# Page:Popular Science Monthly Volume 12.djvu/227

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HISTORY OF DYNAMICAL THEORY OF HEAT.

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 chemical 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 passages, 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. Italicizing 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 comparative 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;"[1] and, although never literally employing such a term, he subsequently 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—

${\displaystyle \scriptstyle 4fp\int r^{2}sin^{-1}{\tfrac {a}{r}}dr}$,

where f denotes the coefficient of friction, p the total pressure between the rubbing surfaces,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—

${\displaystyle \scriptstyle 4fp{\big \{}{\frac {r^{3}}{3}}sin^{-1}{\frac {a}{r}}+{\frac {ar}{6}}{\sqrt {(}}{r^{2}-a^{2}})+{\frac {a^{3}}{6}}log{\frac {r+{\sqrt {(a^{2}-a^{2})}}}{a}}{\big \}}}$,