  In the book [Yu. Safarov and D. Vassiliev, The asymptotic distribution of
eigenvalues of partial differential operators, Amer. Math. Soc., Providence,
RI, 1997], a key and central ``algorithm'' was established, by which the
coefficients of two-term asymptotic expansions of the eigenvalue counting
functions can be explicitly calculated for many partial differential operators
under an additional geometric assumption. In this paper, we give a
counter-example to this ``algorithm'' by discussing the case of elastic
eigenvalues. This implies that the most conclusions in the above book written
by Yu. Safarov and D. Vassiliev are fundamentally wrong because they are based
on the erroneous ``algorithm''.
