Using the technique of Rindler and Perlick we calculate the total precessio
n per revolution of a gyroscope circumventing the source of Weyl metrics. W
e establish thereby a link between the multipole moments of the source and
an "observable" quantity. Special attention deserves the case of the gamma
-metric. As an extension of this result we also present the corresponding e
xpressions for some stationary space-times. (C) 2000 American Institute of
Physics. [S0022- 2488(00)00612-5].