Thanks for the quick replies! Thanks, as well, Chilly, for the info on the banding. The sockets he has have a single band (I think) about a 1/4" from the base, and are numbered as follows:
NT-614 (7/16)
NT-620 (5/8) ,
NT-1222 (11/16),
NT-1226 (13/16),
NT-1230 (15/16),
NT-1232 (1),
NT-1234 (1 1/16),
NT-1236 (1 1/8),
NT-1240, (1 1/4)
He has some others in there that are New Britain, but didn't have numbers on them, so they may have been from an older set, or just worn. They all look similar to me. Is NT the series that these sockets come from, and the number is for that specific size? This is really my first foray into the world of tools, so there's a lot I don't know.
Also, here's a picture that my brother in-law sent of the set. He wasn't really sure which set I was asking him about, so he took it at an angle to include the entire wall, which didn't do well for details of the set in question; the shinier ones are from a different set:
