248 Dr Goring 1 * Remarks on M. Chevalier's Paper. 



than a triple one, that is to say, it performs better upon paral- 

 lel rays when inverted than it does when its concave lens is 

 presented to them to form a telescope ; but to obtain this ap- 

 proximation it must be very thin, and have a very small aper- 

 ture, and is even then a long way off from its true figure. 



As metals are very simple in their action compared with 

 achromatic glasses, I always like to put a case with regard to 

 them in order to settle any theoretical point. Accordingly, I 

 have tried a set of beautifully perfect metals belonging to an 

 Amician reflecting engyscope, inverted as miniature Newto- 

 nian telescopes, and found their figure a great deal too spheri- 

 cal for parallel rays, especially those of the large angles of 

 aperture. 



Had Euler's theory been correct, they ought to have per- 

 formed very well as minute telescopes, because their figure 

 should, in this case, have been parabolical, instead of which 

 it is much nearer the sphere, and, as I presume, elliptical, 

 which harmonizes perfectly with the other trials ; for the dif- 

 ference between the ellipse and the parabola is equivalent to 

 that between the condition of an object-glass perfect in its ac- 

 tion on parallel rays, and another which has too much spheri- 

 cal aberration in its convex lenses to be so. The said metals 

 are, however, not so much out in point of figure as a triple ob- 

 iect-glass is, but about as much as a double one, as far as I 

 can o-uess. The theory of achromatic glasses for diverging 

 rays, is then, I am persuaded, an untried field, in which no 

 mathematician has as yet distinguished himself. * I shall pro- 

 bably be told that a theory would be of no use if we had it, 

 because artists would not zcork to it. This is true with regard 

 to the more minute glasses; but very beautiful and useful en- 

 o-yscopes may be made on a large scale, having object-glasses 

 of so long a focus as four and even six inches, which also act 

 very strikingly in the solar microscope ; and a theory could 



* Money is said to make every thing go ; to be at the bottom of every 

 thing; anil to purchase every thing, (if in sufficient quantity.) Thus all 

 men and all women have their price. When I get rich I shall try if the 

 offer of a <*ood round sum will stimulate the men of numbers and quanti- 

 ties to undertake the theory of a thick aplanatic object-glass for diverging 

 rays. 



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