a Refracting Telescope with ajluid concave lens. 329 



have, when the colour vanishes, - — — = b. 



Where / =: focal length plate lens 



f = focal length fluid lens ; i 



d z= dispersive ratio 

 d = distance of the lenses 

 Or calling/ — d zn nf z=. remaining focus of plate beyond the 



fluid, this becomes ^ = d (1) 



or/' = y (2) 



If now we cally the resulting focus from this combina- 

 tion, reckoning from the fluid, we have by common principles 

 1 a 1 



I = ^^ ~ ^JT/' ^^ f= "^^^^^ ^^"g^^ ^^) 



From which equations all the relations between these six 

 quantities, viz. ff%f", f^^\ n, and d are readily determined; 

 where it may be observed that /' is the focal length of a te- 

 lescope on the usual construction to which this telescope is 

 equivalent, and / the whole length. of the tube. 



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



/ = • = plate focus (6) 



n — I —. n 6 ^ 



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



It is obvious from this last equation, since n and / may be 

 assumed at pleasure, (at least within all practicable limits,) that 

 I 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 ex- 

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

 that the secondary spectrum is reduced as the lenses are open- 

 ed, or as n decreases, but that the general field is enlarged and 

 improved by increasing the value of n. 



