382 Prof. E. Clausius on the Theoretic Determination of 



so that the external work done in the vaporization is equal to 

 that which would be done in the same increase of volume if 

 the pressure changed in accordance with the theoretic iso- 

 thermal*. 



This principle governing the position of the straight line 

 we can now employ in order to derive, from the general theo- 

 retic pressure-formula which holds for all volumes, that pres- 

 sure which is exerted by saturated vapour. The first published 

 research on this subject which has come to my knowledge is 

 found in an interesting essay by Van der Waalsf . The author 

 has, it is true, refrained from communicating in full his calcu- 

 lations and the final equations resulting from them, because 

 the former were too lengthy, and the latter too complicated 

 and, besides, valid only for a limited portion of the curves ; 

 but he has collected a series of important consequences drawn 

 therefrom. Another, likewise very valuable, investigation 

 upon the subject has recently been published by Planck J, in 

 which both the general equations and their special application 

 to carbonic acid are given. 



I also had already, before I became acquainted with these 

 investigations, been for a long time occupied with the same 

 subject ; and the conclusion of my investigation was delayed 

 only by the toilsomeness of the numerical calculations which 

 were necessary for the comparison of the theoretic formulas 

 with the data of observation. But now that those investiga- 

 tions of Van der Waals and Planck are published, I think I 



* When, in my paper on the behaviour of carbonic acid (Wied. Ann. 

 ix. p. 337, 1880), I determined the position of the straight line in the 

 manner above stated, I treated the question as still an open one. At the 

 same time I had derived my knowledge of Maxwell's views from what I 

 could not but consider the most authoritative source, namely his work 

 upon the Theory of Heat, and, indeed, from the last edition, revised by 

 him, published in 1875. In this edition he has omitted a view enunciated 

 in the earlier editions which differs from the above, but without putting 

 another view in its place, from which I was of course obliged to conclude 

 that he recognized that view as erroneous, but had not yet obtained one 

 more satisfactory to him. I have subsequently learned, from a commu- 

 nication kindly made to me by M. van der Waals, that Maxwell has again 

 spoken upon the subject in another place, and there enunciated a view 

 agreeing with the above, — namely, in a lecture delivered at the meeting 

 of the Chemical Society on the 18th February 1875, which lecture is 

 printed in 'Nature,' March 4 and 11, 1875. Why Maxwell has not men- 

 tioned the view there enunciated in the new edition of his work, published 

 in the same year, is unknown to me. 



t Van der Waals, Onderzoekingen omtrent de overeenstemmende eigen- 

 schappen der normale verzadigden-dainp- en vloeistojlijnen, Amsterdam, 

 1880 ; also admitted into Roth's translation of the work entitled Over de 

 continuiteit van den gas- en vloeistoftoestand, Leipzig, 1881. 



t Planck, Wied. Ann. xiii. p. 535 (1881). 



