222 Annual Report of the Council. 



differential equation of the order n - I, which is satisfied by 

 any one of the roots of the algebraic equation. Out of 

 this germ has grown the theory of differential resolvents, 

 a subject treated of by many writers both in the Society's 

 Memoirs and other publications, but which it must be con- 

 fessed is still far from being complete. 



To Cockle also belongs the honour of being the first to 

 discover and develop the properties of those functions of 

 the coefficients of linear differential equations called 

 Criticoids or Differential Invariants, — so called because 

 they remain unaltered when the differential equation is 

 transformed by a change of one of the variables, and are 

 analogous in this respect to the critical functions or 

 semivariant.s of common algebra. Criticoids seem destined 

 to play an important part in the theory of linear 

 differential equations. It would be impossible to discuss 

 in detail Cockle's various discoveries in algebra and 

 the calculus without covering page after page with mathe- 

 matical symbols, which would be quite out of place in a 

 brief obituary notice. Enough to say here that his work 

 was eminently initiatory. He started theories, but left 

 others to elaborate and perfect them. Of his eighty or 

 ninety papers given to the mathematical world, many are 

 no doubt slight and fragmentary ; but there are few, even 

 among the shortest and least complete, which do not 

 contain original and valuable suggestions. Ideas struck 

 out by him have taken root in other minds and borne fruit. 

 The leading events in the life of Sir James Cockle are 

 soon told. He was born at Great Oakley, near Harwich, 

 in Kent, on the 14th January, 1819. Of his early days little 

 is known. From 1825 to 1829 he was educated at Stormond 

 House, Kensington ; thence he was sent to Charterhouse, 

 where he showed considerable power in making Latin verses. 

 At the end of his second year he was removed and placed 

 under the tuition of the Rev. Christian Lenny, D.D., of St. 



