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Buckley and Taylor of Castle Ironworks, Oldham were engineers whose products included mill engines and gear wheel moulding machines
1883 Oldham Exhibition: 'The engines by which the power is applied are situated on the ground floor of No. 1 annexe. The principal are a pair of horizontal compound steam engines driving machinery by ropes. They are each of 40-horse power nominal, and of the type known as Tandem. Having both a high and a low pressure, they possess the advantage of utilising the steam not once but twice. They are further characterised by great regularity and noiselessness in working, and their finish is remarkably good. Although exhibited by Messrs. Buckley and Taylor, they are really the property of Messrs. Marsden, of the Screw Bolt Works, Manchester.'
1884 Horizontal twin tandem compound engine for Fern Mill, Shaw. The engine was removed for preservation, and languished in secure (but open) storage until November 2011 until the parts were recovered for preservation at Ellenroad Mill. The story is told in a well-illustrated article in 'Old Glory' magazine 
1891 Directory: Listed as Cotton Spinner and Manufacturer. [[Cotton Mills in Oldham 1891|More details]
1892 See description of the works in Buckley and Taylor: 1892 Visit to Works
1892 James Taylor died, aged 54 
1898-9 Supplied a cross-compound Corliss-type engine to a cotton mill in Portugal - see Buckley and Taylor engine in Porto. This followed an engine supplied to the mill in 1891.
1901 1500 HP four cylinder triple expansion engine for Wren Mill, Oldham. 
Twin tandem compound engine for Roy Mill, Royton. Approx 2000 HP. Flywheel 24 ft dia, 60 tons. 44 ropes.
1902 Incorporated as a private limited company.
1914 Engineers, millwrights and ironfounders. Specialities: simple, compound and triple expansion steam engines of horizontal and vertical type form 100 to 3,000 hp; mill gearing for driving cotton mills; pumping engines for hydraulic power stations; large gear wheels with cast and cut teeth; rope pulleys for main drives; wheel moulding machines. Employees 300. 
1917 'MAN BURNED TO A SKELETON. terrible affair occurred the engineering works of Messrs. Buckley and Taylor, Oldham, a man named Joseph Henry Penrose, 58, being incinerated before the eyes of helpless fellow workmen. Molten metal for the casting of a 10-ton pump was being conveyed in a ladle attached to a crane, when a chain broke and the vessel fell to the floor. Penrose was buried in the molten metal. Before he could be released the metal had to be cooled with sand, and when the body was recovered it was little more than a skeleton. Flesh had been burned from his bones and his clothes had disappeared.
The sale of Ruby Mill, Oldham, included a 1400 HP Buckley & Taylor engine, with flywheel for 28 ropes.
An excellent summary of the firm's history, with short biographies of the founders, is available on the website of Oldham Engineering Ltd., here.