494 MR. A. E. TUTTON OX THE THERMAL DEFORMATION OF THE CRYSTALLISED 
hy another, compared ivith the larger differences of expansion exhibited in the three 
axial directions of any one salt, together ivith the fact that the change of metal is 
accompanied by considerable modifications of these latter relative expansions for tivo 
of the axial directions, a and c, prevent the coefficients of expamsion 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, the increase of expansion in one of the two directions 
referred to being more or less balanced by the diminution in the other; consequently 
the effect of interchange of the metcds is clearly exhibited by the solid deformation, 
the cubical expansion, the coefficients and increments of which have been shown to 
exhibit a well-defined progression following the order of the atomic weights of the 
three metals. 
Before i3roceeding to siunmarise the interesting analogy between the thermal and 
the optical properties, it may he of advantage to consider what the dimensions 
of the linear change, on replacing one metal by another, would probably be, pro¬ 
vided no directional perturbations occurred. The diflerence between the cubical 
coefficients of expansion of potassium and rubidium sul23hates is 0•00000161, and of 
the rubidium and cmsium salts 0‘00000I44. The mean is O’OOOOOlo, and the linear 
ditferences might be reasonably expected to be about one-third of this, namely 
0’0000005. Even if the linear expansions along the axis b are accepted as free from 
perturbation and unaffected by change of metal, the linear differences for the other 
two directions could not exceed O’OOOOOOS. Now the directional perturbation in 
which the rubidium salt exhibits a reversal of the relative directions of the maximum 
and intermediate thermal axis compared with the potassium salt, amounts to more 
than twice this amount, namely 0'0000017. Hence it is clearly apparent that a 
progressive change, of the maximum possible amount, would be completely masked 
by the larger directional perturbation. A brief summary of the nature of the 
pertui-l^ation and its relation to the optical changes may next be given. 
The chief directional perturbation consists of a reversal, for temperatures below 
50°, of the directions of the maximum and intermediate axes of the thermcd ellipsoid 
in the rubidium scdt, compared with their directions in the qootassium and ccBsium 
scdts. The maximum thermal axis is the crystallographical axis c for the two latter 
salts, but the a axis 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 the 
direction c to the direction a, occurs for similar temperatures, in the case of the 
rubidium, salt. Hence, the maximum thermal axis is identical in all three salts ivith 
the first median line. 
At higher temperatures the same relations still hold for the potassium and casium 
salts, both thermally and opticcdly. But oiving to the increment of expansion cdong 
the axis c being so much greater than for other directions, the exceptional inter¬ 
mediate expansion cdong the axis c of rubidium sidpliate is rapidly brought up to 
