372 M. B. Riemann on Electrodynamics. 



InthisexpressionF'^T + ^canbereplacedbyF^T+^-F^TjT), 

 since 



SSee'-F'Or, r) 



may be neglected. An expression is thereby obtained as a factor 

 of ee', which changes its sign both with e and e 7 ; so that in the 

 additions the members do not cancel one another, and infinitely 

 small fractions of the individual members may be disregarded. 



dd' 



© 



Hence, substituting cr — - — - — for ~E'(t, r + a) — F'(t, t), and in- 



UT UT 



tegrating with respect to cr, we obtain 



C rr dd 'Q) 



P= 22ee'^ 



dTdT .dT- m + K(0), 



to a fraction which may be neglected. 



It is easily seen that H(/) and H(0) may be neglected; for 



F( , +T) , +T+(r)= _^ + _^ T+ _i_ (T+(r)+ ... 



and therefore 



H^-SSee'^ dt 6 ^ 3 df , ^3 dUt 



But here only the first member of the factor of ee' is of the same 

 order with the factor in the first constituent of P ; and this, 

 on account of the summation with respect to e*, yields only a 

 fraction of it which may be neglected. 



The value of P obtained from our theory agrees with the ex- 

 perimental one, 



.rr \r/ , 



2, Zee' - r - r-dr, 



cc dr dr 



-J" 



According to Weber and Kohlrausclr's determination, 



millimetre 



c = 439450. 10 6 



second 



which gives a = 192965 miles in a second, while for the velocity 

 of light Busch has calculated the number 193172 miles from 

 Bradley's observation of aberration, and Fizeau has obtained the 

 number 192757 by direct measurement. 



