The Connections between the Four Transverse Galvanomagnetic and Thermomagnetic Phenomena

Abstract

Three relations are deduced by reasoning of a general character between the four transverse effects, so that each of the effects may be expressed in terms of any other effect. The first relation, $Q=\frac{\mathrm{KP}}{T}$, is obtained from energy considerations by assuming that the source of energy involved in the Nernst effect $Q$ is provided by the Ettingshausen effect $P$, $K$ being the thermal conductivity and $T$ the absolute temperature. It is shown that the Hall effect $R$ and the Righi-Leduc effect $S$ each provides its own source of energy. The second relation, $Q=\frac{\ensuremath{\sigma}R}{\ensuremath{\rho}}$, where $\ensuremath{\sigma}$ is the Thomson coefficient and $\ensuremath{\rho}$ the specific resistance, is that of Moreau, and is obtained by assuming that the level surfaces of the Thomson e.m.f. in a metal carrying a thermal current are rotated by the Hall effect. The third relation, $P=\frac{S\ensuremath{\sigma}T}{K}$, involves the concept, probably new, of a temperature gradient generated by a heat current flowing down a difference of electrical potential. This new effect, which is the thermal analog of the Thomson effect, should be capable of experimental detection. It is proposed to call it the Thomson temperature gradient. The third relation is obtained by assuming that the isothermal lines associated with the Thomson temperature gradient are rotated by the Right-Leduc effect. The experimental data available are not very satisfactory but they agree with the above relations within the experimental error.