It's a california threeway.
Here is a diagram of a double one. You should be able extract the wiring of a single from it. Just ignore the top two switches and light.

Unless you intend to rewire the entire circuit, I would leave it as is. Once you start modifying K&T wiring you need to replace it all. Changing the switches would be OK. If the circuit is fused properly(15 amps) then a short in the switch will simply blow the fuse.
This was a very comon way to wire threeway back in the day.

For those having trouble with chrissmith's "view this in a fixed-width font" instruction:

HÂ --+------------------+Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â
    :                  :              Â
    :             +--- : -----------> L
    :             :    :              Â
    :   #######   :    :   #######    Â
    +---#   C #---+    +---#   C #--> L
        #     #            #     #    Â
        #     #            #     #    Â
    +---#     #        +---#     #    Â
    :   #######        :   #######    Â
    :     SW1          :     SW2      Â
    :                  :              Â
NÂ --+------------------+Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â

Wow, hat's off to both of you for the diagram with ASCII.

I've never seen a California 3 way... it sounds illegal in most southern states.

If this is your duplex, I think you really need to look at upgrading the wiring on this rental unit.

It's not illegal if it's grandfathered in.

Umm, no comment.

"Chicago" 3 way maybe??? The bottom of the stair, bring a 2-wire from an outlet to a 3-way switch. Connect hot from the outlet to the 3-way common. Run a 2-wire from the 3-way to the second 3-way. Travellers. From the 2nd 3-way to the light, connect the common to the light, then use a 2-wire from the light to find a neutral somewhere.

Uggh... the house I'm in right now has one wired that way, and I was never permitted to tear the drywall apart to fix it. The light on the upstairs end is wired correctly, and I ran all the necessary cables to wire the downstairs end correctly, then when I told the homeowner (who is a licensed electrician himself) that I could get to the downstairs light without cutting part of the drywall, his order was "hook the existing hot wire to your new circuit, let it get neutral from wherever it's already hooked." . . . No thanks. I told him I'd leave it open and, if he wanted to halfass it like that, he could do it himself.

He did.

Grrr that one pisses me off every time I flip that switch!

firstly it is illegal to switch the neutral, so any diagram showing the neutral being switch is wrong.
secondly this is 2 way switching and not 3 way.

for 2 way switching the common of switch 1 does to the fuse. The common of the switch 2 goes to the lamp. then two other wires join the other terminals of switch 1 to 2. The switches has 3 terminals. The neutral goes straight from the fuse box to the lamp. For sake of cabling, the neutral may be joined to each other in a spare unused parking terminal in the switches.

Everywhere in North america that I know calls this a three way setup. Only in UK have I heard this called a two way switch.

chezzrob, we must recognize that code wasn't always what it currently is. At some point in history, it was legal to switch the neutral. It was also legal to have individual conductors snaking around the walls and ceilings in all manner of unpredictable directions with twisted, soldered, and taped splices just "hanging around" in there. Think "grandfathered", and remember that we are not required to rewire our houses every time a new edition of NEC comes out. The original poster's installation is legal only because it was legal at the time of installation. You're certainly correct in that it does not, in any way, meet modern code.

Regarding 2/3/4-way switching... the standard terminology applied to switches in the USA is for SPST (normal) swithes to be 2-way, SPDT to be 3-way, and straight/swap to be 4-way. ie, a normal single switch is a 2-way, two switches is a 3-way, and three (or more) switches is a 4-way configuration. I have NO IDEA why "they" decided to refer to them this way, but it is what it is. The only answer I've ever been given is that the number refers to the number of terminals on the switch, not counting ground. I don't believe this explanation myself, but it is nonetheless a good way to remember it.

"I have NO IDEA why "they" decided to refer to them this way, but it is what it is."

By the number of connections on the switch.