NORMAL SULPHATES OF POTASSIUM, RUBIDIUM, AND CESIUM. 
493 
axial directions, brought about by rise of temperature according to a rule common to 
all three salts, result in bringing two of the refractive indices to equality about the 
temperature indicated, and the optic axial angle diminishes until about the same 
temperature the circular rings and rectangular cross of an uniaxial crystal are 
exhibited in convergent polarised light. The exact temperatures at which the 
uniaxial interference figure is produced differ slightly according to the wave-length 
of the light, owing to there being a large amount of dispersion of the optic axes. 
They are respectively 42° for red lithium light, 44° for red C. hydrogen light, 48° for 
sodium light, 52° for green thallium light and 58° for greenish blue F. hydrogen light; 
the average is thus exactly 50°, the temperature at which the crystals of rubidium 
sulphate are thermally uniaxial. But the two ellipsoids of revolution for the two 
properties are not similarly orientated, the principal axis for the optical j)roperty 
being the crystaUographical axis a, while for the thermal property it is the axis b. 
This close parallelism between the thermal and optical properties is of considerable 
importance, inasmuch as the optical constants were shown to exhibit a clear pro¬ 
gression corresponding to the progression of the atomic weights of the three metals, 
the differences between the optical constants for the three salts being much greater 
relatively to their variations in the three axial directions of any one salt, than in the 
case of the thermal properties. 
On following the growth of the coefficients of linear expansion further to 100°, it is 
observed that the continued gain on the part of the c value has now rendered the 
expansion along this axis clearly the maximum, thus reversing the order of the axial 
expansions which had obtained below 50°. The maximum axis of the thermal ellipsoid 
for 100°, and temperatures superior to this, is thus the crystaUographical axis c for 
all three sulphates ; moreover the axis b is the minimum thermal axis, and the axis a 
the axis of intermediate thermal expansion for aU three salts. To complete the paral¬ 
lelism of the thermal and oi^tical properties, it may be mentioned that at temperatures 
superior to the neighbourhood of 50°, where the uniaxial optical interference figure 
is produced, the figure again breaks up into a biaxial one, but with the optic axes 
separated in the plane perpendicular to that which formerly contained them, and the 
optic axes separate more and more in this new plane until about 180° the axis c 
becomes the first median line instead of the axis a. At this temperature, therefore, 
the crystaUographical axis c is the first median line for aU three salts. It has been 
shown that at temjDeratures superior to 100° the axis c is also the direction of 
maxunum thermal expansion. Hence, at higher temperatures the rule observed for 
the lower ones, that the direction of maximum thermal expansion is that of the 
optical first median line, is equaUy valid. 
The foregoing considerations, concerning the relations of the linear coefficients of 
expansion, may be summarised as follows :— 
The smcdlness of the difference in the coefficient of expansion along any particular 
direction in the crystals, ivhich is introduced by the replacement of one idkcdi metal 
