Now Grothendieck has shown that the cohomology of a complex variety may be defined algebraically; in particular if X is a complex affine variety the canonical map from the closed/exact algebraic differentials on X to the DeRham cohomology of X is bijective. The question then naturally arises whether the cohomology sequence above may be recovered algebraically. It is not too difficult to do this, at least when X is affine and Y is principal on X. Namely, let A, B, and A' be the co-ordinate rings of X, Y and X Y, and (t) be the defining principal ideal of Y. Let D(A), D(B), and D(A') be the algebras of algebraic differential forms on X, Y and X Y. The problem amounts to constructing a degree 1 homology isomorphism between the complexes D(B) and D(A')/D(A); for then the exact sequence of complexes