Why have population maps indicated a stark divide in population density of the United States on either side ot the 100th Meridian?

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The answer is related to the map you posted about rainfall. The population of the eastern third of the continental US is denser because of settlement patterns that reflect the local availability of water resources. This quirk of human geography occurs because of the need for irrigation. As detailed by Harvey Leifert in "Dividing line: The past, present and future of the 100th Meridian":

In his 1878 “Report on the Lands of the Arid Region of the United States,” [John Wesley] Powell identified the “arid region” as the land west of the 51-centimeter-per-year rainfall line, which closely tracked the 100th meridian. This amount of rainfall per year is about the minimum that permits farming without irrigation, and it also greatly influences the types of crops that can be grown. The line Powell noted as dividing the arid and humid sections of the continent has become known as the “effective” 100th meridian.

That population is much denser on the east side of the line is apparent in historical demography nearly as soon as masses of settlers arrived there in the mid-1800s; check out this neat animated map.

With more limited water, farms had to be bigger to make money west of the line. Possibly related to farming conditions and market size, insurance was more available east of the line.

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