Some mathematical remarks concerning boundary conditions in the factorial analysis of ability

This paper is a mathematical supplement to the preceding paper by Professor Godfrey H. Thomson. It gives rigorous proofs of theorems enunciated by him and by Dr. J. Ridley Thompson, and extends them. Its basic theorem is that if a matrix of correlations is to be factorized without the aid of higher factors thans-factors (withn-s zero loadings), then the largest latent root of the matrix must not exceed the sum of thes largest communalities on the diagonal.