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M. Huygens lias alfo (hewn, tlir.t the fame aberration is 

 pioiluced by concave lenies as by fimilw convex ones. 



llouover this ipccies of al'erraiion is altogether incon- 

 fidcrablc, compared with the latter ; infoinuch that if the 

 objcft-glafs of a telefcope be plano-convex, and the plane 

 fide he turned towards the ohjcft, and the diameter cf the 

 iphere to which the convex lide of the glafs is ground, be 

 lOO feet, the femidiameter of the aperture be tvyfo inches, 

 and the ratio of the fine of incidence out of glafs into air be 

 to that of reflation as 20 to 3 ! ; the diameter of the circle 



of alierralisns will in this cafe be only parts of 



720CCCOO '^ 



an inch. But the diameter of the little circle, through 

 which the fame rays are fcattcred by unequal refrangibility, 

 will be about the 55th part of the breadth of the aperture 

 of the objeft-glafs, which is here four inches ; and therefore 

 the error arifing from th.e fpherical figure of the glafs is to 

 the error arifing from the different refrangibility of the rays, 



as — i to ■— , that is, as i to C44g. Sec Newton's 



72000000 55 



Optics, p. 83. 8vo. (apudoper. torn. iii. 347. torn. iv. p. 56. 

 Ed. Horfl.) or Smith's Optics, book ii. chap. 6. (vol. i. 

 p. 39.) where thi'i propofition is demonftrated. That objefts 

 fhould appear through telefcopes fo diftinft as they do may 

 feem furpriiing. Newton accounts for the faft by obfcrving, 

 that the rays are not uuifomily difperfed over the whole circu- 

 lar fpace ; in the centre they are more denfe, and they become 

 more and more rare towards the circumference, and on this 

 account they are not viilble, except thofe of them that are in 

 or near the centre. 



In confequence of the difcovery of the unequal refrangibi- 

 lity of light, and the apprehenfion, that equal refraftions 

 muft pAduce equal divergencies in every fort of medium, it 

 was imagined, that all fpherical obietf-glafTes of telefcopes 

 would be equally afFeftcd by the different refrangibility of 

 light, in proportion to their aperture, of whatever materials 

 they might be conftrufted ; and therefore, that the only im- 

 provem.ent of which refratling telefcopes were capable, was 

 that of increal'ing their length. On this account Sir Ifaac 

 Newton, and others after him, defpairing of fuccefs in the 

 manufafture and ufe of refrafting lenfes, direfted their chief 

 attention to the conftrutlion of reflecting telefcopes. How- 

 ever, about the year 1 747, M. Euler apphed himfelf to the 

 fubjeft of refi-attion, and purfuing a hint fuggefted by Sir 

 Ifaac Newton, formed a fcheme of making objeft-glalfes 

 with two lenfes of glafs, inclofing water between them ; 

 hoping, that by conflrufting them of different materials, the 

 refrattions would balance one another, and prevent the ufual 

 aberration. Mr. J. Dollond, an ingenious optician of Lon- 

 don, examined this fcheme, and found that M. Euler's princi- 

 ples were uniatisfaftoiy. M. Clairaut likwife concun-ed in 

 opinion, that his fpeculations were more ingenious than ufeful. 



This controverfy, which promifed to be of great import- 

 ance in the feience of optics, engaged the attention of M. 

 Klingenftierna of Sweden, and induced him carefully to exa- 

 mine the eighth experiment in the fecond part of Newton's 

 Optics, with the conclufions which he draws from it. He 

 found, that the rays of light, in the circumftances there fup- 

 pofed, did not lofe their colour, as Sir Ifaac imagined. 

 This hint of the Swedifli philofopher, led Mr. DoUond to 

 re-examine the fame experiment ; and it appeared, after ac- 

 curate triiils, ttuit difl'erent fubftances made the light to di- 

 verge very differently, in proportion to their general refraftive 

 power: therefore, in the year 1757, he procured wedges of 

 different kinds of glafs, and apphed them together, fo that 

 the refrattions might be made in contrary dlreftions, in 

 order to |difcover, whether the refraftions and divergency of 

 colours would vanifh together. The refult of his firft trials 



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encouraged him to pcrfevert; for he difcovercd a dlfferfnec 

 far htyond his hopes in the refractive qualities of diHerent 

 kinds of gals, with refpcdl to their divergency of colours. 

 The Venice glals^aiid the Englifli crown glafs were found to 

 be nearly allied in this refpcd ; the common Englilh p!:itc 

 glafs made the light diverge more, and the Englidi Hint 

 glafs molt of all. Without enquiring into the caufe of this 

 difference, lie proceeded to adapt wedges of crown glaf«, 

 and of white flint glafs, ground to different angles, to each 

 other, fo as to refract in different directions, till the refiadted 

 light was entirely free from colours. Having ineafiiicd the 

 refraftions of each wedge, he found that of the while glafs 

 to be to that of the crown glafs nearly as iivo to ihree; and 

 he deduced this general conclufion, that any two wedgcj, 

 made in this proportion, and applied together fo as to re- 

 fraft in contrary directions, would refrait the light without 

 any aberrnUon of tlie rays. Mr. Dollond's next objedl was 

 to make limilar trials wilh fpherical glaffes of diflerent ma- 

 terials; and he found that, in order to obtain a refraftion of 

 light in contraiy diredions, one mull be concave, and the 

 other convex; the latter, which was to refratl the molt, 

 that the rays miglit converge to a real focus, was made of 

 crown glafs, and the former of white flint glafs ; and, the rc- 

 fraflions of fpherical glaffes being in an inverfe ratio of their 

 focal diifances, it was necefiary that the focal dillanccs of 

 the two glafles fhould be inverfely as the ratios of the refrac- 

 tions of the wedges; for being thus proportioned, eveiy ray 

 of light that paffes through this combined glafs, at any dif- 

 tance from its axis, will conftantly be refrafted by the dif- 

 ference between two contrary reflations, in the proportion 

 required; and therefore the different refrangibihty of the 

 light will be entirely removed. 



But in the applications of this admirable difcovery to prac- 

 tice, many d'Hiculties occurred. At length, however, by 

 repeated trials, and refolute perfevei-ance, Mr. Dollond fuc 

 ceeded fo far as to conftruft refracT:ing telefcopes much fu- 

 perior to any that had before been ufed; reprefenting objects 

 with great diflinftnefs, and in their true colours. 



M. Clairaut, who interefted himfelf betimes in this dif- 

 covery', endeavoured to afcertain the principles of Mr. Dol- 

 lond's theory, and to lay down rules for facilitating the con- 

 flruftion of thefe new telefcopes. With this view he made 

 feveral experiments, in order to deteniiine the refractive 

 powers of different kinds of glafs, and the proportion m 

 which they feparated the i-ays of light ; and from thefe ex- 

 periments he deduced feveral theorems and problems of ge- 

 neral ufe. M. D'Alembert likewife made a great variety of 

 calculations to the fame purpofe; and fhewed how to cor- 

 reft the errors to which thefe telefcopes are fubjtcf, by 

 placing the objeft-glaffes, in fome cafes, at a fmall diilance 

 from one another, and fometimes by uling eye-glafles of dif- 

 ferent refi-aftive powers. But though foreigners were here- 

 by fupplied with the mofl accurate calculations, they were 

 very defeftivc in praftice. The Englilh telefcopes, made, 

 as they imagined, without any exaft rule, were greatly fu- 

 perior to the befl of their conilru6tion. 



M. Euler, who fu-fl gave occalion to this important and 

 ufeful inquiry, was very reluftant in admitting Mr. Dol- 

 lond's improvements, becaufe they militated again 11 a pre- 

 conceived theory of his own. At lafl, however, convinced 

 of their reality and importance by M. Clairaut, he afTcntcd ; 

 and foon after received farther fatisfa&ion from the experi- 

 ments of M. Zeilier, of Peterlhurgh. 



M. Zeiher demonftrated, that it is the lead, in the com> 

 pofition of glafs, wliich gives it this remarkable property ; 

 fo that, while the refraftlon of the mean rays is nearly the 

 fame, that of the extreme rays confiderably diflers ; and by 

 increafing the lead, he produced a kii.d of glafs, which oc- 



cafioiied 



