Farrington graduated from Huntsville High School in 1891 and SHNI in 1893. He later earned a degree from Vanderbilt University in Nashville (BS, 1897) before marying and returning to Huntsville in 1901. His classroom was on the ground floor of what was then the Science Building, now the Marks Administration Building.

Farrington was also a life-long member of the Methodist Church, where he taught Sunday School for college students for 35 years, and was a member of the Walker County Chamber of Commerce.

The Farrington Science Building honors his memory.