Chap. 3-1 Reflexion from fy&er teal Surfaces. 189 



fleeting furface is an arch or fegment, can be faid to 

 fall perpendicularly upon it, of which the reader may 

 convince himfelf by drawing a ftrait line with a ruler 

 at any point of a given circle or curve. All the reft 

 of the parallel rays therefore falling on the fpherical 

 furface will fall obliquely upon it, and will confe- 

 quently be fubject to the general law of reflexion, and 

 the angle of their reflexion will be. equal to the angle 

 of their incidence. 



Perhaps the fubject will be rendered (till plainer it, 

 purfuing the idea thrown out in the preceding para- 

 graph, that all curved are formed of a number of ftrait 

 lines infinitely fiiort, and inclining to each other like 

 the ftqnes in the arch of a bridge, I prefent to the 

 reader the figures 5, 6, 7, which may be imagined fo 

 many mirrors bent or inclined in the form which is 

 reprefented in the plate. The rays a b and c d (fig. 5.) 

 which are parallel, are from their different points of 

 incidence rendered divergent in h and e\ the angle of 

 reflection with refpect to each being equal to the an- 

 gle of incidence. 



In figure 6 the rays a b and c d are convergent, and 

 would without the interpofition of the reflecting fur- 

 face b d unite in m ; but according to the fame prin- 

 ciple they now proceed to unite in /, which is more 

 diftant from the reflecting furface than the point m ; 

 and it is evident, that if the curvature of the two 

 branches of the reflecting furface b and d was greater 

 they might be reflected parallel or even divergent. la 

 the fame manner in fig. 7, the rays a b and c d which, 

 without the interpcfition of the convex furface b d> 

 would diverge but very little at m> become after re- 

 flexion much more divergent at / ; and the angles of 

 reflexion will be found in all thefe cafes exactly equal 

 to the angles of incidence, if meafured from the re- 



fleet ine 



