Replying on thread to an off-line message from Steph, for the avoidance of duplication of effort.
I was looking for birth records and anything else I can find on David and James.
As for birth records, the best you will get are baptism records, because civil registration didn't start until 1855.
You have David in 1841 aged 20, in a household whose head is Catherine, who I assume is his mother. Adults' ages in the 1841 census were supposed to be rounded down to the nearest 5 years, so he could have been any age from 20 to 24 and therefore born any time between 1816 and 1821. He wasn't born in Angus. However the two youngest children were: James, 13 and John, 8.
In the church records section of Scotland's People (SP) there are baptisms of James Adam, parents David Adam and Catherine Scoone, on 18 November 1827 and John, parents David Adam and Catherine Scone, on 23 September 1832, both in Dundee, who exactly match the census. There is also a Mary Simmers Adam, baptised 10 May 1830, who presumably died young.
There's a marriage of David Adam to Katherine Skene in Alyth, Perthshire, on 10 December 1815, and baptism of James to David Adam and Catharine Skeen in Dundee on 24 July 1825.
There are burials in the Howff Burial Ground in Dundee of
- John Adam on 23 April 1847, son of David Adam, weaver, Smalls Wynd
- Isabella Adam, 91, born Kinnoull, on 12 April 1850, widow of Adam Caird, Shipmaster, Smalls Lane, Smalls Wynd
- James Adam, aged 4 months, on 26 January 1853, son of
James Adam, blacksmith, Smalls Wynd - I do not know if this James is related or not.
However I don't see a burial of either David Adam or of Catherine Scone/Skene or Adam. Check for yourself at
http://www.fdca.org.uk/pdf%20files/HowffA01.pdf just in case I missed them.
From the statutory records of deaths on SP, James Adam, mother's maiden name Scone, died in Dundee in 1863 aged 36. Isabella Adam, other surname David, mmn Skene, died in Dundee in 1895 aged 76. Catherine Skene or Adam, 73, died in Dundee in 1860.
In the 1851 census in Dundee are Catherine Adams, aged 64, born Dundee and her son James, 22, also born in Dundee.
Isabell Adam married Peter David in Dundee on 1 September 1841. In the 1871 census Peter David, mason and his wife Isabella, 52, born Auchterarder, Perthshire, are in Dundee with four of their children.
All this is from transcriptions and indexes. The original documents, and more, can be viewed and downloaded at SP - select Search our records > Advanced People Search and then the type of record you want to see.