1821.] Causes of Calorific Capacity, Latent Heat, Sfc. 201 



Article VII. 



Tables of Temperature, and a Mathematical Development of the 

 Causes and Laics of the Phenomena which have been adduced 

 in Support of the Hypotheses of '* Calorijic Capacity, Latent 

 Heat," S)C By John Herapath, Esq. 



(.Continued from p. 103.) 



Prop. II. Prob. I. 



When portions of the same fluid are mixed at unequal tem- 

 peratures, we have seen by the preceding prop, that the temper- 

 ature of the mixture differs from that which would result if the 

 degrees of Fahrenheit indicated the true increments of tempera- 

 ture : let it now, therefore, be required to determine the most 

 advantageous circumstance under which the mixture can be 

 made with given temperatures ; or the temperatures being 

 given, let it be required to determine the proportion of the quan- 

 tities to be mixed, so that the difference between the resulting 

 temperature and the Fahrenheit theory shall be a maximum. 



If the Fahrenheit thermometer indicated the true increments 

 of temperature, the temperature of the mixture should be 



— — — — — ; W, W,, denoting the weights of the portions 



\V + VV ( 



mixed, and F, F,, their respective temperatures on Fahrenheit. 

 Therefore, when W, = n W, the temperature of the mixture 



H 1 ' i m *F 



becomes -: '• But under these same circumstances, the 



1 • + n 



true indication on Fahrenheit by Cor. 4 to the preceding Prop, 



{l + „ / 448 + F ' ") ~ 

 + " * y 448 + F I _ 448 = 



^ ^418 + F^^x^4 48 + F,y _ 44g> Hen( , e ^^ dmrence be „ 

 . It F + n F, / 1/448 + F + n x ^448 + F>\ 2 



tween these results, or ; I ; 1 



+ 448 is the difference between the two theories ; and, conse- 

 quently, the value of u deduced from the equation 



d . * - +** 1 = d • (JTT?)* ^ &&**?** v'448 + F andp, 



for V 448 + F,) on the supposition of it being the only variable, 

 will show the ratio of W, to W, when that difference is the 



greater. Therefor,, ^ = »*£§ . =*£* mi P, - F 



