1885]. 



Prof. Malet on Rev. R. Harley s Paper. 



211 



II. "Note on Rev. Robert Harley's paper, 'Professor Malet's 

 Classes of Invariants identified with Sir James Cockle's 

 Criticoids." By John C. Malet. Received March 7, 1885. 



In 1882, a paper of mine " On a Class of Invariants " appeared in 

 the " Philosophical Transactions," in which I nsed, for the determina- 

 tion of theorems, two classes of functions of the coefficients of linear 

 differential equations. In consequence of a communication from the 

 Rev. Robert Harley, I appended to the paper the following note : — 



" Since the publication of the abstract of this paper, the Rev. R. 

 Harley has mentioned to me that the first class of functions treated 

 of here have [has] been already investigated by Sir James Cockle ; 

 having consulted the memoirs I was referred to by Mr. Harley, I 

 think little similarity will be found between Sir James Cockle's 

 results and mine. — J. C. M." 



One omission I certainly made,* through ignorance, in this note, 

 and I regret it ; I did not notice that the second class of functions had 

 also been treated of by Sir James Cockle ; this omission, however, 

 appears to me to be a slight one, for anyone treating of the first class 

 would almost as a matter of course be led to treat of the second also, 

 and the existence of the functions is so obvious as hardly to need 

 proof, and the determination of them was with me a process of cal- 

 culation carried on as far as was necessary for the purposes of my 

 paper. 



As far as concerns the mere existence of these functions, certainly 

 those of the first class, the credit of discovering them might be fairly 

 claimed for the writers who first pointed out the strict analogy that 

 exists between linear differential equations and ordinary algebraic 

 equations, for when the second term of an equation is removed, the 

 new coefficients will of course be functions of the old. It never, 

 therefore, occurred to me that anyone reading my note would suppose 

 that I there meant to assert that the functions previously treated of 

 by Sir James Cockle were not identical with those I made use of, and 

 that the latter part of my note referred to the mere calculation of 

 them. 



However, more than two years after the publication of my paper, 

 Mr. Harley communicated to the Royal Society the paper mentioned 

 in the heading of this note, and which I have just seen in the number 

 of the " Proceedings " recently published. In this paper Mr. Harley 

 says : 



" Professor Malet says that having consulted the memoirs to which 

 I referred him, he thinks 'little similarity will be found between Sir 



* Due, no doubt, to oversight on my part. — J. C. M. 



