Advice on threads

[DelombardR]

I am working on a ca 1896 Lenox safety and have trouble with the rear axle.
I thought the threads were 3/8" x 24 but the nut doesn't thread onto a new bolt of that size.
The axle threads are 'rough' so it's hard to get an accurate count and my thread gauge doesn't have every pitch. I have 20, 24, 27, and 28. 
The threading is close to 24 and a new 3/8" x 24 bolt goes about a thread or two into the nut.
Was a 22 pitch or 25 pitch usual back in the 90's?

[Bjd.]

Don't rethreaded either the nut or axle. The cones have to come off for service and they won't if you screw up the axle threads! Find the correct tap and die! There were hundreds of thread combinations, threads pitch etc. talk to Craig Allen. I also have boxes of antique bike taps and dies.

[mike cates]

Use a thread pitch gage and use back lighting to see accurately to establish the threads per inch. A thread micrometer will also show, as Bill has mentioned, "if" the pitch diameter (thread major diameter) is oversize or undersize when referencing dimensions measured to a machinist's handbook on thread size limits.
Mike Cates, CA.

[DelombardR]

The nut threads onto the axle.
The axle threads are 'buggered' up a bit.
After further examination, I'm going to (try to) disassemble the hub and get a new axle made.  The more interior threads will be more easily measured than these outer ones.
It's a tough life being a axle.
On the other hand, the wheel is in good shape with a solid wood rim and a tire (19-teens) that holds air so it may stay 'original' for show when I am not riding it. I'll make up a rideable set of wheels for it that look old but solid for riding.
Front rim needs a 'little' attention (see last photo).