  We investigate forms on supermanifolds defined as Lagrangians of ``copaths''
(that is, systems of equations, which may or may not specify submanifolds). For
this, we consider direct products $M^{n|m}\times\Bbb R^{r|s}$ and study
isomorphisms corresponding to simultaneously advancing the number of additional
parameters $r|s$ and the number of equations. We define an exteriour
differential in terms of variational derivatives w.r.t. a copath and establish
its main properties. In the resulting stable picture we obtain infinite
complexes $\D:\Om{r}{s}\to\Om{r+1}{s}$ for $M^{n|m}$, where $0 \le s \le m$ and
$r$ can be any integer. For $r\ge 0$ a canonical isomorphism with forms
constructed as Lagrangians of $r|s$-paths is established. We discover the
``lacking half'' of forms on supermanifolds: $r|s$-forms with $r<0$, previously
unknown except for $s=m$. (They have been partly replaced earlier by an
augmentation of the ``non-negative'' part of the complexes.) All these results
are new. The study of these questions is in progress now.
