Summary

Oklahoma v. Texas (260 U.S. 606…

In case of doubt,' says Vattel, 'every country, lying upon a river, is presumed to have no other limits but the river itself; because nothing is more natural, than to take a river for boundary, when a state is established on its borders; and wherever there is a doubt, that is always to be presumed which is most natural and most probable.
Source: Wikisource

Oklahoma v. Texas (260 U.S. 606…

It neither takes in overflowed land beyond the bank, nor includes swamps or low grounds liable to be overflowed, but reclaimable for meadows or agriculture, or which, being too low for reclamation, though not always covered with water, may be used for cattle to range upon, as natural or uninclosed pasture. But it may include spots lower than the bluff or bank, whether there is or is not a growth upon them, not forming a part of that land which, whether low or high, we know to be upland or fast lowland, if such spots are within the bed of the river.
Source: Wikisource

Oklahoma v. Texas (260 U.S. 606…

This survey of the physical situation demonstrates that the banks of the river are neither the ranges of bluffs which mark the exterior limits of the valley, nor the low shifting elevations within the sand bed. And that this is the natural and reasonable view of the situation is illustrated by a long course of public and private action.
The valley land always has been dealt with as upland. The United States serveyed and disposed of that on the north side under its public land and Indian laws, and Texas surveyed and disposed of that on the south side under her land laws.
Source: Wikisource

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