Hi again Beckey,
I think I have found your family in 1841.

Ancestry have the name transcribed as
Brown, but FreeCen have decided on
Burns.
Residence: Bambury Close, High Street, Dunbar
James Brown, m, 25, labourer, outside county
Mary, f, 25, -, outside county
Robert, m, 6, -, East Lothian
Adam, m, 4, -, East Lothian
Mary, f, 1, -, East Lothian
hume24