108 Prof. Thomson on the Dynamical Theory of Heat. 



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. Rankiue takes, 

 as the result of Joule's determination, 772, which he estimates 

 must be within g^^ of its own amount, of the truth. If we take 

 772| as the number, we find, by multiplying it by f , 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 fi for 

 different temperatures, it is to be remarked that equation (4) 

 shows that this might be done by experiments upon any sub- 

 stance whatever of indestructible texture, and indicates 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 'shown in Part III. of this paper, the two ex- 

 pressions (6), given in § 30 of my former paper (" Account of 

 Carnot's Theory "), for the value of /j, at any temperature. As 

 yet no experiments have been made upon air which aflbrd the 

 required data for calc\ilating the value of fi through any extensive 

 range of temperature ; but for temperatures between 50° and 

 60° Fahr., Joule's experiments* on the heat evolved by the ex- 

 penditure of a given amount of work on the compression of air 

 kept at a constant temperature, afi'ord 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 t the constant tempera- 

 ture of the fluid, we have by (11) of § 49 of my former paper, 



W.E 



'^=Q(TTW^ ^ ^ 



which is in reality a simple consequence of the other expression 

 for /x in terms of data with reference to air. Remarks upon the 

 determination of fi by such experiments, and by another class of 

 experiments on air originated by Joule, are reserved for a sepa- 

 rate 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 pre- 

 sent paper, shows that /a may be determined for any temperature 

 from determinations for that temperature of — 



* " On the Changes of Temperature produeed by tlie Rarcfaetion and 

 Condensation of Air," Pliil. Mag. vol. xxvi. May 1845. 



