I am looking for information on *how* to determine automatically, via
an electronic circuit, a battery's chemistry (in particular, how to
tell if a battery is secondary NiCd/NiMH, or primary alkaline). This
is useful in chargers, for example, that need to make sure the user
inserted the right type of battery before beginning to charge.

If the only source of information for this "circuit" is that from
being plugged into the positive and negative terminals of the battery,
then I'm pretty sure it is impossible to tell the battery's
chemistry-type.  All it is putting out is current....and electrons are
electrons no matter what molecules they originated from, and so would
offer no help as to the chemical composition.

You might be able to make an educated guess based on measuring the
battery's internal resistance.  It would only be a guess though, and
the battery design would also have an effect.

Ian G.