460 Thaddeus Estreicher on the 



" reduced curves." It appears that these curves are not 

 identical, and the differences between them are too great to 

 be explained by errors of observation. The reason lies else- 

 where, namely, in the disagreement of the quantity / for 

 different bodies. From Prof. Guye's paper *, we know that 

 / in van der Waals's formula 



-log ,r=/-=Z 

 in which it and r are reduced pressure and temperature 

 ( — and m l» is not constant, but differs for different sub- 



stances, and that its value is generally about 3'06, except for 

 associating substances, which have more complex molecules 

 in the liquid than in the gaseous state ; for then f is higher 

 than 3' 06, and may even be higher than 4. In his first 

 paper quoted above, Prof. Guye proves that the curve of 

 pressures of saturation for associating liquids intersects the 

 curves for non-associating bodies (I. c. p. 168). Thence we 

 can easily infer that such a curve, when reduced, is farther 

 from the axis of pressures and nearer the axis of temperatures 

 than a curve for a normal body. And, indeed, the curves for 

 oxygen, carbon bisulphide, ethylene, and other non-associating 

 bodies lie much nearer the axis of it than the curves for 

 water, acetic acid, and alcohols, which bodies are associated, 

 according to Messrs. Ramsay and Shields f. It follows thence 

 that the value of / for associating bodies must differ and be 

 greater than the normal value. For, from the formula of 

 Prof, van der Waals, 



1 — t 1 — r f 



-log7r=/— , and -\ogir'=f-y-, . (1) 



for another body we have at corresponding temperatures, 



/ _ log IT m 



f~\ogir' W 



Similarly, at corresponding pressures, 



f- 1-T W W 



But as, for associating substances, ir is smaller at corre- 



* Archives d. Se. phys. et natiir. d. Geneve, xxxi. pp. 163 and 463. 

 Also Prof. Kamsay, Proc. E. S. April 26, 1894. 



t Phil. Trans, clxxxiv. A. p. 167. Also Zeitschr.f. physik. Chemie, xii. 

 p. 433. 





