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Miller and Co of Vulcan Foundry, Coatbridge
1867 Company founded (presumably as Miller and Anderson at Atlas Works, Coatbridge)
1889 Rolling Mill Engines for the Bowesfield Iron Co and designed by Jeremiah Head of Middlesborough.
1897 Private company.
Supplied one locomotive to the Tudhoe Ironworks. Possibly agents.
1952 Acquired by British Rollmakers Corporation.
1961 Rollmakers, producing chilled iron rolls for paper, rubber, plastic, textile and flour and cereal industries; also chilled iron rollheads for electrical power stations. 270 employees. 
10th January 2013 JO writes:
During the 1960's and perhaps before, through to the 1980's Millers operated from a large foundry in London Road, Edinburgh. They produced chilled iron rolls up to at least 25 tonnes in weight. Their rolls were used by most paper mills, along with makers of linoleum and plastic flooring. They also supplied Kellogg's with rolls to make corn flakes and the producers of oils that ended up in low fat spreads. Their competitors at the time were exclusively German. Despite being old fashioned the degree of precision was remarkable. Consider an iron roll 9 metres long x a metre in diameter ground true with a tolerance of 0.0005" that is one ten thousandth of an inch!