242 ^-ifjpareiit Mao'fili/de of the honzontal Muoit. 



that where tlic sine of incidence was 50, ike sines of refrac- 

 tion of the red and the violet rays were 7 7 and 78. Hence 

 fj _ p 'in lo q + p — In as 1 lo 55. And therefore AB : 



AB 



x>/ :.: Jo : ] ; or xii = - . • 



To elucidate this theorem by examples, let the diameter 

 of the object-glass of a telescope which is four inches be 

 contracted to three inches, and afterwards to two j then the 

 diameters of the circles of aberration formed bv parallel rays 



will be — = •07;?. — = -05-1, and — = -036 respectively- 

 5J 5J 55 



The same Properfi/ of f''"nioii demonstrated otherwise. 



Thus, let // represent the sine of incidence, and p and q 

 the sines of refraction, as before. 



The sine of incidence of every ray is to its sine of refrac- 

 tion in a given ratio *. 



And the sine of incidence- of the extreme ray PA varies 

 with the aperture of the lens: for 7i becomes less as PA 

 approaches the axis of the lens Ew. 



Therefore the sines of refraction p and q, and the angle 

 a: Ay, and its subtense xy, increase or decrease with AB: 

 consequently, the image of the sun or moon upon the retina 

 increases or decreases in magnitude with the pupil of the 

 eye. 



Now as the rays of artificial light are differently refrangi- 

 ble, it is evident from the given ratio of AB to xaj, in which 

 they increase or decrease at the same time, that the image 

 uf a candle formed in the focus of a convex lens decreases 

 with the aperture of the glass. For the rays of thesun and 

 the light of a candle are both governed by the same law in 

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

 does not obtain in the same degree in both objects, in con- 

 sequence of the rays of the latter being in a more diverging 

 state than those of the former. 



Experiment I. 



To prove the truth of this theory by experiment; I took 

 two double convex lenses, each four inches in diameter and 



• Newtoii'f Optics, p. 64. 



24 inches 



