# Page:Popular Science Monthly Volume 12.djvu/228

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THE POPULAR SCIENCE MONTHLY.

about this period,[1]that the heat so generated "is exactly proportional to the force with which the two surfaces are pressed together, and to the rapidity of the friction:" in other words, that the production of heat is "exactly proportional" to the work expended in producing it.

First drawing attention to the absurdity of an apparatus containing or creating an indefinite supply of a material substance; then proving by experiment that the quantities of heat excited in a given time were proportional to the expenditures of an entirely different magnitude—work: he must be credited not only with the first conclusive, but with the most weighty argument initially available, against the existence of caloric, or in favor of the dynamic origin of heat.

 OPEN AIR AND HEALTH.[2]
By Dr. PAUL NIEMEYER.

I SPARE the reader the diffuseness of an introduction, by telling him of a scene in an omnibus, which hinged on the question whether the conductor should open or shut the windows. On the left was

in which the substitution of Count Rumford's data,

 p ${\displaystyle =}$ 10,000lbs., ⁠ a ${\displaystyle =}$ 0.3 inch, ⁠ r ${\displaystyle =}$ 1.75 inches,

gives for the approximate moment of friction of the borer, in foot-pounds,

800 f.

So that, making thirty-two revolutions per minute, a quantity of work, 160,800 f, would be expended during the same interval.
On the other hand, the heat excited in two hours and thirty minutes, and which, dynamically, was to be regarded the equivalent of the work expended, according to Count Rumford's estimate, was sufficient to raise the temperature of 26.58 pounds of water 180° Fahr., or 4,784 heat-units. The production of one heat-unit, therefore, corresponded to the expenditure approximately of an amount of work—

 5041 f, For f ${\displaystyle =}$ 0.15, this would give 756 " f ${\displaystyle =}$ 0.20,⁠"⁠"⁠" 1008

as the equivalents in mechanical units or foot-pounds of one British thermal unit.
Prof. Tait, availing himself of the remark let fall by Rumford, that "the machinery used in this experiment could easily be carried round by the force of one horse," and assuming 30,000 foot-pounds as the value of a horse-power per minute, thus derives 940 foot-pounds as the mechanical value of a rise of temperature of 1° Fahr. in one pound of water. (See "Historical Sketch," p. 9.) But Prof. Thurston regards this calculation as unfair to Rumford, quoting Rankine's estimate of the admissible value of a horse-power, 25,920, from which the value of the equivalent, 812, results. This critique also seems the more allowable, since Rumford neither made corrections for the work expended in friction in "the complicated machinery used" in the determination, nor for "the heat accumulated in the wooden box, nor for that dispersed during the experiment."—(See Journal of the Franklin Institute, 3 lxvii., p. 203.)

1. "Kleine Schriften," 1805, vol. iv., p. 41. "Complete Works," Am. Ac. ed., vol. ii., p. 209.
2. Translated from the German, by J. Fitzgerald, A.M.