  Isostatic equilibrium is commonly defined as the state achieved when there
are no lateral gradients in hydrostatic pressure, and thus no lateral flow, at
depth within the lower viscosity mantle that underlies a planetary body's outer
crust. In a constant-gravity Cartesian framework, this definition is equivalent
to the requirement that columns of equal width contain equal masses. Here we
show, however, that this equivalence breaks down when the spherical geometry of
the problem is taken into account. Imposing the "equal masses" requirement in a
spherical geometry, as is commonly done in the literature, leads to significant
lateral pressure gradients along internal equipotential surfaces, and thus
corresponds to a state of disequilibrium. Compared with the "equal pressures"
model we present here, the "equal masses" model always overestimates the
compensation depth--by ~27% in the case of the lunar highlands and by nearly a
factor of two in the case of Enceladus.
