We start the discussion with just the LM317 3-terminal regulator.
It is designed to produce a voltage of 1.25v above the voltage on the adjust pin (pin 1) and it monitors this voltage accurately.
This means the output voltage will be 1.25v when the adj pin is connected to 0v.
If we add a 180R resistor and 1k pot, we can "jack-up" the output voltage until the output is about 2v less than the input. (This 2v is needed by the circuit inside the IC.) If this voltage is delivered to a load, the chip will deliver up to about 1.5amp.
Now we add the 10 ohm resistor.
This resistor is called the CURRENT LIMITING resistor and normally it is added as shown but the 180R and 1k pot is removed and the adj pin is connected between the 10R and diode.
For a 10R resistor, the maximum current is 125mA
When this is done, the output voltage will rise to any voltage (that is about 2v less than the input voltage) and as the voltage rises, the current through the load will increase and also through the 10R resistor, (because they are in series).
As the current through the 10R increases, the voltage across it increases and when it reaches 1.25v, the circuit inside the IC detects this and the output voltage stops increasing.
When we add the 180R and 1k pot, we have an unusual situation.
We can increase (jack-up) the voltage on the output to about 8v but when we add a load, the 180R alters the current limiting to 35mA.
If the circuit requires 35mA charging current, a 33R resistor can be used and the 180R and 1k pot can be removed.
You cannot add both features at the same time. If you try to set the output voltage, it will decrease rapidly as current is drawn.
Another untried, untested circuit from Electronics For You.