1888-89.] Sir W. Thomson on Constitution of Matter. 701 
§ 27. In this theory* it is shown that in an elastic solid constituted 
by a single homogeneous assemblage of Boscovich atoms, there are 
in general two different rigidities, n , w 15 and one hulk-modulus, k ; 
between which there is essentially the relation 
3k = ?>n + 2 n v 
whatever he the law of force. Here n Y denotes what are called the 
diagonal rigidities, and n the facial rigidities relative to the primi- 
tive cube of § 53 below. By facial and diagonal rigidities relative to 
any given cube I mean rigidities defined in the usual manner,! one 
of them according to shearing parallel to any face of the cube, the 
other according to shearing in planes parallel to any plane-diagonal 
of the cube. 
§ 28. A remarkable result of my mathematical investigation is, 
that the facial rigidity, relatively to the primitive cube of § 52, 
is double the diagonal rigidity in the case in which each atom ex- 
periences force only from its twelve nearest neighbours. The law of 
force may he so adjusted as to make n^ii] and in this case we 
have 3 k — 5n, which is Poisson’s relation. But no such relation is 
obligatory when the elastic solid consists of a homogeneous assem- 
blage of double, or triple, or multiple Boscovich atoms. On the 
contrary, any arbitrarily chosen values may he given to the bulk- 
modulus and to the rigidity, by proper adjustment of the law of 
force, even though we take nothing more complex than the homo- 
geneous assemblage of double Boscovich atoms above described. 
Boscovichian Kinetic Theory of Crystals , Liquids , and Gases. 
§ 29. The most interesting and important part of the subject, the 
kinetic, must, for want of time, he hut slightly touched in the 
present communication. I hope to enter on it more fully in a 
future communication to the Royal Society of Edinburgh. 
§ 30. To avoid circumlocutions, I shall call any velocity moderate , 
which is comparable with the maximum velocity acquired by two 
atoms attracting one another from rest, at distance I. It is the 
velocity that in the circumstances each would have when their 
* See §§ 62-71 below. 
+ Thomson and Tait’s Natural Philosophy, 2nded., vol. i. part 2, §680; also 
reprint of Mathematical and Physical Papers , vol. iii. art. xcii. part 1. 
