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



on the subject in order to procure the results of some experi- 

 ments to compare the present proposition with, but have not 

 been fortunate enough to meet with more than one. Mr. Watt 

 having heated a quantity of water in a Papin's digester to 400° 

 Fahr. suddenly opened the vessel, when about a fifth of the 

 water rushed out in vapour, and the temperature of the rest sunk 

 to 212°. By this experiment, t' = 1172-6, and t = 1329-2; 



13^9*2 1172*6 



and putting w = 1, we have w' = ~ x ^ 9 . 2 6 = fifc or 



-•nearly. This differs from ^ by a pr,th of the whole quantity 



of water ; a difference which philosophers will allow to be suffi- 

 ciently minute for an experiment of this kind. It is observable 

 that the experimental loss exceeds the computed, which is just 

 what we should expect from the manner of making the experi- 

 ment ; for as the vapour rushes out with very great violence, it 

 is highly probable it will force out with it more water, than, if 

 converted into vapour, would be sufficient to reduce the temper- 

 ature to 212°. 



The theorems demonstrated in the present Proposition and its 

 Corollaries furnish us with very easy means of experimentally 

 examining the effects of what is called radiation either to or from 

 water, under peculiar circumstances of temperature, &c. For 

 the quantity evaporated being known, its individual effect on the 

 temperature becomes known, and hence the effect of radiation. 



Prop. XXII.* Prob. VII. 

 ■" Let two vessels communicating with a boiler be filled with 



* This problem, or rather problems, was proposed to me in a very early stage of my 

 inquiries into the laws of vapours by a gentleman, an able mathematician, under cir- 

 cumstances, which, to prevent misconception of their cause on one side, and the motives 

 on the other, it may be necessary to mention. Being one afternoon at the Rev. H. S. 

 Trimmer's, I informed him, that some ideas had just before occurred to me respecting 

 the difference between vapours and permanent airs or gases, which gave me hopes I 

 should, at some period, be able to bring the phenomena of vapours, and with them the 

 theory of the steam-engine, within the pale of mathematical laws. During this conver- 

 sation, I happened to mention that the gentleman alluded to had told me about 1 5 

 months before, that he had a problem connected with steam which he wished to get 

 solved, and which he had proposed to some of the most conversant in these matters for 

 that purpose, but had not received any satisfactory answers. At the same time I 

 observed, that I thought, if I had and knew what this problem was, I could solve it. 

 Mr. Trimmer immediately proposed that I should write to the gentleman, and under- 

 take the solution, and, without scarcely waiting for my reply, placed before me a pen, 

 ink, and paper. While writing this letter, and keeping up a conversation with Mr. 

 and Mrs Trimmer, I inadvertently gave the above gentleman not only liberty to send 

 me the problem in question, but any other of the kind he might choose. The disadvan- 

 tageous situation in which this offer placed me, and the power it gave to a very able 

 man to put my skill to a severe trial, were immediately perceived , but relying on the 

 accuracy of my principles, and the facility with which things flow from them, I deter- 

 mined to send the letter off as it was rather than take the trouble to write another. The 

 consequence was, that about a fortnight afterwards I received the above problems, which 

 I at once saw far transcended the powers of any thing yet published to resolve. How- 

 ever, as soon as I had read them, I felt persuaded my theory would help me out ; and 



