SURFACE TENSION OF AQUEOUS SOLUTIONS.—BARNES. 61 
salts up to an average concentration of 0.8 gramme-equivalent 
per litre at least, can be predicted within the limit of error of 
my observations. 
Specific Gravity and Surface Tension. 
Prof. MacGregor? has proposed, in the case of simple solutions 
of electrolytes, so dilute that the ions and the undissociated 
molecules may be regarded as without mutual action, to express 
any of their physical properties, such as specific gravity, surface 
tension, &e, by the following formula : 
P=Py+k(1—@) nt+len, 
where P is the numerical value of the property for the solution, 
Py that of the same property for water under the same physical 
conditions, n the concentration expressed in gramme-equivalents 
per unit volume, « the ionization coefficient of the electrolyte 
in the solution, and & and lJ constants, called ionization constants. 
He has also shown how to predict the value of any such 
property for a mixture of simple solutions, by the aid of the 
jonization constants determined for the simple solutions.? 
1Trans. N.S. Inst. Sci, 9, 219, 1896. 
2 Note by the communicator of the paper.—The fact that values of k and lin the 
above formula can be found which make the formula represent the observed values of 
a property for simple solutions of an electrolyte has of course little theoretical interest. 
The ionization coefficient, @, is a complex function of the concentration, n. 1f expressed 
in terms of powers of n the expression would involve several powers. (See Trans. N.S. 
I. S., 9, 112). The above expression for P is thus equivalent to an expression in terms 
of three or more powers of n with coefficients which are functions of constants deter- 
mined by the electrical character of the electrolyte and of two additional arbitrary 
constants. As the concentration curves of specific gravity and surface tension for 
Solutions are but slightly curved, it is thus to be expected that the above expression 
would represent them. It 7s of theoretical interest, however, to find whether, when the 
ionization constants for any property have been determined for simple solutions of 
two electrolytes, it is possible to predict the value of the property for mixtures by the 
method referred to. For (1) there are no arbitrary constants in the expression by 
which the prediction is made, (2) the expression itself is derived from the dissociation 
theory, and (3) the ionization coefflcients of the electrolytes in the mixture, involved in 
the expression, are determined by a direct application of that theory. I think it well to 
make this remark because several reviewers of former papers have written under the 
apprehension that the k’s and l’s of the expression for the value of a property fora 
mixture (see p. 65 of this paper) were arbitrary constants determined by the observa- 
tions on the mixtures. They are, however, the ionization constants already determined 
by observations on simple solutions. J. G. M. 
