From whiteout7's earlier mention of a possible 1881 census entry in the Shetlands, this looks to be the family's entry:
John James Hamilton 51, mine manager b. Kirkcudbright
Mary Hamilton 39 b. Brazil
Mary H Hamilton 17 b. Chile
Ellen Hamilton 14 b. Chile
George Hamilton 12 b. Chile
...and two house servants
Address: Leebitton, Dunrossness, Shetland
No sign of a John born 1870 here

Monica
PS: This is the official pay to view site for Scottish BMDs
www.scotlandspeople.gov.uk There are no M*cHamilton BMDs entries showing on it.