Originally Posted by Ford_6L_E350
I don't see the problem there. The diagram shows ground at the bottom, and the middle connection is floating. Both chargers are charging individual 12V batteries in a 24V system. Similar to using two 6V batteries in a 12V system.
In the top diagram (stacked chargers) the middle connection is **only** floating if the chargers don't share an internal ground connection between input and output sides. You can find out with a multimeter, by checking resistance between input and output grounds of the chargers. If not connected, that hookup works. If they **do** connect input and output grounds, then they are sharing a ground via the AC neutral, and the "top" charger will definitely see the combined voltages at the rectifier output.
That schematic assumes there is no internal ground connection in the chargers -- but there may well be. In which case, it doesn't represent reality. Add a wire between the two output grounds to the diagram, and you can see see what really happens in that case.
You'd have the same problem with two 6-volt batteries in series, if you tried to charge them with a pair of 6 volt chargers stacked like that. But most people use a single twelve volt charger attached to each end of the string, which is the right way to do it.
The other issue with stacked chargers is you have to make sure the AC sides are in phase, either by checking for correct hot and neutral connections in the outlets if the charges have 3 prong plugs, or by making sure they are plugged in the same way, in the case of two-prong plugs. Otherwise you will have circulating currents back and forth between the batteries as the chargers work against each other.