496 MR. A. E. TUTTON ON THE THER^IAL DEFORMATION OF THE CRYSTALLISED 
It was therefore concluded that “ the crystals of the three salts, on heating, expand 
most in the direction of the vertical axis c, and least along the macrodiagonal axis h” 
We have seen that this is indeed the case, except for temperatures below 50° in the 
case of X„ and of the rubidium salt, a fact which the method could not possibly 
have indicated, as at 60°, the temperature of the higher density determinations, the 
rule found is really true. 
The actual values now published for the total expansion of potassium sulphate, 
taking this salt as an example, for the 100° between 20° and 120°, calculated by the 
formula a. — a + 26 j, are as follows ; 
= 0-003818, a^= 0-003422, a, = 0-004212. 
The ditference between these highly accurate values and the approximate ones 
obtained by the rougher method is not great considering the nature of the latter, and 
the order is the same. 
An attempt to determine the ex^Dansion of crystals of potassium and rubidium 
sulphates, by means of the weight-thermometer method, has been described by Spring 
(‘Bull, de I’Acad. de Belgique,’ 1882, 197, and ‘ Ber. Deut. Chem. Ges.,’ 15, 1940). 
Olive oil was employed as the liquid, and the density determinations were carried up 
to 100°. The value obtained for the cubical expansion of potassium sulj)hate for 100° 
was 0-0126, and for rubidium sulphate 0-0111. The latter value is extraordinarily 
near the truth according to the results now presented, the value for 0° to 100° being 
actually 0-01108. But the impossibility of trusting this method, equally with aU the 
relatively coarser density methods, to afford correct differences between the values 
for different salts, is clearly demonstrated by the fact that the difference shown 
between the values for the potassium and rubidium salts, namely 0-00150, is seventeen 
times as great as the real difference (-01117-0-01108 — 0-00009), which is now shown 
to exist. 
Summary of Conclusions. 
The principal results of the investigation are presented in the following summary. 
1. The coefficients of cubical expansion of the orthorhombic crystals of the normal 
sulphates of potassium, rubidium and csesium exhibit a progression, corresponding to 
the progression of the atomic weights of the three respective metals. This is true of 
both the constants a and 6 in the general expression for the coefficient of cubical 
expansion, a = a + 26i, for any temperature t. 
2. The order of progression of the two constants is inverted; «, the coefficient for 
0°, diminishes with increasing atomic weight of the metal, while 6, half the increment 
of the coefficient per degree of tenqoerature, increases. 
3. In consequence of rule 2 the coefficients of cubical expansion of the three 
salts converge, with rise of temperature, and attain equality, within the limits of 
