10 Prof. Thomson on the Dynamical Theory of Heat. 



tion of galvanic currents^ tlie same quantity is generated by the 

 same amount of work spent ; and determining the actual amount 

 of work, in foot-])ouncl9, required to generate a unit of heat, 

 which he calls " the mechanical equivalent of heat." Since the 

 publication of that paper, Mr. Joule has made numerous series 

 of experiments for determining with as much accuracy as possible 

 the mechanical equivalent of heat so defined, and has given 

 accounts of them in various communications to the British 

 Association, to the Philosophical Magazine, to the Royal Society, 

 and to the French Institute. 



5. Important contributions to the dynamical theory of heat 

 have recently been made by Rankine and Clausius ; who, by 

 mathematical reasoning analogous to Carnot's on the motive 

 power of heat, but founded on an axiom contrary to his funda- 

 mental axiom, have arrived at some remarkable conclusions. 

 The researches of these authors have been published in the 

 Transactions of this Society, and in Poggendoi-ff's Annalen, du- 

 ring the ])ast year ; and they are more particularly referred to 

 below in connexion with corresponding parts of the investiga- 

 tions at present laid before the Royal Society. 



[Various statements regarding animal heat, and the heat of 

 combustion and chemical combination, are made in the writings 

 of Liebig, (as, for instance, the statement quoted in the foot-note 

 added to § 18 below,) which virtually imply the convertibility 

 of heat into mechanical effect, and which are inconsistent with 

 any other than the dynamical theory of heat.] 



6. The object of the present paper is threefold : — 



(1.) To show what modifications of the conclusions arrived at 

 by Carnot, and by others who have followed his peculiar mode 

 of reasoning regarcbng the motive power of heat, must be made 

 when the hyjiothesis of the dynamical theory, contrary as it is 

 to Carnot's fundamental hypothesis, is adopted. 



(2.) To point out the significance in the dynamical theoiy, of 

 the numerical results deduced from Regnault's observations on 

 steam, and communicated about two years ago to the Society, 

 with an account of Carnot's theory, by the author of the present 

 paper ; and to show that by taking these numbers (subject to 

 correction when accurate experimental data regarding the den- 

 sity of saturated steam shall have been afibrded), in connexion 

 with Joule's mechanical equivalent of a thermal unit, a complete 

 theory of the motive power of heat, within the temperature limits 

 of the experimental data, is obtained. 



(3.) To point out some remarkable relations connecting the 

 physical properties of all substances, established by reasoning 

 analogous to that of Carnot, but founded in part on the contrary 

 principle of the dynamical theory. 



