  It is well known that the equisingularity class of the general polar of a
plane branch is not the same for all branches in a given equisingularity class,
but it is the same for sufficiently general ones and depends upon the analytic
type of the branch. The aim of this paper is to go beyond generality and show
how one could describe the equisingularity classes of (general) polars of all
branches in a given equisingularity class, making use of the analytic
classification of branches as described in previous work by the first two
authors. We will show how this works in some particular equisingularity classes
for which one has the complete explicit analytic classification, and in
particular for all branches of multiplicity less or equal than four.
