ISOTHERMAL EQUATION 113 



there are molecular forces the mean-square speed of the particles necessarily increases 

 with diminution of volume, even when the mean-square speed of a free particle is 

 maintained unaltered ; and this simply because the time during which each particle 

 is free is a smaller fraction of the whole time. But when the whole kinetic energy 

 is treated as constant (as it must be in an Isothermal, when that energy is taken 

 as measuring the absolute temperature), it is clear that isothermal compression must 

 reduce the value of E ____ 



"For the isothermal formation of liquid, heat must in all cases be taken from 

 the group M. This must have the effect of diminishing the value of E. Hence, in a 

 liquid, the temperature is no longer measured by E, but by E + c, where c is a 

 quantity whose value steadily increases, as the temperature is lowered, from the value 

 zero at the critical point..." 



Fritting then E = Rt, where / is the absolute temperature, Tait intro- 

 duced the pressure temperature and volume at the critical point, and threw 

 his equation into the form 



where the barred letters refer to the critical values. He compared this with 

 the corresponding equations of Van der Waals and Clausius and pointed out 

 that, although they all three agreed in form for the critical isothermal, they 

 could not do so for any other. He then found, by direct calculations from 

 Amagat's results for Carbon Dioxide, that the pressures obtained by his 

 formula for given volumes at the critical temperature agree almost perfectly 

 with the measured pressures, between a range of volume from i to 0*003 5. 



This practically finishes the series of papers on the Foundations of 

 the Kinetic Theory of Gases ; for the fifth instalment was printed only in 

 abstract and indicates lines of investigation which were never completed. 



For five full years Tait occupied his mind with these researches ; and 

 if we except his quaternion work there is no other line of investigation which 

 made such serious demands upon both his mathematical powers and his 

 physical intuitions. Throughout the whole series he is essentially the 

 natural philosopher, using mathematics for the elucidation of what might 

 be called the metaphysics of molecular actions. No writer on the subject 

 has put more clearly the assumptions on which the statistical investigation 

 is based ; and apparently he was the first to calculate the rate at which 

 under given conditions the "special state" is restored when disturbed. His 

 abhorrence of long and intricate mathematical operations is strongly expressed 

 more than once. He was convinced of the general accuracy of Maxwell's 

 T. 15 



