12 



Art. 5. — T. Takenouchi 



' dnu ' cnu' 



Also, tlifferentiatiiig (5) witli respect to n, we get 



^'('0 = 



'2 en ;i dn //, 

 snhi 



2 



sn/t sn.v^^sn /ryt 



(6) 



(7) 



Assume that 



//. = a + bp, I 



a=l (mod. 4), h = (mod. 2), J 



« and Z» being rational integers. Then we know that'^ 



su fJ.U 



X = sn/t, 



(8) 



where £.-!„ (.r) = P/^ + J;,,!-- + + A,„_2x""^ + ^ir-'^x"-\ 



Da (x) = 1 + D,„..x- + -f D,x""^+ Bay/ot"'-^x"'-\ 



111 = ^iv/^-)' '' — ^'^ £'=1, 



the coethcients yl's and JJs l)eing integers in IQ', i)'\ such tliat 

 ^^^'"--'+1 = A, i = 3,4, •••, ;;i-2. 



To find the exact value of £, o1)sei've that 

 1 1 



sn-fiu sn-u 





1) Wober: Algebra III, §. 157. 



2) It follows from (9)ou the next pag-e, that the cooffieionts of .4ft{.i), i.e., 



A: 



i = 3, t, , m-2. 



are integers in 7.(p). 



