Abstract
Doubled x-ray lines, produced by the Cauchois focusing spectrograph, have their origin as a result of double curvature of the crystal which causes defocusing of strong surface layer reflections. At the center of the lines shown in this paper, is a single portion, where the surface layer reflections are superimposed as a result of Cauchois exact focusing, showing that the surface layers share in the uniform strain of the crystal. Calculated separation of doubled lines, on the assumption of parallelism of surface layer reflections, shows poor agreement with the actual separations, adding support to the idea of the origin of the doubled lines as a result of crystal warping. The breaking of bent crystals is attributed to the presence of this double curvature. Broadened lines due to light etching are the result of poor resolving power of the thinned surface layers which still do the bulk of reflection.