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
The earliest chant, in the view of the Romans, was that which the leaves sang to themselves in the green solitude of the forest. The whispers and pipings of the "favourable spirit" (-faunus-, from -favere-) in the grove were reproduced for men, by those who had the gift of listening to him, in rhythmically measured language (-casmen-, afterwards -carmen-, from -canere-).
Of a kindred nature to these soothsaying songs of inspired men and women (-vates-) were the incantations properly so called, the formulae for conjuring away diseases and other troubles, and the evil spells by which they prevented rain and called down lightning or even enticed the seed from one field to another; only in these instances, probably from the outset, formulae of mere sounds appear side by side with formulae of words.(3)
3. Thus Cato the Elder (de R. R. 160) gives as potent against sprains the formula: -hauat hauat hauat ista pista sista damia bodannaustra-, which was presumably quite as obscure to its inventor as it is to us. Of course, along with these there were also formulae of words; e. g. it was a remedy for gout, to think, while fasting, on some other person, and thrice nine times to utter the words, touching the earth at the same time and spitting:--"I think of thee, mend my feet. Let the earth receive the ill, let health with me dwell" (-terra pestem teneto, salus hie maneto-. Varro de R. R. i. 2, 27).
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Reference address : https://www.ellopos.net/elpenor/rome/1-15-art.asp?pg=4