6 Time by the Moon

Metonic cycle

The Moon is neglected in the Gregorian calendar but sailors certainly appreciate its importance. Britain as a maritime nation has always been interested in the topic. The earliest recorded attempt at tidal prediction is mentioned in a manuscript entitled Codex Cottonianus JuliusDVII preserved in the British Museum. It contains calendar and other astronomical information including a table giving the time of high water at London Bridge attributed to John Wallingford, who died Abbott of St Albans in 1213.

Tide tables for the port of Liverpool, calculated by the Rev. George Holden, were first published in 1770. Tide tables for a number of ports were published privately by secret methods handed down from father to son for generations. The Hydrographic Department of the Admiralty published tables for the year 1833, more than a century after the British government took action to deal with the problem of longitude at sea.

Tides are divided into species. Those with a period of about a day are called diurnal tides and those with a period of about half a day semidiurnal. The long period species include all tidal oscillations ranging from 14 days to 19 years. The elements are divided into constituents and the difference between mean sea level and high water or mean sea level and low water is called its amplitude. This classification gives rise to the following variations of tidal heights driven by the Moon in any particularly place:

Higher high water , lower high water; higher low water, lower low water.

An old sailors’ rule says the tide rises one twelfth of its range in the first hour, 2 twelfths  in the second hour, 3 twelfths in the third hour, then pauses and retraces the sequence. Spring tides have the greatest range and occur around full Moon and new Moon. (Spring tides don’t necessarily occur in spring.) Neap tides, with a lesser range between high and low water occur with the Moon in first quarter and last quarter. So-called king tides occur in January and July when Oceania is closest to the Sun and farthest from the Sun respectively. At those dates Oceania is orbiting at its fastest rate and slowest rate respectively, or time is accelerating and decelerating. Mean sea level is the benchmark for  survey points ashore but it obviously fluctuates.

Question: Is the water going up and down or is the land going down and up?  Relative to what? You can almost see the Harmonics beloved by Laplace and Kelvin. The graph of the Rule of Twelfths is Gauss’s bell curve of probability related to Pascal’s triangle. It is included in many tide tables along with instructions how to find the height of tide between tabulated times.The standard deviation is one hour or 15 degrees of longitude. A similar bell curve applies to the Sun’s travel north and south in a year.

bell curve

It’s not quite Kepler’s Harmonies of the World but definite rhythms become apparent. Tidal variations associated with lunar declinations have a regular beat of 18.61 years and we have four kinds of month:

  • 29.5306 mean solar days for Moon phases, called lunations.
  • 27.5546 mean solar days for oscillations of lunar distance
  • 27.2122 mean solar days for oscillation of Moon in latitude.
  • 27.3216 mean solar days for revolution in longitude.

Leonardo would not have kept up with that even if he had tried. The Metonic Cycle indicates there are  235/19 months in a year. Of course, 12.236842 is a nasty irrational number  but we can’t begin to understand the real world until we understand the mathematics of the Moon and, indeed, all the other heavenly bodies.  Astrologers have their own rule of twelfths dividing the ecliptic into houses which are believed  to affect human behaviour.  Placing emphasis on the time and place of one’s birth is at least a step towards some kind of inertial or absolute time. It features in various religious and cultural practices around the world. Astronomy has its roots in astrology, applying what we might call the scientific method to mysteries of great importance. There is no greater mystery than time.

Astrology is assured of recognition from psychology without further restrictions because astrology represents the summation of all the psychological knowledge of antiquity.

Doctor Carl Jung