connected with the Theory of the Universe. a7 
the balls, under the influence of the tendency to compression, 
form themselves into small clusters in different kinds of 
closest piling, there will be misfits at the junctions between 
such clusters, involving a waste of space; and adjacent 
clusters will fend to unite and become continuous, so as to 
occupy less room. Such union is most easily effected when 
the tiers of the two clusters are nearly parallel to begin with. 
If each of the two clusters has only one set of tiers (as in the 
‘ease of a cluster not in normal piling), these tiers are very 
unlikely to be nearly parallel. If each of them has 4 sets of 
tiers (as in normal piling) the probability is immensely 
increased. 
The tiers here spoken of are those in triangular formation. 
And the case is strengthened if we include tiers in square 
formation ; for of these each normal cluster has 4, and the 
other clusters have none. 
For these reasons, clusters in normal piling will unite 
together much quicker than other clusters. 
They will thus become larger than other clusters, and 
their increased size will add to the effectiveness of their 
6 sets of battering-rams. 
With these advantages in the struggle for existence, it 
appears to me feasible to maintain that, in the fortuitous 
clashing of a universe of grains, with free paths. gradually 
diminishing, normal piling would_ eventually become the 
prevailing system. 
Prof, O. Reynolds’s theory as it actually stands deals, not 
with remote histor y, but with the universe as it is ; and it 
supposes the great majority of the grains to be at present 
locked in their places, with no opportunity for change except 
at the surfaces of misfit. At these surfaces, the motion is so 
restricted that the stability of the formation does not seem 
to be seriously threatened. et 
I have not made any attempt to verify the elaborate 
statistical calculations with which Prof. Reynolds’s paper 
abounds ; and in the parts of the paper that I have read 
carefully, several conclusions are drawn which to me are not 
obvious, but appear very questionable. 
My present purpose is not controversy, but explanation ; 
and the style of the paper is so excessively technical that a 
good deal of explanation seems necessary before intelligent 
controversy can begin. I have chiefly aimed at an explanation 
of the geometrical conditions which underlie the system 
supposed ; thereby clearing the way for a more searching 
criticism, and helping towards the working out of the very 
fruitful suggestions which the theory contains. 
