CIRCULAR COILS OF RECTANGULAR SECTION. 431 



we find that they become 



} ^efayJdXidfo, j" ^(x^d^dy, and f j" 6(sj/,)d* t di/, 

 respectively, which are equal to 



and 



*(0,0) 

 respectively, where 



(xy) has the same meaning as before. 

 Hence, if 



fk r}6 rk-Y pj*-x 



J-Sc J-}t J-Je-Y J-Jt-X 



is equal to 



This expression, obtained from the function ^>(a;/) by substituting in it b, c, h, c, 

 0, in the way indicated, will, in what follows, be designated by 



2. As an illustration of the above I will indicate the process as applied to the simplest 

 term in P involving log (a^+y 2 ). 



Thus to obtain 



fk (* rk-Y rJA-x 



J_J C J_i J-k-Y J-J6-X 



we find by simple integrations that 



By inspection it is seen that 

 0(00) = 



2*(6, c) = 



(0, c) = * (0, -c) = - |- log c". 



