Well, I never built one...But the theory is...
The transistor's operating point must be set into it's saturation region. You can know the saturation region from the datasheet of the transistor.
A BC547 transistor needs to have about 400+ microampere to drive it into the saturation region. When saturated, there is a maximum limit on the current that can flow through it, for a fixed given voltage. (Voltage across the collector and emitter) However if you do apply a greater load resistance, it shall decrese the current flowing through it and you will need to increase the voltage.
I read of a circuit in my study of the oscilloscopes. It had a saturated transistor that supplied a capacitor a constant current to generate the desired timebase.
I know that this explanation is full of holes but I know nothing better at the timebeing. If you find a good explanation or a circuit, do make it a point to let me know. (You may PM me.)
Thanks.