462 Mr. R. L. Ellis on " TJie Method of Least Squares." 



ing portion. Since, therefore, the presence of a layer of air 

 cannot be here assumed, the darkness of the central spot — 

 even setting aside the consideration that black can never result 

 from the interference of heterogeneous rays — cannot arise 

 from interference, because the latter without an air-layer is 

 impossible. 



The fuller development of the views expressed in the fore- 

 going pages I reserve to a future memoir. In submitting my 

 divergence from received opinions to the judgement of those 

 who understand the subject, my sole object is to bring all 

 optical action, no matter of what particular kind, into coin- 

 cidence with the theory of undulation ; so that the harmony 

 of our thoughts with the divine order of Nature, at least in 

 this department of science, shall remain undisturbed. 



LXIII. Note to a former paper " On an alleged proof of the 

 ' Method of Least Squares.' " Bt/R.L,. Ellis, late Fellow 

 of Trinity College, Cambridge. 



To the Editors of the Philosophical Magazine and Journal. 



Gentlemen, 

 A LLOW me to correct an error in my letter to Professor 

 *■*■ Forbes, published in your last Number. The Edin- 

 burgh 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 pro- 

 bability of a deviation or error r is equal or proportional to a 

 certain constant base raised to the power — ? 2 . 



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. 2h 2 e~ l ' rdr 9 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, 



Brighton, Nov. 7- R. L. ELLIS. 



