  We adapt and generalise results of Loganathan on the cohomology of inverse
semigroups to the cohomology of ordered groupoids. We then derive a five-term
exact sequence in cohomology from an extension of ordered groupoids, and show
that this sequence leads to a classification of extensions by a second
cohomology group. Our methods use structural ideas in cohomology as far as
possible, rather than computation with cocycles.
