The mean symbolical periods of the
various bodies are the length of time
between two successive conjunctions of
that body with the Sun at the same
geocentric longitude, i.e, falling on
the same day of a year. In other words
the Sun in its apparent annual
revolution forms conjunctions with each
of the other bodies as viewed from the
Earth, each successive annual
conjunction with the same body taking
place at an advanced point in the
Zodiac. After a time these conjunctions
themselves form a cycle of conjunctions,
beginning on approximately the same
degree of the Zodiac, or days of the
year. The length of this cycle with
reference to a particular planet
constitutes the planetary periods. These
are:
Moon:
19
years, the Cycle of Meton (q.v.).
Mercury:
79
years, with an inconstant mean advance
of 1°37' each cycle.
Venus:
8
years, with an inconstant mean advance
of 1°32' each cycle.
Mars:
79
years, with an inconstant mean advance
of 1°34' each cycle.
Jupiter:
83
years exact.
Saturn:
59
years, with a mean advance of 1°53'
Uranus:
84
years, with a mean advance of 40'
Neptune:
164
years, 280 days; a mean annual motion of
2°10'54"
Pluto.
247.7
years, with a mean annual motion that,
because of the extreme ellipticity of
its orbit, varies from 1° in Pisces
through Gemini, to 2.5° in Virgo
through Sagittarius.
Ptolemy cites these time-measures as
follows: Moon 4y, Mercury 10y, Venus 8y,
Sun 19y, Mars 15y, Jupiter 12y, Saturn
30y. Those moderns who use his system
add Uranus 90y, Neptune 18oy, Pluto
360y. Lilley alters this, as regards the
Moon to 25y, and Mercury to 20y; others
assign 27y to Mercury.
By means of these periods one is able to
arrive at a rough approximation of a
planet's position at a given date in a
year for which an ephemeris is
unavailable; as follows:
Example:
To determine
the longitude of Uranus on October 15th,
1672 (new style), add multiples of 84y
and subtract the mean advance. To do
this in one operation: assume any year
in this epoch, say 1902. From this
subtract 1672. This gives an interval of
230 years. Divide this by 84; the
result, 2 periods and 62 years. Subtract
62 from 1902, which gives the year 1840:
two Uranus periods subsequent to the
desired date. To illustrate: the
longitude of Uranus, as perceived in the
ephemeris for 1940, on October 15th, is
17°09' Pisces. The 40' advance, times
the two periods, is 1°20'. Subtract
this from 17°09' and you have 15°19'
Pisces as the longitude of Uranus on
October 15th, 1672 (N.S.).
These and additional periods, arranged
in tabular form for reference use, are
as follows:
Planet...Revolutions..Years...Remainder...Other
Periods in Years
Moon.........254.....19....Cycle of
Meton...8-372-1040*#
Mercury......318.....79....+1°37'(a)........7-13-33-46-204*
Venus........13......
8....+1°32'(a)........235-243
Mars.........42......79....+1°34'...........16-32147-205*
Jupiter.......7......83....+0°1'*
Saturn........2......59....+1°53'...........206*
* Unusually exact. # Not an eclipse
cycle. (a) Inconstant mean advance.
The three outer planets are usually
computed by other methods: either (a)
the first return, in even years, with a
plus or minus correction showing excess
over 360 degrees; or (b) the net mean
annual motion.
..Planet..........Period....Remainder...Advance*
..Uranus............84y.......+1°4'.....4°17'55"
..Neptune..........164y.......+0°34'....2°11"55"
..Pluto............245y.......-0°29'....1°28'03"
*Mean annual advance, based on
mean precession.
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