Grumpy_Mike:
The resistor is acting as a feed back mechanism for the transistor and thus supplying a constant current in the light of any changes in the load. The value of this constant current is controlled by the size of this resistor. You want more current, you make that resistor smaller so more current has to flow through it in order to develop sufficient voltage to throttle off the transistor.
So...if I know what the 'drive' voltage is (eg. 5V for an Arduino output pin) I don't need the diodes between the transistor base and ground. I can replace them with whatever resistor gives me 1.4V at the transistor base?
That would give me a constant current with three resistors and a transistor.