The equation in linear vector functions
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was proposed by Tait, and an elegant solution was obtained by him which does not require a determination of the axes of ω. He showed that upon this equation depends the separation of the pure and the rotational parts of a homogeneous strain. The problem appears to be interesting also from the point of view of algebraic analysis. The number and character of the solutions is more varied, given different types of the function ω, than we might at first suppose. In fact there are two forms which may be assigned to M such that the equation does not permit of solution. Otherwise the number of solutions.