Lord Kelvin and His Analog Computer

This tide-predicting machine was one of many advances he made to maritime tech

6 min read

Allison Marsh is a professor at the University of South Carolina and codirector of the university's Ann Johnson Institute for Science, Technology & Society.

Photo of a brass and wood apparatus with multiple dials, cylinders of paper, and a crank on the side.

William Thomson’s ingenious tide-predicting machine could plot a year's worth of tides in just four hours.

Science Museum Group

In 1870, William Thomson, mourning the death of his wife and flush with cash from various patents related to the laying of the first transatlantic telegraph cable, decided to buy a yacht. His schooner, the Lalla Rookh, became Thomson’s summer home and his base for hosting scientific parties. It also gave him firsthand experience with the challenge of accurately predicting tides.

Mariners have always been mindful of the tides lest they find themselves beached on low-lying shoals. Naval admirals guarded tide charts as top-secret information. Civilizations recognized a relationship between the tides and the moon early on, but it wasn’t until 1687 that Isaac Newton explained how the gravitational forces of the sun and the moon caused them. Nine decades later, the French astronomer and mathematician Pierre-Simon Laplace suggested that the tides could be represented as harmonic oscillations. And a century after that, Thomson used that concept to design the first machine for predicting them.

Lord Kelvin’s Rising Tide

William Thomson was born on 26 June 1824, which means this month marks his 200th birthday and a perfect time to reflect on his all-around genius. Thomson was a mathematician, physicist, engineer, and professor of natural philosophy. Queen Victoria knighted him in 1866 for his work on the transatlantic cable, then elevated him to the rank of baron in 1892 for his contributions to thermodynamics, and so he is often remembered as Lord Kelvin. He determined the correct value of absolute zero, for which he is honored by the SI unit of temperature—the kelvin. He dabbled in atmospheric electricity, was a proponent of the vortex theory of the atom, and in the absence of any knowledge of radioactivity made a rather poor estimation of the age of the Earth, which he gave as somewhere between 24 million and 400 million years.

Old photo of an elderly man with a white beard, holding a model of a molecule.William Thomson, also known as Lord Kelvin, is best known for establishing the value of absolute zero. He believed in the practical application of scientific knowledge and invented a wide array of useful, and beautiful, devices. Pictorial Press/Alamy

Thomson’s tide-predicting machine calculated the tide pattern for a given location based on 10 cyclic constituents associated with the periodic motions of the Earth, sun, and moon. (There are actually hundreds of periodic motions associated with these objects, but modern tidal analysis uses only the 37 of them that have the most significant effects.) The most notable one is the lunar semidiurnal, observable in areas that have two high tides and two low tides each day, due to the effects of the moon. The period of a lunar semidiurnal is 12 hours and 25 minutes—half of a lunar day, which lasts 24 hours and 50 minutes.

As Laplace had suggested in 1775, each tidal constituent can be represented as a repeating cosine curve, but those curves are specific to a location and can be calculated only through the collection of tidal data. Luckily for Thomson, many ports had been logging tides for decades. For places that did not have complete logs, Thomson designed both an improved tide gauge and a tidal harmonic analyzer.

On Thomson’s tide-predicting machine, each of 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.

Although Thomson is credited with designing the machine, in his paper “The Tide Gauge, Tidal Harmonic Analyser, and Tide Predicter” (published in Minutes of the Proceedings of the Institution of Civil Engineers), he acknowledges a number of people who helped him solve specific problems. Craftsman Alexander Légé drew up the plan for the screw gearing for the motions of the shafts and constructed the initial prototype machine and subsequent models. Edward Roberts of the Nautical Almanac Office completed the arithmetic to express the ratio of shaft speeds. 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. Thomson’s generous acknowledgments are a reminder that the work of engineers is almost always a team effort.

Photos of two machines. On the left, a machine with a clock face and four smaller dials. On the right, a large machine with multiple metal gears mounted on a long stand.Like Thomson’s tide-prediction machine, these two devices, developed at the U.S. Coast and Geodetic Survey, also looked at tidal harmonic oscillations. William Ferrel’s machine [left] used 19 tidal constituents, while the later machine by Rollin A. Harris and E.G. Fischer [right], relied on 37 constituents. U.S. Coast and Geodetic Survey/NOAA

As with many inventions, the tide predictor was simultaneously and independently developed elsewhere and continued to be improved by others, as did the science of tide prediction. In 1874 in the United States, William Ferrel, a mathematician with the Coast and Geodetic Survey, developed a similar harmonic analysis and prediction device that used 19 harmonic constituents. George Darwin, second son of the famous naturalist, modified and improved the harmonic analysis and published several articles on tides throughout the 1880s. Oceanographer Rollin A. Harris wrote several editions of the Manual of Tidesfor the Coast and Geodetic Survey from 1897 to 1907, and in 1910 he developed, with E.G. Fischer, a tide-predicting machine that used 37 constituents. In the 1920s, Arthur Doodson of the Tidal Institute of the University of Liverpool, in England, and Paul Schureman of the Coast and Geodetic Survey further refined techniques for harmonic analysis and prediction that served for decades. Because of the complexity of the math involved, many of these old brass machines remained in use into the 1950s, when electronic computers finally took over the work of predicting tides.

What Else Did Lord Kelvin Invent?

As regular readers of this column know, I always feature a museum object from the history of computer or electrical engineering and then spin out a story. When I started scouring museum collections for a suitable artifact for Thomson, I was almost paralyzed by the plethora of choices.

I considered Thomson’s double-curb transmitter, which was designed for use with the 1858 transatlantic cable to speed up telegraph signals. Thomson had sailed on the HMS Agamemnon in 1857 on its failed mission to lay a transatlantic cable and was instrumental to the team that finally succeeded.

Photo of a rectangular scientific instrument made of wood and brass. Thomson invented the double-curb transmitter to speed up signals in transatlantic cables.Science Museum Group

I also thought about featuring one of his quadrant electrometers, which measured electrical charge. Indeed, Thomson introduced a number of instruments for measuring electricity, and a good part of his legacy is his work on the precise specifications of electrical units.

But I chose to highlight Thomson’s tide-predicting machine for a number of reasons: Thomson had a lifelong love of seafaring and made many contributions to marine technology that are sometimes overshadowed by his other work. And the tide-predicting machine is an example of an early analog computer that was much more useful than Babbage’s difference engine but not nearly as well known. Also, it is simply a beautiful machine. In fact, Thomson seems to have had a knack for designing stunningly gorgeous devices. (The tide-predicting machine at top and many other Kelvin inventions are in the collection of the Science Museum, in London.)

Photo of a brass scientific instrument with a triangular base supporting a 6-sided cylinder.Thomson devised the quadrant electrometer to measure electric charge. Science Museum Group

The tide-predicting machine was not Thomson’s only contribution to maritime technology. He also patented a compass, an astronomical clock, a sounding machine, and a binnacle (a pedestal that houses nautical instruments). With respect to maritime science, Thomson thought and wrote much about the nature of waves. He mathematically explained the v-shaped wake patterns that ships and waterfowl make as they move across a body of water, which is aptly named the Kelvin wake pattern. He also described what is now known as a Kelvin wave, a type of wave that retains its shape as it moves along the shore due to the balancing of the Earth’s spin against a topographic boundary, such as a coastline.

Considering how much Thomson contributed to all things seafaring, it is amazing that these are some of his lesser known achievements. I guess if you have an insatiable curiosity, a robust grasp of mathematics and physics, and a strong desire to tinker with machinery and apply your scientific knowledge to solving practical problems that benefit humankind, you too have the means to come to great conclusions about the natural world. It can’t hurt to have a nice yacht to spend your summers on.

Part of a continuing serieslooking at historical artifacts that embrace the boundless potential of technology.

An abridged version of this article appears in the June 2024 print issue as “Brass for Brains.”


Before the days of online databases for their collections, museums would periodically publish catalogs of their collections. In 1877, the South Kensington Museum (originator of the collections of the Science Museum, in London, and now known as the Victoria & Albert Museum) published the third edition of its Catalogue of the Special Loan Collection of Scientific Apparatus, which lists a description of Lord Kelvin’s tide-predicting machine on page 11. That description is much more detailed, albeit more confusing, than its current online one.

In 1881, William Thomson published “The Tide Gauge, Tidal Harmonic Analyser, and Tide Predicter” in the Minutes of the Proceedings of the Institute of Civil Engineers,where he gave detailed information on each of those three devices.

I also relied on a number of publications from the National Oceanic and Atmospheric Administration to help me understand tidal analysis and prediction.

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