910 ^- FUJI SA WA. 



The elliptic fnnction.s of vii for ;/ = 2, 3. 4, 5, H. 7. 8 have been 

 calculated by Jiaelir and others* by the primitive method of succes- 

 sively applying the îiddition-eqnati<jn, Ihning found the values 



9 



of r, sn 9?/ may be calculated by the above method without much 

 difficulty. 



§ 16- 



As regards sn nv, n being odd, the analysis contained in the 

 preceding section, whereby the variables are taken to be ^W sn ?/ and a, 

 leaves nothing to be desired ; yet for the other functions, this is not 

 the case, and it is better to have as the variables sn ii and h. For the 

 sake of uniformity, tlierefore, we shall once more investigate Hnnii, but 

 this time consider it as a function of sn u and /.-. 



Changing the variable from f to x, equation (1)(S) takes the form 



(I.I- ax 



Cl/i 



and the equation is satisfied by the numerators and denominator of 



V/'" sn nil, Vp en //?/, -yp= dn 



nv. 



The numerator of sn ////, that is, xA(x-), satisfies the differential 

 equation 



* Se(; the paper of Baelu* tih'oady referred to, and Proooedinsj-s of the Royal Society of 

 London, Vol. XXXIII (1882) pp. 480-489. 



