24 Mr. S. B. McLaren on Hamilton's Equations and the 

 Use (24) next to transform (22), 



ld¥ l „/., ldyjr\ If ,„ ., " 



lrfFx 1 



E' = 



E'=- 



dt 



u, Curl F a - V(/> , 



ere 





Substitute this value o£ E ; in the equations of motion of 

 the 7?th electron 





dp, 

 dt 



+ 





dF 

 dt 



+ 



this 



can 



be 



written 









dp, 

 dt 



■*[■ 



Yc 



dF, 

 dt' 



~*Curl F^+V<l> \pdv n =Q; 



The electron has a movement of translation only, each 



point of it has the same velocity U n , — j \/(b Q pdv n is the 



electrostatic force due to the field of potential <£ . 



Let Ys be the electrostatic energy of this field. It is a 

 function of the positions of the electrons. If q« be the 

 vector position of a point of the nth electron. Then 



J' 



V<l>opaOn=~ • 



Also 



J C 



i(j ">•<-}• 



on the right the differentiation is partial with respect to qu the 

 function being expressed in terms of the velocity u n and 

 the coordinate q n . The equation of motion becomes 



In (35) insert the value of F T from (28), and write 

 -J F r/ >du n =F rnj 



F rn is a function merely of the position of the nth. electron, 



