Jim, a floating ground is exactly what George was after.
Bruce,
The bigger problem is the floating 120Vac output of the transformer. Both leads of the secondary are hot without a true ground reference. For safety the output of the transformer,(if single ended), then one leg must be earth connected. (Balanced the center tap must be grounded). And because the transformer is a separately derived power system fed from the premises main grounded power system one leg of the secondary of the transformer must be connected to the main grounding system of the premises. If the unit plugs into a receptacle, the equipment ground of the receptacle branch circuit is used.
Also at the transformer unit where the output power receptacle/s are located, somewhere in the mix of things, the equipment ground contact of the receptacle/s must also be connected to the grounded leg of the output of the transformer and the equipment ground of the power cord that feeds the transformer. Star grounding.....
Just a quick example what could happen with a 120V floating power system. Say for what ever reason one of the lines feeding a piece of equipment, connected to the floating power source, was to short to the metal case. Nothing would happen right? No fuse would blow. The user of the equipment wouldn't know... No big problem right?
But what if for some reason another piece of equipment also experienced the same problem where the hot wire shorted to the case.... But this time it was the opposite hot wire from the floating 120V power source. Still no fuse will blow... The user will not know a problem may exist.... Only way the user will know if there is a problem if he touches both pieces of equipment at the same time... A 120Vac difference of potential from one to the other....