96 
It was also pointed out that the first was the mini- 
mum density and the second was the maximum density, 
and that between these there were several conditions 
maximinimum density, at one of which the density would 
be 
7T 
It was further stated and illustrated by a model that the 
group could be brought from any density between the 
maximum and minimum into any other by sliding each layer 
of spheres over the adjacent, 'i.e., by a homogeneous strain 
throughout the group. 
Nothing was said in the paper as to whether there was 
more than one arrangement which would result in maximum 
density. The model was such that its action showed that 
there must be two such arrangements, and that the group 
could not be passed from one to the other by a homogeneous 
strain, or general sliding of layer on layer uniformly through- 
out the group. 
It was stated in the paper that the general arrangement 
was one of octahedra and tetrahedra, and that in the case in 
which the centres of the spheres bounding the group were 
in plane surfaces, it was a simple geometrical problem to 
determine the density for any particular arrangement, and 
the dilation consequent on an alteration of the arrangement. 
The construction was not given, as it seemed sufficient to 
have pointed out the method. 
In a paper having the same title as this, Mr. Gwyther has 
discussed the subject of the possible arrangements to give 
maximum density in a manner which seems to be imperfect, 
