In case the 1871 is the correct family:
In 1851:
Tanllidart, Elerch
Isaac Richards, 30, miner
Sophia Richards, 22
Both born Llanbadarnfawr
HO107/2486/9/10
In 1861:
Lleustnewydd, Tyrymynach
Isaac Richards, 40, lead miner, ore dresser and farmer of 40 acres
Sophia Richards, wife, 33, miner's wife
Elizabeth Anne Ricahrds, daughter, 9
Isaac Richards, son, 7
Josiah Richards, son, 6,
Sophia Richards, daughter, 3, b. Llanfihangel geneur glyn
Elinor Winifred Richards, daughter, 1, b. do
All but Sophia and Elinor b. llanbadarnfawr
RG9/4197/9/12
In 1881 :
Penybontchydybeddau (?), Trefeirig
Isaac Richards, 60, formerly lead ore dresser.
Sophia Richards, wife, 53, miner's wife
Josiah Richards, son, 26, lead miner
Evan M Richards, son, 15, lead ore dresser
All b. Llanbadarnfawr
RG11/5449/103/8
Marriage:
Dec q, 1847, Aberystwyth vol 27 p 36
Isaac Richards and Sophia Morgans on the same page
gnu