218 HISTOEY OF COLD AND THE ABSOLUTE ZERO. 



the main preserv^ed the co-vohmie (depending- on the total xolimie of 

 the molecules) unaltered while trying- to niodif}" the constant of molec- 

 ular 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, l)y Kammerlingh Onnes, Korteweg, Jaeger, Boltz- 

 mann, Dieterici, and ileinganum, and others, all directed in the main 

 toward an admitted variation in the value of the co-volume while pre- 

 serving 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 correspond- 

 ence 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 energ}" of the particles inversely in the ratio of the diminution of 

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

 has shown how a " reduced" isothermal may be got by taking two other 

 prominent points as units of measurement instead of the critical 

 coordinates. The most suggestive advance in the improvement of the 

 van der Waals equation has been made by a lady, Mme. Christine 

 Meyer. The idea at the base of this new development may be under- 

 stood from the following general statement: van der Waals brings the 

 van der Waals surfaces for all substances into coincidence at the point 

 where volume, pressure, and temperature are nothing, and then 

 stretches or compresses all the surfaces parallel to the three axes of 

 volume, pressure, and temperature until their critical points coincide. 

 But on this plan the surfaces do not quite coincide, ))ecause the points 

 where the three variables are respectively nothing- are not correspond- 

 ing points. Mme. Meyer's plan is to bring all the critical points first 

 into coincidence, and then to compress or extend all the representative 

 surfaces parallel to the three axes of volume, pressure, and temperature 

 until the surfaces coincide. In this wav, takmg twenty-nine different 

 substances, she completel}' verifies from experiment van der Waals's 

 law of correspondence. The theory of van der Waals has been one of 

 the greatest importance in directing experimental uivestigation and in 

 attacking the difficult pro])lemsof the li(]ucfaction of the most perma- 

 nent gases. One of its greatest triumphs has been the proof that the 

 critical constants and the boiling point of hydrogen theoretically 

 deduced by Wroblewski from a study of the isothermals of the gas 

 taken far above the temperature of li(|uef action are remarkably near 

 the experimental values. We may safely infer, therefore, that if here- 

 after a gas be discovered m small (quantity even four times more volatile 



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