certain High-temperature Boiling-points, 157 



ture exhibited by the phenomena as a whole, and by a 

 diagram such as fig. 3, for instance, then the errors in 

 question assume much smaller importance. In the above 

 pages I have presumed to believe that at the outset the wide 

 temperature comparison is the one which ought first to be 

 made, and some fundamental relation applicable to the whole 

 range of temperature investigated. After this has been done, 

 the said relation may be modified to-suit the individual case. 



I can state this more clearly as follows : — Groshans's deri- 

 vation of his principle * is sufficiently simple. If vapours 

 have identical coefficients of expansion, 1/273 say, and their 

 densities be expressed relatively to the density at the normal 

 boiling-point in each case, then the ratio of absolute boiling- 

 temperatures corresponding to any two given pressures will 

 be the same for all vapours. This inference is incorrect, just 

 in proportion as the application made of the Boyle-Charles 

 law is incorrect. 



However, Dupre in deriving his formula makes virtually 

 the same assumption f. Again, J. J. Thomson % introduces 

 Boyle's law into the mean value of the Lagrangian function 

 investigated for the occurrence of maximum vapour-tension ; 

 but since the form of an arbitrary function of temperature is 

 here determined by experiment, the insertion of Boyle's law 

 suffices Thomson's purposes. Following the model of his 

 work, I hoped to find some suggestion as to a modification of 

 Dupre's equation, such that it may be the outcome of an 

 original type for all substances, by inserting Van der Waals's 

 law instead of Boyle's law into the proper term. It seemed 

 plausible that Dupre's equation could thus be corrected by 

 aid of constants, a and b, the molecular interpretation of 

 which has already been given by Van der Waals. Per- 

 forming the operations, I find, rigorously, 



an equation which, though capable of simplification, essen- 

 tially involves f, and is therefore not suggestive. 

 Physical Laboratory, U.S. Geological Survey, 

 Washington, D. 0., U.S.A. 



* Somewhat similar approximate relations are investigated from Reg- 

 nault's data by Dupre (I. c. pp. 115-117). Groshans used data for water 

 and carbonic acid gas. An older principle due to Dalton (Lit. Soc. 

 Manchester, v. p. 550) is incorrect. The work of Kopp and of Bartoli 

 on corresponding boiling-points has special reference to volumes. 



t Bertrand, /. c. p. 101. X Thomson, /. c. p. 158. 



Phil. Mag. S. 5. Vol. 29. No. 177. Feb. 1890. N 



