  It is easy to find real algebraic varieties with weakly Whitney regular
stratifications which are not Whitney regular, and we give such an example in
section 3 below. No examples are known among complex analytic varieties
however, so that the natural question arises : do Whitney regularity and weak
Whitney regularity coincide in the complex case ? As a test, in this paper we
study the well-known Brian\c{c}on-Speder examples.
  We investigate systematically all of the (infinitely many)
Brian\c{c}on-Speder examples, and establish in particular that none of these
examples are weakly Whitney regular. We determine all the complex curves along
which Whitney regularity fails and all the complex curves along which weak
Whitney regularity fails. It turns out that for each example there are a finite
number of curves $\gamma_i$ such that weak Whitney regularity fails precisely
along those curves tangent to one of the $\gamma_i$ at the origin.
