We obtain the Mellin transform of the Beta statistic used in the test of the univariate general linear hypothesis, assuming that the error distribution is spherically symmetric. From this, the non-null distribution of the statistic is obtained. The normal-errors representation of the Beta as a central Beta with random d.f. is shown to hold iff the error distribution is a normal scale mixture. Closed form expressions for the density are given, without employing this assumption.