TEMPERATURE AND THE PROPERTIES OF GASES 35 



scale of temperature which is either centigrade or Kelvin, and 

 between which there is a relation which is now almost exactly 

 known. However, temperatures are sometimes given in the 

 scales of a particular gas thermometer. 



The difficulties experienced in the determination of the exact 

 values of the critical constants are, as mentioned above, very- 

 great, and this from two causes. In the first place their value 

 varies very much with the presence of only small traces of 

 impurities, traces which would hardly affect any other physical 

 constant ; and in the second place the critical state is so evanes- 

 cent and so exact with pure substances that it is absolutely 

 necessary to have the meniscus under view during the whole 

 time until it disappears with a minute rise of temperature while 

 the pressure is kept constant, or still better is increased very 

 slowly, so that no heating due to compression can take place. 

 It is clear that these conditions are not easily attained in practice, 

 and hence the differences between the results given by even the 

 most careful workers can be understood. 



However, the attainment of these data to a high degree of 

 accuracy is only a matter of time, and a number are now known 

 to a sufficient accuracy to make deductions drawn from their 

 use right in principle if not in actual value. 



In attacking a subject such as this with the desire of de- 

 ducing some general laws, there are always two main lines of 

 advance open, both of which can be usefully followed as each 

 gives the possibility of arriving at some conclusion which would 

 not have been deducible from the other. Thus the simple 

 relation of equation (2) has been of immense value, and really 

 embodies the results of the deductive and the empirical lines of 

 argument in their simplest form. The next step on the de- 

 ductive side was made by J. D. van der Waals in 1873, who 

 from kinetic and thermodynamical reasoning obtained the well- 

 known form : 



(4) (^ + £)(«/-*) = RT = (1 +«)<-i-*)T 



in which a and b are functions of the attraction and of 

 the volume occupied by the molecules respectively, and are 

 supposed to be invariable with temperature and pressure. It is 

 clear from the propositions formulated above that these as- 

 sumptions are not correct, and many attempts have been made 

 by Clausius, Batelli, Berthelot, Boltzmann, Reinganum, and 



