440 Mr. Herapath on True Temperature, and the [Dec. 



CJre's theorem will have the advantage ; because this is made 

 the point of departure in his theorem, whereas in mine it was 

 only used as one of the conditions. Indeed it is questionable, as 

 I shall presently show, whether philosophers are not deceived 

 respecting the actual tension of vapour at 212°. It has com- 

 monly been conceived that the tension of vapour at 212°, and 

 the atmospheric pressure under which water would boil at the 

 same temperature are perfectly equal; but from the views to 

 which I allude, it seems evident that this, strictly speaking, is 

 not the case. The tension, there is no doubt, is at the same 

 temperature greater than the atmospheric pressure of ebullition ; 

 but whether at 212° this difference is appreciable is a question I 

 am not experimentally prepared to prove. Let it be tried at a 

 low pressure, or, for instance, at a few degrees of temperature 

 above ebullition in vacuo, and I feel persuaded the difference 

 will be easily detected. 



Mathematicians can hardly conceive what labour and trouble 

 the investigation of apparently so simple a theorem has cost me. 

 The time indeed which this theorem has consumed out of the 

 small portion, not more than a month, I have had to discover, to 

 investigate, to make my researches, and to write the present 

 theory of evaporation, combined with other avocations, disadvan- 

 tages, and an indifferent state of health, has contributed to 

 render the theory and inquiries much less perfect than I could 

 wish. However, the scientific world will not, I presume, be dis- 

 pleased at my having sacrificed a part that can easily be retrieved 

 for the discovery of a theorem which, with others, I shall in the 

 course of this paper develop, will enable us to give the last 

 stroke of perfection to the theory of one of the most powerful 

 and useful instruments of modern invention, the steam engine. 



By this theorem, we find the temperature of no evaporation is 

 about 813-3 true temperature, and about 131° of Fahrenheit 

 below zero. Dr. Ure's theorem would put the temperature of 

 no evaporation at an infinite distance below 32° Fahr. and again 

 beyond 450° Fahr. it would make the tension decrease instead 

 of increase with an augmentation of temperature — a conclusion 

 decidedly wrong. 



If t denote the tension, then the true temperature T = 



V 



— + 2-21J3714 



; so that the tension being given, we can easily 



•002783313 



find the true temperature corresponding ; by Dr. Ure's theorem, 

 this cannot be done in a direct and general manner. 



This theorem, and those I have already demonstrated, will 

 easily enable us to resolve almost every question relative to 

 evaporation, and the specific gravity, elasticity, &c. of steam ; 

 but the application is so easy 1 forbear entering into it. 



I have already pointed out the difference between evaporation 

 and ebullition ; and have shown that the one arises from a 



