Possibly they were being used to construct a Van de Graaff Electrostatic Generator's top ball electrode with, in case you couldn't acquire a metal ball electrode.
With the use of 2 pie plates to form that electrode, with a traveling belt transferring a charge up to them at the top.
The next device being your aforementioned Tesla coil with its RF boosting technique.
The last one to come to mind would be another electrostatic device called a Wimhurst generator, but its distinct petal shaped electrodes give it away...plus no pie plates involved.
73's de Edd