Finding a replacement bowl for a Century mixer that old would be a stroke of nothing less than pure luck, old mixers and bowls are scrapped and turned into something else so they’re not exactly sitting around in someone’s back room…but you already know that. So, where to go from here? It appears that you have a bowl for the mixer, with that in hand I’d see if I could match it up with an existing bowl from a newer mixer like Hobart, Thunderbird, etc. If you can find a bowl with the same profile the attachment ears can be ground off and new ones made using your old ones as a template. If you can find a bowl that looks like a likely candidate for replacement the next thing to do is to make a cast of the inside of your existing bowl (apply release agent to the inside of your bowl, then make a simple fiberglass shell impression of the inside of the bowl, when cured remove from the bowl and see if it will fit the candidate bowl, if it does, you’re home free, if not, good luck searching some more.
Maybe George Mills can add something too, I think George knows where the final resting site for such old things might be, the only problem with finding an original bowl is that it might not be in any better condition than yours.
One final thought: What’s wrong with the bowl that you have? If it’s just all dented up on the bottom (very common) you can “dolly” the dents out or take it to an auto body repair man and ask him to do it for you, if it’s cracked or split it can be welded, and if it needs to be re-tinned (many times the case) that’s possible too.
Tom Lehmann/The Dough Doctor