TELESCOPE. 



nJ R = I, then the refult will be different, viz. 



108+12+7 



= tV> or nearly ^^ of T. The aberration 



6x9 



Jiere is more than in the former pofition, in the ratio of 

 127 : 67 ; and this is, therefore, called the woijl pofition ; 

 that being always called the iejl, where the firft furface has 

 a fhcK-ter radius than the fecond. If we fuppofe Icnfes of 

 unequal radii to have their focal diftances, their breadth, 

 and confequently their thicknefs the fame, it will be found, 

 by a fimilar procefs, that their aberrations will diminifli, as 

 R continues to exceed r, until /■ is to R as I : 6 ; in which 

 cojiftruftion of a lens, placed in its beft pofition, the aber- 

 ration will be a minimum, i<iz,. 44 of T ; but in its reverfcd 

 or woril pofition, the aberration will be ',V of the fame. 

 A fingle convex lens, in its bell poiition, has its aberration 

 only J of T ; but with the plane fide turned to the radiant, 

 in which r may be faid to be infinite, the aberration will 

 be 4 of T. Alfo a double convex, when its radii r and R 

 are to each other as 2 : 5, has the lame aberration as a fingle 

 convex in its beft pofition, and has lefs fpherical aberration 

 than any menifcus whatever ; but there is no proportion of 

 tlie radii of any one lens that will do away the fpherical 

 aberration altogether. If the refraftive power of any glafs 

 be fuch, that the fines of incidence and of refraftion are not 

 exaftly in the ratio 3:2, the calculated longitudinal aber- 

 ration will differ a little from the true one, fo as to require 

 a corredlion. And with refpeft to the lateral aberration, 

 if m be the fine of incidence, and n the fine of refraiftion zz: i, 

 where two lenfes have equal apertures and radii, then the 

 errors arifing from obliquity of incidence wall refpeftively 

 be as m ■ in one, to 'm ' in the other. 



Likewife, we derive from the foregoing demonilrations of 

 Dr. Smith the following general and important conclu- 

 fions : firfl, that in lenfes of equal apertures, the longitu- 

 dinal aberrations, arifing from figure, are inverfily as the 

 focal diftances (fee Cor. 2. of Prop. II. above quoted); 

 and fecondly, that under hke circumftances, the lateral 

 aberrations are inverfely as the fquares of the faid focal 



diftances (fee Cor. 3. oi the famr Prep.); and, on the con- 

 trary, that when the focal diftances arc the fame, and the 

 apertures differ, then the longitudinal aberrations are a» the 

 fquares (fee Cor. 4.), and the lateral as the cubes of thofe 

 apertures. The utility of thefe proportions will more fully 

 appear in the fequel. 



We proceed now to the moft important part of our 

 article, vi%. to fliew what means have been not only dcvifcd, 

 but praftically applied, for remedying the defeds arifing out 

 of thefe two different kinds of abeirations, and for rcndeniig 

 the apparent objctl, as viewed through a refra^ing telefcope, 

 at the fame time diftina and colourlcfs. Telefcopes of 

 what are called the acbromatic, (from a, priv., and x?="^. 

 colour,) or colourlefs kind, are compofed, hke other tele- 

 Icopes, of two parts requiring fcparate confideration ; a./z. 

 tiie objeft-glafs and the eye-tube : the former being that 

 which produces an image free from colours and miiUnefs; 

 and the latter that which either renders this image vifible, or 

 produces a fecondary one to be viewed, without the repro- 

 duftion of colours. But our prefent confideration is that of 

 the objeft-glafs. 



Before the working optician can proceed to prepare hit 

 tools for making an achromatic objeft-glafs, he mull know 

 the refraftive and difpcrfive powers of his glafs. Various 

 methods have been propofed for determining thefe qualities 

 with accuracy ; but it will be fufficient for our purpofe to 

 explain thofe which have been found moft prafticable. As 

 the ratio between the fine of incidence and the fine of refrac- 

 tion is conftant in the fame glafs, though not the fame ratio 

 in different forts of glafs, the moft certain method of deter- 

 mining this ratio in different fpecimens of glafs is, to grind 

 a piece of each of thofe fpecimens by the fame tool, as 

 Martin and TuUey have done, and then to compare their 

 refracled folar foci with the radius of curvature ; and thofe 

 which have the (hortefl refrafted foci, will have the grcateft 

 refraftive power ; and the contrary. We have already ex- 

 plaine'd, in the firft fedion of our article, how this operation 

 was condutled by Tulley in particular ; and we will now ilate 

 the refults of his experiments in the fubjoined little table. 



Refults of praftical Experiments on the refraftive Powers of different Specimens of Glafs, by C. Tulley. 



If we explain how the numbers in the horizontal column of grinding and partial polifhing, which was all that the 



of flint I. were obtained, the reft of the table will require no glaffes required for viewing the fun, and for adjuftment to 



further explanation. The tool on which the fix fpecimens the folar focus. The firft flint-glafs, after being thus formed 



of glafs were ground at the fame time, was of fpeculum to a curvature on both fides of 33.7 inches radius, equal to 



metal, and did not vary its fhape much during the operation that of the tool, was put into a tube and made into a tcm- 



4 porary 



