Mr. J. Cockle on certain Rcseaiches o/" Murphy. 421 



The letter itself appears (from the folding) to have been 

 placed in a cover, and there is no superscription or direction. 

 Though, therefore, I have supposed that it was addressed to 

 Nourse, I have no other ground for such an opinion than that 

 it was found amongst a mass of letters which were so addressed. 

 My own impression is that Andrew Millar was the early pub- 

 lisher of Goldsmith's work, though I have no means of con- 

 sulting a copy of a date antecedent to this letter. There 

 are, at all events, no other letters to Millar amongst these : 

 and the chief difficulty is to conjecture how a letter addressed 

 to one publisher should get amongst those of his neighbour ; 

 especially as no very friendly feeling existed between the pub- 

 lishers, nor much of sympathy between the scientific and 

 literary classes of that period. 



Royal Military Academy, 

 February 1.5, 1848. 



LVII. On certain Researches o/'Murphy. Bi/ James Cockle, 

 Esq., M.A. of Trinity College, Cambridge, and Barrister-at- 

 Law of the Middle Temple^. 



A T page J 29 of a memoir referred to below f. Murphy has 

 ■'^^ given a rule by means of which we may express in the 

 form of a series a root of any equation containing only positive 

 and integer powers of the unknown quantity. In this memoir 

 there is no allusion to any prior discovery of the rule; and 

 Murphy subsequently:}: refers to the process without mention 

 of any other writer in connexion with it, and appears to regard 

 himself as its originator. The rule seems to have been hi- 

 therto attributed to him §, and I have fallen into the same 

 error at page 363 of the present volume of this Journal ||. It 



« Coironanicated by the Author. 



+ On the Resolution of Algebraic Equations. Published at pp. 126-153 

 ofvol. iv. of the Transactions of the Cambridge Philosophical Society. 

 See more particularly section 1, pp. 129-133. 



} Camb. I'hil. Trans., vol. iv. p. 3i35. See also Murphy's Theory of 

 Equations, p. 77, commencement of article (02.). It is to this article 

 (pp. 77-^2) of Murphy's n-ork that I ought to have made reference supra, 

 page 3G3. 



§ See Dr. Peacock's Report on Analysis (to the British Association, Meet- 

 ing of 1833), p. 350. 



II Among the defects of my paper here referred to, are the having omitted 

 to make mention of the name of Vandermondc. the great rivalof Lagrange in 

 the department of science there discussed, and also of Simpson's (subsitliary) 

 and Professor J. R. Young's (indirect) sohition of a biquadratic. And Mr. 

 Davics has requested me to say, tliat from the haste with which his notes 

 on my paper were written, he omitted to refer to a very neat and elegant 



