In point of fact, dhenry spotted one of the significant problems right off. You cannot
put a 4.2V/1000 = 4.2 mA load on a 1.2A "constant-current" supply and expect to read
correct values. It will drive operation to some boundary condition [unusual operation].
Secondly, I hope you have a truly MASSIVE heatsink on the 317s, as in normal operation
they would be dissipating (16V - (4.2V + 1.2V)) * 1.2A = 13W. This'll cook your 317s
good.
Thirdly, since 317s have the "other" pinout numbering from 7805s, it's easy to wire
them in backwards if not paying attention. These may have all been cooked already
sometime in the past ["I'm not good when it comes to checking the orientation" <- be
more careful, sheesh].
Fourthly, 317s are not biased via driving current into the adjust pin, they are biased
by having 1.2V between Vout and Adjust, and won't regulate unless you have that.
Fifthly, R3 is in the ckt to avoid dumping the entire 1.2A "constant" output current
down the throat of IC2. It limits this current to roughly 4 mA max.
Sixthly, in response to doc's comment, the "constant voltage" aspect comes from the
output voltage feeding back through R5,R4 to shutdown the regulator whenever
Vout goes above ((6.8K + 10K) / 10K) * 2.5V = 4.2V, via IC2 pulling the Adjust pin
to ground, and therefore the Vout pin will be pulled to 1.2V.
Seventhly, this a very common feedback regulator ckt, but I sure wouldn't use it to
charge Li batteries, I'd get a real Li charger for that - one that takes into account
battery chemistry and proper charging cycles.