Mr. Barlow on the Refracting Telescope. 5 



of that imperfection which is generally designated the secon- 

 dary spectrum ; that is, the same proportion, which combines 

 the red and mean rays, will not combine the violet and mean 

 rays, so that there is necessarily a certain quantity of uncor- 

 rected colour when the lenses are in contact, and the disper- 

 sions equal on each side the mean ray, and which, with crown 

 or plate and flint glass, is generally rendered worse by the 

 inequality of the values of ^ and d' in the latter ; the inequality 

 lying on that side which increases the evil : but I have shown 

 in a paper in the ' Philosophical Transactions' for 1828, that 

 by opening the lenses we have a certain command over the 

 artificial dispersion which offers at a least chance of complete 

 correction. 



If, in the above expression, we make/' =p/, and ' = m S, 

 it becomes 



- m(l-f-S) _ 



p (1+niJ) - 



In which A denotes, as before, the dispersion of the red ray 

 in the compound lens, that of the red ray in the plate or 

 crown lens, and m $ that of the other medium, whether it be 

 flint glass, Faraday's glass, or sulphuret of carbon : m and 

 are therefore given quantities, while p is assumable at pleasure 

 within all practicable limits. 



At present we have considered the lenses, whose compound 

 dispersion has been ascertained as being in contact ; let us 

 now inquire into the circumstances of the compound disper- 

 sion due to two lenses placed at a distance from each other. 



Let the focus of the first lens be nf, and let the cone of rays 

 from this lens be intercepted by a second lens at the distance 

 / from the focus of the first ; then n S/will be the coloured 

 focus of this first lens, that is to say, there will be all the 

 colour due to the focus nf, but reckoning only from the place 



of interception the focus being/, we shall have - i=- n $ the 



dispersion of this ray, estimated from the second lens : we have, 

 therefore, only to substitute n instead of S in our former 

 expression, and we shall thus obtain the value of the disper- 

 sion of the compound open lens, viz., in this case we shall have 



