[2] One of the latter's theological pupils, David Hale, brother of Nathan, first instructed Day, and later he continued his preparation for college under John Kingsbury of Waterbury, Connecticut.

During all this time Day had been suffering from tuberculosis, and in July 1801 a hemorrhage brought on by the exertion of preaching caused him to go to Bermuda where he spent nearly a year.

Upon his return Day went to his father's home with little expectation of recovery, but life among the Connecticut hills arrested the disease, and in the summer of 1803 he undertook the duties of the professorship of mathematics and natural philosophy at Yale to which he had been elected shortly after his departure for Bermuda.

Martha died in 1806 and on September 24, 1811, Jeremiah married Olivia, daughter of Major Daniel and Olive (Tinker) Jones of Hartford, Connecticut.

Although, as described by Timothy Dwight V, the younger, "he was a wise disciplinarian, a judicious governor, a thorough and accurate scholar, a valuable teacher, and a man of intelligent and penetrative mind," his influence was due chiefly to his goodness and his reputation for deep wisdom.

Day combined serenity, self-control, modesty, and unselfishness in such a degree that all of the 2,500 students who had been under him, according to President Theodore Dwight Woolsey, would have unquestionably declared him the best man they had ever known.