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 letters, judged to be "eminently distinguished in their subject". This soci ...

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 caus ...

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, structure, space, models, and change. History On ...

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 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 established i ...

, and President of the

Scottish Meteorological Society The Scottish Meteorological Society was founded in 1855 by David Milne-Home with private funding, particularly from wealthy landowners who wished to compile meteorological records in order to improve agriculture. The Society founded the observato ...

Biography

Knott was born in

Penicuik Penicuik ( ; sco, Penicuik; gd, Peighinn na Cuthaig) is a town and former burgh in Midlothian, Scotland, lying on the west bank of the River North Esk. It lies on the A701 midway between Edinburgh and Peebles, east of the Pentland Hills. Na ...

, Midlothian, the son of Pelham Knott, an agent for a paper manufacturer and his wife Ellen. His paternal uncle was the artist

Tavernor Knott Tavernor Knott WSA (occasionally written Taverner Knott) (1816–1890) was a Scottish portrait and genre artist. He was the paternal uncle of Cargill Gilston Knott. Life He was born in Aberdeen in 1816 the son of John Knott (b.1754), a music tea ...

. 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 ( sco, University o Edinburgh, gd, Oilthigh Dhùn Èideann; abbreviated as ''Edin.'' in post-nominals) is a public research university based in Edinburgh, Scotland. Granted a royal charter by King James VI in 15 ...

, 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, '' h ...

. He worked on various aspects of electricity and

magnetism Magnetism is the class of physical attributes that are mediated by a magnetic field, which refers to the capacity to induce attractive and repulsive phenomena in other entities. Electric currents and the magnetic moments of elementary particles ...

, 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 , abbreviated as or UTokyo, is a public research university located in Bunkyō, Tokyo, Japan. Established in 1877, the university was the first Imperial University and is currently a Top Type university of the Top Global University Project by ...

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

Peter Guthrie Tait Peter Guthrie Tait FRSE (28 April 1831 – 4 July 1901) was a Scottish mathematical physicist and early pioneer in thermodynamics. He is best known for the mathematical physics textbook '' Treatise on Natural Philosophy'', which he co-wrote wi ...

Alexander Crum Brown Alexander Crum Brown FRSE FRS (26 March 1838 – 28 October 1922) was a Scottish organic chemist. Alexander Crum Brown Road in Edinburgh's King's Buildings complex is named after him. Early life and education Crum Brown was born at 4 Belle ...

John Gray McKendrick John Gray McKendrick FRS FRSE FRCPE LLD (12 August 1841 – 2 January 1926) was a distinguished Scottish physiologist. He was born and studied in Aberdeen, Scotland, and served as Regius Professor of Physiology at the University of Glasgow fr ...

, 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 mathema ...

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 Je ...

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

Career in Japan

Japan's Public Works was found in October 1871 with 11 departments, one of which was the engineering institution.

Yamao Yozo Yamao (written: ) is a Japanese surname. Notable people with the surname include: *, Japanese rhythmic gymnast *, Japanese cyclist *, Japanese footballer *, Japanese poet *, Japanese politician *, Japanese samurai {{surname Japanese-language sur ...

, head of the institution asked

William Rankine William John Macquorn Rankine (; 5 July 1820 – 24 December 1872) was a Scottish mechanical engineer who also contributed to civil engineering, physics and mathematics. He was a founding contributor, with Rudolf Clausius and William Thomson ( ...

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. Professor of Natural Philosophy (Glasgow), Professor of Natural Philoso ...

to send proper teaching staffs to the technical school through

Hugh Mateson Hugh may refer to: *Hugh (given name) Noblemen and clergy French * Hugh the Great (died 956), Duke of the Franks * Hugh Magnus of France (1007–1025), co-King of France under his father, Robert II * Hugh, Duke of Alsace (died 895), modern-day ...

, and hired 6 instructors lead by

Henry Dyer Henry Dyer (23 August 1848 – 25 September 1918) was a Scottish engineer who contributed much to founding Western-style technical education in Japan and Scottish-Japanese relations. Early life Henry Dyer was born on 16 August 1848, ...

as a principal,

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 in ...

a Professor of Geology and Mining, and

Professor of Physics and Engineering at

from 1878. When Ewing returned to Scotland in 1883, the rector of Tokyo Imperial University wrote to

, 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 was a pioneer Japanese seismologist, second chairman of seismology at the Imperial University of Tokyo and president of the Japanese Imperial Earthquake Investigation Committee. Omori is also known for his observation describing the aftersho ...

in establishing a network of recording seismometers across the

Japanese Empire The also known as the Japanese Empire or Imperial Japan, was a historical nation-state and great power that existed from the Meiji Restoration in 1868 until the enactment of the post-World War II 1947 constitution and subsequent forma ...

. 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. It is the second-strongest of the four fundamental interactions, after the strong force, and it is the dominant force in the interactions of a ...

at the Tokyo Imperial University. Knott also undertook the first

geomagnetic Earth's magnetic field, also known as the geomagnetic field, is the magnetic field that extends from Earth's interior out into space, where it interacts with the solar wind, a stream of charged particles emanating from the Sun. The magnetic ...

survey of Japan, assisted by Japanese

geophysicist Geophysics () is a subject of natural science concerned with the physical processes and physical properties of the Earth and its surrounding space environment, and the use of quantitative methods for their analysis. The term ''geophysics'' som ...

Tanakadate Aikitsu was a Japanese physicist with diverse interests and effect. His given name was also written as Aikitu. Biography Tanakadate was born in Fukuoka hamlet, in what is now part of the city of Ninohe in the northern Iwate Prefecture, Japan. He was ...

, 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 Josep ...

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 right , 235px , James Main Dixon, 1902 James Main Dixon FRSE (1856, Paisley – 27 September 1933) was a Scottish teacher and author, and an important scholar of the Scots language. Life He was born in Paisley in Scotland the son of Rev ...

. On the conclusion of his stay in Japan in 1891, he was awarded the

Order of the Rising Sun The is a 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 features rays of sunlight ...

Emperor Meiji , also called or , was the 122nd emperor of Japan according to the traditional order of succession. Reigning from 13 February 1867 to his death, he was the first monarch of the Empire of Japan and presided over the Meiji era. He was the figur ...

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 is the university press of the University of Cambridge. Granted letters patent by Henry VIII of England, King Henry VIII in 1534, it is the oldest university press A university press is an academic publishing hou ...

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 reflected seismic waves. The method requires a controlled seismi ...

– an important technique in

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

. 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. Hamilton defined a quatern ...

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 matrices. ...

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,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, which means that rearranging the parentheses in an expression will not change the result. In propositional logic, associativity is a valid rule of replacement f ...

in systems like

hyperbolic quaternion In abstract algebra, the algebra of hyperbolic quaternions is a nonassociative algebra over the real numbers with elements of the form :q = a + bi + cj + dk, \quad a,b,c,d \in \mathbb \! where the squares of i, j, and k are +1 and distinct eleme ...

s. 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

coquaternion In abstract algebra, the split-quaternions or coquaternions form an algebraic structure introduced by James Cockle in 1849 under the latter name. They form an associative algebra of dimension four over the real numbers. After introduction in ...

s. 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 is best known as the defining figure of the philosophical school known as process philosophy, which today has found applicat ...

(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'')Lang, ''U ...

. 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 logically the combination of Group (mathematics), groups and Topological space, topological spaces, i.e. they are groups and topological spaces at the same time, such that the Continuous function, continui ...

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

mathematical structure In mathematics, a structure is a set endowed with some additional features on the set (e.g. an operation, relation, metric, or topology). Often, the additional features are attached or related to the set, so as to provide it with some additional ...

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 is an educational institution, usually (but not always) Christian in character. Other religions including Buddhism, Islam, and Judaism have also organised Sunday schools in their temples and mosques, particularly in the West. Su ...

teaching and church affairs with the

United Free Church of Scotland The United Free Church of Scotland (UF Church; gd, An Eaglais Shaor Aonaichte, sco, The Unitit Free Kirk o Scotland) is a Scottish Presbyterian denomination formed in 1900 by the union of the United Presbyterian Church of Scotland (or UP) and ...

. He was finally elected a Fellow of the

in 1920 and was also a member of the

. He died at his home at 42 Upper Gray Street, Newington,

Edinburgh Edinburgh ( ; gd, Dùn Èideann ) is the capital city of Scotland and one of its 32 Council areas of Scotland, council areas. Historically part of the county of Midlothian (interchangeably Edinburghshire before 1921), it is located in Lothian ...

, on 26 October 1922.

Partial bibliography

The

internet archive The Internet Archive is an American digital library with the stated mission of "universal access to all knowledge". It provides free public access to collections of digitized materials, including websites, software applications/games, music, ...

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 Inc. that searches the full text of books and magazines that Google has scanned, converted to text using optical c ...

* 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)" Oxford Dictionary of National Biography, Oxford Univer ...

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 worldwide consortiumof natural history, botanical, research, and national libraries working toge ...

* 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 including content digitized via Google Books and the Internet Archive digitization initiatives, as well as content digitized locally ...

* 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 including content digitized via Google Books and the Internet Archive digitization initiatives, as well as content digitized locally ...

* 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

References

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

American Council of Learned Societies American(s) may refer to: * American, something of, from, or related to the United States of America, commonly known as the "United States" or "America" ** Americans, citizens and nationals of the United States of America ** American ancestry, pe ...

. *

E. T. Whittaker Sir Edmund Taylor Whittaker (24 October 1873 – 24 March 1956) was a British mathematician, physicist, and historian of science. Whittaker was a leading mathematical scholar of the early 20th-century who contributed widely to applied mathema ...

(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-period 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 Scottish mathematicians Alumni of the University of Edinburgh Scottish scholars and academics Academics of the University of Edinburgh University of Tokyo faculty People from Arbroath Recipients of the Order of the Rising Sun