He studied at the Vienna Conservatory with Karl Heissler and Josef Hellmesberger, Sr. from 1873 to 1878.
He worked with Hans Richter, August Manns, Henry Wood, Alexander Mackenzie, York Bowen and Arthur Sullivan.
He taught Spencer Dyke, Albert Sandler, Percy Hilder Miles, E. Florence Whitlock, Lionel Tertis and Rebecca Clarke, (before the latter two changed to viola).
Wessely played on the Deurbroucq Stradivarius violin, 1727, gifted to him in 1903 by pupils and friends at the Royal Academy of Music.
[1] He published A Practical Guide to Violin Playing and Comprehensive Scale Manual.