217] ELECTROMAGNETISM. 423 



respectively 



x-x l y-yi z-z l 

 r > r ' r ' 



dx l dy dz^ 

 ds l ' ds l ' ds l ' 



we have for the components of the vector-product representing the 

 field due to an element ds 1} 



dL = - 8 ( d vi ( z - *0 - d *i (y - 2/i)} 



\ 

 (u) dM = {dzi(x-ocd-dxi(z-zd\, 



dN= - 3 [dad (y - yd - dy^ (x - a^)}. 



We may obtain the same result by the use of Stokes's Theorem, 

 31. Since 



the component of the field in the direction h is 



Let the constant direction cosines of h be a, fi, 7, and those of 

 n be X, /-t, v, variable over the surface of the diaphragm. Then 



a a a a 

 8^ =a 

 (13) 



o ^ ^ ~r M ?; ~r 



dn da? 8 



Now since 



r' = (a? - 

 we have 



_ 

 d%! ' "dy dy l ' dz 



