1821 .] Causes of Calorific Capacity, Latent Heat, fa. 205 

 (2 or , 1 —When V = V, the theorem reduces itself to the 



Sa Co;^ 2 .—Taking V,= t)V and N, = n N, the general theorem 



becomes r = ? + P " T ' 5 aild > therefore, when the volume is so 



taken that v n = It," that V N = V, N„ r = ± (T + T,) ; in 

 which case as we have remarked in the last Scholium, it is 

 immaterial which of the fluids be put at the higher temper- 

 ature the result will be the same. 



^ Co', 3.-Because r (V N + V, NO = TV N + T V, N„ 

 we have N : N, :: r V, - T, V, : T V - r V. Therefore the 

 volumes of two fluids being given, the temperatures at winch 

 they are mixed, and the temperature of the mixture, the ratio of 

 the'numeratoms may be found. # # ' 



q 01 . 4. l n most experiments, it is much easier to determine 



the proportion of the weights than of the volumes, in which case 

 it will be better to have the ratio of the numbers of the particles 

 in equal weights. Let P, P„ denote the numbers of the particles 

 in equal weights, and W, W„ the weights themselves, then the 

 number of particles in each fluid being as W P or W, P„ it is 



TWP+ T,W,P, 

 evident that t = w p + w p • 



Cor. 5.— From the preceding cor. it follows that P : P, :: W, 

 ( T — T ) : W (T — t); and that if W be so taken, that W P = 

 \y p ' T = j. (T + TO a case analogous to that of cor. 2. 



Prop. V. Prob. II. 



Two fluids being given, it is required to investigate the condi- 

 tions of the mixture so that the theory may be examined under 

 the most advantageous circumstances; that is, so that the 

 distances of the resulting temperatures from Fahrenheit s arith- 

 metical mean shall be the most unequal. 



Since the equation r = IXli^A found in Cor. 4 of 



TVN + T.V.N, 



the preceding Prop, is precisely the same as r = v N + v , N, 



in the context of the theorem, by changing W into V, and P into 

 N, it is plain we may in the present inquiry use either. We 

 will, therefore, take that given in the corollary. Let us put 



W, = n W, and we have t = *%;*%*' « % Cor - 2 > Pr0 P' T ' 

 if we put T,« = F, + 448, T» = F + 448, and r* = F„ + 448; 

 therefore, F„ = (IZii^I-)*- 448 ; and the other F n equals 

 /T,P + HTP,y» _ 448 by clianging T, for T, and T for T„ that 



is by reversing the bodies with respect to the temperatures, or, 

 which is the name, the tampamfcurea with respect k> the 



