Page:Philosophical Transactions of the Royal Society A - Volume 184.djvu/840

$q={\frac {\mathrm {P} \left(\cos \epsilon +\alpha \cos \theta \right)^{2}}{4\pi \mathrm {V} r^{2}}}$

$\approx q_{0}\left(1+2\alpha \cos \theta +\alpha ^{2}\cos \ 2\theta -{\tfrac {1}{2}}\alpha ^{3}\sin \theta \sin 2\theta \right)$,

$q_{0}$ being the energy at the same place when there was no drift.

So the energy received per second by a given small area $\mathrm {A}$ at that place, facing the source, i.e., normal to the rays, is

$q\mathrm {V} \;\mathrm {A} \cos \epsilon ={\frac {\mathrm {A} \cos \epsilon }{4\pi r^{2}}}\;\mathrm {P} \left(\cos \epsilon +\alpha \cos \theta \right)^{2}$.

The radiation at distance $r$ from the source is, in fact, the same as what the radiation would be at distance $\rho$ in a stationary medium; except for the small inclination $\epsilon$.

So a pair of similar thermopiles, fore and aft, at equal distances from a source will, on this hypothesis, receive unequal radiation; the difference being equal to $4\alpha \left(\mathrm {PA} /4\pi r^{2}\right)$, or proportional to $4\alpha$.

Fizeau suggested this method, but I am not aware of its having been tried yet.^[1]

Fig. 5.

Thermopile experiment suggested by Fizeau; in two alternative forms.

19. But it is a serious question whether the reasoning establishing the effect is quite sound. It is not unlikely that motion may affect the radiating power of a source. In fact, the theory of exchanges almost necessitates something of the kind, else the two faces of an enclosure would become unequal in temperature by reason of mere motion through the ethereal medium.^[2]

Hence, if, as in fig. 5, we consider a pair of thermopiles with a hot body half-way

1. The suggestion is quoted in a comprehensive, but to me not very intelligible, treatise on the whole subject of aberration: ‘Astronomische Undulationstheorie,’ by Professor Dr. Ketteler, of Bonn.
2. Balfour Stewart (‘Brit. Assoc, Report,’ 1871, Sects, p. 45), argued that this inequality of tempera ture actually occurred; and, since motion thus afforded an available heat engine, he deduced an ethereal friction, dissipating energy. But, as Lord Rayleigh points out (in his Article on “Aberration,” ‘Nature,’ March 1892). it is far more likely that motion should alter radiating and absorbing powers than that it should disturb equality of temperature.