Chap. 6.] EjeBs of fpberical Surfaces. 231 



the focus of diverging rays falling on A B, let x be the 

 focus of rays after refraction found by the proportion 

 before laid down, or by joining H E, and drawing Qj<r 

 parallel to it, In the fame manner the apparent place 

 of R will be found, and a perfon at O will fee the ob- 

 ject QJR apparently in fx, The point Q^he fees by 

 the ray QJ? G O, and the point R by the ray R L, 

 MO. 



When the furfaces are fpherical, a change is made 

 in the apparent places of objects no lefs remarkable 

 than that which we have obferved in objects placed 

 before convex or concave mirrors. To underftand the 

 reafon of thefe appearances, it is necefTary to examine 

 the progrefs of a ray in the fimplcft cafes, and thence 

 to proceed to the more difficult. 



Let ABFD (Fig. 17, 18.) reprefent a medium, 

 rarer or denfer than the furrounding .medium, and. 

 bounded by a fpherical furface A E B 3 and let the ray 

 G H parallel to I E a ray parting through the center 

 of the arch A E B be refracted at H, to or front the. 

 perpendicular, according to the nature of the medium. 

 The fine of the angle C HG is to the fine of the angle 

 CI1 1 in a given ratio, but CI : IH :: S. CHI Ts. 

 C H G, therefore J H : I C in the given ratio of the 

 fine of incidence to the fine of refraction depending on 

 the nature of the mediums. The nearer H is to E the. 

 nearer will the ratio of I H to I C be to that of I E : 

 I C, and consequently by finding a point I in the line 

 C K produced, fuch that IE may be to 1C in the given 

 ratio of the fine of incidence to the fine of refraction, 

 all the rays parallel to I E, which are refracted by the 

 convex furface A E B (Fig. 17.) will after refraction 

 converge to I, or a fmall fpace very near it. The 

 greater the diftance of H from E, the greater will be 

 the diftance of the intei feel ion of the refracted ray and 



line 



