A REFRACTING TELESCOPE WITH A FLUID CONCAVE LENS. 
35 
Where 
Or calling f — d — nf — 
becomes 
f = focal length plate lens 
f = focal length fluid lens 
§ = dispersive ratio 
d — distance of the lenses 
remaining focus of plate beyond the fluid, this 
( 1 ) 
( 2 ) 
If now we call f" the resulting focus from this combination, reckoning from 
the fluid, we have by common principles ~ 
J_ _ J_ 
—f" 
Whence f" = ■ — • ^ = resulting focus (3) 
Consequently f'" = ~ e( l u ^ va ^ en ^ f° cus (4) 
l = ( n 11 ^ f — whole length (5) 
From which equations all the relations between these six quantities, viz. 
n, and l are readily determined ; where it may be observed that f" 
is the focal length of a telescope on the usual construction to which this tele- 
scope is equivalent, and l the whole length of the tube. 
If we consider l, n , and c> as given quantities, we have 
= plate focus 
n — 1 — n S 
( 6 ) 
from which and may be determined. 
It is obvious from this last equation, since n and l 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. 
