TELESCOPE. 



ference being, that in Bofcovich's the lenfcs are of equal 

 convexity ; whereas, in the common improved aftronomical 

 rye-piece, the iinier lens has a longer focus than the outer 

 one, in the ratio of 3 : i, and being both plano-convex, they 

 both have their curved faces turned towards the objeft- 

 glafs. 



From the preceding experiments of the Dollonds, have 

 refulted all th- advantages that the achromatic refrafting 

 tclefcopes pofTefs over the long telefcopes with fimplc 

 objefl-glafTes, and wliich have put them in competition with 

 the beft refleftors in the eflential quahtics of power, light, 

 and diftinclnefs of vifion. There is, however, an iniper- 

 feflion, notwithftanding Dollond's great n<ill and perfever- 

 anco, which remains yet to be overcome, if it is not in- 

 vincible, which is, that while the colours occafioned by the 

 extreme rays are correfted with fufficient accuracy by the 

 compoinid objeft-glafs, yet the intermediate rays are not 

 perfeftly corrcfted ; and if any media can be fo modified as 

 to correft all the rays that fall on every point of the furface 

 of the objeft-glafs, fo as to make them unite at the fame 

 point in the hne of the axis ; then, and not till then, will 

 the objeft-^lafs be quite perfeft. Peter, the fon of John 

 DoUond, who, we have faid, fucceeded to his father's bufi- 

 ncfs, purfued this fubjeft after his father's death ; and in 

 the year 1765, communicated to the Royal Society by letter 

 the rofult of his experiments. He remarks, that when 

 his father had made objeft-glafles of one convex lens of 

 crown-glafs, and of one concave of flint-glafs, to be ufed 

 with convex eye-glaffes, it was found that the excefs of 

 aberration was in the convex portion of the com.pound 

 objcdl-glafs, and that the equaUty of the counterafting 

 aberrations could not be carried to any great diftance from 

 the centre of the glaffes ; he therefore attempted, about the 

 year 1758, to make {hort objeft-glafles of the fame fort, 

 to be ufed with concave eye-glafles ; but it was found, that, 

 as the field of view, in ufing a concave eye-glafs, depended 

 on the aperture of the objeft-glafs, the limits of the aper- 

 ture were too confined with a double objeft-glafs. This 

 trial led the fenior DoUond to a conclufion, which the 

 fon took up, and profited by ; namely, that the excefs of 

 fpherical aberration, occafioned by one double convex lens 

 of crown-glafs, might be diminifhed by fubftituting two 

 plano-convex lenfes of fimilar glafs and curves, placed one 

 at each fide of the double concave of flint-glafs. The 

 fenior Dollond had fucceeded with this conftruftion when 

 a concave eye-glafs was ufed, and when the compound focus 

 was fhort ; but it remained for the fon to complete a long 

 objeft-glafs of this conftruftion, to be ufed with convex 

 eye-glaffes ; which he fucceeded in doing, firft with a tele- 

 fcope of 5-fcet focus, and 3! inches aperture, and afterwards 

 with a 3H-feet one of the fame aperture, which he invited 

 the Royal Society to fee, and which was the prototype of 

 the numerous achromatic telefcopes of the fame dimenfions, 

 which have been fince conftrufted and difperfed by fale 

 through all the regions of the globe. 



Among the firft achromatic telefcopes made by P. Dol- 

 lond, was one purchafed by the due de Chaulnes, who ex- 

 amined very minutely the radii of the refpcftive glafles, and 

 publiftied an account of them in French meafures, which, 

 converted into Enghfti inches, will ftand thus ; 32.4 and 

 40.8 for the outer convex of crown-glafs j 22.2 and 30.6 

 for the double concave of flint ; and 30.6 with 35.5 

 for the inner convex of crown-glafs ; but as the gunlities 

 of the refpeftive glafl'cs are not fpecified, no ufeful in- 

 ference can be drawn for the conftruftion of another tele- 

 fcope, in which the glafs of each lens may be of another 

 quality. This telefcope, we learn from the prefent Mr. 



G. Dollond, had a focal length of 46 inches : and the five- 

 feet telefcopes fubfequently made, have each an aperture of 

 four inches : but the largeft and beft telefcope of the achro- 

 matic kind ever made by P. Dollond, is that of ten-feet 

 focus, and five inches aperture, lately converted into a 

 fuperb tranfit inftrument by Mr. Troughton, and placed in 

 Greenwich Obfervatory. See Transit In/lrumsnt. 



Soon after Peter Dollond's telefcopes began to be in re- 

 pute, namely, in the year 1759, Benjamin Martin, at the 

 fame time a mathematician and a mechanic, who had long 

 turned his attention to the conftruftion of telefcopes, and 

 defcribed various conftruftions, publifli:d his " New Ele- 

 ments of Optics," a book now, like Edwards's Treatife, 

 extremely fcarce, in which he has entered more minutely into 

 the doftrif! ' of both kinds of aberrations, as they relate to 

 praftice,'.han any other author ha", done, cither before or fince. 

 He not only followed the fteps of J. Dollond in determin- 

 ing by glafs wedges or prifms the relative refraftive and dif- 

 perfive powers of different fpecimens of glafs, but ground 

 fingle objeft-gkfles of feveral kinds of glafs, v/ith tools of 

 the fame radius, and then compared the geometrical foci of 

 each with the refrafted or real foci, by nice meafurements : 

 by this means he afcertained the difference between the focus 

 determined theoretically from t'ne known radius, and the 

 real or praftical focus of the refrafted rays in each glafs by 

 meafurement, confidering at the fame time the diftance of the 

 radiant point : and thus he gained, as we ftiall have occafion 

 to fliew more particularly hereafter, the ratio between the 

 fine of the angle of incidence and of the angle of refraftion 

 in each feparate fpecimen, which ratio, in a ray pafllng from 

 air into glafs, had been aflumed in all former optical theo- 

 rems as 3 : 2 in all kinds of glafs, and confequently the 

 focus for parallel rays had been put equal to radius in dou- 

 ble convex lenfes, and alfo equal to the diameter in fingle 

 convex, without regard to the quality of the glafs, with re- 

 fpeft to its refraftive power. The reS'tJication of the old 

 theorem, founded on the conftant ratio 3 : 2, formed the 

 bafis of the " New Elements of Optics," in which one half of 

 the difference between the old theoretic and the refrafted, or 



"p 



praftical foci was called a, and then — = F with parallel 



z a 



rays became the bafis of the reftified theorems, which we pro- 



pofe to give prefently in their proper place. According to 



thefe new elements, and from a meafurement of the angles of 



difperfion, or of the coloured fpeftra contained between the 



extreme rays, as given by a prifm of flint, and another of 



crown-glafs refpeftively, the ratio of which he determined 



to be as 5 : 3, he calculated that " the radii of the lenfes 



muft have the fame proportion as the differences of the fines 



of incidence and refraftion in red and violet rays, in prifms of 



equal refrafting angles of white and crown glafs ;" and that, 



therefore, " the radii [or foci] of the lenfes muft have the 



fame proportion as the angles of diffipation in refraftions by 



fuch prifms ; and, of courfe, the fame proportion as the lengths 



of the coloured fpeftra produced thereby." From thefe 



eonfiderations the author concludes, that " hi all cafes of a 



compound lens for producing vifion without colours, the 



ratio of the radii, r and R, of the concave and convex lenfes 



(when two only are ufed) muft be that of 5 : 3 ; and that 



then the ratio of their focal diftances for parallel rays will be 



that of 3 : 2 nearly. The ratio of the foci of two lenfes 



being thus determined that fhall make the colours vanifh, the 



longitudinal aberration arifing from the refpeftive curves 



was next confidered ; and in doing this, care was taken that 



the comparative foci of the two lenfes was not to be altered 



by an alteration in the curves now to be reftified. By Huy- 



gens's 



