On anomalies in the intensity diffracted spectra

Professor Wood has found that the spectra of an incandescent lamp formed by a grating can have bright and dark lines in them. These occur at the same place in each order of spectrum, and move through the spectrum when the inclination of the grating is altered. The phenomenon has been investigated by Bayleigh,f who discusses the case of diffraction by a grooved reflecting surface. On account of the analytical difficulties he uses approximations. In the present paper a theoretical grating is discussed, the phenomena of which can be investigated accurately, an advantage that is, however, coupled with the drawback that we cannot feel certain how far the phenomena agree with those of the ordinary metallic reflection grating. A theorem that gives the sum of certain infinite series in a finite form, and transforms others into new series, is found in 5.