of the Eye-pieces of Telescopea. 41 



and hence the rays converge after refraction to a line at the distance 



jP"'2 



{U+U' + U"+U"')^ 



Suppose these to be received by the eye, which is adapted to parallel rays. 

 The eye may be correctly represented by a convex lens of invariable focal 

 length K: the rays then would converge to a line at the distance from 

 this lens 



1 K^ R""- 



^+ Jw5 --J- 



But the distance of the retina is K, Hence, the rays intersect at the distance 



before meeting the retina : and if X be the breadth of the pencil which 

 enters the eye, the extent of the diffusion on the retina is 



and the angle which this subtends at the center of the crystalline is 



±,^{U+U'+U"+U"')>^^^. 



Now, let L be the aperture of the object-glass ; p the magnifying 

 power of the telescope (an abstract number); 6 the angular distance of 

 the object from the center of the field of view, not magnified. Then 



(by the known properties of telescopes), ^p^ = tan. apparent distance of 



the object from the center of the field (as magnified) =pQ; and X=— . 



Substituting these, we finally oTbtain for the angular extent of the diffusion, 

 To/. III. Part J. F 



