In a previous paper we have given a complete description of linear liftings of p-forms on n-dimensional manifolds M to q-forms on $T^AM$, where $T^A$ is a Weil functor, for all non-negative integers n, p and q, except the case p = n and q = 0. We now establish formulas connecting such liftings and the exterior derivative of forms. These formulas contain a boundary operator, which enables us to define a homology of the Weil algebra~A. We next study the case p = n and q = 0 under the condition that A is acyclic. Finally, we compute the kernels and the images of the boundary operators for the Weil algebras $𝔻^r_k$ and show that these algebras are acyclic.