I do not see how the heliacal rising of Sirius in any one year could help them to determine its length.
Swart star: the Dogstar, called swarthy because its heliacal rising in ancient times occurred soon after mid-summer.
This was based upon the heliacal rising of Sirius (Sothis) coincident with the beginning of the inundation.
This period, measured thus by the heliacal rising of Sothis, is spoken of as the Sothic cycle.
The heliacal rising of a constellation is when it comes from under the rays of the sun, and begins to appear before daylight.
The dog days were so called because they coincided with the heliacal rising of Sirius or Canicula (the little dog).