For those of you contemplating building a duplicate or are just interested in the RCA Theremin, the following links will interest you. I built an RCA Theremin from scratch so it is possible and subsequently restored an original instrument. I made detailed measurements of the original instrument during the restoration. Art Harrison kindly provided the schematics which I modified as noted.
http://members.tde.com/mmckeown/Theremin/ThereminDwg1.jpg
http://members.tde.com/mmckeown/Theremin/ThereminDwg2.jpg
http://members.tde.com/mmckeown/Theremin/ThereminDwg3.jpg
http://members.tde.com/mmckeown/Theremin/Measure1.jpg
http://members.tde.com/mmckeown/Theremin/Measure2.jpg
http://members.tde.com/mmckeown/Theremin/Schematic1.jpg
http://members.tde.com/mmckeown/Theremin/Schematic2.jpg
http://members.tde.com/mmckeown/Theremin/ThereminDwg1.jpg
http://members.tde.com/mmckeown/Theremin/ThereminDwg2.jpg
http://members.tde.com/mmckeown/Theremin/ThereminDwg3.jpg
http://members.tde.com/mmckeown/Theremin/Measure1.jpg
http://members.tde.com/mmckeown/Theremin/Measure2.jpg
http://members.tde.com/mmckeown/Theremin/Schematic1.jpg
http://members.tde.com/mmckeown/Theremin/Schematic2.jpg