IN a recent communication, B. E. Kelly¹ has directed attention to W. E. Deming's sadly neglected monograph â Statistical Adjustment of Dataâ (1943), and comments that Deming's procedure leads to the solution found by P. A. Wayman² for the best-fitting straight line to a series of observations of two variables both subject to variable error. This is not correct: Deming neglected the variation of his weighting factor Wi with the slope of the fitted line, and his result (p. 180) is a weighted regression. We have re-examined the problem of multivariate linear relations: when both variables are subject to independently variable errors we obtain a result the bivariate case of which agrees with Wayman's (which so far as we can find had not previously been described); when the ratio of the standard deviations of error in the several variables is constant for all sets of measurements, we find that for n variables connected by ν linear relations the best-fitting (n â ν)-flat is defined by the ν latent vectors of the covariance matrix corresponding to its ν smallest latent roots; and we have been able to find a procedure suitable when not all the variables were measured at every point (a situation very common in studies of the correlation of chemical composition and physical properties of minerals). Certain non-linear relations of mineralogical importance are under investigation.