Hi Brian,
With all that info , makes life a wee bit easier, here is some that you may already have by the sound of it, but will help other reseachers to give all info known at outset.
Parents were James Carmichael & Margaret Shaw.
Andrew Halliday Carmichael 10 Mar 1824 St Cuthbert’s, Edinburgh, Midlothian (Extracted)
Margaret Carmichael 11 May 1825 St Cuthbert’s, Edinburgh, Midlothian (Extracted)
Lauchlan Carmichael born 01 Oct 1826 St Cuthbert’s, Edinburgh, Midlothian (Extracted)
Duncan Carmichael 20 May 1828 St Cuthbert’s, Edinburgh, Midlothian (Extracted)
Helen Halliday Carmichael 31 Mar 1830 St Cuthbert’s, Edinburgh, Midlothian (Extracted)
Janet Carmichael 30 Mar 1836 St Cuthbert’s, Edinburgh, Midlothian (Extracted)
Lauchlan Carmichael married Margaret Steel 20 Jun 1851 St Cuthbert’s, Edinburgh, Midlothian (Extracted)
In the 1841 census at Beaumont Cottage, Edinburgh
James Carmichael 60 b 1781 Scotland Cl Stamp & Tax Office
Margaret Carmichael 45 b 1796 Midlothian wife
Andrew Carmichael 15 b 1826 Midlothian Student of Medicine
Margaret Carmichael 15 b 1826 Midlothian
Helen Carmichael 10 b 1841 Midlothian
Janet Carmichael 5 b 1836 Midlothian
Alexander Carmichael 5 b 1836 Midlothian
It would appear that they have rounded all ages to nearest 5 not just 20 and over.
In the 1851 census at Mexborough Yorkshire,
Andrew H Carmichael 28 b 1824 Edinburgh General Practitioner
Margaret Carmichael 20 b 1831Edinburgh sister, should be 26
In the 1861 still at Mexborough, still unmarried,
Andrew H Carmichael 36 b 1825 Edinburgh General Practitioner
No other family with him.
In the 1871 England census at 17 Newgate St, Chester
Andrew H Carmichael 47 b 1824 Edinburgh, Physician & Surgeon
Maria Hancock 28 b 1843 Brample, Derbyshire Niece and House keeper
I can see where Andrew Halliday Carmichael went, but struggling with the rest. There are 2 IGI searches I did in North America.
Lachlan Carmichael married Christine McLean 21 Oct 1885 Buchanan, Missouri (Extracted)
Lachlan Alexander Carmichael b 03 Dec 1890 Green Leaf, Kansas m Annie Laurie Pelletier 27 Nov 1916 and died 22 Jun 1973
Not sure if they are connected but food for thought.
Tom