35 
Ordinary Meeting, November 3rd, 1885. 
Professor W. C. Williamson, LL.D., F.RS., President, 
in the Chair. 
“ On the different arrangements in a state of maximum 
density of equal spherical granules,” by P. F. Gwythee, 
M.A. 
Imagine the spheres to be initially in a state of minimum 
density consistent with being in contact with surrounding 
spheres, and then imagine the spheres moved in layers into 
positions of greater density. This can be done in different 
ways. 
First, letting the spheres in each layer remain in the 
position of minimum density, let the alternate layers be 
shifted till the centres occupy the positions 1, 2, 3 in the 
accompanying diagram A, and call the different states Ai, 
A2, A3. 
We will consider the volume of the parallelepiped formed 
by joining the centres of eight spheres, which originally 
form the angular points of a cube, as the element of volume 
Pkoceedings— Lit. & Phil. Soc.— Vol. XXV.—No, 3.— Session 1885-6, 
