Gaseous, Liquid, and Solid States of Water. 45 1 



pressure for change of temperature is independent of whether 

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

 perature 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 —rr to denote 



the rate of increase of the pressure per unit increase of temperature 

 for steam with water at the triple point (0° Centigrade nearly), and 

 M to denote the rate of absorption at which heat must be sup- 

 plied to a body consisting of steam and water at the triple point, 

 per unit augmentation of volume of that whole heterogeneous 

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

 dp 

 -77, and M' to denote the corresponding rates for steam with ice 



at the triple point, we have 



dp 



dp' — M'* 

 ~dt 



The latent heat of evaporation of one pound of water at the 

 freezing-point (or triple point) into steam at the same temperature, 

 as determined by Begnault, is 606*5 thermic units, the thermic 

 unit being here taken as the heat which would raise the tempera- 

 ture of one pound of water one degree Centigrade ; and the latent 

 heat of fusion of ice is about 78 or 79 of the same thermic units. 

 Hence, though M and M' belong each to a cubic foot of steam at 



M 



the triple point, not to a pound mass of it, still the ratio ^v-, is 



606 



79 + 606 

 Hence 



dp 



~dt 606 1 



dp'" 79 + 606 = 143' 

 dt 



This shows that for any small descent in temperature from the 

 triple point (where the pressure of steam with ice is the same as 

 that of steam with water), the pressure of steam with ice falls off 

 1*13 times as much as does the pressure of steam with water. 



In submitting the quantitative calculation now given, I have pre- 

 ferred to adopt the method proposed and developed by my brother 

 rather than that which I had myself previously devised, because his 

 method is simpler, and brings out the results more briefly by estab- 



2G2 



