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It is an invalid condition for a 555 trigger to stay low for longer than the 555's output pulse duration. I needed a way to ensure that no matter how long a button is pushed, the trigger will always have a valid length.
With a DPST switch, this would easy: one end is connected to high, one to low, and the capacitor takes care of the rest. I included this circuit in the TOP for comparison. But I wanted to do this with a push button.
I achieved a similar effect with a push button in the BOTTOM circuit by using a voltage divider. Initially, the voltage at the capacitor is high. However, the push button opens a parallel circuit in the lower part of the divider, drastically lowering its resistance, lowering the voltage at the capacitor. The voltage drop isn't really "low", but it's low enough to trigger another 555.
Thus, a chain of 555s can be triggered (the next 555 by connecting it's trigger to the capacitor), with always-same output pulses regardless of input pulse length.
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