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On Achromatic Telescopes. 



Having perused, in the last number of the Quarterly Journal, 

 Signor Santini's very scientific discussion on a new construction 

 of the achromatic telescope, from which it would appear that 

 the spherical aberration cannot always be destroyed by the 

 separation of the lenses of the correcting glass, I beg leave to 

 observe that this arises from the data upon which his calcula- 

 tions proceed being somewhat different from those which I 

 adopted. 



Signor Santini supposes that the foci of the two lenses of the 

 correcting glass are exactly equal for mean rays. This can 

 only take place when the thickness of these lenses is evanescent : 

 when they are of a sensible thickness, the focus of the concave 

 must be shorter than that of the convex, otherwise their foci 

 cannot coincide, and the combination cannot act as a plane, 

 but as a convex lens ; and it is expressly slated in the paper 

 which was read before the Astronomical Society, that to make 

 allowance for the thickness of the lenses, I assumed the focus 

 of the concave lens a quarter of an inch shorter than that of the 

 convex. Our calculations, therefore, proceeding on the dif- 

 ferent suppositions of 9 + v = 0, and 9 + v = 0*25 inch, have 

 led to different results. 



It is not necessary to limit the construction to the condition 

 of the correcting lens acting as a plane ; it is rather advan- 

 tageous to render it slightly concave by making the difference 

 of the foci of its component lenses somewhat greater than is 

 necessary to compensate for the thickness of these lenses. This 

 enables us, with the smallest possible curvatures, to create an 

 excess of concave spherical aberrations, which can always be 

 removed by reducing the aperture of the concave lens, and this 

 is done by separating the two lenses. 



I consider myself indebted to Signor Santini for the interest 

 he has taken in the construction ; and should be happy if so 

 eminent a mathematician were to repeat his calculations, assign- 

 ing a shorter focus to the concave lens ; when, 1 hope, our 

 results would no longer disagree. 



If the destruction of the aberrations could not be completed 

 OCT.— dec 1829. 2 G 



