The first practical self contained cartridge was invented around 1845 in France. It was a rimfire CB cap , very low powered. By the civil war 25 years or so later the cartridges had progressed to a slightly larger caliber and other style ignition systems were being developed.Also by the Civil war there were numerous manual repeaters such as the Spencer and even the Henry and 1866 winchester, and the gatling gun was being developed. By the turn of the century there were working machine guns designed. So at the birth of our nation in 1776 it was about 70-80 years before cartridge development came to where practical repeaters were feasible, and within about 120 years machine guns as we know them were being developed.