It points to St. Audoen's Church (as a side note, you can see video of the church here: http://tr.im/ECauhttp://tr.im/ECau ) as being the location of Hugh and Mary Ann Hamilton's (MAH) wedding on February 10th, 1763. I'm fairly new to this, so bare with me.
I looked at William's file there and come up with this: http://is.gd/4R3pShttp://is.gd/4R3pS that lists William's mother as: Mary Ann McCullough (MAM). I've often seen references to a Mary Burns as well( http://is.gd/4R8vzhttp://is.gd/4R8vz ), for example.
The marriage date, if correct, would give a starting point. I'm working with extremes in marriage and birth ages first.Even in those days I don't think a child younger than ten would be likely to get married. If we go with the wedding date of Hugh to MAH, that would make MAH born in 1753. Let's say she was able to bare children until she was 50. Any children over 1803 aren't hers.
I've seen in places where Mary's said to be born in 1770, but had kids in 1775. If the age time-line I'm going with here (and I know it's based on a lot of assumptions, but they are reasonable ones) is correct, if MAM was born in 1770, she'd only have been 39 when Mary Elizabeth was born (Hugh and MAH's last child).
But I don't think If you're STILL with me, looking at the time-line of births, there's a gap between Isabel and William of 7 years. It seems to stick out like a sore thumb given the rhythm of births before and after. If MAH died between Isabel and William (a middle point would be 1791), MAM would have been 20 and Hugh would have been 48. At the birth of their last child, Samuel, she would have been 44 years old and Hugh would have been 70.
Thoughts? Holes in my theory? Opinions? All are welcomed.