This transformation will be recognized as being the same as that used by Geary (1932) as a partial result in his "eqn viii " but whose derivation and limitations were hardly explained. Thus the first part of Geary's transformation to approximate Gaussianity in the previous section is actually exact and not dependent on the positivity of "Y". The offset result is also consistent with the "Cauchy" correlated zero-mean Gaussian ratio distribution in the first section. Marsaglia has applied the same result but using a nonlinear method to achieve it.