tii Places of Images. [Book HI. 



each other, and the point q will then be very near -to 

 T, the point bifecting the radius of the fur face. The 

 parallel rays then falling upon the concave fu'rface 1 

 very near to D will converge, after reflexion, very 

 nearly to the point T, and that point may be confi- 

 de red, and is confidered, as the focus after reflexion 

 gf ihoie rays ; the aberration of every other ray, or the 

 diilance q T fhall be afterwards confidered. The pa- 

 rallel rays falling on the convex fide will alfo, after 

 reflexion,, appear to have diverged from this point T, 

 without any very material error. We may lay it 

 do-wn, therefore, as a principle, that rays falling upon 

 a reflecting furface will, by the concave fide, be made 

 to converge to a point bifecting a radius drawn pa- 

 rallel to them, and by the convex fide will be reflected 

 fo as to appear to diverge from a point bifecting the 

 radius drawn parallel to them. 



Let now (fig. 6.) the rays diverging from a cer- 

 tain point be intercepted by a fpherical reflecting fur- 

 face, and let Q^be that point, and A B the furface of 

 which C is the center ; and let q E be the reflected 

 ray. Draw C m parallel to q E, and C ;/ parallel to 

 Q^E. By the principle above mentioned a ray di- 

 verging from the point m will, after reflexion, cut the 

 parallel radius Cn in #, bifecting the radius in that 

 point ; and, if a ray diverges from , it will, after re- 

 flexion, cut the parallel radius C m in m, bifecting that 

 radius; therefore C;;;,Cw, CT are equal. Since 

 the triangles Qjn C, C n q are fimilar, Qj : m C, or 

 C T : : C , or C T : 7; q. The nearer E is to D, the 

 nearer will the points m and n be to T j Q^nt will be 

 nearly equal to QJ, and q n to q T. Therefore the 

 focus of rays, after reflexion, will be found, without 

 very material error, by. faying, as QJT : C T : : C T 

 : T q. Calling therefore T the principal focu^, its 



diftance 



