472 MR. A. E. TUTTON ON THE THERMAL DEFORMATION OF THE CRYSTALLISED 
refei'ence of the interference band observations, and so any error due to minute lack 
of parallelism of the surfaces involved was obviated. 
An example taken at random from the actual measurements will render the process 
quite clear. It refers to the fourth crystal of caesium sulphate along the direction of 
the morphological axis h. 
millims. millims. 
Height of top of glass disc 
Known thickness of glass disc 
Height of screws . . . . 
,, top of compensator 
„ „ crystal . . 
,, ,, tripod table. 
40-857 
6-117 
34-740 d = 0-145 
34-595 4 = 5-253 
29-342 8-379 
20-963 I = 13-777 
The Nature of the Problem ivith reference to the Crystallographical Symmetry. 
The symmetry of the three salts under investigation being orthorhombic, the three 
axes of the thermal ellipsoid coincide in direction in each case with the crystallo¬ 
graphical axes, just as do the axes of the optical ellipsoid already fully elucidated in 
a previous memoir. The amounts of thermal deformation along these three axial 
directions should not, from general considerations, be. equal, as in crystals belonging 
to the cubic system, nor even would any two of them be likely to exhibit the same 
amount of expansion, as in the case of crystals exhibiting tetragonal or hexagonal 
symmetry. Orthorhombic symmetry requires that if a sphere of the substance of any 
one of these crystallised salts could be procured at any specific temperature, at any 
other temperature such sphere would have become converted into an ellipsoid with 
three unequal axes, and that these axes would coincide in direction with the three 
rectangular crystallographical axes. One of these morphological axes would thus be 
the direction of maximum expansion or contraction, another that of minimum and the 
remaining one that of intermediate deformation. The problem of the determination 
of the nature and amount of this thermal deformation consequently resolves itself 
into the determination of the amount of linear thermal expansion or contraction along 
the respective directions of the three morphological axes. From these fundamental 
data can be calculated the cubical expansion, in other words, the difference in volume 
between the sphere of unit radius and the deformation ellipsoid produced therefrom 
as the effect of change of temperature. 
The Determinations and Computations. 
The work has thus consisted in the determination of nine quantities, namely, the 
linear coefficients of thermal expansion or contraction along each of the three crystal¬ 
lographical axes of each of the three salts. It may be at once stated that in no 
case has contraction been observed, expansion in every direction having been found 
to be the invariable rule with regard to all three sulphates. Every one of the nine 
