Another solution is to rewind the transformer. So long as you get the winding counts within 5% or so you should be fine. Also, be sure you wind in the same direction as the original!
If in the end, it doesn't work, try swapping connections 3 and 4, or 5 and 6.
I would not recommend using a disposable camera capacitor, they are cheap, only charge to about 120 or so volts and they wouldnnt even work as a transformer. What I recommend you do is look around the internet (eBay, radioshack, etc) and see if you can find a transformer that has the same input to output ratio as what you need. Also, of you can get a part number off the transformer, that will make it a lot easier to find a replacement for it.
You can use the transformer out of disposable camera to get about 400-450V that you need. A good guide is in my source.
I can't help you with your first question and I don't know how it's called but the relation between voltage and the windigs is: Voltage-In / Voltage-Out = Windings-In / Windings-out sorry I can't help you any further, I just don't have experience with GM's.
First, please be very careful with this. The capacitor can hold a charge long after the battery is removed. It's enough to kill you.
If you are not completely familiar with how to discharge -- and keep discharged -- the capacitor, or if you cannot find a friend with this knowledge, you're better off walking away from this. Next, are you sure the transformer is bad and not Q3? Unless you are certain, that transistor is also a prime suspect.
The circuit is a astable multivibrator which drives a step-up transformer, followed by a rectifier and filter. In whole, it's called a DC-to-DC converter. The transistor circuit converts the battery's DC to AC which the transformer needs.
The transformer step up the 3 volts to over 400 volts. The rectifier re-converts the AC to DC, and the filter smooths out the ripples in the DC. End to end, the DC converter converts "smooth" low voltage to "smooth" high voltage because the Geiger tube won't work on just 3 volts.
You could, in fact, put 150 or so 3-volt batteries in series to make a 450-volt DC battery and this would work. DON'T do that, however. You'll have the voltage right, but available current will kill you on contact.So, if it's really the transformer that's bad, carefully examine it and note any numbers.
Search them on the Internet and see if you can't find a direct replacement. It's a neat circuit, and if you simply cannot find the transformer you can built a voltage multiplier circuit with new components and get the job done that way. I have no idea what the counter is worth, so I can't say at what point you should just buy a new one.
Again, whatever you do, please be very careful.
I cant really gove you an answer,but what I can give you is a way to a solution, that is you have to find the anglde that you relate to or peaks your interest. A good paper is one that people get drawn into because it reaches them ln some way.As for me WW11 to me, I think of the holocaust and the effect it had on the survivors, their families and those who stood by and did nothing until it was too late.