I'm a novice trying to repair a Philco 37-60 found on riders 7-19. Both the field coil and the primary of the output transformer is open. At least that is what I think they are called. They are all mounted on the speaker. Any suggestions for repair?

You may try to repair the field coil if you can unwind it a bit to find a broken winding near the top of the windings. Otherwise...The field coil for this model is 1140 ohms and could easily be replaced with a 1200 ohm 2 watt resistor if you want to use a Permanent Magnet type speaker.
The output transformer is probably available at "oldradioparts.com" or AES