Again, we have 7,200 to count forward from the known coefficient, in this
case 13 (the coefficient of the ending day of the second katun). But we
have seen above that if we deduct all the 13s possible from 7,200 there
will be a remainder of 11; consequently this remainder 11 must be added to
13, the known coefficient. 13 + 11 = 24; but since this number is above 13,
we must deduct 13 from it in order to find out the resulting coefficient.
24 - 13 = 11, and 11 is the coefficient of the ending day of the third
katun in Table IX. By applying the above rule, all of the coefficients of
the ending days of the katuns could be shown to follow the sequence
indicated in Table IX. And since the ending days of the katuns determined
their names, this same sequence is also that of the katuns themselves.
The above table enables us to establish a constant by means of which we can
always find the name of the next katun. Since 7,200 is always the number of
days in any katun, after deducting all the 13s possible the remainder will
always be 11, which has to be added to the known coefficient to find the
unknown. But since 13 has to be deducted from the resulting number when it
is above 13, subtracting 2 will always give us exactly the same coefficient
as adding 11; consequently we may formulate for determining the numerical
coefficients of the ending days of katuns the following simple rule:
Subtract 2 from the coefficient of the ending day of the preceding katun in
every case. A glance at Table IX will demonstrate the truth of this rule.
Public-domain text, read in full here on John Shaqi.
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