In the 1910 Federal Census, this family is living at 243 Chalkstone Ave., Ward 10, Providence, RI. I have made an assumption that this wife and four children belong to this particular Henry Remington, because the age and location match. (needs research to confirm)
In 1920 the family is in Providence as follows: Henry Remington 45, Lena 44, Harold 24, Carol 20, and Beatrice 15.
In 1930 the family is in Providence as follows: Henry R. Remington 57, Lena 55, Beatrice 24, Malinda 34 dtr-in-law, Frances 12 gr-dtr, and Clarence W. 6 gr-son, all born RI.