Davison (Can. J. Phys. 35: 576), gave an expression for the constants of integration, in terms of the moments applicable to the spherical harmonics method, in an arbitrary odd order of approximation in cylindrical geometry. This inversion of the matrix which expresses the moments in terms of the constants of integration is most useful in problems invoiving neutron diffusion in several coaxial regions. His inversion formula contains an error which it is thought useful to correct. A proof of the inversion is sketched, in so far as is needed to establish the correct result. The proof consists in showing that the product of two given matrices is the unit matrix. (W.D.M.)