PETIN M.I.

The PETIN - METON calendar

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`Contents - http://Petin1Mikhail.narod.ru/index.htm                 `
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`                   The accuracy of the PETIN-METON Calendar `
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3. The results of calculations (Part 3).

3.3. For the summands L and s , b,  cycles M1-M4  of compensation, 855-year cycle (see item 2.5 which have been mentioned above) misalignment dT are accordingly equal to

for:

-  L :            dT =  -0,3116935 day,

-  s :            dT = +0,6883071 day,

-  b :            dT =  -0,3116935 + 0,6883071 + (-0,3116935) = 0,0649201 day,

-  M1 cycle:                        dT = + 0,0649201 day,

-  M2 cycle:                        dT = + 0,0778271 day,

-  M3 cycle:                        dT = - 0,1560935 day,

-  M4 cycle:                        dT = - 0,0003851 day,

-  855-year cycle:               dT = - 0,0261991 day.

3.4. For compensation of the accumulated residual misalignments of base cycles the following cycles are packed in the calendar:

-  for combinations M1 - M4 (see item 2.5 above):

- cycle M5 = 1463 x 260 = 380 380 lunar years.

-  for combinations 1 ¢ 3:

- cycle P3 =       304 x 24 + L = 7 315 lunar years,

- cycle P4 = 52 [ 304 x 24 + L ] = 380 380 lunar years.

-  for combinations 4 - 9 :

- cycle ą5 = 855 § 38 = 32 490 lunar years, in which

in 16 250-th lunar year Month 12 has 29 instead of 30 days.

3.5. The rules of the misalignment compensation of calendar lunar cycles with natural cycles are formulated as follows (for example, for combinations M1-M4, 1-3,  4 and 7 in item 2.5):

Combination M1¢M4:      Duration of Month 12 is equal to 30 days in  1, 5, 9, 13-th years

of each Meton cycle, but:

-                                                     - 29 days - in 57n + 20-th year of  each 361-year  M2 cycle

in each 741-year M3 cycle of each 1463-year M4 cycle

(where:  n - integers from 0 up to 5,

M1 - M4 cycles  - Petin cycles);

Combination 1-3: Duration of Month 12 is equal to 30 days in  1, 5, 9, 13-th years of each Meton cycle, but:

- 29 days - in 57n + 20-th year of each 57-year M1 cycle of each 304-year  Hipparh cycle,

(where:  n - integers from 0 up to 4);

See also the formula:  52{24[5(L+s+L) +L] +L}=380 380 lunar years.

Combination 4: Duration of Month 12 is equal to 30 days 1, 5, 9, 13-th years of each Meton cycle, but:

- 29 days - in 57n+20 years of each 304-year Hipparh cycle in each 855-year cycle B

(where:  n - integers from 0 up to 4);

- 29 days - in 16 250-th year of each 32 490-year cycle C (B, C - Petin cycles).

Combination 7: Duration of Month 12 is equal to 30 days 1, 5, 9, 13-th years of each Meton cycle, but:

- 29 days - in 1-st year of each 57-year cycle A in each 418-year cycle D;

- 30 days - in 400-th year of each 418-year cycle D,

- 30 days - in 837-th year of each 855-year cycle B,

- 29 days - in 16 250-th year of each 32 490-year cycle C (A, B, C, D - Petin cycles).

3.6. The misalignment ranges for the combinations 1 - 9  (see item 2.5 above) and the misalignment values at the end of cycles are equal to:

The misalignment                   dT, day

range, day

Cycle  L (years SimpleM1 ¢ M19)             =  -1,1058 -  +0,3670          !  -0,3117       ,

½      s (years LeapM1  -   M19)             =   -0,1058 -  +1,3659          !  +0,6883       ,

½      b (57 lunar years)                            =  -1,1058 -  +1,0542          !  +0,0649       ,

Cycle M2 (  361 lunar years)               =  -1,1058 -  +1,0542          !  +0,0778       ,

Cycle M3 (  741 lunar years)               =  -1,1058 -  +1,4566          !  - 0,1561

Cycle M4 (1463 lunar years)               =  -1,2619 -  +1,4566          !  - 0,00038     ,

Cycle M5 (380380 lunar years)           =  -1,3616 -  +1,4566          !  - 0,1001      ,

Cycle 2 (   304 lunar years)               =  -1,1058 -  +1,3139          !  +0,0129       ,

Cycle  24§═2 (7315 lunar years)         =  -1,1058 -  +1,6107          !  +0,0019       ,

Cycle  77§═2 (380380 lunar years)     =  -1,2040 -  +1,6107          !   -0,1001       ,

3.7. The combinations M1-M4 and 1-3 have the best accuracy (the least misalignment range) and symmetry of misalignment concerning the mean natural lunar cycle.

3.8. On the basis of the calculations executed according to the variant - the combinations 1-3 ¢ the auxiliary tables are made and the examples of some calculations with the use of the PETIN-METON calendar are given:

Tables 3 - 5 -

Examples V-VI -

Examples VII - VIII -

Examples IX - X -

Example XI -    etc.

Note.  The materials of variants - the combinations M1-M4,  4 and 7 - are being executed for publication in the Internet.

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