  Calculations of the Casimir energy for spherical geometries which are based
on integrations of the stress tensor are critically examined. It is shown that
despite their apparent agreement with numerical results obtained from mode
summation methods, they contain a number of serious errors. Specifically, these
include (1) an improper application of the stress tensor to spherical
boundaries, (2) the neglect of pole terms in contour integrations, and (3) the
imposition of inappropriate boundary conditions upon the relevant propagators.
A calculation which is based on the stress tensor and which avoids such
problems is shown to be possible. It is, however, equivalent to the mode
summation method and does not therefore constitute an independent calculation
of the Casimir energy.
