Page:Elementary Text-book of Physics (Anthony, 1897).djvu/398

384 force indicated by the area is from copper to the other metal across the hot junction. At the point where the lines $$AA'$$ and $$BB'$$ intersect, the thermoelectric power for the two metals vanishes. The temperature at which this occurs is called the neutral temperature, and is designated by $$t_{n}.$$ When the temperature $$t_{x}$$ lies on the other side of the neutral temperature from $$t_{0},$$ the thermoelectric power becomes negative, and the electromotive force due to the rise in temperature from $$t_{n}$$ to $$t_{x}$$ is negative. In Fig. 91 it is at once seen that $$A'B'$$ is negative for $$t_{x},$$ and that the area $$NA'B'$$ is also negative. The electromotive force due to a rise of temperature from $$t_{0}$$ increases until the temperature of the hot junction is $$t_{n},$$ when it is a maximum, and then decreases. When the area $$NA'B'$$ becomes equal to the area $$ANB$$ the total electromotive force is zero; when $$NA'B'$$ is greater than $$ANB,$$ the electromotive force becomes negative, and the current is reversed. In case $$AA'$$ and $$BB'$$ are straight lines, it is plain that the temperature $$t_{x},$$ at which this reversal occurs, will be such that the neutral temperature $$t_{n}$$ is a mean between $$t_{0}$$ and $$t_{n}.$$

The same facts can be represented by a general formula. Thomson first pointed out that the fact of thermoelectric inversion necessitates the view that the thermoelectric power at a junction is a function of the temperature of that junction. Avenarius embodied this idea in a formula, which his own researches, and those of Tait, show to be closely in agreement with experiment. Let us call the hot junction 1 and the cool junction 2, and set the electromotive force at each junction as a quadratic function of the absolute temperatures. We have $$E_{1} = A + bt_{1} + ct_{1}^2$$ and $$E_{2} = A + bt_{2} + ct_{2}^2,$$ where $$A, b,$$ and $$c$$ are constants. The difference $$E_{1} - E_{2},$$ or the electromotive force in the circuit, is $$E_{1} - E_{2} = b(t_{1} - t_{2}) + c(t_{1}^2 - t_{2}^2) = (t_{1} - t_{2}) (b + c(t_{1} + t_{2})).$$