CHARACTERISTIC EQUATION 17 



needed to agree with the facts, and such were suggested 

 by Sarrau l , Batelli 2 , and Jager 3 . 



Van der Waals 4 endeavours to take this circumstance 

 into account by the expression 



but then b appears only to be constant to a first approxi- 

 mation, and should be replaced by 5 



b b 2 6 3 



in which a = , j3 = 0-0958 6 ; 



o 



whilst lately, Amagat 7 , Rose-Innes 8 , and Lewis 9 have made 

 other suggestions. 



None of these equations can be regarded as the ex- 

 pression of a natural law : in deducing them, simplifying 

 assumptions are always made, and in none of them has 

 complete agreement with the facts been proved. Under 

 these circumstances it is best to choose the one which forms 

 the best compromise between accuracy and simplicity. 



The equation 



seems the most suitable. This expresses the qualitative 

 behaviour, indicating the gaseous state, the critical phe- 

 nomena, and the formation of liquid ; only the solid state 

 of aggregation is not accounted for, which is due to the 

 deduction assuming spherical molecules, and consequently 



1 Zeitschr.f. Phys. Chem. 12. 280. 2 Memorie di Torino, 1893, p. 27. 



3 Wien. Akad. Ber. 1892, p. 1675 ; see also p. 35. 



4 Van Laar, Die Thermo-dynamik in der Chemie, 1893, p. 50 ; Zeitschr. f. Phys. 

 Chem. ii. 433. 



5 Van der Waals, Verslagen Kon. Akad. Amsterdam, 1898. 



6 Van Laar, Archives Teyler, 1899. 



7 Comptes Rendus, 1894, p. 566. 8 Phil. Hag. 1899. p. 367. 



9 Amer. Acad. of Sc. 1899 ; see also 0. E. Meyer, Kinetic Theory of Gases, 

 1899; Thiessen, ' Zustandsgleichungen/ Wied.Ann. 1898. 



B 



