TELESCOPE. 



gens's general theorem, the aberration arifing from the curves 

 of any lens may be determined and compated ; and it being 

 known from this theorem, that the longitudinal abeh-ation is 

 equal to ':ds of the thicknefs of a double convex lens of 

 equal radii, a double concave was determined from an equa- 

 tion of this aberration fuch, that its contrary aberration 

 might counteract the aberration of the alTumed convex lens 

 of equal radii ; and the numbers thus produced for tlie radii 

 of the double convex of crown-glafs, and of tlie double 

 concave of flint refpcclively, were 8.36, 8.36, 10, and 23 

 inches, in which the focal diltances of tlie two lenfes are faid 

 to be nearly as 2 : 3. In this combination, the compound 

 focus is ftated to be 23.3 inches, and the radius r = 22 

 is contiguous to the convex glafs. Other calculations were 

 alfo made where the radii of the convex lens were unequal, 

 as well as thofe of the concave, but we do not learn that 

 a good achromatic objeft-glafs, put together agreeably to 

 Martin's calculations, was ever yet conftrudled. In the in- 

 ftance before us, it is evident that the curve 8.36, coming in 

 contaft with the concave 23, muft touch it in the middle, 

 and therefore the proportions are imprafticable. 



While thefe various improvements in the conftruftion af a 

 telefcope were going on, we muft. not omit to mention that 

 different kinds of micrometers were applied to it fucceflively, 

 by different ingenious men, for the purpofe of meafuring 

 fmall angles ; by which addition, the fcience of aflronomy 

 has been greatly promoted. Among thofe promoters of this 

 noble fcience, may be enumerated|Auzout,Gafcoigne,Hooke, 

 Le Fevre, Kirchius, Caffini, Fouchy, HoUman, B. Martin, 

 Savery, J. Dollond, Dr. Maflcelyne, Ramfden, Dr. Her- 

 fchel, Smeaton, Rochon, Kjcftner, Cavallo, Troughton, 

 and Arago, the prefent aflronomer royal of France. 



But it remained for the ingenious optician of Iflington, 

 C. Tulley, to whom we are indebted for much valuable in- 

 formation on the fubjeft of our prefent inquiries, to calcu- 

 late and manufafture, from any two given fpecimens of 

 crown and flint glafs, a double objeft-glafs that fhall, gene- 

 rally fpeaking, be found both achromatic, and alio as free 

 from the effects of fpherical aberration as art can make it. 



After this artiil had made himfelf mafter of Martin's 

 propofed plan of compounding cm achromatic objeft-glafs, 

 he found that the curves calculated for this purpofe woidd 

 not produce their defired effeft with any fpecimens of glafs 

 that could be procured ; but ftill he thought that a careful 

 repetition of Martin's experiments might lead to refults fa- 

 vourable to his views, when fome modification was made in 

 their application. He therefore, in the year 1800, obtamed 

 fix forts of glafs, differing in fpecilic gravity, and ground 

 them all to the fame radius by a toolof fpeculiim metal, that 

 did not much alter its figure by attrition in grinding, and in 

 giving a partial polifh : thefe lenfes were fitted fucceflively 

 to one cell, that was received by a tube having an eye-piece 

 at the oppofite end, in order that the folar focus of the re- 

 frafted rays might be the more accurately meafured with 

 each glafs ufed as an objeft-glafs of a telefcope ; and though 

 the pohfh was imperfetl in thefe lenfes, ground and partially 

 polifhed by the fame tool, yet the image of the fun was 

 clearly defined by them. Thefe focal diflances, limited by 

 the folar image, were in the next place meafured carefully by 

 a nicely divided fcale, and were found to differ from one an- 

 other conliderably, as we fhall hereafter have occafion to 

 Hate more particularly : the radius of curvature of the tool 

 was alfo afcertained with equal care, and ft,und to exceed in 

 length the longeft of the focal lengths of the ref rafted rays. 

 The radius of the tool was then divided by each of the re- 

 frafted focal lengths, and the quotients were called fo many 

 divifors or multipliers, accordingly as tlic geometrical was 



to be determined from the rcfrafted focus, or the contrary. 

 Thefe quotients, therefore, bore the fame proportion to 

 unity, that the geometrical focus bore to the refrafted focus 

 of each lens, and turned out to be very nearly the fame quan- 

 tities that Martin had determined with glaffes of fimilar 

 qualities, and th.it he denoted by the exprefTion : n in his 

 reftihed theorems. In faft, they were the numbers from 

 which the ratio of the fines of tlie angles of incidrnce to the 

 fines of the angles of refraction were accurately determined, 

 as will be explained hereafter. The fpecific gravities of the 

 different lenfes were then taken with a good liydroftatic 

 balance, and were found to iiicreafe with their correfpond- 

 ing divifors, but not in a regular proportion. From thefe 

 experiments a fet of tables was conftrufted, containing in 

 parallel columns, both for crown and flint glafs, tlie fpecific 

 gravities, varying from 3.466 to 2.428, together with the 

 correfponding ratios of the lines of the angles of incidence 

 and of refraction ; and alfo the ratios of the two curves, 

 that fhall produce an alTigiied longitudinal fpherical aber- 

 ration in any lens ; all which calculations are extended from 

 the ratios 1:1,1: i.oi, i : 1.02, &c. in fucccflion, up 

 to 1:6, where the aberration is a minimum, as was long 

 ago determined by Huygens : and wliat is worthy of re- 

 mark, the French plate-glafs, wliicli had the fpecific gra- 

 vity lowefl, and its divlfor only 1.004, '""^ which, confe- 

 quently, had its refracted focus nearly equal to its geometri- 

 cal focus, was, in all probability, fimilar to the glafs manu- 

 factured at the time when the experiments of fir Ifaac New- 

 ton were made, from which the original optical theorems 

 were framed. From thefe tables, our Ikilful optician takes his 

 curves by infpeftion fuitable for glafs of any given fpecific 

 gravity, fuch as will fuit his tools for telefcopes of difl"erent 

 lengths ; and having as it were the command of the whole 

 range of varying ratios, he can immciliately fix on fuitable 

 curves for any glafs, and for any compound focal length, or 

 even afTign a fellow that fhall match any practicable lens, con- 

 vex or concave, that has been previoufly poliflied. Such is 

 the faciUty which this ingenious and perievcring optician has 

 attained in the highcfl branch of his art, whilll, at the fame 

 time, his fliill in grinding, pohfhing, and centering his glalfes, 

 is not exceeded by any other artifl. The principal deviation 

 from Martin's rules, that Tulley found it neceflary to adopt 

 in his practice, is the application of a corrt-iling number to the 

 calculated or tabulated aberration arifing from the figure of 

 the fiint-glafs, on account of its difference of refractive power, 

 as compared with that of the crown-glals : in order to gain 

 which correcting number in all different cafes, he firR reduces 

 the geometrical foci of the two feparate lenfes into the re- 

 fraCted foci by his divifor = Martin's 2 a, and extr.iCts the 

 fquare root of the cubes of thofe refraCted foci refpectively ; 

 then dividing the root of the flint-glafs by the root of the 

 crown-glafs, he gains the correSing divifor, by which the 

 calculated aberration of the flint-glais is divided, to pro- 

 duce the corrected aberration for the concave lens ; which lens 

 mull now have its radii determined agreeably to this cor- 

 rected aberration from the general theorem, or may be 

 taken from the tables to be fubflituted for the radii that 

 would have been requilite, if the proportional aberration had 

 remained uncorrected. And lallly, that the foci of the fepa- 

 rate lenfes may be fo proportioned to each other, and to the 

 compound focus of both the lenfes, which is ulually given 

 when a telefcope is to be made, the ratio between the tocus 

 of the crown-glafs and of the compound glafs, having been 

 calculated by an appropriate theorem, as will be explained, 

 is tabulated to fuit different forts of glafs agreeably to 

 their fpecific gravities ; fo that Martin's conflant ratio 

 of 5 : 3 is varied according to the variation of the fpe- 



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