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A heliacal rise of Sirius was recorded by Censorinus as having happened on the Egyptian New Year's Day between 140-142.
Thus he was able to compare the day on which Sirius rose in the Egyptian calendar to the day on which Sirius ought to have risen in the Julian calendar, count the number of intercalary days needed, and determine how many years were between the beginning of a cycle and the observation.
The slow rate of change from this value is also of note.
If observations and records could have been maintained during predynastic times the Sothic rise would optimally return to the same calendar day after 1461 calendar years.
If the axis swings the observer closer to the event its observational year will be shortened.
This observation was almost certainly made at Itj-Tawy, the Twelfth Dynasty capital, which would date the Twelfth Dynasty from 1963 to 1786 The Sothic cycle is a specific example of two cycles of differing length interacting to cycle together, here called a tertiary cycle.
The length of time for a star to make a yearly path can be marked when it rises to a defined altitude above a local horizon at the time of sunrise.
This altitude does not have to be the altitude of first possible visibility.
The first is the aforementioned ivory tablet from the reign of Djer which supposedly indicates the beginning of a Sothic cycle, the rising of Sirius on the same day as the new year.
If this does indicate the beginning of a Sothic cycle, it must date to about 17 July 2773 However, this date is too late for Djer's reign, so many scholars believe that it indicates a correlation between the rising of Sirius and the Egyptian lunar calendar, instead of the solar civil calendar, which would render the tablet essentially devoid of chronological value.
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This cycle was first noticed by Eduard Meyer in 1904, who then carefully combed known Egyptian inscriptions and written materials to find any mention of the calendar dates when Sirius rose at dawn.