory 

 of nuclear scattering, and has been verified for j3 rays by 

 observations made in a very direct manner by Dr. Crowther. 

 The agreement of Schmidt's results with these direct obser- 

 vations seems to be prima facie evidence of the substantial 

 accuracy of bis theory and experiments. 



Cavendish Laboratory, 

 Cambridge. 



Nov. 3rd, 1921. 



XLII. Reply to Sir Oliver Lodge's paper on the Einstein 

 Spectral Shift. 



[Phil. Mag. June 1921.] 



SIR OLIVER LODGE'S criticism of my paper on the 

 Einstein Spectral Line effect appears to be sound in so 

 far as my argument is stated more briefly and more roughly 

 than would be justifiable if the work were given as a theorem 

 in Pure Mathematics. Strictly speaking, if ds = 0, the limit 



of -K- does not exist, and there is no differential coefficient -r 

 bs as' 



In the problem under consideration, however, there is the 

 underlying physical assumption that the path corresponding 

 to an initial velocity c is the limit, as v tends to c, of the path 

 corresponding to an initial velocity v. This assumption 

 appears to be supported by the transformations of the Special 

 Theory of Relativity and it is difficult to imagine any 

 alternative. 



Equations (5) and (6) of my paper lead to 



C-J+^H-v'] 



where k and h depend on the initial velocity v but not on 

 the coordinates. 



