324 Mr. W-. Hibbert on the Gladstone 



It is at, once apparent that the introduction of /3 tends 

 to remove the anomalies, and also evident why cases 1, 2, 

 and 3 in the above summary are satisfied by the uncorrected 

 formulae. 



In 1 and 3, that is in the case of gases and dissolved salts 

 respectively, the value /3 is negligible compared with v. 



In 2, owing to the very slight compressibility of the liquids, 

 the changes in v are always exceedingly small. Hence v— /3 

 will change almost as much as v, if, as is probable, /3 is not a 

 large fraction of v. 



In 4, the case of liquids undergoing thermal expansion, 

 the changes in v are great enough, as compared with the 

 value of /5, to cause an appreciable difference between the 

 ratios v/i\ and (v—ff)/(y 1 —$). 



In 5, the case of vaporization, we have v for the liquid 

 comparatively small, changing into a very large value in the 

 vapour. Here there is a decided and altogether disturbing 

 difference between the ratios v/v 1 and (y—(3)l(i\—(3)*. 



Evidently, then, if the numerical data are found to be of 

 the right order, the introduction of /3 will remove the reserva- 

 tions with which the Gladstone law is usually stated. More- 

 over, the physical conditions under which ft needs to be 

 introduced render it probable that /3 has, or may have, a 

 physical meaning, and is not merely of the nature of an 

 arbitrary constant. But the real justification for introducing 

 /3 must be, h posteriori, by showing that the calculated values 

 are not improbable, and that they have relations to other 

 physical quantities. 



We can determine j3 for any one substance from observa- 

 tions on a liquid at two different temperatures. 



Let fi l9 fJL 2 be the refractive indices ; v 1} v 2 the volumes of 



unit mass I = -. J at the temperatures of two experiments, 



* This paper was written out before I recalled the fact that Ketteler 

 suggested the same solution for the discrepancies experienced in applying 

 the expression (/z 2 — l)t*= constant. Writing it (/x* — 1) {v— /3) he examined 

 a series of experiments made by "Weegmann (Zeit. phys. Chem. ii. p. 905). 

 The result was not very encouraging. But I am of opinion that there 

 are two reasons for that discouragement. First, "Weegmann happened to 

 work on substances of exceptional density, a fact which ought to fore- 

 shadow the probability of exceptional results in any volume deduced 

 from them. Secondly, the expression (/i 2 — l)v is surely not so good a 

 basis for the investigation as the simpler one due to Gladstone and Dale. 

 In ordinary liquids it is not so constant ; it is not supported by Quincke's 

 experiments on liquids under pressure {comp. Sutherland, Phil. Mag. 

 1888) ; nor does it render such service in Physical Chemistry as either the 

 Gladstone or Lorentz expression. 



