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Joined: Jun 2007
This will lead you to a discussion (among other things) of some battery current measurements which several of us made on the HP35S. (Go towards the middle of the thread.)
I was impressed with how similar the current delivered by each of the batteries is. As close as I could measure it, it is identical.
As you both note, the batteries are certainly not in series. I suspect they are in some sort of parallel, using a circuit which isolates the batteries from each other but balances the load.
I just tried my calculator with one battery at a time - and that works, briefly! I get a couple of seconds on either one until it shuts itself off. Whether it shuts off after sensing that a battery is low or missing or whether it is running on residual charge I don't know, except that I was able to turn it back on (in the single battery mode) several times.