368 Dr. J. Larinor. Complete Scheme of Electrodynamic 



the spacial differential coefficients of (F, Gr, H) are also involved 

 in the forcives of the eethereal field, and with them the case is 

 different : the transformation by parts is then analytically wrong, 

 owing to neglect of the infinite elements at the origin, while 

 in actuality a finite portion of the whole effect arises from the 

 influence of the neighbouring molecules. We have, therefore, by the 

 molecular principle, to separate the infinite elements from the 

 integrals and leave them out of account ; and this is effected by 

 employing the second form above for F, which differs from the first 

 form only in having got rid of the local terms at the origin in its 

 differential coefficients. Thus it is not merely convenient, but even 

 necessary for a mechanical theory, which considers distributions 

 instead of individual molecules, to replace magnetism by its equival- 

 ent continuous current system as here. The g^m'-magnetism arising 

 from electric convection adds to this equivalent current system 

 the additional bodily terms 



together with surface sheets : thus the volume current so added has 

 for aj-component 



dx 



_ 

 dy V*' 



where ~- represents -: + -r- + -5 + -7- > or the rate of cnan g e 



~- represents -4: + -^r- + -5 + -7- 

 dt dt dx dy dz 



f supposed associated with the moving matter. Combining all 

 these parts, the current and magnetism together are completely 

 represented as regards determination of electric effect by what we 

 may call the total effective current ( 15 v h w\) where 



dC dE 



Bf 



dpg' dph' 



together with superficial current sheets arising from the true 

 magnetism (A, B, C) and the electric convection. Since p is 

 equal to 



d(ff)_ 

 dx 



dz 



we may write 



in 



which the last term may be expressed as 



