Cargill Gilston Knott FRS,

FRSE Fellowship of the Royal Society of Edinburgh (FRSE) is an award granted to individuals that the Royal Society of Edinburgh, Scotland's national academy of science and Literature, letters, judged to be "eminently distinguished in their subject". ...

LLD (30 June 1856 – 26 October 1922) was a Scottish

physicist A physicist is a scientist who specializes in the field of physics, which encompasses the interactions of matter and energy at all length and time scales in the physical universe. Physicists generally are interested in the root or ultimate cau ...

and

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

who was a pioneer in seismological research. He spent his early career in Japan. He later became a Fellow of the

Royal Society The Royal Society, formally The Royal Society of London for Improving Natural Knowledge, is a learned society and the United Kingdom's national academy of sciences. The society fulfils a number of roles: promoting science and its benefits, re ...

, Secretary of the

Royal Society of Edinburgh The Royal Society of Edinburgh (RSE) is Scotland's national academy of science and letters. It is a registered charity that operates on a wholly independent and non-partisan basis and provides public benefit throughout Scotland. It was establis ...

, and President of the Scottish Meteorological Society.

Biography

Knott was born in Penicuik, Midlothian, the son of Pelham Knott, an agent for a paper manufacturer and his wife Ellen. His paternal uncle was the artist Tavernor Knott. He was educated at

Arbroath High School Arbroath High School is a six-year, all-through comprehensive school situated on the west side of Arbroath, Angus, Scotland. It moved into its present building in 1985. Accommodation The new building was opened in 1985 to serve the west side of ...

in Angus, and attended the

University of Edinburgh The University of Edinburgh (, ; abbreviated as ''Edin.'' in Post-nominal letters, post-nominals) is a Public university, public research university based in Edinburgh, Scotland. Founded by the City of Edinburgh Council, town council under th ...

, where he studied alongside

James Alfred Ewing Sir James Alfred Ewing MInstitCE (27 March 1855 − 7 January 1935) 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, ''hy ...

. He worked on various aspects of electricity and

magnetism Magnetism is the class of physical attributes that occur through a magnetic field, which allows objects to attract or repel each other. Because both electric currents and magnetic moments of elementary particles give rise to a magnetic field, ...

, obtaining his doctorate in 1879. He was appointed as an assistant in Natural Philosophy at the University of Edinburgh in 1879, and held this post until 1883, when he left to take up a post at

Tokyo Imperial University The University of Tokyo (, abbreviated as in Japanese and UTokyo in English) is a public university, public research university in Bunkyō, Tokyo, Japan. Founded in 1877 as the nation's first modern university by the merger of several Edo peri ...

. He was elected as a Fellow of the Royal Society of Edinburgh in 1880 after being proposed by

Peter Guthrie Tait Peter Guthrie Tait (28 April 18314 July 1901) was a Scottish Mathematical physics, mathematical physicist and early pioneer in thermodynamics. He is best known for the mathematical physics textbook ''Treatise on Natural Philosophy'', which he ...

Alexander Crum Brown Alexander Crum Brown Fellow of the Royal Society of Edinburgh, FRSE Fellow of the Royal Society, FRS (26 March 1838 – 28 October 1922) was a Scottish Organic chemistry, organic chemist. Alexander Crum Brown Road in Edinburgh's King's Buildi ...

, John Gray McKendrick, and Alexander Buchan. He won the Society's

Keith Prize The Keith Medal was a prize awarded by the Royal Society of Edinburgh, Scotland's national academy, for a scientific paper published in the society's scientific journals, preference being given to a paper containing a discovery, either in mathem ...

for the period 1893–95. He served as Secretary 1905-1912 and General Secretary 1912–1922. He was also a founder of the

Edinburgh Mathematical Society The Edinburgh Mathematical Society is a mathematical society for academics in Scotland. History The Society was founded in 1883 by a group of Edinburgh school teachers and academics, on the initiative of Alexander Yule Fraser FRSE and Andrew ...

, taking the chair for its first meeting on Friday 2 February 1883.

Career in Japan

Japan's Ministry of Public Works was founded in October 1871 with 11 departments, one of which was an engineering college. College head Yamao Yōzō invited British scientists William Rankine and

Lord Kelvin William Thomson, 1st Baron Kelvin (26 June 182417 December 1907), was a British mathematician, Mathematical physics, mathematical physicist and engineer. Born in Belfast, he was the Professor of Natural Philosophy (Glasgow), professor of Natur ...

to send British instructors. Six came, including geologist

John Milne John Milne (30 December 1850 – 31 July 1913) was a British geologist and mining engineer who worked on a horizontal seismograph. Biography Milne was born in Liverpool, England, the only child of John Milne of Milnrow, and at first raised ...

and physicist

, who became professors at the college, which became part of

. Ewing returned to Scotland in 1883 and the University rector asked

to recommend a successor. Kelvin recommended Knott, which 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 in establishing a network of recording seismometers across the

Japanese Empire The Empire of Japan, also known as the Japanese Empire or Imperial Japan, was the Japanese nation state that existed from the Meiji Restoration on January 3, 1868, until the Constitution of Japan took effect on May 3, 1947. From 1910 to ...

. Knott also taught courses in mathematics,

acoustics Acoustics is a branch of physics that deals with the study of mechanical waves in gases, liquids, and solids including topics such as vibration, sound, ultrasound and infrasound. A scientist who works in the field of acoustics is an acoustician ...

, and

electromagnetism In physics, electromagnetism is an interaction that occurs between particles with electric charge via electromagnetic fields. The electromagnetic force is one of the four fundamental forces of nature. It is the dominant force in the interacti ...

at the Tokyo Imperial University. Knott also undertook the first geomagnetic survey of Japan, assisted by Japanese

geophysicist Geophysics () is a subject of natural science concerned with the physical processes and properties of Earth and its surrounding space environment, and the use of quantitative methods for their analysis. Geophysicists conduct investigations acros ...

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 In mathematics, Fourier analysis () is the study of the way general functions may be represented or approximated by sums of simpler trigonometric functions. Fourier analysis grew from the study of Fourier series, and is named after Joseph Fo ...

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. Cargil Knott married Mary Dixon in 1885, becoming the brother-in-law of the literary scholar James Main Dixon. On the conclusion of his stay in Japan in 1891, he was awarded the

Order of the Rising Sun The is a Japanese honors system, Japanese order, established in 1875 by Emperor Meiji. The Order was the first national decoration awarded by the Japanese government, created on 10 April 1875 by decree of the Council of State. The badge feat ...

Emperor Meiji , posthumously honored as , was the 122nd emperor of Japan according to the List of emperors of Japan, traditional order of succession, reigning from 1867 until his death in 1912. His reign is associated with the Meiji Restoration of 1868, which ...

Return to Edinburgh

On his return to Edinburgh, Knott took up the position of a Reader in Applied Mathematics at the University of Edinburgh, holding the post until his death in 1922. While in Japan, Knott began to develop mathematical equations describing how seismic vibrations are reflected and transmitted across the boundary between seawater and seabed. After returning to the University of Edinburgh in 1892, he expanded upon this research to describe the behaviour of earthquake waves at the interface between two different types of rock. Knott's equations, derived in terms of potentials, were the first to describe the amplitudes of reflected and refracted waves at non-normal incidenceSheriff, R. E., Geldart, L. P., (1995), 2nd edition, ''Exploration Seismology'',

Cambridge University Press Cambridge University Press was the university press of the University of Cambridge. Granted a letters patent by King Henry VIII in 1534, it was the oldest university press in the world. Cambridge University Press merged with Cambridge Assessme ...

and together with the Zoeppritz equations are now the basis for modern

reflection seismology Reflection seismology (or seismic reflection) is a method of exploration geophysics that uses the principles of seismology to estimate the properties of the Earth's subsurface from reflection (physics), reflected seismic waves. The method requir ...

– an important technique in

hydrocarbon exploration Hydrocarbon exploration (or oil and gas exploration) is the search by petroleum geologists and geophysicists for hydrocarbon deposits, particularly petroleum and natural gas, in the Earth's crust using petroleum geology. Exploration methods ...

. Knott continued his work as a mathematician, including

quaternion In mathematics, the quaternion number system extends the complex numbers. Quaternions were first described by the Irish mathematician William Rowan Hamilton in 1843 and applied to mechanics in three-dimensional space. The algebra of quater ...

methods of his professor and mentor

. When the tight constraints of a single

linear algebra Linear algebra is the branch of mathematics concerning linear equations such as :a_1x_1+\cdots +a_nx_n=b, linear maps such as :(x_1, \ldots, x_n) \mapsto a_1x_1+\cdots +a_nx_n, and their representations in vector spaces and through matrix (mathemat ...

began to be felt in the 1890s, and revisionists began publishing, Knott contributed the pivotal article "Recent Innovations in Vector Theory". As Michael J. Crowe describes,M.J. Crowe (1967)

A History of Vector Analysis ''A History of Vector Analysis'' (1967) is a book on the history of vector analysis by Michael J. Crowe, originally published by the University of Notre Dame Press. As a scholarly treatment of a reformation in technical communication, the text i ...

, esp. pp. 200–5 this paper set straight wayward theorists that expected to find

associativity In mathematics, the associative property is a property of some binary operations that rearranging the parentheses in an expression will not change the result. In propositional logic, associativity is a Validity (logic), valid rule of replaceme ...

in systems like hyperbolic quaternions. Knott wrote: :: e 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 coquaternions. Nevertheless, Crowe states 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 (15 February 1861 – 30 December 1947) was an English mathematician and philosopher. He created the philosophical school known as process philosophy, which has been applied in a wide variety of disciplines, inclu ...

(1898) presumed some grounding in quaternions as students encountered

matrix algebra In abstract algebra, a matrix ring is a set of matrices with entries in a ring ''R'' that form a ring under matrix addition and matrix multiplication. The set of all matrices with entries in ''R'' is a matrix ring denoted M''n''(''R'') (alterna ...

. 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 In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted , called the imaginary unit and satisfying the equation i^= -1; every complex number can be expressed in the form a ...

and

continuous group In mathematics, topological groups are the combination of groups and topological spaces, i.e. they are groups and topological spaces at the same time, such that the continuity condition for the group operations connects these two structures ...

s,...". Thus he was aware of the diversity to be encountered in modern

mathematical structure In mathematics, a structure on a set (or on some sets) refers to providing or endowing it (or them) with certain additional features (e.g. an operation, relation, metric, or topology). Τhe additional features are attached or related to the ...

s, and that quaternions stand as a milestone on the way to others. He became more active in the Royal Society of Edinburgh, serving on the council from 1894 to 1905, moving up to a Secretary to Ordinary Meetings in 1905 and finally becoming its general secretary in 1912 until his death in 1922. Knott also took an active social role in his community including

Sunday school ] A Sunday school, sometimes known as a Sabbath school, is an educational institution, usually Christianity, Christian in character and intended for children or neophytes. Sunday school classes usually precede a Sunday church service and are u ...

teaching and church affairs with the

United Free Church of Scotland The United Free Church of Scotland (UF Church; , ) is a Scottish Presbyterian denomination formed in 1900 by the union of the United Presbyterian Church of Scotland (or UP) and the Free Church of Scotland (1843–1900), majority of the 19th-cen ...

. He was finally elected a Fellow of the

in 1920 and was also a member of the Scottish Meteorological Society. He died at his home at 42 Upper Gray Street, Newington,

Edinburgh Edinburgh is the capital city of Scotland and one of its 32 Council areas of Scotland, council areas. The city is located in southeast Scotland and is bounded to the north by the Firth of Forth and to the south by the Pentland Hills. Edinburgh ...

, on 26 October 1922.

Partial bibliography

The

internet archive The Internet Archive is an American 501(c)(3) organization, non-profit organization founded in 1996 by Brewster Kahle that runs a digital library website, archive.org. It provides free access to collections of digitized media including web ...

and other web sources now offer some of Knott's works: * 1890
M. Ballore’s Calculations on Earthquake Frequency
from

Google Books Google Books (previously known as Google Book Search, Google Print, and by its code-name Project Ocean) is a service from Google that searches the full text of books and magazines that Google has scanned, converted to text using optical charac ...

* 1899
Reflection and Refraction of Elastic Waves with Seismological Applications

Philosophical Magazine The ''Philosophical Magazine'' is one of the oldest scientific journals published in English. It was established by Alexander Tilloch in 1798;John Burnett"Tilloch, Alexander (1759–1825)" Dictionary of National Biography#Oxford Dictionary of ...

48: 64–97 via

Biodiversity Heritage Library The Biodiversity Heritage Library (BHL) is the world’s largest open-access digital library for biodiversity literature and archives. BHL operates as a worldwide consortium of natural history, botanical, research, and national libraries working ...

* 1904: (as editor
Introduction to Quaternions, 3rd edition
via

Hathi Trust HathiTrust Digital Library is a large-scale collaborative repository of digital content from research libraries. Its holdings include content digitized via Google Books and the Internet Archive digitization initiatives, as well as content digit ...

* 1908
The Physics of Earthquake Phenomena
* 1911
Life and Scientific Work of Peter Gutherie Tait. Supplementing the Two Volumes of Scientific Papers Published in 1898 and 1900
* 1913
Physics, An Elementary Textbook for University Classes
from

HathiTrust HathiTrust Digital Library is a large-scale collaborative repository of digital content from research libraries. Its holdings include content digitized via Google Books and the Internet Archive digitization initiatives, as well as content digit ...

* 1915
Napier Tercentenary Memorial Volume
* 1919: "The Propagation of Earthquake Waves through the Earth and connected problems", ''Proceedings of the Royal Society of Edinburgh'' 39: 157–208

Family

In 1885, Cargill married Mary Dixon, sister of James Main Dixon.

References

* K.E. Bullen (1973) "Knott, Cargill Gilston" in ''Dictionary of Scientific Biography'', C.C. Gillespie editor, published by

American Council of Learned Societies The American Council of Learned Societies (ACLS) is a private, nonprofit federation of 75 scholarly organizations in the humanities and related social sciences founded in 1919. It is best known for its fellowship competitions which provide a ra ...

. * E. T. Whittaker (1922) "Cargill Gilston Knott" (obituary) ''Proceedings of the Royal Society of Edinburgh'' 43:237 – 48. Includes a substantial but partial bibliography. * A Milne (1922) " Cargill G Knott, D.Sc., LL.D., F.R.S. (obituary)", Proceedings of the Edinburgh Math. Soc. 40 (1921–22), 50–51 *

External links

* *
Penicuik Community Development Trust essay on C.G. Knott and ties to Japan
{{DEFAULTSORT:Knott, Cargill Gilston Scottish physicists 1856 births 1922 deaths Foreign advisors to the government in Meiji-era Japan Foreign educators in Japan Scottish expatriates in Japan Fellows of the Royal Society of Edinburgh Fellows of the Royal Society People from Penicuik British seismologists 19th-century Scottish mathematicians Alumni of the University of Edinburgh Scottish scholars and academics Academics of the University of Edinburgh Academic staff of the University of Tokyo People from Arbroath Recipients of the Order of the Rising Sun 20th-century Scottish mathematicians