http://www.allaboutcircuits.com/vol_6/chpt_8/7.html

The first multivibrator controls the second. Both are designed for minimum current, as well as the inverter made using Q1. Both the oscillators are very similar, the first has been covered in previous experiments. The problem is it stays on, or is high, 97% of the time. On the previous circuits we used the low state to light the LED, in this case the high is what turns the second multivibrator on. Using a simple transistor inverter designed for extra low current solves this problem.

Maybe I'm not seeing it right, but when the first timer output goes high that should switch off Q1, pulling Pin 4 of the second timer to ground, and shutting off the second oscillator.

So it's the high of the Inverter Q1 turning on the second timer, rather than the high of the first timer, which shuts off the second timer.

I think this needs to be explained more clearly.

 

I am the author of that little piece. Q1 is a simple logic inverter. I think I explained that pretty clearly, the 97% on time for the first astable multvibrator had to be inverted. Definition of logic inverter, logic 1 in = logic 0 out.