1888 - 89 .] Sir W. Thomson on Constitution of Matter. 717 
edge of the base, there are three lines of globes in contact along the 
lines bisecting the three vertical angles of the sides of the pyramid 
and ending in the single crowning globe. 
§ 56. If instead of building the second layer as in § 55, we place 
a second layer over all the black dots ( ° ), a third layer over all the 
white dots ( ° ), a fourth layer over centres of globes of the first 
layer, a fifth over black dots ( * ) again; a sixth over white 
dots ( ° ), and the last a single globe as in § 55, we make an 
ordinary triangular pyramid having three equilateral triangles for its 
slant sides and a fourth for base ; and having the globes arranged 
in equilateral triangular order not only in the base as in § 55, but 
also in each of the three slant sides. 
§ 57. The ordinary square pyramid of globes has for its base the 
same square order structure as the slant sides of the triangular 
pyramid of § 55, while its four slant sides have the same equilateral 
triangular structure as each of the three slant sides and the base of 
the pyramid of § 56. If we divide the ordinary square pyramid 
into four parts by two diagonal vertical planes through its centre, 
and turn one of these parts over till it rests on its triangular slant 
side, it becomes the triangular pyramid of § 55. 
§ 58. In considering Baumhauer’s splendid discovery of the arti- 
ficial twinning of Iceland spar, by means of a knife, published 
about 22 years ago, soon after Beusch’s fundamental discovery 
(1867) of the artificial twinning of Iceland spar by pressure, I 
endeavoured to picture to myself the molecular tactics called into 
play in the wonderful change of shape thus produced. It was 
necessary first to suppose known the molecular arrangement in the 
natural crystal. Two distinct hypotheses presented themselves, 
each perfectly definite ; and it seems certain that the structure is 
one or other of these two. 
Hypothesis (1). — Imagine an equilateral tetrahedron of a close 
packed homogeneous assemblage of globes. To avoid circumlocution 
let one of its faces rest on a horizontal plane. Let the whole system 
be shrunk homogeneously in lines perpendicular to this plane till 
the originally acute trihedral angle of the triangular pyramid of 
globes becomes the obtuse trihedral angle of the rhomb of Iceland 
spar. The shrinkage ratio required to do this would be exactly 
JS to 1 if the inclination of each slant face to the base were exactly 
