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[March 11,
Mr. H. Bateman

or all the quantities of type are zero, and that either

or all the quantities of type are zero. It follows from this that either (1) the six quantities (αβ) are zero or (2) that the thirty-six quantities are all zero or (3) that there is a set of relations

It is easy to see, however, that in the latter case we also have

Hence, in all cases,

Again, we have

hence, since the last term is zero,

This gives

say, and there are similar equations in . It follows that

These conditions, combined with the previous set, imply that the sixteen quantities are the elements of an orthogonal matrix.