SOR 
II. On Normal Piling, as connected with Osborne Reynolds’s 
Theory of the Oniverse. By Prof. J. D. Everett, 
PG... 
ROF. O. REYNOLDS’S theory was set forth in an 
elaborate paper communicated to the Royal Society in 
Feb. 1902, and accepted for the Transactions. It is published 
as a separate volume of about 250 quarto pages, under the title 
“The Sub-Mechanies of the Universe.” It is briefly summarised 
‘in the Rede Lecture for 1902, which is published as a small 
book, with excellent pictorial illustrations, under the title “On 
an Inversion of Ideas as to the Structure of the Universe” 
(Camb. Univ. Press). Its fundamental supposition is that 
the universe consists of equal small and perfectly hard 
spherical grains, arranged for the most part in the manner 
usually adopted for piles of shot, hence called by Prof. 
Reynolds NoRMAL PILING. As a knowledge of the structure 
of such piles is essential to an intelligent discussion of the 
theory, and is unfamiliar to most students of physics, I propose 
to commence by giving a full description of it. 
When 4 equal spheres touch one another, their centres are 
at the 4 corners of a regular tetrahedron. ‘The tetrahedron 
has 6 edges, each joining the centres of a pair of spheres ; 
and if the 4 spheres are a portion of a normal pile, each of 
these pairs belongs to a continuous line of spheres in contact, 
extending all through the pile. The whole pile can thus be 
resolved in 6 different ways into parallel lines of spheres in 
contact. Every sphere in the interior of the pile belongs to 
6 of these lines, and is therefore touched by 12 spheres, at 
the opposite ends of 6 diameters. Its centre is the meeting- 
point of the vertices of 8 of the tetrahedrons; and the gaps 
between these tetrahedrons would be exactly filled by 
6 square pyramids ; all the 8 edges of a square pyramid 
being of the same length as an edge of a tetrahedron. 
The pile can be split up into planes of spheres, either 
parallel to the base of a square pyramid, or to any face of a 
tetrahedron. In the former case the spheres in the plane 
layer are in square formation, so that each touches 4. In the 
other case the spheres in the plane tier are in triangular 
formation and each touches 6, whose centres are at the 
corners of a regular hexagon. This last is the arrangement 
which gives the closest possible packing of spheres in plano. 
The tiers which have this formation are parallel to a face of 
the fundamental tetrahedron; and as a tetrahedron has 
A faces, we have our choice of 4 ways of splitting up a normal 
pile into tiers of closest formation. 
* Communicated by the Physical Society : read April 22, 1904. 
