62 On the UNEQUAL 
Ir appears from the preceding experiments, that in com- 
pound: object-glafles of crown and flint-glafs, there is only a 
partial correétion of the aberration from unequal refrangibi- 
lity, and therefore in them, and others of that kind, the aper- 
tures and magnifying powers muft only be increafed in a fub-_ 
duplicate ratio of the increafe of length, as in fingle lenfes. 
I writ not pretend to ftate with abfolute certainty the pre- 
cife aperture which an achromatic telefcope of a given length 
ought to have. This muft be determined by experience. If 
two inches be taken for the greateft aperture which ought to be 
given to a telefcope of this kind two and thirty inches long, 
then three inches will be too much for one of forty-two inches, . 
as hath been already obferved. But whichfoever of thefe - 
lengths and apertures be taken as the ftandard, it is certain, 
that if we would avoid a greater degree of that indiftinétnefs 
which is occafioned by the aberration from difference of refran- 
gibility, the aperture and magnifying power muft not be in- 
creafed in a greater proportion than the fquare root of the in- - 
creafed length. Befides, therefore, that this imperfect correc- 
tion renders fuch telefcopes incapable of bearing high magni- 
fying powers for thofe of moderate lengths, large inftruments, 
if they were to be attempted, would ftill be unmanageable, on _ 
account of their immoderate lengths. The focal length of an 
objedt-glafs of this kind, four feet in diameter, would require 
to be upwards of fifteen hundred feet, im order to enable it to 
bear the magnifying power adapted to that aperture, with the 
fame diftinétnefs that is found in an object-glafs two inches in 
diameter, and thirty-two inches in focal length. But when 
the aberration from difference of refrangibility is totally re- 
moved, the focal length of an objett-glafs four feet in diame- 
ter, need not exceed twenty feet. 
Havine mentioned to fome friends the imperfect correction 
of the aberration from difference of refrangibility, which 1s 
obtained by the common combination of two mediums: which 
differ 
