I just felt the need to throw an equation in the description for fun! Math is so much cooler when you're not in school anymore. I once calculated the vector force acted upon a driver after she was in a car accident. It made her boyfriend, who was with me at work, feel much better.
I couldn't do that now though. It's been far too many years since I've used those formulae. (That's "formulas" for the degenerate yanks who are kneecapping their language *grins* It's colours, not colors! I truly expect them to drop the "k" in "knife" next.)
This is why your empire fell apart.