The Crystal as Diffraction Grating

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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.

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