IN THE DOUBLE ACHROMATIC OBJECT-GLASS. .555 



it is important to correct as accurately as possible the spherical aber- 

 ration, an error, which amounts to any sensible part of it, must also 

 merit discussion. 



Of the two methods before spoken of, I shall here detail the one 

 winch appears the more regular process, and only indicate the other 

 which however has the advantage of being more continuous in thJ 

 working out. 



Let B, A R, be a double convex lens, whose axis is q, O, 0„ 

 (see Fig. 1), O, and O. being respectively the centers of its spherical 

 surfaces, 



and 0,i?, = rA ^, . 



O.R, = rJ t'^"»''«dn. 



Let QR, be a ray of a pencil incident parallel to the axis, and let 

 It be refracted at /?, in the direction R, R, q, meeting the axis in ry,. 



J, If i^J' f^;^^ ^^ *^"^'""'' ^* ^' ^"^ ^ respectively, draw 

 A-.ili,, RM. and Im, perpendicular to the axis; 



and put R, 3/, = y, 



RM, = y„ 



also put the distance ^i^, = />,, 



and let n = refractive index. 



Then 1\RJR,T., represents the virtual prism by which the ray is 

 retracted, and its angle / is thus found : 



^ / - z TJm + z Tim 



= ^ R,0,M, + I R,0,M, 



0,R, "*" O.R, 



= f; + ^, nearly, 



since these angles are always small. 

 Vol. VI. Part III. 4B 



