  The Hartshorne--Hirschowitz theorem says that a generic union of lines in
$\mathbb{P}^n$, $(n\geq 3)$, has good postulation. The proof of Hartshorne and
Hirschowitz in the initial case $\mathbb{P}^3$ is difficult and so long, which
is handled by a method of specialization via a smooth quadric surface with the
property of having two rulings of skew lines. We provide a proof in the case
$\mathbb{P}^3$ based on a new degeneration of disjoint lines via a plane
$H\cong\mathbb{P}^2$, which we call $(2,s)$-cone configuration, that is a
schematic union of $s$ intersecting lines passing through a single point $P$
together with the trace of an $s$-multiple point supported at $P$ on the double
plane $2H$. In the first part of this paper, we discuss our degeneration
inductive approach. We prove that a $(2,s)$-cone configuration is a
degeneration of $s$ disjoint lines in $\mathbb{P}^3$, or more generally in
$\mathbb{P}^n$. In the second part of the paper, we use this degeneration in an
effective method to show that a generic union of lines in $\mathbb{P}^3$
imposes independent conditions on the linear system
$|\mathbb{O}_{\mathbb{P}^3}(d)|$ of surfaces of given degree $d$. The basic
motivation behind our degeneration approach is that it looks more systematic
that gives some hope of extensions to the analogous problem in higher
dimensional spaces, that is the postulation problem for $m$-dimensional planes
in $\mathbb{P}^{2m+1}$.
