Sometimes you want to find the optimum size power factor correction capacitor to put across a particular load and you end up trying various discreet values until a suitable value is found. Or maybe you need a set of big variable capacitors to excite a stand alone induction generator. What about the following approach? Get a variac and put a suitable (but relatively small) capacitor permanently across the mains input side so the variac draws essentially zero reactive power. Then connect a relatively large power factor cap across the output of the variac. Connect the variac input to whatever needs an adjustable capacitor.
According to my way of thinking, as the variac is adjusted up and down, the voltage on the output side capacitor varies accordingly, and so it draws an adjustable amount of reactive power. This adjustable amount of reactive power appears at the variac input and so appears as a continuously variable capacitor.
I might have posted this idea some time ago and forgotten about it.