John Hay was born 10 Apr 1810 at Seaton, a farm NE of Arbroath, and christened 3 May 1810 in Inverkeilor, son of John Hay and Janet Doig. There is no marriage of record and no other children listed which ususally indicates the child is illegitimate. I suggest you check the original parish records (available through LDS Family History Centers) which should list if child is "lawful" or "natural", the later indicating illegitimate. There may also be witnesses, places of residence, etc. There is more on the Doig family at www.doig.net.