Cargill Gilston Knott
Encyclopedia
Cargill Gilston Knott was a Scottish
Scotland
Scotland is a country that is part of the United Kingdom. Occupying the northern third of the island of Great Britain, it shares a border with England to the south and is bounded by the North Sea to the east, the Atlantic Ocean to the north and west, and the North Channel and Irish Sea to the...

 physicist
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

 and mathematician who was a pioneer in seismological
Seismology
Seismology is the scientific study of earthquakes and the propagation of elastic waves through the Earth or through other planet-like bodies. The field also includes studies of earthquake effects, such as tsunamis as well as diverse seismic sources such as volcanic, tectonic, oceanic,...

 research. He spent his early career in Japan
Japan
Japan is an island nation in East Asia. Located in the Pacific Ocean, it lies to the east of the Sea of Japan, China, North Korea, South Korea and Russia, stretching from the Sea of Okhotsk in the north to the East China Sea and Taiwan in the south...

. He later became a Fellow of the Royal Society
Royal Society
The Royal Society of London for Improving Natural Knowledge, known simply as the Royal Society, is a learned society for science, and is possibly the oldest such society in existence. Founded in November 1660, it was granted a Royal Charter by King Charles II as the "Royal Society of London"...

, Secretary of the Royal Society of Edinburgh
Royal Society of Edinburgh
The Royal Society of Edinburgh is Scotland's national academy of science and letters. It is a registered charity, operating on a wholly independent and non-party-political basis and providing public benefit throughout Scotland...

, and President of the Scottish Meteorological Society
Scottish Meteorological Society
The Scottish Meteorological Society was founded in 1855 with private funding, particularly from wealthy landowners who wished to compile meteorological records in order to improve agriculture....

.

Biography

Knott was born at Penicuik
Penicuik
Penicuik is a burgh and civil parish in Midlothian, Scotland, lying on the west bank of the River North Esk. The town was developed as a planned village in 1770 by Sir James Clerk of Penicuik. It became a burgh in 1867. The town was well known for its paper mills, the last of which closed in 2005....

, Midlothian
Midlothian
Midlothian is one of the 32 council areas of Scotland, and a lieutenancy area. It borders the Scottish Borders, East Lothian and the City of Edinburgh council areas....

, educated at Arbroath High School
Arbroath High School
Arbroath High School is a six-year state run school in Arbroath, north-east Scotland.-Admissions:The school has around 1000 pupils and serves the west-end of Arbroath...

 in Angus
Angus
Angus is one of the 32 local government council areas of Scotland, a registration county and a lieutenancy area. The council area borders Aberdeenshire, Perth and Kinross and Dundee City...

, and attended the University of Edinburgh
University of Edinburgh
The University of Edinburgh, founded in 1583, is a public research university located in Edinburgh, the capital of Scotland, and a UNESCO World Heritage Site. The university is deeply embedded in the fabric of the city, with many of the buildings in the historic Old Town belonging to the university...

, where he studied alongside James Alfred Ewing
James Alfred Ewing
Sir James Alfred Ewing KCB FRS FRSE MInstitCE was a Scottish physicist and engineer, best known for his work on the magnetic properties of metals and, in particular, for his discovery of, and coinage of the word, hysteresis.It was said of Ewing that he was 'Careful at all times of his appearance,...

. He worked on various aspects of electricity
Electricity
Electricity is a general term encompassing a variety of phenomena resulting from the presence and flow of electric charge. These include many easily recognizable phenomena, such as lightning, static electricity, and the flow of electrical current in an electrical wire...

 and magnetism
Magnetism
Magnetism is a property of materials that respond at an atomic or subatomic level to an applied magnetic field. Ferromagnetism is the strongest and most familiar type of magnetism. It is responsible for the behavior of permanent magnets, which produce their own persistent magnetic fields, as well...

, obtaining his doctorate
Doctorate
A doctorate is an academic degree or professional degree that in most countries refers to a class of degrees which qualify the holder to teach in a specific field, A doctorate is an academic degree or professional degree that in most countries refers to a class of degrees which qualify the holder...

 in 1879.

Knott was the brother-in-law of the literary scholar James Main Dixon
James Main Dixon
James Main Dixon FRSE was a Scottish teacher and author, and an important scholar of the Scots language. He graduated at St...

.

Career in Japan

Soon after the Meiji Restoration
Meiji Restoration
The , also known as the Meiji Ishin, Revolution, Reform or Renewal, was a chain of events that restored imperial rule to Japan in 1868...

 in Japan
Japan
Japan is an island nation in East Asia. Located in the Pacific Ocean, it lies to the east of the Sea of Japan, China, North Korea, South Korea and Russia, stretching from the Sea of Okhotsk in the north to the East China Sea and Taiwan in the south...

, the new Meiji government began a program for building lighthouse
Lighthouse
A lighthouse is a tower, building, or other type of structure designed to emit light from a system of lamps and lenses or, in older times, from a fire, and used as an aid to navigation for maritime pilots at sea or on inland waterways....

s to facilitate trade and navigation, hiring Scottish engineer Richard Henry Brunton
Richard Henry Brunton
Richard Henry Brunton FRGS MICE was the so-called "Father of Japanese lighthouses". Brunton was born in Muchalls, Kincardineshire, Scotland...

 in 1868. Brunton soon realized that the new lighthouses would need to be designed against the frequent earthquake
Earthquake
An earthquake is the result of a sudden release of energy in the Earth's crust that creates seismic waves. The seismicity, seismism or seismic activity of an area refers to the frequency, type and size of earthquakes experienced over a period of time...

s that strike Japan, and at his urging the Japanese government began to recruit British scientists to contribute the latest ideas of western science to better understand, predict, and possibly mitigate the effects of earthquakes. John Milne
John Milne
For other uses, see John Milne .John Milne was the British geologist and mining engineer who worked on a horizontal seismograph.-Biography:...

 was hired in 1874 as a Professor of Geology and Mining, and in 1878, James Alfred Ewing was appointed Professor of Physics and Engineering at Tokyo Imperial University. With Japanese colleagues, Milne, Ewing and another Briton, Thomas Lomas Gray, devised the prototype instruments which evolved into the modern seismograph.

When Ewing returned to Scotland in 1883, the rector of Tokyo Imperial University wrote to Lord Kelvin, asking for his recommendation for a successor, Lord Kelvin recommended Knott, and the recommendation was supported by Ewing. Thus, Knott replaced Ewing as Professor of Physics and Engineering at Tokyo Imperial University. For the next nine years, he worked closely with Milne, Gray and the Japanese seismologist Fusakichi Omori
Fusakichi Omori
was a pioneer Japanese seismologist, second chairman of seismology at the Imperial University of Tokyo and president of the Japanese Imperial Earthquake Investigation Committee.-Education:...

 in establishing a network of recording seismometers across the Japanese Empire. Knott also taught courses in mathematics, acoustics
Acoustics
Acoustics is the interdisciplinary science that deals with the study of all mechanical waves in gases, liquids, and solids including vibration, sound, ultrasound and infrasound. A scientist who works in the field of acoustics is an acoustician while someone working in the field of acoustics...

, and electromagnetism
Electromagnetism
Electromagnetism is one of the four fundamental interactions in nature. The other three are the strong interaction, the weak interaction and gravitation...

 at the Tokyo Imperial University.

Knott also undertook the first geomagnetic survey of Japan, assisted by Japanese geophysicist
Geophysics
Geophysics is the physics of the Earth and its environment in space; also the study of the Earth using quantitative physical methods. The term geophysics sometimes refers only to the geological applications: Earth's shape; its gravitational and magnetic fields; its internal structure and...

 Tanakadate Aikitsu, from which was developed the first earthquake hazard map of Japan. Knott's key contribution was his background in mathematics and data analysis. One of his innovations was to apply the technique of Fourier analysis to the occurrence of earthquakes. Two chapters in his 1908 book The Physics of Earthquake Phenomena were devoted to this subject, which Knott hoped would enable him to deduce the probability of when future earthquakes would occur.

On the conclusion of his stay in Japan in 1891, he was awarded the Order of the Rising Sun
Order of the Rising Sun
The is a Japanese order, established in 1875 by Emperor Meiji of Japan. The Order was the first national decoration awarded by the Japanese Government, created on April 10, 1875 by decree of the Council of State. The badge features rays of sunlight from the rising sun...

 by Emperor Meiji
Emperor Meiji
The or was the 122nd emperor of Japan according to the traditional order of succession, reigning from 3 February 1867 until his death...

.

Later career

While in Japan, Knott began to develop mathematical equations describing of how seismic vibrations are reflected and transmitted across the boundary between seawater and seabed. After returning to Edinburgh University in 1892, he expanded upon this research to describe the behavior of earthquake waves at the interface between two different types of rock. The "Knott equations" are now the basis for many new developments in seismology, including modern seismic exploration tools for petroleum
Petroleum
Petroleum or crude oil is a naturally occurring, flammable liquid consisting of a complex mixture of hydrocarbons of various molecular weights and other liquid organic compounds, that are found in geologic formations beneath the Earth's surface. Petroleum is recovered mostly through oil drilling...

 and natural gas
Natural gas
Natural gas is a naturally occurring gas mixture consisting primarily of methane, typically with 0–20% higher hydrocarbons . It is found associated with other hydrocarbon fuel, in coal beds, as methane clathrates, and is an important fuel source and a major feedstock for fertilizers.Most natural...

.

After his return to Scotland, Knott resumed his work as a mathematician, expanding on the quaternion
Quaternion
In mathematics, the quaternions are a number system that extends the complex numbers. They were first described by Irish mathematician Sir William Rowan Hamilton in 1843 and applied to mechanics in three-dimensional space...

 algebra
Algebra
Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures...

 developments of his professor and mentor Peter Guthrie Tait
Peter Guthrie Tait
Peter Guthrie Tait FRSE was a Scottish mathematical physicist, best known for the seminal energy physics textbook Treatise on Natural Philosophy, which he co-wrote with Kelvin, and his early investigations into knot theory, which contributed to the eventual formation of topology as a mathematical...

. When the tight constraints of a single linear algebra
Linear algebra
Linear algebra is a branch of mathematics that studies vector spaces, also called linear spaces, along with linear functions that input one vector and output another. Such functions are called linear maps and can be represented by matrices if a basis is given. Thus matrix theory is often...

 began to be felt in the 1890s and revisionists began publishing, Knott contributed the pivotal article "Recent Innovations in Vector Theory". As M.J. Crowe describes in his book (pp. 200–5), this paper set straight wayward theorists that expected to find associativity
Associativity
In mathematics, associativity is a property of some binary operations. It means that, within an expression containing two or more occurrences in a row of the same associative operator, the order in which the operations are performed does not matter as long as the sequence of the operands is not...

 in systems like hyperbolic quaternion
Hyperbolic quaternion
In the abstract algebra of algebras over a field, the hyperbolic quaternionq = a + bi + cj + dk, \quad a,b,c,d \in R \!is a mutated quaternion wherei^2 = j^2 = k^2 = +1 \! instead of the usual −1....

s. Knott wrote:
[T]he assumption that the square of a unit vector is positive unity leads to an algebra whose characteristic quantities are non-associative.

Evidently Knott overlooked the existence of the ring of coquaternion
Coquaternion
In abstract algebra, the split-quaternions or coquaternions are elements of a 4-dimensional associative algebra introduced by James Cockle in 1849 under the latter name. Like the quaternions introduced by Hamilton in 1843, they form a four dimensional real vector space equipped with a...

s. Nevertheless, Crowe states (p. 216) that Knott "wrote with care and thoroughness" and that "only Knott was well acquainted with his opponents system".

For a textbook on quaternions, lecturers and students relied on Tait and Kelland's Introduction to Quaternions which had editions in 1873 and 1882. It fell to Knott to prepare a third edition in 1904. By then the Universal Algebra of Alfred North Whitehead
Alfred North Whitehead
Alfred North Whitehead, OM FRS was an English mathematician who became a philosopher. He wrote on algebra, logic, foundations of mathematics, philosophy of science, physics, metaphysics, and education...

 (1898) presumed some grounding in quaternions as students encountered matrix algebra
Matrix (mathematics)
In mathematics, a matrix is a rectangular array of numbers, symbols, or expressions. The individual items in a matrix are called its elements or entries. An example of a matrix with six elements isMatrices of the same size can be added or subtracted element by element...

. In Knott's introduction to his textbook edition he says "Analytically the quaternion is now known to take its place in the general theory of complex numbers
Hypercomplex number
In mathematics, a hypercomplex number is a traditional term for an element of an algebra over a field where the field is the real numbers or the complex numbers. In the nineteenth century number systems called quaternions, tessarines, coquaternions, biquaternions, and octonions became established...

 and continuous groups,...". Thus he was aware of the diversity to be encountered in modern mathematical structure
Mathematical structure
In mathematics, a structure on a set, or more generally a type, consists of additional mathematical objects that in some manner attach to the set, making it easier to visualize or work with, or endowing the collection with meaning or significance....

s, and that quaternions stand as a milestone on the way to others.

While in Japan, Knott had been elected a Fellow of the Royal Society of Edinburgh. He became its General Secretary in 1912. He was also a founder of the Edinburgh Mathematical Society
Edinburgh Mathematical Society
The Edinburgh Mathematical Society is the leading mathematical society in Scotland.The Society was founded in 1883 by a group of Edinburgh schoolteachers and academics, on the initiative of A. Y. Fraser and A. J. G. Barclay, teachers at George Watson's College and Cargill Gilston Knott, who was the...

. Knott took an active social role in his community including Sunday school
Sunday school
Sunday school is the generic name for many different types of religious education pursued on Sundays by various denominations.-England:The first Sunday school may have been opened in 1751 in St. Mary's Church, Nottingham. Another early start was made by Hannah Ball, a native of High Wycombe in...

 teaching and church affairs with the United Free Church of Scotland
United Free Church of Scotland
The United Free Church of Scotland is a Scottish Presbyterian denomination formed in 1900 by the union of the United Presbyterian Church of Scotland and the Free Church of Scotland...

. He died at his home in Newington, Edinburgh
Edinburgh
Edinburgh is the capital city of Scotland, the second largest city in Scotland, and the eighth most populous in the United Kingdom. The City of Edinburgh Council governs one of Scotland's 32 local government council areas. The council area includes urban Edinburgh and a rural area...

, on October 26, 1922.

Partial bibliography

  • Earthquake Frequency (1886)
  • Electricity and Magnetism (1893)
  • The Physics of Earthquake Phenomena (1908)
  • Life and Scientific Work of Peter Gutherie Tait. Supplementing the Two Volumes of Scientific Papers Published in 1898 and 1900 (1911)
  • Physics, An Elementary Textbook (1913)
  • Napier tercentenary memorial volume (1915)
  • The Propagation of Earthquake Waves through the Earth (1920)

External links

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