1888 - 89 .] Sir W. Thomson on Constitution of Matter. 713 
the given ellipsoid. Every possible configuration of closest homo- 
geneous packing of the given ellipsoids is clearly to he thus found ; 
and is specified in terms of three independent variables, — the three 
orientational coordinates, relative to the equilateral tetrahedron of 
the system of rectangular lines. 
§ 48. In §§ 46, 47 we have a solution of the problem given four 
points , 0, P, Q, R, not in one plane , to place con-orientationally four 
equal and similar ellipsoids with their centres at the four points , and 
the surface of every one touching the surface of each of the three 
others. From it we have the following perfectly simple construction 
for the answer. Bisect OP, OQ, OR, in F, G, H, and QR, RP, PQ, 
in F', G', H', and join FF', GG', II H'. These three lines meet in one 
point S. The planes GSH, HSF, FSG are parallel to conjugate 
diametral planes of the required ellipsoids. These ellipsoids touch 
one another in the points F, F', G, G', H, H'. To construct them, 
first make four parallelepipeds, having a common corner at S, and 
their half-edges which meet in S, and their- centres, as follows : — 
Half-edges. 
SF 
SG 
SH 
SG 7 
SIT 
SF 
Inscribe within the twelve edges of each parallelepiped an ellipsoid, 
touching them at their middle points. This construction is interest- 
ing as showing, in the middle points of the twelve edges of the 
parallelepiped, the twelve points of contact of the ellipsoid with its 
twelve next neighbours. 
The ellipsoid touching the twelve edges is, it need scarcely be 
remarked, similar to the inscribed ellipsoid touching the surfaces, 
but of J 2 times the linear dimensions. 
§ 49. To understand the configuration of a closely packed homo- 
geneous assemblage of ellipsoids, it is convenient to consider the 
assemblage of globes to which it is reduced by strain (geometrical 
distortion), in § 46. The assemblage of ellipsoids has all characteristic 
features the same, except the inequalities of lines and angles involved 
in the distortional transition from one configuration to the other. 
Centres. 
Half-edges. 
Centres. 
I 
SH' 
) 
- o 
SF' 
r 
f 
SG 
SF' 
I 
i p 
SG' 
y e 
f 
SH 
( 
