Given n observations of m-variates having known errors, the envelope of primes, associated with a given probability level, is shown to be a quadric primal the nature of which determines the acceptability or otherwise of a prime as a structural relation. If the variates derive from r independent linear equations, i.e. an (m−r)-fold, the rational definition proposed is that the (m−r)-fold is an acceptable structural relation if every prime through it is acceptable. The consequences of the rational definition are shown to be consistent and are contrasted with some less satisfactory properties of Tintner's method. The coefficients in the relation are not estimated in the usual way, although a ‘best’ relation can be given. Certain practical advantages are noted. The connexion with canonical correlations, confluence analysis and other qualitative methods is discussed briefly.