  For some classical solutions $\Psi_\mathrm{sol}$ in Witten's bosonic string
field theory, it was proven that energy of the solution is proportional to the
Ellwood invariant $\mathrm{Tr}(\mathcal{V}\Psi_\mathrm{sol})$ with
$\mathcal{V}=c\bar{c}\partial X^0\bar{\partial}X^0$. We examine the relation
for solutions involving $X^0$ variables. As a result, we obtain that the
relation may not hold for such solutions. Namely, there is a possibility that
the energy is not proportional to the Ellwood invariant.
