274 PROFESSOR WILLIAM THOMSON ON THE 
produce more mechanical effect from a given quantity of heat, with a given 
available range of temperatures, than an engine satisfying the criterion stated in 
the enunciation of the proposition. 
29. The mechanical equivalent of a thermal unit Fahrenheit, or the quantity of 
heat necessary to raise the temperature of a pound of water from 32° to 33° Fahr., 
has been determined by JouLE in foot-pounds at Manchester, and the value 
which he gives as his best determination is 772°69. Mr Rankine takes, as the 
result of Jouz’s determination, 772, which he estimates must be within 3g of its 
own amount, of the truth. If we take 7723 as the number, we find, by mul- 
tiplying it by 3, 1390 as the equivalent of the thermal unit centigrade, which is 
taken as the value of J in the numerical applications contained in the present. . 
paper. 
30. With regard to the determination of the values of y for different tem- 
peratures, it is to be remarked that equation (4) shews that this might be done 
by experiments upon any substance whatever of indestructible texture, and indi- 
cates exactly the experimental data required in each case. For instance, by first 
supposing the medium to be air; and again, by supposing it to consist partly of 
liquid water and partly of saturated vapour, we deduce, as is shewn in Part III. 
of this paper, the two expressions (6), given in § 30 of my former paper, for the 
value of » at any temperature. As yet no experiments have been made upon 
air which afford the required data for calculating the value of u through any 
extensive range of temperature; but for temperatures between 50° and 60° 
Fahrenheit, JouLe’s experiments* on the heat evolved by the expenditure of a 
given amount of work on the compression of air kept at a constant temperature, 
afford the most direct data for this object which have yet been obtained; since, 
if Q be the quantity of heat evolved by the compression of a fluid subject to “ the 
gaseous laws” of expansion and compressibility, W the amount of mechanical 
work spent, and ¢ the constant temperature of the fluid, we have, by (11) of § 49 
of my former paper, 
WwW. 
i = Qe OMe, Sno ees ay aaa 
which is in reality a simple consequence of the other expression for ~ in terms 
of data with reference to air. Remarks upon the determination of » by such 
experiments, and by another class of experiments on air originated by JouLE, 
are reserved for a separate communication, which I hope to be able to make to the 
Royal Society on another occasion. 
31. The second of the expressions (6), in § 30 of my former paper, or the 
equivalent expression (32), given below in the present paper, shews that » may 
be determined for any temperature from determinations for that temperature of; 
* « Qn the Changes of Temperature produced by the Rarefaction and Condensation of Air,” 
Phil. Mag., vol. xxvi. May 1846. 

