The HP 115BR divider and clock uses very unusual analog RF dividers, electro-mechanical  resolvers, optics, synchronous motors and mechanical clockwork to achieve its amazing performance with early 1960's technology. 

The dividers use regenerative frequency dividers, consisting of RF mixers and frequency multipliers to make divide-by-ten circuits, which need to be manually jump-started in order to work! 

How the analog dividers work is mind bending and very clever. It would be a bit confusing to explain them with words alone, but the diagram animation in the first video should get you up to speed. 

Two of these divide-by-ten are used to downshift the 100 kHz input frequency to 1 kHz. The 1 kHz then drives a synchronous motor, which you also need to spin up manually to jump start. This then drives an almost conventional mechanical clock that displays down to 0.01s (stroboscope required to read it!).

But how do you generate the super precise 1s tick? By a clever combination of optical pickup and RF tricks. A photodiode picks up the top of the second, when two holes in two different gears align for a very short moment every second. But that is nowhere precise enough. So, this optically-derived pulse is used as a gate to let just one of the much shorter 1 kHz pulses through. The 1 kHz pulse train is obtained from the output of the 1 kHz electronic divider, and therefore has atomic-derived precision.

But there is more. A continuously adjustable phase shifter is inserted between the first and the second divider, in the 10 kHz sine wave. The phase shifter is cleverly implemented with a resolver, an electro-mechanical contraption that is also better understood by watching the video. The result is that you can shift the pulses coming out of the following 1 kHz divider to 1 us precision. The amazing trick is that the resolvers are continuously rotating and adjustable, with no end stop. So you can keep spinning it and achieve seconds of advance or delay, in a continuous way, without ever skipping a beat. Analog rules!

However our unit did not work - that's why it ended up on my bench, I guess. To make our life even harder, it did not follow the published schematics either. We later found out, by reverse engineering, that it had been modified by HP for the 1 us tick delay resolution (the regular unit had 10 us resolution). 

We also found out that it had a second undocumented HP modification, which to our surprise turned out to be an atomically precise 60 Hz output signal generation. Was this unit was used in a power plant, to regulate the 60 Hz grid? Or, more prosaically, as a master clock to drive other synchronous clocks that would normally expect 60 Hz from the grid, and upgrade them to atomic precision. 

Finally, it had a third undocumented modification, this time by the previous owner and generous donor of this unit, who disconnected the dividers and drove the synchronous motor at 1000 Hz, to just "get it going". 

It took us two episodes to revert it to its original configuration and get it going again, as changing early faulty germanium transistors wasn't enough to fix our stubborn divider. It took us most of episode 2 to corner a slightly leaky mil-spec tantalum cap, which was the culprit for an almost-but-not-quite working RF mixer. But the chase was well worth it, as it got us to understand and admire the finer points of these ingenious RF circuits. 

So all was well in the end, and we finally got to admire our atomic, continuously adjustable tick. We even sync'ed it to the atomic signal from NIST in Fort Collins, using the WWW radio signal. From a 1957 vintage tube receiver, of course. The startup and sync procedure itself is quite an adventure.

The project is still ongoing as of this writing. We are now trying to replicate the Hafele and Keating flying clock experiments from 1974. These were done with vastly improved electronic dividers, now precise to a few...