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Although illiteracy is felt to be surprisingly high at present in Canada, we pretty much take it for granted that the great majority of us know basic arithmetic reasonably well. While Lowland Scotland had a relatively good educational system in general 300 or so years ago, counting and measuring by the masses were still founded largely on such everyday things as the typical hand or foot. There was relatively little immediate need for complex measurements and calculations. As the cash economy crept into everyday affairs, it became more and more important for people to do more and more with numbers.

Here, we have a snapshot of Ayrshire folk who took a special interest in "The New Math". A solid majority of the subscribers to this book were from Ayrshire. Most of the people listed below lived in the villages, as stated. It is important to note that we only show those farms that could reliably be identified as in Cumnock Parish. So, the number of farmers who subscribed is very under-represented in the following data. Some of the people listed here did not live in Ayrshire at the time, but their information is inserted below for various illustrative purposes.

Refer to our Lesson Plan: Classification and Properties of a Class of Objects. For the purposes of this Lesson Plan and the Exercises, you can consider the data below to represent a crude sampling of Ayrshire people who were interested in improving their grasp of arithmetic at the close of the eighteenth century.


Ayrshire Subscribers to
The Practical Figurer
Or An Improved System of Arithmetic

by William Halbert, Paisley 1789


  Name Place Occupation
Adderton Richard Adderton Ayr Lieutenant
Allan Robert Allan Catrine Engineer
Anderson Adam Anderson Ayr Farmer
Anderson James Anderson Dunlop School master
Andrew William Andrew Tarbolton Mason
Baird James Baird Ayr Merchant
Ballantine John Ballantine, Esq. Ayr Provost
Begg James Begg Sorn Mason
Blackwood Thomas Blackwood Irvine  
Borland John Borland Mauchline Weaver
Boswell John Boswell Ayr Writer, literature
Boyman James Boyman Auchinleck Wright, wood/carriage trades
Brown James Brown Berryhill, Auchinleck  
Brown Thomas Brown Stewarton Merchant
Buchanan John Buchanan Irvine Writing master, literature
Burns George Burns Auchinleck Mason
Burns Robert Burns Parnassus  
Campbell John Campbell, Esq Tobago (West Indies: Note 1) Doctor
Campbell William Campbell Dalquhanna  
Cowan Hugh Cowan Paisley  
Cowan William Cowan Ayr Banker
Crosse John Crosse Drumpelier, Old Monkland (Lanarkshire: Note 1)  
Culbertson Mrs. Culbertson Cumnock, Dumfries House  
Cunninghame David Cunninghame Auchinleck Shoe maker
Dean John Dean Stewartson Writer, legal
Dimmock James Dimmock Mauchline Teacher
Donald William Donald Ayr Merchant
Douglas George Douglas Ayr Teacher of mathematics
Dun Dun Maybole School master
Dun James Dun Ayr Banker
Dun Reverend John Dun Auchinleck Minister of Auchinleck
Duncan Rev. John Duncan Saltcoats Minister of Saltcoats
Elder James Elder Miltoun Book engraver, printing trades
Ewen James Ewen Cumnock, Dumfries House Gardener
Ferguson James Ferguson Ochiltree Mason
Finlay James Finlay Cumnock, Dumfries House Gardener
Gibb James Gibb Kirkwood Mason
Gibb William Gibb Tarbolton Excise Officer
Gillies William Gillies Townhead  
Gray James Gray Newtown School master
Greenshields Thomas Greenshields Kilmarnock Baillie
Hair Andrew Hair Barhill  
Hamilton Captain James Hamilton   Army/naval officer
Harkness Adam Harkness Cummock Merchant
Harvey Francis Harvey Irvine Wright, wood/carriage trades
Henry John Henry Ayr Merchant
Herbert George Herbert Catrine Carter
Hewand John Hewand Auchinleck Joiner, wood trades
Hewand Robert Hewand Glasgow Manufacturer, textiles
(Note 2)
Hodge Archibald Hodge Mauchline Silk weaver
Hutchinson John Hutchinson Auchinleck Merchant
Hutchinson William Hutchinson Cumnock, Dumfries House Carter
Hutchinson William Hutchinson   Drover, livestock
Irvine Alexander Irvine Catrine  
Irvine Joseph Irvine Knockrrom  
Johnston Thomas Johnston Gowklee Moss Surveyor
Kennedy John Kennedy Cumnock (Dumfries House) Factor to Earl of Dumfries
King John King Cummock Dyer, textiles
Lambie Gavin Lambie Mauchline Messenger
Lambie John Lambie Mauchline Tailor
Lapraick John Lapraick Defram  
Lawson Hugh Lawson Newtown, Ayrshire Baker
Logan William Logan Maybole  
Lorimer Charles Lorimer Drumbowie  
  Lord Lyle    
M'Adam Quintin McAdam, Esq.    
M'Harg Anthony McHarg Ayr Writer, legal
M'Ilwraith Thomas McIlwraith Ayr  
M'Kee William McKee Ayr  
M'Kelvin John McKelvin Dumfries House Gardener
M'Kerrow James McKerrow Barskimming Game keeper
M'William Alexander McWilliam Ayr  
Macome Ebenezer Macome Paisley (Renfrewshire) Accountant, writing master
Macome Robert Macome Paisley (Renfrewshire) Accountant, writing master
Mair James Mair Irvine Merchant
Marshall Robert Marshall Mauchline Brazier, metal work
Maxwell Thomas Maxwell Stewarton Minister of Stewarton
Maul Benjamin Maul Irvine Master of the English School
Mcars Alexander Mcars   Soldier, army
Mcaul Thomas Mcaul Ayr Merchant
Mclatchie William Mclatchie Sykefide Wright, wood/carriage trades
Mclure John Mclure Kilmarnock Plasterer
Mcowan Robert Mcowan Knocknab (Cumnock) Note 3
Mcreath James Mcreath Mauchline Messenger
Mavitie Charles Mavitie Cumnock Overseer to the Earl of Dumfries
Mcrone John Mcrone Ochiltree Wright, wood/carriage trades
Mdougal Colin Mcdougal Cumnock Merchant
Mgavin John Mcgavin Paisley (Renfrewshire) Accountant, writing master
Mitchell Captain Hugh Mitchell Dallegles Army/naval officer
Mitchell John Mitchell Auchinleck Silk weaver
McMath John McMath Mauchline Surgeon
Montgomery Col. Montgomery, Esq. Coylsfield Army/naval officer
Montgomery Major William Montgomery Ayr Army/naval officer
Morton John Morton Barskimming Stone cutter
Muire James Muire Muirkirk School master
Muire John Muire Barskimming Game keeper
Murdoch David Murdoch Auchinleck Mason
Murdoch Robert Murdoch jun. Auchinleck Mason
Murdoch Robert Murdoch Auchinleck Mason
Murdoch William Murdoch Auchinleck Mason
Murdoch William Murdoch Auchinleck Wright, wood /carriage trades
Murray Alexander Murray Ayr School master
Murray William Murray Auchinleck Wright, wood/carriage trades
Neil William Neil Ayr School master
Nimmo William Nimmo Sorn Mason
Noble Andrew Noble Mauchline School master
Paterson Robert Paterson Mauchline Merchant
Picken John Picken Stewarton Merchant
Pollique William Pollique Knockroon  
Ramsay Rev. John Ramsay Kirkmichael Minister of Kirkmichael
Ranken Andrew Ranken Burnside, Cumnock  
Rankin Whitehill    
Rankin John Rankin Cumnock Watch maker
Rankine Crichton Rankin Bridgend, Cumnock  
Reid Matthew Reid Irvine Merchant
Reid Patrick Reid Ayr Merchant
Richardson James Richardson   Lieutenant of Marines
Richmond Rev. James Richmond Irvine Minister of Irvine
Richmont David Richmont Cumnock, Dumfries House Carter
Ritchie Stuart Ritchie Cumnock, Dumfries House Gardener
Rob Allan Rob Mauchline Carrier
Robinson Duncan Robinson   Ditcher, agriculture
Robinson Robert Robinson Catrine  
Roison William Roison Ayr Merchant
Ronald William Ronald Mauchline Tobacconist
Rowan Rev. Stephen Rowan Irvine Preacher assistant
Roxburgh William Roxburgh Fenwick Surveyor
Scot David Scot Ayr Banker
Shaw James Shaw Irvine Baillie
Siller David Siller Irvine Merchant
Simson William Simson Cumnock School master
Smith James Smith Knocknab (Cumnock)  
Smith John Smith Sorn Mason
Smith John Smith Mauchline Mason
Smith Robert Smith Galstoun School master
Stevenson Robert Stevenson Ayr  
Stevenson William Stevenson Arran castle  
Stirling John Stirling Stevenston Farmer
Stodart William Stodart Cumnock Stocking maker
Struthers John Struthers Sorn School master
Sutor Robert Sutor Cumnock Mason
Tarbet James Tarbet Ayr  
Templeton Andrew Templeton Cumnock Merchant
Templeton William Templeton Mauchline Merchant
Templeton William Templeton Irvine Book seller
Vez Sous Vez Barskimming  
Wait James Wait Ayr Painter
Watt James Watt Dumbarton Officer of his Majesty's Excise  (Note 4)
Weir John Weir Sanquhar (Dumfriesshire)  
Weir John Weir    
Weir Mason Weir Cumnock  
Weir Robert Weir Ayr Mason
White James White Cumnock, Dumfries-house Postillion, carriage/transport
Whiteford James Whiteford Douglas School master (Lanarkshire:  Note 5)
Wilkins James Wilkins Dumbarton Officer of his Majesty's Excise
Williams Frederick Williams Irvine  
Wilson John Wilson Mauchline Toll gatherer
Wilson Quintine Wilson Cumnock, Dumfries house Postillion, carriage/transport
Wilson Samuel Wilson Ayr Treasurer
Wood Alexander Wood Dumbarton Officer of his Majesty's Excise
Wood James Haig Wood Dumbarton Officer of his Majesty's Excise
Wood John Wood Ayr Merchant
Wright Donald Wright Cumnock, Dumfries house Gardener
Wylie John Wylie Auchinleck Silk weaver
Young James Young Irvine Baillie
Young John Young Auchinleck Merchant
  1. Further notes in a future issue.
  2. There were also three subscribers in Liverpool named Hewand, two of them joiners. Included to show migration to the industrial south.
  3. There is a small possibility that this is Robert McCowan, father of James McCowan, later Coalmaster in Lesmahagow. James McCowan's library included a similar book.
  4. Not in Ayrshire, but included to show the importance of trade.
  5. Not in Ayrshire, but included because James Whiteford became a good friend and mentor of James McCowan. As a professional land surveyor and factor of Blackwood Estate in Lesmahagow, Whiteford (1760 app-1819/9/30) would be well-equipped to help the young entrepreneur in his negotiations with the landowner, James Corbet of Stockbriggs.
  6. Not in Ayrshire. In fact Parnassus was probably just a fictitious residence chosen by poet Robert Burns. He had written his famous love poem, "O, Were I on Parnassus Hill" in 1788 shortly before Mr. Halbert's "Practical Figurer" was published. Burns had leased Ellisland farm in Dumfriesshire starting in 1788, but first had to spend a good number of months building a farmhouse. Twenty five miles up the Nith Valley, in New Cumnock Parish, is Corsincon Hill, made famous in that Burns' love poem -- "On Corsincon I'll glow'r and spell, And write how dear I love thee". It appears that Corsincon was Burns' substitute for Mount Parnassus in ancient Greece, for which he yearns in the poem.


Overall Distribution of Place of Residence of the Subscribers (Summary by D.B. McCowan):

  • Ayrshire  156
  • County Undetermined or Residence Not Stated   91
  • Renfrewshire   21
  • Dumbartonshire   15
  • Glasgow   11
  • Lanarkshire   4
  • England   4
  • Dumfriesshire   2
  • Edinburgh   2
  • West Indies   1
  • Galloway   1
  • Argyleshire   1

Note: Dumfries House is in Cumnock Parish, Ayrshire -- not in Dumfriesshire.


Related Lessons


The Scarboro Heights Record V12 #2