TELESCOPE. 



frotn the gweral theorem of Huygens, we find A = 1.374 



X T.and 1.374 X 1.59 = 2.184 x 'T = 'A ratioual, which 



2.184 'A . 



is yet to be corrcded ; then -~ = — = 2.535, the cor- 



X 2 = J a = 1. 147, or a divifor for the flint ; sdfo 



1.623 



reded aberration. By getting the root of the quadratic arif- 

 ing from this aberration agreeably to the general theorem, as 

 before, the ratio of the radii '11 : V comes out i : 2.375. 



-— = .002 = F refrafted ; and 



1.088 ' 1-147 



1.415 = 'F 



2r R 



2 X I X 2.375 



Laftly, by the tlieorem ^^-^ we get , ^ ^^^^ 



= I.A07 = 'F rational, and i^^^ = 10.89 = 'R, and 



^^' i'407 



alfo 10.89 X 2.375 = 25.864 =.V. We have, therefore, 



R = ^IT.} -^ ^ - 9.643- 

 Hence the next table is fuitable for double achromatic 



F X 'F 

 refraded. Again, — — — = = 3.318 = <P rational; alfo 



V' .992' = X = .3124, and ( = -872 ) V -872' 



V1.147 / 



= y- 



wife — =^— 



47 

 V . 2 c 7 c 

 2575 ; whence — = — ^-^ — .824 = z. Like- 



•3124 

 = 9.03 = F, md 9.03 X 1.623 = 14-65 ='F. 



>-F „ , R 



2r -F = ^ = ■'•34. and — 



= 1.51, or r : R ;: i : 1.51 ; hence A, by the general 

 theorem of Huygens, =: 1.376 x T, and 'A ^1.376 x 1.623 

 = 2.233 X 'T = the aberration of the concave correded 



3-318 

 Put r = 7.5 ; then 



obiecl-glaffes of various focal lengtlis, where m : « in the for tlie difference of refradive power. The root arifing from 



crown-glafs is as 1.528 : i, and in the flint as 1.584 : i ; a quadratic equation of this aberration is 'r = 2.78, when 



and their refpedive difperfive powers as I : 1.590. _^ ^ , 2rR 



Table III Radii of double Objed-^glafles in Inches. 



'R = I, confequently =; 1-47' = 'F rational, and 



— — - =: 9.96 :=; 'F geometrical ; alfo 9.96 x 2.78 ;= 

 27.68 = 'F geometrical. Thus, 



R = 1 1^34 I ^ ^ 9.03 geometrical. 



>r = 27!68 } 'F = 14-65 geometrical. 



Table IV Radii of double Objed-glafles, with Lenfes 



of Plate and Flint, in Inches. • 



Example 4. — Let us next take an example, in which 

 plate-glafs is fubftituted for crown, and let the fines of the 

 angles of incidence and of refradion in it be as 1.504 : I, 

 while m : n in the flint is as 1.573 : i, and their difperfive 

 powers I : 1.623 ; and let the length of the telefcope be 



required to be 30 inches, as before ? Then — ^^^— x 2 



n 



= 2*7 = 1.008, is the divifor for the plate-glafs; and 



Exatr.pli 



