AC Motor Capacitor Confusion on a 1956 Sewing Machine

[APAudVid]

YouTube - Machine Motor

Hey Guys! working on a sewing machine (motor) and am running into a bit of confusion as to the use of the motor cap.... The main resistor is cracked and useless now, though I can't say that I mind digging into this whole thing as the speed controller never really worked that well. I'll be wanting to add (already have it) a "Two wire" rheostat / foot pedal...
The new foot pedal rheostat is designed for this and has an "open / NC" point on the start of the travel. Then it hits the point of full resistance until, (fully depressed) no resistance.
The issue I'm having is understanding the Capacitor in this AC Motor set-up... I did draw up a diagram and what it says on the capacitor (It's a Swiss machine so it says "Capacity"). For the sake of simplicity, I put the whole shooting match (pictures and schematics too) in a You Tube video to really give an idea of what's going on here...
If somehow I can streamline the cap situation and either get rid of it all together (probably not) I would at least like to put some new caps in for the sake of longevity) (I'm guessing they would have to be non-polarized?)
YouTube - Machine Motor

Anyway, thanks in advance! As always, I'm appreciative of the help I get here.

AP



PS, the video works best set up (on the You Tube viewer) displayed at 480p instead of 360p and full screen looks good too. You can pause to take a look at the schematics I drew.

 

[crutschow]

The motor is likely a capacitor run type induction motor, where the capacitor provides a phase-shift in one of the fields to generate a rotating magnetic field. Some method of doing this is required for all single-phase motors which can also be done by a shaded-pole (shorting coil around one pole.) Thus the cap is required and is a non-polarized (AC) type. See single-phase motors for more info.

 

[APAudVid]

Thanks... But....

In regards to my situation and the schematics and the info on the cap, what should I do?
If you haven't, have a look at the vid I posted (or jump to the end where I posted my drawings). I did the google thing before, but wanted some direct input. (IE what to make of the marks on the existing cap {schema and size}, what size would be the best replacement, etc... and what is the solder point on the motor?)
Or if someone could post a new drawing for me, that would be most insightful / helpful!
Thanks again
AP