GO THE VOYAGE OF H.M.S. CHALLENGER. 



ADDENDUM (8/8/88). 



The reader has already seen that I have, more than once in the course of the inquiry, found myself 

 reproducing the results of others. A few days ago I showed the proof-sheets of this Report to Dr. H. du 

 Bois, who happened to visit my laboratory, and was informed by him that one of Van der WaaJs' papers 

 (he did not know which, but thought it was a recent one) contains an elaborate study of the molecular 

 pressure in fluids. I had been under the impression, strongly forced on me by the reception which my 

 speculations (Appendix E., below) met with both at home and abroad, that Laplace's views had gone 

 entirely out of fashion ; — having made, perhaps, their final appearance in Miller's Hydrostatics, where I first 

 became acquainted with them about 1850. In Van der Waals' memoir " On the Continuity of the Gaseous 

 and Liquid States," which I have just rapidly perused in a German translation, the author expresses himself 

 somewhat to the following effect : If I here give values of K for some bodies, I do it not from the 

 conviction that they are satisfactory, but because I think it important to make a commencement in a 

 matter where our ignorance is so complete that not even a single opinion, based on probable grounds, has 

 yet been expressed about it. 



Van der Waals gives, as the value of K in water, 10,500 atmospheres; and, in a subsequent paper, 

 10,700 atm.; while the value given in the text above is about half, viz. 5180 atm. So far as I can see, 

 he does not state how these values were obtained, though he gives the data and the calculations for other 

 liquids. It is to be presumed, however, that his result for water was obtained, like those for ether and 

 alcohol, from Cagniard de la Tour's data as to any two of the critical temperature, volume, and pressure. 

 Van der Waals forms, by a very ingenious process, a general equation of the isothermals of a fluid, in which 

 there are but two disposable constants. This is a cubic in r, whose three roots are real and equal at the 

 critical point. Thus the critical temperature, volume, and pressure can all be expressed in terms of the 

 two constants, so that one relation exists among them. Two being given, the equation of the isothermals 

 can be formed, and from it A' can be at once found. 



My process, as explained above, was very different. I formed the equation of the isothermal of 

 water at 0° C. from the empirical formula for the average compressibility under large additional pressures ; 

 and by comparing this, and the corresponding equation for various salt solutions, with an elementary 

 formula of the Kinetic theory of gases, I was led to interpret, as the internal pressure, a numerical 

 quantity which appears in the equations. 



I have left the passages, in the text and Appendix alike, which refer to this subject in the form in 

 which they stood before I became acquainted with Van der Waals' work. I have not sufficiently studied 

 Ms memoir to be able as yet to form a definite opinion whether the difficulty (connected with the non- 

 hydrostatic nature of the pressure in surface films) which is raised in Appendix E. can, or cannot, be 

 satisfactorily met by Van der Waals' methods. Anyhow, the isothermals spoken of in that Appendix are 

 totally different from those given by Van der Waals' equation, inasmuch as the whole pressure, and not 

 merely the external pressure, is introduced graphically in my proposed construction. 



