HISTORY OF COLD AND THE ABSOLUTE ZERO. 217 



agreement with the experimental values of Andrews. Tliis o-ave 

 chemists the means of ascertainino- the critical constants, provided suf- 

 ficiently accurate data derived from the study of a few ])roperly dis- 

 tributed isothermals of the gaseous substance were available. Such 

 important data came into the possession of chemists when Amagat 

 pul)lishcd his valuable paper on "The isothermals of hydrogen, nitro- 

 gen, oxygen, ethylene, etc.,'"' in the year 18.S0. It now l)ecame possi- 

 ble to calculate the critical data with comparative accuracy for the 

 so-calk'd piM'manent gases oxygen and nitrogen, and this was done l)y 

 Sari-au in ISS'i. Jn the meantime a great impulse had been given to a 

 further attaclc upon the so-called permanent gases by the suggestive 

 experiments made by Pictet and Cailletet. The static lic[uefaction of 

 oxygen was efl'ected by Wroblewski in 1883, and thereby the theo- 

 retical conclusions derived from van der Waals's ecpiation were su))- 

 stantially confirmed. The liquefaction of oxygen and air was achieved 

 through the use of liquid ethylene as a cooling agent, which enabled a 

 temperature of minus l-to'^ to be maintained l)y its steady evaporation 

 in vacuo. From this time liquid oxygen and air came to l)e regarded 

 as the potential cooling agents for future research, commanding as 

 they did a temperature of 200'^ 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 sul>stances as those in which the ratios of the tempera- 

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

 volume, respectively, were the same for the two substances, and in cor- 

 responding 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 faidty though approximate laws. 

 As examples, he succeeded in calculating the boiling point of carbonic 

 acid from observations on ether vapor, proved Kopp's law of molec- 

 ular volumes, and showed that at corresponding temperatures the 

 molecular latent heats of vaporization are proportional to the absolute 

 critical temperature, and that under the same conditions the coeffi- 

 cients of liquid expansion are inversely proportional to the absolute 

 critical temperature, and that the coefficients of liquid compressibility 

 are inversely proportional to the critical pressure. All these proposi- 

 tions and deductions are in the main correct, though further experi- 

 mental investigation has shown minor discrepancies requiring expla- 

 nation. Various proposals have ^been made to supplement van der 

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

 being entirely empiric, others theoretical. Clausius, Sarrau, Wro- 

 blewski, Batteli,> and others attacked the question empirically, and in 



