In chap. 45 of the Decline and Fall, when Tiberius is made Augustus 4 years before the death of Justin II, Gibbon's marginal note reads "Association of Tiberius, A.D. 574". As far as I've been able to determine, all editions use the word 'association', but I suspect it may be a misprint for 'accession'. Is this a misprint -- perhaps a misreading of Gibbon's MS -- or a technical (or rare) use of 'association'?
Gibbon uses the word association a lot, in many ways. One sense he uses is listed in my OED as sense 6: "Law. The appointment of additional legal officials to act as colleagues on any occasion; the writ appointing them." (It lists citations from 1613 and 1809 books about the law.) Gibbon seems to use it in this sense in chap 48 part I (my emphasis):
Constantine, his eldest son, enjoyed in a mature age the title of Augustus; but the weakness of his constitution required a colleague and a guardian, and he yielded with secret reluctance to the partition of the empire. The senate was summoned to the palace to ratify or attest the association of Heracleonas, the son of Martina: the imposition of the diadem was consecrated by the prayer and blessing of the patriarch; the senators and patricians adored the majesty of the great emperor and the partners of his reign; and as soon as the doors were thrown open, they were hailed by the tumultuary but important voice of the soldiers. After an interval of five months, the pompous ceremonies which formed the essence of the Byzantine state were celebrated in the cathedral and the hippodrome; the concord of the royal brothers was affectedly displayed by the younger leaning on the arm of the elder; and the name of Martina was mingled in the reluctant or venal acclamations of the people. Heraclius survived this association about two years: his last testimony declared his two sons the equal heirs of the Eastern empire, and commanded them to honor his widow Martina as their mother and their sovereign.
and in chap 49 part V, about the successors of Charlemagne:
But the association of his son Lewis the Pious asserts the independent right of monarchy and conquest, and the emperor seems on this occasion to have foreseen and prevented the latent claims of the clergy. The royal youth was commanded to take the crown from the altar, and with his own hands to place it on his head, as a gift which he held from God, his father, and the nation. The same ceremony was repeated, though with less energy, in the subsequent associations of Lothaire and Lewis the Second: the Carlovingian sceptre was transmitted from father to son in a lineal descent of four generations; and the ambition of the popes was reduced to the empty honor of crowning and anointing these hereditary princes, who were already invested with their power and dominions.
So it seems reasonable to me that he uses it this way in chapter 45, to mean the official appointment of Tiberius to Caesar-hood. According to the all-knowing and infallible Delphic Oracle, Tiberius was made Caesar in 574 and Augustus in 578, which bears out the marginal note under my proposed interpretation. (Thanks to Joshua Engel for pointing this out.)