NORMAL SULPHATES OF POTASSIUM, RUBIDIUM, AND CAESIUM. 
487 
expression for the product of the expansions in the three rectangular axial directions, 
which naturally gives the expansion of the solid, is examined, it is found to consist of 
a large number of terms of which the only ones that alfect the fourth and last place 
of significant figures in the coefficient of expansion for any temperature are the sums 
of the constants a and 6 respectively. 
In the next table is presented a summary of the constants of the cubical coefficients 
of expansion, and of the cubical coefficients for 50°, in a form which readily admits of 
a comparison of the values for the three salts. 
Coefficients of the Cubical Expansion of the three Sulphates. 
a. 
h. 
^ 50 =. 
KoSOi . . . 
0-000 104 75 
0-000 000 069 8 
0-000 111 73 
Diflf. 161 
Diff. 69 
Diff. 92 
Rb2S04 . . . 
0-000 103 14 
0-000 000 076 7 
0-000 110 81 
Diff. 144 
Diff. 43 
DifL 101 
CS 2 SO 4 . . . 
0-000 101 70 
0-000 000 081 0 
0-000 109 80 
The mean coefficients of the cubical expansion of the three salts between 0° and f 
are therefore as follows : 
For potassium sulphate . O'OOO 104 75 + O’OOO 000 069 8^ or 10“® (10475 + 6’98^). 
,, rubidium sulphate . O'OOO 103 14 + O'OOO 000 076 7t, or 10“® (10314 -[- 7'67i). 
,, csesium sulphate . O'OOO 101 70 + O'OOO 000 081 Ot, or 10“® (10170 + 8'10^). 
The actual coefficients of cubical expansion, a, at any temperature t, and also the 
mean coefficients of cubical expansion between any two temperatures whose mean is t, 
are the following, in which a = a 2ht: 
For potassium sulphate . O'OOO 104 75 + O'OOO 000 139 6^, or 10“® (10475 + 13'96^). 
,, rubidium sulphate . O'OOO 103 14 + O'OOO 000 153 it, or 10“® (10314 fi- 15'34i). 
,, csesium sulphate . O'OOO 101 70 + O'OOO 000 162 Ot, or 10“® (10170 + 16'20^). 
Discussion of the Results, and Conclusions Thekefrom. 
Uie Cubical Expansion. 
The most striking result of the investigation is apparent from an inspection of the 
comparative table of the cubical coefficients of expansion. It may be stated in the 
following words : 
The coefficients of cubical- expa^ision of the normal sulphates of j^otassium, 
