175 watt halide wiring

[scuglass]

ok so i understand all that u are saying but i dont know if it was wired properly when i bought it. hereis a drawing hopefully u can understand it.

from how it is wired right now there are 2 commons from each ballast. 2 of thes(one from each runs up to the lights(which is correct.) and one leads to the plug(correct). then from the 120v one goes up to the lights (INCORECT??) and one to the plug(correct.)

so there are 2 wires one from each cap going up to the lights (one to each socket) and then 1 common (correct) a ground(correct) and a hot(incorrect????)

heres a pic(sorry its confusing)