200 A. Mi\kho\yddhj'dj—'Reply to Lt.-Col. GiinningTiam. [Nov. 



moment. Let ns see, then, what the plain facts of the case are. In 

 the first place we find that the Mongian equation, though first given 

 about eighty years ago, remained for a long series of years unsolved in 

 any direct and elementary way. You will remember that in July 1887, 

 I read a paper before our Society, in which I gave, I believe for the 

 first time, among other things, a direct elementary solution of the Mon- 

 gian equation ; this paper, read in July, was published on the 2nd 

 November 1887, though in the preceding August I had distributed to 

 my friends both here and in England, the extra copies of the paper with 

 which I had been furnished by the Society. Now, in April last I found 

 that in the February Number of the Messenger of Mathematics (which 

 had been published in Cambridge in March) there was a paper by Col. 

 Cunningham giving exactly the same solution of the Mongian equation 

 as had been given before by me, and the transformation not only 

 appeared in the Colonel's paper, but it appeared without any acknow- 

 ledgement that it had been given before ; I, therefore, put a note in 

 our February Proceedings (which were then passing through, the 

 press), calling attention to this point; in this note I stated that my 

 transformation was reproduced in the Messenger without any ac- 

 knowledgement, though Col. Cunningham was fully acquainted with 

 my paper at the date of publication of his article. Of course, as I had 

 expected, he takes objection to this remark, and tries to explain it 

 away ; but, gentlemen, I will presently show you that it is impossible 

 to escape. We have, then, the two facts that my paper was published 

 in Calcutta in November and his in Cambridge four months later. Of 

 course, these two facts taken together prove nothing ; for he being 

 in England and not a member of our Society, it does not follow that 

 he had an opportunity of seeing my paper before his article was pub- 

 lished. You will, therefore, expect me to produce some direct evi- 

 dence on the point, and under ordinary circumstances, it would be 

 impossible for me to do so. But, gentlemen, in this case, the Colonel 

 himself has been good enough to furnish us with a very satisfactory 

 evidence. If you refer to the February Number of our Proceedings, 

 you will find on page 73, a letter from Col. Cunningham, in which 

 he criticizes that very paper of mine on the Mongian equation 

 which contains the transformation in question ; and you will see that his 

 letter was written on the 29th December 1887; it follows, therefore, 

 that in December 1887, that is to say, two clear months before the date 

 of publication of his paper, he had studied my memoir. This, then, 

 substantiates the statement I made ; how is it, I ask, that knowing my 

 solution in December, he published the same thing in February, with- 

 out the slightest acknowledgement that it had been given before by me. 



