With the purchase of Louisiana (30th April 1803) the United States gained a clear title to the land between the Mississippi and the Rocky Mountains as far north as 49° and, because of contiguity, a shadowy claim to the region west of the mountains.
2 It is then in connexion with the history of inheritance and adoption, and of the gradual evolution from societies held together only by blood-kinship to societies consolidated on other bases, especially on that of local contiguity, that ancestor-worship chiefly calls for investigation.
But he also recognizes association by similarity, or assimilation, or " apperception " in Herbart's more confined sense of the word, and association by contiguity, or complication.
If n +4 be positive, the attraction of infinitely distant parts contributes to the result; while if n+4 be negative, the parts in immediate contiguity act with infinite power.
The elementary spatial relation Herbart conceives to be "the contiguity (Aneinander) of two points," so that every "pure and independent line" is discrete.