Thanks everyone!
I'm interested in learning how to use a capacitor in series, and I was researching it for the last 10 minutes, but I feel like it's too complex for me for now. I'm still working on the beginners' electronics books.
Is the main idea that the capacitor lowers the voltage across the circuit? If so, how do we know what kind of voltage drop would be able to dim eight 60-watt incandescents to anywhere between 40-60% of their regular output? Is it straightforward, like where 60 volts (instead of 120) would result in a 50% reduction of light output?
Also, how do we calculate what size capacitor to choose?