HISTORY OF DYNAMICAL THEORY OF HEAT 215 



component elastic fluids (most probably inflammable air) must at the same time 

 have been set at liberty, and, in making its escape into the atmosphere, would 

 have been detected ; but, though I frequently examined the water to see if any 

 air-bubbles rose up through it, and had even made preparations for catching 

 them, in order to examine them, if any should appear, I could perceive none ; 

 nor was there any sign of decomposition of any kind whatever, or other chemi- 

 cal process, going on in the water. 



" Is it possible that the heat could have been supplied by means of the iron 

 bar, to the end of which the blunt steel borer was fixed, or by the small neck 

 of gun-metal by which the hollow cylinder was united to the cannon ? These 

 suppositions appear more improbable even than either of those before mentioned ; 

 for heat was continually going off, or out of the machinery, by both these pas- 

 sages, during the whole time the experiment lasted. 



" And, in reasoning on this subject, we must not forget to consider that most 

 remarkable circumstance, that the source of the heat generated by friction, in 

 these experiments, appeared evidently to be inexhaustible. 



"It is hardly necessary to add that anything which any insulated body, or 

 system of bodies, can continue to furnish without limitation, cannot possibly be 

 a material substance ; and it appears to me to be extremely difficult, if not quite 

 impossible, to form any distinct idea of anything capable of being excited and 

 communicated in the manner the heat was excited and communicated in these 

 experiments, except it be motion." 



From this quotation we see, then, that Rumford, with a sagacity 

 indeed consummate, had seized upon the most notable circumstance 

 presented by these experiments, against the materiality of heat. Ital- 

 icizing the word inexhaustible a far more significant proceeding than 

 the use of any acids would have been he showed most incontestably 

 that, to still further reconcile the doctrine of caloric with experience, 

 it would be necessary to admit the creation of it a substance in 

 the production of heat by friction. But, even against so absurd a 

 proposition, he proceeded to prepare, when he subjected to a com- 

 parative investigation the quantities of energy expended and heat 

 produced in such an operation. 



In his " Experiment No. 3 " he made, as may have been already 

 noticed, nearly all the observations and corrections necessary for 

 an entirely trustworthy estimate of the " mechanical equivalent of 

 heat ;" * and, although never literally employing such a term, he sub- 

 sequently stated, in reviewing still other experiments undertaken at 



1 Its value from the data given may be calculated as follows : 



Considering the shape of the borer, and its contact with the bottom of the cylinder, 

 we see that the moment of friction may be represented by the expression 



4fp I j* 2 sin -1 d r, 



where/ denotes the coefficient of friction, p the total pressure between the rubbing sur- 

 faces, r the variable distance from the axis, of any rubbing particle, and a the half-width 

 of the borer: when, moreover, the superior value of r alone is substituted. 

 The integral indicated is 



4fp ) sin - 1 _ + Y (r z a-) + _ log LA 1 f j 



\ 3 r 6 6 a ) 



