[wonderwrench]

This is a 116X not a 37-116 or 38-116 correct? If so see below.
Do the two cabinets accept the same size speaker? If so PN 36-3088 is the field coil with speaker. The output transformer was mounted to the speaker so you do not have a output transformer PN is 32-7446. As far as other Philco's that use the same speaker I did a little checking and found zip. There may be other models that use the same parts but without a cross reference it would take more time than I have at this point. Maybe Ron will know. You could always use a PM speaker and a 1000 ohm, 25 watt (minimum) resistor (fixed per Ron's advice) as a fake field coil but you still need a output transformer as it was attached to the speaker you do not have.

If you want to research your self get copies of most Philco models service info here. http://www.theoldradiofixerupperguy.com/...nloads.htm
If they do not have the model you are looking for try here.
http://www.nostalgiaair.org/Resources/

Hope you get it figured out!

Edited to correct info