The distribution of the ratio of normal random variables and the ellipticity of the Earth

In this paper we consider inference regarding the ratio of two normal and the ratio of two t-distributed random variables, using both the popular Fieller interval, as well as, exact distributions. We apply these methods to a historical dataset regarding the shape of the Earth, and estimate the Earth's flatness coefficient as a ratio of regression coefficients. We demonstrate the equivalence of the inference using the exact density of this ratio with that using the Fieller interval.