I'd never seen this application of a coil, but the theory you'll read about for Experiment 28 makes sense.
In the first part of the exercise, I simply wired up the circuit on page 247 and pressed the button. As expected, a single LED lit up on the button press and the other LED lit up on release of the button. It happens quickly. The author recommends against holding down the button because the resistor will get hot fast. You can see this in action in the first video.
The second part of the exercise involves hooking up a capacitor in place of the 220 ohm resistor (don't forget to add in the single 1K resistor). The author states that capacitance works the opposite of self-inductance, so you would think that based on the first exercise, we should see the 2nd LED (on the right in the video) light up first, and then the 1st LED (on the left) after the button is released. The second video shows my results.
What happened? As I understand it, capacitance resists at first and wants to take most of the current to charge up - so the first LED does light up, but not as bright. Releasing the button causes the capacitor to discharge and I can only guess that the resistance in the coil is very low (compared to LED 1) so the current flows through the coil and then through LED 2. Of course, I could be completely wrong as I expected LED 2 to light up first... then LED 1. Goes to show that electronics don't always behave in the ways we expect them to... (or maybe I wired up this modification incorrectly - if anyone knows, please let me know so I can try again.)
A fun experiment... just be sure to wire up that capacitor correctly (for polarity).
Finally, I got my copy of 'Practical Electronics for Inventors' by Paul Scherz. A quick scan of the entire book and a read of the first few pages tells me that although the material is quite dry (compared to Make: Electronics), it should be very useful. I can already tell that this book should be easier to read and understand after having completed Make: Electronics.