The first Coke-Smyth was artist John Richard Coke Smyth (the hyphen was brought in by the next generation) perhaps best known for his water colours of Canada which he visited in 1838 as Drawing Master to the daughters of Governor General, the Earl of Durham. These have sometimes been mistakenly ascribed to WH Bartlett as a result of forgery discovered by The Royal Ontario Museum which houses the originals.
Coke Smyth produced many historical dress water colours including ones of those who attended Queen Victoria's Silver Jubilee fancy dress ball, which can be seen in the Victoria & Albert Museum in London. He did various sketches and water colours around Europe and particularly Turkey. The sketch above is of himself and contemporaries.
In the background history of the family, the interest is rather more in connections than direct ancestry. This is no doubt just as well in view of the extent to which males lines have come to a halt down the centuries. In an age where feminism is bringing the family matriarchs out of the shadows and into the forefront on an equal basis, for most at least, male primogeniture is unfamiliar and less relevant. The attached family tree carries two strands: the paternal coke Smyth lines and the maternal Crowe line.
The latter also has its artistic members including the better known Eyre Crowe ARA (1824-1910) covered by the excellent site of Kathryn J Summerwill at http://eyrecrowe.com/.
Some pictures from the Crowe side of the family can be found by following the Crowe pictures link.