On the Reflection and Transmission of Electric Waves by a Metallic Grating

The main problem of this paper consists in the calculation of the disturbance produced in a train of electric waves by a plane grating composed of parallel, equal, and equidistant metallic strips.The treatment is approximate, and involves the assumption that the wave-length is large compared with the distance between the centres of consecutive strips; the application is, therefore, rather to Hertzian waves than to phenomena of ordinary Optics.The previous mathematical litemture bearing directly on the subject consists of an investigation by Prof. J. J. Thomson,* and of two papers by Lord Rayleigh.fIt will be seen that the author is under great obligations to each of these sources.The work of § § 1, 2, 3 is preliminary, and consists in the solution of several electrostatical problems.With modern methods these pi'esent no difficulty; but the results appeared to possess sufficient interest of their own to warrant the expenditure of a little trouble in the way of graphical representation.The diagrams obtained serve, moreover, to illustrate very clearly some of the conclusions arrived at afterwards in the discussion of the wave problem.The problem of § 4 is introduced on account of its close connexion with what precedes, although it has no bearing on the main subject of the paper.