128 Proceedings of Royal Society of Edinburgh. [sess. 
2. Take six fine straight rods, and six straight tubes, all of the 
same length, the internal diameter of the tubes exactly equal to the 
external diameter of the rods. Joint all the twelve together with 
ends to one point P. Mechanically this might be done (but it 
would not he worth the doing) by a ball-and-twelve-socket 
mechanism. The condition to he fulfilled is simply that the axes 
of the six rods and of the six tubes all pass through the one point 
P. Make a vast number of such clusters of six tubes and six rods, 
and, to begin with, place their jointed ends so as to constitute an 
equilateral homogeneous assemblage* of points P, P' . . . . , each con- 
nected to its twelve nearest neighbours by a rod of one sliding into 
a tube of another. This assemblage of points we shall call our 
primary assemblage. The mechanical connections between them do 
not impose any constraint ; each point of the assemblage may be 
moved arbitrarily in any direction, while all the others are at rest. 
The mechanical connections are required merely for the sake of pro- 
viding us with rigid lines joining the points, or more properly rigid 
cylindric surfaces having their axes in the joining lines. Make 
now a rigid frame, G, of three rods fixed together at right angles to 
one another through one point O. Place it with its three bars in 
contact with the three pairs of rigid sides of any tetrahedron, 
(PP', P"P"'), (PP", P'"F), (PP"', FT') of our primary assem- 
blage. Place similarly other similar rigid frames, G', G", &c., 
on the edges of all the tetrahedrons congener f to the one first 
chosen. The points 0, O', 0", &c., form a second homogeneous 
assemblage related to the assemblage of Ps, just as the reds are re- 
lated to the blues in § 69 of the Article referred to in the footnotes. 
3. The position of the frame G — that is to say, its orientation 
and the position of its centre O (six disposables) — is completely 
determined by the four points P, P', P", P"' (Thomson and Tait’s 
Natural Philosophy , § 198; or Elements, § 168). If its bars were 
allowed to break away from contact with the three pairs of edges of 
the tetrahedron, we might chose, as its six co-ordinates, the six dis- 
tances of its three bars from the three pairs of edges; but we suppose 
it to be constrained to preserve these contacts. And now let any 
* See “Molecular Constitution of Matter,” §§ 45 (a) . . (j), Proc. Boy. Soc. 
Edin. for July 1889, to be republished as Art. XCVII. of Yol. III. of my Papers. 
+ Ibid., § 13. 
