Melville was born in Merchiston in Edinburgh, the elder daughter of Francis Suther Melville, a depute clerk of the Court of Session, and Helen Alexandrina Kerr. Melville was one of seven children; five brothers and two sister. She spent her childhood in Edinburgh, where she was educated at George Watson's Ladies' College and later studied music for a year in Germany.
Education
Following the 1889 Universities Act which allowed women to graduate from universities in Scotland, Melville became one of the first women to matriculate at the University of Edinburgh in 1892. She graduated five years later in 1897 with a first class MA Honours degree in Philosophy. In 1910 Melville was awarded a Bachelor of Divinity degree by the University of St Andrews, the first woman in Scotland to graduate with this degree.
Academic career
Following graduation, Melville worked as a tutor at the University of Edinburgh from 1896 to 1899, where she taught classes on logic, psychology, and metaphysics run by Professor Andrew Seth Pringle-Pattinson. From 1899 to 1909 Melville held the post of Warden of University Hall at the University of St Andrews. On her departure she wrote a "Memorandum on the duties of the warden of University Hall" which is held by the University of St Andrews Archives. After a short spell as lecturer in Mental and Moral Science at Cheltenham Ladies' College, Melville succeeded Janet Anne Galloway as Mistress of Queen Margaret College, University of Glasgow, in 1909 a post she held until the closure of the college in 1935. After becoming Head of the Women's Department at the University of Glasgow, Melville was asked to gather information on the suitability of women for diplomatic and consular service positions. This led to a lengthy correspondence between Melville and educationist Marjorie Rackstraw, warden of Masson House at the University of Edinburgh. Rackstraw was hoping to compile data from all Scottish universities in support of women's potential for governmental service and sought Melville's help to provide information on Glasgow's female graduates. At the height of her career Melville was the most senior female academic in Scotland, notable for her academic achievements and administrative abilities. In 1927 she was awarded an honorary LL.D by the University of Glasgow. She was the first woman academic to receive an honorary degree from the University. In King's Birthday Honours list of 1935 Melville was awarded an OBE.
The women have been admitted to graduation in several of the faculties of the universities and their names have been placed on the Register of the General Council. They have attended and voted at the meetings of the General Council, and they have hitherto enjoyed and exercised all the privileges possessed by male graduates of the universities.
During her retirement, Melville lived in Dalry in Kirkcudbrightshire, before moving back to Edinburgh where she died on 7 March 1962 at her home on Merchiston Place. She is buried in Warriston Cemetery, Edinburgh.
Legacy
Melville House at the University of Glasgow is named in honour of Frances Melville and the University awards the Frances Melville medal annually to the most distinguished honours candidate in Mental Philosophy.