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.
A later usage developed in the early 20th century among Marxists, who saw imperialism as the economic and political dominance of monopolistic finance capital in the most advanced countries and its acquisition â and enforcement through the state â of control of the means (and hence the returns) of production in less developed regions.