Hello everyone! Does anybody out there still use solid axles?

Alright, I have a solid rear axle that served me well on an old 26" mountain bike wheel. Now I was wondering if my solid rear axle would be transferable to a vintage road bike I have my eye on at the local bike shop. The only problem with this road bike is the broken axle, but it appears to have an over sized rear axle hub (similar to the picture, though not identical).

Any thoughts?