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SCIENCE. 



[N. S. Vol. XVI. No. 406. 



corresponding temperatures the molecular 

 latent heats of vaporization are propor- 

 tional to the absolute critical temperature, 

 and that under the same conditions the 

 coefficients of liquid expansion are in- 

 versely proportional to the absolute criti- 

 cal temperature, and that the coefficients 

 of liquid compressibility are inversely pro- 

 portional to the critical pressure. All 

 these propositions and deductions are in 

 the main correct, though further experi- 

 mental investigation has shown minor dis- 

 crepancies requiring explanation. Various 

 proposals have been made to supplement 

 van der Waals' equation so as to bring it 

 into line with experiments, some being en- 

 tirely empiric, others theoretical. Clausi- 

 us, Sarrau, Wroblewski, Batteli, and oth- 

 ers attacked the question empirically, and 

 in the main preserved the co- volume (de- 

 pending on the total volume of the mole- 

 cules) 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 in- 

 creased 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, Die- 

 terici, and Rienganum, and others, all 

 directed in the main towards an admitted 

 variation 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 sim- 

 plest extension is that made by Rein- 



ganum, in which he increased the press- 

 ure 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 how a 'reduced' iso- 

 thermal may be got by taking two other 

 prominent points as units of measurement 

 instead of the critical coordinates. The 

 most suggestive advance in the improve- 

 ment of the van der Waals equation has 

 been made by a lady, Mme. Christine Mey- 

 er. The idea at the base of this new devel- 

 opment may be understood from the fol- 

 lowing 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 com- 

 presses all the surfaces parallel to the 

 three axes of volume, pressure, and tem- 

 perature, until their critical points coin- 

 cide. But on this plan the surfaces do not 

 quite coincide, because the points where 

 the three variables are respectively noth- 

 ing are not corresponding 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 vol- 

 ume, pi'essure, and temperature, until the 

 surfaces coincide. In this way, taking 

 twenty-nine different substances, she com- 

 pletely verifies from experiment van der 

 Waals' law of correspondence. The theory 

 of van der Waals has been one of the great- 

 est importance in directing experimental 

 investigation, and in attacking the difficult 

 problems of the liquefaction of the most 

 permanent gases. One of its greatest tri- 

 umphs has been the proof that the critical 

 constants and the boiling-point of hydro- 

 gen theoretically deduced by Wroblewski 

 from a study of the isothermals of the gas 

 taken far above the temperature of lique- 

 faction are remarkably near the experi- 



