usually consist of two opposite wound coils with their ends joined to form a centre tapping. A 10,000 volt NST consisting of two 5,000 volt coils, a 15,000 volt one would be two 7,500 volt coils etc. This way the voltage across each coil is reduced, this in turn bringing down construction cost by way of lower insulation requirements.
you can see in the main top picture I went overboard somewhat on the construction of this. Three spaced nails in a piece of wood would work just as well. I had recently purchased a knurling tool and a spherical turning attachment for my lathe, so this seemed like a good excuse to try them out.
you have a Variac that is capable of giving out a slightly higher voltage than the input (most will) then a good way to adjust the safety gap is as follows. Set the Variac so its output voltage to the NST is the normal mains voltage that the NST is designed for. At this setting the safety gap should not be firing. Then increase the Variac's output voltage to the NST a little and the gap should now fire regularly. In the UK (235 volts ~ ) the NST steps up the voltage by a factor of 42 approx' for a 10Kv NST. So a 12 volt increase to the NST's primary winding will give nearly 500 volts of over-voltage on the secondary, so don't go too mad with the voltage control!
safety gap shown at the top of the page is best suited to centre tapped transformers like NSTs. For my PDT
or PIG I used a ordinary horn gap. This tends to act like a Jacob's ladder when it fires and thus extinguishes better.