140 Prof. 0. W. Richardson : 



letters negative charges. For an electron charge e' mass m r 

 revolving round a nucleus containing positive electrons of 

 total charge E and mass M and negative electrons of total 

 charge e and mass m 9 the force at distance r apart is 



+ fl [(E+07%/(f + 7)]+^M+»y} l . 



For isotopes E + <?, e', and m! have the same value but 

 M, m, E, and e are different. The difference in F for two 

 isotopes is thus 



SF = 4^3 { ^'8(M. -f m)+ce'§(^ + ^) +? m'a(M + m) j . 



To a first approximation M/E and ???/<? are respectively 

 constant, being the oxygen nucleus and negative electron 

 values, also ra/M is small, so that 



47T7' 2 ' 



1 A ■ I ' ,M , 



where A = a<? +c<? ^t + #wi 



and W = M + w. 



The forces will thus be the same as it" the nuclear charge 

 were increased by an amount 



According to Bohr's theory the frequency of any particular 

 spectral line is 



imJjW ( 1 Jo 

 l, + m 1 )A r lT r » t,»J-' 



, = w WVf i 



(M, 



ei and ??ii being the charge and mass of the circulating elec- 

 tron and Ej and M x the charge and mass of the nucleus and 

 electron system about which it circulates. r r and t s are 

 positive integers and h is Planck's constant. The corre- 

 sponding frequency for the isotope is 



„,_ 2 2 (M 1 + gW)m,(EH-BgW)V fl JO 



