theres a few different ways of hooking them up especially with magnetic ballasts like you have , the capacitor is to change the power factor to make the tubes run efficiently otherwise they will draw more power than what they need too. you were right about bulbs being connected in series to a certain degree sometimes tubes use a single ballast to run both ( although im not sure if they are connected in series or parallel )
it would normally state on the ballast most of the combinations its capable of being set up with ie 1x40w, A, pwerfactor
2x20w,A.power factor
yours only states one and while it may be capable of being used in a different configuration its probaby not worth it as you would need to figure out the power factor and get a capacitor to suit and thats some good mathematics in itself i wish i could help ya more but i cant rmember enough about it to feel comfortable helping you out