He was the son of Alexander Brough and Jane Dandie Brough. He emigrated to the United States in 1882, and settled in Providence, Rhode Island. He attended Brown University, and graduated from Amherst College in 1887.
In 1916, he was appointed by Mayor John Purroy Mitchel as a City Magistrate. Brough retired from the bench in June 1939.
- Official New York from Cleveland to Hughes by Charles Elliott Fitch (Hurd Publishing Co., New York and Buffalo, 1911, Vol. IV; pg. 354 and 367)
- ALEX. BROUGH, 77, AN EX-MAGISTRATE in NYT on February 28, 1940 (subscription required)
|New York Assembly|
Mervin C. Stanley
| New York State Assembly
New York County, 19th District
William B. Donihee
|New York State Senate|
| New York State Senate
Henry W. Pollock
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