  We consider trigonometric solutions of the KP hierarchy. It is known that
their poles move as particles of the Calogero-Moser model with trigonometric
potential. We show that this correspondence can be extended to the level of
hierarchies: the evolution of the poles with respect to the $k$-th hierarchical
time of the KP hierarchy is governed by a Hamiltonian which is a linear
combination of the first $k$ higher Hamiltonians of the trigonometric
Calogero-Moser hierarchy.
