IN THE DOUBLE ACHROMATIC OBJECT-GLASS. 563 



A residual circle of dispersion of this magnitude is such as would 

 never be tolerated in a telescope like the Northumberland one from 

 which we have taken our example. The observations made by Professor 

 btruve with the Dorpat telescope, on most difficult double stars, shew 

 that no uncorrected dispersion to an amount like the above could exist 

 in that telescope; and the Northumberland telescope may be reason- 

 ably expected to be no ways inferior. 



From this we are led to conclude, that practical opticians have 

 through experience adopted curvatures for their lenses of much greater 

 accuracy than those given by any theoretical computations hitherto 

 published, and the production of critical defining power in an object 

 glass must be left to their skill and patience in finding the forms which 

 produce the desired effect. 



To shew the effect of our correction on the radius of any one of 

 the surfaces, I shall now give, as example, a case in which the convex 

 crown lens is taken of a greater thickness than would occur in any 

 modern object-glass, namely 



/, = 4 inch, 4=1 inch for an aperture of 6 inches, and focal length 10 feet. 

 Calculating with these, we find 



^(Z)-Z>) = .0000011629, 

 and the diameter of the least circle of residual dispersion 



= .000011629 of a foot. 



Now the diameter of the least circle of spherical aberration in a 

 crossed lens of plate-glass, refractive index = 1.5, is for the same focal 

 length and aperture =.00008.^70; 



so that the former correction would amount to about one-seventh of 

 the spherical aberration in an equivalent lens of the best form, and 

 yet to correct this large residual dispersion would require only a' very 

 small alteration in the radius of one of the surfaces. To find this 

 alteration, we must now take the value of S(D-jy) = o, and as both 

 the term.s in the residual value are positive, we cannot fulfil this con- 



dition whilst (^--^J is separately = 0, but must make the whole 

 Vol.. VI. Part III. 4C 



