Chap. 4.] Coavergijie Rajs on a convex Surface. 207 



If their convergence is exactly proportioned to the 

 convexity of the furface, they will not fuffer any re- 

 fraction j (fee fig. 2.) becaufe in that cafe one of 

 the efTentials is wanting to refraction, viz. the obliquity 

 of the incidence, and each ray proceeds in a direct line 

 to the center of that circle, of which the convex fur- 

 face is an arch or fegment. For inflance, the rays ef t 

 and dh y (fig. 7.) which tend to unite at C, the center 

 of the convex furface, may be confidered as. perpendi- 

 cular, being the radii of the circle. 



If the rays have a tendency to converge before they 

 reach the center of the convexity, xhey will then be. 

 rendered lefs convergent ; for inftead of converging to 

 a point at b (fig. 3.) they will converge at B. The 

 reafon of this is evident, for the ray ib (fig. 7.) which, 

 if not intercepted, would meet the axis at k, nearer the 

 lurface of the refracting medium than the center of con- 

 vexity C, being refracted towards the perpendicular or 

 radius dC, meets the axis only at o. 



If, on the contrary, the rays have a tendency to con- 

 verge beyond the center of the convexity, they will 

 then, by the law of refraction, be rendered ftill more 

 convergent, as in fig. 4, where their point of union, 

 if not intercepted, would be c, but where, by the influ- 

 ence of the refraction, they are found to converge at C. 

 For the ray gb (fig. 7.) the tendency of which is to- 

 wards /, is refracted towards the perpendicular dC f 

 and joins the axis zip. 



If diverging rays fall on the convex furface of a 

 denfer medium, they are always rendered lefs divergent,, 

 as in fig. 5.; and they may be rendered parallel, or 

 even convergent, according to the degree of divergence 

 compared with the convexity of the refracting furface, 

 on the principles already explained. 



If 



