motor reversing wiring diagram

I just purchased a 1940s(?) South Bend heavy 10. The previous owner's son cut the wires (grrrr....) from the motor to the reversing drum switch to remove the lathe from the bench. Unfortunately, the wires were all red and unmarked (as seen in drum switch photo). I have attached a photo of the...

I give up. I watched a couple videos and determined with my limited electric motor knowledge that this motor should be able to be reversed. Reason: there are four leads coming from the starting coil and running coil. It is a 115V 1/2hp Hercules motor. OK, here is the photo: So, am I right in...