74 Pyoceedings of the Roynl Irisli Academy. 



where f%) = 0, 



and /rXi) ^ ' a-r2\, h g I 



I I + 2Ai / m 



g f c + 2X1 n 



I T/i n d — Xi' 



Consider 



K T7^^ [ ^' + y' + 2' - ;^ (^-^ - ^ry + ^Vj - A,i^2 



i), = 8X/ + &c. . . . f{K) = - 8 A/ + &c. ; 



hence the coefficient of (i-- + ^'^ -^ z^/ vanishes ; and for the same 



reason the coefficient of {x- + y- + z"^) tc [ar, y, 2] also vanishes. 



The coefficient of 



, , ^, A, . A ^5 Z/- 

 t^-ar^ = 22 +4.2 . 



But since 



f{K) = 0, 



Z,2 - A J), = 0, 



L 



Hence 



2X^, + 



p = ^, = - 4A/ + &c. 



4 . Z,2 



= (16- 16)A^^+ &c.; 



therefore the coefficient of vP-x^ also vanishes. 

 The coefficient of 



w'xy = 2j ^, ., .. - = 2 



hut 



i);-f'{x;) ^ JDj'ix;)' 



LJI^ - S^D^ = 0. 



B. 



= E = - -IhXJ^ + &c. . . 



Hence the coefficients of w^ [zu, yz, zx'] all vanish ; and hence 



5_A_ r , 



, 2w;[Z^ + Jr^y 4 i\> 



z. 



-r A>2^-' 



that is, that the squares of these five Jacohian Quadrics are connected 

 by a linear relation. 



