93 
1891-92.] Hon. Lord McLaren on the Elli^se-Glissdte. 
(W + C2)v4 + (4CV - 2BX2 + 
+ 2(BaX - C/5A + Ca/x — B/?/x)i/^ 
+ (2X^^^ + + A.‘^)y^ - 2(aA.^ + aX^j? + /?A^/x + B/x^)yv 
+ (a2A2 + iS V + + « w 
+ (2BCA/X - 2B2A2 - C^A2 - C 
+ 2 (B^X^fjL — BaA^ + Cf3X^ — 2BaA/x^ + Ca/x^) 1/ + 2 (BA^ — C/xA^ 
+ BA^/x^ — CA/x^)y 
+ C2AV^ - 2BCAV + B2A4 + 2a/5AV - /S^A^/x^ - - 2a/5A/x3 
-a2A4-y82^4:=.0. 
The terms of the 8th degree in x and y are all contained in the 
first four lines of the preceding formula, and these only need to he 
expressed in terms of x and y. Substituting for a, yS, A, /x, in the 
above factors, and retaining only the highest terms of the expressions 
which are represented by v^, yr^, we have 
(B^ + C^)(x^ + ix^y^ + ^xhj^ + + y^ -h &c.) 
- (8{Bfe2 _ 2Ci9^}x2 + 16{C092 - q^) - 2By9g}^ry + 8{B{p^ - q^) 
+ 2Cy>5'}y2 j. X + 2a?2y4 + y<5 _j_ 
- {8{C(^^ -p^) + 2 Bpg}icy + 8 {B(^ 2 - 2 Cp 2 '}y^ j- x (x^ -i- 8x‘^y^ 
+ 3xhj‘^ + y^) 
+ 1 6(p2 + g2^2^^4 ^ 2x‘^y^ + y^) x (y^ + &c. ) 
- 32(|;2 -p q^YipchJ^ + y^) x (sc^y^ + y^ + &c.) 
+ 1 6(y2 + q^Yix^y^ + x + 2 ir^y^ + y^ + etc.) + / 0 (a?j^y) 
+/4(*i2/)+/"2(*i2') = 0- 
Observing that C = - 2 j:»^, B = the coefficients of 
the powers are seen to be 
For 
x^ , (B^ + C^) = (cP- -tP -p^ + q^Y + {8qoqY = O 
x^y , 8 (C(jy^ - q^) - 2 Bpg) = - \ <opq{oP‘ - 6 ^) 
Xhf , 4(B2 + C 2 + 4B(i;2 _ ^ 2 ) + j_ ^ 2 ) + 
= i(n + i{p^-q^)(a?-V) ) 
= 4(a^ - + {ipqf / 
x?y ^ , - 1 ^pq(a^ - Ir) 
xhj\ 6(B2 + C2) + 32B(p2_^2) + 32(^;2 + 22)2 + 64Cyg = 8r - 2Q, 
x^y^ , + 16py(a^ - V^) 
xhf, 4r . . =4r 
xy " , + 1 ^p)q{a? - IP) 
y^ , {a^ - IP - p^ q^)"^ -\- {2pqY .... =0 
These are the same values which are found in Dr Muir’s paper.* 
* There are two errata in the page referred to (p. 27, below the Table). 
Line 6 should be {a^ -IP+p^ - q^p-\-{2p>qy‘ \ and the expression in the 10th line 
is meant to be equited to 4r. 
