Sampling experiments are done on the maximum likelihood estimator, k = tan (f), of the slope of the bivariate normal major axis, which is often used on log-transformed data to estimate ailometry exponents. The slope tan (f) becomes highly variable in small samples from populations with low correlations. Moreover, the corresponding angle, f= arc tan (k), is biased toward zero because it has an axial distribution of which the axial mode is not situated at zero and in which angles falling outside of the [-90 ยฐ, +90 ยฐ] range are interpreted as narrower angles of the opposi~te sign. However, the usual notions of linear (scalar) average and bias are not appropriate for directional or axial data. If the axial distribution of angle f is transformed into a directional distribution by doubling angles, the vector of the numerators of the direction cosines of the doubled angle 2f is unbiased, and the corresponding expected vector of direction cosines points in the proper direction to within order O(N-2). For the preceding reasons, the utilization of the usual estimators k = tan (f) and f = arc tan (k) may be considered as legitimate. Procedures are suggested for combining independent estimates of the slope of the major axis validly into a single estimate.