connected with the Theory of the Universe. dd 
the edges of the base of our tetrahedron of reference. The 
other 3 are parallel to the edges which meet in the vertex of 
the tetrahedron; and as soon as we depart from normal piling 
these lines of spheres are broken. Moreover, in normal 
piling there are, in addition to the assumed set of parallel 
tiers, 3 other sets parailel to the 3 faces of the tetrahedron 
that meet in the vertex. In departing from normal piling, 
we twist these faces alternately one way and the other through 
60°, and thus destroy these 3 sets of parallel tiers. 
As regards the 3 sets of parallel planes containing sphere- 
centres in square formation, they have all disappeared. In 
place of the regular equidistant planes of this kind, we have 
to draw planes 3 times as close, if we wish to include all the 
sphere-centres ; the distribution of centres in each plane being 
in alternate stripes of greater and less closeness, the average 
closeness being of course one third of what it was in normal 
piling. 
If, instead of attending to the centres of the spheres, we 
attend to the tangent planes at every point of contact of 
2 spheres, we find that, in normal piling, each sphere is 
inscribed in a dodecahedron, whose faces are equal and 
similar rhombuses, the point of contact being in each case 
the centre of the rhombus. Space is thus partitioned into 
equal and congruent cells. The dodecahedron has 24 edges 
consisting of 4 sets of 6 parallels; and if we take a section 
across one of these sets, each of the two halves has the shape 
of a bees’ cell. If we rotate one half through 60°, the halves 
will still fit together ; and in their new position they form 
the dodecahedron in which each sphere is inscribed in anti- 
normal piling. 
According to Prof. O. Reynolds’s theory, the material 
universe (including ether as well as ordinary matter) consists 
of equal spherical grains, exactly alike, and infinitely hard, 
so that when they collide the rebound is instantaneous, without 
loss of kinetic energy. 
For the most part, their free paths are infinitesimal com- 
pared with their diameters ; and their packing differs only 
infinitesimally from normal piling, so that each grain is 
securely hedged in by its 12 neighbours, with extremely 
little room to disport itself between them. But though this 
is the prevailing condition, there are exceptional spots where 
there is a crack or loose joint in the piling, affording oppor- 
tunity for grains to pass across it, and thus partially change 
their neighbours. “Surfaces of misfit” is a name frequently 
applied to these places of weakness ; and according to the 
theory they are closed surfaces, approximating to the form of 
Phil. Mag. 8. 6. Vol. 8. No. 43. July 1904. D 
