The old National Park Service Popular Study Series monograph "Rifle Making in the Smokey Mountains" notes:
"The calibre of the mountain rifles deserves a word of mention. Strictly speaking, these rifles had no calibre in the ordinary sense of the word. Usually, however, four kinds of rifles were made: one of about .35 calibre (0.35 inch) which was called a squirrel gun; one about .40 calibre (0.40 inch) called a turkey rifle; one about .45 calibre (0.45 inch) called a deer rifle; and one of approximately .50 calibre (0.50 inch) called a bear gun."
It is a bit of an odd caliber--a little too much for small game, and not quite enough for large game unless you are really, really close.