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James Cockle was best known to us. He wrote on the Indian Astro- 

 nomical Literature, on the Indian Cycles and Lunar Calendar, on the 

 date of the Vedas and Jyotish Sastra, and on the Ages of Grarga and 

 Parasara. He also published four elaborate memoirs on the Motion 

 of Fluids, and some notes on Light under the Action of Magnetism, 

 &c, but in general he confined himself to problems in pure mathe- 

 matics. His analytical researches were concerned for the most part 

 with two subjects^ viz., Common Algebra and the Theory of Differ- 

 ential Equations. In algebra he worked mainly among the higher 

 equations, and for many years his labours in this department were 

 inspired and directed by the hope of being able to " solve the 

 quintic," or, in other words, to express a root of the general equation 

 of the fifth degree by a finite combination of radicals and rational 

 functions. The problem had long engaged the attention of mathe- 

 maticians, and was attacked by the most celebrated analysts of the 

 last century with great skill and vigour, but without success. In the 

 early part of the present century, Abel, the young and gifted Nor- 

 wegian mathematician, attempted to show that a finite algebraic solu- 

 tion of the problem was impossible. Cockle considered the argument 

 with care, and reproduced it as modified by Sir W. R. Hamilton, in 

 the 'Quarterly Journal of Mathematics' (vol. 5). To prove a nega- 

 tive, however, is proverbially difficult, and despite Abel's " demon- 

 stration," and the non-success of preceding investigators, Cockle for 

 many years clung to the conviction that what had been done for the 

 lower equations might be done also for the equation of the fifth degree. 

 He laboured long and hard at the problem ; and although he failed, 

 as others before him had failed, to effect a general solution, and came 

 finally to the conclusion that such a solution was " absolutely 

 unattainable," yet his labour was not lost. He found not the thing 

 he sought for, but other things which amply repaid the toil of effort, 

 and he opened up new methods of working, and new lines of research 

 which are of acknowledged value in themselves. A result which he 

 obtained in the fifties attracted much attention at the time, on 

 account of its remarkable simplicity. By an indirect but ingenious 

 process he succeeded in determining the explicit form of a certain 

 sextic equation on the solution of which that of the general quintic 

 may be shown to depend. The accuracy of this sextic or " auxiliary" 

 equation (whose coefficients are all monomials save one, which is a 

 binomial) was shortly afterwards confirmed by an independent calcu- 

 lation. The writer of this notice was led to consider the problem in 

 connection with some researches of his own on the finite solution of 

 algebraic equations, in the course of which he calculated Cockle's 

 sextic by a direct process. His researches were published in the 

 ' Memoirs of the Manchester Literary and Philosophical Society,' to 

 which Cockle had contributed his remarkable result, and the subject 



