I bet the long one is lower to higher (3V to 12V) and the short is Polarity.
Can you measure with a multimeter? If you get a +x.xx reading with Black test lead on outer and red on inner, you are on Centre Positive. Your equipment should match.
Voltage may be higher than expected on 'no-load'. It drops to correct value when you connect.
Google for a .pdf User Guide. The label will give you a model number.
Or post an photo via Imageshack or similar.