498 ON THE THERMAL DEFORMATION OF CRYSTALLISED NORMAL SULPHATES. 
along the axis c being so much greater than for the other directions, the intermediate 
expansion along c for rubidium sulphate attains equality at 50° with the exj)ansion 
along a, and beyond this temperature c becomes the maximum thermal axis for this salt, 
as it is for the other two sulj)hates. Consequently, at 50° the crystals of rubidium 
sulphate are apparently thermally uniaxial. At temperatures varying 10° each side 
of 50° for different wave-lengths of light, they have previously been shown to simulate 
uniaxial optical properties. The thermal and optical ellipsoids of revolution are not, 
however, identically orientated, the axis of the former being the axis h and of the 
latter a. Further, the change of direction of the maximum thermal axis of rubidium 
sulphate from a to c is followed ojffically at 180° by the change of the first median 
line from a to c, rendering the last sentence of rule 9 again valid. 
11. A close jDarallelism between the linear thermal expansion and the directional 
optical behaviour is thus shown to exist, and is indicative that the same progressive 
effect of variation of the atomic weight of the metal is in operation with regard to the 
former, as was clearly demonstrated in a former memoir with respect to the latter, 
and that this effect would be manifest in the former were it not masked by the larger 
eflect indicated under 6. 
12. The thermal deformation constants best capable of indicating the effect of the 
replacement of one alkali metal by aiiotlier, in the crystals of the normal alkali 
sulphates, have thus been shown to be the cubical coefficients of expansion and their 
increments ; and these have been further demonstrated to exhibit a regular progres¬ 
sion, which follows the order of j^rogression of the atomic weights of the metals in 
question. Moreover, the linear coefficients and their increments have been shown to 
exhibit var iations which present a remarkable analogy to those of the optical con¬ 
stants, for which, the values for the three salts being very much more widely 
separated and consequently undisturbed by the modification of the directional differ¬ 
ences for the same salt which are relatively so much more important in the case of 
the linear thermal constants, a clear progression according to the atomic weight of 
the alkali metals has been proved. 
The final conclusion of this investigation, therefore, is that: 
The thermal deformation constants of the crystals of the normal sulphates of 
potassium, rubidium, and ccBsium exhibit variations, ivhich, in common ivith the 
morphological, optical, and other physical properties previously investigated, follow the 
order of progression of the atomic iveights of the alkali metals ivhich the salts contain. 
This result is, therefore, in perfect agreement with the principle enunciated at the 
conclusion of the memoir concerning the alkaline selenates (‘ Journ. Chem. Soc., Trans.,’ 
1897, p. 920), which reads as follows : 
The difference in the nature of the elements of the same family group which is 
manifested in their regularly varying atomic weights, is also expressed in the similarly 
regular variation of the characters of the crystals of an isomorphous series of salts of 
which these elements are the interchangeable'constituents. 
