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[The Devil]

Azztech has just about explained it all other than the switching unit I use. I'm using a black box t/stat as the switch, the inverter is on standby while the incubator is running.
This t/stat is dual wired to the lights and set .5C below the main t/stat, I figure that most eggs will cope with a .5C drop in temp.
An electrician I'm not, but I was under the impression that a standard mains outlet was rated at about 10amps, therefor I'm not sure about 2X50W heat cords drawing 8 amps. Should that be correct I could be in trouble running 5X100W lights from the same point.

With the batteries you need to use deep cycle, I use 2X6V 220 amp hour, wire together this gives 12V 220a.h. Using deep cycle batteries gives you much longer running time as they will hold 12V down to about 40% capacity . The inverter needs about 12V input to work and deep cycle will outlast a normal battery by a country mile.

Another thing I did was to sit beside the incubators with a stop watch and time the on/off cycle of the lights. Knowing that, enables you to work how long the batteries will last.
Further, when using deep cycle batteries you need a good battery charger to to top them up weekly. Given that I'm told these batteries have high resistance plates the smallest charger would need to be about 15AH