204 Mr. Herapath on True Temperature, and the [Sept. 



same way, that any errors which had crept into one would pro- 

 portionally run through the rest, and thence, in a similar way, 

 affect the theory with all. Dr. Henry has indeed not told us 

 whether the numbers he has given be the results of experiment 

 or calculation ; but from the way in which he has introduced 

 them, I should think they were derived from experiment. 



A beautiful case presents itself for ascertaining the truth of 

 our theory to any one who chooses to undertake it. When 

 water and mercury are mixed at a great interval of temperature, 

 180° for instance, the results, if our theory be true, by first put- 

 ting the one body and then the other at the higher tempera- 

 ture, will unequally differ from the arithmetical mean of 

 Fahrenheit. Thus, supposing the above ratio of the numera- 

 toms to be correct, a volume of water at 212° mixed with an equal 

 volume of mercury at 32° should give a temperature of 148 - 9°, 

 and a volume of mercuiy at 212° mixed with an equal volume of 

 water at 32° should produce a temperature of 88-8°. These 

 numbers differ from the arithmetical mean 122° by 26*7° and 

 33 - 2°. A slight difference in the ratio of the numeratoms would 

 but triflingly affect the discordance of these differences. It is 

 manifest, therefore, if experiments can be correctly made with 

 about this difference of temperature, the results will be suffi- 

 ciently marked to decide the truth of our theory respecting the 

 cause of the phamoniena attributed to " Calorific Capacity." 

 Were the present notions of capacities true, the results, if I 

 understand correctly the doctrine, should be equidistant from the 

 arithmetical mean. But to ascertain this inequality of distances, 

 we are not obliged to use water and mercury ; we may use water 

 alone by substituting for the mercury half its volume of water, 

 or mercury alone by substituting for the water double its volume 

 of mercury. 



If the same temperatures were used, 32° and 212° of Fahr. 

 and water or mercury alone was used in quantities in the pro- 

 portion of 6 to 6i, one of the temperatures would come out 122° 

 Fahrenheit's arithmetical mean, and the other no less than 7-3° 

 below it. This inequality would be very striking ; and as it is 

 closely connected with the doctrine of capacities, it would alone, 

 it appears to me, decide the fate of that hypothesis. 



Prop. IV. Theok. III. 



Denoting the volumes mixed by V V,, and the numeratoms 

 and true temperatures as before by N N, and T T„ the true tem- 

 perature (t) of the mixture will be equal to — — — - — ! — ! — ! . 



A ^ VN + V,N, 



By the same train of reasoning as in the last Proposition, 

 x (V N + V, N,) = T V N + T, N, V , and, therefore, t *= 



TVN + T,V,N, 

 VN + V,N, * 



