You can find census and passenger list records as well as some other federal records on familysearch.org. This is a free research site, you just need to sign up for a free username and password. The paper of Albert Payson Terhune are at the Library of Congress in Washington DC Albert Payson Terhune papers, | Library of Congress (loc.gov)
Dear Mr. Artis,
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At the National Archives, Census Records may provide more information on Albert Payson Terhune and his family. We searched the National Archives Catalog and located the Population Schedules for the 1870 Census, the Population Schedules for the 1880 Census, the Population Schedules for the 1890 Census; the Population Schedules for the 1900 Census, and the Population Schedules for the 1910 Census, the Population Schedules for the 1920 Census, the Population Schedules for the 1930 Census, and the Population Schedules for the 1940 Census in the Records of the Bureau of the Census (Record Group 29) that may contain information about Albert Payson Terhune in New Jersey. The 1940 Census schedules are digitized and available using the Catalog. For more information about the non-digitized schedules, please contact the National Archives at Washington, DC - Textual Reference (RDT1) via email at email@example.com.
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We searched Chronicling America and located 3,126 references to Albert Payson Terhune that include ads for his books plus articles he wrote for “The Evening World” newspaper. As noted by Ms. Brooks, the Albert Payson Terhune papers are located at the Library of Congress Manuscript Division.
Also you may be interested in his estate, Sunnybank, that is now a part of Terhune Memorial Park - Sunnybank located in Wayne, New Jersey. The site notes that the Van Riper-Hopper House Museum in the park includes an Albert Payson Terhune Collection.
Plus, the FamilySearch Research wiki for New Jersey Genealogy may be useful.
We hope this is helpful. Best of luck with your research!