278 
rOPULAR SCIENCE REVIEW. 
regions — a northern and a southern — so markedly, that the dis- 
tribution of stars within these regions is richer than the 
distribution over the rest of the heavens, in the proportion of 
about five to two. 
3. The stars of these orders are associated in the most 
intimate manner with the Milky Way, insomuch that when the 
Milky Way is included with the two rich regions above-named, 
it appears that stars in the single division thus formed are dis- 
tributed about three times as richly as over the remaining 
portion of the heavens. 
These results cannot be regarded as due to mere chance-dis- 
tribution, unless we are to forget all the rules which the 
science of probabilities lays down for our guidance in such 
cases.* And if once we admit that they result from real laws 
of aggregation, our estimate of the nature of the sidereal system 
is wholly altered. We see at once that we are not dealing 
with a system that can be gauged ; for if within the limits of 
naked-eye vision there exist these aggregations and these 
lacunce , we may be full sure that throughout the sidereal 
system they exist also, and what confidence can we have in 
any system of gauging applied to depths so diversely occupied ? 
Our sounding-line may light on a rich stream or clustering 
aggregation of stars, or it may pass through relatively vacant 
spaces, yet we can by no means conclude from the richness of 
the one region or the poverty of the other, that the line reaches 
either very far off or relatively very near the limits of the 
sidereal scheme. 
Again, regarding either of the rich regions referred to above 
as consisting wholly or in part of a definite aggregation 
of stars happening to lie relatively near to us, is it not abun- 
dantly evident that other such aggregations at different orders 
of distance would exhibit many of the features which we see in 
the nebulae, and have been in the habit of associating with 
regions lying beyond the sidereal system ? Or — to arrive at a 
similar conclusion from different evidence — if the Milky Way be 
• The effect of numbers in diminishing the probability of such signs of 
law resulting from mere chance-distribution, must here again be insisted 
upon. It is most important to notice how it bears upon the conclusions we 
are to form. Here is a simple illustration of the law of probabilities in 
question. — Suppose we toss a coin 4, 8, 12, and 16 times, and inquire what 
is the chance that in the several cases either heads or tails will preponderate 
in the proportion of 3 to 1. Now the exact mathematical solution of this 
problem shows that when 4 trials take place, the chance is f, or more than \ 
when 8, the chance is or less than J ; when 12, the chance is 5 2 6 fl ~,or little 
more than * ; while when 16 trials take place, the chance is reduced to ■£££& 
or less than ^ . The chance would become indefinitely small if, instead of 
16, we took several thousand trials. 
