Gravitational acceleration perpendicular to the galactic plane

A new method for the determination of the gravitational acceleration perpendicular to the galactic plane is formulated in terms of a set of virial equations governing the perpendicular structure of a stellar subsystem of the Galaxy. The formulation properly takes account of the facts (often neglected) that the equations of galactic dynamics govern expectation values of observable quantities and that applications of the equations involve replacing those expectation values with observed values in the Galaxy. When applied to a sample of A-type stars in the general direction of the North Galactic Pole, the method yields values in the range 0.19-0.28 for the density of matter in the solar neighborhood. The apparent discrepancy between this result and the conventional value 0.13 is found to be marginal when the statistics of the sample is considered.