Ian,
Something is very odd about that first trace. With the globe in the circuit, are you only getting 1V AC p-p out of the transformer secondary?
That seems amazingly low.
Is that still the voltage on the 15V secondary?
I should have explained more thoroughly perhaps. I put the transformer's secondary in series with the 4 W bulb, and I put a 100 ohm resistor across the primary. I traced the voltage across that resistor. I didn't check the voltage though, so let me try now.
The 4 W bulb at 120 V should pass about 33 mA through the secondary. That should produce a current in the primary of 14/120 * 33 = 3.9 mA. Passing this through the 100 ohm resistor should produce an RMS voltage of 390 mV, and therefore a peak voltage of about 550 mV. At 20 mV (200 mV?) per division, that is about what the scope shows. Phew! The world works as it should
(Note that I previously measured the open circuit voltage of the secondary at 14 V, which is where the 14/120 factor comes from. I am trusting my mains voltage to be 120 V, which it usually is--a spot check just now gives 121 V)
Edit: I just noticed that 20 mV/200 mV mix up. I thought the scope was on the 10X scale, but maybe not. I'll have to check.
Edit2: Oh, it looks like the scope had reverted to 1X on the scale factor instead of 10X. I feel sure I had previously set it to 10X. Perhaps it got reset later.