Why do we say "Keep a stiff upper lip"?

Meaning:

Don't show that you're upset, in the face of adversity be self-reliant, remain calm.

Background:

Just before starting to cry the lips tend to tremble. In which case, why does this expression refer only to the top lip? One theory is that, in the 19th century, most men had moustaches which would have made a quivering top lip more noticeable than the bottom.

Similar in meaning to "chin up", "keep a stiff upper lip" would see seem to be the epitome of Englishness (e.g. The Jeeves novel, Stiff Upper Lip by P. G. Wodehouse). However, apparently it originates in the USA, having been traced back as far as 1815.

"What's the use of boohooin'.... keep a stiff upper lip no bones broke -- don't I know?"
- Down Easters (1833) by John Neal.

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