Gerry: I'll take a stab at it.
I'm not sure his explanation was exactly correct, but then I'm not sure either what was exactly wrong with it.
Thinking about it . . . I suppose that . . . the primary function of the coil is to multiply the voltage from the primary winding to the secondary winding. The primary current finds its path to ground through the points, as long as they are closed, when the points open, I think the following things happen:
1. Since the primary winding is an inductor, the polarity of the voltage INSTANTLY reverses.
2. The DC current starts charging the "condenser" (actually the component is called a capacitor, but it can be conceptualized as "condensing" the electricity, see below), which takes a period of time (there's a formula to calculate the time, but I don't have my textbook out).
3. In this rather neat little system, the points are opening ever wider, but the voltage across the capacitor is also growing until such point as it gains the "potential" (another word for voltage) to leap across the gap of the open points, which, if you're watching, appears to the naked eye as a tiny spark, no more than 12 volts, and likely a bit less.
4. On the next point I'm not clear, but when the spark jumps the open points gap, the field around the primary coil either collapses or reverses direction again, but in either case a much larger spark is "induced" in the secondary winding which can only find its path to ground across the electrode at the spark plug.
I think it is an awesome example of an electro-mechanical system which demonstrates the properties of both inductors and capacitors. Technically, it is an "LC Network" and I think it is a shame they never taught us the finer workings of it in Community College, but they did equip us to understand enough about it to know that without the condenser you will never get a spark at the plug, and if the points don't open, you'll never charge the condenser, and if the point gap is too large, there is not enough time available to "reset the system" by letting it "dwell" long enough for the capacitor to lose its charge through the closed points.
Note there has to be voltage at the capacitor in order to charge it, and there is no voltage at the capacitor when the points are closed. Capacitors block current, but pass voltage; conversely, inductors pass DC current, but store DC voltage (although they reverse its polarity).
At least that is my theory about how it works, but if you know better, I would be happy to hear it explained, as I like to learn things as much as the next guy.
Fine day here in Eastern North Carolina, and I'm stepping out to enjoy it and study up on setting the governor on a Kohler M18.
Edit 1: Never mind, I see you explained it.
Edit 2: Final thought, if you need your tractor to do some work ANY condensor is better than NO condenser, that's all I'm saying.