410 Mr Kleeman, The Work done in the Formation of a 
Before considering the application of this equation to mixtures it | 
will be useful to reconsider its deduction. 
The true law of molecular attraction is probably not given by. 
a law of such simplicity as the foregoing. But there is nothing 
against supposing for purposes of calculation that the molecules 
are replaced by a set of molecules obeying such a law pro- | 
vided that the surface tension in question and the value of U) 
remain unaltered. This can be realized since we have two) 
variables at our disposal, namely k and vr. Equation (1) is thus\ 
fundamentally correct. It then remains to find the equivalent’ 
law of molecular attraction of the form given. This need only) 
be approximately realized for the reasons given. To see how’ 
the value of the eae depends on the value of r it was | 
calculated for the case r=2, which gave ‘71. When r=o it) 
will be easily seen that it is equal to unity. The correct value | 
thus lies between ‘7 and 1. The attraction varies much more 
rapidly with the distance of separation of the molecules than 
corresponding to r= 2, r being approximately equal to 5*, or 4 to’ 
which corresponds van der Waals’ equation of state. It is evident, 
therefore that the approximately correct value of 5 for r should 
give within a few per cent. the correct value of the expression. | 
When we are dealing with a mixture of substances we may | 
suppose as before that the molecules are replaced by a set of) 
molecules equal to one another and which obey a law of attraction | 
of the form given. This is evidently possible for the same 
reasons as stated above. The equivalent law of attraction will 
obviously be very approximately the same as for a pure substance, | 
and the value of the expression discussed practically not altered. | 
The molecular weight mg occurs in connection with the number | 
of molecules in the substance. In the case of a mixture it 1s: 
therefore only necessary to substitute for mg the average mole-— 
cular weight. The quantity U refers in all cases to a gram of the | 
substance. 
When the ingredients of the mixture consist of liquids whose — 
heats of evaporation in the pure state are known for temperatures : 
at which their vapours approximately obey the laws of a perfect | 
gas, the values of U may be approximately calculated corresponding — 
to this region of temperatures. The heat of evaporation of a: 
substance whose vapour approximately obeys the laws of a perfect 
gas is equal to the energy expended in separating the molecules” 
an infinite distance from one another. This heat is expended in 
overcoming the attraction between the molecules and producing 
changes in their internal energy. I have shownt that the latter 
* Toc. cit., May 1910, p. 807. 
+ Previous paper in this volume. 
