|(/Q OPTICAL ABERRATION, 



From this given ratio of A B to xy it follows, that the 

 image of the fun within a telefcope varies vvlth the aperture 

 Qi' the obj«6l glafs. 



Sir Jfaac Newton fqund by moft accurate experiments that 



■where the fine of incidence was 50, the fines of refradion of 



(he red and the violet rays were 77 and 78. Hence q—p is to 



q-\-p—2n as 1 to 55. And therefore A B : 3:3/ :: 55 ; 1 ; or 



AB 



To elucidate this theorem by examples, let the diameter of 

 the objc6l glafs of a telefcope, which is 4. inches, be con- 

 tracted to 3 inches, and afterwards to 2; then the diameters 

 of the circles by aberration formed by parallel rays, will be 

 ^^ = .072, -^ = ,054, and /^ = '036 refpeaively. 



The fame Pnoperty of Vifion demonjlrated othenvife. 

 Thus, let n rejjrefent the fine of iAcidence, andj) and^ the 

 MtL lines of refraclion, as before. 



The fine of incidence of every ray, is to its fine of refrac- 

 tion in a given ratio.* 



And the fine of incidence of the extreme ray PA, varies 

 with the aperture of the lens. For n becomes lefs as P A ap*. 

 proaches the axis of the lens E v. 



Therefore the fines of refra61ion p and q, the angle xAy, 

 and its fubtenfe xy increafe or decreafe wira A B. Confe- 

 quently the image of the fun or moon, upon the retina in- 

 treafes or decreafes in magnitude with the pupil of the eye, 

 Deduaion' Now as the rays of artificialligh tare differently refrangi- 



ble, {^evident from the given ratio of A B to xy, in which 

 they increafe or decreafe at the fame time that the image of a 

 candle formed in the focus of a convex lens decreafes with 

 the aperture of the glafs. For the rays of the fun and the 

 li^ht of a candle are boCfi governed by the fame law, in th^ 

 formation of images in the focus of a lens; but this law does 

 not obtain in the fame degree in both obje6ls, in confoquence 

 <)f the rays of the latter being in a more diverging liate than 

 thofe of the former, 

 ^applied In ' Hence the truth of the refult of my experiments, which 

 fupport of the were publiftied in Vol. IX. page 161- of this Journal, is proved 

 menu? "^'"' ^fom the difcoveries of Sir Jfaac Newton. 



* Newton's Optics, page 64. 



4 What 



