Part 33

+----------------------------------------------------+ | TABLE VII. _The number of Days, reckoned | | from the beginning of_ March, _answering to | | the Days of all the mean New and Full Moons_. | +----+---+---+---+---+---+---+---+---+---+---+---+---+ |Days|Mar|Apr|May|Jun|Jul|Aug|Sep|Oct|Nov|Dec|Jan|Feb| +----+---+---+---+---+---+---+---+---+---+---+---+---+ | 1 | 1| 32| 62| 93|123|154|185|215|246|276|307|338| | 2 | 2| 33| 63| 94|124|155|186|216|247|277|308|339| | 3 | 3| 34| 64| 95|125|156|187|217|248|278|309|340| | 4 | 4| 35| 65| 96|126|157|188|218|249|279|310|341| | 5 | 5| 36| 66| 97|127|158|189|219|250|280|311|342| +----+---+---+---+---+---+---+---+---+---+---+---+---+ | 6 | 6| 37| 67| 98|128|159|190|220|251|281|312|343| | 7 | 7| 38| 68| 99|129|160|191|221|252|282|313|344| | 8 | 8| 39| 69|100|130|161|192|222|253|283|314|345| | 9 | 9| 40| 70|101|131|162|193|223|254|284|315|346| | 10 | 10| 41| 71|102|132|163|194|224|255|285|316|347| +----+---+---+---+---+---+---+---+---+---+---+---+---+ | 11 | 11| 42| 72|103|133|164|195|225|256|286|317|348| | 12 | 12| 43| 73|104|134|165|196|226|257|287|318|349| | 13 | 13| 44| 74|105|135|166|197|227|258|288|319|350| | 14 | 14| 45| 75|106|136|167|198|228|259|289|320|351| | 15 | 15| 46| 76|107|137|168|199|229|260|290|321|352| +----+---+---+---+---+---+---+---+---+---+---+---+---+ | 16 | 16| 47| 77|108|138|169|200|230|261|291|322|353| | 17 | 17| 48| 78|109|139|170|201|231|262|292|323|354| | 18 | 18| 49| 79|110|140|171|202|232|263|293|324|355| | 19 | 19| 50| 80|111|141|172|203|233|264|294|325|356| | 20 | 20| 51| 81|112|142|173|204|234|265|295|326|357| +----+---+---+---+---+---+---+---+---+---+---+---+---+ | 21 | 21| 52| 82|113|143|174|205|235|266|296|327|358| | 22 | 22| 53| 83|114|144|175|206|236|267|297|328|359| | 23 | 23| 54| 84|115|145|176|207|237|268|298|329|360| | 24 | 24| 55| 85|116|146|177|208|238|269|299|330|361| | 25 | 25| 56| 86|117|147|178|209|239|270|300|331|362| +----+---+---+---+---+---+---+---+---+---+---+---+---+ | 26 | 26| 57| 87|118|148|179|210|240|271|301|332|363| | 27 | 27| 58| 88|119|149|180|211|241|272|302|333|364| | 28 | 28| 59| 89|120|150|181|212|242|273|303|334|365| | 29 | 29| 60| 90|121|151|182|213|243|274|304|335|366| | 30 | 30| 61| 91|122|152|183|214|244|275|305|336|---| | 31 | 31| --| 92|---|153|184|---|245|---|306|337|---| +----+---+---+---+---+---+---+---+---+---+---+---+---+ +-----------------------------------------+ |TABLE VIII. _The Moon’s annual Equation._| +-----+-----------------------------+-----+ |Sun’s| Subtract |Sun’s| |Ano. +----+----+----+----+----+----+Ano. | | | 0 | 1 | 2 | 3 | 4 | 5 | | | | S. | S. | S. | S. | S. | S. | | +-----+----+----+----+----+----+----+-----+ | D. | M. | M. | M. | M. | M. | M. | D. | +-----+----+----+----+----+----+----+-----+ | 0 | 0 | 11 | 18 | 22 | 19 | 11 | 30 | | 1 | 0 | 11 | 19 | 22 | 19 | 11 | 29 | | 2 | 1 | 11 | 19 | 22 | 18 | 10 | 28 | | 3 | 1 | 11 | 19 | 22 | 18 | 10 | 27 | | 4 | 1 | 12 | 19 | 22 | 18 | 10 | 26 | | 5 | 2 | 12 | 19 | 22 | 18 | 9 | 25 | | 6 | 2 | 12 | 19 | 21 | 18 | 9 | 24 | | 7 | 3 | 13 | 20 | 21 | 17 | 9 | 23 | | 8 | 3 | 13 | 20 | 21 | 17 | 8 | 22 | | 9 | 3 | 13 | 20 | 21 | 17 | 8 | 21 | | 10 | 4 | 14 | 20 | 21 | 17 | 8 | 20 | | 11 | 4 | 14 | 20 | 21 | 16 | 7 | 19 | | 12 | 4 | 14 | 20 | 21 | 16 | 7 | 18 | | 13 | 5 | 14 | 20 | 21 | 16 | 6 | 17 | | 14 | 5 | 15 | 20 | 21 | 16 | 6 | 16 | | 15 | 5 | 15 | 21 | 21 | 15 | 6 | 15 | | 16 | 6 | 15 | 21 | 21 | 15 | 5 | 14 | | 17 | 6 | 15 | 21 | 21 | 15 | 5 | 13 | | 18 | 6 | 16 | 21 | 21 | 15 | 5 | 12 | | 19 | 7 | 16 | 21 | 20 | 14 | 4 | 11 | | 20 | 7 | 16 | 21 | 20 | 14 | 4 | 10 | | 21 | 7 | 16 | 21 | 20 | 14 | 3 | 9 | | 22 | 8 | 17 | 21 | 20 | 13 | 3 | 8 | | 23 | 8 | 17 | 21 | 20 | 13 | 3 | 7 | | 24 | 9 | 17 | 21 | 20 | 13 | 2 | 6 | | 25 | 9 | 17 | 21 | 20 | 13 | 2 | 5 | | 26 | 9 | 18 | 21 | 20 | 12 | 2 | 4 | | 27 | 10 | 18 | 21 | 19 | 12 | 1 | 3 | | 28 | 10 | 18 | 21 | 19 | 12 | 1 | 2 | | 29 | 10 | 18 | 22 | 19 | 11 | 0 | 1 | | 30 | 11 | 18 | 22 | 19 | 11 | 0 | 0 | +-----+----+----+----+----+----+----+-----+ |Sun’s| 11 | 10 | 9 | 8 | 7 | 6 |Sun’s| |Ano. | S. | S. | S. | S. | S. | S. |Ano. | | +----+----+----+----+----+----+ | | | Add | | +-----+-----------------------------+-----+ +-----------------------------------------+ | TABLE IX. _Equation of the Moon’s | | mean Anomaly._ | +-----+-----------------------------+-----+ |Sun’s| |Sun’s| |Anom.| Add |Anom.| +-----+----+----+----+----+----+----+-----+ | | 0 | 1 | 2 | 3 | 4 | 5 | | | | S. | S. | S. | S. | S. | S. | | +-----+----+----+----+----+----+----+-----+ | ° | ʹ | ʹ | ʹ | ʹ | ʹ | ʹ | ° | +-----+----+----+----+----+----+----+-----+ | 0 | 0 | 10 | 17 | 20 | 17 | 10 | 30 | | 1 | 0 | 10 | 17 | 20 | 17 | 10 | 29 | | 2 | 1 | 11 | 17 | 20 | 17 | 9 | 28 | | 3 | 1 | 11 | 18 | 20 | 17 | 9 | 27 | | 4 | 1 | 11 | 18 | 20 | 17 | 9 | 26 | | 5 | 2 | 12 | 18 | 20 | 17 | 9 | 25 | | 6 | 2 | 12 | 18 | 20 | 16 | 8 | 24 | | 7 | 2 | 12 | 18 | 20 | 16 | 8 | 23 | | 8 | 3 | 12 | 18 | 20 | 16 | 8 | 22 | | 9 | 3 | 12 | 19 | 20 | 16 | 7 | 21 | | 10 | 3 | 13 | 19 | 20 | 16 | 7 | 20 | | 11 | 4 | 13 | 19 | 20 | 15 | 7 | 19 | | 12 | 4 | 13 | 19 | 20 | 15 | 6 | 18 | | 13 | 4 | 13 | 19 | 19 | 15 | 6 | 17 | | 14 | 5 | 14 | 19 | 19 | 15 | 6 | 16 | | 15 | 5 | 14 | 19 | 19 | 14 | 5 | 15 | | 16 | 5 | 14 | 19 | 19 | 14 | 5 | 14 | | 17 | 6 | 14 | 19 | 19 | 14 | 5 | 13 | | 18 | 6 | 15 | 19 | 19 | 14 | 4 | 12 | | 19 | 6 | 15 | 20 | 19 | 13 | 4 | 11 | | 20 | 7 | 15 | 20 | 19 | 13 | 4 | 10 | | 21 | 7 | 15 | 20 | 19 | 13 | 3 | 9 | | 22 | 7 | 16 | 20 | 19 | 13 | 3 | 8 | | 23 | 8 | 16 | 20 | 19 | 12 | 3 | 7 | | 24 | 8 | 16 | 20 | 18 | 12 | 2 | 6 | | 25 | 8 | 16 | 20 | 18 | 12 | 2 | 5 | | 26 | 9 | 16 | 20 | 18 | 11 | 1 | 4 | | 27 | 9 | 17 | 20 | 18 | 11 | 1 | 3 | | 28 | 9 | 17 | 20 | 18 | 11 | 1 | 2 | | 29 | 10 | 17 | 20 | 18 | 10 | 0 | 1 | | 30 | 10 | 17 | 20 | 17 | 10 | 0 | 0 | +-----+----+----+----+----+----+----+-----+ | | 11 | 10 | 9 | 8 | 7 | 6 | | |Sun’s| S. | S. | S. | S. | S. | S.|Sun’s| |Anom.+----+----+----+----+----+----+Anom.| | | Subtract | | +-----+-----------------------------+-----+ +-------------------------------------------------------------+ | TABLE X. _The Moon’s elliptic Equation._ | +------+-----------------------------------------------+------+ | | | | |Moon’s| Add |Moon’s| | +-------+-------+-------+-------+-------+-------+ | | Ano. | 0 | 1 | 2 | 3 | 4 | 5 |Ano. | | | Signs | Signs | Signs | Signs | Signs | Signs | | +------+-------+-------+-------+-------+-------+-------+------+ | ° | H. M. | H. M. | H. M. | H. M. | H. M. | H. M. | ° | +------+-------+-------+-------+-------+-------+-------+------+ | 0 | 0 0 | 4 49 | 8 8 | 9 2 | 7 32 | 4 14 | 30 | | 1 | 0 10 | 4 57 | 8 12 | 9 1 | 7 27 | 4 6 | 29 | | 2 | 0 20 | 5 5 | 8 16 | 9 0 | 7 22 | 3 58 | 28 | | 3 | 0 30 | 5 13 | 8 20 | 8 59 | 7 17 | 3 50 | 27 | | 4 | 0 40 | 5 21 | 8 24 | 8 58 | 7 12 | 3 42 | 26 | | 5 | 0 50 | 5 29 | 8 28 | 8 57 | 7 6 | 3 34 | 25 | | 6 | 1 0 | 5 37 | 8 31 | 8 55 | 7 0 | 3 26 | 24 | | 7 | 1 10 | 5 45 | 8 34 | 8 53 | 6 54 | 3 18 | 23 | | 8 | 1 20 | 5 53 | 8 37 | 8 51 | 6 48 | 3 10 | 22 | | 9 | 1 30 | 6 1 | 8 40 | 8 49 | 6 42 | 3 2 | 21 | | 10 | 1 40 | 6 9 | 8 43 | 8 47 | 6 36 | 2 53 | 20 | | 11 | 1 50 | 6 16 | 8 45 | 8 44 | 6 30 | 2 45 | 19 | | 12 | 2 0 | 6 23 | 8 47 | 8 41 | 6 24 | 2 37 | 18 | | 13 | 2 10 | 6 30 | 8 49 | 8 38 | 6 18 | 2 29 | 17 | | 14 | 2 20 | 6 37 | 8 51 | 8 35 | 6 11 | 2 21 | 16 | | 15 | 2 30 | 6 44 | 8 53 | 8 32 | 6 4 | 2 12 | 15 | | 16 | 2 40 | 6 51 | 8 55 | 8 29 | 5 57 | 2 3 | 14 | | 17 | 2 50 | 6 58 | 8 57 | 8 26 | 5 50 | 1 54 | 13 | | 18 | 3 0 | 7 4 | 8 59 | 8 23 | 5 43 | 1 45 | 12 | | 19 | 3 10 | 7 10 | 9 0 | 8 20 | 5 36 | 1 36 | 11 | | 20 | 3 19 | 7 16 | 9 1 | 8 16 | 5 29 | 1 27 | 10 | | 21 | 3 28 | 7 22 | 9 2 | 8 12 | 5 22 | 1 19 | 9 | | 22 | 3 37 | 7 28 | 9 2 | 8 8 | 5 15 | 1 11 | 8 | | 23 | 3 46 | 7 33 | 9 3 | 8 4 | 5 8 | 1 3 | 7 | | 24 | 3 55 | 7 38 | 9 3 | 8 0 | 5 1 | 0 54 | 6 | | 25 | 4 4 | 7 43 | 9 4 | 7 56 | 4 54 | 0 45 | 5 | | 26 | 4 13 | 7 48 | 9 4 | 7 52 | 4 46 | 0 36 | 4 | | 27 | 4 22 | 7 53 | 9 4 | 7 47 | 4 38 | 0 27 | 3 | | 28 | 4 31 | 7 58 | 9 3 | 7 42 | 4 30 | 0 18 | 2 | | 29 | 4 40 | 8 3 | 9 3 | 7 37 | 4 22 | 0 9 | 1 | | 30 | 4 49 | 8 8 | 9 2 | 7 32 | 4 14 | 0 0 | 0 | +------+-------+-------+-------+-------+-------+-------+------+ | | 11 | 10 | 9 | 8 | 7 | 6 | | |Moon’s| Signs | Signs | Signs | Signs | Signs | Signs |Moon’s| | +-------+-------+-------+-------+-------+-------+ | | Ano. | Subtract | Ano. | +------+-----------------------------------------------+------+ +---------------------------------------------------------------+ | TABLE XI. _The Sun’s Equation at the time of | | New and Full Moon._ | +-------+-----------------------------------------------+-------+ | | Subtract | | | Sun’s +-------+-------+-------+-------+-------+-------+ Sun’s | | Anom. | 0 | 1 | 2 | 3 | 4 | 5 | Anom. | | | Signs | Signs | Signs | Signs | Signs | Signs | | +-------+-------+-------+-------+-------+-------+-------+-------+ | ° | H. M. | H. M. | H. M. | H. M. | H. M. | H. M. | ° | +-------+-------+-------+-------+-------+-------+-------+-------+ | 0 | 0 0 | 1 44 | 3 2 | 3 32 | 3 5 | 1 48 | 30 | | 1 | 0 4 | 1 47 | 3 3 | 3 32 | 3 3 | 1 45 | 29 | | 2 | 0 7 | 1 50 | 3 5 | 3 32 | 3 2 | 1 42 | 28 | | 3 | 0 11 | 1 53 | 3 7 | 3 32 | 3 0 | 1 38 | 27 | | 4 | 0 14 | 1 57 | 3 9 | 3 32 | 2 58 | 1 35 | 26 | | 5 | 0 18 | 2 0 | 3 10 | 3 31 | 2 56 | 1 31 | 25 | | 6 | 0 22 | 2 3 | 3 12 | 3 31 | 2 54 | 1 28 | 24 | | 7 | 0 25 | 2 6 | 3 14 | 3 31 | 2 52 | 1 24 | 23 | | 8 | 0 29 | 2 8 | 3 16 | 3 30 | 2 50 | 1 21 | 22 | | 9 | 0 32 | 2 11 | 3 17 | 4 30 | 2 48 | 1 17 | 21 | | 10 | 0 36 | 2 14 | 3 18 | 3 30 | 2 45 | 1 14 | 20 | | 11 | 0 40 | 2 17 | 3 19 | 3 29 | 2 43 | 1 11 | 19 | | 12 | 0 43 | 2 20 | 3 20 | 3 29 | 2 40 | 1 7 | 18 | | 13 | 0 47 | 2 22 | 3 21 | 3 28 | 2 37 | 1 4 | 17 | | 14 | 0 50 | 2 25 | 3 22 | 3 27 | 2 35 | 1 0 | 16 | | 15 | 0 54 | 2 28 | 3 23 | 3 26 | 2 32 | 0 56 | 15 | | 16 | 0 57 | 2 30 | 3 24 | 3 25 | 2 29 | 0 52 | 14 | | 17 | 1 0 | 2 32 | 3 25 | 3 24 | 2 26 | 0 49 | 13 | | 18 | 1 4 | 2 35 | 3 26 | 3 23 | 2 23 | 0 45 | 12 | | 19 | 1 7 | 2 38 | 3 27 | 3 22 | 2 21 | 0 41 | 11 | | 20 | 1 11 | 2 40 | 3 28 | 3 21 | 2 18 | 0 38 | 10 | | 21 | 1 14 | 2 43 | 3 28 | 3 20 | 2 15 | 0 34 | 9 | | 22 | 1 17 | 2 45 | 3 29 | 3 19 | 2 12 | 0 30 | 8 | | 23 | 1 21 | 2 47 | 3 29 | 3 18 | 2 10 | 0 26 | 7 | | 24 | 1 24 | 2 49 | 3 30 | 3 17 | 2 7 | 0 23 | 6 | | 25 | 1 28 | 2 51 | 3 30 | 3 15 | 2 4 | 0 19 | 5 | | 26 | 1 31 | 2 54 | 3 31 | 3 13 | 2 1 | 0 15 | 4 | | 27 | 1 34 | 2 57 | 3 31 | 3 11 | 1 58 | 0 11 | 3 | | 28 | 1 38 | 2 59 | 3 31 | 3 9 | 1 55 | 0 7 | 2 | | 29 | 1 41 | 3 1 | 3 32 | 3 7 | 1 52 | 0 4 | 1 | | 30 | 1 44 | 3 2 | 3 32 | 3 5 | 1 48 | 0 0 | 0 | +-------+-------+-------+-------+-------+-------+-------+-------+ | | 11 | 10 | 9 | 8 | 7 | 6 | | | Sun’s | Signs | Signs | Signs | Signs | Signs | Signs | Sun’s | | Anom. +-------+-------+-------+-------+-------+-------+ Anom. | | | Add | | +-------+-----------------------------------------------+-------+ +---------------------------------------------------------------+ | TABLE XII. _Equation of the Sun’s mean Place._ | +-------+-----------------------------------------------+-------+ | | Subtract | | | Sun’s +-------+-------+-------+-------+-------+-------+ Sun’s | | Anom. | 0 | 1 | 2 | 3 | 4 | 5 | Anom. | | | Signs | Signs | Signs | Signs | Signs | Signs | | +-------+-------+-------+-------+-------+-------+-------+-------+ | ° | ° ʹ | ° ʹ | ° ʹ | ° ʹ | ° ʹ | ° ʹ | ° | +-------+-------+-------+-------+-------+-------+-------+-------+ | 0 | 0 0 | 0 57 | 1 40 | 1 56 | 1 42 | 0 59 | 30 | | 1 | 0 2 | 0 59 | 1 41 | 1 56 | 1 41 | 0 57 | 29 | | 2 | 0 4 | 1 0 | 1 42 | 1 56 | 1 40 | 0 56 | 28 | | 3 | 0 6 | 1 1 | 1 43 | 1 56 | 1 39 | 0 54 | 27 | | 4 | 0 8 | 1 2 | 1 44 | 1 56 | 1 38 | 0 52 | 26 | | 5 | 0 10 | 1 4 | 1 45 | 1 56 | 1 36 | 0 50 | 25 | | 6 | 0 12 | 1 6 | 1 45 | 1 56 | 1 35 | 0 48 | 24 | | 7 | 0 14 | 1 7 | 1 46 | 1 55 | 1 34 | 0 46 | 23 | | 8 | 0 16 | 1 9 | 1 47 | 1 55 | 1 33 | 0 44 | 22 | | 9 | 0 18 | 1 10 | 1 48 | 1 55 | 1 32 | 0 42 | 21 | | 10 | 0 20 | 1 12 | 1 48 | 1 54 | 1 30 | 0 41 | 20 | | 11 | 0 22 | 1 14 | 1 49 | 1 54 | 1 29 | 0 39 | 19 | | 12 | 0 24 | 1 15 | 1 50 | 1 54 | 1 28 | 0 37 | 18 | | 13 | 0 26 | 1 17 | 1 51 | 1 53 | 1 26 | 0 35 | 17 | | 14 | 0 28 | 1 18 | 1 51 | 1 53 | 1 25 | 0 33 | 16 | | 15 | 0 30 | 1 20 | 1 52 | 1 52 | 1 23 | 0 31 | 15 | | 16 | 0 31 | 1 21 | 1 52 | 1 52 | 1 22 | 0 29 | 14 | | 17 | 0 33 | 1 22 | 1 53 | 1 51 | 1 21 | 0 27 | 13 | | 18 | 0 35 | 1 24 | 1 53 | 1 51 | 1 19 | 0 25 | 12 | | 19 | 0 37 | 1 25 | 1 54 | 1 50 | 1 18 | 0 23 | 11 | | 20 | 0 39 | 1 27 | 1 54 | 1 49 | 1 16 | 0 21 | 10 | | 21 | 0 41 | 1 28 | 1 55 | 1 49 | 1 14 | 0 19 | 9 | | 22 | 0 43 | 1 29 | 1 55 | 1 48 | 1 13 | 0 17 | 8 | | 23 | 0 45 | 1 30 | 1 55 | 1 47 | 1 11 | 0 14 | 7 | | 24 | 0 46 | 1 32 | 1 56 | 1 46 | 1 10 | 0 12 | 6 | | 25 | 0 48 | 1 33 | 1 56 | 1 46 | 1 8 | 0 10 | 5 | | 26 | 0 50 | 1 34 | 1 56 | 1 45 | 1 6 | 0 8 | 4 | | 27 | 0 52 | 1 35 | 1 56 | 1 45 | 1 5 | 0 6 | 3 | | 28 | 0 54 | 1 36 | 1 56 | 1 44 | 1 3 | 0 4 | 2 | | 29 | 0 55 | 1 38 | 1 56 | 1 43 | 1 1 | 0 2 | 1 | | 30 | 0 57 | 1 40 | 1 56 | 1 42 | 0 59 | 0 0 | 0 | +-------+-------+-------+-------+-------+-------+-------+-------+ | | 11 | 10 | 9 | 8 | 7 | 6 | | | Sun’s | Signs | Signs | Signs | Signs | Signs | Signs | Sun’s | | Anom. +-------+-------+-------+-------+-------+-------+ Anom. | | | Add | | +-------+-----------------------------------------------+-------+ +-----------------------------------------+ | TABLE XIII. _Equation of the | | Moon’s Nodes._ | +-----+-----------------------------+-----+ | | Subtract | | |Sun’s+----+----+----+----+----+----+Sun’s| |Ano. | 0 | 1 | 2 | 3 | 4 | 5 |Ano. | | | S. | S. | S. | S. | S. | S. | | +-----+----+----+----+----+----+----+-----+ | ° | ʹ | ʹ | ʹ | ʹ | ʹ | ʹ | ° | +-----+----+----+----+----+----+----+-----+ | 0 | 0 | 5 | 8 | 10 | 8 | 5 | 30 | | 1 | 0 | 5 | 8 | 10 | 8 | 5 | 29 | | 2 | 0 | 5 | 8 | 10 | 8 | 5 | 28 | | 3 | 0 | 5 | 8 | 10 | 8 | 4 | 27 | | 4 | 1 | 5 | 8 | 10 | 8 | 4 | 26 | | 5 | 1 | 5 | 8 | 10 | 8 | 4 | 25 | | 6 | 1 | 6 | 9 | 10 | 8 | 4 | 24 | | 7 | 1 | 6 | 9 | 9 | 8 | 4 | 23 | | 8 | 1 | 6 | 9 | 9 | 8 | 4 | 22 | | 9 | 1 | 6 | 9 | 9 | 7 | 3 | 21 | | 10 | 2 | 6 | 9 | 9 | 7 | 3 | 20 | | 11 | 2 | 6 | 9 | 9 | 7 | 3 | 19 | | 12 | 2 | 6 | 9 | 9 | 7 | 3 | 18 | | 13 | 2 | 6 | 9 | 9 | 7 | 3 | 17 | | 14 | 2 | 7 | 9 | 9 | 7 | 3 | 16 | | 15 | 2 | 7 | 9 | 9 | 7 | 3 | 15 | | 16 | 2 | 7 | 9 | 9 | 7 | 2 | 14 | | 17 | 3 | 7 | 9 | 9 | 7 | 2 | 13 | | 18 | 3 | 7 | 9 | 9 | 6 | 2 | 12 | | 19 | 3 | 7 | 9 | 9 | 6 | 2 | 11 | | 20 | 3 | 7 | 9 | 9 | 6 | 2 | 10 | | 21 | 3 | 7 | 9 | 9 | 6 | 2 | 9 | | 22 | 4 | 7 | 9 | 9 | 6 | 1 | 8 | | 23 | 4 | 8 | 9 | 9 | 6 | 1 | 7 | | 24 | 4 | 8 | 9 | 9 | 6 | 1 | 6 | | 25 | 4 | 8 | 9 | 9 | 6 | 1 | 5 | | 26 | 4 | 8 | 10 | 9 | 5 | 1 | 4 | | 27 | 4 | 8 | 10 | 9 | 5 | 1 | 3 | | 28 | 4 | 8 | 10 | 8 | 5 | 0 | 2 | | 29 | 5 | 8 | 10 | 8 | 5 | 0 | 1 | | 30 | 5 | 8 | 10 | 8 | 5 | 0 | 0 | +-----+----+----+----+----+----+----+-----+ | | 11 | 10 | 9 | 8 | 7 | 6 | | |Sun’s| S. | S. | S. | S. | S. | S. |Sun’s| |Ano. +----+----+----+----+----+----+Ano. | | | Add | | +-----------------------------------+-----+ | The above titles, _Add_ and _Subtract_, | | are right when the Equation is applied | | to the Sun’s mean distance from the | | Node; but when it is applied to the | | mean place of the Node, the titles must | | be changed. | +-----------------------------------------+ +------------------------+ | TAB. XIV. _The | | Moon’s latitude | | in Eclipses._ | +------------------------+ | Argument of Latit. | +------+-----------------+ | Moon | | | fr. | Sig. 0 N. A. | | the | Sig. 6 S. D. | | Node.| | +------+----------+------+ | ° | ° ʹ ʺ | ° | +------+----------+------+ | 0 | 0 0 0 | 30 | | 1 | 0 5 15 | 29 | | 2 | 0 10 30 | 28 | | 3 | 0 15 44 | 27 | | 4 | 0 20 59 | 26 | | 5 | 0 26 13 | 25 | | 6 | 0 31 26 | 24 | | 7 | 0 36 39 | 23 | | 8 | 0 41 51 | 22 | | 9 | 0 47 2 | 21 | | 10 | 0 52 13 | 20 | | 11 | 0 57 23 | 19 | | 12 | 1 2 31 | 18 | | 13 | 1 7 38 | 17 | | 14 | 1 12 44 | 16 | | 15 | 1 17 49 | 15 | | 16 | 1 22 52 | 14 | | 17 | 1 27 53 | 13 | | 18 | 1 32 54 | 12 | +------+----------+------+ | | Moon | | N. D. Sig. 5 | fr. | | S. A. Sig. 11 | the | | | Node.| +-----------------+------+ | Argument of Latit. | +------------------------+ | This Table extends | | no farther than the | | limits of Eclipses. | | N. A. signifies North | | Ascending Lat. S. A. | | South Ascending; N. D. | | North Descending; | | and S. D. South | | Descending. | +------------------------+ +--------------------------------------------------------+ | TABLE XV. _The Moons Horizontal Parallax; | | the Semidiameters and true Horary motions | | of the Sun and Moon._ | +--------------------------------------------------------+ | Anomaly of the Sun and Moon. | | +------------------------------------------------+ | | Moon’s Horizontal Parallax. | | | +----------------------------------------+ | | | Sun’s Semidiameter. | | | | +--------------------------------+ | | | | Moon’s Semidiamet. | | | | | +------------------------+ | | | | | Moon’s horary Mot. | | | | | | +----------------+ | | | | | | Sun’s | | | | | | | horary Mot. | | | | | | | +---------+ | | | | | | | Anomaly | | | | | | | | of the | | | | | | | | Sun and | | | | | | | | Moon. | +-------+-------+-------+-------+-------+------+---------+ | ^s ° | ʹ ʺ | ʹ ʺ | ʹ ʺ | ʹ ʺ | ʹ ʺ | ^s ° | +-------+-------+-------+-------+-------+------+---------+ | 0 0 | 54 59 | 15 50 | 14 54 | 30 10 | 2 23 | 12 0 | | 6 | 54 59 | 15 50 | 14 55 | 30 12 | 2 23 | 24 | | 12 | 55 0 | 15 50 | 14 56 | 30 15 | 2 23 | 18 | | 18 | 55 4 | 15 51 | 14 57 | 30 18 | 2 23 | 12 | | 24 | 55 11 | 15 51 | 14 58 | 30 26 | 2 23 | 6 | | 1 0 | 55 20 | 15 52 | 14 59 | 30 34 | 2 23 | 11 0 | | 6 | 55 30 | 15 53 | 15 1 | 30 44 | 2 24 | 24 | | 12 | 55 40 | 13 54 | 15 4 | 30 55 | 2 24 | 18 | | 18 | 55 51 | 15 55 | 15 8 | 31 9 | 2 24 | 12 | | 24 | 56 0 | 15 56 | 15 12 | 31 23 | 2 25 | 6 | | 2 0 | 56 11 | 15 58 | 15 17 | 31 40 | 2 25 | 10 0 | | 6 | 56 24 | 15 59 | 15 22 | 31 58 | 2 26 | 24 | | 12 | 56 41 | 16 1 | 15 26 | 32 17 | 2 27 | 18 | | 18 | 57 12 | 16 2 | 15 30 | 32 39 | 2 27 | 12 | | 24 | 57 30 | 16 4 | 15 36 | 33 11 | 2 28 | 6 | | 3 0 | 57 49 | 16 6 | 15 41 | 33 23 | 2 28 | 9 0 | | 6 | 58 10 | 16 8 | 15 46 | 33 47 | 2 29 | 24 | | 12 | 58 31 | 16 9 | 15 52 | 34 11 | 2 29 | 18 | | 18 | 58 52 | 16 11 | 15 58 | 34 34 | 2 29 | 12 | | 24 | 59 11 | 16 13 | 16 3 | 34 58 | 2 30 | 6 | | 4 0 | 59 30 | 16 14 | 16 9 | 35 22 | 2 30 | 8 0 | | 6 | 59 52 | 16 15 | 16 14 | 35 45 | 2 31 | 24 | | 12 | 60 9 | 16 17 | 16 19 | 36 0 | 2 31 | 18 | | 18 | 60 26 | 16 19 | 16 24 | 36 20 | 2 32 | 12 | | 24 | 60 40 | 16 20 | 16 28 | 36 40 | 2 32 | 6 | | 5 0 | 60 54 | 16 21 | 16 31 | 37 0 | 2 32 | 7 0 | | 6 | 61 4 | 16 21 | 16 34 | 37 10 | 2 33 | 24 | | 12 | 61 11 | 16 22 | 16 37 | 37 19 | 2 33 | 18 | | 18 | 61 16 | 16 22 | 16 38 | 37 28 | 2 33 | 12 | | 24 | 61 20 | 16 23 | 16 39 | 37 36 | 2 33 | 6 | | 6 0 | 61 24 | 16 23 | 16 39 | 37 40 | 2 33 | 6 0 | +-------+-------+-------+-------+-------+------+---------+ | The gradual increase or decrease of the above numbers | | being so small, it is sufficient to have them to every | | sixth degree; the proportions for the intermediate | | degrees being easily made by sight. | +--------------------------------------------------------+ +----------------------------------+ | TABLE XVI. _The Sun’s mean | | Motion and Anomaly._ | +---------+-------------+----------+ | | Sun’s mean | Sun’s | |Years of | Longitude | mean | |Christ | from Aries. | Anomaly. | |beginning+-------------+----------+ | | ^s ° ʹ ʺ | ^s ° ʹ| +---------+-------------+----------+ O.S. | 1 | 9 7 53 10 | 6 29 54 | | 1301 | 9 17 42 30 | 6 16 58 | | 1401 | 9 18 27 50 | 6 15 59 | | 1501 | 9 19 13 10 | 6 14 59 | | 1601 | 9 19 58 30 | 6 13 59 | | 1701 | 9 20 43 50 | 6 12 59 | N.S. | 1753 | 9 10 16 52 | 6 1 38 | | 1801 | 9 9 39 39 | 6 0 10 | Old Style +---------+-------------+----------+ to the | | Sun’s mean | Sun’s | beginning |Years of | Motion. | mean | of A. D. |Christ | | Anomaly. | 1753; |compleat +-------------+----------+ then | | ^s ° ʹ ʺ | ^s ° ʹ| New Style +---------+-------------+----------+ | 1 | 11 29 45 40 | 11 29 45 | | 2 | 11 29 31 20 | 11 29 29 | | 3 | 11 29 17 0 | 11 29 14 | | 4 | 0 0 1 49 | 11 29 58 | | 5 | 11 29 47 29 | 11 29 42 | | 6 | 11 29 33 9 | 11 29 27 | | 7 | 11 29 18 49 | 11 29 11 | | 8 | 0 0 3 38 | 11 29 55 | | 9 | 11 29 49 18 | 11 29 40 | | 10 | 11 29 34 58 | 11 29 24 | | 11 | 11 29 20 38 | 11 29 9 | | 12 | 0 0 5 26 | 11 29 53 | | 13 | 11 29 51 7 | 11 29 37 | | 14 | 11 29 36 47 | 11 29 22 | | 15 | 11 29 22 27 | 11 29 7 | | 16 | 0 0 7 15 | 11 29 50 | | 17 | 11 29 52 55 | 11 29 35 | | 18 | 11 29 38 35 | 11 29 20 | | 19 | 11 29 24 16 | 11 29 4 | | 20 | 0 0 9 4 | 11 29 48 | | 40 | 0 0 18 8 | 11 29 36 | | 60 | 0 0 27 12 | 11 29 24 | | 80 | 0 0 36 16 | 11 29 12 | | 100 | 0 0 45 20 | 11 29 0 | | 200 | 0 1 30 40 | 11 28 1 | | 300 | 0 2 16 0 | 11 27 1 | | 400 | 0 3 1 20 | 11 26 1 | | 500 | 0 3 46 40 | 11 25 2 | | 600 | 0 4 32 0 | 11 24 2 | | 700 | 0 5 17 20 | 11 23 2 | | 800 | 0 6 2 40 | 11 22 3 | | 900 | 0 6 48 0 | 11 21 3 | | 1000 | 0 7 33 20 | 11 20 3 | | 2000 | 0 15 6 40 | 11 10 7 | | 3000 | 0 22 40 0 | 11 0 10 | | 4000 | 1 0 13 20 | 10 20 13 | | 5000 | 1 7 46 40 | 10 10 16 | | 6000 | 1 15 20 0 | 10 0 19 | +---------+-------------+----------+ | | Sun’s mean | Sun’s | | | Motion. | mean | | | | Anomaly. | | Months +-------------+----------+ | | ^s ° ʹ ʺ | ^s ° ʹ| +---------+-------------+----------+ | Jan. | 0 0 0 0 | 0 0 0 | | Feb. | 1 0 33 18 | 1 0 33 | | Mar. | 1 28 9 11 | 1 28 9 | | Apr. | 2 28 42 30 | 2 28 42 | | May. | 3 28 16 40 | 3 28 17 | | June | 4 28 49 58 | 4 28 50 | | July | 5 28 24 8 | 5 28 24 | | Aug. | 6 28 57 26 | 6 28 57 | | Sep. | 7 29 30 44 | 7 29 30 | | Oct. | 8 29 4 54 | 8 29 4 | | Nov. | 9 29 38 12 | 9 29 37 | | Dec. | 10 29 12 22 | 10 29 11 | +---------+-------------+----------+ +-----+-------------+ | | Sun’s mean | | | Motion and | | | Anomaly. | |Days.+-------------+ | | ^s ° ʹ ʺ | +-----+-------------+ | 1 | 0 0 59 8 | | 2 | 0 1 58 17 | | 3 | 0 2 57 25 | | 4 | 0 3 56 33 | | 5 | 0 4 55 42 | | 6 | 0 5 54 50 | | 7 | 0 5 53 58 | | 8 | 0 7 53 7 | | 9 | 0 8 52 15 | | 10 | 0 9 51 23 | | 11 | 0 10 50 32 | | 12 | 0 11 49 40 | | 13 | 0 12 48 48 | | 14 | 0 13 47 57 | | 15 | 0 14 47 5 | | 16 | 0 15 46 13 | | 17 | 0 16 45 22 | | 18 | 0 17 44 30 | | 19 | 0 18 43 38 | | 20 | 0 19 42 47 | | 21 | 0 20 41 55 | | 22 | 0 21 41 3 | | 23 | 0 22 40 12 | | 24 | 0 23 39 20 | | 25 | 0 24 38 28 | | 26 | 0 25 37 37 | | 27 | 0 26 36 45 | | 28 | 0 27 35 53 | | 29 | 0 28 35 2 | | 30 | 0 29 34 10 | | 31 | 1 0 33 18 | +-----+-------------+ | In Leap-years, | | after _February_, | | add one Day and | | one Day’s motion. | +-------------------+ +----------------------+ | Sun’s mean Motion | | and Anomaly. | +------+---------------+ |Hours.| Mot. & Ano. | | +---------------+ | | ° ʹ ʺ | | ʹ | ʹ ʺ ʺʹ | | ʺ | ʺ ʺʹ ʺʺ | +------+---------------+ | 1 | 0 2 28 | | 2 | 0 4 56 | | 3 | 0 7 24 | | 4 | 0 9 51 | | 5 | 0 12 19 | | 6 | 0 14 47 | | 7 | 0 17 15 | | 8 | 0 19 43 | | 9 | 0 22 11 | | 10 | 0 24 38 | | 11 | 0 27 6 | | 12 | 0 29 34 | | 13 | 0 32 2 | | 14 | 0 34 30 | | 15 | 0 36 58 | | 16 | 0 39 26 | | 17 | 0 41 53 | | 18 | 0 44 21 | | 19 | 0 46 49 | | 20 | 0 49 17 | | 21 | 0 51 45 | | 22 | 0 54 13 | | 23 | 0 56 40 | | 24 | 0 59 8 | | 25 | 1 1 36 | | 26 | 1 4 4 | | 27 | 1 6 32 | | 28 | 1 9 0 | | 29 | 1 11 28 | | 30 | 1 13 55 | | 31 | 1 16 23 | | 32 | 1 18 51 | | 33 | 1 21 19 | | 34 | 1 23 47 | | 35 | 1 26 15 | | 36 | 1 28 42 | | 37 | 1 31 10 | | 38 | 1 33 38 | | 39 | 1 36 6 | | 40 | 1 38 34 | | 41 | 1 41 2 | | 42 | 1 43 30 | | 43 | 1 45 57 | | 44 | 1 48 25 | | 45 | 1 50 53 | | 46 | 1 53 21 | | 47 | 1 55 49 | | 48 | 1 58 17 | | 49 | 2 0 44 | | 50 | 2 3 12 | | 51 | 2 5 40 | | 52 | 2 8 8 | | 53 | 2 10 36 | | 54 | 2 13 4 | | 55 | 2 15 32 | | 56 | 2 17 59 | | 57 | 2 20 27 | | 58 | 2 22 55 | | 59 | 2 25 23 | | 60 | 2 27 51 | +------+---------------+ | In Leap-years, after | | _February_, add one | | Day and one Day’s | | motion. | +----------------------+ +----------------------------------------------+ | TABLE XVII. _The Sun’s Declination | | in every Degree of the Ecliptic._ | +-----+-----------+-----------+-----------+----+ | | ♈ ♎ | ♉ ♏ | ♊ ♐ | | |Signs| 0 6 | 1 7 | 2 8 | | | | Nor. Sou. | Nor. Sou. | Nor. Sou. | | +-----+-----------+-----------+-----------+----+ | ° | ° ʹ ʺ | ° ʹ ʺ | ° ʹ ʺ | ° | +-----+-----------+-----------+-----------+----+ | 0 | 0 0 0 | 11 29 33 | 20 11 16 | 30 | | 1 | 0 23 54 | 11 50 35 | 20 23 49 | 29 | | 2 | 0 47 48 | 12 11 26 | 20 36 0 | 28 | | 3 | 1 11 42 | 12 32 5 | 20 47 48 | 27 | | 4 | 1 35 34 | 12 52 31 | 20 59 13 | 26 | | 5 | 1 59 25 | 13 12 44 | 21 10 15 | 25 | | 6 | 2 23 14 | 13 32 54 | 21 20 53 | 24 | | 7 | 2 47 1 | 13 52 32 | 21 31 7 | 23 | | 8 | 3 10 45 | 14 12 5 | 21 40 58 | 22 | | 9 | 3 34 26 | 14 31 24 | 21 50 24 | 21 | | 10 | 3 58 4 | 14 50 28 | 21 59 25 | 20 | | 11 | 4 21 38 | 15 9 17 | 22 8 2 | 19 | | 12 | 4 45 8 | 15 27 51 | 22 16 14 | 18 | | 13 | 5 8 34 | 15 46 9 | 22 24 0 | 17 | | 14 | 5 31 55 | 16 4 11 | 22 31 21 | 16 | | 15 | 5 55 11 | 16 21 57 | 22 38 16 | 15 | | 16 | 6 18 21 | 16 39 26 | 22 44 45 | 14 | | 17 | 6 41 25 | 16 56 37 | 22 50 49 | 13 | | 18 | 7 4 23 | 17 13 31 | 22 56 26 | 12 | | 19 | 7 27 15 | 17 30 7 | 23 1 36 | 11 | | 20 | 7 50 0 | 17 46 15 | 23 6 20 | 10 | | 21 | 8 12 36 | 18 2 24 | 23 10 38 | 9 | | 22 | 8 35 5 | 18 18 3 | 23 14 29 | 8 | | 23 | 8 57 26 | 18 33 24 | 23 17 52 | 7 | | 24 | 9 19 39 | 18 48 25 | 23 20 49 | 6 | | 25 | 9 41 43 | 19 3 5 | 23 23 19 | 5 | | 26 | 10 3 37 | 19 17 26 | 23 25 22 | 4 | | 27 | 10 25 21 | 19 31 25 | 23 26 57 | 3 | | 28 | 10 46 56 | 19 45 3 | 23 28 5 | 2 | | 29 | 11 8 20 | 19 58 20 | 23 28 46 | 1 | | 30 | 11 29 33 | 20 11 16 | 23 29 0 | 0 | +-----+-----------+-----------+-----------+----+ | | ♓ ♍ | ♒ ♌ | ♑ ♋ | | |Signs| 1 5 | 10 4 | 9 3 | | | | Sou. Nor. | Sou. Nor. | Sou. Nor. | | +-----+-----------+-----------+-----------+----+ | If the Sun’s place be taken from the Tables | | on pag. 114 and 115, his declination may be | | had thereby, near enough for common use, | | from this Table, by entering it with the | | signs at the head and degrees at the left | | hand; or with the signs at the foot and | | degrees at the right hand. Thus, _March_ | | the 5th, the Sun’s place is ♓ 14° 53ʹ | | (call it 15°, being so near) to which | | answers 5° 55ʹ 11ʺ of the south | | declination. | +---------------------------------------------+ +---------------------------------+ | TABLE XVIII. _Lunations | | from 1 to 100000._ | +--------+---------+----+----+----+ | Lunat. | Days. | H. | M. | S. | +--------+---------+----+----+----+ | | Contain | | | | | 1 | 29 | 12 | 44 | 3 | | 2 | 59 | 1 | 28 | 6 | | 3 | 88 | 14 | 12 | 9 | | 4 | 118 | 2 | 56 | 13 | | 5 | 147 | 15 | 40 | 16 | +--------+---------+----+----+----+ | 6 | 177 | 4 | 24 | 19 | | 7 | 206 | 17 | 8 | 22 | | 8 | 236 | 5 | 52 | 25 | | 9 | 265 | 18 | 36 | 28 | | 10 | 295 | 7 | 20 | 31 | +--------+---------+----+----+----+ | 20 | 590 | 14 | 41 | 3 | | 30 | 885 | 22 | 1 | 34 | | 40 | 1181 | 5 | 22 | 6 | | 50 | 1476 | 12 | 42 | 37 | | 60 | 1771 | 20 | 3 | 9 | +--------+---------+----+----+----+ | 70 | 2067 | 3 | 23 | 40 | | 80 | 2362 | 10 | 44 | 12 | | 90 | 2657 | 18 | 4 | 43 | | 100 | 2953 | 1 | 25 | 15 | | 200 | 5906 | 2 | 50 | 30 | +--------+---------+----+----+----+ | 300 | 8859 | 4 | 15 | 45 | | 400 | 11812 | 5 | 41 | 0 | | 500 | 14765 | 7 | 6 | 15 | | 600 | 17718 | 8 | 31 | 30 | | 700 | 20671 | 9 | 56 | 45 | +--------+---------+----+----+----+ | 800 | 23624 | 11 | 22 | 0 | | 900 | 26577 | 12 | 47 | 15 | | 1000 | 29530 | 14 | 12 | 30 | | 2000 | 59061 | 4 | 25 | 0 | | 3000 | 88591 | 18 | 37 | 30 | +--------+---------+----+----+----+ | 4000 | 118122 | 8 | 50 | 0 | | 5000 | 147652 | 23 | 2 | 30 | | 6000 | 177183 | 13 | 15 | 0 | | 7000 | 206714 | 3 | 27 | 30 | | 8000 | 236244 | 17 | 40 | 0 | +--------+---------+----+----+----+ | 9000 | 265775 | 7 | 52 | 30 | | 10000 | 295305 | 22 | 5 | | | 20000 | 590611 | 20 | 10 | | | 30000 | 885917 | 18 | 15 | | | 40000 | 1181223 | 16 | 20 | | +--------+---------+----+----+----+ | 50000 | 1476529 | 14 | 25 | | | 60000 | 1771835 | 12 | 30 | | | 70000 | 2067141 | 10 | 35 | | | 80000 | 2362447 | 8 | 40 | | | 90000 | 2657753 | 6 | 45 | | | 100000 | 2953059 | 4 | 50 | | +--------+---------+----+----+----+ | By comparing this Table with | | the Table on page 113, it is | | easy to find how many Lunations | | are contained in any given | | number of Sidereal, Julian, and | | Solar years, from 1 to 8000. | +---------------------------------+