third way to determine how many equivalent protons there are is to look at the atom attached to. the proton (usually a carbon) and observe what that atom is bonded to, and then the atom bonded. to that, all the way until a difference is observed.
The goal of imperialism is  to exercise economic and political control over a dependent territory. Such control is often accomplished through settlement, sovereignty or less direct methods.
Imperialism was a good force in terms of technology because the nationalist fervor led to an arms race in Europe. European power expanded and the nations who raced for power spawned inventions that were meant to trump the inventions of other nations.