6 Mr. Barlow on the Refracting Telescope. 



for the red ray with a positive and negative lens, 



/'(I 

 for the violet ray, 



for the red ray, both lenses being positive, we shall have 

 f'n $(1+80 + /S'(l-f-rcS) - A . 



~7 r (l + ^)+/(l+7i^) 

 for the violet ray 



where it is assumed that the dispersion is equal on each side 

 the mean ray, as is the case in crown or plate glass, which is 

 the medium to which this principle is more particularly appli- 

 cable ; and here again, as we cannot completely answer both 

 conditions, so as to combine the red and violet with the mean 

 ray, we must, as in the case of the common double or triple 

 object-glass, take a mean value of A by rejecting n 3 and $ as 

 inconsiderably ; this reduces the expressions to 

 /nS/y _ A 



f'f 



the upper signs applying to the case of two positive lenses, and 

 the lower to a positive and negative lens. 



Taking this view of the subject, we must, in the combination 

 of two lenses to correct the front lens of an object-glass, con- 

 sider it rather as a combination of the two distant crown 

 lenses, to be corrected by the simple flint lens, at least this will 

 be the most convenient form for computation. For example, 

 the focus of the compound lens will be 



its dispersion = A ; and calling the dispersion of the flint I", 

 we have only to compute its focus f f " by the common analogy 

 adopted in the usual form of telescope, viz. 

 A : J" :: /" :/'" 



that is w = ^' *" 



