696 Proceedings of Royal Society of Edinburgh. [sess. 
lines, the partitional polyhedron to which it leads is a parallele- 
piped. 
§ 12. If the three points chosen are nearest neighbours of P 
(§ 45 i below), we are led to the best conditioned (or least oblique) of 
all the infinity of parallelepipedal partitions possible. This is the 
most obvious and the best known of the periodic partitions of space. 
§13. Taking the parallelepipedal partitioning of §11, let P' he 
the farthest corner from P, so that PP' is the longest diagonal of the 
parallelepiped. Let PA, PB, PC he conterminous edges and A'P', 
B'P', C'P' their opposites conterminous in P'. Draw the planes 
ABC, A'B'C'. We thus divide the parallelepiped into three parts — 
an octohedron ABCA'B'C' ; and two tetrahedrons, PABC, P' A'B'C', 
which are parallel mutual perverts (footnote on § 45a below). 
This grouping of eight points of a homogeneous assemblage is, as 
we shall see later, important in the dynamics of molecular structure, 
or at all events in Boscovich’s theory.* 
On Boscovich’s Theory (§§ 14-44 and §§ 62-71). 
§14. Without accepting Boscovich’s fundamental doctrine that 
the ultimate atoms of matter are points endowed each with inertia 
and with mutual attractions or repulsions dependent on mutual 
distances, and that all the properties of matter are due to equilibrium 
of these forces, and to motions, or changes of motion, produced by 
them when they are not balanced; we can learn something towards 
an understanding of the real molecular structure of matter, and of 
some of its thermodynamic properties, by consideration of the static 
and kinetic problems which it suggests. Hooke’s exhibition of the 
forms of crystals by piles of globes, Navier’s and Poisson’s theory of 
the elasticity of solids, Maxwell’s and Clausius’ work in the kinetic 
theory of gases, and Tait’s more recent work on the same subject — 
all developments of Boscovich’s theory pure and simple — amply 
justify this statement. 
§ 15. Boscovich made it an essential in his theory that at the 
* Theoria Philosophise Naturalis redacta ad unicam legem virium in natura 
existentium, auctore P. Rogerio Josepho Boscovich, Societatis Jesu, nunc ab 
ipso perpolita, et aucta, ac a plurimis prseeendentium editionum mendis ex- 
purgata. Editio Yeneta prima ipso auctore prsesentm, etcorrigente. Yenetiis, 
mdcclxiii. Ex Typographia Remondiniana superiorum permissu, ac privi- 
legio. 
