ON ABERRATION AT A CURVED SURFACE. 2L 



To prevent mistakes may I recommend to your readers to 

 strike out from vol. vi, p. 89, line ten from the bottom, the 

 words " or striate/' which are intended to apply to EupleuHa 

 incurvata, since removed to Gephyria. 



The Fundamental Proposition in the Theory of Aberra- 

 tion (in Refraction) at a Curved Surface simply 

 Demonstrated ; and a Test established whereby the 

 Insufficiency of the Approximate Formulae (noiv in 

 use) for Calculating the Aberration at a Spherical 

 Glass Surface may be correctly ascertained. By 

 H. M. 



In the following paper I propose to treat on a subject of 

 great importance to working opticians, and which appears 

 to me to have been not very successfully handled by writers 

 on Optics. 



Instead of giving a decided answer to the question I 

 propose to solve, mathematicians have hitherto considered 

 it sufficient to offer an approximate solution, supposed to be 

 correct enough for practical purposes. This is a point on 

 which I entertain a doubt, and my object in the present 

 paper is to give a completely satisfactory answer to the ques- 

 tion proposed, and to show, by an example, illustrating the 

 formula deduced, how far the usual approximation falls short 

 of the truth — in an extreme case. 



I have added a geometrical proof of the truthfulness of 

 the formula, which may contribute to excite attention to 

 a subject the difficulty of which has, I think, been unneces- 

 sarily magnified. 



For convenience I have also appended the arithmetical 

 working of the example. 



Although I have not Potter's book at hand, the correct- 

 ness of the substitution of the figures in his formula, which 

 is identical with Sir J. Herschel's in 'Encyclop. Metrop.,' 

 and Wood's, &c, may be relied on. 



PROBLEM. 



Trace accurately the course of a given ray of light, QA, 

 after refraction at a given point, A, on the surface of a given 



