Joly was born at St Catherine's Rectory, Hop Hill, Tullamore, County Offaly, the eldest of six children of Rev. John Swift Joly (1818-1887) and Elizabeth Slator (1835-1904). He was a second cousin to John Joly. He was educated at Galway Grammar School. In 1882, he was enrolled at Trinity College Dublin on a mathematical scholarship and graduated with first place in mathematics in 1886. Winning a studentship and following his great interest in experimental physics, he moved to Berlin to work in Helmholtz’s laboratory.[4]
Over the next five years, he wrote numerous mathematical papers, particularly on the applicability of the theory of quaternions to several areas of mathematics: theory of strain, spherical harmonics, hydrodynamics and electromagnetism.
In 1900, he went on the RIA/RDS eclipse expedition to Spain and later took part in the British Association visit to South Africa in 1905.