Learn English – “On the principle” versus “Under the principle”

“On the principle” outpolls “under the principle” by pretty wide margins in published books scanned by Google Books, as shown in this graph. So odd did the latter phrase seem to me that I even threw in “under the principal”—which might well occur, for instance, in discussing the organization chart of an American public school, or in elaborating a taxonomy—as a phrase that you might have mistaken for it; but that too was used in this corpus far less than “on the principle.” My native-speaker sense and this statistical survey strongly agree in strongly preferring “on the principle.”

Martin Smith, however, cites in a comment the usage “under the principle of comity, one nation defers and gives effect to the laws and judicial decrees of another country” (from here). This usage does seem normal to me: I suspect it is fairly specific to legal and similar contexts, where the principles in question are rather normative than natural. I disagree with Martin, though, in thinking that on would do nicely here as well.