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Maximum Likelihood estimation of the bulk flow from radial peculiar motionsof galaxies, generally assumes a constant velocity field inside the surveyvolume. The assumption is inconsistent with the definition of the bulk flow asthe average of the peculiar velocity field over the relevant volume. Thisfollows from a straightforward mathematical relation between the bulk flow of asphere and the velocity potential on its surface. The inconsistency exists alsofor ideal data with exact radial velocities and full spatial coverage.  Based on the same relation we propose a simple modification to correct forthis inconsistency.

An Inconsistency in standard Maximum Likelihood Estimation of Bulk Flows