22 Mr Greenhill, Multiplication of Elliptic Functions. [Oct. 29, 

 and equivalent to the transformation 



1 +* \1 + - 



ic a 



a transformation which is capable of affording an independent 

 verification. 



(l--\ 2 

 c- c + /3 7 



1-ic \-z l X ~J$ K 



~ l '' 1 + Z\ ^ z 



1 + o V+W 



, ff=cnl(K + iK'); 



and therefore 



l + x\ a 



or 



i; (i?»M . 1 ~ cn {w' ,x ) 



M- 



1 + cn 



or, en 



(a? ,x ) 1+cn (l"" x ') 



(£•*)«* (y.v)-i. 



where 10 = ^ (2 — % a/5) u. 



In the same way, from the expression of y = en -J (1 + 1\/7) w 

 in terms of x = en w, we can obtain a; = en \ (1 — i \/7) v in terms 

 of 2/ = cn , y by the solution of a quadratic; and also from the ex- 

 pression of y = en i (1 + i \/lS) ?t in terms of x — en ?/, we can 

 obtain x = en ^ (1 — i a/15) v in terms of y = cn v, also by the solu- 

 tion of a quadratic equation. 



