202 Mr. llerapalh on True Temperature, and the [Sept. 



= 2 (p { — p) •'~~f 5 fr° m which we easily get n (F, — F) 

 + F, - F = 2 u {p J - ;;, p) + 2 ( Pl p - f), and n = 



2 /' P ~! P ',~ (1 p'~~*r - Now by putting p = T, we have Cor. 2 

 of the preceding Piop.p, = T„ and F, — F = T,'- — T 2 ; whence 



n — 2T t T - 2T,H (TV - T") T 2 T, T - T a - X, 3 ~ m0St 



advantageous method, therefore, of examining the truth of the 

 theory is when the weights of the portions mixed are equal, as I 

 have stated at p. 406 of the last volume of the Annals ; for under 

 this circumstance, the difference between the Fahrenheit theory 

 and mine is a maximum. 



Prop. III. Theou. II. 



Let N, N,, denote the numeratoms of any two fluids which do 

 not act chemically on one another, and T, T,, their true temper- 

 atures, then if r be the true temperature of the mixture of equal 

 volumes of these fluids, N : N, :: t — T, : T — t. 



For no motion being supposed to be gained or lost by the 

 mixture, the sum of the motions of all the particles of the mix- 

 ture will be equal to the sum of the motions of all the particles 

 in the two fluids before the mixture. But the volumes of the 

 two fluids being equal, the sum of all the motions of each fluid 

 will be as its temperature and numeratom conjointly ; and the 

 temperature of the mixture being supposed to be uniform, the 

 sum of all the motions of the mixture will be as the sum of 

 the two numeratoms multiplied by the common temperature ; 

 therefore, t (N + N ) = T N + T, N„ and, consequently, N : 

 N, :: T - T, : T - r. 



Cor. — Hence the numeratoms and temperatures of equal 

 volumes of anv two fluids which have no chemical action on one 

 another being given, the temperature of the mixture may be 

 found; for since N : N, :: t *- T, : T — r f we have t = 



T N + T N 



— ^ — r7-^- J . P>v this cor. as soon as we have determined by 



N + N, •' J 



one experiment the ratio of the numeratoms, we can employ it 

 to examine the accuracy of the theory by other experiments. 



Scholium. 



In Dr. Henry's Chemistry, it is said that if equal portions in 

 volume of mercury at 100° F and water at 40° be mixed toge- 

 ther, the temperature of the mixture will be 60°. Hence if N 

 denote the numeratom of this water, the preceding tables give 

 T, = 1068-5, T = 1008-3, and t = 1028-8; and, therefore, 

 N, : N :: 20-5 : 39-7 :: 1 : P94, or as 1 : 2 nearly. Taking this 

 ratio as correct, v/e shall be able to compare the theory with the 

 experiment from which it has been deduced, as well as with the 

 Other experiments mentioned by Dr. Henry. For, by the pre- 



