Note on Gravitation. 141 



Thus 



X 1 v' r nii „ B 



\ 



B m, W- 



v ^ LMi(M! + m x ) EJ 



6VV LM 1 (M 1 + m 1 ) 2+- E l M 1 (M 1 + m 1 ) ' E : 2 



+ 

 and the relative shift 



^-SWT ^ + 2—1 



+ S W " LM7(M7 + ^ + 2 "Ei M^M^-t-^y + E?J + ' • ' 



The atomic weights of the different leads tested by Merton 

 do not appear to have been measured, but we need not go 

 beyond the order of magnitude of the different terms, and 

 for this accuracy it will be sufficient to put 



-8\/\=l'2xl0-\ SW = 0-5, M 1 = 207, — = 1860. 



The first term on the right represents the Bohr shift. It 

 amounts to about 6 x 10~ 9 and therefore forms only a small 

 fraction of the observed S\/\. It appears that all the other 

 terms are small except the second which has to account for 

 practically the whole of 8\/X. On the type of view here 

 considered then it appears that B/E x must be of the order 

 10~ 6 . 



If B/Ex were as large as this it would have several notable 

 consequences. In terms of the coefficients the value of B/E x 



is ™~( <2 + -n c + g~ t ) • The last term in this expression 

 Ei\ Jif \e J 



represents the ordinary Newtonian gravitational force due 



to the mass m' of the electron. On substituting the 



numerical data the value of §= -. is found to be 2*5 x 10" 16 . 



sSi X e 



It is thus a very minute fraction of the whole of B/Ej. This 

 would mean that in a gravitational field positive and nega- 

 tive electrons would be acted on by opposite torces of nearly 

 equal magnitude but much larger than the Newtonian forces 

 for neutral particles of equal masses. In an insulator at rest 

 this would give rise to an electric polarization proportional 

 to the gravitational intensity. In a conductor in equilibrium 

 we should expect a separation of the charges giving rise to 

 an equilibrating electric field. In the earth's gravitational 



