50 



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 rea- 

 soning regarding the motive power of heat, must be made when the 

 hypothesis of the Dynamical Theory, contrary as it is to Carnot s 

 fundamental hypothesis, is adopted. 



(2.) To point out the significance in the Dynamical Theory, 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 density of saturated steam 

 shall have been afforded), in connection with Joule's mechanical equi- 

 valent 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 phy- 

 sical properties of all substances, established by reasoning analogous 

 to that of Carnot, but founded on the contrary principle of the Dy- 

 namical Theory. 



In tlie first part of the paper Mr Joule's principle regarding the 

 mechanical equivalent of heat is shown to be in reality as certainly 

 true as Carnot"'s would be if the hypothesis that heat is matter were 

 not false ; and it is therefore adopted by the author, not as Carnot's 

 principle was adopted by him temporarily " as the most probable 

 basis for an investigation of the motive power of heat" without a 

 belief in its rigorous exactness ; but, with implicit confidence, as a 

 true law of nature. 



The following axiom is also adopted : — 



It is impossible by mecuis of inanimate material agency to derive 

 mechanical effect from any portion of matter by cooling it below the 

 temperature of the coldest of the surrounding objects. 



From Joule's principle, and from this axiom, the two following pro- 

 positions, which constitute the foundation of the theory, are deduced. 



Prop. I. — When equal quantities of mechanical effect are pro- 

 duced by any means whatever from purely thermal sources, or lost 

 in purely thermal effects, equal quantities of heat are put out of 

 existence, or are generated. 



Pkop. II. — If an engine be such that when it is worked back, 

 wards the physical and mechanical agencies in every part of its 



