U.S. Census Office, The Progress of the Nation 1830-1840 (1874)

These maps were featured in the U.S. Census Offices's Statistical Atlas of the United States Based on the Results of the Ninth Census, 1870. This Statistical Atlas, the first of several, was published in 1874 under the supervision of Superintendent Francis Walker, who wanted to mark the upcoming centennial of the United States by illustrating its progress over the last century, including the expansion of settlement. His statisticians did so by plotting the westward encroachment of population density data from each census on a series of maps over eight decades. These maps depict two decades: 1830 and 1840. They can be compared with data maps from 1790-1820 and then 1850 and 1860, also featured on this site. The grayscale on the maps uses darker colors to indicate higher population densities, with the darkest shade indicating 90 or more inhabitants per square mile and the lightest gray indicating 2 to 5 inhabitants per square mile. The white indicates fewer than 2 inhabitants per square mile. In an accompanying section of the Statistical Atlas titled "The Progress of the Nation: 1790-1870," Walker famously discusses the  population line separating the area of European-American settlement (colored in different shades of gray) and the frontier (shown in white), which would become known as the "frontier line." In that same section (see p. 2), Walker calculated that the total settled area of the United States in 1830 was 632,717 square miles, with a population (not counting Native Americans) of 12,866,0120, and an average density of 20.3 inhabitants per square mile.  In 1840, he calculated the settled area to have grown to 807,292 square miles, with a population of 17,069,453, and an average density of settlement of 21.2 inhabitants to the square mile.