Stone remained at the McCormick Observatory until 1912. In his time there, he taught various astronomy courses for the university; founded the "Annals of Mathematics" in 1884, funding the publication with his own money, and edited the journal until 1899 (after which he served on the editorial board); founded the Philosophical Society at the university; and spent much of the final ten years of his directorship in the cause for secondary education in Virginia. He was a member of the American Association for the Advancement of Science (Member: 1875; Fellow: 1876; Chair, Committee on Standard Time: 1880; Member of Committee on Stellar Magnitudes: 1880; Vice-President, Astronomy and Mathematics: 1887; Vice-President of Section A: Astrometry, of Department 11: Astronomy: 1888; Chair: 1901 Councilor, Section A, Mathematics and Astronomy: 1902-1905; Sectional Committee, Section A: 1905-1907; Emeritus Life Member: 1927), the American Astronomical and Astrophysical Society, now known as the American Astronomical Society (Councilor 1899-1909), and the American Mathematical Society (Councilor 1897), among many other academic societies. He served on the Board of Visitors (as Secretary) for the United States Naval Observatory from 1901 to 1903, served on the first Advisory Committee on Mathematics for the Carnegie Institution of Washington starting in 1902, and was a trustee of Harrisonburg Normal College (now James Madison University). He also maintained contacts with people of influence across the country, including his brother Melville E. Stone, the founder of the "Chicago Daily News", who became well known as the General Manager of Associated Press.