30 Prof. J. Thomson on the [Dec. 11, 



ments, which I was seeking to obtain. On his attention being thus 

 turned to the matter, he noticed that the desired quantitative relation 

 could be obtained very directly and easily from a simple formula which 

 he had given in his paper on the Dynamical Theory of Heat, Transac- 

 tions of the Epyal Society of Edinburgh, March 17, 1851, 21 (3), to 

 express the second law of thermodynamics for a body of uniform tem- 

 perature throughout, exposed to pressure equal in all directions. 

 That formula is 



J>=CM ; 



in which p denotes the amount of the pressure, and -f ^ s ra * e ^ ^ n ~ 



crease per unit increase of temperature, the volume being kept constant ; 

 C denotes Carnot's function ; and M denotes the rate of absorption at 

 which heat must be supplied to the substance per unit augmentation 

 of volume, to let it expand without varying in temperature. The body 

 may be either homogeneous throughout, as a continuous solid, or liquid, 

 or gas ; or it may be heterogeneous, as a mass of water and aqueous 

 vapour (t. e. steam), or ice and water, or ice and aqueous vapour (i. e. 



Now apply that formula, 1st, to steam with water, and, 2nd, to steam 

 with ice, the temperature of the heterogeneous body in each case being 

 that of the triple point ; or we may, for the present purpose, say Centi- 

 grade, which is almost exactly the same. It is to be observed that while 

 in the general application of the formula the rate of increase of the pres- 

 sure with increase of temperature, when the volume is kept constant, has 



been denoted by -J?, y e t in each of the two particular cases now 



brought under consideration, it is a matter of indifference whether the 

 volume be kept constant or not ; because the pressure of steam in con- 

 tact either with water or with ice, for any given temperature, is inde- 

 pendent of the volume of the whole heterogeneous body ; so that the 

 change of pressure for change of temperature is independent of whether 

 there be change of volume or not. As C is a function of the tempera- 

 ture which has the same value for all substances at the same temperature, 

 it has the same value for the two cases now under consideration. Hence, 

 retaining for the first case (that, namely, of steam with water) the same 

 notation as before, but modifying it by the use of an accent where 

 distinction is necessary in the second case (that of steam with ice), and 



thus using jj- to denote the rate of increase of the pressure per unit 

 increase of temperature for steam with water at the triple point (0 Cen- 

 tigrade nearly), and M to denote the rate of absorption at which heat 

 must be supplied to a body consisting of steam and water at the triple 

 point, per unit augmentation of volume of that whole heterogeneous 



dp 

 body, to let it expand without varying in temperature, and using -^ 



