of the Eye-pieces of Telescopes. 13 



3d. If the lens be plano-convex, its plane side towards the 

 object-glass, v=—f, and 



^_ 588 g* 

 "~ \6S- F" 



4th. If the lens be equi-convex, v = 0, and 



^~ 168 -F^- 



5th. If the lens be plano-conve.x, its convex side towards the 

 object-glass, v=f, and 



168' F'- 



Of the common forms, then, the equi-convex is the best : it would be 

 somewhat improved by increasing the curvature of the surface next the 

 object-glass. 



Ex. 3. Suppose two convex lenses of equal focal length are 

 placed in contact. 



If we suppose k = 1,5, the equations of Prop. 1, and 2, may be put 

 under this form : 



Q=^ib-BHa^{lfv+lfe^Cf(lv^^l^ev+'-§e-+lr)}; 



b'-B'=^ib-B)+a\CY(lv^'-^ev+fe^ + ^^f); 



, B' 



" = c "• 



In the present instance, 



C=F, B'= -F, C'= f , e= - I, e'= - ^, b -B = o, «' = «. 

 First, then, we find 



u-B'=.^:-y-lf.^lr]: 



