Griffith's birthplace in Wales, Merthyr Tydfil, was a booming industrial town which, at the time, was a part of the historic county of Glamorgan.

He was instructed in elementary subjects by a private teacher and subsequently graduated from Allegheny College in Meadville, Pennsylvania.

At the age of fifty-six, he campaigned as a Democrat to represent his congressional district and was elected to the 42nd United States Congress in November 1870.

After an unsuccessful reelection campaign in 1872, he resumed law practice in Mercer.

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