6 Art. 6.— E. Kaibara : 



;^o= +1-8974390607 



a, = -0-l673'2092 



a., = -0-4747820 



a. = +0-380062 



a,= +0-40908 



a-^ = —0-3475 



«e = -0-894. 



By means of the equation just obtained, the vahie of z can be 

 determined for an assigned vahie of h, provided the latter is not 

 near unity. 



5. Formula? for jo's and e's given in (13) and thence those 

 for i? and i given in (5), (6) and (9) can be adapted to numerical 

 calculation, by quadratic transformation of the ;?-functions and l^y 

 introducing auxiliary angles. 



With a pair of corresponding values of h and z, let the follow- 

 ing four functions be computed: 



d, = 2^Ti{l + ¥ + h''+ ), 



/?3 = l + 2,V + 27t«+ , 



d^^v) = 2v/î(cos^ + 7i-'cos3^ + 7t'2cos5,?+ ■■■') 

 6,(2v) = 1 + 27r cos 2^ + 27i' cos 4,s + , 



where the symbol 6 signifies that the modulus of the function is 2r, 

 i. e., 



6, = â,iO ! 2r), dX^v) = mv 1 2r), {i = 2, 3). 



All these series converge very rapidly; in most cases, the first two 

 terms of each series will give a sufficiently accurate value of the 

 function. Next, let angles «, ß l)e determined by the equations 



6. 



(18) 



tail a = 



(19) 



^3 



tan ^y = — — =^^ — — ; 

 ^3(2^) 



then, we have the formulée: 



ê.? = 16. ß., = ;;^sin2«, 



7%^ = di+di = X\ \ (20) 



