440 
n= 5, it is 
n— 7, it is 
PROFESSOR CAYLEY ON THE TRANSFORMATION 
(l + « 2 )(l + « 4 
1 + a 2 + «*+« 
fl +ct 2 ) (l+« 4 )(l + « 6 ) 1+a + a 2 + a 3 + a 4 + a 5 + 2a 6^_ i 
— . rzz — -I. 
a . otr . cC 
and so on. The term in question thus is 
V ' ■ ( v'2) rt_1 ^ r 1 + ? 2 . . 1+?”. 
that is 
( + 2 
n 
This has to be multiplied by u", =(< v /2)”j i /*(2). and we thus obtain 
%=(-)“”- V%V(2')> 
agreeing with a former result. 
We have in what precedes a complete ^-transcendental solution for the trcmsformatio 
prima ; viz. the original modulus k 2 [=ti 8 ) being given as a function of then, as well 
the new modulus >^(— 'Co) and the multiplier M 0 , as also the several functions which 
enter into the expression 
* r / ~ \ / vn 
l-y__ l~* j (* S nc 2 a> 0 ) ••• j 1 snc(rc-l)«J I 
1 + 2/ 1+#| / n , x \ , a? \ j 
^”^snc2w 0 ) ’ ‘ ’ » 
[y -1- 1 snc2co 0/ / * ’ ' snc(« 
are all of them expressed as functions of q. 
60. I consider in like manner the expression 
11 dn 2 ffw n 
snc2^w„ sn(K — 2ffcu n ) 5 cu 2goo n ‘ 
2K£ 
21v? 
Here, writing 2 ga n =-^~ (| instead of Jacobi’s x as before), that is 
and thence 
9/7 iK ' — 2/^K' 
?_ 2K n ~ nK ’ 
_z ^ 
" K , =£», 
1 2K£ . cn 2Kf 
snc 2gw n 7r " 7r 
=/%) • ^4- (i+? 4 ’" 
*g ,,zM 
i +q n (i + 5? (i+s ”)■• 
we have 
