Williams father, John Murdoch was millwright and tenant of Bello Mill in Lugar, in the Parish of Auchenleck, which John took over in 1754 and operated for James Boswell (Lord Auchenleck). 

Six years later in 1760, Bello Mill was the most technically advanced mill in Britain for John cast and installed his own cast iron-toothed gearing wheels. 

The wheels were cast to John's design at John Roebuck's Carron Foundry at Falkirk, some fifty miles away. These were probably the first castings done at the Carron Foundry for the first air-furnace was fired in April 1760 and the first blast furnace on Boxing Day. 

The wheels are thought to still be in situ in Bello Mill, but it is difficult to say if the wheels in the ruins of Bello Mill are the wheels cast at the Carron Foundry or later ones cast at nearby Muirkirk. 

The confusion comes from William himself who claimed he had one of them taken out and brought to him at Sycamore House in Handsworth, which William had just built, where he had it set in stone and installed on the lawn 

REFERENCES :

1817 - Inscription on the stone at Sycamore House. 

"Cast at Carron Ironworks for John Murdoch of Bellow Mill Ayrshire A.D.1760 being the first toothed gearing used in Millwork in Great Britian."

What became of the gearwheel at Handsworth is not known, nor if it is still in existence. 

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John Murdoch was also involved in other technical projects for Lord Auchenleck as well as his own mechanical contrivences: 

1760's, - Murdoch's "Wooden Horse on Wheels"

1780's - The "Corn-Engined Chariot"

1783 - Designed and installed Corn Drying Kiln

1786 - "Small Fire Engine" installed at Birnieknowe

1788 - "Small Fire Engine" installed at Gasswater

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According to one account, (paper: Auchenleck, Helen Steven, 1898), John Murdoch was the son of David Murdoch who was the Kirk of Session Clerk and registrar and who kept a school in Auchenleck until 1759 and who later became teacher to the well known Scots poet Robert Burns.

1725 - Born Bello Mill, Lugar
1744 - Jan; Apprentice inWoolwich Co. - Trains of Artillery 
1744 - Sept; became Gunner
1746 - April : Fought at the Battle of Culloden
1747 - Married Anna Bruce, (sister of Boswell's agent)
1748 - Birth of First child, Jean
1749 - Birth of second child, Andrew (died in infancy)
1751 - Recorded on muster roll as "sick at Perth"
1752 - July -  Recorded as "On furla" (demob)
1752 - August - Returns to Bello Mill
1754 - Takes over as Millwright from his father, David
1754 - August 21st- Birth of third child, William
1757 - Birth of fourth child, Robert
1759 - Birth of fifth child, Mungo
1760's Builds "Wooden Horse on Wheels"
1762 - Birth of sixth child, Euphemia (died in infancy)
1763 - Casts & installs iron-toothed gearing wheels
1766 - Birth of seventh child, James (baptised 1768)
1767 - "Wheel & cylinder pumps" installed at Birnieknowe
1769 - "Water machine for drying coal" installed at Gasswater
1774 - Construction contractor for Ayrshire Turnpike Act
1777 - Allows William to leave Bello Mill for Birmingham
1780's Builds the "Corn-Engined Chariot"
1783 - Designed and installed Corn Drying Kiln
1784 - Contract to repair "Craikston Bridge & Publik road"
1786 - "Small Fire Engine" installed at Birnieknowe
1788 - "Small Fire Engine" installed at Gasswater
1790-1805 - retired from active business circa 1790
1806 - Deceased

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