If you mean it wobbles sideways back and forth as it runs, that's natural for a short wheelbase 0-4-0 due to the amount of slack between the wheels and rail.
Even prototype 0-4-0 and 0-6-0 steam engines had some sideways wobble to them.
Do exactly what Bob suggests, get the thing upside down in a cradle of some kind. I have an old Hornby 0-6-0 tank which wobbled like crazy. Turning it upside down and applying power revealed that one of the driver wheels was not straight on the axle. It was very hard to get it back to being close to straight. Also the wheels were way under gauge and had to be widened a bit.
Simon Modelling CB&Q and Wabash See my slowly evolving layout on my picturetrail site http://www.picturetrail.com/simontrains and our videos at http://www.youtube.com/user/MrCrispybake?feature=mhum
It would be helpful to know the manufacturer. If it is really old it could be a Varney. The secret to identifying Varney is to look at the builder's plate cast on each side of the smoke box. Varney put a V in that. All other knock off's left it blank or smooth.
My guess is if it really that old, and gallops as much as you say, it probably has a warped zinc cast spoke assembly in one or more wheels, causing it to go out of round.
Hold the loco up side down and run a pair of wires to the drivers and power it up. You should be able to see it.
see ya
Bob
Traction tires are always not the same thickness and have a hump sometimes?. A drive wheel might be out of round ? Drive wheel not mounted/pressed on axel correctly? Drive wheels out of quarter?? If it is real bad might be more than one problem or wheel.
h o scale
What scale is the locomotive? I know on some early N Scale locomotives, the traction tires caused the wobbling.
Modeling the Pennsylvania Railroad in N Scale.
www.prr-nscale.blogspot.com
I recently purchased a used 0-4-0 docksider,manufacturer unknown. while this little engine runs great, it has a tremendous wobble while running. it reminds of a salmon trying to swim upstream.Does anybody know how to correct this problem?