114 
ON A CERTAIN SEXTIC TORSE. 
[436 
+ (/3 8 + 9/3V + 9/3Y + 7 s ) (1, a 6 ^y^ 3 , f 3 &> 3 ) 
+ (7 s + 97 4 a 2 + 97 2 a 4 4- a 8 ) (1, /3 8 $yf 3 , r) 3 a> 3 ) 
+ (a 8 + 9a 4 /3 2 + 9a 2 /3 4 + /3 8 ) (1, 7 6 $fY £ 3 a> 3 ) 
4- 3 {a 8 + 3a 4 (2/3 2 + 7 2 ) + 3a 2 (/3 4 - 7/3y) +/3y} (1, /3 2 , 7 4 , WW'vV, V e <*T, *>V£ 4 ) 
+ 3 {/3 8 + 3/3 4 (27 2 + a 2 ) 4- 3/3 2 (7 4 - 77 2 a 2 ) + T 4 a 2 } (1, 7' 3 , a 4 , 7 2 a 4 ][ J7 8 £ 4 £ 2 , £ 8 û>y, f 8 «y 4 ?? 2 , tu 8 ^ 2 | 4 ) 
4- 3 Y + 3 7 4 (2a 2 + /3 2 ) 4- 3 7 2 (a 4 - 7a 2 /3 2 ) 4- a 4 /3 2 } (1, a 2 , £ 4 , a 2 /3 4 $£ 8 | 4 >f, f 8 ar£ 4 , t/W^ 2 , a> 8 £y) 
4- 3 {a 8 + 3a 4 (2r + /3 2 ) + 3a 2 ( 7 4 - 7/3 2 7 2 ) + /3y} (1, 7 2 , /3 4 , PY^vV, «VP) 
+ 3 {/3 8 + 3/3 4 (2a 2 + 7 2 ) + 3/3 2 (a 4 - 77 2 a 2 ) + 7 2 a 4 } (1, a 2 , y 4 , y 4 a 2 ^yf 2 ! 4 , f 8 « 2 ?? 4 , Ç 6 m 4 rf, et> 8 £ 4 f 2 ) 
4- 3 { 7 8 4- 3 7 4 (2yS 2 + a 2 ) + 3 7 2 (/3 4 - 7a 2 /3 2 ) 4- a 2 /3 4 } (1, /3 2 , a 4 , a 4 /3 2 ££ 6 £y, V WÇ 4 , ®W) 
4- 9 (/3 J 7 2 4- /3y + 7 4 a 2 + 7 2 a 4 4- a 4 /3 2 4- a 2 /3 4 — 14a 2 /3y) 
(1, /3y, 7 2 a 2 , aYWvV, vT< №» 4 , ÏVY 
( — 3 |62a 2 /3y — 28 (/3y 4- 7 s « 3 + a :i /3 3 )} (a 2 , /3 2 , 7 2 , a 2 /3y][|f 4 , Y £ 4 , a» 4 ) ^ 
! + 3 (3a 8 - 14a 8 /3 7 + 130a 4 /3y + 136a 2 /3y - 42/3Y) (1, a 2 $y£ 2 , fW) 
4- £ 2 V 2 £ 2a)2 : r- 
j + 3 (3/3 8 - 14/3 8 7a + 130/3 4 7 2 a 2 +136 y 3 2 7 3 a 3 - 427 4 a 4 ) (1, /3 2 ££ 2 £ 2 , t?W) 
-f 3 (37 8 — 147 8 a/3 + 130T 4 a 2 /3 2 + 1367 2 a 3 /3 3 — 42a 4 /3 4 ) (1, 7 2 $yy, Ç’ 3 « 2 ) , 
This agrees with the result given in Salmon’s Solid Geometry, Ed. 2, p. 151, [Ed. 4, 
p. 178], and Quarterly Mathematical Journal, vol. 11. p. 220 (1858); in the latter place, 
however, the term 
/3Y£ 4 + ŸvV + a T°> 4 + «WY« 8 
is by mistake written 
/Syf 4 4- 7 2 ?? 4 £ 8 4- a 8 £ 8 &) 4 4- /3y| 4 û> 8 ; 
viz. a factor a 8 is omitted in one of the coefficients. 
Some of the coefficients are presented under slightly different forms ; viz. instead of 
62a 2 /3 2 y 2 — 28 (/3y + y' ! a :! 4- a 3 /3 3 ) 
Salmon has 
14 (/3 4 y 2 4- /3y 4- 7 4 a 2 4- 7 2 a 4 4- a 4 /3 2 4- a 2 /3 4 ) 4- 20a 2 /3 2 y' 2 ; 
and instead of 
3a 8 — 14a 8 /37 4- 130a 4 /3y 4- 136a 2 /3Y — 42/3Y, 
he has 
— 4a 8 + 7a 8 (/3 2 4- 7 2 ) + 196a 4 /3Y — 68a 2 /3Y (/3 2 4- 7 2 ) — 42/3y, 
but these different forms are respectively equivalent in virtue of the relation 
a 4- /3 4- 7 = 0.