Barnett was born in Woodson County, Kansas, the son of a minister.
In 1903 he published his book Elements of Electromagnetic Theory, which he dedicated to his friend Professor Francis H. Smith at the University of Virginia.
His wife, Mrs. Lelia Jefferson Harvie Barnett, was a scientific co-collaborator, and together they worked in a magnetic metal-free lab at the California Institute of Technology from 1924 to 1953.
[1] He was elected a Fellow of the American Academy of Arts and Sciences in 1921.
[1] They had no children, but their adopted daughter, Ann, also died shortly after Barnett's retirement from the university.