The rigorous calculation of the temperature diffuse scattering pattern of a crystal presupposes a knowledge of the propagation velocities and of the polarization directions. It is shown how these quantities can be found for a simple cubic lattice of the Born-Kármán type. When the elastic constants satisfy the condition $c_{11}=3\mathrm{}{c}_{12}$ the formula for the intensity distribution in the diffraction maxima is particularly simple and this case is therefore treated in some detail. Expressions for the positions and half-widths of the intensity maxima have been developed. Also the case $c_{11}\gg 3c_{12}$ has received special attention. For lattices of this type the diffuse diffraction maxima have a complex structure, each maximum consisting in the general case of three peaks. Formulae are given for the position and intensity of these peaks. Under proper conditions only one or two of the three peaks composing a maximum will be observable. An intensity expression for very small scattering angles has been developed. According to theory there is no diffuse halo around the forward beam. Such a halo has been reported by some experimenters, and it is suggested that the observed diffuse ring is not connected with the temperature diffuse scattering, but is due to continuous radiation in the incident beam and scattering from the air.

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