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III. On Professor Stokes's proof of Clairaut's Theorem. 

 By Archdeacon Pratt, F.K.S. 



To the Editors of the Philosophical Magazine and Journal. 

 Gentlemen, 

 A BOUT a year ago I expressed an opinion in your Magazine, 

 **- that Professor Stokes's proof of Clairaut's theorem is not 

 more general than Laplace's. In this I was wrong. My show- 

 ing you in few words how I came to make this mistake will 

 illustrate the great disadvantage under which those labour who 

 are far away by thousands of miles from intercourse with the 

 leaders of scientific thought, and from libraries where books and 

 journals of the higher branches of mathematical investigation 

 can be regularly consulted. 



Several years ago Professor Stokes wrote two papers on Clai- 

 raut's theorem and attractions, — one of them in the Cambridge 

 and Dublin Mathematical Journal, and the other in the Cam- 

 bridge Philosophical Transactions. In the first paper he an- 

 nounced that the second was under preparation. But in the 

 second there is no allusion to the "first. He was kind enough to 

 send me copies of both ; but the second only reached me. The 

 first, by some accident which it is impossible at this distant date 

 to trace, never came to hand, and I did not know of its existence. 

 As to any allusions I saw elsewhere to the new investigation, 

 I had no reason for supposing that what I had received (viz. the 

 paper in the Cambridge Philosophical Transactions) did not con- 

 tain everything. It was the other paper which gave a complete 

 view of the new method. In the paper which did reach me 

 there was a step which I thought inconclusive. But I see now 

 that this arose from my misconceiving the author's meaning, 

 from which I should have been saved had I possessed the first 

 paper. Subsequent correspondence with Professor Stokes brought 

 to light that there was a paper missing. I have made every effort 

 to get a copy and have at last succeeded, but only at the end of 

 last March ! I take this early opportunity of recalling the opi- 

 nion which I expressed. 



On the same authority I must yield the point that the sphere 

 is the only surface which regulates the redistribution of the mass 

 so as to leave the external attraction unaltered. Complicated as 

 is the function in page 263* of your ^Number for April last, an 

 a priori demonstration by Professor Stokes, which I have just 

 received from him, shows that it must be capable of being made 



* For 4- -4--* - read r*+3 #+3 ±. 



