W. and J. Beardmore
of Glasgow, Iron Masters
Presumably the name is a misprint for W. and I. Beardmore
c1871 Isaac Beardmore (who for a number of years had been managing the forge department at Parkhead Forge) became a partner and the company was called W. and I. Beardmore.
1877 William Beardmore senior died, Isaac became sole proprietor of the Parkhead Forge. William junior inherited his father's share in the business but he first completed his education and only then returned to Glasgow (in 1879) to become the junior partner in the company.
Subsequently I. and W. Beardmore