Bridge Pinger with one side grounded?

["Tesla list" <tesla-at-pupman-dot-com>]

Original poster: "Jolyon Vater Cox by way of Terry Fritz <twftesla-at-qwest-dot-net>" <jolyon-at-vatercox.freeserve.co.uk>

Is it possible to build a ping tester with a bridge output where one side 
of the bridge is grounded?
I am thinking of adding another 555 to my 555 astable pinger to act as a 
phase inverter to get a squarewave (between Pins 3 of the two ICs) of twice 
the voltage of the 555 astable alone.
I understand that grounding one side of a bridge makes the DC rails "live" 
at 1/2 the bridge AC output voltage -is this correct?
If I use "floating" batteries to power the pinger will this be OK?

Jolyon