46 MR. ROBERT RAWSON ON DIFFERENTIAL 



Then 



V 27 



And 



Therefore 



2 a 3 „ 



27 



=-a+K/^i) 



The value of y in (23) agrees with Cardan's formula. 



The process of obtaining the first and second differential 

 resolvents is a direct process ; and it is only fair to state 

 that it has been gathered entirely from the correspond- 

 ence with Sir James Cockle, F.R.S. &c, and the Rev. 

 Robert Harley, F.R.S. &c, with whom originated the 

 important invention of differential resolvents of algebraical 

 equations. 



I am not sure whether the results in Arts. (4) and (5) 

 have been published by either Sir James Cockle or the 

 Rev. Robert Harley. 



It is more than curious that Cardan's formula should 

 be reached as it has been, without the slightest assump- 

 tion, by means of the second differential resolvent. And 

 the method which has been adopted is, in my opinion, 

 very suggestive in the theory of higher algebraical equations, 

 especially so when several independent variables are made 

 use of. 



6. If in (14) we put 



— 2«m' lar . . 



• • • (24) 



V4« 3 + 27m a V27' 

 where (r) is another function of x, 



