Lathe Motor Wiring Help

I'm cleaning up an old Atlas/Craftsman Lathe and had a quick question about the Craftsman motor. Generally for these old flat start capacitors, does it mater which terminals the two wires are connected to? In other words, if you swap the two wires, would it still function?

This is the motor I'm working on: http://www.vintagemachinery.org/pubs/222/3331.pdf

upload_2022-6-13_9-40-52.png

upload_2022-6-13_9-41-3.png

I also found this hand-drawn wiring diagram online. Not sure if it's correct though.

cm_100_c13.jpg