306 



calculated by tables of double entry. In fact, we have the 

 following formulae, 



e^- log(l + eot^6lsi nV) _ 



iTY{k',e) -2F{k)Y{k',e) - {E{k) ~Fik)] {v{k',e)Y 



- ^irHk') - ^ik) log (k sin^e) 

 C^' log(l-(l -k'^s in^d) sin» _ 



7rr(A',0) - 2f(A) Y(A',0) - {e(^) - r(A)} {f(A', B)}^ 



P log(l — ;^^sin"e sin» 



•^0 V ( 1 -A^sin^^) "^ ~ 



e(A)Jf(A,0)P_2f(A)Y(A, 0). (3) 



In equation (3) if we put 6 = ^tt, we will have, recollect- 

 ing that 



r(h^)=iF{k)E{k)-l\0gk', 

 f l^-=i!^!l) rf^ = log(k') .(k). (4) 



Again, 6, being the amplitude of the semi-complete function, 

 we have 



and, 



f2k' s/y 



so that 



Y(0,) = iF(^)EW-ilog(^^') 



r"log(cosV + ^'sinV) , ,, f1h'^k'\ ,, 

 The values of the definite integrals (4) and (5) have been 



