  A description of Orthogonal Tensor Hermite Polynomials in 3-D is presented.
These polynomials, as introduced by Grad in 1949 [1], can be used to obtain a
series solution to the Boltzmann Transport Equation. The properties that are
explored are scaling, translation and rotation. Order 6 Hermite Tensors are
studied while obtaining the rotation relations. From the scaling of the
independent variables of particle velocities, a criterion on temperature is
obtained which implies that the equation can be applied to binary gas mixtures
only if the temperature of the hotter constituent is less than four times that
of the cooler one. This criterion and other properties of the tensor hermite
polynomials obtained in this paper can be used to study gas dynamics in the
thermosphere.
