3^ Art. 7. — K. Terazawa : 



OO. = -^ . -^"y- ■ -'-{^ fe + -».)-^». } (78) 

 Tzar 'A(À+u)u -vi« ara' ) 



2(/l + /.)/. 



where 



2 \J 



a = 



ar 



cr + r- «- + ?•■ — 6ar (X" + r- + 6a>- 



3<xra " 6ar« Gar« 



At the surface the vahie of / Ijecomes simply 



(>• + «)*+ lr—a|* 



so that the use of the ^'-series is very advantageous for the calculat- 

 ion, especially at the points near the origin or at a distance from 

 it. For example, at the point r = 3«, we have 



— = 0-085786, q = 0-085796 ; 



thus, even for the value ;- = 3a,, we may neglect the terms after /^ 

 and rf in the series. For larger values of r the ^-series converge of 

 course very rapidly." 



§27. The formula for {ih\ can he transformed into the form 

 which is convenient for the nse of Legendre's table of elhptic 

 integrals. If we remember that 



-fj^ + eiw^ = ^'e^ — e-^E, 

 K 



Ä'and jË* being the tirst and the second complete elliptic integrals 

 with the moduli k and k' , and 



the expression for {;uz\ beccwmes 



1) For the point near the edge of the circle, the calculation may be undertaken by 

 using similar series, specified by qi and /j. See below. 



