I have no idea of the model (since I know nothing of A&I reels), but it has the Trademark pattern from trademarks issued in 1877 & 1881, rather than the later pattern issued in 1909.
Al, sorry this took so long to get to but i was hoping someone would jump in before now. In any event, i don't believe there would have been any model name associated with these early reels... just "small raised pillar reel" comes about as close as you can come! In the book " The Origins of American Angling by Mary Kelly ( available via whitefish press), Mary did an article on the logos of A&I. Yours is the earliest, from mid 1870s, based on the figure i have pasted below. Nice find and a definite keeper!
Ps: you probably already own this book... ask your wife where she put it
ORCA member since 1999 Honorary Life Member
Specializing in saltwater reels...and fly reels...and oh, yeah, kentucky style reels.....and those tiny little RP reels.....oh, heck...i collect fishing reels!...and fly rods....and lures