NOTE TO A FORMER PAPER ON AN ALLEGED 

 PROOF OF THE METHOD OF LEAST 

 SQUARES*. 



To the Editors of the Philosophical Magazine and Journal. 



GENTLEMEN, 



ALLOW me to correct an error in my letter to Professor Fortes, 

 published in your last Number. The Edinburgh reviewer, on 

 whose proof of the method of least squares I was commenting, 

 says that the most probable position of the wafer is the centre 

 of gravity of the shot-marks ; of course on the supposition that 

 in this, as in all other cases, the probability of a deviation or 

 error r is equal or proportional to a certain constant base raised 

 to the power r z . 



Now, admitting this supposition to be true, the centre of 

 gravity is not the most probable position of the wafer. But, 

 on the contrary, if the function mentioned at the close of my 

 former communication, viz. Zffe** 1 * 1 * rdr, expresses the proba- 

 bility of an error r, then the centre of gravity is the most pro- 

 bable position. I thus not only omitted to notice that the 

 reviewer's conclusion would not follow from his own hypo- 

 thesis, but by this omission was led to introduce an error of 

 my own. 



It is unnecessary to trouble you with a proof of what I have 

 now said, as the matter does not affect the general question. 



I am, Gentlemen, 



Your obedient Servant, 



E. L. ELLIS. 



BRIGHTON, Nov. 7. 



* Philosophical Magazine, December, 1850. 



