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12. DEMONSTRATION OF THE 3RD MEAN MOTION AND SIDEREAL YEAR
The kaliyuga of 432000 years is the unit of reference for determining the length of the sidereal year in Hindu cosmological time cycles.

There are seven rotations of the 3rd mean solar motion, counted separately through the sidereal year, in 10000 sidereal years. For a single year the count is 0.2563795... diurnal revolutions of the Earth. For two years it is 2(0.2563795...). For a complete rotation there are

The integral part of this interval, 1428 years, summed 432000(7) times is equal to 14 manus (see Table III). Thus The fractional part of this interval, 4/7 years, summed 432000(7) times is equal to the introductory dawn (see Table III). Thus, Thus, 1428 4/7 weeks of kaliyugas = 1 kalpa.
2. This is the Sothic cycle of the Egyptians but with the difference that the cycle is reckoned using sidereal days instead of mean solar days. Calculate this cycle using any reasonably accurate determination of the sidereal year measured in sidereal days, e.g., Newcomb's 366.2564 sidereal days. Thus, 366.2564/.2564 = 1428.4571 sidereal years. Note that this is very nearly 10000/7. Now, the 3rd mean motion of the Sun used in Hindu cosmological time cycles may be found by solving (366 + x)/x = 10000/7, x = 0.2563795...
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