NORMAL SULPHATES OF POTASSIUM, RUBIDIUM, AND CESIUM. 
407 
experimental error, at 136°. Beyond the temperature of identity divergence occurs 
and an increase of atomic weight is now accompanied by an increase in the coefficient 
of cubical expansion. 
4. The thermal deformation is of the nature of an expansion in all directions in the 
crystals of all three sulphates. 
5. The differences between the coefficients of linear expansion along the three 
crystallographical axial directions of any one salt, although only amounting to one- 
eighth of the total coefficient, are large compared with the differences between the 
values for the same direction of the three salts. 
6. The operation of rule 5, together with the fact that the replacement of one 
metal by another is accompanied by considerable modifications of the relations of two 
of the three values for the original salt, those corresponding to the axes a and c*, 
prevent the coefficients of linear expansion for any one direction of the three salts 
from exhibiting any progression corresponding to that of the atomic weights of the 
three metals. These directional perturbations are, however, mutually compensative, 
so that the effect of interchange of the metals is clearly exhibited by the solid defor¬ 
mation, the cubical expansion, the coefficients of which and their increments have 
been shown to exhibit a progression according to the atomic weight of the metal, as 
stated in rule 1. 
7. The increment of the linear coefficient of expansion for the direction of the 
vertical axis c of each salt, is about twice as large as the increments for the other two 
directions a and 6, for which latter the increments are nearly equal. This thermal 
property is analogous to the optical behaviour, the refractive power being altered 
(diminished) by rise of temperature much more in the direction of the axis c than in 
the other two directions, in which the lesser amounts of change are nearly equal. 
8. The amount of expansion along the direction of the crystallograpldeal axis h is 
approximately identical for all three sulphates, indicating that interchange of the 
metals is without influence on the thermal behaviour along the macrodiao;onal axis of 
the crystals. The crystals of all three salts also expand least in this direction, which 
is therefore the common minimum axis of the thermal ellipsoid. 
9. The chief of the directional perturlDations, referred to under 6, consists of a 
reversal, for temperatures below 50°, of the directions of the maximum and inter¬ 
mediate axes of the thermal ellipsoid for rubidium sulphate, compared witli their 
directions in the potassium and emsium salts. The maximum thermal axis is the 
crystallographical axis c for the two latter salts, but a for the rubidium salt. A 
similar reversal of the direction of the first median line, the maximum axis of the 
optical ellipsoid (the indicatrix), from c to a occurs for the same temperatures, in the 
case of rubidium sulphate. The maximum thermal axis is identical in all three salts 
with the optical first median line. 
10. At higher temperatures the same relations still olffain for the potassium and 
ernsium salts, both thermally and o})tlcally. But ov/ing to the Increment of expansion 
VOL. cxcii.—A. 3 s 
