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[Philosophical, Magazine, Vol. xxxix. pp. 225233, 1920.]
[Note.This paper, written in 1919, was left by the Author ready for press except that the first two pages were missing. The preliminary sentences, taken from a separate rough sheet, were perhaps meant to be expanded.
Prof. Wood* had observed highly coloured effects in the reflexion from a granular film of sodium or potassium, which he attributed to resonance from the cavities of a serrated structure of rod-like crystals.]
THIS investigation was intended to illustrate some points discussed with Prof. R. W. Wood. But it does not seem to have much application to the transverse vibrations of light. Electric resonators could be got from thin conducting rods |X long; but it would seem that these must be disposed with their lengths perpendicular to the direction of propagation, not apparently leading to any probable structure.
The case of sound might perhaps be dealt with experimentally with birdcall and sensitive flame. A sort of wire brush would be used.
The investigation follows the same lines as in Theory of Sound, 2nd ed.  351 (1896), where the effect of porosity of walls on the reflecting power for sound is considered. In the complete absence of dissipative influences, what is not transmitted must be reflected, whatever may be the irregularities in the structure of the wall. In the paragraph referred to, the dissipation regarded is that due to gaseous viscosity and heat conduction, both of which causes act with exaggerated power in narrow channels. For the present purpose it seems sufficient to employ a simpler law of dissipation.
Let us conceive an otherwise continuous wall, presenting a flat face at cc~Q, to be perforated by a great number of similar narrow channels, uniformly
* [See Phil. Mag. July 1919, pp. 98112, especially p. Ill, where a verbal opinion of Lord Eayleigh. is quoted that in certain cases the grooves of gratings might possibly act as resonators. The explanation of the absorption of sound by porous bodies such as curtains, given in Theory of Sound, second edition,  348351, dates back to 1883: see Scientific Papers, Vol. n. No. 103, pp. 2205, " On porous bodies in relation to Sound."] can involve the concentrations only as ratios; otherwise the element of mass would enter into the result uncompensated. In like manner the diffusibilities can be involved only as ratios, or the element of time would enter. And since these ratios are all pure numbers, dx must be proportional to x. In words, the linear period at any place is proportional, cceteris paribus, to the distance from the original boundary. In this argument the thickness of the film another linear quantityis omitted, as is probably for the most part legitimate. In imagination we may suppose the film to be infinitely thin or, if it be of finite thickness, that the diffusion takes place strictly in one dimension.