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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
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Page 178
Reform of the Calendar
Of a kindred nature was the reform of the calendar. The republican calendar, which strangely enough was still the old decemviral calendar--an imperfect adoption of the -octaeteris- that preceded Meton (117)--had by a combination of wretched mathematics and wretched administration come to anticipate the true time by 67 whole days, so that e. g. the festival of Flora was celebrated on the 11th July instead of the 28th April.
117. Cf. III. III. Illyrian Piracy
Caesar finally removed this evil, and with the help of the Greek mathematician Sosigenes introduced the Italian farmer's year regulated according to the Egyptian calendar of Eudoxus, as well as a rational system of intercalation, into religious and official use; while at the same time the beginning of the year on the 1st March of the old calendar was abolished, and the date of the 1st January--fixed at first as the official term for changing the supreme magistrates and, in consequence of this, long since prevailing in civil life-- was assumed also as the calendar-period for commencing the year. Both changes came into effect on the 1st January 709, and along with them the use of the Julian calendar so named after its author, which long after the fall of the monarchy of Caesar remained the regulative standard of the civilized world and in the main is so still.
By way of explanation there was added in a detailed edict a star-calendar derived from the Egyptian astronomical observations and transferred--not indeed very skilfully--to Italy, which fixed the rising and setting of the stars named according to days of the calendar.(118) In this domain also the Roman and Greek worlds were thus placed on a par.
118. The identity of this edict drawn up perhaps by Marcus Flavius (Macrob. Sat. i. 14, 2) and the alleged treatise of Caesar, De Stellis, is shown by the joke of Cicero (Plutarch, Caes. 59) that now the Lyre rises according to edict.
We may add that it was known even before Caesar that the solar year of 365 days 6 hours, which was the basis of the Egyptian calendar, and which he made the basis of his, was somewhat too long. the most exact calculation of the tropical year which the ancient world was acquainted with, that of Hipparchus, put it at 365 d. 5 h. 52' 12"; the true length is 365 d. 5 h. 48' 48".
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Reference address : https://www.ellopos.net/elpenor/rome/5-11-old-republic-new-monarchy.asp?pg=178
