500 
PROFESSOR J. J. THOMSON ON SOME APPLICATIONS OF 
for every degree above 0°, so that at 15° C. an increase of 2 per cent, would cause 
an increase of ‘348 part in 10 - 9, which is about 3‘2 per cent., so that in this case the 
agreement is almost closer than we could have expected. 
In the case of NaCl we have, getting the data from the same sources as before— 
X = 20 X 4-2 X 10 7 , 
d (v + v')/dq = ‘05 ; 
hence the change in temperature required to produce the same change as 100 atmo¬ 
spheres at 15° 
288 x 10 8 x 5 x 10- 2 
20 x 4-2 x 10 7 
= 1'6° approximately. 
Now, according to the curve of solubility of NaCl given in Ostwald’s £ Lehrbuch der 
AUgemeinen Chemie,’ vol. 1, p. 380, about 34 parts dissolve at 15°, and the increase 
is about ^ of a part per degree Centigrade, so that for 1*6° the increase would be 
about ’13 in 34 : this is '40 per cent. The value found by Sorby was - 419 per cent., 
so that the agreement is again very close. 
Ch emiccd Combincttion. 
§ 11. We can apply Hamilton’s principle to the case of chemical combination. 
I jet us in the first place take cases of the type studied by Guldberg and Waage in 
/ 
their theory of chemical combination (‘Etudes sur les Affinites Chimiques’). 
In these cases there is equilibrium between various chemical actions which tend to 
reverse each other : a good example of such cases is that of a mixture of dilute solutions 
of sulphuric and nitric acids, sodium nitrate, and sodium sulphate. When the sulphuric 
acid acts on the sodium nitrate it produces nitric acid and sodium sulphate, while 
nitric acid by its action on sodium sulphate produces sulphuric acid and sodium 
nitrate. The problem is, given four substances of this kind, to find the quantity of 
each when there is equilibrium. Let us begin with the case of four gases, which we 
will call A, B, O, D, such that A by its action on B produces C and D, while C by its 
action on I) produces A and B. 
Let qr), r£, se, be the number of molecules of A, B, C, D, respectively, when 
p, q, r, s, are the numbers of molecules in equivalent molecules. By equivalent 
molecules we mean molecules, or groups of molecules, such that, {A} being the 
equivalent molecule of the gas A, with a corresponding notation for the others, the 
chemical action which goes on may be expressed by the equation 
{A} + {B} = {C} + {D}. 
