The breadth of the frontier zone is indicative of the activity of growth on the one side and the corresponding decline on the other, because extensive encroachment in the same degree disintegrates the territory of the neighbor at whose cost such encroachment is made. A straight, narrow race boundary, especially if it is nearly coincident with a political boundary, points to an equilibrium of forces which means, for the time being at least, a cessation of growth. Such boundaries are found in old, thickly populated countries, while the wide, ragged border zone belongs to new, and especially to colonial peoples. In the oldest and most densely populated seats of the Germans, where they are found in the Rhine Valley, the boundaries of race and empire are straight and simple; but the younger, eastern border, which for centuries has been steadily advancing at the cost of the unequally matched Slavs, has the ragged outline and sparse population of a true colonial frontier. Between two peoples who have had a long period of growth behind them, the oscillations of the boundary decrease in amplitude, as it were, and finally approach a state of rest. Each people tends to fill out its area evenly; every advance in civilization, every increase of population, increases the stability of their tenure, and hence the equilibrium of the pressure upon the boundary. Therefore, in such countries, racial, linguistic and cultural boundaries tend to become simpler and straighter. [Sidenote: The broad frontier zone of active expansion.] The growth is more apparent, or, in other words, the border zone is widest and most irregular, where a superior people intrudes upon the territory of an interior race. Such was the broad zone of thinly scattered farms and villages amid a prevailing wilderness and hostile Indian tribes which, in 1810 and 1820, surrounded our Trans-Allegheny area of continuous settlement in a one to two hundred mile wide girdle. Such has been the wide, mobile frontier of the Russian advance in Siberia and until recently in Manchuria, which aimed to include within a dotted line of widely separated railway-guard stations, Cossack barracks, and penal colonies, the vast territory which later generations were fully to occupy. Similar, too, is the frontier of the Dutch and English settlements in South Africa, which has been pushed forward into the Kaffir country--a broad belt of scattered cattle ranches and isolated mining hives, dropped down amid Kaffir hunting and grazing lands. Broader still was that shadowy belt of American occupation which for four decades immediately succeeding the purchase of Louisiana stretched in the form of isolated fur-stations, lonely trappers' camps, and shifting traders' _rendezvous_ from the Mississippi to the western slope of the Rockies and the northern watershed of the Missouri, where it met the corresponding nebulous outskirts of the far-away Canadian state on the St. Lawrence River.