C hap. $.] Places of Images made by Reflexion. 2 If 



veral images of the fame object appearing to be placed 

 in a circle, whofe center is the vertex of the acute 

 angle, and radius the diftance of the object from that 

 vertex. Let M N O P, Plate XII. (fig. 4-) two fur- 

 faces produced, meet in b, and let QJbe an object, and 

 <7, c its images in the refpective glafTes. Join bq, 

 b Q^> and the triangles Q^a b, q a b, having twd fides 

 and an angle rcfpectively equal, the third fide Q is 

 equal to q b. So b c is equal to b Qj and in the 

 fame manner the images of q, and c found in the op- 

 pofite glaffes, will be equidiftant from b. 



The places of images, made by the reflexion of the 

 rays of light from plane furfaces, are cafily determin- 

 ed: but when rays are reflected by curvilinear fur- 

 faces, the diffisulty of determining the place of the 

 image is confiderably increafed. I fhall endeavour to 

 fhew the manner of inveftigating this fubject in the 

 fimpleft cafes. 



Let A B (fig. 5.) be a fpherical furface, of which C 

 is the center, reflecting the rays of light both on the 

 concave and convex fide ; and let QE, a ray of light 

 parallel to the radius C D, be incident on the furface 

 at E. After reflexion on the concave fide, the ray 

 will proceed in the direction E q> making the angle 

 y E C equal to QJE C ; but the ray Q^E reflected by 

 the convex furface will proceed in the direction E K, 

 making the angle K E I equal to the angle Q^E I. 

 The greater the diftance of E, the point of incidence, 

 is from D, the vertex of the furface, the farther will the 

 interfection of the reflected ray and the radius C D be 

 from the center of the furface. Since QJi, is parallel 

 to C D, the angle QJE C is equal to the angle E C q ; 

 therefore the angles q E C, q C E are equal to each 

 other, and confequently q C is equal to q E. If E is 

 very near to D, q D and q E will be very nearly equal 



to 



