PARTICULARLY THOSE OE TWO VARIABLES. 
823 
and therefore 
that is 
Now 
and thus, by (108), 
1 d 2n+2 6 __ 2n dK d^d _ cl d*»0 
4cc' dx 0 2n+2 K dc dx 0 2n dc dx 0 2n 
= —K _2 ”y • K a 
do 
d 2n d 
t _ 
dx 0 2n 
TZ2 n+2Z __ — 
1 * • 7 OmJ.0 
%n +2 
lit Uq 
- 4ccK * K W 
= (—4oc'K s —) 6(0) 
e 0 ,o(o )=(|/k* 
<U0)=(!)W 
4cc'K^)”K* 
(108). 
(109). 
K 2? 
rttnf) 
U Q, 1 
dx 0 2n 
K 3 
rThlfi 
,n ° J V.O . 
dx^ n 
(_l)»g)*(4oo'K^)”KV‘. 
(-l).g)*(4co'K^)“K¥ . 
( 110 ). 
( 111 ). 
Similarly, if X 3 =y, A.' 3 =y', 
A^=(-i)«(^( 4 ry'A^)V. 
^=(- i )<!) V A ^ Ayi 
. . . ( 112 ) 
. . . (113) 
d^P) /2W ,7\» 
A^=(-l)*g)(WA^)AV.(114). 
Next, let 0 he the uneven function; differentiating the equation (2w+l) times 
with regard to a and putting a; zero 
^ +3 6> 11 „ , ,^ 2w+1 6» in , n d d 2n ^6 ,, n 
M -2 a (2»+l)—Jf+fe -^r“=0 
ffry, 2W+3 
t/l/ tA'Q 
5 N 
do dx 0 2n+1 
MDCCCLXXXII, 
