The Dillingham Commission is today little known. But a century ago, it stood at the center of a transformation in immigration policy, exemplifying Americans’ simultaneous feelings of fascination and fear toward the millions of migrants who have made the United States their home.

In 1911, the Dillingham Commission produced perhaps the most extensive investigation of immigration in the history of the country, an exhaustive 41-volume study that demonstrated just how vital 19th-century and early-20th-century immigrants were to the U.S. economy. But …