ON THE CONSERVATION OF FORCE. 301 



by intermediate stages. This also agreed very well with the 

 assumption, which was the basis of the theory of heat, that 

 heat is a substance entirely unchangeable in quantity. The 

 natural processes which have here been briefly mentioned, were 

 the subject of extensive experimental and mathematical investi- 

 gations, 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 pro- 

 cesses 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 Revolu- 

 tion, had indeed endeavoured to deduce the work which heat 

 performs, by assuming that the hypothetical 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 carriage 

 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 powerful degree of friction is not, 

 indeed, necessary to disengage 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 the dry hands together to feel the heat produced by friction, 



