200 Dr. Rankine on Saturated Vapours. 



where b is a constant to be found by experiment, d the specific 

 heat of the vapour at constant pressure, and J the dynamical 

 equivalent of a unit of heat, t being the absolute temperature, 

 as before. In a paper read to the Royal Society of Edinburgh 

 in 1855, but not published, the same formula was shown to ex- 

 press in dynamical units the total heat of gasefication of any sub- 

 stance under any constant pressure when the final absolute tem- 

 perature is t. In the present paper the author equates that 

 expression to another expression for the total heat of evaporation 

 from the absolute zero, at a given absolute temperature t, as 

 follows, 



U + M = J P c U dt + t^ (v-v JI ) ; 



in which v and v" are the volumes of unity of weight of the sub- 

 stance in the gaseous and liquid states respectively, under the 

 pressure p and at the absolute temperature t. Then putting for 

 v its value in the perfectly gaseous state, namely 



J(c'-c)t 



P 

 where c is the specific heat of the gas at constant volume, and 

 neglecting v" as very small in comparison with v, there is found 

 by integration the following value of the hyperbolic logarithm 

 of the pressure of saturation (a being a constant to be deduced 

 from one experiment for each fluid), 



b c f 1 C*dt C* 



hyplog^-^^+^.hyplog*-^.^ ¥ yj<dt. (A) 



When c u is constant (as is approximately the case in some in- 

 stances), the preceding equation beeomes 



b c n — c ! 



hyplog^ = «-^— ^--^— ^hyplogt . . (B) 



The pressures of various vapours as calculated, on the supposi- 

 tion of their being perfectly gaseous, by means of the preceding 

 equations, are compared with their actual pressures — the general 

 result being that when the vapours are rare the differences are 

 small, and that when the densities increase the differences in- 

 crease. For example, in the case of steam, the pressures calcu- 

 lated by equation (B) agree very closely with the actual pres- 

 sures from 0° to 160° Centigrade ; but above the latter tempera- 

 ture the difference gradually becomes considerable, and at 220° C. 

 is about one-fiftieth part of the whole pressure. At 0° C. one 

 pound of saturated steam occupies about 3400 cubic feet ; at 

 160° C. about 5 cubic feet; and at 220° C. about 1*4 cubic foot. 



The author also makes some comparisons between the actual 



