1888 - 89 .] Sir W. Thomson on Constitution of Matter. 721 
On the Equilibrium of a Homogeneous Assemblage of mutually 
Attracting Points (§§ 62-71). 
§ 62. The chief object of this communication is to find the simplest 
possible way of realising, by means of an assemblage of points act- 
ing upon one another with forces in the lines joining them, and 
depending merely on the lengths of the joining lines, an elastic 
solid which shall not be subject to Poisson’s restriction of the bulk- 
modulus to be exactly -f of the rigidity-modulus ; but which may 
on the contrary have, with given rigidity, any magnitude of bulk- 
modulus through the whole range from - of the rigidity to + oo, 
shown to be imaginable by Green. That the thing can be done I 
showed in my Baltimore Lectures (1884), and I gave an easily con- 
ceived although a somewhat complex way of doing it. I now find 
that the next-to-the-simplest-possible mode of arranging an assem- 
blage of points to produce an elastic solid realises Green’s ideal; 
while the very simplest possible is restricted by Poisson’s 
limitation. 
§ 63. The simplest possible arrangement of points to make a homo- 
geneous elastic solid, is a single homogeneous assemblage as defined 
in § 45 a-d above. In the first place, for simplicity we shall suppose 
it to be elastically isotropic, or as nearly isotropic as we can make it. 
§ 64. To make the solid as nearly as may be isotropic, the unstrained 
equilibrium distribution must be the equilateral homogeneous assem- 
blage of § 21 above. Consider now a finite assemblage containing a 
very great number of points thus distributed. To take the very 
simplest possible case, let there be no force exerted between others 
than nearest neighbours. For the case of equilibrium, no force acts 
from without on any of the points, whether on the boundary or in 
the interior; and therefore clearly there is no mutual action between 
any of the points according to our present supposition of forces 
between nearest neighbours only. Suppose now the assemblage to 
he in equilibrium under the influence of forces acting on points in 
the boundary, giving rise to infinitesimal deviations from the equi- 
lateral homogeneous grouping. Instead of zero force in each 
shortest distance, there will now he a force which, for stability of 
equilibrium, must be pull or thrust, according as the distance is 
greater or less than that which we had in the zero-equilibrium. 
