554 Mr potter, ON A NEW CORRECTION 



It must have struck most persons conversant with the subject, that 

 the effect of the lenses, in an achromatic combination of two or three 

 lenses in contact, must be sensibly different near their edges, on account 

 of the oblique passage of the rays, from what it is near their centers; 

 and this difference will be the more important, as the area of that 

 part of the surface of the lens, with this unconsidered effect, is so 

 much more than that part of the surface near the center for which 

 the common theorem is accurate, or nearly so. 



In the present paper, I have investigated the conditions of achroma- 

 tism in a double object-glass for a ray passing through it at a distance 

 from the center of its aperture, on the supposition that we may neglect 

 powers, of the small quantities which enter the expressions, above the 

 first, and also their products. It is also necessary to consider the 

 thicknesses of the lenses, as that of their edges, for all parts at which 

 the new correction rises to any important magnitude. 



I have ai-rived, by two different methods, at the same result, which 

 involves the expression obtained by the ordinary mode, together with 

 others depending on the thicknesses of the lenses. The spaces, through 

 which a ray has passed within the lenses, have on the achromatism 

 an effect which is precisely similar to that of the distance of the lenses 

 in achromatic eye-pieces. If the lens have great thickness, a ray of 

 light after an oblique passage through the glass, will meet the second 

 surface at a different angle to what it would have done if that thick- 

 ness had been small; and hence, if we consider a virtual prism to be 

 formed by the tangent planes to the surfaces of the lens, at the points 

 at which the ray is incident and emergent, the angle of this virtual 

 prism will depend on the thickness of the lens, as well as on the radii 

 of the surfaces and the distance of the point of incidence from the 

 center of its aperture. We may easily conceive, that this variable angle 

 of the virtual prism will need more accurate consideration when we 

 pass beyond the ordinary first approximation. 



The new correction, which we thus arrive at, supposing the thick- 

 nesses of the lenses in a double object-glass such as might arise in 

 practice, is however not very large in magnitude. But nevertheless, if 



