217] ELECTEOMAGNETISM. 425 



(16) V h 



w " 



making Q h the resultant of Uh, F^, Wh equal to / times the 

 vector product of the unit vector h and the vector parameter of 

 1/r, the force in the direction h is 



(17) 



= - J|(curl Q A ) cos (curl &, n) ^. 

 But by Stokes's theorem this is equal to the line integral 

 (18) - (Uifa + V h d yi + WhdzJ^-QhCos (Q h ds) d Sl , 



around the current circuit. 



Accordingly attributing to each element ds the amount of field 



(19) dH cos (dH, h) = adL + 0dM + jdN 



and since this must hold for every value of a, /3, 7, equating their 

 coefficients we obtain 



T 



dL = 



dM = 



a - 



fyi 



which give the values obtained in (11). 



