398 J. W. Gibbs — Equilibrium of Heterogeneous Substances. 



differential equation from which the vahaes of //sd), ^2(1)5 ^'scd? 

 etc. in terms of ^, yUj, ja^^ etc., may be at once obtained by comparison 

 with (514).* 



* If liquid mercury meets the mixed vapors of water and mercury in a plane sur- 

 face, and we use /z, and fi.i to denote the potentials of mercury' and water respec- 

 tively, and place the dividing surface so that T, =0, i. e., so that the total quantity of 

 mercury is the same as if the liquid mercury reached this surface on one side and the 

 mercury vapor on the other without change of density on either side, then r2(i) will 

 represent the amount of water in the vicinity of this surface, per unit of surface, 

 above that which there would be, if the water-vapor just reached the surface without 

 change of density, and this quantity (which we may call the quantity of water con- 

 densed upon the surface of the mercury) will be determined by the equation 



da 

 ^2(1)= -^• 



(In this differential coefficient as well as the following, the temperature is supposed 

 to remain constant and the surface of discontinuity plane. Practically, the latter con- 

 dition may be regarded as fulfilled in the case of any ordinary curvatures.) 



If the pressure in the mixed vapors conforms to the law of Dalton (see pp. 215, 218), 

 we shall have for constant temperature 



dp-2 = 7i '^¥2, 

 where j).i denotes the part of the pressure in the vapor due to the water-vapor, and 

 y.2 the density of the water-vapor. Hence we obtain 



da 

 ^2(1)= ~>'2^- 



For temperatures below 100° centigrade, this will certainly be accurate, since the pres- 

 sure due to the vapor of mercury may be neglected, 



The value of a for^2=0 and the temperature of 20° centigrade must be nearly the 

 same as the superficial tension of mercury in contact with air, or 55.03 grammes per 

 linear metre according to Quincke (Pogg. Ann., Bd. 139, p. 27). The value of a at the 

 same temperatiwe, when the condensed water begins to have the properties of water 

 in mass, will be equal to the sum of the superficial tensions of mercury in contact 

 with water and of water in contact with its own vapor. This will be, according to 

 the same authority, 42.58 + 8.25, or 50.83 grammes per metre, if we neglect the differ- 

 ence of the tensions of water with its vapor and water with air. As p.^, therefore, 

 increases from zero to 236400 grammes per square metre (when water begins to be 

 condensed in mass), a diminishes from about 55.03 to about 50.83 grammes per linear 

 metre. If the general course of the values of a for intermediate values of j^i vvere 

 determined by experiment, we could easily form an approximate estimate of the 

 values of the superficial density T^n) for different pressures less than that of satu- 

 rated vapor. It will be observed that the determination of the superficial density 

 does not by any means depend upon inappreciable differences of superficial tension. 

 The greatest difficulty in the determination would doubtless be that of distinguishing 

 between the diminution of superficial tension due to the water and that due to other 

 substances which might accidentally be present. Such determinations are of con- 

 sideraV)le practical importance on account of the use of mercury in measurements of 

 the specific gravity of vapors. 



