A REFRACTING TELESCOPE WITH A FLUID CONCAVE LENS. 35 



Where / = focal length plate lens 



y = focal length fluid lens 



5 = dispersive ratio 



d = distance of the lenses 

 Or calling / — d = nf = remaining focus of plate beyond the fluid, this 

 becomes ^ — g n") 



or y' = ^ (2) 



~ 8 

 If now we call/" the resulting focus from this combination, reckoning from 



1 s 1 



the fluid, we have by common principles —j, —j, = -^ 



Whence /" = -^^ = resulting focus (3) 



Consequently/'" = ^£ = equivalent focus (4) 



/ = (" - ^_- " ^)/= whole length (5) 



From which equations all the relations between these six quantities, viz. 

 /}/'}/ "^/'"j ^} ^^^ ^ ^i"^ readily determined ; where it may be observed that/'" 

 is the focal length of a telescope on the usual construction to which this tele- 

 scope is equivalent, and I the whole length of the tube. 



If we consider I, n, and h as given quantities, we have 



from which/',/", and/'" may be determined. 



It is obvious from this last equation, since n and I may be assumed at 

 pleasure, (at least within all practicable limits,) that this form of telescope 

 will admit of great variety of proportions between the different quantities, and 

 that some classes of these have a practical advantage over others may be 

 reasonably expected. From the experiments I have made, it appears to me 

 that the secondary spectrum is reduced as the lenses are opened, or as n de- 

 creases, but that the general field is enlarged and improved by increasing the 

 value of n. 



f2 



