Historically, population growth had been quite slow. From A.D. 1 to A.D. 1000, the population of Western Europe had increased by only 6%. In the next seven centuries, its population more than doubled. By 1700, statistics suggested that England's population was going to double once every 360 years.
After Britain established its first permanent North American settlement at Jamestown in 1607, disease took so many lives that it wasn't until the 1690s that births outpaced deaths.
Population growth was slow enough that Thomas Jefferson could claim in his First Inaugural Address in 1801 that there was "room enough for descendants to the thousand and thousand generation." At the time, America's Western boundary was the Mississippi River.
In 1803, the Louisiana purchase effectively doubled the size of the country. Jefferson and Washington assumed that whites could settle the land "compactly", by staying east of the boundary, whilst the Native Americans were coaxed to move west through treaties. They wanted to avoid costly wars.
What happened instead was that ...
> a small population of English-speaking whites and their black slaves was going supernova. They inhabited a continent substantially cleared of its indigenous population by disease, they possessed powerful agricultural technologies, and they enjoyed close economic ties to Britain, the center of the Industrial Revolution. The combination was explosive.
> [T]he population of the United States at its independence was between three and four million –roughly one-tenth the size of France. And yet by 1900 it was seventy-six million, nearly twice France’s size.
> Although the frontier had advanced by fewer than two miles a year in the 150 years following Jamestown’s establishment, in the first half of the nineteenth century it shot west at nearly forty miles a year, stopping only when settlers reached the Pacific Coast.
> With arable land stretching to the horizon, settlers spread like bacteria.
> You could see it in the cities the settlers built. Cincinnati, a village in 1810, had a nine-story steampowered mill by 1815 and a fleet of 150 steamboats by 1830. Chicago grew from a settlement of fewer than a hundred people (and fourteen taxpayers) in 1830 to a towering megalopolis with the world’s first dense cluster of skyscrapers and more than a million residents in 1890—despite having burned to the ground in 1871.
>
> That phoenix-from-the-ashes routine was surprisingly common. Constructed with maximal haste and minimal regard for the principles of zoning, settler cities burst into flame with alarming frequency. But not even fire could stop the endless torrent.
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Source: [[How to Hide an Empire]]