32 THE SCIENTIFIC PAPERS OF 



publications. Carnot and Clapeyron produced the first general 

 formula?, which contained, however, an uncertain function, and 

 were still based upon the supposition that heat was material.* 

 Holtzman, of Manheim, in pursuing the views of Carnot and 

 Clapeyron, obtained a complete mathematical solution in 1845.f 

 Joule, of Manchester, solved the problem experimentally about 

 the same time.J 



The " dynamical theory " was more fully developed by Helm- 

 holtz in 1847, and Mayer.|| Mr. W. J. M. Eankine, C.E., and 

 Professor Thomson, of Edinburgh, have much extended the 

 dynamical theory of heat, and applied the same to calculate the 

 power of steam and air engines. IF 



M. Regnault, of Paris, has, by careful experimental researches 

 on the total heat of steam, &c.,** provided some important data for 

 the development of the dynamical theory of heat. 



The following are the results obtained in units of power, or foot 

 Ibs., for one unit of heat, by different authors : 



The comparatively small effect produced by the steam-engine of 

 the present day would seem to indicate that there is still much 

 room for improvement. 



Practical engineers will probably receive with incredulity, and 



* Vide Annales de Chimie et Physique, XXIII. 



t Vide his pamphlet ' ' Ueber die Waerme und Elasticitaet der Gase und 

 Daempf e. " 



J Vide Transactions of the Philosophical Society of Manchester, Vol. XVIII. 



Vide Ueber die Erhaltung der Kraft. 



|| Vide Mechanische Aequivalent der Waerme, 1851. 



\ Vide Transactions of Royal Society of Edinburgh, 1849-1850 and 1850-1851. 



** Vide Comptes Rendus. 



