The exact distribution of the square sum of Dirichlet random variables is
given by two different univariate integral representations. Alternatively,
three representations by orthogonal series with Jacobi or Legendre polynomials
are derived. As a special case the distribution of the square sum of spacings -
also called Greenwood's statistic - is obtained. Nine quantiles of this
statistic are tabulated with eight digits where the number of squares ranges
from 10 to 100.