714 Proceedings of Royal Society of Edinburgh. [sess. 
§ 50. In the close homogeneous assemblage of globes, we may first 
remark, that each globe is touched by its neighbours, at twelve points, 
being the points in which its surface is cut by diameters parallel to 
the six edges of the tetrahedron. If we place a number of small 
globes (hoys’ marbles, or billiard balls) on a table in close triangular 
order, and three as close as they can be together above them, we see 
nine of the twelve points of contact on the ball below the middle of 
the triangle of these three ; six points on the circle in which it is cut 
by a horizontal plane through its centre, and three symmetrically 
ranged on a small circle above it. The other ends of the diameters* 
through these three are the remaining three of the twelve. Or if 
we join the upper three by great circles, making a spherical triangle 
of 60° side, and complete these circles, they make another spherical 
triangle of 60° side, whose angular points are the lower three of the 
twelve contact points. The three great circles thus drawn cut the 
horizontal great circle in the first six points. Thus we see that the 
* In the compound assemblage of two homogeneous assemblages described 
in the preceding footnote, there are twelve points of contact on each globe, of 
which nine are placed as those described in the text for the homogeneous single 
assemblage, and the remaining three are not “at the other ends of the 
diameters” as described in the text, but are at the opposite points of the small 
circle on which lie the ends of the diameters referred to. 
