OF ELECTRO-DYNAMIC FORCKS. 525 



r^ "~rf = — u sin — u' sin e' cos oo — v sin »] cos y, 



do, 

 dt 



r^ -~ = — u' sin B' — u sin 6 cos w — t; sin ») cos (w + y), 



/•4 -3-^ = — v sin rj — M sin e cos y — u' sin 6' cos (w + 7). 



Now since for the moment under consideration /-j = rg = /"g = r4 = r, 

 we thus get 



/do, dOc, de.,~?de\ . , . «, 



{de. de^ de^ deA , . 



again: 



/c?e\ rfe^_rfe;3_rfe;4\ _ 

 \dt ^ dt dt dt J ~ ' 



tly: 



(dyh_ , dr^ _ <^'!3_ _ ^\ _ rt 

 \dt ^ dt dt dt ) ~ ' 



These values by substitution become 



/ddr, , ddr^ ddr<, ddr\ „ , ■ ^ ■ , 



^ v-^?~ + "^F" - "^- ^;=-^^^^^^^'^°^ '^'^^"'^ 



(ddr. ddvc, ddr<, ddrA „ • ^ . 



— 4r cos O.^-r. 

 a/ 



With these values, the sum of the forces which act upon the 

 positive and negative electricity in the element «' is 



= 7 .aeu.a'e'u' (sin sin 0' cos «> — ^ cos © cos 0' t)). 



If in this equation the angle which the directions of the two 

 elements « and a' form with each other be denoted by e, and, as 



r 



lastly : 

 r 



