This article has been adapted from Chapter 3 of my research project entitled ‘An historic analysis of tide prediction machines using an adapted prosopographic approach and digital humanities tools’, which I wrote during the first year of my Master’s degree. A copy of the full text can be found at: http://doi.org/10.5281/zenodo.3265011.

The tides

It would be difficult to talk about the history of tidal prediction without first introducing the notion of tides. Tides on Earth can be observed in bodies of water such as oceans, seas and lakes. Physically they appear as vertical movements of the surface of the water, the maximum and minimum of which are known as high water and low water, and alternating horizontal movements of the water, known as tidal currents (Gordon et al. 2015).

To understand why tides exist on Earth, it is necessary to have some knowledge of the interactions between the Earth, the Moon and the Sun. The Moon is attracted to the Earth because of gravitational attraction but is also repulsed by the Earth due to the centrifugal force that results from the Moon spinning around it. The diagram below shows the Earth (large circle on the left), the water on the surface of the Earth (oval) the Moon (small circle on the right) and the forces in play between them: the red arrows represent the direction and the intensity of the force of gravitational attraction, the blue arrows represent the direction and the intensity of the centrifugal force and the green arrows represent the direction and the intensity of the resultant tide-causing force. The intensity of the centrifugal force on the Earth is constant whilst the intensity of the gravitational attraction varies proportionally to the changing distance between the Earth and the Moon. It is the combination of these two forces that results in the tides: when the resulting force is directed towards the centre of the Earth, the water level falls, and when the force is directed away from the centre of the Earth in the plane of the Moon, the water level rises, as shown by the green arrows in the diagram. The Sun contributes to tides on Earth in exactly the same way as the Moon does, but to a lesser extent. At most locations on Earth tides are semidiurnal, which means that low tide and high tide each occur twice per day. This effect is a result of the rotation of the Earth itself and the fact that there is always high water on two opposite sides of the Earth at any one time. There is also a diurnal component to the tides, which is because of the asymmetry of the high water directed towards and away from the Moon (Ifremer 2004).

There are also certain geographical features on Earth that affect the height of the tides and their fluctuation in time. These features include the shape of the specific beach, the angle of the seabed leading up to the beach, the shape and depth of the surrounding coastline and the prevailing ocean currents (Byrd 2019). As well as these predictable astronomical and geographical tidal influences, the climate and weather have very unpredictable influences on the tides on Earth.

For all the astronomical, geographical and meteorological reasons aforementioned, the tides on Earth do not follow a repeated pattern (National Oceanography Centre 2019[b]). This means that the only way of knowing the times and heights of future tides is to forecast or predict them using an equation that takes into account the factors that cause them.

History of tidal science and prediction

Before tide prediction machines

Tidal theory is the result of centuries of observations, hypotheses, empirical research and contributions from dozens of the brightest minds from a multitude of locations across the world.

The first attempts at predicting the tides were made by those occupying lands next to tidal waters in the form of rule-of-thumb methods linked to the phase of the moon. There is evidence from centuries and millennia before the Christian era of early Indian and Arabic civilisations recognising the influence of the moon over the tides, and of their interaction with and efforts to manage the tides (Cartwright 2000, p. 1-6). The Copernican Revolution, which stemmed from an idea by Nikolaus Copernicus (1473–1543) that the Earth is not located at the centre of the universe but that it revolves around the Sun with other planets, allowed for the development of a new genre of physical theories of the tides from the sixteenth century. Distinguished polymaths and natural philosophers of the time such as Francis Bacon (1561–1626), Galileo Galilei (1564–1642), Johannes Kepler (1571–1630) and René Descartes (1596–1650) all contributed their theories of the tides, with varying levels of success (Cartwright 2000, p. 25-34). These attempts were eclipsed by a tidal theory by Isaac Newton (1643–1727), developed in the seventeenth century as part of his gravitational theory. The fundamental principles of Newton’s tidal theory remain in accordance with scientific understanding today, although some deductions drawn from them are erroneous (Cartwright 2000, p. 35). Around a century later and following many suggestions and modifications by other natural philosophers, Pierre-Simon de Laplace (1749–1827) proposed a dynamic theory of the tides, which for the first time took into account the dynamicity of the response of the ocean to tidal forces. Laplace translated his theory into a set of equations, today known as the Laplace Tidal Equations, which describe this dynamic response of the ocean (Cartwright 2000, p. 68-81).

From theories to analysis and prediction

The nineteenth century saw a shift in focus from tidal theories to the more practical analysis and prediction of tides. By expanding upon the base of data used by Laplace and making careful refinements to established theories, John William Lubbock (1803–1865) devised the so-called synthetic method of tidal analysis and prediction in the 1830s, which gave the most accurate predictions for tides at Liverpool at the time and therefore became the preferred method for calculating tide tables for British ports (Cartwright 2000, p. 91-92). The next significant advancement came in 1867 from Thomson in the form of a harmonic method of tidal analysis, based upon Laplace’s equations and works by Thomas Young (1773– 1829) and George Biddell Airy (1801–1892) (Cartwright 2000, p. 82-83, 97). This development attracted the interest of the British Association for the Advancement of Science (BAAS), who in the same year established a committee for the improvement and promotion of this newly discovered method (NOAA 2018).

The harmonic method of analysis, based upon observations of sea levels (Pouvreau 2008, p. 37), allows for the individual factors causing the tides to be isolated as unique mathematical components and provides better results for a wider range of locations than the synthetic model, but is a much more complicated calculation. Its complexity meant that doing the calculation by hand was time-consuming and prone to errors, which was part of the motivation for devising a mechanical device capable of doing this calculation.

Development of tide Prediction machines

The development of the first tide prediction machine was made possible thanks to funding from the BAAS who decided that calculations done by hand alone could no longer be relied upon to predict the tides at ports around the country. This was because of the increasing pressure from commercial shipping lines towards the middle of the nineteenth century, who wanted a greater number of more accurate predictions more quickly.

The first ever tide prediction machine, which features in the photograph below, was developed in Great Britain during a period when science and industry were growing closer together, a period of widespread mechanisation (Durand-Richard 2016, p. 127-128). However, the idea of a mechanical calculating machine was not new; Charles Babbage had already conceived the idea half a century earlier with his Difference Engine and Analytical Engine (Dasgupta 2014, p. 22). More specifically, it is known that the design for the first tide prediction machine was inspired by a mechanical device devised by Charles Wheatstone for telegraphy purposes (Cartwright 2000, p. 104).

The construction of the first operational tide prediction machine was completed in 1873. It was designed by Thomson with the help of Edward Roberts and Alexander Légé, whose company A. Légé & Co. manufactured it in London (Woodworth 2016, p. 14). Lubbock’s synthetic method was relied upon for producing British tide tables until around 1920, by which time six further tide prediction machines had been constructed. These machines were primarily kept in Great Britain but were used to predict the tides at British colonial ports. Meanwhile, William E. Ferrel (1817–1891) and George Howard Darwin (1845–1912) were making modifications and improvements to Thomson’s harmonic method, and later Joseph Proudman (1888–1975) and Arthur Thomas Doodson (1890–1968) made significant contributions to tidal studies, and Doodson in particular to the improvement of tide prediction machines (Doodson 1921; Reidy 2008, p. 188). Eventually the transition from the synthetic method to the harmonic method in Great Britain was made, and thus the adoption of tide prediction machines for domestic ports (Cartwright 2000, p. 97-108).

Tidal prediction today

Tidal predictions today are calculated using specially-made software that run on digital computers. They use the same harmonic method as the analogue machines of the last century, but are able to take into account many more constituents. The NOC has developed a software called POLTIPS-3 that can calculate predictions for anywhere in the world using up to 240 different constituents (National Oceanography Centre 2019[a]) whilst the SHOM uses a software called MAS that uses up to 541 constituents (Pouvreau 2008, p. 39-40).

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