TELESCOPE. 



Neither is it dofireable, in a };ootl achromatic objc dt-gl^ifs, to 

 ulc varnifh of any defcripliou, a» has bceu rccommciidrd. 



As \vc have iheun tliat profeflor Robifon's data, and the 

 calculations foinided on them, do not produce curves proper 

 for an acliromatic double objcdt-j;lafs, we will conclude this 

 pai-t of our I'ubji tt by examinuig if his calculations for a 

 triple objeil-t-glafs are any better adapted for praflice. In 

 Dr. Brewller's Table V. (Appendix to his edition of 

 Fergufon's Lectures, vol. ii. p. 418.) a thirty-incli triple 

 objeA-glafs is calculated, according to profeflor Robifon's 

 report of the radii ufed by the London artills, to have 

 r= 18.84, (printed by milhike 18.34,) R = 22.47, V and 

 'R each 17.37, and the fecond convex tlie fame as tlie firll ; 

 where, as before, the ratio m :.n in the crown is taken as 

 1.526 : I, and in the flint as 1.604 • '» ^nd the ratio of the 

 difperfive powers as l : 1.65. If thefe numbers will make 

 an achromatic objeCl-glafs, we fliall have i : 1.65 :: F : 'F 

 exaftly ; /'. e. the ratio of the difperfive power will alfo 

 be the ratio of the geometrical focal diflaiiccs, agree- 

 ably both to theory and practice ; but we iiave, by the theo- 



2 )• R 2 X 18.84 X 22.47 846.6696 



'■^" r^TR' • - 



In like manner, any number of tables might be com- 

 puted for tlie focal lengths of a triple objefl-glafs, where 

 the l^nfes have given refraftive and difperfive powers, and 

 where the radii aflumcd for one of the lenfes are taken at 

 pleafure ; but it will be always defireable to fix on a 

 concave lens firft in a triple objeft-glafs, notwithftanding we 

 hare fhewn that it is better to affume a convex one firft, 

 where a double obje£t-glafs is calculated : for by attending 

 to this direftion, the optician will find that countcrading 

 aberrations will be within his reach ; and though he may 

 fix on radii in the affumed lens that will not be the beft in 

 praftice, yet, by changing the ratio of the afliimed radii, he 

 will find prafticable lenfes that will anfwer his purpofe. 

 In our tables of triple objeft-glafTes, the numbers come out 

 very convenient for praftice ; for in each, both fides of the 

 convex lenfes have longer radii than either face of the 

 concave has got, fo that there will be no point of contaft, 

 in the middle of any of the curves, when they are placed 

 contiguous to one another ; and in Table IX. there is juft 

 difference enough, between the radii of each of the convex 

 glafles, to allow one of them to be reverfed, if it is found 

 that the errors of workmanlhip, or imperfeftion of the 

 glafs, ftiould require fuch corretlion, when the objeft-glafs 

 comes to b^- finally adjufted. Indeed all the furfaces might 

 be calculated to be a little different from one another, and 

 then there would be the option of eight changes in the final 

 adjuftment : but if the glals is homogeneal, and the work 

 well pecformed, it will always be found beil to adhere to the 

 pofitions for whicli the lenfes have had their radii calculated. 



5 



18.84 + 22.47 



41-43 



= 20.495 



for the focus of one convex lens, and therefore — - = 



2 



10.247 for the compound focus of the two ; alfo we have 

 tlie focus of the concave = 17.37 in the table, the radii 

 being equal; hence we have as i : 1.65 :: 10.247 : 16.90, 

 inftead of 17.37 ; therefore the objeft-glafs is not tluly cor- 

 reSed for the prifmalic aberration. This conclufion, which 

 is intelligible by every common reader, corroborates our 

 former inference reipeCling the want of achromatifm in the 

 double obje£l-glanes made from Robifon's calculations ; 

 but let us purfue the enquiry a little farther, and fee what 

 focal diftancc will accord with thefe numbers : tiie refrac- 

 tive power of the convex being .604 = a, we have — ^— 5- 

 =: 9.74 for the refraBcd iocM^ ihtreoi ; and the refradtive 

 power of the concave being .526 



'F X F 



17.^7 

 b, we have — ■■ •; ■ = 

 2 b 



14.38 for its refrafted focus, and by our theorem , 



, 14.38 X 9.74 140.0612 ^ 



= *, we have — l^^- ^~- = -^—^ = 30.18, &c. for 



14.38 - 9.74 4.64 



the focal length of the objeft-glafs ; which is much nearer 

 to the propofed length than the focus of the double objoft- 

 glafs was wliich we before examined. If we calculate tliis 

 triple objeft-glafs according to our method, as pradifed by 

 Tulley, we mull begin with 16.9 as the proper focus for the 

 concave, of which we difregai'd the negative fign, as of no 

 importance in our mode of calculating ; we fliall then have as 

 1.65 : 1 :: 16.9 : 10.247, and this ratio muft not be com- 

 promifed, on any confideration, as being the achromatic ratio, 

 on a fuppofition that the rcfradive and difperfive powers, as 

 above ftated, are in natural proportion ; then as the radii V 

 and 'R are affumed equal, the aberration of the concave will be 



1.666 X T, and z = .826; therefore -■,-> = 1.376 = 'A 



.020 



correfted; and — ^— = .834 = A of the fubftituted fingle 

 1.65 



lens E, which, as before, is an impolTible quantity to be in 

 one lens ; but this being doubled, will be 1.668 x T for the 

 proper quantity of each lens ; or multiplied by 4, will be a 



proper 



