Page:Elementary Text-book of Physics (Anthony, 1897).djvu/397

§ 316] where $$t_{1}$$ and $$t_{0}$$ are indefinitely near one another. Hence if we lay off on the axis of abscissas (Fig. 90) an infinitesimal length $$t_{1} - t_{0},$$ and erect as ordinate the corresponding thermoelectric power $$\theta_{1},$$ the area of the rectangle formed by the two lines wiH represent the electromotive force $$E_{1} - E_{0},$$ due to the change in temperature. If, beginning at the point $$t_{1},$$ we layoff the similar infinitesimal length $$t_{2} - t_{1},$$ and erect as ordinate the thermoelectric power $$\theta_{2},$$ we shall obtain another rectangle representing the electromotive force $$E_{2} - E_{1}.$$ So for any temperature changes the total area of the figure bounded by the axis of temperatures, by the ordinates representing the thermoelectric powers at the temperatures $$t_{0}$$ and $$t_{x},$$ and by the curve $$AA'$$ passing through the summits of the rectangles so obtained, will represent the electromotive force due to the heating of the junction from $$t_{0}$$ to $$t_{x}.$$

It was found by Tait and Le Roux that the thermoelectric power, referred to lead as a standard, of all metals but iron and nickel, is proportional to the rise in temperature. The curve $$AA'$$ is therefore for those metals a straight line. For iron and nickel the curve is not straight.

For another metal in comparison with lead, the line $$BB',$$ corresponding to the line $$AA'$$ for copper, may have a different direction. From what has been said about the possibility of arranging the metals in a thermoelectric series, it is evident that the thermoelectric power between copper and the other metal is the difference of their thermoelectric powers referred to lead, and that the electromotive force at the junction of the two metals, due to a rise of temperature from $$t_{0}$$ to $$t_{x},$$ is represented by the area of the figure contained by the two terminal ordinates and the two lines $$AA'$$ and $$BB'.$$ The thermoelectric power is reckoned positive when the current sets from lead to copper across the hot junction. In the diagram the thermoelectric power $$AB$$ is positive, and the