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"