183 



and which also enables us with ease to calculate the resolvent 

 for the cubic {?i =. 3), viz. 



Results (1) and (3) were first calculated by a different process 

 by Mr. Cockle, The following are now published for the 

 ■first time. For the biquadratic {n — 4) the differential 

 resolvent is 



• 2=(:-.,g-...3v3-..43.|+5, = 0...(3) 



And for the quintic (n = 5) the resolvent is 



— 3.5^M7.r^H-3.7-lly=:0...(4) 

 ax 



The Boolian form of (3) is 



("-| )("-t)(^-t) 3. „ ,, ■ 



^ D(D— 1)(D — 2) *" ^ 



d e 



where D is the differential symbol — , and £ =j:. 



" do 



I notice also tlie following remarkable relations among the 



' differential coefficients for the general case, viz., 



+ 3(/i — l)(?i-!-2)(2n+l)y 



— (2;i.-l)(3?2'4-3?i — 8):^ 



dx 



The investigations on this subject^ which I intend to 

 publish shortly, embrace a curious and anomalous result in 



