In the first paper of this series, the effect of experimental errors in the Fourier coefficients, upon the derived atomic co-ordinates was investigated. The assumption was made that the probable errors were independent of the magnitudes of their parent Bragg reflexions. It has been suggested that a more accurate assumption would be to take the probable error of any coefficient as being proportional to the magnitude of that coefficient. The present paper develops the theory on this basis, and a solution in closed form is obtained. The question of how the experimental error in the co-ordinates varies with the position of the atom in relation to its neighbours is also investigated, and it is shown that the variation is much smaller than that previously derived for finite summation errors.