Our well-founded claim, grounded on continuity, has greatly strengthened, during the same period, by the rapid advance of our population toward the territoryits great increase, especially in the valley of the Mississippias well as the greatly increased facility of passing to the territory by more accessible routes, and the far stronger and rapidly-swelling tide of population that has recently commenced flowing into it.

Summary

The quote highlights how the claim of a particular group has become even more solidified over time. The claim is based on the idea of continuity, and this claim has been fortified by several factors. Firstly, the population has grown significantly, particularly in the Mississippi Valley. Secondly, there are now more convenient and accessible routes for people to reach the territory in question. Finally, there is a noticeable and increasingly large influx of people into this territory. Overall, these developments contribute to the strengthening of the claim, adding weight and credibility to it.