Discovered in 1872, these two marble reliefs (plutei Trajani), which now are shelted inside the Curia, date from the time of Hadrian. The one on the right commemorates Trajan's program of food relief (alimenta) for children of the poor. The emperor sites in a draped chair on a low platform (suggestum), his foot on a stool, and is approached by the allegorical figure of a woman with a child in her arm and leading another by the hand. On the other half of the relief, a figure stands on a rostrate platform (the beak of a ship can be seen), addressing an assembly who lift their hands in acclamation.
"Moreover, he [Hadrian] used every means of gaining popularity. He remitted to private debtors in Rome and in Italy immense sums of money owed to the privy-purse, and in the provinces he remitted large amounts of arrears; and he ordered the promissory notes to be burned in the Forum of the Deified Trajan, in order that the general sense of security might thereby be increased. He gave orders that the property of condemned persons should not accrue to the privy-purse, and in each case deposited the whole amount in the public treasury. He made additional appropriations for the children to whom Trajan had allotted grants of money."
Historia Augusta, Hadrian (I.7.5-8); also Dio (LXIX.8.1)
The relief on the left depicts the burning of records (syngraphae, written acknowledgments of debt) from the Tabularium in a remission of tax debt, probably by Hadrian in AD 118, who remitted nine hundred million sesterces owed the State (although after the conquest of Dacia, Trajan also forgave debt, cf. Pliny the Younger, Panegyric, XXXVII.1ff). Here, the top part of the middle and the end block are missing, and only a portion of the suggestum can be seen. On the back of both reliefs, the three animals of the suovetaurilia, the sow, sheep, and bull (sus, ovis, and taurus), are shown garlanded and with a broad girdle over the backs of the sow and bull.
Because the reliefs were found in an area of the Forum Romanum thought to be the location of the statue of Marsyas and the Ficus, Olea, Vitis, and both depict Marsyas beside a fig tree (the Ficus Ruminalis), it has been argued that the reliefs enclosed that plot of ground. Or the base of the tree may not represent an enclosure but be the pedestal for its statue, in which case the plutei may have adorned the ends of the Rostra, even though their size would not seem appropriate for that location.
Symbolic of the Forum Romanum, the figure of Marsyas and the Ficus Ruminalis provide a point of reference for its topography. On the left-hand relief, the fig tree precedes the figure of Marsyas, with the arcades of the Basilica Julia in the background. An empty space represents the Vicus Jugarius, then the Temple of Saturn (as can be discerned by its Ionic capitals) and the Temple of Vespasian and its Corinthian order. Between the two is an arch, which likely is from the loggia of the Tabularium. The missing end section may have shown the Temple of Concord.
On the right-hand relief, the order is reversed and Marsyas is shown first. Now, one is looking in the opposite direction. From this perspective, the Basilica Julia is again represented, with a gap in the relief corresponding to the Vicus Tuscus, which ran between the basilica and the Temple of Castor and Pollux, which is shown next. Finally, there is the Arch of Augustus and the rostra in front of the Temple of Divine Julius.
Reference: "The 'Trajan-Reliefs' in the Roman Forum" (1901) by Anna Spalding Jenkins, American Journal of Archaeology, 5(1), 58-82. The article provides an early overview of the reliefs but stumbles when the rostrate platform (Rostra Julia) in the relief is identified as the one completed by Augustus (Rostra Augusti). This obliges the author to assume that the Basilica Aemilia is represented in the right-hand relief, with the Curia and an unknown arch next to it. Rather, it is the Basilica Julia that is depicted in both cases. See "The So-Called Balustrades of Trajan" (1910) by Jesse Benedict Carter, American Journal of Archaeology, 14(3), 310-317.
