517 
1898-99.] Sulphuric Acid and Sulphates in Solution. 
The values of the new constant A lf obtained by introducing the 
concentrations into this expression are given in the next table. 
The increase in A x , from the first to the last experiment, has not 
yet altogether disappeared, but it is not nearly so marked nor so 
regular. Of course the exaggeration of the experimental errors 
which the expression causes and which has already been pointed 
out, holds good here also, and a really good constant is hardly to 
be expected. 
h 2 so 4 
Na 2 S0 4 
A! 
0-025 
+ o-i 
0-0594 
0-05 
jj 
0-0600 
o-i 
jj 
0-0624 
0-2 
55 
0-0708 
0-35 
55 
0-0617 
The most probable value of A 1} calculated in the same manner 
as before, by assigning a “ weight ” to each individual constant, 
is 0’0618, and the complete expression for the equilibrium between 
the undissociated portions of the free sulphuric acid, sodium 
sulphate and sodium acid sulphate which exist in mixed solutions 
of the acid and neutral salt is accordingly given by the equation 
{aH^O^l-eq)} 0 * 85 0*0618 
C.NaHS0 4 (l - a 3 ) { a.Na 2 S0 4 (l - a 2 )} 1 ^ * 
The real test of the accuracy and value of this expression is the 
comparison of the results obtained by means of it with those 
actually observed, for example, by calculating the percentage of 
free acid which ought to exist in the various solutions and noting 
the agreement between this series of numbers with those found by 
experiment. This was done, and the results are shown in the next 
table. It will be seen from a comparison of the two series of 
numbers, and also at once in the curves of the accompanying 
diagram, that the agreement within the limits of the experiments 
is particularly good. The same general feature which was noticed 
in the case of potassium sulphate solutions is present here also, 
namely, that at the lower percentages the calculated values are 
too high, and vice versa. The mean real percentage difference 
between them is, however, considerably less than 1 per cent. 
