TELESCOPE. 



In this and the (Ix preceding tables, the radn are calcu- 

 lated for an aperture of three inches for a focal diftance ot 

 thirty inches ; and the optician who may ufe any of them, 

 with fimilar glafs, may incrcafe or diminini his aperture 

 accordingly as the focal length is greater or lefs than thirty 

 inches. .. 



If we examine and compare the refpeftivc radn r and K, 

 and alfo V and 'R of the convex and concave lenfes m the 

 preceding tables, whlcli are all calculated by the fame pro- 

 cefs that ii ufcd by TuUey, and feveral of which have been 

 ufed in pradicc, we {hall' perceive that a difference in the 

 quality of the glafs, as to difpt-rfive and refrafltve powers, 

 makes the curves of the lenfes widely different ; and that a 

 fmall alteration in the affumed value of ;•, the firft face of 

 the convex lens, alfo produces a great alteration in the 

 curves of the three other faces of the compound objeft- 

 glafs. For inftance, if we compare the radii in Table I. 

 with thofe in Table VI., where r is affumed equal, toz. 7. J, 

 in both, and where the fame crown-glafs is ufed, and the 

 fint-glafs alone taken different, the former being No. 2. 

 and the latter No. I ; the radii in the former are /- = 7.5, 

 R = 11.63, 'R = 10.43, ^"^ ''' = 20.86, in a telefcope of 

 thirty inches focal length ; whereas in Table VI. there is r = 

 7.5, as before, but R :^ 22.34, 'R = 14.56, .-mdV= 30.58; 

 vhich curves are very widely different. And if we compare 

 Table II. with Table VII., in both which r is again 

 affumed equal, as well as the crown, wiiilc the two flints are 

 rei'erfed, viz. the former having No. I. and the latter 

 No. 2, the comparifon will ffaiul thus in telefcopes of 

 thirty inches focal length : in Table II. there is r — 9.00, 

 R = 14.92, 'R = 13.06, and'r =r 40.15; but m Table VI I. 

 r = 9.00, as before, while R is — 9.24, 'R = 9- 1 3) aid 

 '/• 1= 29.30. Hence it is maiiifcft, that it is not only u/ele/s 

 but detrimental to copy the radii of a double objeft-glafs of 

 even the beft telefcope that ever was made by any artift, 

 unlefs the refraRi'ae and difperfme powers of both forts 

 of glafs be precifely the fame, in the given and propofed 

 telefcopes intended to be equally good : but when different 

 fpecimens of glafs are neceffarily ufed by different artifts, it 

 is hardly to be expefted that both the requifite qualities of 

 each piece of glafs will be found alike, or even fufficiently 

 near a perfcfi: fimilarity, to authorife the copying of the 

 radii of a ftandard telefcope, even if thofe radii could be 

 meafured by mechanical means with fuflicient accuracy ; 

 but the meafurement from the folar focus of a lens, as is 

 ufual, does not afford data for obtaining the geometrical 

 focus, and from it the radii of curvature, unlefs the quantity 

 2 a be previoully known ; though the converfe operation, 

 we have before feen, is not difficult to a praftical optician. 

 We have no hefitation, therefore, in condemning the praftice 

 of analyfing a telefcope for the purpofe of copying it ; for 

 it is the certain guide to irrational conilruftions ; and 

 feldom will an inftrument fo made be free from either 

 colours or indiftinftnefs. 



Neither is it fafe to copy tables, fuch as thofe publifhed 

 by Dr, Brewfter, in his edition of Fergufon's Leftures, of 

 which the forms are alfo given under the article Achro- 

 matic Telefcopes, (in the Edinburgh Encyclopaedia,) until 

 the fpecimens of glafs to be ufed are afcertained to have 

 the^ fame refraaive and difperfme powers, as thofe from 

 which the tables are calculated. On comparing thefe tables 

 with the refults of profeffor Robifon's calculations, given 

 in the Encyclopxdia Britannica under the article Tele- 

 scope, we find not only that the bafis of thefe tables is 

 derived from this fourcc, but that the calculations them- 

 felves are adopted, without further modification than what 

 ii neceffary for adapting them to given focal lengths of the 



compound objeft-glafs. As profeffor Robifon's article on 

 our prefent fubje£t has hitherto been confidered to be the 

 only article in our language that has difclofed the fteps by 

 which an achromatic objeH-glafs may be conftrufted direftly 

 from mathematical calculations ; it will be fatisfaftor)' to 

 our readers that we fhould try what curves will refult from 

 TuUey's praftical mode of proceeding, w-hcn the fame data 

 are taken that Robifon has ufed in one of his examples. 

 In an example worked according to Bofcovich's formula, 

 the ratio of m : n in the crown-glafs is taken as 1.526 : I, 

 and in the flint, fo high as 1.604 : l ; while the ratio of the 

 difperfive powers, when converted into the proper terms, are 



I 



only in the ratio i : 1.65, or I : — ; let us fee what 



' .6054 



will bo the curves of a thirty-inch telefcope, when r is 

 affumed =z 9.7, and R = 954, according to Dr. Brewller's 

 Table VI., derived from Robifon's numbers 0.32325 x 

 30 = 9-6975. a"d 0.31798 X 30 = 9-5394- 



As r is greater than R in this affumption, the convex 

 lens is in its worft pofition, and the fpherical aberration, Ai 

 determined by the general theorem of Huygens, will be 

 1.682 X T : and as the geometrical foci of the two lenfes 

 mufl: be direftly as their difperfive powers, and as T and 

 'T are inverfely as thofe foci, we fliall have 1.682 x 1.65 

 r= 2-775 ^'"" '^^ proportional aberration 'A uncorrefted ;. 

 then as the correfting number, for flint of 1.599 : I, which 

 is the molt denfe that TuUey has met with, is .826, we may 

 take this without apparent error for that of 1.604 • ' > '^"'i 



2.77 ? 



= 3.26 = 'A is the correSed aberration of the 



then 



.826 



concave ; and according to this aberration, the root of the 



2r R 



quadratic will give 'R : V as I : 5.40 ; and by theorem 



the rational focus will be 



2 X 5.40 X I 



+ R 



= 1.68S ; then 

 5.40 X I 



having r = 9.7, and R = 9.54, by the fame theorem 

 we have F of the convex = 9.618, and F x 1. 65 =r 

 15.8697 = 'F, or focus of the concave. Alfo we have 



' = 9.401 = 'R, or fhorter radius of the concave ; 



1.688 



and 9.401 X 5.4 = 50.76 = 'r, or longer radius of the con- 

 cave. Lafl;ly, to obtain the compound focus <I), we muft 

 reduce the geometrical focus of each lens into its refrafted 

 focui, by the proper divifors i .052 for the crown, and 1.208 



for the flint ; then we fhall have =0.14 for the re- 



1.052 



frafted focus of the convex, and ' — i ^04 for the 



1.208 



F X 'F 



refrafted focus of the concave ; and by the theorem -= •- 



'r — r 



thefe numbers will give 



9.14 X 13.04 



= 30-53 



*. 



13.04-9.14 



We have now obtained numbers that will enable us tq 

 form the defired comparifon ; thus, according to Robifon^ 



r = 9.7, R = 9.54, 'R = y.54, V = 47.47 ; 



but according to Tulley, 



r = 9.7, R — 9.54, 'R = 9.4c, V = 50.7. 



Alfo, according to Robifon we have F = 9.618 and 

 'F = 13.25 geometrical, and the compound focus* — 29.1. 

 But according to Tulley, F :r: 9,618 and 'F = 15.8697 

 geometrical, while the coropeund focus * = 30'53' 



2 Now 



