Boundary conditions in the common-factor-space,in the factorial analysis of ability

The author arrives at a simple rule for ascertaining when a matrix of correlations, with communalities reducing it to minimum rank, cannot be analyzed into factors such that every column of loadings has at least as many zeros as the number of common factors, as required by Thurstone. A more exact but arithmetically tedious rule is also deduced from Ridley Thompson's boundary conditions, and a correction is made to the latter.