William Thomson

If you can not measure it, you can not improve it.
Lord Kelvin

Sir William Thomson, Baron Kelvin (1824-1907)
Sir William Thomson, Baron Kelvin (1824-1907)

At the present time, predictions of tides and tidal currents are generated by computer. The prediction of the periodic tides is the oldest form of oceanic prediction. How were such predictions made before the electronic age?

Ancient civilizations recognized the relationship between the rise and set of the Moon and the rise and fall of the tides. Initially, tide predictions used rule-of-thumb to relate the times of the tides to the rise and set of the Moon. Such techniques indicate that the high tide would occur a certain number of hours after the Moon had passed overhead, or that the low tide had occurred a certain number of hours after the Moon rose or set. However, such methods provide general information which may not be accurate. A more precise, harmonic method of predicting tides was developed in the mid-1800s.

The first scientist to explain how tides are generated by the gravitational forces of the moon and sun was Isaac Newton (in the 1690s). In 1775 Pierre Laplace suggested, that tides should be represented as a series of harmonic oscillations. However, it was the British mathematician, physicist, and engineer William Thomson (later known as Lord Kelvin) who announced, in 1867, that he had developed a method for harmonic analysis and prediction.

The harmonic method of predicting tides is based on the fact that tides are the result of the gravitational forces of the Moon and Sun. The magnitude of these forces is due to the changing positions of the Earth, Moon, and Sun relative to each other. As the gravitational forces change, so do tides. The orbits of the Earth, Moon, and Sun are in constant motion, following repeating patterns of different frequencies that can be observed, analyzed, and predicted.

Some of these are orbiting patterns we are familiar with—the daily rotation of the Earth relative to the Sun (24 hours—a solar day); the rotation of the Earth relative to the Moon (24 hours and 50 minutes—a sidereal day); the orbit of the Moon around the Earth (29.5 days—the changing phases of the Moon); the orbit of the Earth around the Sun (365.25 days—a calendar year). There are many more—some with periods of a few hours, others with periods of months—which are harder to describe and visualize.

Using the timing of these different and periodic changes in the positions of the Earth, Moon, and Sun, scientists analyzed tide observations for changes that occur with the same frequencies. They were able to connect changes in the tides to specific changes in the positions of the Earth, Sun, and Moon, representing them as several sine curves, each with a frequency matching the frequency of one of the periodic motions of the Earth, Sun, and Moon, and with an amplitude equalling the contribution of a particular motion to the tides at a given location.

These “connections” are called “tidal harmonic constituents.” By combining the effect of all the constituents for a location, i.e., by adding and subtracting the various sine curves, the tides at that location can be predicted—for the present but also for dates in the future or in the past to assist in an analysis of past or future events. More than 200 tidal harmonic constituents have been mathematically defined. However, for most locations, many of these constituents have no real effect on the tides and can thus be safely discounted.

10-component tide-predicting machine of 1872-73, conceived by Sir William Thomson, Science Museum, London
Thomson’s 10-component tide-predicting machine of 1872, Science Museum, London

Manually adding and subtracting the effects of multiple sine curves is a daunting task. William Thomson made use of the very regular nature of the harmonic constituents to automate tide predictions.

Sine curves have a very well-defined period and amplitude, thus the effects could be mechanically reproduced using a gear, attached pin, and pulley. This developed into a machine made up of dozens of gears and pulleys, each gear designed to have the same period as one of the tidal harmonic constituents. The pin made it possible to set the amplitude of the constituent, while a chain ran over a pulley with a pen attached to it. The gears and pins pulled on the pulley and chain, thus moving the pen and tracing a curve on a roll paper—a curve which was the resulting tide prediction.

The machines built to predict the tides were finely crafted of brass and iron. The first such machine, a kind of analog computer, was built in London (1872) and calculated the tides using 10 harmonic constituents. This machine, designed by Thomson with the collaboration of Edward Roberts (1845-1933, assistant at the Nautical Almanac Office), and craftsman Alexander Légé, who constructed it, used a pen and paper trace to record the predicted tides. Thomson’s older brother, James, a professor of civil engineering at Queen’s College Belfast, designed the disk-globe-and-cylinder integrator that was used for the tidal harmonic analyzer.

In the machine, each of the 10 components was associated with a specific tidal constituent and had its own gearing to set the amplitude. The components were geared together so that their periods were proportional to the periods of the tidal constituents. A single crank turned all of the gears simultaneously, having the effect of summing each of the cosine curves. As the user turned the crank, an ink pen traced the resulting complex curve on a moving roll of paper. The device marked each hour with a small horizontal mark, making a deeper notch each day at noon. Turning the wheel rapidly allowed the user to run a year’s worth of tide readings in about 4 hours.