37 
In the case A3 these centres are the angular points of a 
network of regular octohedra, the centres grouping them." 
regularly in sets of 6. 
In the case Bg these centres are the angular points of 
regular tetrahedra, the centres falling into sets of 4. But 
taking a part of the diagram as far as it relates to 3 
adjacent layers, we see that they may be related in either 
of the two ways shown in the figures 1 and 2 — ■ 
where the equilateral triangles in a plane join the centres 
of the spheres in a layer, the apices of the tetrahedra with 
full lines are the centres of the spheres in the upper layer; 
those of the dotted lines are the centres of the spheres in 
the lower layer. This subject was suggested to me by 
Professor Eeynolds’ paper “ On the Dilatancy of a Granular 
Medium,” read before the British Association at Aberdeen 
this year, and my object is to show that a given volume' can 
be filled with the same set of equal spherical granules in 
different ways, and that if even the boundaries were fixed 
and rigid the difference would amount only to multiples of 
a granule, and would not be expressed as a fraction of the 
whole mass. 
Note. (Nov. 4, 1885.) — In consequence of the remarks of 
Professor Eeynolds when this paper was read, I have 
reconsidered the question, and now find that the variation 
which I mentioned in the state Bg (shown in fig. 2) reduces 
it to the state Ag. This variation ought therefore to be 
omitted, but it shows how the two states may be combined 
and how passage may be made from one state to the other 
