Saturated Steam expressed by a New Formula, 7 



we may find the temperature at which d . log PV becomes equal 

 to d.logp ; that is, the temperature at which the rate of incre- 

 ment of the expansive force of a unit weight of saturated steam 

 is equal to the rate of increment of expansive force of a unit 

 weight of a perfectly elastic gas maintained at a constant volume. 

 Since 



we shall have d . logPV = </. logp, when 



(/ \ T302585 

 1+ 376) =- 8084 °- 



The value of / which satisfies the above equation is negative, and 



equals — 56°. Consequently the absolute temperature at which 



<£.logPV = ^. log;? is (376 — 56), or 320°, which corresponds to 



(320 — 276), or 44° of the Centigrade thermometer. The ratio 



d. log PV 

 * . — is less than unity for all temperatures above 44° C, 



and greater than unity for all temperatures below that point. 



In Tables II. and III., the values at different temperatures 

 of V and PV given by the new formulae are compared with 

 similar values obtained from the published Tables of Professor 

 Rankine, and with similar values obtained from the formula 

 for volume by M. Clausius, in combination with the new for- 

 mula for pressure of saturated steam. On comparing together 

 the three series of results, it will be perceived that for all tempe- 

 ratures above 60° C. the three series of results may be said to be 

 identical one with another. At temperatures below 60° C, the 

 two series of M. Clausius and Professor Rankine continue to 

 agree with one another, but they disagree slightly with the 

 results of the new formula. This disagreement arises from the 

 circumstance that the first two series of results are regulated by 

 the law of latent heat adopted by M. Regnault, which law is in 

 complete accordance with the formula h = VYp~ n for all tempe- 

 ratures above 60° C, whilst it deviates slightly from such for- 

 mulae for all lower temperatures. 



In Table IV. will be seen, for various intervals of tempera- 

 ture from 0° C. to 220° C, the relation between the numbers 

 for latent heat given by M. Regnault, and the true numbers 

 for latent heat which flow from the adoption of M. Clausius's 

 formula for volume in combination with the new formula for 

 pressure of saturated steam. It will be seen that for all tem- 

 peratures above 60° C. there is no appreciable difference be- 

 tween experimental and theoretical numbers. At temperatures 

 below 60° C. there is a slight discrepancy between the alleged 



