Effect of failing/failed condensor?

[Graham O]

John is right, a failed capacitor generally has a spurious discharge path (which might only show under operation, not with a multimeter's test voltage). That discharge path will stop a good capacitor from helping.

The capacitor does two things:
it eliminates sparking at the breaker points 
it creates a form of resonance with the coil primary winding inductance to increase the spark level.

This resonance starts when the breaker points open and the coil primary winding's magnetic field collapses due to a lack of current.  The collapsing magnetic field creates a high primary voltage that discharges through the capacitor.  When the capacitor charges up to this new voltage (higher than the initial 6v from the battery), it then discharges back through the coil's primary winding to create a reverse voltage in the primary and hence the secondary.  So the capacitor and coil primary inductance work together to increase the initial 6V to a higher level to increase the spark.

You can check this by playing with a good system and removing the capacitor.  There will be a spark, but it is much better with the capacitor.