454 Mr. Herapath on True Temperature, and the [Dec. 



itself is homogeneous) is equal to — * / Y; in which V denotes 



the specific gravity of vapour, and G that of the gas in question. 



Though this formula must be considered as mathematically 

 true only in the case of perfect homogeneity, yet it would not 

 differ very materially in compound cases ; and, therefore, in any 

 airs with which we are acquainted. 



Those baromerins, as I have repeatedly stated, are proportional 

 to what is understood by the " calorific capacities or specific 

 heats." The discordance, however, in the determinations of the 

 " specific heats " of gases by different philosophers is so great, 

 that it is absurd, if not ridiculous, to attempt to compare the 

 theory with them. For instance, Crawford, who is conceived by 

 the British philosophers to be the most accurate in his experi- 

 ments of this kind, makes the " specificheat" of hydrogen 21*4, 

 while De Laroche and Berard, who obtained the prize of the 

 Jtoyal Institute of France for their experiments on this subject, 

 make it only 3*2936, which is something better than a seventh 

 part of Crawford's. Again, by the former, oxygen comes out 

 4*749, and by the latter, *2361 ; so that here Crawford's number 

 is not only six or seven times, as in the instance of hydrogen, as 

 great, but upwards of 20 times. Our theorem gives 1*375 for 

 oxygen, and 5*50 for hydrogen ; but philosophers will have the 

 goodness to recollect, that these numbers rest on the supposition 

 of the individual homogeneity of vapour, oxygen, and hydrogen. 

 A theorem might be easily given for any degree of complexity 

 or compoundness of composition in the airs, from which some 

 interesting conclusions may be drawn ; but these things I shall 

 reserve for another opportunity. One point may be observed, in 

 which our theory agrees with the general results of both parties, 

 namely, that the " specific heats " of the lighter airs exceed 

 those of the heavier. 



If we wish to have a theorem which will include the laws of 

 any changes on the body in its three states at once, we can 

 easily obtain it. For since by Cor. 1, Prop. 16, when B = 19, 

 b = 22 ; and since by Cor. 1 of the present Prop, when b = 6, 

 V = 11, we have B = 19, b = 22, and V = 22 x y - 40 i; 

 or if we prefer whole numbers, B = 57, b — 66, and b' = 121. 

 From these data we get the general equations t = 



19 T W + 28 t to + 40i t' mj' 19 T W + 22 t to + 40j t' to' _ 



19 (W + to + to" 7 ) ' 0f 22 (W + to + to') 



19 T W + 22 t to + \Q\ t' w' j. ,, , „ vj 



^ , according as tne mixture is wholly solid, 



40£ (W + to + to') ' & J 



wholly fluid, or wholly vapour. Several interesting phsenomena 

 connected with these general equations brevity obliges me to 

 leave unnoticed. 



Prop. XXI. Prob. VI. 



The temperature of a given weight of water being known, to 



