Crosby was born in New York City in 1826. He graduated in 1844 from New York University where he was one of the founding fathers of the Gamma Chapter of the Delta Phi fraternity, and became professor of Greek at NYU in 1851. In 1859, he was appointed professor of Greek at Rutgers College, New Brunswick, New Jersey, where two years later he was ordained pastor of the First Presbyterian Church of New Brunswick. From 1863 until his death he was pastor of Fourth Avenue Presbyterian Church, New York. From 1870 to 1881 Crosby was chancellor of New York University, then known as the University of the City of New York. He was one of the American revisers of the English version of the New Testament. Crosby took a prominent part in politics. He urged to excise reform and opposed total abstinence. He was one of the founders and the first president of the New York Society for the Prevention of Crime, and pleaded for better management of Indian affairs and international copyright. Among his publications are The Lands of the Moslem, Bible Companion, Jesus: His Life and Works, True Temperance Reform, True Humanity of Christ, and commentaries on the book of Joshua, Nehemiah and the New Testament. He was also president of the American Philological Association and in 1871 gave a presidential address, excerpted in the Proceedings of the American Philological Association. "Linguistics or philology may be considered either as a science or as a philosophy. Under the first aspect we may gain some idea of its extent by thinking of the vast number of languages which are to be investigated, not only those now spoken, but also many of which we have but the fossils. It touches here psychology and history, and enables us to know the unseen. A linguistic criticism is the source of all true commentary. By philology we can reconstruct prehistoric man, and read the history of times before the Olympiads and Nabonassar. Languages are never lost. By this science, the original unity of the human race is already nearly proved….Again philology as a philosophy speculates on the value of language to man, and its relations to his mind. These speculations are not to be confounded with the facts of the science….Every profound thinker has found himself fettered by language. Hence disputes and misunderstandings have arisen. Also in poetry, in devotion, in music, language is shown to be imperfect; it can never be made sufficient for the whole realm of thought. Man in his development, must have a nobler and fuller language than he has to-day. This may be in a new creation with spiritual bodies." The President, in conclusion, referred to the field of American languages as especially open to the researches of the Association, suggesting its division into sections and the organization of local branches. From 1872 to 1880 Crosby was a member of the New Testament Company of the American Revision Committee. Crosby married Margaret Evertson Givan, a daughter of John Givan and Mary Ann Evertson, she a granddaughter of Jacob Evertson of Amenia, New York.