The Circuits Today description of the LM317 circuit is horribly mixed up.

That circuit has been around for years, and they just reprinted it with a wrong description and lack of attribution.

That circuit has a major design flaw. Think about what happens if the input supply voltage drops below the battery voltage plus the drop-out voltage of the LM317!

The battery discharges backwards through the voltage divider resistors... Very poor design...

Here is a better circuit.

 

yes sir but after limiting current by changing 0.51 ohm resistor to 2 ohm then this will limit the current.
and how could we limit the current at supply.By introducing resistor???

 

I do not understand your last question. Limiting the current to the load serves to limit the current drawn at the supply.

The LM317 should be protected by a reverse biased diode from output to input. This will save it if/when the supply is removed while the battery (or output capacitor) is still connected. Applying power to the output without an input can damage the LM317.