David Rumsey's fantastic map website has many examples of demographic statistics on cartographic beauties. One example I came across is an 1874 creation based on statistics from the 1870 U.S. federal census.
For the Irish, the page has two measurements - absolute (number per square mile) and relative (number as a percentage of the whole population) numbers east of the 100th meridian, the line that roughly divides the U.S. in two.
You can access the map here.
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