28 REPORT— 1902. 



as they did a temperature of 200 degrees below melting ice. The theoretical 

 side of the question received at the hands of van der Waals a second 

 contribution, which was even more important than his original essay, and 

 that was his novel and ingenious development of what he calls 'The 

 Theory of Corresponding States.' He defined the corresponding states of 

 two substances as those in which the ratios of the temperature, pressure, 

 and volume to the critical temperature, pressure, and volume respectively 

 were the same for the two substances, and in corresponding states he 

 showed that the three pairs of ratios all coincided. From this a series of 

 remarkable propositions were developed, some new, some proving previous 

 laws that were hitherto only empiric, and some completing and correcting 

 faulty though approximate laws. As examples, he succeeded in calculating 

 the boiling-point of carbonic acid from observations on ether vapour, 

 proved Kopp'slawof molecular volumes, and showed that at corresponding 

 temperatures the molecular latent heats of vaporisation are proportional 

 to the absolute critical temperature, and that under the same conditions 

 the coefficients of liquid expansion are inversely proportional to the 

 absolute critical temperature, and that the coefficients of liquid compres- 

 sibility are inversely proportional to the critical pressure. All these 

 propositions and deductions are in the main correct, though further 

 experimental investigation has shown minor discrepancies requiring 

 explanation. Various proposals have been made to supplement van der 

 Waals' equation so as to bring it into line with experiments, some being 

 entirely empiric, others theoretical. Clausius, Sari-au, AVroblewski, Batteli, 

 and others attacked the question empirically, and in the main preserved 

 the CO- volume (depending on the total volume of the molecules) unaltered 

 while trying to modify the constant of molecular attraction. Their success 

 depended entirely on the fact that, instead of limiting the number of 

 constants to three, some of them have increased them to as many as ten. 

 On the other hand, a series of very remarkable theoretical investigations 

 has been made by van der Waals himself, by Kammerlingh Onnes, 

 Korteweg, Jaeger, Boltzmann, Dieterici, and Rienganum, and others, all 

 directed in the main towards an admitted A^ariation in the value of the 

 co-volume while preserving the molecular attraction constant. The 

 theoretical deductions of Tait lead to the conclusion that a substance 

 below its critical point ought to have two different equations of the van 

 der Waals type, one referring to the liquid and the other to the gaseous 

 phase. One important fact was soon elicited — namely, that the law of 

 correspondence demanded only that the equation should contain not more 

 than three constants for each body. The simplest extension is that made 

 by Reinganum, in which he increased the pressure for a given mean 

 kinetic energy of the particles inversely in the ratio of the diminution of 

 free volume, due to the molecules possessing linear extension. Berthelot 

 has shown bow a ' reduced ' isothermal may be got by taking two other 

 prominent points as units of measurement instead of the critical co- 

 ordinates. The most suggestive advance in the improvement of the 



