202 MR. DOLLOND ON A CONCAVE ACHROMATIC LENS. 



Power. 

 295 + 40 — 4-2 Meanof all = 4P-33, which =!"• 143. 



N.B. The plus and minus measures are taken alternately, and not one rejected or altered. 



" Though 600 did well for the angles^ the stars were not sharp enough with that 

 high power for accurate bisection. The parallel threads are sweetly fine and sharp 

 with 295 (formerly 140). Indeed, this is a very efficient and generally useful power. 



" Thus you will see, my dear Sir, that a long-lamented desideratum has been effi- 

 ciently supplied by your elegant invention. I have thus nearly all the advantages, 

 and none of the disadvantages, of a ten-feet telescope of the same aperture. 



" I remain, my dear Sir, 



" Yours faithfully, 

 (Signed) "W.R.Dawes." 



I shall now introduce some extracts from a letter I have since received from Pro- 

 fessor Barlow, in which his formulae for constructing the lens are given. 



" Woolwich, February 1st, 1834. 



" Dear Sir, — In answer to your letter of January 30th, 1834, 1 will endeavour to state 

 the views which led to my requesting you to make the achromatic concave lens you 

 allude to, and explain the formulae and principles on which I computed the curves. 



" First, with regard to my views. Every one is aware of the ease and comfort of 

 observing objects in a long telescope in comparison with viewing the same in a short 

 one, supposing the powers equal in both instruments ; and my object was to produce 

 this effect by taking up the rays before they arrived at their focus, extending them 

 to a greater distance, and thereby increasing the size of the image, which is of course 

 the same as increasing the length of the telescope in a like proportion. 



" In order to render this lens achromatic, it is only necessary to make the foci of 

 the lenses proportional to their dispersive powers, as in the object-glass itself; except 

 that here the crown lens must be made concave and the flint lens convex. 



" Suppose, for example, the compound lens is to be placed at a distance, d, from the 

 focus, and that the image is to be doubled, then the focal length of the compound lens 



must be 2 J ; for -j — ^^ = ^ : again, I being the dispersive ratio, we have 



f =.2 d{\ —I) =z focal length of the crown lens, 



f = — -^ = focal length of the flint lens. 



" To correct the spherical aberration requires more labour. Let us suppose the crown 

 lens placed towards the object-glass. Assume its radii r,/, or rather their ratio ^ = ^, 



