  For a polynomial mapping from S^{n-k} to the Stiefel manifold
\widetilde{V}_k(\R^{n}), where n-k is even, there is presented an effective
method of expressing the corresponding element of the homotopy group
\pi_{n-k}\widetilde{V}_k(\R^{n})\simeq\Z in terms of signatures of quadratic
forms. There is also given a method of computing the intersection number for a
polynomial immersion from S^m to \R^{2m}.
