1891 - 92 .] 
Dr Muir on a Prollem of Elimination. 
27 
a;8 
x! 
a;6 
a;5 
a:-! 
«3 
»2 
a: 
a:'’ 
y° 
0 
-4® 
2x 
-40-2® 
cr^n 
y'- 
- 16pg(a2 - 62) 
32^>2(a2 - 62)p 
- 16pg(a2 - &2)a 
y^ 
4r 
_4<^ 
4A 
- 4cr20 
2/3 
-16pf/(a2_62) 
16i9g(a2_ 62 )a 
yi 
24> 
-4^ 
2x 
2/5 
16pg(a2_&2) 
- 32^g(«2 - 62)p 
2/6 
4r 
-4® 
y" 
16pg(c(2- 62) 
2/8 
0 
where 
= + h^ + 2&^_p^ - 2l)^cf + 
= {p^ + - q^){a‘^ - 5^) + (a^ - l)^Y , 
= {(P - IP -qP + q^Y + {fpqf ; 
r = Cfc4 + &4 +^4 + ^4 _ 2«2^2 + 2a2p2 _ 2a2^2 _ 2Pp^ + Wf + 
= (p2 + g2^2 ^ 2(p2 _ ^2^(^^2 _ ^2^ _|_ ^^2 _ ^2j2 ^ 
= {(P - &2 +^2 _ ^2^ _j_ (2pqY , 
= O + 4(p2 - g2^^^2 _ 52^ ^ 
$ = + 3^4 + 3^4 + 3^4 0^252 + 10a2p2 _ 10^2^2 _ lQJj2^p + I0]pg2 + 0^2^2 ^ 
= 3(i?2 + ^2)2 + 10(p2 _ ^2)(^2 _ ^2) + 3(^2 _ ^2)2^ 
= 3r + 4(p2_^2)(^2_ J2). and .-. d) + ^ = 4T; 
0 = a^ + P -\- -\- q^ - aPP — Pp^ + a^q^ - hhi^ + Z>4p2 _ 54^2 
-qpp ppH/^ + 3p4g2 ^ - q%'^ + 3g'4^2 j" ^ 
= (292 + 2'2)3 _ (p4 - 2'4)(a2 - &2^ _ (^4 _ 54)(^2 _ ^2^ ^ ^^4 _ ^4)(^2 _ 52^ . 
4^ = Za^ + 3// + Zp^ + Zq^ ~ 3a^^2 ^ Qa^qP - - ZPP - bh^p^^ + blAq^ 
+ 5 j 9%2 - bp^^P + 9j?4^2 _ 5^4^2 _j_ 5^4^, 2 ^ 9^4^2 J ^ 
=- 3(2^2 _|_ ^2^3 + 5(p4 _ ^4)^^2 _ JP'^ 5(^4 _ P)(jP - q2^ + 3(^4 _ ^4^(^2 _ ^ 
= ZO + 8{p^-q‘^)(a^-P)p; 
p = a^-\-P +^2 + ^2 . 
X = 3a^ + 3i^^ + Zp^ + 3^^ - 4a^p2 ._ 456^2 _ 4^6^2 _ 4^q%2 ^ 2 2p^q^ + 1 2q^p^ 1 
- Za'^P + 2^4^94 + 2 u 4^4 _[_ 2^4p4 ^ 264^4 _j_ 1 8^4^4 I 
+ 4a4&2^2 _ 4-Pp'2q^ 4- APa^p^— iPp'^q - ip^^Pq^ > 
- 8p^a^^q^ - iqPPp)^ - 8q^h\P I 
+ 16a2Z>229Vj • I 
