  Let A be a union of smooth plane curves C_i, such that each singular point of
A is quasihomogeneous. We prove that if C is a smooth curve such that each
singular point of A U C is also quasihomogeneous, then there is an elementary
modification of rank two bundles, which relates the O_{P^2} module Der(log A)
of vector fields on P^2 tangent to A to the module Der(log A U C). This yields
an inductive tool for studying the splitting of the bundles Der(log A) and
Der(log A U C), depending on the geometry of the divisor A|_C on C.
