366 



by making R approach zero at the same time as T in an appro- 

 priate manner. A variation of R of that nature for a definite 

 amount ^) of substance means that the molecules combine to aggre- 

 gates (association) ^) or undergo a different process, which resembles 

 the former very closely (quasi-associalion) and was repeatedly assumed 

 by VAN DER Waals ") and his pupils ") for the purpose of explaining 

 the incomplete numerical correspondence between the original equation 

 of state and the actual course of the isothermal. It was, however, 

 always assumed, that only one kind of molecular aggregate was 

 formed ^), whereas for R to fall to zero a much more complex 

 association (or quasi-association) is required, viz. a process in which 

 the molecular groups which are formed become more and more 

 complex, according as the temperature falls, until finally at 7'=:0 

 the substance behaves as if consisting of only one molecule, at least 

 at small volumes '). 



On this ground 1 have made an attempt to extend the theory of 

 association by introducing the hypothesis, that instead of one special 

 aggregate all possible molecular complexes are formed: double 

 molecules, triple, quadruple, etc. ') In this attempt 1 think I have 

 succeeded, proceeding logically on the lines followed by van der 

 Waals in his theory of "quasi-association or molecular aggregation" 



1) R is only then a universal constant (the gas constant) when it refers to a 

 gram mol of the substance. When the molecules form groups, the number of 

 gram-mols in a given mass diminishes and R for that mass changes proportio- 

 nally to that number. 



2) Previously F. Richakz (ZS. f. anorg. Ghem., 58 (190S) p. 356; (1908) p. 

 146) has explained the fall of the specific heat by association. Comp. also J. 

 DucLAUx, CR. 155 (1912) p. 1015. The same hypothesis was shown by G. Benedicks 

 (Ann. d Phys., (4), 42 (1913) p. 133) to be capable of giving an explanation of 

 Planck's law of energy-distribution. 



3) Gontinuitat, II, p. 27. These Proceedings (1), p. 107 and 494. 



*) J. J. VAN L\ar, ZS. f. physik. Ghem., 31, (1899) p. 1; Arch. Teyler, (2), 

 XI, 1908. 



G. VAN RiJ, Proefschrift, Amsterdam, 1908. 



'") This assumption was made for the sake of simplicity, although the probabi- 

 lity of different molecular complexes being formed was recognised. (See for in- 

 stance VAN DER Waals, These Proceedings, XIII (1), p. 494). 



S) Gomp H. Kamerlingh Onnes and W. H Keesom. Die Zustandsgleichung. 

 Encyklopadie der Mathematischen Wissenschaften, V, 10, p. 886. Suppl. 23 of the 

 Gomm. from the Phys. Lab. of Leiden, p. 272 



We shall not dwell on the difficulty which may be involved in imagining the 

 state in which during the transition to the molecular condition of one solid lump 

 the substance must have consisted of a small number of molecules. 



''} This thought I developed many years ago for an associating substance 

 guch as water iq the dissolved condition (Acad. Roy. de Bruxelles, Mém. cour., 1896). 



