Hi Ian and all,
I decided to have a look at all Cheynes affiliated with the police in 1901. See if anyone can get some ideas from this:
1901
4 Morrin Sq, Glasgow Robertson Memorial, Blackfriars, Lanarkshire
William Cheyne, 32, Head, born Turiff, Aberdeenshire, Inspector of Police
Helen M Cheyne, 16, Wife, born Mertoun, Berwickshire
James A Cheyne, 5, son, born Glasgow, scholar
Thomas H Cheyne, 4, son, born Glasgow
Isobel M S Cheyne, 2, Daur, born Glasgow, Lanarkshire
George Cheyne, 1, son, born Glasgow, Lanarkshire, Scholar
1901
Police Station, Hamilton, Lanarkshire
Charles Cheyne, 33, Head, born Fyvie, Aberdeenshire, Police Sergeant
Margaret Cheyne, 33, Wife, born Biggar, Lanarkshire
Charles George Cheyne, 4, Son, born Hamilton, Lanarkshire, Scholar
Margaret Spence Cheyne, 2, Daur, born Hamilton, Lanarkshire
William Elrick, 26, Boarder, born Peterhead, Aberdeenshire, Police Constable
Robert Tennion, 22, Boarder, born Keith, Banffshire, Police Constable
Going back with these two chaps:
1891
Constab: Buildings, Jedburgh, Roxburghshire
George Dickson, 33, Head, born Beath, Fifeshire, Police Constable
Thomas Currie, 28, Boarder, born Ireland, Police Constable
John McDonald, 22, Boarder, born Cawdor, Nairnshire, Police Constable
John Morrison, 21, Boarder, born Alvah, Banffshire, Police Constable
William Cheyne, 21, Boarder, born Turiff, Aberdeenshire, Police Constable
1891
Braehead, Carnwath, Lanarkshire
Annie H Weir, 36, Head, born Carnwath, Lanarkshire, Fancy Knitting & Crocheting
Alexander Weir, 10, Son, born Carnwath, Lanarkshire, scholar
Annie R Weir, 5, Daur, born Carnwath, Lanarkshire
Charles Cheyne, 23, Lodger, born Aberdeenshire, Police Constable
Both William and Charles are going to be a bit young in 1886... but still possible.
Charles is a farm servant in Fyvie in 1881, which sounds good from what we know:
1881
Cow Hill Farm, Fyvie, Aberdeenshire
Charles Cheyne, 13, Servant, born Fyvie, Aberdeen, Farm Servant
William is still at home with his parents, a scholar. I really think he is too young...
1881
Touchar, Monquihitter, Aberdeenshire
George Cheyne, 34, Head, born Monquhitter, Aberdeenshire, Farmer of 10 Acres
Mary Cheyne, 34, Wife, born Marnoch, Banffshire, Farmers Wife
William Cheyne, 11, Son, born Turiff, Aberdeenshire, Scholar
Jane Cheyne, 7, Daughter, born Turiff, Aberdeenshire, Scholar
George Cheyne, 6, Son, born Monquhitter, Aberdeenshire, Scholar
Elizabeth Cheyne, 3, Daughter, born Monquhitter, Aberdeenshire
Mary Cheyne, 1, Daughter, born Monquhitter, Aberdeenshire
There is also this one, born England, although he doesn't seem very likely:
1881
37 So Albion St (Police Barracks) Glasgow Blackfriars, Lanarkshire
John Chenay, 38, born England, Sergeant of Police
Charles appears to be the illegitimate son of Agnes George. He was born 10 Sep 1867 in Fyvie. In 1871 he is with his grandmother Jane George in Fyvie. She is 73 years old and has a houseful of grandchildren, each with a different surname
So... no link with the James born Methlick, as far as we know (although we don't know who Charles' father was).
Not sure I have got us anywhere, but at least I did find a Cheyne who was a farm servant in the Fyvie area and then later a police sergeant!
Cheers,
Sarah