352 PHILOSOPHICAL TRANSACTIONS. [ANNO 1783. 



figure of the lens e will be eg 3 — eh 3 , but as the lens approaches towards f, eg 

 and eh becoming equal, this cause of aberration vanishes accordingly. The 

 effects of the lens k will be altogether insensible from the smallness of its aper- 

 ture; or it might be corrected in the figure of the object-glass, by making its 

 aberration negative as much as this is affirmative. 



It has been usual to consider that form and position of the eye-glasses best 

 that would make the pencils from every part of the field intersect each other in 

 the axis of the telescope at the place of the eye ; but this will be found of little 

 consequence, seeing the diameter o( a pencil here is generally much less than 

 the pupil, nothing more is requisite than that the eye may take in the pencils 

 from the different parts of the field at the same time : but the field of a teles- 

 cope will be most perfect when the construction of the eye-glasses is such, that 

 the focus of an extreme and of a central pencil are at the same distance from the 

 eye. The disposition above described will be found conformable to that idea. 



Let ab fig. 4, represent an image formed by the object-glass of a telescope, 

 v the first eye-glass, as already described, with its plane side towards the image ; 

 let ac be the axis of a pencil of rays incident on the first surface of the lens v, 

 and Ae an extreme ray of the same pencil. Take cf to ca, as the sine of inci- 

 dence out of the air into glass, to the sine of refraction, and f will be the focus 

 of this pencil after passing through the first surface of the lens v. From the 

 point f draw the angle CFe, the incident pencil on the second surface of this 

 lens, continue the lines fc and Fe to b and r respectively, and draw the perpen- 

 diculars oi and ok, on the point c describe the arc nd. and making cd to ab, as 

 the sine of refraction out of glass into air, to the sine of incidence, draw cd 

 continued till it cuts the axis in p. In like manner, on a centre e describe-the 

 arc mg, and making yg to or as the sine of the angle of refraction to that of 

 incidence, draw the line ego; continue it and the line cd backward till they meet 

 each other in h, and it will be the focus of the emergent pencil from the second 

 surface of the lens v. On the axis cf set off the distance cs equal to ch, and 

 draw es and ce. Now it is evident from the figure, that the focus of the emer- 

 gent pencil will be nearer to c than the object itself, in proportion as the angle 

 cse exceeds the angle cac Thus, from the great angle of incidence of the 

 oblique pencil on the second surface of the lens, the focus of the emergent pencil 

 is brought nearer to p the second eye-glass, while that of the principal pencil 

 remains the same, or very nearly so; and the image will become more distinct 

 towards the edge of the field the nearer ph and pt approach to equality. 



To give a proper demonstration and theorem for the exact form of the first 

 lens, according to its distance from the image, would require more leisure than 

 is consistent witli the situation of one not very conversant with mathematics. 

 That distance in proportion to the focal length of the lens, so that any una- 



