142 Mr Glazebrook, On the general equations [April 28, 



April 28, 1884. 

 Mr Glaisher, President, in the chair. 

 J. C. Bose, B.A., Christ's College, was elected a fellow. 



The following communications were made : 



(1) On the general equations of the electromagnetic field. By 

 E. T. Glazebrook, M.A., F.RS. 



In a paper read before this Society on February 25, 1884, I 

 compared the general equations of the electromagnetic field as 

 obtained by Maxwell and Helmholtz. The object of the present 

 communication is to obtain the more general equations of Helm- 

 holtz in a manner analogous to that employed by Maxwell. We 

 shall use the notation of the latter freed however from the restric- 

 tion that 



du dv dw . 



t- + -j- + -^- is zero. 



dx dy dz 



We shall further assume with Maxwell that the current in a 

 dielectric is represented by/ not by \ as in Helmholtz' work. 



The electromagnetic effects depend on the values of F, 0, and 

 H the components of the electrokinetic momentum, and we have 

 if we integrate completely round a closed curve with the usual 

 notation 



r Co cos € 

 \Fdx + Ody + Hdz = /j, I dsda. 



Let ds coincide with the axes in turn, then we obtain 



F=!*Jfflax>dyW+^...., (1), 



etc 



% being any single -valued function of x, y, z and t. 

 Let % be given by the equation 



X=t- \\\-dxdydz (2), 



47T J J J r 



so that x is the potential of matter of density \ distributed 

 throughout the space. Then 



