  If the integrals of a one-form over all lines meeting a small open set vanish
and the form is closed in this set, then the one-form is exact in the whole
Euclidean space. We obtain a unique continuation result for the normal operator
of the X-ray transform of one-forms, and this leads to one of our two proofs of
the partial data result. Our proofs apply to compactly supported
covector-valued distributions.
