James Adam and Janet Shedden lived in the Parish of Beith, Ayrshire, The Isle of Lewis and Edinburgh. Three of their children emigrated to New Zealand (James, Elizabeth and John).
This family is of interest because ancestry.co.uk has found a DNA match between a descendant of Janet and James Adam's Son, John Shedden Adam, and a descendant of Alexander Hall Shedden from Trivandrum in South East India.
So far, I have not been able to find any documentation to prove the connection.
The most credible source of information I have found regarding John Shedden and Barbara Wilson comes from the Memoir of William Wilson of Crummock.
Some of the dates in the memoir can be confirmed from the Old Parish records of Scotland available at scotlandspeople.gov.uk
I copy below extracts from that memoir:
Janet (Shedden), born 28th March 1788; married, 10th August 1807, James Adam, W.S., and factor on the Drummond estates in Perthshire. Mr Adam gave up the factorship, and, on his own account, entered into extensive speculations and improvements in land in his native parish of Lochwinnoch, which financially proved disastrous. He afterwards for a time became factor in Lewis for Mackenzie of Seaforth, but ultimately resided and practised as W.S. in Edinburgh.
A man of considerable originality, he invented the screw propeller, and, along with his son James, experimented successfully on a fishing boat at Leith. In 1832, the result was laid before the Admiralty as being an invention eminently adapted for moving ships of war, but it was not approved of. Unfortunately Mr Adam took out no patent for his invention, which was afterwards applied for by, and granted to, Francis Potter Smith, of Hendon, in 1836. The correspondence between Mr Adam and the Board of Admiralty was printed in pamphlet form by Ballantyne & Hughes, Edinburgh, circa 1837.
Mr and Mrs Adam had surviving issue:
Mr Adam died in Edinburgh on 3rd December 1849, and Mrs Adam in 1863