Page:Elementary Text-book of Physics (Anthony, 1897).djvu/218

204 section, and is equal to the heat which escapes from the portion of the bar beyond the section.

178. Measurement of Conductivity.—A bar heated at one end furnishes a convenient means of measuring conductivity. In Fig. 69 let $$AB$$ represent a bar heated at $$A.$$ Let the ordinates $$aa', bb', cc'$$, represent the excess of temperatures above the temperature of the air at the points from which they are drawn. These temperatures may be determined by means of thermometers inserted in cavities in the bar, or by means of a thermopile. Draw the curve $$a'b'c'd' \dots$$ through the summits of the ordinates. The inclination of this curve at any point represents the rate of fall of temperature at that point. The ordinates to the line $$b'm,$$ drawn tangent to the curve at the point $$b',$$ show what would be the temperatures at various points of the bar if the fall were uniform and at the same rate as at $$b'.$$ It shows that, at the rate of fall at $$b',$$ the bar would at $$m$$ be at the temperature of the air; or, in the length $$bm,$$ the fall of temperature would equal the amount represented by $$bb'.$$ The rate of fall is, therefore, $$\frac{bb'}{bm}\cdot$$ If $$Q$$ represent the quantity of heat passing the section at $$b$$ in the unit time, we have, from § 176, $$Q$$ is equal to the quantity of heat that escapes in unit time from all that portion of the bar beyond $$b.$$ It may be found by heating a short piece of the same bar to a high temperature, allowing it to cool under the same conditions that surround the bar $$AB,$$ and observing its temperature from minute to minute as it falls. These observations furnish the data for computing the quantity of heat which escapes per minute from unit length of the bar at different temperatures. It is then easy to compute the amount of heat that escapes per minute from each portion, $$bc, cd$$, etc., of the bar beyond $$b;$$ each portion being taken so short that its