Every digital wristwatch I've ever owned since being old enough to take them apart has a screw adjustment. Are you saying they aren't digital?
I don't know how to design digital clock circuits, but it seems like something simple to design a circuit which could: calculate the time elapsed since the last time adjustment, divide the amount of time adjusted into that, and then have the clock do some math operations to correctly adjust the speed of the clock.
I just assumed it was a POT of some sort and it modulated the signal from the quartz in some way that was meaningful to the processor.
DC-powered digital clocks? I've never met one, especially clock in cars. They notoriously suck at keeping accurate time. They lose more time than my dollar store wall clocks.
Yeah, that's my gripe. Some of the innovations that were developed in mechanical clocks, seem to have no equivalent in digital clocks. It's disappointing that digital clocks sometimes fail to keep time as accurately as the old mechanical ones. I bought a battery-operated mechanical clock at a yard sale about 2 years ago, and I haven't had to adjust it once in 2 years. Another digital clock in the house is gaining about 5 minutes a month, even worst than the dollar-store clock I keep beside it as a reminder of how bad it is.
The clock on my microwave oven gains about a minute every two days. I hate resetting that stupid thing every day.
This works adequately well when the ambient temperature patterns don't change. But it cannot adjust for changing seasonal temperature patterns that cause frequency shifts in the quart crystal. One of my parents' old cars had that self adjusting mechanical clock system you mentioned. I do seem to remember it being more accurate than other mechanical clocks, but not more accurate than some of the quartz wristwatches since. ??? Please elaborate on what you mean. All my quartz-type clocks use DC power, specifically batteries of some sort. Some have fairly good crystals, some have cheap crystals. None have special high accuracy crystals. Plug-in wall clocks use either a synchronous AC motor, or a powerline cycle counter. Their 'accuracy' is merely a reflection of the AC power grid, which in most of North America is very well regulated. Phase noise may be awful, but long interval timekeeping is usually almost 'perfect' under normal conditions. One of my college EE profs told stories of some winters in the 1950s where capacity problems caused mild brownouts and frequency drops. Every morning, the radio news would tell listeners how many tens of minutes everybody's plug-in clocks fell behind overnight. At my old workplace, a newly arrived facilities manager reamed several of her staff for being two minutes late for a Monday morning meeting. She didn't understand that the overhead clocks were simply tied to the AC grid. During a weekend power failure, the plant's backup diesel generators kicked in for an extended period, and those clocks gained 4 minutes. Everyone but her had long known that those overhead clocks were frequently off, due to occasional outages. That is why the rest of us ignored those, and used any of hundreds of PCs or UXs synced daily to online NBS servers via NNTP.
Mechanical clocks cope quite well with temperature changes. Electronic circuits can monitor temperature with thermistors.
Temperature compensated movements can cope well. Earlier mechanical movements were not compensated. Semiconductor junctions can too. Digital clocks accurate to +/- 50 ppm (a half hour per year) can be built for pennies. Accuracy can be increased almost without limit. It just takes money. But in an era of ubiquitous handheld communication devices, wireless synchronized via a traceable calibration path to national reference standards, consumer demand for accurate standalone clocks has plummeted. Much of the population doesn't even wear watches anymore, they just pull out their cellphones to check time. This is even how thieves now get potential victims to show their phones. If you want to buck this trend, you can. Just add money. But beware that when asking for something that few other consumers are willing to pay for, you may have to add a lot of money.