In Chapter eleven of A Companion to Roman Religion, "Religion and Roman Coins," Jonathan Williams says the earliest Roman coins, from the late fourth and early third century B.C., resembled their Greek counterparts in showing the head or profile bust of a god or goddess on the obverse and religious symbols on the reverse. Starting with the introduction of the denarius, in about 212 [sometime after 269, according to the Encyclopedic Dictionary of Roman Law, by Adolf Berger, "Denarius"; Transactions of the American Philosophical Society, New Series, Vol. 43, No. 2 (1953), pp. 333-809.] -- and then worth ten copper asses or four sestertii nummi -- the reverses of the denarii displayed action scenes. Almost a century later, in about 130, coins began to change annually, when Rome instituted a panel of new magistrates, the tres viri monetales (the board of three in charge of the mint).
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