of the Eye-pieces of Telescopes. 57 



than the confusion produced by spherical aberration. The latter 

 varies as the square of the distance from the center: but the former 

 varies as the distance (as the variation of tan FHC, p. 243 of tht 

 former Memoir, is proportional to k). And in this conflision 

 there is nothing to point out the center of the coloured line. If 

 an object-glass be not perfectly achromatic, there is always one 

 brilliant point in the coloured circle which can be fixed on as 

 the image of a star : but if an eye-piece be not achromatic, a star 

 appears a coloured line, with no diiference of intensity of light, 

 except that depending on the nature of the colours. It appears 

 to me, therefore, that the first thing to be aimed at for the mi- 

 crometer eye-piece (supposing the first image formed before the 

 rays enter the eye-piece), is the removal of colour. The only 

 eye-piece now in use which will secure this, is that with four 

 glasses. Its spherical aberration would be three times as great 

 as that of the positive eye-piece, and there would be the loss 

 of light resulting from two additional glasses, but I believe that 

 these defects would be well compensated by the removal of the 

 coloured fringes. The field-glass ought to be plano-convex; the 

 first and fourth, crossed lenses with their more convex sides turned 

 toward each other, and the third, a deep meniscus with its con- 

 vexity towards the field-glass. 



I shall make one more remark, suggested by the expression 

 for the extent of the confusion. It appears that the impossibility 

 of making telescopes perfect depends on this circumstance ; that 

 the sum of the powers of the lenses is positive. Now, would it be 

 possible to construct an eye-piece, satisfying the conditions of 

 achromatism, &c., in which some of the lenses were concave?* 



• There is another reason which makes it probable that concave lenses might be ad- 

 vantageously introduced. The value of V contains an arbitrary square (depending on v) 

 VolAll. Parti. H *^'"'S'= 



