(483 ) 



c /Y d(p\ c f 



^^ 2r%v+c)J y ^ ^ d.v) ^rU 



O u 



c rf d(p\ c(v—2c) r 



- pt -j f 2r/ -f .'• £] ^hv + ;.^ ---T" j V" '/''• 



-?^^ 



2rt 2n 



-|- six other integrals which are obtained bv siibstitiitiiig — c for c 



and .v^ for .i\ in the above. 



The signification of the symbols is as follows : a is the radius of the 



spherical electron \vhich is supposed to be charged with homogeneons 



cubic density ; g is the charge of the electron, c the \elocity of 



1 .v"" 

 light, r the numeric value of 53 : <f the function '2a — ./-I ^ • 



X, is (r -|- c) t -\- \', pf and ,/■, = {r — c) t -\- \/, ;J^^ In the expres- 

 sions for .i\ and .i'.^ the term ^ , yV- may, however, be neglected. 



Without performing the integrations completely we mav di-aw the 

 following conclusions : 



1^^. All the terms of A.^ contain t as a factor. So we have A = A^ 

 if t vanishes. No sudden inci-ease of the force is therefore I'eipdred 

 if the motion is suddenly accelerated, as is the case with a bodv with 

 positive mass; neither a sudden diminution of the force as would 

 be the case with a l)ody with negative mass. The force remains 

 unchanged. 



2'"'. Xo terms with the first powei- of f occur in a.,, lliei-efore 



^tf , . . '/a . 



— =0. Eveji the derivative is therefore continuous at the point 



dt'^t = 0) 'ft 



t=zO. This agrees with our remark that a discontimiity in the 



derivative of A only occurs if the velocity changes discontinuously. 



3»''. For establishing the sign of a, for / = very small, we have 



only to take into account the terms with f. There are also terms 



with t'- 1(1) but the sum of their coefficients is zei-o. If we perform 



the integrations as far as is required we find : 



o V* V V — c\ 



