done during the Evaporation of a Liquid. 407 
with increase of temperature, and that it follows from the Joule- 
Thomson effect that it varies approximately inversely as the 
temperature. This effect is more likely to be brought about, as 
pointed out in the paper quoted, by a relative displacement of the 
atoms of each molecule with change of temperature than by a true 
change in the forces of attraction. It follows therefore that the 
intrinsic pressure term in the equation of state is a function of 
the temperature as well as the volume of the substance. Also the 
variation of the viscosity of a gas with change of temperature is 
not due only to a change in the velocity of translation of the 
molecules but also toa variation of the forces of attraction between 
them. 
A formula for the intrinsic pressure was also obtained which 
gives the quantity to the same degree of approximation that 
U+u—U, is equal to U. 
Since w—Uq is small in comparison with U it is possible to 
obtain some information about the law of molecular attraction 
from a study of the internal heats of evaporation of liquids. This 
I have carried out in previous papers assuming the foregoing. 
It was shown* that if no other assumption is made besides the 
one mentioned it is mathematically impossible to determine com- 
pletely the law of molecular attraction from internal heat of 
evaporation data, in other words the law obtained should contain 
an arbitrary function of the temperature and distance of separation 
of the molecules. ‘This arises from the fact that we do not know 
a priort how the attraction varies with the temperature, other 
conditions remaining the same. And this point cannot be deter- 
mined from the data in question because we cannot say how much 
of the change in internal heat of evaporation with rise of tempera- 
ture is due to a separation of the molecules of the liquid due to 
its decrease in density, and how much due to a change in the 
attraction of the molecules. But even if this poimt were deter- 
mined the law would still contain an arbitrary function. For the 
internal heat of evaporation is the difference of two quantities, 
viz. the potential energies of attraction in the states of liquid and 
saturated vapour, and we evidently cannot recover a curve given 
the difference between certain ordinates. It is therefore of primary 
importance to obtain the law of attraction in the form involving 
an arbitrary function for we can then be sure that the part of the 
law outside the function is correct. On the other hand if we obtain 
a definite law by the help of assumptions, say assuming the form 
of the law, an agreement with the facts does not mean that our 
assumptions are correct. This follows from the mathematical 
theorem so often ignored by scientists that an infinite number of 
formulae can be found to express a set of facts equally well, each 
* Phil. Mag., Jan. 1911, pp. 83—102. 
