moon was furthest from the plane of the Equator. All this despite the relatively small amplitude of Mediterranean basin tides. (The strong currents through the Euripus Strait and the Strait of Messina puzzled Aristotle.) Philostratus discussed tides in Book Five of The Life of Apollonius of Tyana. Philostratus mentions the moon, but attributes tides to "spirits". In Europe around 730 AD, the Venerable Bede described how the rising tide on one coast of the British Isles coincided with the fall on the other and described the time progression of high water along the Northumbrian coast. The first tide table in China was recorded in 1056 AD primarily for visitors wishing to see the famous tidal bore in the Qiantang River. The first known British tide table is thought to be that of John Wallingford, who died Abbot of St. Albans in 1213, based on high water occurring 48 minutes later each day, and three hours earlier at the Thames mouth than upriver at London. In 1614 Claude d'Abbeville published the work “”, where he exposed that the Tupinambá people already had an understanding of the relation between the Moon and the tides before Europe. William Thomson (Lord Kelvin) led the first systematic harmonic analysis of tidal records starting in 1867. The main result was the building of a tide-predicting machine using a system of pulleys to add together six harmonic time functions. It was "programmed" by resetting gears and chains to adjust phasing and amplitudes. Similar machines were used until the 1960s. The first known sea-level record of an entire spring–neap cycle was made in 1831 on the Navy Dock in the Thames Estuary. Many large ports had automatic tide gauge stations by 1850. John Lubbock was one of the first to map co-tidal lines, for Great Britain, Ireland and adjacent coasts, in 1840. William Whewell expanded this work ending with a nearly global chart in 1836. In order to make these maps consistent, he hypothesized the existence of a region with no tidal rise or fall where co-tidal lines meet in the mid-ocean. The existence of such an amphidromic point, as they are now known, was confirmed in 1840 by Captain William Hewett, RN, from careful soundings in the North Sea. Physics Forces The tidal force produced by a massive object (Moon, hereafter) on a small particle located on or in an extensive body (Earth, hereafter) is the vector