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XXIII. Astronomical observations and experiments , selected for 
the purpose of ascertaining the relative distances of clusters of 
stars , and of investigating how far the power of our telescopes 
may be expected to reach into space , when directed to ambiguous 
celestial objects. By Sir William Herschel, Knt. Guelp. 
LL.D . F. R. S. 
Read June 11, 1818. 
In my last paper on the local arrangement of the celestial 
bodies in space, I have shown how, by an equalization of the 
light of stars of different brightness, we may ascertain their 
relative distances from the observer, in the direction of the 
line in which they are seen ; and from this equalization, a 
method of turning the space-penetrating power of a telescope 
into a gradually increasing series of gaging powers has been 
deduced, by which means the profundity in space, of every 
object consisting of stars, can be ascertained, as far as the 
light of the instrument which is used upon this occasion will 
reach. This method has already been applied to fathom the 
milky way, and may with equal propriety be used to ascertain 
the profundity of globular and other clusters of stars in 
space ; I shall therefore make use of some of the numerous 
observations, contained in my journals and sweeps of the 
heavens, to show how the distances of these objects may be 
obtained ; and shall also attempt to represent their situation 
in space by a figure, in which their distances are made pro- 
portional to the diameter of a globular space, sufficiently large 
