...Drillings. These guns would have been common place around the time of the Mexican war.

Bullshit.

from wehich I glean that the Sharps and the Henry were both flintlocks of the falling-block design

Then you - or they- gather wrong.

It may come as a shock to some people that the sum of all human knowledge is not available on-line and that a good deal of what IS posted on websites is complete and utter crap- reposted and perpetuated- but crap none the less.

Some times ya just gotta resort to -GASP! BOOKS! for the straight dope. Preferably books by knowledgeable authors known in the field & who actually know & understand what they're writing about.