Scottish Champion 1886; edited a chess column in the Glasgow Weekly Citizen; held the West of Scotland Challenge Cup for several successive years; Glasgow Chess Club champion (Outram Cup) 1892 and 1893; served as president of Glasgow Chess Club.
Barbier is connected to the famous Saavedra study; it was in one of his columns in the Glasgow Weekly Citizen in 1895 that Barbier showed a position (remembered wrongly from a Fenton-Potter game). Later, the amateur player Fernando Saavedra pointed out an improvement, which changed the assessment to a win.
Early in life he came to London with his father, the incumbent of a French Protestant church there. He was for some time a journalist, but in 1883 accepted the appointment of teacher of French at the Glasgow Athenaeum. He was highly regarded both as a player and problem composer. A few weeks before his death he had gone to France in the hope of improving his health.
Historian, Chess Scotland