1821.] Causes of Calorific Capacity, Latent Heat, fyc. 457 



steam of any temperature, and heated themselves to the same 

 degree, say 212°. Let one be detached from the boiler, and let 

 the other continue to communicate with it. Let the elastic force 

 of the steam be doubled, trebled, &c. in both ; required the cor- 

 responding densities of the steam in each vessel, one of course 

 being constant; their capacities for heat, and quantities of latent 

 heat above what is present at the temperature of 212°." 



Case 1. — Let it be required to determine the ratio of the capa- 

 cities. Suppose F,, F + n, F„ F, +?i, to denote any Fahrenheit 

 temperatures, and t, t u f a , t a , the corresponding true ones. 

 Them because t : t, :: V F + 448 : ^F + n + 448, and t : t ' 



__ ' 4 J 



:: v F, + 448 : \/ F, + n + 448, we have t. — t : t — t :: 



3 2 



V F + « + 448 - V F + 448 : V F, +n + 448 - ^FT+448; 



tj-t, V F, -r n + 44« - V F, + 448 /F + 448 



and, therefore, - = — = * / 



■ *i-t VF + n + 448- VF -r 448 V F, + 448 



when n = o, which is, therefore, the capacity at F„ that at F 

 being unity. 



The above theorem gives the ratio of the capacities in terms of 

 the Fahrenheit temperatures ; but as the proposer requires it in 

 terms of the elasticities, and of the capacity at 212°, that also 

 may be given. 



First, in the case of the detached boiler. By Prop. 8 of my 



e -p, F, + 448 F, + 448 . nn 



former paper, E = e f + 448 = — — — , accounting e = 30 



when F = 212°. Hence by substitution 



t 3 -t 2 >/ 22 B + n — V~1%1[ /~30 



T— i" ' y/' 660 + h - v~mo 

 when n = o. 



Secondly, in the case of the attached boiler, we have Prop. 

 21, Cor. 2, true temperature = cp~ ' E; and, therefore, F,+448 



- <f~ ' E > 2 X : TiSooo = <*~ ' E > 3 x & when F = 21 2°, and 

 the corresponding elasticity = 30. Hence 



= * / -|r the capacity sought, 



4 / (3-' E)* . + n - A /(*-' E)* 



'3 - U X/ * 6250 \/ V? ; 6250 1 172-6 ., 



rZT = — — — = rzT5> the 



'»• ' V 660 + n - V 660 <p-'E' 



capacity sought, when n = o. 



Case 2. — To determine the latent heats in terms of the elasti- 



6 w t + \\ w' t' 

 6 (io + ui') 



steam being condensed ; and by Prop. 1, Cor. 2, we have t = 



cities. By Prop. 20, Cor. 2, we have t' = , all the 



b (to + w') 



though I had not then solved tire principal part (our 1 5th Prop.) I replied that as soon 

 as I was released from a mathematical investigation of Mr. Dalton's laws of evapora- 

 tion, which I was then husily trying to discover and arrange for the press, I would 

 endeavour to send him the solutions he desired. 



