When the Roman calendar was expanded from 10 to 12 months, two months were added to accommodate the changes. This expansion took place around 713 BC when King Numa Pompilius added the months of January and February to the existing calendar.

The original Roman calendar, known as the Romulus calendar, had only 10 months and a total of 304 days. The months in this calendar were Martius, Aprilis, Maius, Junius, Quintilis, Sextilis, September, October, November, and December. However, this calendar did not align with the lunar cycles and needed adjustments.

King Numa Pompilius, the second king of Rome, recognized the need for a more accurate calendar system. He consulted with the high priest and added two months to the calendar to bring the total number of months to 12. January was named after Janus, the Roman god of doorways and beginnings, while February was named after Februa, a purification ritual held on February 15.

With the addition of these two months, the Roman calendar now had a total of 355 days, divided into 12 months. This new calendar, known as the Julian calendar, was more aligned with the solar year and allowed for more accurate timekeeping.

Despite these changes, the Roman calendar continued to undergo revisions over the centuries. In 46 BC, Julius Caesar introduced the Julian calendar, which included a leap year system to account for the extra quarter day in the solar year. This calendar remained in use until the Gregorian calendar was introduced in 1582.

In conclusion, the expansion of the Roman calendar from 10 to 12 months was a significant development in the history of timekeeping. The addition of January and February helped to align the calendar with the solar year and improve accuracy in tracking time. These changes laid the foundation for the modern calendar systems used today.

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