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POPULAR SCIENCE REVIEW. 
by handfuls, and both hands full,” and each increase of power 
adding fresh riches to the display. According to the Herschelian 
hypothesis, there is but one explanation of these wonders ; we 
are looking into a widely extended part of the sidereal system,, 
and those different orders of stars lie at different orders of 
distance — the farthest at distances so enormous that we cannot 
attain to them. But, in what a different light we must regard 
the scene if we remember the possibility that that wondrous 
wealth of stellar display need by no means argue enormous 
extension. All these sparkling orbs may be gathered into one 
region of space, their various orders of apparent lustre arguing 
various orders of real magnitude. Instead of looking into 
star-lit depths, which extend linearly from the eye, far out into 
space beyond the ordinary limits of distance separating from 
us the outer bounds of the sidereal system, we may in fact be 
contemplating a wondrously variegated star-group. 
But the conclusions we are to form must be founded not on 
the consideration of what may be, but on our observation of 
what is. There is abundant evidence for forming probable 
views respecting the general laws prevailing within the sidereal 
system ; at any rate, for deciding whether it is more probable 
that there is or not any general uniformity of distribution 
within its limits. 
One direct consequence of the laws of probability has been 
very much lost sight of in dealing with the subject we are now 
engaged upon. It has been urged that where so many stars 
are spread over the heavens, at so many various distances, we 
ought not to be surprised if very great varieties of distribution 
should be observed, nor conclude, therefore, that the general 
uniformity predicated by Sir William Herschel may not pre- 
vail as respects distribution in space. It has been forgotten 
that the vastness of the numbers in question should tend to a 
uniformity of apparent distribution, instead of the reverse. 
I had been led myself to overlook this consideration, obvious 
as it is, until it was impressed upon me in a very striking 
manner during a somewhat novel process of research. 
I wished to determine what peculiarities of distribution 
might be expected to appear among a number of points spread 
over a plane surface perfectly at random. It is clear that this 
is a preliminary consideration very necessary for the purpose of 
determining whether the laws of distribution seen among the 
stars are accidental or not. Now, the problem of determining 
by purely mathematical considerations what peculiarities would 
probably appear in a chance distribution of any given number 
of points, is one which may be regarded as altogether too 
difficult for solution. Very simple problems of probability 
have been found perplexing, insomuch that two eminent ma- 
