OF ELECTRO-DYNAMIC FORCES. 515 



ducting M-ires, and which consequently are again functions of 



the time t. On developing their complete differentials, we 



have 



, dr. J dr. . , 



dr, = -j^ds, + -^ds!, 



, dr., J , dr., , , 



" ds, ' dSfl "' 



moreover, 



ddr, , 2 , rt ddr, , , , ddr, , „ 



, ddr,, , 9 , _ c?c?r, , . , ddr,, , ,, 



If these differentials are respectively divided by the elements 

 of the time d t, and their squares d f^, and admitting that 



ds, _ ds„_ ds} _ ds,l _ , 

 'dt~llt~'^' U ~ 1T~^ 



we have 



/ > 



dr, dr, , , dr, 



dt ds, ds 



dr„ dr„ , , dr,, 



dt ds, ds,. 



dt dSi, ds,l' 



"''"'nil __ j^ "''"'mi ^ ,^/ ^^/ . 

 dt ds„ dsj ' 



