Hi, found these births in case you don't have them.
Births:
George Waddell  bap. 5 Jan 1848  Airdrie, Lanark
Susan Rankin  bap. 23 April 1850  Airdrie, Lanark
Christopher  bap. 23 July 1852  Airdrie, Lanark
Margrate  bap. 28 March 1857  Whitburn, West Lothian
Janet  bap. 18 August 1859  Whitburn, West Lothian
John  bap. 14 August 1862  Whitburn, West Lothian
James  bap. 10 December 1865  Whitburn, West Lothian
William  bap. 13 March 1868  Whitburn, West Lothian
Agnes Brittan  bap. 16 April 1871  Whitburn, West Lothian
children to Christopher & Susan (Rankine) Brittan:
Janet  born: 30 April 1825  bap. 5 June 1825
Margaret born: 24 March 1827  bap. 19 April 1827
* both girls born in Shotts, Lanark
** the parents married 14 August 1820 in Dalserf, Lanark
I found this marriage and think perhaps the man may be related to George;
John Newlands
married
Christian Brunton (Brittan)
2 March 1820
in Glasgow, Lanark
As for George, I am thinking that perhaps he had relations living in Airdrie, so that after he married Margaret they set up house there. Later, they moved to West Lothian which has me thinking that he may have actually been born up that way. Going by naming patterns (not that everyone uses them), his dad may also have been a George. If so, there are 2 good births for him; 1822 to George & Margaret Bennet and 1825 to George & Grace Thomson. Hope something may help, Kim