Answers:
Why guess at it when there's census data available?
I can't find data for 1875. Census data is done every ten years, so there's data for 1870, which has these cities:
1 New York city, NY *.... 942,292
2 Philadelphia city, PA..... 674,022
3 Brooklyn city, NY *.... 396,099
4 St. Louis city, MO..... 310,864
5 Chicago city, IL....... 298,977
6 Baltimore city, MD..... 267,354
7 Boston city, MA *...... 250,526
8 Cincinnati city, OH.... 216,239
9 New Orleans city, LA...... 191,418
10 San Francisco city, CA.... 149,473
and 1880, which has these cities:
1 New York city, NY *.... 1,206,299
2 Philadelphia city, PA..... 847,170
3 Brooklyn city, NY *.... 566,663
4 Chicago city, IL....... 503,185
5 Boston city, MA *...... 362,839
6 St. Louis city, MO..... 350,518
7 Baltimore city, MD..... 332,313
8 Cincinnati city, OH.... 255,139
9 San Francisco city, CA.... 233,959
10 New Orleans city, LA...... 216,090
New York City
Boston
Charlotte
Raleigh
San Francisco
San Antonio
Atlanta
Philadelphia
Chicago
Just guessing.
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