488 MR. A. E. TUTTON ON THE THERMAL DEFORMATION OF THE CRYSTALLISED 
rubidium, and ccesium 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 
b in the genercd expression for the coeffcient of cubical expansion, the values of each 
constant for the rubidium salt being intermediate between the corresponding values for 
the potassium omd ccesium salts. 
It may be further stated that: 
The differences between the values of the constant a, which represents the coefficient 
of cidjical expansion for ()°,for the three salts, are small, amounting to only one and 
a half per cent.; this is an amount, however, which is five times as great as the 
possible experimental error in the detemninations. 
Also that : 
The order of progression of the two constants of the cubiccd coefficient of 
expansion is inverted; a, the coefficient at 0°, diminishes tvith increasing atomic 
weight of the metal contained in the scdt, ivhile b, half the increment of the 
coefficient per degree, increases. 
This latter fact leads to an interesting residt, namely, that the coefficients, in 
increasing with rise of temperature, approach each other in value, until for three 
certain temperatures between 110° and 170° they become identical in pairs; more¬ 
over, in the neighbourhood of the second of these temperatures the three values 
approximate so closely to each other that their difference comes within the limits of 
experimental error. For temperatures higher than those of coincidence, the values 
diverge and exhibit an inverted order of progression. This will be rendered clear by 
a table shovdng the true coefficients of cubical expansion, a + ‘2bt, for intervals of 
50° up to 200°, and for the three temperatures of coincidence. These latter are 114° 
for the identity of cubical expansion of potassium and rubidium sulphates, 136° for 
potassium and caesium sulphates, and 168° for the coincidence of expansion of the 
rubidium and caesiuni salts. 
Coefficients of Cubical Expansion for Various Temperatures from 0° to 200° 
Salt. 
0°. 
o 
o 
100°. 
114°. 
136°. 
150°. 
168°. 
200°. 
K.,SO, 
10-810475 
11173 
11871 
12066 
12373 
12569 
12820 
13267 
Rb,SO^ 
10-810314 
11081 
11848 
12065 
12400 
12615 
12891 
13382 
cs.;so^ 
10-810170 
10980 
11790 
12017 
12373 
12600 
12891 
13410 
The point may be grapbically demonstrated l)y plotting out the values on curve 
paper, taking temperatures as abscissae and coefficients of cubical expansion as 
ordinates. The three straight lines thus obtained, shown in the reproduction given, 
will he observed to converge from 0° towards the three temperatures of coincidence, 
where crossing of the lines in pairs occurs, beyond which they diverge. The relative 
nearness of tlie lines to each other in tlie middle of the part where crossing occurs. 
