Chapter IX: Part 9

+-----------------------------------------------------------------------------------------+ | A TABLE of the Equation of natural Days, shewing what Time it ought to | | be by the Clock when the Sun is on the Meridian. | +-----------------------------------------------------------------------------------------+ | The first after Leap-year. | +----+--------+----+--------+----+---------+----+--------+----+--------+----+--------+----+ |Days| July |Dif.| August |Dif.|September|Dif.| October|Dif.|November|Dif.|December|Dif.| | +--------+----+--------+----+---------+----+--------+----+--------+----+--------+----+ | |H. M. S.| S. |H. M. S.| S. | H. M. S.| S. |H. M. S.| S. |H. M. S.| S. |H. M. S.| S. | +----+--------+----+--------+----+---------+----+--------+----+--------+----+--------+----+ | | |Inc.| |Dec.| |Dec.| |Dec.| |Dec.| |Inc.| | 1 |12 3 15| |12 5 48| |11 59 38 | |11 49 33| |11 43 49| |11 49 36| | | | | 12 | | 4 | | 19 | | 19 | | 0 | | 24 | | 2 |12 3 27| |12 5 44| |11 59 19 | |11 49 14| |11 43 49| |11 50 0| | | | | 11 | | 5 | | 19 | | 19 | |Inc.| | 24 | | 3 |12 3 38| |12 5 39| |11 59 0 | |11 48 55| |11 43 49| |11 50 24| | | | | 11 | | 5 | | 19 | | 18 | | 1 | | 25 | | 4 |12 3 49| |12 5 34| |11 58 41 | |11 48 37| |11 43 50| |11 50 49| | | | | 10 | | 6 | | 20 | | 17 | | 2 | | 25 | | 5 |12 3 59| |12 5 28| |11 58 21 | |11 48 20| |11 43 52| |11 51 14| | +----+--------+ 10 +--------+ 6 +---------+ 20 +--------+ 17 +--------+ 3 +--------+ 26 + | 6 |12 4 9| |12 5 22| |11 58 1 | |11 48 3| |11 43 55| |11 51 40| | | | | 10 | | 7 | | 20 | | 17 | | 3 | | 26 | | 7 |12 4 19| |12 5 15| |11 57 41 | |11 47 46| |11 43 58| |11 52 6| | | | | 10 | | 7 | | 20 | | 17 | | 4 | | 27 | | 8 |12 4 29| |12 5 8| |11 57 21 | |11 47 29| |11 44 2| |11 52 33| | | | | 9 | | 8 | | 20 | | 16 | | 5 | | 27 | | 9 |12 4 38| |12 5 0| |11 57 1 | |11 47 13| |11 44 7| |11 53 0| | | | | 8 | | 9 | | 20 | | 15 | | 6 | | 27 | | 10 |12 4 46| |12 4 51| |11 56 41 | |11 46 58| |11 44 13| |11 53 27| | +----+--------+ 8 +--------+ 9 +---------+ 20 +--------+ 15 +--------+ 7 +--------+ 28 + | 11 |12 4 54| |12 4 42| |11 56 21 | |11 46 43| |11 44 20| |11 53 35| | | | | 8 | | 10 | | 21 | | 14 | | 8 | | 28 | | 12 |12 5 2| |12 4 32| |11 56 0 | |11 46 29| |11 44 28| |11 54 23| | | | | 8 | | 10 | | 21 | | 13 | | 9 | | 29 | | 13 |12 5 10| |12 4 22| |11 55 39 | |11 46 16| |11 44 37| |11 54 52| | | | | 7 | | 11 | | 21 | | 13 | | 10 | | 29 | | 14 |12 5 17| |12 4 11| |11 55 18 | |11 46 3| |11 44 47| |11 55 21| | | | | 6 | | 11 | | 21 | | 13 | | 11 | | 29 | | 15 |12 5 23| |12 4 0| |11 54 57 | |11 45 50| |11 44 58| |11 55 50| | +----+--------+ 6 +--------+ 12 +---------+ 21 +--------+ 13 +--------+ 12 +--------+ 30 + | 16 |12 5 29| |12 3 48| |11 54 36 | |11 45 37| |11 45 10| |11 56 19| | | | | 5 | | 12 | | 21 | | 12 | | 13 | | 30 | | 17 |12 5 34| |12 3 36| |11 54 15 | |11 45 25| |11 45 23| |11 56 49| | | | | 5 | | 13 | | 21 | | 11 | | 13 | | 30 | | 18 |12 5 39| |12 3 23| |11 53 54 | |11 45 14| |11 45 36| |11 57 19| | | | | 4 | | 13 | | 21 | | 11 | | 14 | | 30 | | 19 |12 5 43| |12 3 10| |11 53 33 | |11 45 3| |33 45 50| |11 57 49| | | | | 4 | | 14 | | 21 | | 10 | | 14 | | 30 | | 20 |12 5 47| |12 2 56| |11 53 12 | |11 44 53| |11 46 4| |11 58 19| | +----+--------+ 4 +--------+ 14 +---------+ 21 +--------+ 10 +--------+ 15 +--------+ 30 + | 21 |12 5 51| |12 2 42| |11 52 51 | |11 44 43| |11 46 19| |11 58 49| | | | | 3 | | 15 | | 20 | | 9 | | 16 | | 30 | | 22 |12 5 54| |12 2 17| |11 52 31 | |11 44 34| |11 46 35| |11 59 19| | | | | 2 | | 15 | | 20 | | 8 | | 17 | | 30 | | 23 |12 5 56| |12 2 12| |11 52 11 | |11 44 26| |11 46 52| |11 59 49| | | | | 1 | | 16 | | 21 | | 7 | | 18 | | 30 | | 24 |12 5 57| |12 1 56| |11 51 50 | |11 44 19| |11 47 10| |12 0 19| | | | | 1 | | 16 | | 21 | | 6 | | 19 | | 30 | | 25 |12 5 58| |12 1 40| |11 51 29 | |11 44 13| |11 47 29| |12 0 49| | +----+--------+Dec.+--------+ 16 +---------+ 20 +--------+ 6 +--------+ 19 +--------+ 30 + | 26 |12 5 59| |12 1 24| |11 51 9 | |11 44 7| |11 47 48| |12 1 19| | | | | 1 | | 17 | | 20 | | 5 | | 20 | | 30 | | 27 |12 5 58| |12 1 7| |11 50 40 | |11 44 2| |11 48 8| |12 1 49| | | | | 1 | | 17 | | 19 | | 4 | | 21 | | 29 | | 28 |12 5 57| |12 1 50| |11 50 30 | |11 43 58| |11 48 29| |12 2 18| | | | | 2 | | 18 | | 19 | | 3 | | 22 | | 29 | | 29 |12 5 55| |12 1 32| |11 50 11 | |11 43 55| |11 48 51| |12 2 47| | | | | 2 | | 18 | | 19 | | 3 | | 22 | | 29 | | 30 |12 5 53| |12 0 14| |11 49 52 | |11 43 52| |11 49 13| |12 3 16| | +----+--------+ 2 +--------+ 18 +---------+ 19 +--------+ 2 +--------+ 23 +--------+ 29 + | 31 |12 5 51| |11 59 56| | | |11 43 50| | | |12 3 45| | | | | 3 | | 18 | | | | 1 | | | | 29 | +----+--------+----+--------+----+---------+----+--------+----+--------+----+--------+----+ Incr. 2ʹ 43ʺ Decr. 5ʹ 52ʺ Decr. 9ʹ 46ʺ Decr. 5ʹ 43ʺ Decr. 0ʹ 0ʺ Incr. 14ʹ 9ʺ Decr. 0 8 Incr. 5 24 +----------------------------------------------------------------------------------------+ | A TABLE of the Equation of natural Days, shewing what Time it ought to | | be by the Clock when the Sun is on the Meridian. | +----------------------------------------------------------------------------------------+ | The second after Leap-year. | +----+--------+----+--------+----+--------+----+--------+----+--------+----+--------+----+ |Days| January|Dif.|February|Dif.| March |Dif.| April |Dif.| May |Dif.| June |Dif.| | +--------+----+--------+----+--------+----+--------+----+--------+----+--------+----+ | |H. M. S.| S. |H. M. S.| S. |H. M. S.| S. |H. M. S.| S. |H. M. S.| S. |H. M. S.| S. | +----+--------+----+--------+----+--------+----+--------+----+--------+----+--------+----+ | | |Inc.| |Dec.| |Inc.| |Dec.| |Dec.| |Inc.| | 1 |12 4 14| |12 14 9| |12 12 42| |12 3 56| |11 56 50| |11 57 16| | | | | 28 | | 7 | | 13 | | 18 | | 8 | | 9 | | 2 |12 4 42| |12 14 16| |12 12 20| |12 3 38| |11 56 42| |11 57 25| | | | | 28 | | 6 | | 13 | | 18 | | 7 | | 10 | | 3 |12 5 10| |12 14 22| |12 12 16| |12 3 20| |11 56 35| |11 57 35| | | | | 27 | | 5 | | 13 | | 18 | | 6 | | 10 | | 4 |12 5 37| |12 14 27| |12 12 3| |12 3 2| |11 56 29| |11 57 45| | | | | 27 | | 5 | | 14 | | 18 | | 6 | | 10 | | 5 |12 6 4| |12 14 32| |12 11 49| |12 2 44| |11 56 23| |11 57 55| | +----+--------+ 27 +--------+ 4 +--------+ 14 +--------+ 18 +--------+ 5 +--------+ 10 + | 6 |12 6 30| |12 14 36| |12 11 35| |12 2 26| |11 56 18| |11 58 5| | | | | 26 | | 3 | | 15 | | 17 | | 5 | | 11 | | 7 |12 6 56| |12 14 39| |12 11 20| |12 2 9| |11 56 23| |11 58 16| | | | | 26 | | 2 | | 15 | | 17 | | 4 | | 11 | | 8 |12 7 22| |12 14 41| |12 11 5| |12 1 52| |11 56 9| |11 58 27| | | | | 25 | | 2 | | 15 | | 17 | | 3 | | 11 | | 9 |12 7 47| |12 14 43| |12 10 50| |12 1 35| |11 56 6| |11 58 38| | | | | 24 | | 1 | | 16 | | 17 | | 3 | | 12 | | 10 |12 8 11| |12 14 44| |12 10 34| |12 1 18| |11 56 3| |11 58 50| | +----+--------+ 24 +--------+Dec.+--------+ 16 +--------+ 17 +--------+ 2 +--------+ 12 + | 11 |12 8 35| |12 14 44| |12 10 18| |12 1 1| |11 56 1| |11 59 2| | | | | 23 | | 1 | | 17 | | 16 | | 2 | | 12 | | 12 |12 8 58| |12 14 43| |12 10 1| |12 0 45| |11 55 59| |11 59 14| | | | | 22 | | 2 | | 17 | | 16 | | 2 | | 12 | | 13 |12 9 20| |12 14 41| |12 9 44| |12 0 29| |11 55 57| |11 59 26| | | | | 22 | | 3 | | 17 | | 16 | | 1 | | 12 | | 14 |12 9 42| |12 14 38| |12 9 27| |12 0 13| |11 55 56| |11 59 38| | | | | 21 | | 3 | | 17 | | 15 | |Inc.| | 12 | | 15 |12 10 3| |12 14 35| |12 9 10| |11 59 58| |11 55 56| |11 59 50| +----+--------+ 21 +--------+ 4 +--------+ 18 +--------+ 15 +--------+ 1 +--------+ 13 + | 16 |12 10 24| |12 14 31| |12 8 52| |11 59 43| |11 55 57| |12 0 3| | | | | 20 | | 4 | | 18 | | 14 | | 1 | | 13 | | 17 |12 10 44| |12 14 27| |12 8 34| |11 59 29| |11 55 58| |12 0 16| | | | | 19 | | 5 | | 18 | | 14 | | 2 | | 13 | | 18 |12 11 3| |12 14 22| |12 8 16| |11 59 15| |11 56 0| |12 0 29| | | | | 18 | | 6 | | 18 | | 14 | | 2 | | 13 | | 19 |12 11 21| |12 14 16| |12 7 58| |11 59 1| |11 56 2| |12 0 42| | | | | 18 | | 7 | | 18 | | 14 | | 3 | | 13 | | 20 |12 11 39| |12 14 9| |12 7 40| |11 58 47| |11 56 5| |12 0 55| | +----+--------+ 17 +--------+ 7 +--------+ 18 +--------+ 13 +--------+ 3 +--------+ 13 + | 21 |12 11 56| |12 14 2| |12 7 22| |11 58 34| |11 56 8| |12 1 8| | | | | 16 | | 8 | | 18 | | 12 | | 3 | | 13 | | 22 |12 12 12| |12 13 54| |12 7 4| |11 58 22| |11 56 11| |12 1 21| | | | | 15 | | 9 | | 19 | | 12 | | 4 | | 13 | | 23 |12 12 27 |12 13 45| |12 6 45| |11 58 10| |11 56 15| |12 1 34| | | | | 15 | | 9 | | 19 | | 12 | | 5 | | 13 | | 24 |12 12 42| |12 13 36| |12 6 26| |11 57 58| |11 56 20| |12 1 47| | | | | 14 | | 10 | | 19 | | 11 | | 6 | | 12 | | 25 |12 12 56| |12 13 26| |12 6 7| |11 57 47| |11 56 26| |12 1 59| | +----+--------+ 13 +--------+ 10 +--------+ 19 +--------+ 11 +--------+ 6 +--------+ 13 + | 26 |12 13 9| |12 13 16| |12 5 48| |11 57 36| |11 56 32| |12 2 12| | | | | 12 | | 11 | | 19 | | 10 | | 6 | | 13 | | 27 |12 13 21| |12 13 5| |12 5 29| |11 57 26| |11 56 38| |12 2 25| | | | | 11 | | 11 | | 19 | | 10 | | 7 | | 12 | | 28 |12 13 32| |12 12 54| |12 5 10| |11 57 16| |11 56 45| |12 2 37| | | | | 10 | | 12 | | 19 | | 9 | | 7 | | 12 | | 29 |12 13 42| | | |12 4 51| |11 57 7| |11 56 52| |12 2 49| | | | | 10 | | | | 18 | | 9 | | 8 | | 12 | | 30 |12 13 52| | | |12 4 33| |11 56 58| |11 57 0| |12 3 1| | +----+--------+ 9 +--------+----+--------+ 18 +--------+ 8 +--------+ 8 +--------+ 11 + | 31 |12 14 1| | | |12 4 15| | | |11 57 8| | | | | | | 8 | | | | 18 | | | | 8 | | | +----+--------+----+--------+----+--------+----+--------+----+--------+----+--------+----+ Incr. 9ʹ 47ʺ Incr. 0ʹ 35ʺ Decr. 8ʹ 27ʺ Decr. 6ʹ 58ʺ Decr. 0ʹ 54ʺ Incr. 5ʹ 45ʺ Decr. 1 50 Incr. 1 12 +-----------------------------------------------------------------------------------------+ | A TABLE of the Equation of natural Days, shewing what Time it ought to | | be by the Clock when the Sun is on the Meridian. | +-----------------------------------------------------------------------------------------+ | The second after Leap-year. | +----+--------+----+--------+----+---------+----+--------+----+--------+----+--------+----+ |Days| July |Dif.| August |Dif.|September|Dif.| October|Dif.|November|Dif.|December|Dif.| | +--------+----+--------+----+---------+----+--------+----+--------+----+--------+----+ | |H. M. S.| S. |H. M. S.| S. |H. M. S. | S. |H. M. S.| S. |H. M. S.| S. |H. M. S.| S. | +----+--------+----+--------+----+---------+----+--------+----+--------+----+--------+----+ | | |Inc.| |Dec.| |Dec.| |Dec.| |Dec.| |Inc.| | 1 |12 3 12| |12 5 48| |11 59 43 | |11 49 37| |11 43 49| |11 49 30| | | | | 12 | | 4 | | 19 | | 19 | | 1 | | 23 | | 2 |12 3 24| |12 5 44| |11 59 24 | |11 49 18| |11 43 48| |11 49 53| | | | | 11 | | 4 | | 19 | | 18 | |Inc.| | 24 | | 3 |12 3 35| |12 5 40| |11 59 5 | |11 49 0| |11 43 49| |11 50 17| | | | | 11 | | 5 | | 19 | | 18 | | 1 | | 25 | | 4 |12 3 46| |12 5 35| |11 58 46 | |11 48 42| |11 43 50| |11 50 42| | | | | 11 | | 5 | | 20 | | 18 | | 2 | | 25 | | 5 |12 3 57| |12 5 30| |11 58 26 | |11 48 24| |11 43 52| |11 51 7| | +-------------+ 10 +--------+ 6 +---------+ 20 +--------+ 17 +--------+ 3 +--------+ 26 + | 6 |12 4 7| |12 5 24| |11 58 6 | |11 48 7| |11 43 55| |11 51 33| | | | | 10 | | 7 | | 20 | | 17 | | 3 | | 26 | | 7 |12 4 17| |12 5 17| |11 57 46 | |11 47 50| |11 43 58| |11 51 59| | | | | 9 | | 7 | | 20 | | 17 | | 4 | | 26 | | 8 |12 4 26| |12 5 10| |11 57 26 | |11 47 33| |11 44 2| |11 52 25| | | | | 9 | | 8 | | 21 | | 16 | | 5 | | 27 | | 9 |12 4 35| |12 5 2| |11 57 5 | |11 47 17| |11 44 7| |11 52 52| | | | | 9 | | 9 | | 20 | | 16 | | 6 | | 28 | | 10 |12 4 44| |12 4 53| |11 56 45 | |11 47 1| |11 44 13| |11 53 20| | +----+--------+ 8 +--------+ 9 +---------+ 21 +--------+ 15 +--------+ 7 +--------+ 28 + | 11 |12 4 52| |12 4 44| |11 56 24 | |11 46 46| |11 44 20| |11 53 48| | | | | 8 | | 9 | | 21 | | 14 | | 8 | | 28 | | 12 |12 5 0| |12 4 35| |11 56 3 | |11 46 32| |11 44 28| |11 54 16| | | | | 8 | | 10 | | 21 | | 14 | | 9 | | 28 | | 13 |12 5 8| |12 4 25| |11 55 42 | |11 46 18| |11 44 37| |11 54 44| | | | | 7 | | 11 | | 20 | | 13 | | 9 | | 29 | | 14 |12 5 15| |12 4 13| |11 55 22 | |11 46 5| |11 44 46| |11 54 13| | | | | 6 | | 11 | | 20 | | 13 | | 10 | | 29 | | 15 |12 5 21| |12 4 3| |11 55 2 | |11 45 52| |11 44 56| |11 55 42| | +----+--------+ 6 +--------+ 12 +---------+ 21 +--------+ 13 +--------+ 11 +--------+ 29 + | 16 |12 5 27| |12 3 51| |11 54 41 | |11 45 39| |11 45 7| |11 56 11| | | | | 6 | | 12 | | 21 | | 12 | | 12 | | 30 | | 17 |12 5 33| |12 3 39| |11 54 20 | |11 45 27| |11 45 19| |11 56 41| | | | | 5 | | 12 | | 21 | | 11 | | 13 | | 30 | | 18 |12 5 38| |12 3 27| |11 53 59 | |11 45 16| |11 45 32| |11 57 11| | | | | 4 | | 13 | | 20 | | 10 | | 14 | | 30 | | 19 |12 5 42| |12 3 14| |11 53 39 | |11 45 6| |11 45 46| |11 57 41| | | | | 4 | | 14 | | 21 | | 10 | | 15 | | 30 | | 20 |12 5 46| |12 3 0| |11 53 18 | |11 44 56| |11 46 1| |11 58 11| | +----+--------+ 3 +--------+ 14 +---------+ 21 +--------+ 10 +--------+ 15 +--------+ 30 + | 21 |12 5 49| |12 2 46| |11 52 57 | |11 44 46| |11 46 16| |11 58 41| | | | | 3 | | 15 | | 20 | | 9 | | 16 | | 30 | | 22 |12 5 52| |12 2 31| |11 52 37 | |11 44 37| |11 46 32| |11 59 11| | | | | 2 | | 15 | | 21 | | 8 | | 17 | | 30 | | 23 |12 5 54| |12 2 16| |11 52 16 | |11 44 29| |11 46 49| |11 59 41| | | | | 2 | | 15 | | 21 | | 7 | | 18 | | 30 | | 24 |12 5 56| |12 2 1| |11 51 55 | |11 44 22| |11 47 7| |12 0 11| | | | | 2 | | 16 | | 21 | | 7 | | 18 | | 30 | | 25 |12 5 58| |12 1 45| |11 51 34 | |11 44 15| |11 47 25| |12 0 41| | +----+--------+ 1 +--------+ 16 +---------+ 20 +--------+ 6 +--------+ 19 +--------+ 30 + | 26 |12 5 59| |12 1 29| |11 51 14 | |11 44 9| |11 47 44| |12 1 11| | | | |Dec.| | 17 | | 20 | | 5 | | 20 | | 30 | | 27 |12 5 58| |12 1 12| |11 50 54 | |11 44 4| |11 48 4| |12 1 41| | | | | 1 | | 17 | | 20 | | 5 | | 21 | | 30 | | 28 |12 5 57| |12 0 55| |11 50 34 | |11 43 59| |11 48 25| |12 2 11| | | | | 1 | | 18 | | 19 | | 4 | | 21 | | 29 | | 29 |12 5 56| |12 0 37| |11 50 15 | |11 43 55| |11 48 46| |12 2 40| | | | | 2 | | 18 | | 19 | | 3 | | 22 | | 29 | | 30 |12 5 54| |12 0 19| |11 49 56 | |11 43 52| |11 49 8| |12 3 9| | +----+--------+ 3 +--------+ 18 +---------+ 19 +--------+ 2 +--------+ 22 +--------+ 29 + | 31 |12 5 51| |12 0 1| | | |11 43 50| | | |12 3 38| | | | | 3 | | 18 | | | | 1 | | | | 29 | +----+--------+----+--------+----+---------+----+--------+----+--------+----+--------+----+ Incr. 2ʹ 46ʺ Decr. 5ʹ 47ʺ Decr. 9ʹ 47ʺ Decr. 5ʹ 47ʺ Decr. 0ʹ 1ʺ Incr. 14ʹ 8ʺ Decr. 0 8 Incr. 5 19 +----------------------------------------------------------------------------------------+ | A TABLE of the Equation of natural Days, shewing what Time it ought to | | be by the Clock when the Sun is on the Meridian. | +----------------------------------------------------------------------------------------+ | The third after Leap-year. | +----+--------+----+--------+----+--------+----+--------+----+--------+----+--------+----+ |Days| January|Dif.|February|Dif.| March |Dif.| April |Dif.| May |Dif.| June |Dif.| | +--------+----+--------+----+--------+----+--------+----+--------+----+--------+----+ | |H. M. S.| S. |H. M. S.| S. |H. M. S.| S. |H. M. S.| S. |H. M. S.| S. |H. M. S.| S. | +----+--------+----+--------+----+--------+----+--------+----+--------+----+--------+----+ | | |Inc.| |Inc.| |Dec.| |Dec.| |Dec.| |Inc.| | 1 |12 4 7| |12 14 6| |12 12 44| |12 4 1| |11 56 52| |11 57 15| | | | | 28 | | 7 | | 12 | | 18 | | 8 | | 9 | | 2 |12 4 35| |12 14 13| |12 12 32| |12 3 43| |11 56 44| |11 57 24| | | | | 28 | | 7 | | 13 | | 18 | | 7 | | 9 | | 3 |12 5 3| |12 14 20| |12 12 19| |12 3 25| |11 56 37| |11 57 33| | | | | 27 | | 6 | | 13 | | 18 | | 7 | | 9 | | 4 |12 5 30| |12 14 26| |12 12 6| |12 3 7| |11 56 30| |11 57 42| | | | | 27 | | 5 | | 14 | | 18 | | 6 | | 10 | | 5 |12 5 57| |12 14 31| |12 11 52| |12 2 49| |11 56 24| |11 57 52| | +----+--------+ 27 +--------+ 4 +--------+ 14 +--------+ 18 +--------+ 5 +--------+ 10 + | 6 |12 6 24| |12 14 35| |12 11 38| |12 2 31| |11 56 19| |11 58 2| | | | | 26 | | 3 | | 14 | | 18 | | 5 | | 11 | | 7 |12 6 50| |12 14 38| |12 11 24| |12 2 13| |11 56 14| |11 58 13| | | | | 25 | | 2 | | 15 | | 18 | | 4 | | 11 | | 8 |12 7 15| |12 14 41| |12 11 9| |12 1 55| |11 56 10| |11 58 24| | | | | 25 | | 1 | | 16 | | 17 | | 4 | | 11 | | 9 |12 7 40| |12 14 43| |12 10 53| |12 1 38| |11 56 6| |11 58 35| | | | | 25 | | 1 | | 16 | | 17 | | 3 | | 11 | | 10 |12 8 5| |12 14 44| |12 10 37| |12 1 21| |11 56 3| |11 58 46| | +----+--------+ 24 +--------+Dec.+--------+ 16 +--------+ 16 +--------+ 2 +--------+ 12 + | 11 |12 8 29| |12 14 44| |12 10 21| |12 1 5| |11 56 1| |11 58 58| | | | | 23 | | 1 | | 16 | | 16 | | 2 | | 12 | | 12 |12 8 52| |12 14 43| |12 10 5| |12 0 49| |11 55 59| |11 59 10| | | | | 23 | | 2 | | 17 | | 16 | | 2 | | 12 | | 13 |12 9 15| |12 14 41| |12 10 48| |12 0 33| |11 55 57| |11 59 22| | | | | 22 | | 2 | | 17 | | 16 | | 1 | | 12 | | 14 |12 9 37| |12 14 39| |12 9 31| |12 0 17| |11 55 56| |11 59 34| | | | | 21 | | 3 | | 17 | | 15 | |Inc.| | 13 | | 15 |12 9 58| |12 14 36| |12 9 14| |12 0 2| |11 55 56| |11 59 47| | +----+--------+ 21 +--------+ 4 +--------+ 17 +--------+ 15 +--------+ 1 +--------+ 13 + | 16 |12 10 19| |12 14 32| |12 8 57| |11 59 47| |11 55 57| |12 0 0| | | | | 20 | | 4 | | 18 | | 15 | | 1 | | 13 | | 17 |12 10 39| |12 14 28| |12 8 39| |11 59 32| |11 55 58| |12 0 13| | | | | 19 | | 5 | | 18 | | 14 | | 1 | | 13 | | 18 |12 10 58| |12 14 23| |12 8 21| |11 59 18| |11 55 59| |12 0 26| | | | | 18 | | 6 | | 18 | | 14 | | 2 | | 13 | | 19 |12 11 16| |12 14 17| |12 8 3| |11 59 4| |11 56 1| |12 0 39| | | | | 18 | | 7 | | 18 | | 14 | | 2 | | 13 | | 20 |12 11 34| |12 14 10| |12 7 45| |11 58 50| |11 56 3| |12 0 52| | +----+--------+ 17 +--------+ 7 +--------+ 18 +--------+ 13 +--------+ 3 +--------+ 13 + | 21 |12 11 51| |12 14 3| |12 7 27| |11 58 37| |11 56 6| |12 1 5| | | | | 16 | | 8 | | 19 | | 13 | | 4 | | 12 | | 22 |12 12 7| |12 13 55| |12 7 8| |11 58 24| |11 56 10| |12 1 17| | | | | 16 | | 8 | | 19 | | 12 | | 4 | | 13 | | 23 |12 12 23| |12 13 47| |12 6 49| |11 58 12| |11 56 14| |12 1 30| | | | | 15 | | 9 | | 19 | | 12 | | 5 | | 13 | | 24 |12 12 38| |12 13 38| |12 6 30| |11 58 0| |11 56 19| |12 1 43| | | | | 14 | | 9 | | 19 | | 11 | | 5 | | 13 | | 25 |12 12 52| |12 13 29| |12 6 11| |11 57 49| |11 56 24| |12 1 56| | +----+--------+ 13 +--------+ 10 +--------+ 18 +--------+ 11 +--------+ 6 +--------+ 13 + | 26 |12 13 5| |12 13 19| |12 5 53| |11 57 38| |11 56 30| |12 2 9| | | | | 12 | | 11 | | 19 | | 10 | | 6 | | 13 | | 27 |12 13 17| |12 13 8| |12 5 34| |11 57 28| |11 56 36| |12 2 22| | | | | 11 | | 12 | | 19 | | 10 | | 7 | | 12 | | 28 |12 13 28| |12 12 56| |12 5 15| |11 57 18| |11 56 43| |12 2 34| | | | | 11 | | 12 | | 18 | | 9 | | 7 | | 12 | | 29 |12 13 39| | | |12 4 57| |11 57 9| |11 56 50| |12 2 46| | | | | 10 | | | | 19 | | 9 | | 8 | | 12 | | 30 |12 13 49| | | |12 4 38| |11 57 0| |11 56 58| |12 2 58| | +----+--------+ 9 +--------+----+--------+ 19 +--------+ 8 +--------+ 8 +--------+ 12 + | 31 |12 13 58| | | |12 4 19| | | |11 57 6| | | | | | | 8 | | | | 18 | | | | 9 | | | +----+--------+----+--------+----+--------+----+--------+----+--------+----+--------+----+ Incr. 9ʹ 51ʺ Incr. 0ʹ 38ʺ Decr. 8ʹ 25ʺ Decr. 7ʹ 1ʺ Decr. 0ʹ 56ʺ Incr. 5ʹ 43ʺ Decr. 1 48 Incr. 1 10 +-----------------------------------------------------------------------------------------+ | A TABLE of the Equation of natural Days, shewing what Time it ought to | | be by the Clock when the Sun is on the Meridian. | +-----------------------------------------------------------------------------------------+ | The third after Leap-year. | +----+--------+----+--------+----+---------+----+--------+----+--------+----+--------+----+ |Days| July |Dif.| August |Dif.|September|Dif.| October|Dif.|November|Dif.|December|Dif.| | +--------+----+--------+----+---------+----+--------+----+--------+----+--------+----+ | |H. M. S.| S. |H. M. S.| S. |H. M. S. | S. |H. M. S.| S. |H. M. S.| S. |H. M. S.| S. | +----+--------+----+--------+----+---------+----+--------+----+--------+----+--------+----+ | | |Inc.| |Dec.| |Dec.| |Dec.| |Dec.| |Inc.| | 1 |12 3 10| |12 5 49| |11 59 47 | |11 49 42| |11 43 49| |11 49 25| | | | | 11 | | 4 | | 19 | | 18 | | 1 | | 23 | | 2 |12 3 21| |12 5 45| |11 59 28 | |11 49 24| |11 43 48| |11 49 48| | | | | 11 | | 4 | | 19 | | 18 | |Inc.| | 24 | | 3 |12 3 32| |12 5 41| |11 59 9 | |11 49 6| |11 43 48| |11 50 12| | | | | 11 | | 5 | | 19 | | 18 | | 1 | | 24 | | 4 |12 3 43| |12 5 36| |11 58 50 | |11 48 48| |11 43 49| |11 50 36| | | | | 11 | | 5 | | 19 | | 18 | | 2 | | 25 | | 5 |12 3 54| |12 5 31| |11 58 31 | |11 48 30| |11 43 51| |11 51 1| | +----+--------+ 10 +--------+ 6 +---------+ 20 +--------+ 18 +--------+ 2 +--------+ 25 + | 6 |12 4 4| |12 5 25| |11 58 11 | |11 48 12| |11 43 53| |11 51 26| | | | | 10 | | 7 | | 20 | | 17 | | 3 | | 26 | | 7 |12 4 14| |12 5 18| |11 57 51 | |11 47 55| |11 43 56| |11 52 52| | | | | 10 | | 7 | | 20 | | 16 | | 4 | | 27 | | 8 |12 4 24| |12 5 11| |11 57 31 | |11 47 39| |11 44 0| |11 52 19| | | | | 9 | | 7 | | 20 | | 16 | | 5 | | 27 | | 9 |12 4 33| |12 5 4| |11 57 11 | |11 47 23| |11 44 5| |11 52 46| | | | | 9 | | 8 | | 20 | | 16 | | 6 | | 27 | | 10 |12 4 42| |12 4 56| |11 56 51 | |11 47 7| |11 44 11| |11 53 13| | +----+--------+ 8 +--------+ 8 +---------+ 20 +--------+ 15 +--------+ 7 +--------+ 28 + | 11 |12 4 50| |12 4 48| |11 56 31 | |11 46 52| |11 44 18| |11 53 41| | | | | 8 | | 9 | | 21 | | 15 | | 8 | | 28 | | 12 |12 4 58| |12 4 37| |11 56 10 | |11 46 37| |11 44 26| |11 54 9| | | | | 8 | | 10 | | 21 | | 14 | | 8 | | 28 | | 13 |12 5 6| |12 4 27| |11 55 49 | |11 46 23| |11 44 34| |11 54 37| | | | | 7 | | 10 | | 21 | | 14 | | 9 | | 29 | | 14 |12 5 13| |12 4 17| |11 55 28 | |11 46 9| |11 44 43| |11 55 6| | | | | 6 | | 11 | | 21 | | 13 | | 10 | | 30 | | 15 |12 5 19| |12 4 6| |11 55 7 | |11 45 56| |11 44 53| |11 55 36| | +----+--------+ 6 +--------+ 12 +---------+ 20 +--------+ 12 +--------+ 11 +--------+ 29 + | 16 |12 5 25| |12 3 54| |11 54 47 | |11 45 44| |11 45 4| |11 56 6| | | | | 6 | | 12 | | 21 | | 12 | | 12 | | 30 | | 17 |12 5 31| |12 3 42| |11 54 26 | |11 45 32| |11 45 16| |11 56 36| | | | | 5 | | 13 | | 21 | | 12 | | 13 | | 30 | | 18 |12 5 36| |12 3 29| |11 54 5 | |11 45 20| |11 45 29| |11 57 6| | | | | 5 | | 13 | | 21 | | 11 | | 14 | | 29 | | 19 |12 5 41| |12 3 16| |11 53 44 | |11 45 9| |11 45 43| |11 57 35| | | | | 4 | | 13 | | 21 | | 10 | | 14 | | 30 | | 20 |12 5 45| |12 3 3| |11 53 23 | |11 44 59| |11 45 57| |11 58 5| | +----+--------+ 4 +--------+ 14 +---------+ 20 +--------+ 9 +--------+ 15 +--------+ 30 + | 21 |12 5 49| |12 2 49| |11 53 3 | |11 44 50| |11 46 12| |11 58 34| | | | | 3 | | 15 | | 21 | | 9 | | 16 | | 30 | | 22 |12 5 52| |13 2 34| |11 52 42 | |11 44 41| |11 46 28| |11 59 4| | | | | 3 | | 15 | | 21 | | 9 | | 17 | | 30 | | 23 |12 5 55| |12 2 19| |11 52 21 | |11 44 32| |11 46 45| |11 59 34| | | | | 2 | | 15 | | 20 | | 8 | | 17 | | 30 | | 24 |12 5 57| |12 2 4| |11 52 1 | |11 44 24| |11 47 2| |12 0 4| | | | | 1 | | 16 | | 21 | | 7 | | 18 | | 30 | | 25 |12 5 58| |12 1 48| |11 51 40 | |11 44 17| |11 47 20| |12 0 34| | +----+--------+ 1 +--------+ 16 +---------+ 20 +--------+ 6 +--------+ 19 +--------+ 30 + | 26 |12 5 59| |12 1 32| |11 51 20 | |11 44 11| |11 47 39| |12 1 4| | | | |Dec.| | 16 | | 20 | | 5 | | 20 | | 30 | | 27 |12 5 58| |12 1 16| |11 51 0 | |11 44 6| |11 47 59| |12 1 34| | | | | 1 | | 17 | | 20 | | 5 | | 20 | | 30 | | 28 |12 5 57| |12 0 59| |11 50 40 | |11 44 1| |11 48 19| |12 2 4| | | | | 1 | | 17 | | 20 | | 4 | | 21 | | 29 | | 29 |12 5 56| |12 0 42| |11 50 20 | |11 43 57| |11 48 40| |12 2 33| | | | | 2 | | 18 | | 19 | | 3 | | 22 | | 29 | | 30 |12 5 54| |12 0 24| |11 50 1 | |11 43 54| |11 49 2| |12 3 2| | +----+--------+ 2 +--------+ 18 +---------+ 19 +--------+ 3 +--------+ 23 +--------+ 29 + | 31 |12 5 52| |12 0 6| | | |11 43 51| | | |12 3 31| | | | | 3 | | 19 | | | | 2 | | | | 29 | +----+--------+----+--------+----+---------+----+--------+----+--------+----+--------+----+ Incr. 2ʹ 48ʺ Decr. 5ʹ 43ʺ Decr. 9ʹ 46ʺ Decr. 5ʹ 51ʺ Decr. 0ʹ 1ʺ Incr. 14ʹ 6ʺ Decr. 0 7 Incr. 5 14

CHAP. XV.

_The Moon’s surface mountainous: Her Phases described: Her path, and the
paths of Jupiter’s Moons delineated: The proportions of the Diameters of
their Orbits, and those of Saturn’s Moons, to each other; and to the
Diameter of the Sun._

[Sidenote: PL. VII.

The Moon’s surface mountainous.]

252. By looking at the Moon with an ordinary telescope we perceive that her surface is diversified with long tracts of prodigious high mountains and deep cavities. Some of her mountains, by comparing their height with her diameter (which is 2180 miles) are found to be three times higher than the highest hills on our Earth. This ruggedness of the Moon’s surface is of great use to us, by reflecting the Sun’s light to all sides: for if the Moon were smooth and polished like a looking-glass, or covered with water, she could never distribute the Sun’s light all round; only in some positions she would shew us his image, no bigger than a point, but with such a lustre as would be hurtful to our eyes.

[Sidenote: Why no hills appear on her edge.]

253. The Moon’s surface being so uneven, many have wondered why her edge appears not jagged, as well as the curve bounding the light and dark places. But if we consider, that what we call the edge of the Moon’s Disc is not a single line set round with mountains, in which case it would appear irregularly indented, but a large Zone having many mountains lying behind one another from the observer’s eye, we shall find that the mountains in some rows will be opposite to the vales in others; and so fill up the inequalities as to make her appear quite round: just as when one looks at an orange, although it’s roughness be very discernible on the side next the eye, especially if the Sun or a Candle shines obliquely on that side, yet the line terminating the visible part still appears smooth and even.

_J. Ferguson delin._ _J. Mynde Sculp._]

[Sidenote: The Moon has no twilight.

Fig. I.]

254. As the Sun can only enlighten that half of the Earth which is at any moment turned towards him, and being withdrawn from the opposite half leaves it in darkness; so he likewise doth to the Moon: only with this difference, that the Earth being surrounded by an Atmosphere, and the Moon having none, we have twilight after the Sun sets; but the Lunar Inhabitants have an immediate transition from the brightest Sun-shine to the blackest darkness § 177. For, let _tkrsw_ be the Earth, and _A_, _B_, _C_, _D_, _E_, _F_, _G_, _H_ the Moon in eight different parts of her Orbit. As the Earth turns round its Axis, from west to east, when any place comes to _t_ the twilight begins there, and when it revolves from thence to _r_ the Sun _S_ rises; when the place comes to _s_ the Sun sets, and when it comes to _w_ the twilight ends. But as the Moon turns round her Axis, which is only once a month, the moment that any point of her surface comes to _r_ (see the Moon at _G_) the Sun rises there without any previous warning by twilight; and when the same point comes to _s_ the Sun sets, and that point goes into darkness as black as at midnight.

[Sidenote: The Moon’s Phases.]

255. The Moon being an opaque spherical body, (for her hills take off no more from her roundness than the inequalities on the surface of an orange takes off from its roundness) we can only see that part of the enlightened half of her which is towards the Earth. And therefore, when the Moon is at _A_, in conjunction with the Sun _S_, her dark half is towards the Earth, and she disappears as at _a_, there being no light on that half to render it visible. When she comes to her first Octant at _B_, or has gone an eighth part of her orbit from her Conjunction, a quarter of her enlightened side is towards the Earth, and she appears horned as at _b_. When she has gone a quarter of her orbit from between the Earth and Sun to _C_, she shews us one half of her enlightened side as at _c_, and we say, she is a quarter old. At _D_ she is in her second Octant, and by shewing us more of her enlightened side she appears gibbous as at _d_. At _E_ her whole enlightened side is towards the Earth, and therefore she appears round as at _e_, when we say, it is Full Moon. In her third Octant at _F_, part of her dark side being towards the Earth, she again appears gibbous, and is on the decrease, as at _f_. At _G_ we see just one half of her enlightened side, and she appears half decreased, or in her third Quarter, as at _g_. At _H_ we only see a quarter of her enlightened side, being in her fourth Octant, where she appears horned as at _h_. And at _A_, having compleated her course from the Sun to the Sun again, she disappears; and we say, it is New Moon. Thus in going from _A_ to _E_ the Moon seems continually to increase; and in going from _E_ to _A_, to decrease in the same proportion; having like Phases at equal distances from _A_ or _E_, but as seen from the Sun _S_, she is always Full.

[Sidenote: The Moon’s Disc not always quite round when full.]

256. The Moon appears not perfectly round when she is Full in the highest or lowest part of her Orbit, because we have not a direct view of her enlightened side at that time. When Full in the highest part of her orbit, a small deficiency appears on her lower edge; and the contrary when Full in the lowest part of her Orbit.

[Sidenote: The Phases of the Earth and Moon contrary.]

257. ’Tis plain by the Figure, that when the Moon changes to the Earth, the Earth appears Full to the Moon; and _vice versâ_. For when the Moon is at _A_, _New_ to the Earth, the whole enlightened side of the Earth is towards the Moon: and when the Moon is at _E_, _Full_ to the Earth, it’s dark side is towards her. Hence a _New Moon_ answers to a _Full Earth_, and a _Full Moon_ to a _New Earth_. The _Quarters_ are also reversed to each other.

[Sidenote: An agreeable Phenomenon.]

258. Between the third Quarter and Change, the Moon is frequently visible in the forenoon, even when the Sun shines; and then she affords us an opportunity of seeing a very agreeable appearance, wherever we find a globular stone above the level of the eye, as suppose on the top of a gate. For, if the Sun shines on the stone, and we place ourselves so as the upper part of the stone may just seem to touch the point of the Moon’s lowermost horn, we shall then see the enlightened part of the stone exactly of the same shape with the Moon; horned as she is, and inclining the same way to the Horizon. The reason is plain; for the Sun enlightens the stone the same way as he does the Moon: and both being Globes, when we put ourselves into the above situation, the Moon and stone have the same position to our eyes; and therefore we must see as much of the illuminated part of the one as of the other.

[Sidenote: The nonagesimal Degree, what.]

259. The position of the Moon’s Cusps, or a right line touching the points of her horns, is very differently inclined to the Horizon at different hours of the same days of her age. Sometimes she stands, as it were, upright on her lower horn, and then such a line is perpendicular to the Horizon: when this, happens, she is in what the Astronomers call _the Nonagesimal Degree_; which is the highest point of the Ecliptic above the Horizon at that time, and is 90 degrees from both sides of the Horizon where it is then cut by the Ecliptic. But this never happens when the Moon is on the Meridian, except when she is at the very beginning of Cancer or Capricorn.

[Sidenote: How the inclination of the Ecliptic may be found by the
position of the Moon horns.

PL. VII.]

260. The inclination of that part of the Ecliptic to the Horizon in which the Moon is at any time when horned, may be known by the position of her horns; for a right line touching their points is perpendicular to the Ecliptic. And as the Angle that the Moon’s orbit makes with the Ecliptic can never raise her above, nor depress her below the Ecliptic, more than two minutes of a degree, as seen from the Sun; it can have no sensible effect upon the position of her horns. Therefore, if a Quadrant be held up, so as one of it’s edges may seem to touch the Moon’s horns, the graduated side being kept towards the eye, and as far from the eye as it can be conveniently held, the arc between the Plumb-line and that edge of the Quadrant which seems to touch the Moon’s horns will shew the inclination of that part of the Ecliptic to the Horizon. And the arc between the other edge of the Quadrant and Plumb-line will shew the inclination of the Moon’s horns to the Horizon at that time also.

[Sidenote: Fig. I.

Why the Moon appears as big as the Sun.]

261. The Moon generally appears as large as the Sun; for the Angle _vkA_, under which the Moon is seen from the Earth, is the same with the Angle _LkM_, under which the Sun is seen from it. And therefore the Moon may hide the Sun’s whole Disc from us, as she sometimes does in solar Eclipses. The reason why she does not eclipse the Sun at every Change shall be explained afterwards. If the Moon were farther from the Earth as at _a_, she could never hide the whole of the Sun from us; for then she would appear under the Angle _NkO_, eclipsing only that part of the Sun which lies between _N_ and _O_: were she still further from the Earth, as at _X_, she would appear under the small Angle _TkW_, like a spot on the Sun, hiding only the part _TW_ from our sight.

[Sidenote: A proof of the Moon’s turning round her Axis.]

262. The Moon turns round her Axis in the time that she goes round her orbit; which is evident from hence, that a spectator at rest, without the periphery of the Moon’s orbit, would see all her sides turned regularly towards him in that time. She turns round her Axis from any Star to the same Star again in 27 days 8 hours; from the Sun to the Sun again in 29-1/2 days: the former is the length of her sidereal day, and the latter the length of her solar day. A body moving round the Sun would have a solar day in every revolution, without turning on it’s Axis; the same as if it had kept all the while at rest, and the Sun moved round it: but without turning round it’s Axis it could never have one sidereal day, because it would always keep the same side towards any given Star.

[Sidenote: Her periodical and synodical Revolution.]

263. If the Earth had no annual motion, the Moon would go round it so as to compleat a Lunation, a sidereal, and a solar day, all in the same time. But, because the Earth goes forward in it’s orbit while the Moon goes round the Earth in her orbit, the Moon must go as much more than round her orbit from Change to Change in compleating a solar day as the Earth has gone forward in it’s orbit during that time, _i. e._ almost a twelfth part of a Circle.

[Sidenote: Familiarly represented.

A Table shewing the times that the hour and minute hands of a
watch are in conjunction.

A machine for shewing the motions of the Sun and Moon.

PL. VII.]