for ascertaining the distances of clusters of stars , &c. 4% 
Jar manner of its appearance of any cluster of stars in a 
finder or in a small telescope of any known gaging power is 
ascertained ; and when also by any superior instrument its 
profundity in space has been assigned, so that it maybe reduced 
to the station at which it would be visible to the eye, it may 
then be viewed with any telescope of which the space-pene- 
trating power is known ; and if we put e for the power of 
the eye,/ for that of the telescope which acts the part of the 
finder, p for the ascertained profundity of the cluster, and S 
for the space-penetrating power of a superior telescope, then 
will the extent E of this telescope to reach the same cluster, 
as an ambiguous object of any required appearance, be had 
by the formula E = 
It will not be necessary to calculate, by this formula, the 
order of distances at which in large telescopes some of the 
clusters of stars would be seen like telescopic comets ; others 
as large stellar nebulae, and others again as ill defined stars 
surrounded by nebulosity, as all these appearances must fall 
within the compass of the full stretch of their power ; I shall 
therefore only add a calculation of the ambiguous visibility of 
one of the very distant clusters of stars. 
The 75th of the connoissance is not visible to the eye, but 
may be seen in the finder ; and the telescopic observations of 
it have ascertained its profundity to be of the 734th order ; 
the station to which it should be brought, that it might be 
visible to the eye, is therefore of the 183.5th order. From 
this it follows, that with any telescope which has the space- 
penetrating power of the front view of my 20 feet reflector, 
this cluster might still be perceived if it were removed to the 
