  The sunspot drawings of Johann Staudacher of 1749--1799 were used to
determine the solar differential rotation in that period. These drawings of the
full disk lack any indication of their orientation. We used a Bayesian
estimator to obtain the position angles of the drawings, the corresponding
heliographic spot positions, a time offset between the drawings and the
differential rotation parameter \delta\Omega, assuming the equatorial rotation
period is the same as today. The drawings are grouped in pairs, and the
resulting marginal distributions for \delta\Omega were multiplied. We obtain
\delta\Omega=-0.048 \pm 0.025 d^-1 (-2.75^o/d) for the entire period. There is
no significant difference to the value of the present Sun. We find an
(insignificant) indication for a change of \delta\Omega throughout the
observing period from strong differential rotation, \delta\Omega\approx -0.07
d^-1, to weaker differential rotation, \delta\Omega\approx-0.04 d^-1.
