450 Royal Society : — Prof. J. Thomson on the 



f erred to (the one read at the Brighton Meeting, 1872), I gave 

 demonstrations showing that these two curves L T and N T should 

 meet, as shown in the accompanying figure, with a re-entrant angle 

 at T, not with a salient angle such as is exemplified in the vertex of 

 a pointed arch, and offered in conclusion the suggestion that the 

 reasoning which had been adduced might be followed up by a quan- 

 titative calculation founded on experimental data, by which calcu- 

 lation the difference of the pressures of steam with water and steam 

 with ice for any given temperature very near the triple point may 

 be found with a very close approximation to the truth. 



In the month of last October (October 1872) I explained to my 

 brother, Sir William Thomson, the nature of that contemplated 

 quantitative calculation : I mentioned to him the method which I 

 had prepared for carrying out the intended investigation, and in- 

 quired of him for some of the experimental data, or data already 

 deduced by theory from experiments, which I was seeking to ob- 

 tain. On his attention being thus turned to the matter, he noticed 

 that the desired quantitative relation could be obtained very di- 

 rectly and easily from a simple formula which he had given in his 

 paper on the Dynamical Theory of Heat, Transactions of the 

 Eoyal Society of Edinburgh, March 17, 1851, § 21 (3), to express 

 the second law of thermodynamics for a body of uniform tempe- 

 rature throughout, exposed to pressure equal in all directions. 



That formula is 



J=cm ; 



in which p denotes the amount of the pressure, and -n its rate 



of increase 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 (i. e. steam), or ice and 

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



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 pur- 

 pose, say 0° Centigrade, 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 pressure with increase of temperature, 



when the volume is Jcej>t constant, has been denoted by ~, yet 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 contact either with water 

 or with ice, for any given temperature, is independent of the 

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



