Thank you for getting in touch. I did know about the three children born to John Gardner and Janet Black. What happened to Janet after John's death ? Did she remarry ?
What you have found is my first post about this family which brought in no response. I therefore reposted in May 2014 and this second post brought in a great deal of helpful information, particularly about Agnes Gardner (your g g grandfather's sister). Agnes and her husband, William Wilson, did not in fact emigrate, as I had thought, although some of their children probably did. Agnes died in Wishaw in 1911.
Your g g grandfather also had a half-sibling. After Mary Taylor's death in childbirth in 1856, John Gardner married Margaret Dunbar and they had a daughter, Anne Gardner.
If you are interested in knowing more, I can PM you once I have excavated my notes and put them in order (may take a little time !)
All good wishes,
Margow