LM317 constant current source

This LM317 constant current source circuit is using transistors and can be used as a driver for LED strings. The following LM317 constant current source circuit is splitting up the current sense resistor into three resistors, one for each leg of the LED string.
Current through any one of the LED strings of LM317 constant current source circuit is set using this equation: Iout= (1.25V+ Vsat)/Rsense .
Vsat is saturation voltage for transistor used in circuit .
When the circuit works properly all the LEDs are running, all three sense resistors have about 1.25 V across
them, which turns the transistor switches ‘on’.
When this happens all three sense resistors are connected back to the Vadj pin allowing the proper current to go through each leg. If one string opens up, the sense resistor for that leg won’t have any voltage across
it, turning ‘off’ the transistor and disconnecting its sense resistor from the Vadj pin. Therefore, the other two LED strings are unaffected by the fault.