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
Colleges of Sacred Lore
There was thus enough of priesthood and of priests in Rome. Those, however, who had business with a god resorted to the god, and not to the priest. Every suppliant and inquirer addressed himself directly to the divinity--the community of course by the king as its mouthpiece, just as the -curia- by the -curio- and the -equites-by their colonels; no intervention of a priest was allowed to conceal or to obscure this original and simple relation. But it was no easy matter to hold converse with a god.
The god had his own way of speaking, which was intelligible only to the man acquainted with it; but one who did rightly understand it knew not only how to ascertain, but also how to manage, the will of the god, and even in case of need to overreach or to constrain him. It was natural, therefore, that the worshipper of the god should regularly consult such men of skill and listen to their advice; and thence arose the corporations or colleges of men specially skilled in religious lore, a thoroughly national Italian institution, which had a far more important influence on political development than the individual priests and priesthoods.
These colleges have been often, but erroneously, confounded with the priesthoods. The priesthoods were charged with the worship of a specific divinity; the skilled colleges, on the other hand, were charged with the preservation of traditional rules regarding those more general religious observances, the proper fulfilment of which implied a certain amount of knowledge and rendered it necessary that the state in its own interest should provide for the faithful transmission of that knowledge. These close corporations supplying their own vacancies, of course from the ranks of the burgesses, became in this way the depositaries of skilled arts and sciences.
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Reference address : https://www.ellopos.net/elpenor/rome/1-12-religion.asp?pg=16