4 Mr. Barlow on the Refracting Telescope. 



/:/':: S : y 

 as stated in the first page of this paper. 



2. If /=/' 



we have A = 1, which is Mr. Rogers' correcting lens. 



3. If / : /' :: 1 + S : 1 + $' 

 the denominator vanishes, and A is infinite. 



And between these limits lies an immense range of disper- 

 sive powers, almost entirely unexplored ; and out of which a 

 well directed course of experiments could not fail of eliciting 

 many valuable practical results. 



If the lenses are both positive, the expression becomes 



/*(! + *') +/*'(! + *) _ A . (2 ) 



In this case A can never become zero, but it must neces- 

 sarily fall between the two values of and $', and will conse- 

 quently be less than the greater of the two. 



The above deductions, it will be observed, relate only to the 

 red ray, but by everywhere changing into d, and &' into d' t 

 they apply equally to the violet ray. The expression (I) there- 

 fore, for the violet ray, with a positive and negative lens, is 



and with two positive lenses it is 



'(l-d) _ A 



The former, of course, becomes zero when 

 /:// :: ddd' : d'-dd', 



which, rejecting as before dd ', as inconsiderable, gives as in the 

 red ray 



f:f':d:d f :: &V&V/ 



It follows from these formula? and equations, that although 

 in two media we should have 



$' = d' y and 5= d, 



yet, as the combination of the red ray with the mean, would 

 require the proportion 



/:/' :: (! + $')* : (! + $)*' 

 and the combination of violet ray with the mean, the proportion 



/:/' :: (!-*')* : (I-*)*' 

 we see at once, in this change of sign from + to , the origin 



