4

Which of the following sentences is correct?

  1. The numbers are experimentally determined.
  2. The numbers are determined experimentally.

Are both (not) correct and if only one of them is correct, what is the underlying rule?

5

There's no significant difference. It's just a matter of style.

LATER: OP's particular word-pair doesn't occur often enough to easily establish usage figures for the two alternative orders, but I think this NGram shows a clear tendency to write arbitrarily chosen rather than chosen arbitrarily (a grammatically and semantically similar example).

On no authority but my own, I suggest the choice of word order may sometimes be influenced by a tendency to write the contextually more significant word first. In my particular example, for instance, I believe the arbitrary nature of the choice is likely to be more in the writer's mind than the fact of a 'choice' being made at all.

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