SOME PROBLEMS CONCERNING THE MUTUAL INFLUENCE OF RESONATORS EXPOSED TO PRIMARY PLANE WAVES.
[Philosophical Magazine, Vol. xxix. pp. 209—222, 1915.]
RECENT investigations, especially the beautiful work of Wood on " Radiation of Gas Molecules excited by Light"*, have raised questions as to the behaviour of a cloud of resonators under the influence of plane waves of their own period. Such questions are indeed of fundamental importance. Until they are answered we can hardly approach the consideration of absorption, viz. the conversion of radiant into thermal energy. The first action is upon the molecule. We may ask whether this can involve on the average an increase of translatory energy. It does not seem likely. If not., the transformation into thermal energy must await collisions.
The difficulties in the way of answering the questions which naturally arise are formidable. In the first place we do not understand what kind of vibration is assumed by the molecule. But it seems desirable that a beginning should be made ; and for this purpose I here consider the case of the simple aerial resonator vibrating symmetrically. The results cannot be regarded as even roughly applicable in a quantitative sense to radiation, inasmuch as this type is inadmissible for transverse vibrations. Nevertheless they may afford suggestions.
The action of a simple resonator under the influence of suitably tuned primary aerial waves was considered in Theory of Sound, § 319 (1878). The primary waves were supposed to issue from a simple source at a finite distance c from the resonator. With suppression of the time-factor, and at a distance r from their source, they are represented! by the potential
* A convenient summary of many of the more important results is given in the Guthrie Lecture, Proo. Phys. Soc. Vol. xxvi. p. 185 (1914). t A slight change of notation is introduced. — f = 2cov + — , .............................. (7)