As James MATTHEWS was a Coal Miner, on the 1871 census, working at the Steam Mills .... he probably moved briefly for work - (with or without his family at times)
On the Census, Lysias place of birth, is Hafod Side, Glamorgan. ***
There is on Google, information of Hafod Copperworks etc
Lysias William MATTHEWS - on the GRO Index he has been transcribed as Lynas William MATTHEWS - mother's maiden name SLADEN - and was registered: Jan/Feb/March Qtr 1868 Pont Y Pridd, Volume 11A and Page 310.
The birth certificate would give their address, father's occupation, mother's maiden name etc.
James MATTHEWS and Rebecaa Elizabeth Harriet (nee SLADEN) - had 4 children christened on the same day at Drybrook i.e. 25 February 1871
Elizabeth Olivia Louisa MATTHEWS - mother's maiden name listed as SLADIN - M Qtr 1864, Westbury on Severn
Alonza James MATTHEWS - M Qtr - 1866, Westbury on Severn
Lionel Agustus MATTHEWS - M Qtr, 1870 Westbury on Severn
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Using the Advance Search, there are various baptism on the records, where the parents are living in Glamorgan.