534 Mr. G. H. Livens on the Electron Theory 



present writer in another connexion in a previous communi- 

 cation. The present method of deduction, however, appears 

 to bring out more clearly the essential character of the 

 assumption on which the results are based. 



If we adopt the notations of vector analysis and use 

 u, E, H to denote the vectors of electronic velocity, electric 

 force, and magnetic force respectively, this expression may 

 be more concisely written in the form 



f-f. + rfe {^ E >- i(«v)A +M >v) ? } 



wherein V denotes the usual Hamiltonian vector operator 

 whose components are 





4. The general expressions for the currents of electricity 

 and heat. 



The various constituents of the complete flux of electricity 

 and heat are now easily obtained, being calculated along 

 exactly the same lines as developed by Lorentz for the 

 simpler example of the same principles and by Grans in his 

 analysis of the present problem. It will not, therefore, be 

 necessary for me to enter into a detailed examination of each 

 calculation. According to Lorentz, if 



then the current of electricity is a vector whose components 

 are 



— oo 



whilst the current of heat is a vector with components 



+ 00 



