  We consider the problem of bounding the dimension of the linear system of
curves in ${\bf P}^2$ of degree $d$ with prescribed multiplicities
$m_1,...,m_n$ at $n$ general points (\cite{Hir1},\cite{Hir2}). We propose a new
method, based on the work of Ciliberto and Miranda (\cite {CM1}, \cite {CM2}),
by specializing the general points to an elliptic curve in ${\bf P}^2$.
