The latest Burke’s Peerage (of 2003) has the first wife of Richard Bourke as a dau. of Murrough O’Madden and which lady they state to be the mother of the first earl.  CP in vol III pub 1913, clearly states that the mother of the first earl was Margaret Butler, the second wife according to Burke.  The CP Corrigenda volume of 1998 has no correction, nor are there any corrections to this on Chris Phillips’ web-site, www.medievalgenealogy.org.uk/cp/ .  I will allow that a slight question mark is under this crucial part of the Hamilton ancestry and would like to find some further confirmation.