98 
But on closer examination it is impossible to say what 
is meant. If the given volume is filled with the same 
set of equal spheres, the mean density must be the same 
however they are arranged or whatever the boundaries 
may be, so the difference referred to cannot be that of 
density ; it cannot be that of volume, for that is to be 
the given volume. 
Is it meant that a given volume can be filled in different 
ways with the same spheres provided the boundaries are 
variable, but if the boundaries are fixed and rigid the differ- 
ence of the number of spheres contained under the different 
arrangement would not be expressed as a fraction of the 
whole. 
If this is what is meant it is true, provided the number 
of spheres each way through the group is sufficient; and 
true not only for the two arrangements of max. densities 
to which the author refers, but for every possible arrange- 
ment of max. density to anything similar. But then, it 
has no bearing on the subject of dilatancy ; because it is 
impossible to pass from the one arrangement of max. density 
to another, with the boundaries fined. And to pass by any 
uniform distortion of the boundaries, or sliding of the layers, 
is impossible in the cases considered by Mr. Gwyther, and in 
any case it is impossible without passing through a condition 
of minimum or maximum density. This is at once evident 
from the model, but is difficult to express or realize by 
figures. 
At the end of the page (37) in the note, it is said, it 
shows how passage may be made from one state to another 
by the sliding of the layers. 
