724 Proceedings of Royal Society of Edinburgh. [sess. 
§§ 45, 60) being considered each tetrahedron of reds is vacant of 
blue, and each tetrahedron of blues is vacant of reds.* 
§ 70. Imagine the springs removed and the struts left; but now all 
properly jointed by fours of ends with perfect frictionless ball-and- 
socket triple-joints. We have a perfectly non-rigid three-dimensional 
skeleton frame-work, analogous to idealised plane netting consisting 
of stiff straight sides of hexagons perfectly jointed in threes of 
ends. 
§ 71. Leaving mechanism now, return to the purely ideal mutually 
attracting points of Boscovich. 
The group is placed at rest in simple equilateral homogeneous 
distribution : — shortest distance £. It will be in stable equilibrium, 
constituting a solid with the compressibility, and the two rigidities 
referred to in § 27 above. Condense it to a certain degree to be 
found by measurements made on the Boscovich curve, and it will 
become unstable. Let there be some means of consuming energy, 
or carrying away energy ; and it will fall into a stable allotropic 
condition. The Boscovich curve may be such that this condition 
is the configuration of absolute minimum energy ; and may be such 
that this configuration is the double homogeneous assemblage of 
reds and blues described above. Though marked red and blue, 
to avoid circumlocutions, these points are equal and similar in all 
qualities. 
The mathematical investigation must be deferred for a future 
communication, when I hope to give it with some further develop- 
ments. 
* An interesting structure is suggested by adding another homogeneous 
assemblage, marked green ; giving a green in the centre of each hitherto 
vacant tetrahedron of reds. It is the same assemblage of triplets as that 
described in § 24 above. It does not (as long as we have mere jointed struts 
of constant length between the greens and reds) modify our rigidity-modulus, 
nor otherwise help us at present, so, having inevitably noticed it, we leave it. 
