314 ON THE CONSERVATION OF FOKCE. 



which have here been briefly mentioned, were the subject 

 of extensive experimental and mathematical investiga- 

 tions, especially of the great French physicists in the 

 last decade of the former, and the first decade of the 

 present, century ; and a rich and accurately-worked chapter 

 of physics had been developed, in which everything agreed 

 excellently with the hypothesis that heat is a substance. 

 On the other hand, the invariability in the quantity of 

 heat in all these processes could at that time be explained 

 in no other manner than that heat is a substance. 



But one relation of heat namely, that to mechanical 

 work had not been accurately investigated. A French 

 engineer, Sadi Carnot, son of the celebrated War Minister 

 of the Revolution, had indeed endeavoured to deduce the 

 work which heat performs, by assuming that the hypo- 

 thetical caloric endeavoured to expand like a gas ; and 

 from this assumption he deduced in fact a remarkable 

 law as to the capacity of heat for work, which even now, 

 though with an essential alteration introduced by Clausius, 

 is among the bases of the modern mechanical theory of 

 heat, and the practical conclusions from which, so far as 

 they could at that time be compared with experiments, 

 have held good. 



But it was already known that whenever two bodies 

 in motion rubbed against each other, heat was developed 

 anew, and it could not be said whence it came. 



The fact is universally recognised ; the axle of a car- 

 riage which is badly greased and where the friction is 

 great, becomes hot so hot, indeed, that it may take fire ; 

 machine-wheels with iron axles going at a great rate may 

 become so hot that they weld to their sockets. A power- 

 ful degree of friction is not, indeed, necessary to disen- 

 gage an appreciable degree of heat ; thus, a lucifer- 

 match, which by rubbing is so heated that the phosphoric 

 mass ignites, teaches this fact. Nay, it is enough to rub 



