Linky to Cecil column My questions are:
Does anyone have a link to pictures of A and B batteries so we can see what they look like? Are the square nine-volt batteries part of this lettering scheme? And if I did pry apart a 6-volt lantern battery, are the “F” batteries inside in packaged modular units, or are they integral to the whole lantern battery?
The four F cells in a six-volt lantern battery are self-contained cylinders, like D cells, but bigger. Similarly, nine-volt transistor batteries are usually made of six AAAA cells.
One contributing reason that A and B cells disappeared may have been that “A battery”, “B battery”, and “C battery” had another, completely different, meaning in the early days of radio, when an “A battery” was the battery used to light up a triode filament, a “B battery” was used to provide the positive plate voltage, and a “C battery” was used to bias the grid. (This obviously leaves the question of why C cells survive, but, historically, the C bias battery was both introduced later and replaced earlier than the other two.)
Or maybe it simply wasn’t necessary to have a battery that was smaller than C, unless you were using something that needed something as small as AA, which, by Occam’s razor, would be my starting guess.
There may be no A cells about the place, but 2/3A (two-thirds the height of an A, same thickness as A) are widely used in modelling. 4/5C are seen a fair bit too. Electric model aircraft have a very heavy current draw and thinner cells aren’t as good for providing this.
There’s a thread over in MPSIMS, I believe, about what the inside of a 9V looks like but I can’t find it.
Which is why I said “contributing”.
Of course, back in the 1950s, when I was a kid, the main use of dry cells was flashlights. (They were normally called “flashlight batteries”.) Back then, even C was relatively uncommon. Either you used big, manly D’s, or you used AAs in eensy-weensy puny-gurly “penlights”, or you used AAAs in keyfob lights that looked rather like modern disposable butane lighters.
A little later, you used to see a fair few 4.5V batteries that were just three AAs bundled in a flat package with a couple of brass strip terminals on the top. They were used quite a lot in bike lights if I remember right.
The explanation I read was that the earliest portable radio sets had four batteries, which were sensibly labeled A B C and D from smallest to largest.
What battery did what I don’t recall, except I’m sure the D’s were for the speaker.
No, I’ve already explained that.[ul]
[li]It wasn’t just portable radios; lots of early electronic equipment ran on batteries because of voltage-control and smoothing problems.[/li][li]There were three.[/li][li]The A battery ran the cathode filament.[/li][li]The B battery charged the plate.[/li][li]The C battery biased the grid.[/li][li]There was no D battery, and you couldn’t use a battery “to power the speakers” in the first place. Running DC through the speaker coils would just burn them out.[/li][li]The A battery, powering a heat source, took the most power; the A battery, in fact, was often a lead-acid affair.[/li][li]As the last item imlies, the A, B, and C radio batteries had nothing to do with A, B, and C dry-cell sizes, except that (perhaps) the ambiguity may have contributed to the demise of the A and B sizes.[/li][/ul]
And then the vibrator came along and guaranteed a market for C batteries for all time. 
Except for those wimpy ones that take AAs, whose only virtue is that they are quiet.
We had a different code for batteries, and the US one only seems to have taken off here in recent years. C cells were SP11, D cells were SP2, AAs were HP7s, AAAs were HP17s, I can’t recall the rest
Really old radios from the 1920s and maybe a bit later sometimes used a tiny “C” battery, in addition to the “A” and “B” batteries under the chassis innards for some arcane portion of the circuit of just a very low current similar to a watch battery. That’s what’s used for replacement today, but they last fairly much forever. In a pinch the restorers just add a tiny bit of water to the battery and they almost always work fine.
Usually people would have cables running from the basement to the radio upstairs, because keeping lead-acid batteries around the house is hard on the carpet, and noxious fumes. Farm or rural folks would often run windmills with generators to keep whole banks of batteries charged. 32 volt radios and other devices were sold so the whole household could run on battery power (no Television yet!) The higher battery voltages were multiples of 1.56, a standard dry cell voltage, and called “B” voltage/battery. Coupled in series parallel combinations a whole range of voltages can be applied. 3, 6, 9, 45, 90, etc. The tube filaments called “A” voltage/battery drew a lot more current so a heavy duty battery of the lead-acid kind (and rechargeable) was most often used.
People stopped using/manufacturing certain types of batteries because (in part) their names were already in use?
If you curse enough users for not understanding why a “B battery” doesn’t mean a “B battery”, yeah, such things happen.