# John Scott Russell - The Wave of Translation

The Wave of Translation

In 1834, while conducting experiments to determine the most efficient design for canal boats, he discovered a phenomenon that he described as the wave of translation. In fluid dynamics the wave is now called a Scott Russell solitary wave or soliton. The discovery is described here in his own words:

I was observing the motion of a boat which was rapidly drawn along a narrow channel by a pair of horses, when the boat suddenly stopped—not so the mass of water in the channel which it had put in motion; it accumulated round the prow of the vessel in a state of violent agitation, then suddenly leaving it behind, rolled forward with great velocity, assuming the form of a large solitary elevation, a rounded, smooth and well-defined heap of water, which continued its course along the channel apparently without change of form or diminution of speed. I followed it on horseback, and overtook it still rolling on at a rate of some eight or nine miles an hour, preserving its original figure some thirty feet long and a foot to a foot and a half in height. Its height gradually diminished, and after a chase of one or two miles I lost it in the windings of the channel. Such, in the month of August 1834, was my first chance interview with that singular and beautiful phenomenon which I have called the Wave of Translation.

Scott Russell spent some time making practical and theoretical investigations of these waves. He built wave tanks at his home and noticed some key properties:

• The waves are stable, and can travel over very large distances (normal waves would tend to either flatten out, or steepen and topple over)
• The speed depends on the size of the wave, and its width on the depth of water.
• Unlike normal waves they will never merge—so a small wave is overtaken by a large one, rather than the two combining.
• If a wave is too big for the depth of water, it splits into two, one big and one small.

Scott Russell's experimental work seemed at contrast with the Isaac Newton and Daniel Bernoulli's theories of hydrodynamics. George Biddell Airy and George Gabriel Stokes had difficulty to accept Scott Russell's experimental observations because Scott Russell's observations could not be explained by the existing water-wave theories. His contemporaries spent some time attempting to extend the theory but it would take until the 1870s before an explanation was provided.

Lord Rayleigh published a paper in Philosophical Magazine in 1876 to support John Scott Russell's experimental observation with his mathematical theory. In his 1876 paper, Lord Rayleigh mentioned Scott Russell's name and also admitted that the first theoretical treatment was by Joseph Valentin Boussinesq in 1871. Joseph Boussinesq mentioned Scott Russell's name in his 1871 paper. Thus Scott Russell's observations on solitons were accepted as true by some prominent scientists within his own lifetime.

Korteweg and de Vries did not mention John Scott Russell's name at all in their 1895 paper but they did quote Boussinesq's paper in 1871 and Lord Rayleigh's paper in 1876. Although the paper by Korteweg and de Vries in 1895 was not the first theoretical treatment of this subject, it was a very important milestone in the history of the development of soliton theory.

It was not until the 1960s and the advent of modern computers that the significance of Scott Russell's discovery in physics, electronics, biology and especially fibre optics started to become understood, leading to the modern general theory of solitons.

A book was written by George Sinclair Emmerson on Scott Russell with the title John Scott Russell: a great Victorian engineer and naval architect, which was published in 1977. However, this book has very little discussion on the discovery of solitons by John Scott Russell. In 2005, Olivier Darrigol published a book Worlds of Flow, which covers the history of hydrodynamics from the years before John Scott Russell and to many years after his death. Inside this book, Darrigol provided a comprehensive list of classical papers written by John Scott Russell and other scientists on hydrodynamics. The book by Darrigol has a much better discussion on the discovery of solitons.