Hi Siani,
I looked at the 1841 census for Kerry and was unable to find Arthur. I could only find one Thomas Williams who had a wife named Ann...........
HO107/1439/6, Upper Kerry, Enumeration Dist 3, page 5
The address appeared to be Cutsoid Commune but was badly written, faint and partially obscured

All surnames Williams, all born in county apart from Ann
Thomas, 45, Ag Lab
Ann, 45
David, 10
Catharina, 8
Pryce, 6
Sarah, 2............Not much help I'm afraid.
The plot thickens with the 1851 census HO107/2497, folio 58, page1, Kerry Parish. All surnames Williams, address Goitre Hall (sounds painful)
Arthur, h, m, Ag Lab, MGY Kerry
Mary, w, m, 30, MGY Kerry
George, s, 3, MON Bedwallte (how strange)
Thomas, s, 3 (yes 3), MGY Kerry
Edward, s, 3mths................
Then in 1861, RG9/4249, folio 27, page 1, Kerry
All surnames Williams, address Kerry Village
Arthur, h, m, 37, Labourer, MGY Carno
Mary, w, m, MGY Llandyssil
Edward, s, 10, MGY Kerry
Ann, d, 8, MGY Kerry............seems like more errors
The enumerators don't seem to be consistent or there was more than one family.
I looked in Carno in the 1841 for Arthur and his family but no joy. The 1881 gives Kerry as Athur's birthplace.
I have Trows in my family but from the Welshpool/Berriew area. I'm trying to trace Joseph Trow a butcher whose daughter Jane was born about 1836 in Berriew.
Cheers Dave
