You're referring to "hook edge" rims vs......er, uh, well, "non-hook edge" rims , or straight walled rims. I had a concern about this not long ago myself, and did a little research on the various old wheels in my basement. First, a couple of guidelines: straight-walled rims, because they don't have a hook edge, won't hold the bead under very high pressures; for a 27 x 1 1/4" tire, the max. safe pressure will be about 75-80 psi. Hook edge rims will generally hold whatever the max pressure rating is on the tire. When I did my little research, I found that straight-walled rims are indeed that, there's absolutely no obvious bump along the edge for holding the tire's bead. I did find some slight variation between one "hook edge" and another, but what you're looking for is an obvious, well defined hump at the edge of the rim, which serves to keep the bead from climbing over the wall of the rim.........I had thought that I owned more straight-walled rims than I actually did, I found that the only rims I have that are straight-walled were on an '82 Schwinn Super le tour(27") and an '83 Schwinn le tour luxe(27"). I've long since replaced these OEM rims on the '83. I found hook-edge rims on my '83 Centurion Pro Tour (27"), '85 Centurion Accordo (27"), and all my mountain bikes, some of which go back to the late '80's. I did find that the hook edge is more pronounced on the modern 700c clincher rims (Sun M13II rims) I'm now using on the le tour luxe than it is on the various mountain bike rims and older 27" hook-edge road rims, including the most modern mountain bike rims I own (Mavic X517). It was rather interesting "research," I had even started a thread here asking about the various pressures, etc., because I knew that I had used straight-walled rims on my old road bikes, but I hadn't given all that much thought to it until I started building up the Centurion Pro Tour and I wanted to run pressures over 90psi. Interestingly, the stock tires that came on the '83 le tour luxe were 90psi tires, despite the straight-walled rims. I have no explanation for that. Given that your bike is an '82 Fuji, I'd say there's a fair chance for either type of rim, check closely to see what the inside wall of the rims looks like-