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Full-text online articles are available for free for 1851 to 1922 and 1981-date. For other years, with the date and page number from your search you can locate articles on the library's microfilm - at AP 2.N657 in the Periodicals Area.
In the Crumb Library Reference Area at Ref AI 21.N45 Indexes the contents of the paper from its beginning in 1851. Includes news summaries. Get the date, page, and column numbers for articles in The New York Times - on microfilm at AP 2.N657 in the Periodicals Area.