I 33 ] 



the refradiion of the central rays remaining the fame as before. 

 And perhaps it will appear that thefe effedls may be produced 

 by a concavo-convex glafs of greater curvature on the concave 

 fide than on the convex, efpecially if the thicknefs of fuch a 

 lens be made greater'tHan ufual ; becaufe the thicker the lens 

 is, the nearer will an exterior ray be brought to the vertex of the 

 fecond furface, and therefore its incidence, and confequently its 

 refradion by that furface, will be the lefs, as in Fig. VI. • 

 vice verfa in Fig. VII. 



We fee that in the double concave the refradion of an exte- 

 rior ray, by |the firft furface, is greater than that of a central 

 ray, and as its efied is to caufc a divergence, the refradion of 

 the firft furface will add more to the effed of the fecond furface 

 (which is ,alfo to cai^fe divergence) upon the exterior rays than 

 upon the central. 



I. In the fame manner in the concavo-convex (the rays 

 falling on the convex fide) the refradion of the exterior rays 

 by the firft furface is greater than that of the central rays ; 

 but thefe refradions are decrements of the divergence caufed 

 by the fecond furface ; therefore the divergence of the exterior 

 rays is more diminifhed than that of the central rays, and there- 

 fore may be made lefs than that of the exterior rays made by 

 a double concave, while the divergence of the central rays 

 caufed by both is the fame. 



,2. Let the rays fall on the concave fide, Fig. VIII. In this cafe 

 the divergence of the exterior rays by the concave is greater than 



F ' that 



