  The computation of long range linear self-interaction forces in string and
higher dimensional brane models requires the evaluation of the gradients of
regularised values of divergent self-interaction potentials. It is shown that
the appropriately regularised gradient in directions orthogonal to the brane
surface will always be obtainable simply by multiplying the regularised
potential components by just half the trace of the second fundamental tensor,
except in the hypermembrane case for which the method fails. Whatever the
dimension of the background this result is valid provided the codimension is
two (the hyperstring case) or more, so it can be used for investigating
brane-world scenarios with more than one extra space dimension.
