This chapter is concerned with tests of goodness of fit based on , b2 in sampling from the normal or other distributions such as members of the Pearson system. It deals with theoretical aspects of the omnibus contours, including evaluation of the moments of b1 and b2, their correlation, and the construction of equivalent normal deviates for b1 and b2. In sampling from fairly symmetric distributions, one might expect the kurtosis to reflect the nonnormality. Asymptotic or slowly convergent series may be approximated by the ratio of polynomials in the variable, and there has been a resurgence of interest in the last decade in the subject, basically initiated by Pade. The surprising feature is the largeness of the correlation especially at parameter points not in the neighborhood of the normal point. The editors have provided 17 random samples of 100 from specified populations for discussion.