Hi John -- and welcome to the thread!
I am interested by the fact that you found an abstract of the will of Thomas Williams of Arddwyfaen on the National Archives website. Would you mind sharing a link to the relevant page, or at least specifying where on that huge site you located it? As will abstracts are not often to be found there, I am wondering whether it lies within a broader collection of relevant papers that I ought to know about!
I am assuming that the will concerned is the one that was proved in 1806 at the Diocese of St Asaph's Consistory Court, but correct me if I have that wrong.
Other readers of this thread may wish to be aware that the full original text of the 1806 will is available free online via The National Library of Wales's website -- and this is the direct hypertext link:http://hdl.handle.net/10107/83306
As will be seen via that link, the abstract you saw -- if about the same will -- seems to have omitted the names of three other children who were bequeathed only token legacies, probably indicating that they were older than the others and had already been provided for during the testator's lifetime (presumably on marriage). They were called William, Cadwalader and Elizabeth.
I see that the two photo links that I posted above (on 19 Nov. 2011) were broken. Now repaired.