  In previous work, the conformal-gauge two-dimensional quantum gravity in the
BRS formalism has been solved completely in terms of Wightman functions. In the
present paper, this result is extended to the closed and open bosonic strings
of finite length; the open-string case is nothing but the Kato-Ogawa string
theory. The field-equation anomaly found previously, which means a slight
violation of a field equation at the level of Wightman functions, remains
existent also in the finite-string cases. By using this fact, a BRS charge
nilpotent even for $D\not=26$ is explicitly constructed in the framework of the
Kato-Ogawa string theory. The FP-ghost vacuum structure of the Kato-Ogawa
theory is made more transparent; the appearance of half-integral ghost numbers
and the artificial introduction of indefinite metric are avoided.
