TELESCOPE. 



r 



NowasF :'F:: I : 1.65 (tlierefpeftivedifperfivepon'crs), 

 let us fee if either of thefe refults will make an achroma- 



tic telefcope : thus, as -J , ^„ ^^f- 



^ ' li : 1.65 :: 9.618 : 15.8697J 



which fiievvs that Tulley's foci are exadly as the Jifpcrfive 

 poiven, and therefore would be achromatic, if the dlfpctfive 

 power had been truly proportioned to the refractive power ; 

 but from long experience he knows, that the difperfive 

 power of flint-glafs of the greateft denfity, compiu-ed with 

 that of crown, which feldom varies, is not lefs than 1.759 • '• 

 Hence Robifon's difperiive power is in the iirft place taken 

 too low ; and in the next, allowing it to be truly taken, he 

 has not preferved the two feparate focal dillances in fuch 

 ratio, agreeably to that of the difperfive powers, as will 

 nmke an achromatic telefcope. And this is further proved by 

 the circuniilance, that the compound focus does not come 

 out exaftly 30, which it will always do by Tulley's procefs, 

 if the proportions are all rational. If we fubftitute the 

 ratio 1.759 • '• hiftead of 1.65 : I, for the difperfive power, 

 which Tulley's table of difperfive powers gives, to corre- 

 Ipciid with the refractive powers, when m : ?i as 1.599 • ■ • 

 and if we take the convex lens of Robifon in the worft po- 

 iition, as before, with r = 9.7, and R = 9-54) the radii of 

 the concave, by Tulley's mode of calculating, will be 

 'R = 9.65, and 'r — 68.04, and the compound tocus * = 

 25.6 ; with which curves and focal length the telefcope 

 would be achromatic, and truly correBed for fpherical aber- 

 ration ; but as R comes out a deeper curve than 'R, thefe 

 furfaces would come in contaft at the centre, and therefore 

 are not in a prafticable form. Hence we infer that the con- 

 ftruftion of an achromatic telefcope with Robifon's convex 

 lens in its -woifl pofition is impradticable, though a concave 

 might be determined to fuit it in its beft pofition ; w's. 

 when its faces are reverfed. There is, indeed, no form of 

 a double convex lens, but a concave may be calculated to fuit 

 it, provided the curves come out in a prafticable form ; but, 

 oi) the contrary, a concave may be fixed on that, in its worit 

 pofition, (which is always its pofition in a double objeil- 

 glafs, ) can have no convex that will match it. Martin has 



ihcwn, that if the aberration of a given concave be — x 'T, 



then 



'T 



whence a : b :. 

 A.a 



6 

 ^ T 



6.43 



4 a 



. = 6.42857 will be a minimum ; 







4:: i6:tonearly. Therefore, vrhen 

 is lefj than 6.43, the problem will be impofiible. For 



inftance, in a plano-concave lens, the aberration is J- of T, 

 and -J- X 4 = 4.66 only, which (hould not be lefs than 6.43 ; 

 and therefore this lens cannot be ufed fingly with a convex 

 of any defeription ; much lefs can a concave in its befl; 

 form, where ;•: R :: I : 6, be ufed; for its aberration 



4^1 



4.284 only. But either of thefe may 



-^ X i gives 

 14 ft 



be ufed in their worft pofition, becaufe then either of them 

 will have aben-ation enough for any convex. And this pre- 

 vious confideration will enable the Ikilful optici^'.n to fix on a 

 proper ratio of V : 'R, before he proceeds to his calculation. 

 Should it be aiked, why we prefer Tulley's difperfive 

 powers to profefTor Robifon's ? our anfwer is this ; that 

 Tplley's were not gained fimply by prifmatic meafurement 

 of the fpeftrum, like Robifon's, where fome errors are ob- 

 vioufly unavoidable ; but have been correfted by repeated 

 pomparifon of the focal lengths of the convex and concave 

 Jcnfes in the very beft achromatic telefcopes felefted for the 

 Vol, XXXV. 



purpofe, where, when a high magnifying power was ufed, 

 tlie leaft difcolouration would have been obferv.iblc ; and 

 as thefe foci are always in the fame ratio as the difperfive 

 powers, no other method of determining thefe powers can 

 have fimilar pretcnfions to accuracy. 



When the convex and concave lenfes are both ground and 

 poliflicd (fee Glas.s and Gkinding), they require fome care 

 in putting them properly into the tube, fo that they may 

 have their common axis coinciding with the axis of the cye- 

 glalfes, in order that every part of the field of view may 

 be equally diftinft and free from colour : and as there will 

 always be fome errors of worknianfliip, and as both lenfes, 

 but particularly the flint, may not be perfetlly homogeneal, 

 one of the lenfes muft be turned round in the common 

 cell, till the faults of one lens are obfcrved to correft 

 thofeof the other as much as pofiible ; which will be known 

 when the viiion is moft diftindt, or the objedl bell defined. 

 Should any colour remain about the edges of tlie objedt, 

 the prifmatic aberration is not correfted ; and if indif- 

 tinftnefs does not take place foon, and at equnl diftances 

 from the point of diftindt vifion, when the eye-tube is moved 

 in and out, the corredtion for fpherical aberration is not per- 

 fedt. A double object-glafs is much more cafily adjufted for 

 a good central pofition, and for the counteradtion of oppo- 

 fite errors of workmanlhip and imporfedlion of glafs, than a 

 triple one, and has moreover more light, in confequence of 

 having but four refledting furfaces ; but as it does not admit 

 of any change of the faces in the final adjuftment, the lenfes 

 require to be both truly calculated and nicely worked, in 

 order to make the pradtice correfpond with the theory ; 

 which is probably the reafon why triple objedt-glaffcs, that 

 admit of changes in their pofitions, ai-emo(t frequently made, 

 particularly for lliort telefcopes : befides, half a dozen of 

 thefe lenfes may be ground and polifiied at the fame time 5 

 whereas, for a double objedt -glafs, each lens requires to be 

 ground and polilhed feparately, and with the greateft 

 care. 



Triple achromatic Ohjed-glaffes After having explained 



the theory, and exemplified the conftrudtion of a double 

 achromatic objedt -glafs with great minutencfs, we come now 

 to treat of triple objedt -glaffes, that fhall have the achro- 

 matic property ; but it will not be neceftary to give fo many 

 examples, nor fuch minute explanation, as feemed requifitc 

 in our preceding part of this fubjedt, feeing that the cal- 

 culations for a triple objedt -glafs are grounded on thofe that 

 we have given for a double one, and do not materially differ 

 from them. It will, however, be proper to Ihew how the 

 compound focus of three lenfes is determined, before we 

 proceed to find the aphromatic proportions of the refpeflive 

 radii. 



Firft, we muft have recourfe to our fundamental theorem, 

 (of Table I. of theorems for the rcfradtive foci of lenfes,) 



11/s;. f = — = — — =-— , where p is the reciprocal of 



■' dK -\- dr — p^r -^ 



the refradting power of the medium employed, or of 

 , the meafure of that power, r and R the radii, as 



before, and d the radiant diftance. To apply this theorem 

 to a fyftem of glafTes, as B, C, D, &c. which we propofe 

 doing, it is convenient to fubftitute, for the general expref- 



fion — , the letters a, b, and e, as peculiar to each medium 



refpeAively. Supp ofing now our three lenfes arranged in 

 the order B, C, D, with B next the radiant objedt (as in 



