An aluminum electrolytic capacitor that hasn't been in service for a long time may need to be brought back to service by very slowly raising its voltage up to rating. If you try to bring one up too rapidly, the capacitor can be destroyed.
This circuit enabled the resurrection of a very old, spider webbed, dust covered 14000 µF capacitor that had been sitting idle in a storage closet for how long, nobody knew.
The 0.1 µF, the two diodes and the 14000 µF capacitor itself form a half-wave, Cockcroft-Walton voltage doubler circuit. However, because the 0.1 µF is so small compared to the 14000 µF, the voltage rise time across the 14000 µF is something around fifteen minutes for the 60 Hz line frequency.
In use, you apply the input line voltage (120VAC at 60 Hz in my case) and turn the autotransformer up just a little bit. Maybe half an hour later, you raise the autotransformer setting upward a little bit, after another half hour you do it again and so on and so on.
Since the risetime is so slow, you don't need quick reflexes if you happen to raise the autotransformer a bit more than you had intended. You can just lower the setting back down again.
Also, if the 14000 µF were to short circuit itself, the AC line would simply be loaded at most by the 0.1 µF which poses no safety hazard.
Just do be sure to put the capacitor inside of something safe in case the capacitor does fail. An empty metal can might suffice.