Input = Two Eveready "C" Nimh cells, v=2.52 volts, i=116 mA. They
              discharge at fairly stable voltage.

              Output = Two Nichia white leds in parallel,
              LED1: 3.46 volts, 24.8 mA,
              LED2: 3.41 volts, 27.1 mA

              I'm using an FP ferrite bead. Hole=.184", length=1/8", OD=3/8".
              I don't know
              what kind of ferrite it is. I got it from Hosfelt Electronics for 15 cents.

              I have more test results for the two transistor circuit.

              I swapped the NTE11 for an ECG128P. It started well but the output led
              current dropped about in half. Then I switched to rechargable alkalines
              instead of Nimh. I got a little more output current but it started harder.

              I switched back to NTE11 / NTE12 and made a new coil with
              about  40 turns
              instead of 20. I got about 15 more mA through the leds so
              I increased R2 to
              5k to get 27 mA in each led.

              Next I varied C2. With 47 micro F it almost doesn't run. I can
              jump start it
              but then it fades and goes out.

              With C2=4.7 micro F it runs fine after a jump start by pulsing R2 to 3k.

              Without C2 it starts perfectly.

              Results:

              NTE11/12
              R2=5k
              C2=4.7 micro F
              LED current = 27 mA each (3.5 v)
              Battery input = 3 volts, 122 mA with C2=4.7, 116 mA with no C2.
              Light quality = high

              There's some kind of pattern emerging here. The 47 micro F
              capacitor works
              fine with the one transistor circuit, then for the two transistor
              circuit, as the
              number of coil turns increases, there's a preference for a lower
              value C2.

              A larger coil might mean lower frequency so maybe lower
              frequencies like
              smaller C2 values. There's a little more light, but not much more,
              with the 4.7
              micro F C2 compared to no C2.

              I guess I gotta go find a smaller C2 capacitor. What is another
              size C1 to try?
              Is there a size relationship between C1 and C2?

              There isnt really any size relationship
              between C1 and C2, except when ripple
              is a concern.

              For the purpose of understanding C1 a little better, Q2 has two
              distinct states:
              1. Q2 turned on
              2. Q2 turned off

              When Q2 is on, C1 charges very quickly though the base emitter of Q1
              and through Q2 collector emitter.
              When Q2 is off, C1 discharges through the 10k resistor.

              At very low input voltages like 1.2 volts, R1=5k does appear to
              work better then 10k.
              A value of 500pf appears to work with inductor values from
              200uH to 3200uH, but i would try 1000pf with larger inductances
              also. Stick to 500pf or so for lower inductances.
              Apparently, the lower the value of C1 the lower the ripple output.

             I think I've got it.

             It seems to be starting very well under all conditions. I think there is a
             relationship between C1 and C2.

             Here's two things:

             1. Sometimes my brain doesn't work very well. One of my capacitors,
             the 4.7 micro F, is a polarized electrolytic. I tried hard, but for some of
             my testing, I had it in backwards. Sorry.

             2. It's starting right up now with C2 = 47 micro F. I put a second 680
             pico F capacitor in parallel with the first C1. That gives it a little more
             something that I've got to think about, but it's working. It starts right
             up. Zoom.

             Q1=nte12
             Q2=nte11
             R1=10k
             R2=5k
             R3=10 ohms
             #leds = 2
             2 x 1.5 volt batteries
             C1= two 680 pico F in parallel
             C2= 47 micro F
             D1=nte585

             Here's numbers for the two transistor circuit using a 47 micro F filter
             capacitor on both the battery side and the LED side:

             Two Alkaline batteries in series:

             Vbattery = 3.06v
             Ibattery = 114.7 mA
             LED1: i=32.8 mA, v=3.58 volts
             LED2: i=35.6 mA, v=3.54 volts

             Two Nimh batteries in series:

             Vbattery = 2.46v
             Ibattery = 72.5 mA
             LED1: i=18.5 mA, v=3.37 volts
             LED2: i=16.6 mA, v=3.35 volts

             Ibattery with and without the inlet filter capacitor was almost identical.