Mr. Barlow on the Refracting Telescope. 7 



It would extend this article to too great a length to enter 

 into the various cases that arise by giving different values to 

 n and/' in this expression. I shall therefore, simply for illus- 

 tration, take the particular case proposed by Mr. Rogers, in 

 which it is assumed that = ', the first and second lens being 

 both crown, and /=/'", the foci of the second and third lens 

 being equal : this gives 



/ ff'V . 





As an example, suppose the correcting lens to be placed at 

 half the focal length of the front lens ; and the focus of the 

 front lens n/= 84 inches, and that the correcting lens is com- 

 posed of crown and English flint glass, of which the relative 

 dispersions are as 2 to 3, that is = 2, S" = 3 and n = 2, con- 

 sequently, /= 42, we should have 



/' = 3 "" 2 x 42=10-25 inches, 

 4 



that is, the focus of each of the lenses forming the compound 

 correcting lens must be 10 inches, the whole length of the 

 telescope being 84 inches. 



As another example, let the correcting lens be composed of 

 crown and Faraday's glass, of which the relative dispersions 

 are as 10 to 19. Then we should have 



/>= 19-10 /- 18.9 inches, 



2x10 



that is, the focus of each of the correcting lenses must be 18.9 

 inches. 



Lastly, let the correcting lens be crown glass and sulphuret 

 of carbon, the relative dispersions being as 3 to 10. Here we 

 should have 



/'= 10 ~ 3 /=: 49 inches. 

 2X3* 7 



We see thus the great advantage of a high dispersive power 

 in this form of construction : for, in consequence of the depths 

 of the curves required in the first example, it would be prac- 

 cally impossible to take n greater, or at least very little greater, 



