Don't know about the external horn Disc Graphophones, but my three Grafonola's all have serial numbers stamped into the motor-plate.
My little Columbia "Jewel" ($35 table-top with lid) still had enough of the label on the bottom that specifically ID'd it as a "Jewel"...
A friend has an Eclipse (more expensive "hornless Grafonola"), which does not have a motor plate - the motor is fastened directly to the wooden deck, as with Victor. I don't know if his machine has a serial # anywhere...
My other two G-fonolas are uprights, the smaller one probably a Mignonette, the larger probably a "late" Nonpareil. Both definitely preceede the alpha-numeric model system...
One of the variances between both my uprights and Baumbach's book is that neither of them have cabinet-knobs on the face of the tone-leaves (as shown in most catalogue cuts), just the knob on the side of the cabinet at the front.
I guess I'll have to learn how to do this data-base stuff and be the guy to create one, "for the good of the order"...
