of the Eye-pieces of Telescopes. 56 



6th. The most advantageous combination, therefore, of common 

 lenses is, ail plano-convex, the first and second with their plane sides 

 towards the object-glass, and the third and fourth with their con- 

 vexities the same way. With this, 2 (^) =mx,1190, whence 



"th. The eye-piece would be much improved by giving a slight 

 curvature to that side of the fourth lens next the eye, and by making 

 the second lens a meniscus, in which the radius of the concave surface 

 next the first lens is more than double that of the other. 



8th. A single lens, for the same power, must have the focal 



length Mx 2,l6, and, therefore, its smallest values of U and Y 



.1,08 2,62 



would be -j^ , and -^ . 



The instances which we have used as examples to our formulae 

 are taken from the eye-pieces which are, or have been, commonly 

 in use. And the numerical results which we have obtained enable 

 us to judge of their comparative merits, and of the improvements 

 which have been introduced in this branch of telescope-making. 

 Of these, the most remarkable is that of the positive eye-piece. 

 In the form which we have given as the best, two plano-convex 

 lenses, with their convexities towards each other, (and which is, 

 in fact, the common construction), the ratio of its value of 2(f/) 

 to that for a single lens is about i : 5 ; whereas, if the lenses be 

 placed in contact, it is 4 : 15 ; in the Hiiygenian eye-piece, it is 

 15 : 31 ; in the old three-glass eye-piece, 3 : i, and in the four- 

 glass eye-piece, 2:3. The chance, or the reasoning, which led 

 to this construction, avowedly for the purpose of making the 



