ted:
so multiplier for spherical will not work with pointed electrodes ?
the more the electrodes are sharp, the smaller the distance is needed to start the arc.
It all comes down to the ionization of the air surrounding the charged metal. The critical measurement is the area of the charged material. A point has very little area, but the voltage is the same as for a sphere or a point. So the air or gas will ionize at a lower voltage because the surface is tiny.
In the 1950's a group at Linfield College discovered they could create X-rays between two sharp pointed electrodes sealed in a vacuum tube with a rather low DC voltage applied. The points were sharpened to a single metal molecule at the point. Google "field emission".
Paul