NORMAL SULPHATES OF POTASSIUM, RUBIDIUM, AND CESIUM. 
495 
equality, at 50°, ivith the expansion along the axis a; and heyond this temperature c 
becomes the maximum thermal ctxis for the rubidium salt, as it is for the other tivo 
sulphates. Hence, at 50° the crystals of rubidium sulphate are apparently thermally 
uniaxial. At temperatures varying 10° each side of 50° for different uKive-lengths 
of light, they are cdso ap)parently optically uniaxial. The thermal and optical 
elliptsoids of revolution, however, are not identically orientated, the axis of the former 
being the crystcdlographical axis b, and of the latter a. Further, the change of 
direction of the maximum thermal axis of rubidium sulphate, from a to c, is folloived 
op>tically at 180° by the change of the first median line from a to c. Thus the first 
optical median line corresponds, as at lower temperatures, to the maximum thermal 
axis, for all three sulphates. 
This parallelism between the linear thermal expansions and the opticcd coiistants 
is of significance, inasmuch as the latter constants, which, unlike the former ones, 
exhibit differences between the three salts of much greater magnitude than the 
directional differences for any one salt, show a clear progression, in the order of the 
atomic weights of the metals contained in the three sulphates. 
It will be interesting in conclusion, to compare the results for the thermal deforma¬ 
tion thus obtained by the refined interference method, with those jDreviously obtained 
from the much cruder method of combining determinations of specific gravity at the 
ordinary and higher temperatures with measurements of the morphological angles 
at those temperatures. Such an attempt to determine the coefficients of expansion 
was described in the j^revious memoir on the sulphates (‘Journ. Chem. Soc., Trans.,’ 
1894, p. 653). It naturally depended for success on the possibility of employing a 
liquid in the pyknometer which was absolutely without action on the salts, as well 
as upon the degree of accuracy with which such determinations and angular measure¬ 
ments, the latter involving total deviations of less than two minutes of arc, can be 
carried out, even with the aid of the extremely delicate insti’uments employed. 
The actual values found for the total cubical expansion for 40° (hetweeii 20° and 
60°) were :— 
For potassium sulphate . . . 0'0053 
,, rubidium ,, ... 0'0052 
,, csesium ,, ... 0'0051. 
Thus a diminution of expansion was found to occur as the atomic weight of the 
metal increa.sed, a result which is fully borne out by the more accurate determinations 
now presented. The figures for the three salts were so near, however, that they were 
taken as identical, having reference to the method Ijy which they were obtained, for 
the purpose of calculating the coefficients of linear expansion with the aid of the 
angular deviations for the same temperatures. For the linear coefficients of expansion 
X for 100° the following numbers were given :— 
X, = 0-00437, 
X, = 0-00385, 
X, = 0-00479. 
