PARTICULARLY THOSE OP TWO VARIABLES. 
831 
where 
Lastly 
where 
• ^14— C l^ xJ r G 'l4f — o I (^14,03 Ql4i 1» ^14,2> ^14, 2/) "+ • • ■ 
+ 2 n TjTi;(ri4,oi Pi*i. ^14, i’ • • • > Pi4,» • • • ’ 2/)-' ,+1 + . . . (186), 
/KA, , , 1 , J /7rVdc'*K» „ D ^ 
cu=^rKrV^) -y- .( 187 ), 
c' M =|Ai-c‘KVV*A».(188), 
p••'••■ ('“)• 
P i 4 > s,+ i = a(k) (!) d^d^‘ Kc ’ u .( 19 °^ 
'^15 ==C 15 2~|(^15,0> ®15,1> ® 15,2X^J V ) 3 
H - -^r(N 15)0J ^"15,1? ^15, 2 ’ • • •»-^15,« ■ • * > y) s "+ • • • (191), 
c 15 =^A 3 .cVy/*K*A*.(192), 
^15, 2s — 
7T \ / 7r\ 25 
K; 
A/ dp' n ~ s dq' s 
'15 
(193), 
N 
__ 1 _ 
15’2 ,+ 1“KA 
7r\ 2 ( n-s-i y tt\ 2s d n ~ Y 
K/ \A/ dp' n ~ s ~ 1 dq' s 
A^cVy/WA* . 
(194). 
37. The formulae (42), (43), (44) give expressions for #c x , k 2 , k 3 in terms of the c’s; 
and therefore, by the preceding, all the ks of § 13 can be expressed in terms of K, A. 
In fact, we have > 
_ (A : . KM¥) x (A 1 , KM¥ 7 *) 
’ 1— (ApKLV) x (A 1 .K i Ay) 
, _ (A 1 .K*AV*) x (A lt K>AVy) 
!l— (A^EAA*) x (Aj.K^AV) 
(195) 
_ (Aj.KWcy) X (Aj.KWcV*) 1 
' 3 ” (A^K^AV) x (Ai.KtAV* 
, _ (A x . K 4 AVV) x (A,. KMVy*) 
' 3 “ (A^K^AV) x (A^KMy*) 
(196) 
(A x . KW) x (Aj. UA^V) 1 
13 — (A x . KM 4 ) x (A a . KMy *) ' 
, _(A X .K*AV*) x (A^KMVy*) | 
:3— ( A t . KM) x (A L . KMy *) j 
5 o 
(197) 
MDCCCLXXXII. 
