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