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Pytheas of Massalia (4th century BC), Greek geographer and explorer: is maybe the earliest to state that tides are caused by the moon.
Seleucus of Seleucia (190 BC - 150 BC), Hellenistic astronomer and philosopher: was the first to link tides to lunar attraction, earth's motion, moon's position relative to the sun and that tides varied in time and strength in different parts of the world.
John Wallingford (12th-13th century AD): introduced he first British tide table based on high water occurring 48 minutes later each day, and three hours earlier at the Thames mouth than upriver at London. However, an earlier tide table was recorded in China in 1056 AD for visitors wishing to see the famous tidal bore in the Qiantang River.
Pierre-Simon Laplace (1749 - 1827), French mathematician and astronomer: developed was is known today as Laplace's tidal equations which detailed the motion of tidal waters that occurs in response to the tide-generating forces due to the Moon and Sun.
William Whewell (1794 - 1866), English polymath and scientist: first mapped co-tidal lines (lines on a map passing through places that have high tide at the same time) ending with a nearly global chart in 1836.
Captain William Hewett, British naval surveyor: confirmed in 1840 the existence of amphidromes (amphidromic points) where co-tidal lines meet in the mid-ocean where the height difference between high tide and low tide is zero. The amphidromes were hypothesized by William Whewell in order to make his maps consistent (see above).
William Thomson (Lord Kelvin) (1824 - 1907), British physicist and engineer: built the first tide-predicting machine (a mechanical analog computer) in 1872 using a system of pulleys, gears and chains. Similar machines were used until the 1960s. In 1867 Thomson led the first systematic harmonic analysis of tidal records (a mathematics technique concerned with the representation of functions or signals as the superposition of basic waves using Fourier series).
William Ferrel (1817 – 1891), American meteorologist: built another tide predicting machine, in 1881-2. Ferrel's machine delivered predictions by telling the times and heights of successive high and low waters, shown by pointer-readings on dials and scales. These were read by an operator who copied the readings on to forms, to be sent to the printer of the US tide-tables.
George Darwin (1845 - 1912), English astronomer and mathematician (son of Charles Darwin): extended Laplace's and Thomson's analysis of tides (see above) in 1884 based on the lunar theory of his time. His symbols for the tidal harmonic constituents (tidal constants) are still used today. Each constituent is represented by a symbol with a numerical value 0, 1, or 2, which designates whether the constituent is long-period, diurnal (daily), or semidiurnal (occurring once every 12 hours).
Ernest William Brown (1866 - 1938), British mathematician and astronomer: improved significantly lunar theory of the motion of the moon.
Arthur Thomas Doodson (1890 - 1968), British oceanographer: introduced the Doodson Numbers, in 1921, in order to specify the different harmonic components of the tide-generating potential - Doodson attributed numerical values to six basic variables like mean lunar time, mean longitude of the sun, etc. Doodson's system is still in use. He also designed the Doodson-Légé Tide Predicting Machine in 1949.
Tidal Prediction Resources
Introduction to Tides
The Factors Contributing to the level of Confidence in the Tidal Predictions Accuracy
Tidal theory Introduction
Admiralty EasyTide - United Kingdom Hydrographic Office (UKHO)
Tidal predictions are available for UK & Irish locations for the next 28 days
Water Level Tidal Predictions - NOAA Tides and Currents
Tide-Predicting Machine Resources
Tide-predicting machine - Wikipedia
JAVA simulation of Kelvin's Tide Predicting Machine
Tide Predicting Machines - NOAA
2nd German Tide-predicting Machine (1935-39)
Mechanical prediction of tides - NOAA
Tide Prediction In America
Short-term Tide Prediction
The Doodson-Légé Tide Predicting Machine