Page:A history of the theories of aether and electricity. Whittacker E.T. (1910).pdf/287

Since the metals A and B are quite independent, this gives

${\frac {\textstyle \prod _{A}(T+\delta T)}{T+\delta T}}-{\frac {\textstyle \prod _{A}(T)}{T}}-S_{A}(T){\frac {\delta T}{T}}=0$,

or $S_{A}(T)=T{\frac {d}{dT}}\left\{{\frac {\textstyle \prod _{A}(T)}{T}}\right\}$. This equation connects Thomson's "specific heat of electricity" S_A(T) with the Peltier effect.

In 1870 P. G. Tait^[1] found experimentally that the specific heat of electricity in pure metals is proportional to the absolute temperature. We may therefore write $S_{A}(T)=\rho _{A}T$, where $\rho _{A}$, denotes a constant characteristic of the metal $A$. The thermodynamical equation then becomes

${\frac {d}{dT}}\left\{{\frac {\textstyle \prod _{A}(T)}{T}}\right\}=\sigma _{A}$,

or $\textstyle \prod _{A}(T)=\pi _{A}T+\sigma _{A}T^{2}$. where π_A denotes another constant characteristic of the metal. The chief part of the Peltier effect arises from the term π_AT.

By the investigations which have been described in the present chapter, the theory of electric currents was considerably advanced in several directions. In all these researches, however, attention was fixed on the conductor carrying the current as the seat of the phenomenon. In the following period, interest was centred not so much on the conductors which carry charges and currents, as on the processes which take place in the dielectric media around them.

1. Proc. R. S. Edinb. vži (1870), p. 308. Cf. also Batelli, Atti della R. Acc. di Torino, xxii (1886), p. 48, translated Pbil. Mag. xxiv (1887), p. 296.