230 MR. W. SPOTTISWOODE ON DIFFERENTIAL RESOLVENTS. 



The developed values of A, E, F^ G are as follow : — 

 A 



a 



= — 3i*c* + 4^56?— 6abcd-\- 4«c' -f a*c?*. 



-6b'a{bd-c^) 

 — '^ca{bc—ad) 

 ^2d'a{aC'-b^), 



^=a:{^bcd-ad''-6c') ; 



-\-'^b\lbc^ — 2b'^d—acd) 



+ 3<^( — 3^^^ + 2ac* + abd) 

 + d'{-'jabc + a^d+6b^). 



^=2a'd{bd-c^) 



+ 2b'd{bc—ad) 

 + 6c'd{ac-b^) 

 4- 6?'( — 4ac* + 3^ V + «*6?) . 



Now Mr. Harley has shown in a recent letter, that the 

 coefficients of a? and i in (12) are divisible by A (the dis- 

 criminant of the original cubic) ; the result, after various 

 reductions, is 



AE^" 

 + I A'E - AE' - 3EF + 6^E* I ^' 



4--{9(E'F-EF) 



^2:E[a''-(-ad^-gc^ + gbcd) 



+ gb"-a(2bd—2c'-) 



— gc"-a^c 



-d"-a} 



+ Za^b\ — ^b'-d +gbc^— acd) 



