  We compare Hofer's geometries on two spaces associated with a closed
symplectic manifold M. The first space is the group of Hamiltonian
diffeomorphisms. The second space L consists of all Lagrangian submanifolds of
$M \times M$ which are exact Lagrangian isotopic to the diagonal. We show that
in the case of a closed symplectic manifold with $\pi_2(M) = 0$, the canonical
embedding of Ham(M) into L, f $\mapsto$ graph(f) is not an isometric embedding,
although it preserves Hofer's length of smooth paths.
