Cargill Gilston Knott
|Cargill Gilston Knott|
Cargill Gilston Knott
|Born||30 June 1856
|Died||26 October 1922
|Fields||physics, mathematics, seismology|
|Alma mater||University of Edinburgh|
|Notable awards||Order of the Rising Sun|
Cargill Gilston Knott FRS, FRSE (30 June 1856 – 26 October 1922) was a Scottish physicist and mathematician who was a pioneer in seismological research. He spent his early career in Japan. He later became a Fellow of the Royal Society, Secretary of the Royal Society of Edinburgh, and President of the Scottish Meteorological Society.
Knott was born at Penicuik, Midlothian, educated at Arbroath High School in Angus, and attended the University of Edinburgh, where he studied alongside James Alfred Ewing. He worked on various aspects of electricity and magnetism, obtaining his doctorate in 1879.
He was appointed as an assistant in Natural Philosophy at Edinburgh University in 1879 and held this post until 1883, when he left to take up a post at Tokyo Imperial University. He was elected as a Fellow of the Royal Society of Edinburgh in 1880 after being proposed by Peter Guthrie Tait, Alexander Crum Brown, John Gray McKendrick, and Alexander Buchan. He was also a founder of the Edinburgh Mathematical Society, taking the chair for its first meeting on Friday 2 February 1883.
Career in Japan
Soon after the Meiji Restoration in Japan, the new Meiji government began a program for building lighthouses to facilitate trade and navigation, hiring Scottish engineer Richard Henry Brunton in 1868. Brunton soon realised that the new lighthouses would need to be designed against the frequent earthquakes 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 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 Lomar 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 in establishing a network of recording seismometers across the Japanese Empire. Knott also taught courses in mathematics, acoustics, and electromagnetism at the Tokyo Imperial University.
Knott also undertook the first geomagnetic survey of Japan, assisted by Japanese geophysicist 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.
Return to Edinburgh
Upon his return to Edinburgh, Knott took up the position of a Reader in Applied Mathematics at Edinburgh University and held this 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 Edinburgh University 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 incidence and together with the Zoeppritz equations are now the basis for modern reflection seismology – an important technique in hydrocarbon exploration.
Knott continued his work as a mathematician, expanding on the quaternion algebra developments of his professor and mentor Peter Guthrie Tait. When the tight constraints of a single linear algebra 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 in systems like hyperbolic quaternions. 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 coquaternions. 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 (1898) presumed some grounding in quaternions as students encountered matrix algebra. 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 and continuous groups,...". Thus he was aware of the diversity to be encountered in modern mathematical structures, 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 teaching and church affairs with the United Free Church of Scotland. He was finally elected a Fellow of the Royal Society in 1920 and was also a member of the Scottish Meteorological Society.
- 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)
- History of Edinburgh Mathematical Society.
- Flood, Kelvin, Labor; Labors and Legacy. Pp.218
- "Former Fellows of the Royal Society of Edinburgh". Royal Society of Edinburgh. Retrieved 2 September 2010.
- Penicuik Community Development Trust (UK): Cargill Gilston Knott
- Sheriff, R. E., Geldart, L. P., (1995), 2nd Edition. Exploration Seismology. Cambridge University Press.
- St. Andrews University. School of Mathematics and Statistics. Cargill Gilston Knott. http://www-history.mcs.st-andrews.ac.uk/Biographies/Knott.html
- K.E. Bullen (1973) "Knott, Cargill Gilston" in Dictionary of Scientific Biography, C.C. Gillespie editor, published by American Council of Learned Societies.
- M.J. Crowe (1967) A History of Vector Analysis, esp. pp. 200–5 .
- C.G. Knott (1893) "Recent innovations in vector theory" Proceedings of the Royal Society of Edinburgh 9:212–37.Synopsis in Nature 47:590–3.
- 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
- Flood, Raymond (2008). Kelvin: Life, Labours and Legacy. Oxford University Press. ISBN 0-19-923125-7.
- Works written by or about Cargill Gilston Knott at Wikisource
- Quotations related to Cargill Gilston Knott at Wikiquote
- Penicuik Community Development Trust essay on C.G. Knott and ties to Japan