THE 

 LONDON, EDINBURGH and DUBLIN 



PHILOSOPHICAL MAGAZINE 



AND 



JOURNAL OF SCIENCE. 



[THIRD SERIES.] 



NOVEMBER 1850. 



XL. Remarks on an alleged proof of the " Method of Least 

 Squares" contained in a late Number of the Edinburgh Re- 

 view. In a Letter addressed to Professor J. D. Forbes, by 

 R. L. Ellis, Esq., late Fellow of Trinity College, Cam- 

 bridge*. 



My dear Sir, 



THE review of Quetelet's " Lettres a S. A. R. le Due 

 regnant de Saxe Cobourg et Gotha," which appeared 

 in the July Number of the Edinburgh Review, contains a new 

 demonstration of the method of least squares which ought not, 

 I think, to pass unnoticed. If it is correct, it is so much 

 simpler than those which have hitherto been received, that it 

 ought to supersede them ; and if not, the sooner its incor- 

 rectness is pointed out the better. 



Some years since, in a paper published in the Cambridge 

 Transactions for 1844, I made an analysis of all the demon- 

 strations, or professed demonstrations of the method of least 

 squares, with which I was then acquainted, and I therefore 

 read this new one with more attention than you perhaps have 

 given to it. 



The reviewer gives some account of the history of the sub- 

 ject, and remarks that the demonstration of the least squares 

 was first attempted by Gauss, but that his proof is no proof 

 at all, because it assumes that in the case of a single element 

 the arithmetical mean of the observed values is in all cases the 

 most probable value, "a thing to be demonstrated, not as- 

 sumed." Gauss afterwards gave another demonstration, which 

 is perfectly rigorous; but of this the reviewer takes no notice, 

 though it is mentioned in at least one of the works on the 

 * Communicated by the Author. 



Phil. Mag. S. 3. Vol. 37. No. 251. Nov. 1850. Y 



