718 Proceedings of Royal Society of Edinburgh. [sess. 
45°* in the triangular pyramid obtained by truncating the obtuse 
trihedral angle of Iceland spar perpendicularly to the “ axis ” (or line 
equally inclined to the three edges meeting in the trihedral angle). 
Hence if, instead of globes to begin with we take oblate ellipsoids 
of revolution, each having its equatorial diameter J 8 (= 2*83) 
times its polar axis, and make a pyramid of them by laying a 
number of them flat on a horizontal plane and putting them to- 
gether and building others up on them according to the rule of § 56, 
we have an obviously conceivable structure for Iceland spar. This 
is Hypothesis (1). 
This Hypothesis I now find was given 200 years ago by Huyghens 
in his Traite de la Lumiere (Leyden, 1690), and independently by 
Wollaston in the Bakerian Lecture for 1812, Philosophical Trans- 
actions Royal Society for the year 1813, Part 1, but with priority 
attributed to Huyghens. I had thought of it independently, but 
did not feel altogether satisfied with it, in the first place because of 
the great internal commotion which it would imply in the tactics of 
Baumhauer’s twinning. Then it occurred to me to think of the 
subject thus. It seems as if the aeolotropic quality of Iceland spar, 
according to which there are differences of quality for directional 
actions along and perpendicular to the shortest line-diagonal of the 
rhomb, may be naturally supposed to depend on the rhomb not being 
a cube ; and that the change from a cube to the Iceland spar rhomb 
should be looked to as the cause of the seolotropy. If this is so we 
must begin with a cube which is isotropic in respect to its four line- 
diagonals. This is the case with the cube described in § 53, but it 
is not the case with the cube which we find if in the shrinkage! of 
Hypothesis (1) we pause at the stage in which the acute trihedral 
angle of the equilateral tetrahedron is rectangular on its way to be- 
coming obtuse ; on the contrary, in this configuration each globe is 
* At ordinary temperatures the angle is 44° 36'’6 (Phillips, Brooke, and 
Miller’s Mineralogy, § 407); and at temperature 300° it is almost exactly 45°. 
Huyghens must have taken it as exactly 45°, as he gave \/8 for the ratio of 
the equatorial to the polar diameter in the statement of his hypothesis. 
t The shrinkages to pass from the equilateral triangular pyramid to the 
pyramid with rectangular vertex and to the triangular pyramid for Iceland spar, 
will be understood in a moment by remarking that the tangents of inclinations 
of slant sides to base in the three cases are respectively \/8, v% and 1 ; and 
therefore the distances of vertex from base are as these numbers, the base being 
unchanged in the simple shrinkage specified in the text. 
