He served as the editor of the Annals of Mathematics and towards the end of his life made donations which led to the founding of the Fairfax Public Library System.

While attending Chicago High School, he met Truman Henry Safford, an astronomer at the recently completed Dearborn Observatory.

It was on this trip to Des Moines, Iowa, with Safford that he met astronomers from the United States Naval Observatory (USNO).

In 1882, Stone was offered the position of director at the brand new observatory being built at the University of Virginia, and was accompanied from Cincinnati by John Jones and Frank P. Leavenworth.

Stone oversaw the final stages of construction on the observatory, which was completed in 1885, but began astronomical work almost immediately upon his arrival in Charlottesville.

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.

In November 1929, Professor Stone and his friend, lawyer Thomas Keith, approached the Fairfax County Board of Supervisors to request space to begin a library.

He died just six days after his eighty-sixth birthday, when he was struck and instantly killed by the driver of a C&P Telephone Company vehicle while walking along the road near his farm in Centreville.