1901-2.] Lord Kelvin on Molecular Dynamics of a Crystal. 217 
equilibrium is stable. Build up now a quasi infinite number of 
such cubes with coincident corners to form one large cube or a 
crystal of any other shape. Join ideally, to make one atom, each 
set of eight particles in contact which we find in this structure. 
The ■whole system is in stable equilibrium. The four forces in 
each set of four coincident edges of the primitive cubes become 
one force equal to the force between atom and atom at distance A. 
The two forces in either diagonal of the coincident square faces 
of two cubes in contact make one force equal to the force between 
atoms at distance A J2. The single force in each body-diagonal 
of any one of the cubes is the force between atom and atom at 
■distance A^/3. The three moduluses of elasticity (compressibility- 
modulus, modulus with reference to change of angles of the 
square faces, and modulus with reference to change of angles 
between their diagonals) are all easily found by consideration of 
the dynamics of a single primitive cube, or they may be found 
by the general method given in “On the Elasticity of a Crystal 
according to Boscovich.” * (In passing, remark that neither in 
this nor in other cases is it to be assumed without proof that 
stability is ensured by positive values of the elasticity moduluses.) 
§ 22. Now while it is obvious that our cubic system is in stable 
equilibrium if the eight particles constituting a detached primitive 
oube are in stable equilibrium, it is not obvious without proof that 
this condition, though sufficient, is necessary for the stability of 
the combined assemblage. It might be that though each primitive 
cube by itself is unstable, the combined assemblage is stable in 
virtue of mutual support given by the joinings of eight particles 
into one at the corners of the cubes which we have put together. 
§ 23. The simplest possible illustration of the stability question 
of § 20 is presented by the exceedingly interesting problem of the 
equilibrium of an infinite row of similar particles, free to move 
only in a straight line. The consideration of this linear problem 
we shall find also useful (§§ 28, 29 below) for investigation of the 
disturbance from homogeneousness in the neighbourhood of the 
bounding surface, experienced by a three-dimensional homogeneous 
assemblage in equilibrium. First let us find a, the distance, or 
one of the distances, from atom to atom at which the atoms must 
* Proc. R.S.L . , vol. 54, June 8, 1893. 
