October 10, 1902.] 



SCIENCE. 



569 



shown to be the results of the laws of 

 dynamics. Andrews applied the new 

 equation to the consideration of the coeffi- 

 cients of expansion with temperature and 

 of pressure with temperature, showing that 

 although they were nearly equal, neverthe- 

 less they were almost independent quan- 

 tities. His investigation of the capillarity 

 constant was masterly, and he added 

 further to our knowledge of the magni- 

 tudes of the molecules of gases and of their 

 mean free paths. Following up the ex- 

 periments of Joule and Kelvin, he showed 

 how their cooling coefficients could be de- 

 duced, and proved that they vanished at ^ 

 temperature in each case which is a con- 

 stant multiple of the specific critical tem- 

 perature. The equation of continuity de- 

 veloped by van der Waals involved the 

 use of three constants instead of one, as 

 in the old law of Boyle and Chai'les, the 

 latter being only utilized to express the re- 

 lation of temperature, pressure, and vol- 

 ume, when the gas is far removed from its 

 point of liquefaction. Of the two new 

 constants one represents the molecular 

 pressure arising from the attraction be- 

 tween the molecules, the other foiir times 

 the volume of the molecules. Given these 

 constants of a gas, van der Waals showed 

 that his equation not only fitted into the 

 general characters of the isothermals, but 

 also gave the values of the critical temper- 

 ature, the critical pressure, and the critical 

 volume. In the case of carbonic acid the 

 theoretical results were found to be in re- 

 markable agreement with the experimental 

 values of Andrews. This gave chem- 

 ists the means of ascertaining the crit- 

 ical constants, provided sufficiently ac- 

 curate data derived from the study of a 

 few properly distributed isothermals of the 

 gaseous substance were available. Such 

 important data came into the possession of 

 chemists when Amagat published his valu- 

 able paper on 'The Isothermals of Hydro- 



gen, Nitrogen, Oxygen, Ethylene, etc.,' in 

 the year 1880. It now became possible to 

 calculate the critical data with comparative 

 accuracy for the so-called permanent gases 

 oxygen and nitrogen, and this was done by 

 Sarrau in 1882. In the meantime a great 

 impulse had been given to a further attack 

 upon the so-called permanent gases by the 

 suggestive experiments made by Pictet and 

 Cailletet. The static liquefaction of oxy- 

 gen was eifected by Wroblewski in 1883, 

 and thereby the theoretical conclusions de- 

 rived from van der Waals' equation were 

 substantially 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 140 degrees to be maintained by its 

 steady evaporation in vacuo. From this 

 time liquid oxygen and air came to be re- 

 garded as the potential cooling agents for 

 future research, commanding as they did 

 a temperature of 200 degrees below melt- 

 ing ice. The theoretical side of the ques- 

 tion 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 de- 

 velopment of what he calls 'The Theory 

 of Corresponding States.' He defitned 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 respec- 

 tively 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 em- 

 piric, and some completing and correcting 

 faulty though approximate laws. As ex- 

 amples, he succeeded in calculating the 

 boiling-point of carbonic acid from obser- 

 vations on ether vapor, proved Kopp 's law 

 of molecular volumes, and showed that at 



