I am constructing this apparatus over the weekend possibly even to use later this year in a science fair. I want to make as many things variable so that I can best experiment with this however I don't want to make something variable that doesn't influence effects. Would you be able to tell me what of the following has some sort of influence on the effects produced;
Copper Bar Length
Spark Gap Length
Capacitance(C and C1 as per Tesla's lecture)

Tesla states "These results, as I have pointed out previously, should not be considered to be due exactly to frequency but rather to the time rate of change which may be great, even with low frequencies." so I'd say a variac would be a good component to use however I'll just use a simple variable 555 timer circuit driving an ignition coil for the transformer in this circuit.

Also is there anything more you'd suggest I look at? Oh and by the way, awesome reconstruction. I did see this a little while ago and was quiet impressed.