  We present an integrable nonholonomic case of rolling without sliding of a
gyroscopic ball over a sphere. This case was introduced and studied in detail
by Vasilije Demchenko in his 1923 doctoral dissertation defended at the
University of Belgrade, with Anton Bilimovic as the advisor. These results are
absolutely unknown to modern researchers. The study is based on the C. Neumann
coordinates and the Voronec principle. By using involved technique of elliptic
functions, a detailed study of motion is performed. Several special classes of
trajectories are distinguished, including regular and pseudo-regular
precessions. So-called remarkable trajectories, introduced by Paul Painleve and
Anton Bilimovic, are described in the present case. The historic context as
well as the place of the results in contemporary mechanics are outlined.
