IN THE DOUBLE ACHROMATIC OBJECT-GLASS. 559 



and .-. /?,3/, = y,, 



&c. &c. 

 Also let mM, = i the aperture of the lens 



= (t. 



Calling AB the thickness of the lens at its edge --= T„ we shall have 

 the central thickness 



and R,R. = f, = i T, + 'lnVl , f^JZi^l __J__ 

 ( 2r, 2/-2 ]' cos R,q,M, 



1.2.(<7,M,)'^ 



Now if it were necessary to retain the variable quantities y, and y, 

 in this expression of the value of f,. and similarly ij., and y, in that of /„ 

 we should, from <! (Z>- Z>') = 0, have the radii ;•„ r,, r„ to be expressed 

 in terms of constants, and y„ y„ ij^, or the surfaces would be surfaces of 

 revolution generated by curves of variable curvature, in place of por- 

 tions of surfaces of spheres. 



But the dispersion near the edge of a lens is always very great in 

 amount compared with that near the center of its aperture; and it 

 becomes proportionally more important that it should be accurately 

 corrected for the edge, and especially as the enlargement of the aper- 

 tures of our telescopes may depend upon it. In the example I have 



calculated, further on in the paper, ^ and ^ are considerably smaller 

 than 7',, and accordingly "^^' and " ~ ^' are very small coni])ared 



