The Crystal as Diffraction Grating

Abstract

THE use of a crystal as a grating for measuring the wave-lengths of Röntgen rays affords a beautiful illustration of the value of a second reference frame that may be associated with the customary reference frame of vector analysis. Let e₁ e₂ e₃ be the prime vectors of the customary frame. The second or derived frame, the prime vectors of which we will denote by e¹ e² e³ with superior affixes, is such that the scalar products x.e₁ x.e₂ x.e₃ of any vector x and the original prime vectors are the cartesian components of the vector in the derived frame, and the scalar products x.e¹ x.e² x.e³ of the vector x and the derived prime vectors are the cartesian components of the vector in the original frame.