"Wider still, and wider, shall thy bounds be set;" if this refers to the British Empire I believe it means that it is commenting on the expanding boundaries of this Empire as new lands are conquered and turned into colonies. At one time, Britain had far flung colonies in Africa, Asia and also the 13 colonies and Canada before the independence movements of the late 18th century in America and also 20th century in Africa. In other words, at one time the world was colonized by primarily the Spanish, the Portuguese and the British and the colonies had to supply the raw materials to the colonizers and were an appendage of the big powers.
