An extra doorbell ringer.

All you need to do is confirm that the 3-wire cable does indeed go from the transformer directly up to the existing bell. If it does, the unused Red wire can "return" the bell signal down to the baasement with no rewiring.

Jim

OP> As far as I can see, the red wire does run from the transformer to the ringer, and both ends of the red wire are unused and wrapped around the brown cable. I suspect that I would connect it to the FRONT (door) terminal in the ringer, and in series to one or the other wires at the transformer. I'll pick up a cheap ringer in the next few days and try it, and let you know how it works. Thanks

Here's a couple of links to some sites about doorbell wiring (watch for wrap):

Thanks.

Connect the red unused wire to the wire that comes from the switch to the old ringer. The basement end of that wire will go to the new ringer. The return wire from the new ringer will then go to a transformer tap. If you get the wrong transformer tap it won't ring. What I mean is that it will not short out anything.

direct. This is why polarity doesn't matter.

That's good. That way he'll always be ready.

The thing is that one of the two wires connected to the bell now goes to the button. The other one goes to the transformer in the basement.

Either that, which is the way mine was, or they all go to the basement and there is another pair of wires from the button to the basement.

Figure out which wire is which and connect the second bell to the two connections on the first bell. If your house is like mine, you can use the unused red wire to go from the bell (the screw that is connected to the button) to the basement bell.

And the other wire to the first bell already runs to the basement. You can use that for the second wire to the new bell.

I had the same problem you did and first go a little bell with a circle at the top and a clapper at the side. It worked well enough that I knew someone was there, and the main floor ding dong also worked. Years later Home Depot had 75% off a nicer ding dong than the one I had, so I put the new one on the first floor and moved the old one to the basement. Then neither rang! So I had to go to the next bigger transformer, which is an inconvenience, but not impossible. Althought in your case it might mean taking the cover off the fuse box, which is also possible but requires extra safety things we'd have to go over.

That was fine but then came the intennet, and I needed a bell on the second floor. No wires already run and no easy way to run wires. So I used my mother's old wireless doorbell, but without batteries.

I took the 18 volt transformer, put a little diode in the circuit to make 9 volts DC (ripple doesn't matter) and ran parallel to the wires on the downstairs bell to the 9 volt battery conector of the wireless push button. This means when somone pushes the front door button, the wirelss button is activated. Oh, yeah, I soldered a little wire to short out the wireless pushbutton button, so that switch is always closed. Then I plugged in the receiver in the 2nd floor hall and everything works fine. No batteries to worry about.

I paid 3 dollars iirc from Sunset House for this wireless one 18 years ago.