He was elected a Petrean fellow of Exeter College, Oxford, on 30 June that year and was mathematical examiner in the university from 1832 to 1833 and again from 1836 to 1838.
In 1839, he opened the Petrean fellowships at Exeter College to natives of Cheshire by conveying a small incorporeal hereditament to Lord Petre for that purpose.
He married in 1840 Isabella, daughter of J. Robinson, and widow of W. S. Douglas; she died at St. Alessi, near Pistoja in Tuscany, 7 February 1869.
The first six books by Hans Claude Hamilton, and the remainder by Falconer, with a complete index, appeared in Bohn's Classical Library in 1854–57 in three volumes.
The text of Strabo had been edited in 1807 by his father, Thomas Falconer, who had also prepared a translation, the manuscript of which was used by his son.