NORMAL SULPHATES OF POTASSIUM, RUBIDIUM, AND CESIUM. 
491 
of expansion is found to be prevented by the slight directional perturbations due to 
the different natures of the molecules of the three salts. The replacement of the 
atoms of one metal by those of another of higher atomic weight is possibly, and even 
probably, accompanied by movement of the relative positions of the constituents of 
the molecules of their spheres of motion, as well as by the purely chemical change; 
for not only is the substitution accompanied by an increase of mass, but also by an 
increase in the electro-positive energy of the metallic atoms, which may very reason¬ 
ably be expected to result in a closer approximation to the negative atoms, probably 
of oxygen, to which they are attracted. There are, however, several interesting facts 
exhibited by the linear coefficients, which connect their relations very intimately with 
those of the optical constants, for which a true progression in the order of atomic 
weight has been clearly demonstrated. Before passing to the consideration of these 
indications of parahelism between the thermal and optical behaviour of the crystals of 
the three salts, attention must be drawn to the two following salient facts which are 
apparent from an inspection of the linear coefficients. It is that : 
The amount of expansion along the dwection of the crystallographical axis h is 
practically identical for all three sulphates, indicating that the interchange of the 
three metcds is ivithout influence on the thermcd behaviour along the macrodiagonal 
axis of the crystals. Moreover, the crystals of cdl three salts expand least along this 
direction, which is therefore that of the minimum axis of the thermal ellipsoid. 
These two facts are doubtless of significance with respect to the structure of the 
molecule, apparently indicating absence of the metallic atoms or their spheres of 
motion from the immediate proximity of the axis b. The significance becomes 
enhanced in view of the fact that the author has shown (‘Journ. Chem. Soc. Trans.,’ 
1896, p. 507) that the whole of the work on the sulphates and double sulphates 
points to the conclusion that the structural unit of the crystals of the simple sulphates 
is the simple chemical molecule, a conclusion which is supported by the work of Fock 
(referred to loc. cit.) on the solubility of mixed crystals. 
The relations between the amounts of expansion along the directions of the other 
two crystallographical axes, a and c, are much more complicated, and are evidently 
influenced by the replacement of one metal by another. Considering the coefficients 
of expansion for 0°, the amount of expansion along the direction of the axis c is the 
greater in the case of both the potassium and csesium salts ; and for all three salts the 
increment is, as already indicated, greater for this than for any other direction. But 
in the case of the rubidium salt a remarkable excess of expansion is observed to occur 
along the direction of the a axis, which is the maximum thermal axis at 0°, at the 
expense of that along the c axis, which becomes reduced to the intermediate thermal 
axis. The increments per degree, however, for these two directions in the rubidium 
salt, remain of the same order as for the other two salts. Now it is an interesting 
fact, and doubtless not without significance, that the directions of maximum thermal 
effect coincide with those of the first median line of the optic axial angles of all three 
3 E 2 
