Matching the influx of foreign immigrants into larger cities of the United States during the late nineteenth century was a domestic migration，from town and farm to city，within the United States.
(倒装句：Matching the influx…was a domestic migration…=a domestic migration…was matching the influx…)
19世纪晚期，与外国移民流入美国较大城市相媲美的，是美国本土移民从小镇和乡村到城市的国内迁移。
解析：
倒装，主干正常顺序是a domestic migration was Matching the influx of foreign
immigrants….
从句1：from town and farm to city，
从句2：within the United States
从句1，2共同修饰主干中的a domestic migration
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