This article complements the introductory article on the chi-square distribution, with details of its derivation as the distribution of the sum of squares of standard normal deviates, the density being a gamma function, and the relationship between its distribution function and that of the Poisson distribution. When the component normal distributions have nonzero mean, the sum of squares has a noncentral chi-square distribution, depending on a noncentrality parameter, the sum of squares of the normal means. This plays a role in determining the power of a chi-square test.