It used to be widely held by people with a little learning that to say "under the circumstances" must be wrong because what is around us cannot be over us. "In the circumstances" was the only correct expression. This argument is characterised by Fowler as puerile. Its major premiss is not true (" a threatening sky is a circumstance no less than a threatening bulldog") and even if it were true it would be irrelevant, because, as cannot be too often repeated, English idiom has a contempt for logic. There is good authority for under the circumstances, and if some of us prefer in the circumstances (as I do), that is a matter of taste, not of rule.