MB. J. J. WALKKK ON THE DIAMETERS OF A PLANE CUBIC. 169 



4 ( _ Ayz - Fx> + Gxy + Hzx) 

 so that 



4 (be' + b'c-2ff')/ 2 +... 

 a*w a*M 3 



+ u ? - w 



9M \ 



1 



+ f 

 \&u(d*\* ,^f/3v 3^ aa\ K, 



' 1 9^ h 



o _ . j 



J " *" + " 



the negative term in which being the result of substituting n ds/dy m dsjdz for x' . . . 

 in 



is (30) 



-Ct>; .... (46) 



consequently, (45) (46), sixteen times the eliminant (44) is 



..... (47) 



As was mentioned, (38), 31, the terms multiplied by 4s within [ ] a in (47) are 

 equal to 



-6PL, 



so that the elimiuant is simply, after division by 36, 



or 



v (v + 8PLs) = 0. 



MDCCCLXXXVIII. A. Z 



