Thanks again to all of you.  I have a lot more confidence after getting your advice.  I ordered a new switch.  I should have it within a week or so.  I'm pretty sure that once that switch is installed the lathe will be operational.  I'll let you know how it works out.

Matchless, thanks for the offer of the switch.  If the one I ordered falls through, I will get in touch with you.  These DPST toggle switches are really a poor selection for starting a motor.  It really needs something more on the order of a spring loaded contact that slams the contacts closed.  But this DPST switch has been working good for about 20 years.

The lathe was delivered with a rotary switch that incorporated a spring loaded contact system.  It self destructed in short order.  That thing had killer springs.  I replaced it with a system that uses two DPDT switches to select direction of rotation, and the one DPST switch to energize the system.

Again, thanks.  I appreciate the help.  Electrons are not my forte.  

Thanks for the link on the capacitors.  I'll measure the dimensions on mine and see if these Grainger units will fit.  The ones on there now don't have the resistor, is that a problem?

Aren't the caps out of the loop almost as soon as the rotor starts turning?  The centrifugal switch seems to cycle almost instantaneously.