Hi James
Yes, descend on somewhere like the engineering or physics schools!
I had better explain how the circuit works: it is actually rather sophisticated and NOT obvious. Note that I am not sure what the nominal output of the solar cells is: I only THINK it is 6 V. It might be 8 V.
The solar panel generates a voltage which can go way over the 6 V on the two Tenergy cells. But while charging those cells through the Schottky diode the solar cell voltage is restricted to whatever the Tenergy cells 'want'. Note that the Schottky must be able to take 1 – 2 A. That bit is easy.
Now while this is happening the voltage from the solar cells is restricted to about 7 to 8 volts, and the rest of the circuit does nothing. In fact, you could use just the solar cell and the Schottky diode and skip the rest. Doing so would leave you not knowing what the state of charge was however.
Now for the really obscure bit. When the Tenergy cells are fully charged the safety circuit hidden inside each cell will turn off. No more charging current will enter the cells. This behaviour is unique to rechargable lithium cells.
Without the current load, the voltage on the solar cells will rise quite a bit. There will be enough voltage in fact to turn the 7808 voltage regulator on, and this will put 8 volts across the resistor. But the solar cell voltage will go even higher, up to about 11 volts (which is why the solar cell may actually be rated higher than 6 volts).
Now, with 11+ V on one side of the white LED and 8 volts on the other side, we have enough voltage to turn the white LED on. So when you see the white LED turned ON, you know the Tenergy cells are fully charged. Of course, if the sun goes away, so does everything else!
I used this charger during our 3 month walk in France in 2007. Tt was quite robust. The solar cell is mounted on some blank FRP circuit board. At the edge there is a battery holder to take two Tenergy cells. You can't buy anything suitable, so I made this by hacking an AA cell holder and stretching it. I bolted the battery holder down onto the FRP board with some 210 denier nylon sandwiched. The nylon has hook & loop fastening on it which closes oveer the top of the batteries, to make sure they don't fall out. The rest you can see. Ah – the LED and the 7808 are tucked in beside the battery holder.
Cheers