216 HISTORY OF COLD AND THE ABSOLUTE ZERO. 



dynamics, for a long-continued series of motions, either oscillator3^ or 

 changino- exceedingly slowly with time, applied it to the consideration 

 of the molecular movements of the particles of the gaseous substance, 

 and after much retined investigation, and the fullest experimental 

 calculation available at the time, devised his well-known equation of 

 continuity. Its paramount merit is that it is based entirely on a 

 mechanical foundation, and is in no sense empiric; we may therefore 

 look upon it as having a secure foundation in fact, but as being capable 

 of extension and improvement. James Thomson, realizing that the 

 straight-line breach of continuous curvature in the Andrews isother- 

 mals was untenable to the physical mind, propounded his emendation 

 of the Andrews curves — namely, that they were continuous and of S 

 form. AVe also owe to James Thomson the conception and execution 

 of a three-dimensional model of Andrews's results, which has been of 

 the greatest service in exhibiting the three variables by means of a 

 specific surface afterwards greatly extended and developed by Prof. 

 Willard Gibbs. The suggestive work of James Thomson undoubt- 

 edly was a valuable aid to van der Waals, for as soon as he reached the 

 point where his equation had to show the continuity of the two states 

 this was the first difficulty he had to encounter, and he succeeded in 

 giving the explanation. He also gave a satisfactory reason for the 

 existence of a minimum value of the product of volume and pressure 

 in the Regnault isothermals. His isothermals, with James Thomson's 

 completion of them, were now shown to be the results of the laws of 

 dynamics. Van der Waals applied the new equation to the considera- 

 tion of the coefficients of expansion with temperature and of pressure 

 with temperature, showing that although they were nearl}^ equal, nev- 

 ertheless they were almost independent quantities. His investigation 

 of the capillarity constant was masterly, and he added further to our 

 knowledge of the magnitudes of the molecules of gases and of their 

 mean free paths. Following up the experiments of Joule and Kelvin, 

 he showed how their cooling coefficients could be deduced, and proved 

 that they vanished at a temperature in each case which is a constant 

 multiple of the specific critical temperature. The equation of conti- 

 nuity developed by van der Waals involved the use of three constants 

 instead of one, as in the old law of Boyle and Charles, the latter ))eing 

 only utilized to express the relation of temperature, pressure, and 

 volume, when the gas is far removed from its point of liquefaction. 

 Of the two new constants one represents the molecular pressure aris- 

 ing from the attraction between the molecules, the other four 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 char- 

 acters of th(> isothermals, but also gave the Aalues of the critical tem- 

 perature, the critical pressure, and the critical volume. In the case 

 of carbonic acid the theoretical results were found to be in remarkable 



