Eaton graduated from Williams College in 1799 and settled in Catskill, N.Y., as a lawyer, but later abandoned his law practice to pursue his great interest in the natural sciences.
He instituted a course of popular lectures in botany and published a manual that succeeded through eight editions. He surveyed the district along the Erie Canal in 1824, the same year he co-founded the Rensselaer School with the support and patronage of Stephen Van Rensselaer. As senior professor, he created unique methods of instruction that placed the student in the role of teacher and stressed laboratory and field observation.
Eaton had a remarkable gift of arousing interest and enthusiasm in others. A friend of Emma Willard, Troy’s pioneer in the education of women, Eaton wrote often of his belief in educating women in the sciences.