1. Summary. In Biometrika (1948) a paper [1] by H. L. Seal contained a theorem applying to “n random variables normally distributed about zero mean with unit variance, these variables being connected by means of k linear relations.” Arising from this is the question of how to obtain a set of normal variates connected by k linear relations and such that each variate has unit variance: or, more generally, connected by k linear relations and such that each variate has a given variance.