YRASKK—JRe'fnrfio)!. of a Quartic Surfaco fn a Canonical For)ii. 75 



Again, consider 



-^1 Wi 



/(A,.) 

 tlie coefficient of 



the coefficient of 



rr^ + y- + z2 _ 2 ^-^- ^f ^ w + A,«<;2 | z»_, = gA^ + &c., 



A 



8A * + (fee 



hence the terms 



wljir', y^, z^, x^y, xH, y'^x, y\ z^x, z^y'] 



do not appear, as their coefficients all vanish for the same reason. 



The coefficient of 



urx^ = ^ 77; 



2Ar + 4 



/(ML " A J 



= % 





.-. A J), - Z,2 = 



■2A^2 j 8A,^ + 4A,^ (« f ^ + g)} + &c. - 4A,{4A/ + 4A,^ {b + g)^}' 



AK) 



= :§ 



« . 8A,.'' 



and of course the coefficient of tv^y'^ = - i, and of m^V = - <;. 

 The coefficient of 



8A,Z,J/, 



/(A.). A L/(A,.)J 



"8A, . m 



= :s 



8A,[-A(c + 2A,)(a-A,'') + &c.] 



= :§ 



h. 16A,* + 

 7TM 



27?. 



Similarly the coefficient of w'^y'^z = - 2/, and of w-zx = - 2y. 

 The coefficient of 



^.'4^" 



■/(A.)' 



X, = - 4/A/ + &c. ; 



hence this coefficient = - 21, that of iv^y = - 2m, and of ivH = - 2». 

 The coefficient of 



w^ = 2i^ ^^' ^Z + «?Jf + wi\^+ (d - A^) Z = /(A) ; 



L, Jf, iV are only quadratics in A ; hence 



A,^Z, = - AJ(A,) + A^[^Z, + mM, ^ nX^ + r/ZJ = d . 8A/ + &c. ; 



