458 Mr. Herapath 071 True Temperature, and ihe [Dec. 



. — , supposing w' to be water instead of steam. Therefore, 



*? — r = — - is the rise of temperature due to the conden- 

 sation of vt. weight of vapour ; and consequently - — is the 



rise due to the condensation of unity weight of steam. But this 



condensation raises not merely w weight of water from t to t 7 , 



but to + 1 weight. Whence the rise of unity weight would be 



&t' 



— , which expresses the effect of condensation in terms of the 



true temperature. Consequently in the detached boiler the effect 



in units of true temperature = — — , and in the attached 



6 V30 



boiler it = f.f'E; accounting E the elasticity. And if we 



suppose the effect of condensation at 212° Fahr. = 1, in the 



former case it will =\A^, and in the latter *"]^ or y^§. 



To express the same things in Fahrenheit degrees, we may 



multiply each expression by ~- — = — = nearly, supposing F, 



the Fahr. degree corresponding with t', and F the same thing 

 corresponding with t ; and the products will nearly give the 

 latent heats according to the common views. 



If it be required to give a correct expression in terms of Fah- 

 renheit, that also may be done. Let us suppose the weight of 

 vapour = 1, that of water being to; and let F, F„ and F,, be 

 the Fahrenheit temperatures of the water, vapour, and mixture. 

 Suppose also that F 3 is the Fahrenheit temperature which would 

 result from mixing one of water instead of steam at F, with to of 

 water at F. Then F^ — F 3 is manifestly the increase of tem- 

 perature occasioned by the condensation, and is, therefore, the 

 whole latent heat developed by the condensation of unity weight 

 of vapour. But this latent heat acts not on the to weight of 

 water only, but on the whole mass of water and condensed 

 steam; * for if there were no latent heat developed, the whole 



* It is curious that this circumstance has escaped the notice of Dr. lire in his calcu- 

 lation of the latent heat of water, in the Transactions of the Royal Society for 1818, 

 p. 388. He computes the latent heat from the formula (F., — F 3 ) ir, instead of 

 t*» — F3) . (10 + I). But just above, in the same page, another error of a more 



" 84 



extraordinary kind appears. The Doctor says, = -52 is the elevation of tem- 

 perature which 1 of water at 2 ! 2° would occasion on 1 C 1 -7 of water at 42-5°." Now the 

 , . 212 - 4 2-5 169-5 

 IS J6I-7 + 1 = ifio.r- = 1 '01 * s tne proper elevation according to the old doc- 

 trine, or double what Dr. Ure has computed it to be. These errors rectified give the 

 Doctor's latent heat cf water 6-o°- 1 -04° x 162-7 = 888 J, instead of 967°. 'Whether 

 like errors pervade die other latent heats he has there given, I cannot sav ; I have not 



