Please note that Mommsen uses the AUC chronology (Ab Urbe Condita), i.e. from the founding of the City of Rome. You can use this reference table to have the B.C. dates
From: The History of Rome, by Theodor Mommsen
Translated with the sanction of the author by William Purdie Dickson
We have already stated how the army of aggression, the "gathering" (-legio-), was formed. In the tripartite Roman community it consisted of three "hundreds" (-centuriae-) of horsemen (-celeres-, "the swift," or -flexuntes-, "the wheelers") under the three leaders-of-division of the horsemen (-tribuni celerum-)(10) and three "thousands" of footmen (-milties-) under the three leaders-of-division of the infantry (-tribuni militum-), the latter were probably from the first the flower of the general levy.
10. Among the eight ritual institutions of Numa, Dionysius (ii. 64) after naming the Curiones and Flamines, specifies as the third the leaders of the horsemen (--oi eigemones ton Kelerion--). According to the Praenestine calendar a festival was celebrated at the Comitium on the 19th March [adstantibus pon]tificibus et trib(unis) celer(um). Valerius Antias (in Dionys. i. 13, comp. iii. 41) assigns to the earliest Roman cavalry a leader, Celer, and three centurions; whereas in the treatise De viris ill. i, Celer himself is termed -centurio-.
Moreover Brutus is affirmed to have been -tribunus celerum- at the expulsion of the kings (Liv. i. 59), and according to Dionysius (iv. 71) to have even by virtue of this office made the proposal to banish the Tarquins. And, lastly, Pomponius (Dig. i. 2, 2, 15, 19) and Lydus in a similar way, partly perhaps borrowing from him (De Mag. i. 14, 37), identify the -tribunus celerum- with the Celer of Antias, the -magister equitum- of the dictator under the republic, and the -Praefectus praetorio- of the empire.
Of these-the only statements which are extant regarding the -tribuni celerum- --the last mentioned not only proceeds from late and quite untrustworthy authorities, but is inconsistent with the meaning of the term, which can only signify "divisional leaders of horsemen," and above all the master of the horse of the republican period, who was nominated only on extraordinary occasions and was in later times no longer nominated at all, cannot possibly have been identical with the magistracy that was required for the annual festival of the 19th March and was consequently a standing office.
Laying aside, as we necessarily must, the account of Pomponius, which has evidently arisen solely out of the anecdote of Brutus dressed up with ever-increasing ignorance as history, we reach the simple result that the -tribuni celerum- entirely correspond in number and character to the -tribuni militum-, and that they were the leaders-of-division of the horsemen, consequently quite distinct from the -magister equitum-.
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Reference address : https://www.ellopos.net/elpenor/rome/1-05-original-constitution-rome.asp?pg=20