The arithmetic theory of quadratic forms may be said to have begun with Fermat in 1654 who showed, among other things, that every prime of the form*x*and*y*integers. Gauss was the first systematically to deal with quadratic forms and from that time, names associated with quadratic forms were most of the names in mathematics, with Dirichlet playing a leading role. H. J. S. Smith, in the latter part of the nineteenth century and Minkowski, in the first part of this, made notable and systematic contributions to the theory. In