The transition amplitude for the gravitational field as given by the Feynman sum over histories expression is analyzed in analogy to the electromagnetic transition amplitude. The analysis is based on an explicit representation of the Feynman sum by means of a lattice. The measure is found by consistency requirements and differs from those proposed by other workers. Particular attention is paid to the subsidiary conditions associated with the gauge group. It is shown, that the present approach is equivalent to the quantization by means of canonical variables as proposed by Dirac.