Spark,
I assume you mean on the 240v secondary side of the 1 phase xfmr. What is it powering? I assume from your comment that you have measured this b4 and never saw any voltage? So something changed? Did you add some device/load to the xfmr that was not there last time you measured?
Lots of assumption per above, but based on them, it sounds like the 240v side of the xfmr was never referenced to ground - which is not a bad thing by itself. Lots of stuff is not referenced to ground. But perhaps you want it referenced to ground? Why? I am not suggesting do so is bad, just curious why the change now?
with power off, did you OHM from 240 side to earth? Any resistance?
If it is electronic equipment powered by this 240, electronics often have capacitors from power input legs to earth or ground; so that may be where you are seeing the 60v from - if there is no resistance to ground.
If you have some resistance to ground and you did not have that before, and you did not add something new, perhaps something is breaking down some (motor coil?)
just my various rambling thoughts on the subject....