362 



NATURE 



[Feb. 20, 1890 



contains an elaborate study of the molecular pressure in 

 fluids " ; and a few lines further down he refers to " Van 

 der Waals' memoir * On the Continuity of the Gaseous 

 and Liquid States,' which I have just rapidly perused in a 

 German translation." 



In view of the fact that Prof. Tait published a book on 

 " Heat" in 1884, these statements are so astonishing that 

 his interview with the visitor from whom he heard of Van 

 der Waals can only be described, in the words of Mr- 

 Montague Tigg when he discovered that Martin Chuzzle- 

 wit was in the next box in the pawn-shop, as "one of 

 the most tremendous meetings in Ancient or Modern 

 History." 



Other indications of a lack of acquaintance with what 

 has been done by others are not wanting. Taking 

 p{zr - a) = constant, as the equation to the isothermal 

 of a gas, and assuming that it applies approximately 

 to a liquid, the author concludes " that water [at 0° C.] 

 can be compressed to somewhat less than three-fourths 

 of its original bulk, but not further." He adds that " the 

 whole of this speculation is of the roughest character,'' 

 but makes no reference to the converging lines of evidence 

 which indicate that liquids could be compressed to from 

 o"2 to o'3 of their bulk at ordinary temperatures and 

 pressures. The numbers which lead to this conclusion 

 are frequently in good accord, whether they are deduced 

 from direct observation on the specific inductive capaci- 

 ties or the refractive indices of the liquids themselves, or 

 from those of their vapours, or from the molecular 

 volumes of the elements of which they are composed. 

 The latter, however, as calculated in the few cases 

 he discussed from Van der Waals' theory, are larger^ 

 except in the case of hydrogen, than the corre- 

 sponding numbers obtained from optical or electrical 

 measurements. Van der Waals did not deal with water- 

 vapour, but if we use the molecular volumes for Hg and 

 air obtained by means of O. Meyer's modification of his 

 theory, and take the molecular volumes of air and O2 as 

 identical (an assumption which will certainly make the 

 result too large), we obtain the following values :— 



Volume of the Matter in the Unit Volume of Water 

 tinder Standard Conditions. 



Deduced from observations on the refractive index of) , 



liquid water (L. Lorentz) ... J ° ^°°'- 



Deduced from observations on the refractive index of) ro 



water-vapour (L. Lorentz) jO 2005. 



Deduced from the molecular volumes of Hg and 0.{\ 



obtained from refractive index or specific inductive rO'23. 



capacity... ... ... ... ... ... ...j 



Deduced from the molecular volumes of H2 and air | .„ 



given by Van der Waals' theory J^-' 



'ZZ- 



Prof. Tait's value is 0717. It is certainly unfortunate 

 that a number so widely divergent from the results of a 

 whole literature of optical, electrical, and thermal re- 

 searches should be published in a Challenger Report 

 without any reference to the discrepancy. It is still more 

 unfortunate that in discussing the theory on which this 

 result is based the opinion should be registered that " the 

 quantity a [in the formula p{v - a) = constant] obviously 

 denotes the ultimate volume " (p. 48). This was published 

 sixteen years after Van der Waals had given reasons for 

 believing that a (or, as he calls it, b) is four times the 

 ultimate volume, and twelve years after O. Meyer had 



argued that the multiplier ought to be increased to 4^/2. 

 The best theories on the subject are no doubt tentative, 

 their agreement with facts is imperfect, but it is esta- 

 blished beyond the possibility of doubt that the constant 

 in question need not have the meaning which is here said 

 to be obvious. 



Two papers in which the compressibilities of solutions 

 of NaCl are discussed had appeared in Wiedemann's 

 Annalen some little time before the conclusion of Prof. 

 Tait's work. Rontgen and Schneider (Wied. Ann. 

 xxix. 165, 1886) determined the relative compressibilities 

 of water and of a number of different salt-solutions, and 

 Schumann ( Wied. Ann., xxxi. 14, May 1887) gave absolute 

 measures. Both researches were carried on at low 

 pressures only, but they are interesting in their relation 

 to Prof. Tait's conclusions, inasmuch as his compressi- 

 bihties at low pressures are obtained (as he fully explains) 

 by an extrapolation, and it is therefore desirable to compare 

 them with the values given by direct observation. 



In the following table the compressibihties obtained by 

 Schumann for solutions containing given percentages of 

 NaCl {i.e. parts of salt to 100 of solution) are compared 

 with the values deduced from Prof. Tait's formula : — 



It is to be observed that the number 50*3 is assumed 

 by Schumann from Grassi, and that it was employed in 

 experiments made with water, for determining the effect of 

 pressure on the internal volume of the piezometers. If it 

 had been replaced by Prof. Tait's value, the close agree- 

 ment between the results for mean percentages would be 

 destroyed. Schumann also obtains maxima of com- 

 pressibility for low percentages of certain salts, though he 

 seems very doubtful about the validity of these results. 

 We have no intention of entering into a detailed discus- 

 sion of his work which certainly appears to require con- 

 firmation, but there is no doubt that nobody could have 

 made a critical comparison between his own experiments 

 and those of Schumann so well as Prof. Tait, when he had 

 the whole subject at his fingers' ends. It is thus a real 

 loss to science when a man of his great ability ignores an 

 investigation published nearly a year before the date of 

 his own paper. 



The form of the formula given by Prof. Tait for the 

 compressibility of salt-solutions is closely analogous to 

 that deduced from theory by Prof J. J. Thomson in his 

 " Applications of Dynamics to Physics and Chemistry '' 

 (p. 184). He shows that if k' is the compressibility of 

 water, and P is the internal pressure due to the solution 

 of a salt, the compressibility of the solution is k'jil + Vk'). 

 If then we put k' = o"ooi86/(36 + p), Prof. Tait's formula 



for a salt-solution becomes k\ 



0"00I{ 



since P is proportional to very similar to J. J . Thomson's. 



4 



I + k'- 



\ , which. 



