1888-89.] Sir W. Thomson on Constitution of Matter. 715 
twelve points are the intersections of four great circles, which divide 
the spherical surface into eight equilateral triangles, and six squares ; 
all with arcs of 60° for boundaries. Fig. 3 shows an orthogonal 
projection of these circles on the plane of one of them; each an 
ellipse whose minor axis is J of its major axis. The eight equi- 
lateral spherical triangles are abc, ahg', bfh ' , cgf, a'b'c', ali'g , b'fh, 
cg'f. The six squares are begh calif , abfg', b'cg'h, calif, a'b'fg. 
§ 51. Draw planes through the centre of the sphere, parallel to the 
pairs of planes of the angular points of the eight spherical triangles ; 
these are four planes, the four planes in which the assemblage is 
found in close triangular order. They are parallel to the sides of 
the tetrahedron A BCD. 
§ 52. Draw planes through the centre of the sphere, parallel to the 
pairs of planes of the angular points of the six spherical squares ; 
these are three planes, the three planes, in which the assemblage is 
found in square order. They are parallel to the pairs (AB,CD), 
(AC,BD), (AD,BC) of the edges of the tetrahedron ; and are 
mutually orthogonal. 
§ 53. Take a cube of the assemblage, having its sides parallel to the 
planes of § 51. It will present on every side, arrangement of the 
globes in square order, with rows along and parallel to the diagonals 
of the square sides of the cube. This I call the primitive cube of 
Fig. 4. Fig. 5. 
a homogeneous assemblage of closely packed globes. It is seen in 
fig. 4 taken from a paper published in Nature (Dec. 20, 1883), by 
Mr Barlow, who, so far as I know, was the first to show a cubic 
part of the close-packed homogeneous assemblage of equal globes. 
§ 54. Bevel the corners of the primitive cube perpendicularly to its 
four line- diagonals as shown for one only of the corners bevelled in 
