146.

In establishing the dynamical law, it will be rational to proceed in such a way as to make the deviation from the laws of classical electrodynamics, which was recognized as necessary, as slight as possible.

Hence, as regards the influence of the field of radiation on an oscillator, we follow that theory closely.

If the oscillator vibrates under the influence of any external electromagnetic field whatever, its energy $U$ will not in general remain constant, but the energy equation [eqn:(205a)] (205a) must be extended to include the work which the external electromagnetic field does on the oscillator, and, if the axis of the electric doublet coincides with the $z$ -axis, this work is expressed by the term $⋿_{z} d f = ⋿_{z} \dot{f} d t$ .

Here $⋿_{z}$ denotes the $z$ component of the external electric field-strength at the position of the oscillator, that is, that electric field-strength which would exist at the position of the oscillator, if the latter were not there at all.

The other components of the external field have no influence on the vibrations of the oscillator.

Hence the complete energy equation reads:

$K f d f + L \dot{f} d \dot{f} = ⋿_{z} d f$

or:

$K f + L \ddot{f} = ⋿_{z}, \Label [e q n] (233) \upshape (233)$

and the energy absorbed by the oscillator during the time element $d t$ is:

$⋿_{z} \dot{f} d t . \Label [e q n] (234) \upshape (234)$

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