Uniqueness of the projective plane with 57 points

Professor Gunter Pickert has pointed out to me that there is an error in my paper [Proc. Amer. Math. Soc. vol. 4 (1953) pp. 912-916]. The equation on page 915 which reads 12+3s + 2£ = 24 should read 12+3s + 2£+w = 24. This invalidates my conclusion w = 0 from which I deduce U = 0, which is necessary for the rest of the paper. I give here a new proof that £7 = 0. We must show that in a 57 point plane a line containing points A CC is not possible, or that U = 0. The proof is by showing that if there is a line ACC we reach a contradiction. We may take ACC as .41C4C6 by numbering points appropriately. We now reletter by the following rule: