  We provide a new proof of the following results of H. Schubert: If K is a
satellite knot with companion J and pattern L that lies in a solid torus T in
which it has index k, then the bridge numbers satisfy the following: 1) The
bridge number of K is greater than or equal to the product of k and the bridge
number of J; 2) If K is a composite knot (this is the case k = 1), then the
bridge number of K is one less than the sum of the bridge numbers of J and L.
