He graduated at Harvard in 1856, studied one year at the Harvard Law School, was admitted to the Michigan bar and practised in Marshall, Michigan, until 1865, when he was appointed tutor in Latin at Harvard. In 1873 he became assistant professor, and in 1883 professor of Latin, a post which he resigned hardly six weeks before his death at Cambridge, Massachusetts.
Following the lead of Goodwin's Moods and Tenses (1860), he set himself to study Latin historical syntax, and in 1870 published Analysis of the Latin Subjunctive, a brief treatise, privately printed, of much originality and value, and in many ways coinciding with Berthold Delbrück's Gebrauch des Conjunctivs und Optativs in Sanskrit und Griechischen (1871), which, however, quite overshadowed the Analysis.
In 1872 appeared A Latin Grammar for Schools and Colleges, founded on Comparative Grammar, by Joseph A. Allen and James B. Greenough, a work of great critical carefulness. His theory of cum-constructions is that adopted and developed by William Gardner Hale. In 1872-1880 Greenough offered the first courses in Sanskrit and comparative philology given at Harvard.
His fine abilities for advanced scholarship were used outside the classroom in editing the Allen and Greenough Latin Series of text-books, although he occasionally contributed to Harvard Studies in Classical Philology (founded in 1889 and endowed at his instance by his own class) papers on Latin syntax, prosody and etymology— a subject on which he planned a long work on Roman archaeology and on Greek religion at the time of the New Comedy.
He assisted largely in the founding of Radcliffe College. An able English scholar and an excellent etymologist, he collaborated with Professor George L Kittredge on Words and their Ways in English Speech (1901), one of the best books on the subject in the language.
He wrote clever light verse, including:
Selections from the Poems of Ovid (1882)
Select Orations of Cicero (1886)