If only we could now find one!  This has been one of the most exciting articles I have ever read.
The circuit was a typical "kicking coil" circuit using a large electromagnet that had a tungsten interrupter
to turn itself on and off.  The self-inductance of the electromagnet was used to charge the cap which in turn discharged
through the primary of the Tesla Coil.  The circuit was commonly used in the quack "Violet Ray" machines of the time and operated on AC or DC.

(http://www.electrotherapymuseum.com/2006/MiscOscillators/images/TeslaOscillatorFig7.jpg)

This would be of similar construction:

XI. Exhibition of a Tesla Coil. By Prof. Silvanus Thompson, D.Sc., FM.S*

This apparatus is intended to replace the two induction coils and spark-gap arrangements used by Mr. Tesla for high frequency experiments. It consists of an induction-coil, with a separate self-inductance coil in the primary circuit. This self-inductance coil is also used as an electromagnet for the separate interrupter of the primary circuit. A condenser of 2.27 microfarads capacity is connected between one end of the primary coil and one terminal of the interrupter, so as to include both of them between its terminals. The primary consists of 5 turns of copper strip. The secondary has 2000 turns of thick wire. The supply current, about half an ampere, may be taken from the electric-light mains at almost any voltage from 50 to 200, direct or alternating.

 Discussion.

Prof. Lodge said that he believed Sir W. Crookes had found it work quite well at 10 volts. He pointed out also that if the straight discharge rods at the spark-gap were free to slide, the discharge drove them back into their sockets.

Prof. Fitzgekald said it was stated at Toronto that the spark was broken at the interrupter when the condenser was charged, and that by the time the condenser was ready to discharge, the contact at the interrupter had been made again. It had seemed to him at first that the condenser discharges and surgings must take place at a rate far higher than the period of the mechanical movement of the interrupter ; but he perceived afterwards that it was not so.

Prof. Herschel asked if such an apparatus was suitable for work with Rontgen rays.

Dr. Thompson, in reply, congratulated Mr. Tesla upon the perfect working and compactness of his invention. The present form was not suited for Rontgen ray experiments, with ordinary focus-tubes, but Mr. Tesla had designed a special tube that was excellent for that purpose.
 

* January 21, 1898


Enjoy!
I would be happy to build a reproduction of this apparatus to exhibit on the forum, but am  in need of some magnet wire - 26 awg and 18 awg, or something near there for the magnet coil and Tesla secondary Pancake Coil...
Jeff Behary