The Quaternion Society was a scientific society, self-described as an "International Association for Promoting the Study of Quaternions and Allied Systems of Mathematics". At its peak it consisted of about 60 mathematicians spread throughout the academic world that were experimenting with quaternions and other hypercomplex number systems. The group's guiding light was Alexander Macfarlane who served as its secretary initially, and became president in 1909. The association published a Bibliography in 1904 and a Bulletin (annual report) from 1900 to 1913.
The Bulletin became a review journal for topics in vector analysis and abstract algebra such as the theory of equipollence. The mathematical work reviewed pertained largely to matrices and linear algebra as the methods were in rapid development at the time.
In 1895, Professor P. Molenbroek of The Hague, Holland, and Shinkichi Kimura studying at Yale put out a call for scholars to form the society in widely circulated journals: Nature,Science, and the Bulletin of the American Mathematical Society. Giuseppe Peano also announced the society formation in his Rivista di Matematica.
The call to form an Association was encouraged by Macfarlane in 1896:
In 1897 the British Association met in Toronto where vector products were discussed:
A system of national secretaries was announced in the AMS Bulletin in 1899: Alexander McAulay for Australasia, Victor Schlegel for Germany, Joly for Great Britain and Ireland, Giuseppe Peano for Italy, Kimura for Japan, Aleksandr Kotelnikov for Russia, F. Kraft for Switzerland, and Arthur Stafford Hathaway for the USA. For France the national secretary was Paul Genty, an engineer with the division of Ponts et Chaussees, and a quaternion collaborator with Charles-Ange Laisant, author of Methode des Quaterniones (1881).
Victor Schlegel reportedon the new institution in the Monatshefte für Mathematik.
When the society was organized in 1899, Peter Guthrie Tait was chosen as president, but he declined for reasons of poor health.
The first president was Robert Stawell Ball, and Alexander Macfarlane served as secretary and treasurer. In 1905 Charles Jasper Joly took over as president and L. van Elfrinkhof as treasurer, while Macfarlane continued as secretary. In 1909 Macfarlane became president, James Byrnie Shaw became secretary, and van Elfrinkhof continued as treasurer. The next year Macfarlane and Shaw continued in their posts, while Macfarlane also absorbed the office of treasurer. When Macfarlane died in 1913 after nearly completing the issue of the Bulletin, Shaw completed it and wound up the association.
The rules state that the president had the power of veto.
The Bulletin of the Association Promoting the Study of Quaternions and Allied Systems of Mathematics was issued nine times under the editorship of Alexander Macfarlane. Every issue listed the officers of the Association, governing council, rules, members, and a financial statement from the treasurer. Today HathiTrust provides access to these publications that are mainly of historical interest:
Published in 1904 at Dublin, cradle of quaternions, the 86 page Bibliography of Quaternions and Allied Systems of Mathematics :cited some one thousand references. The publication set a professional standard; for instance the Manual of Quaternions (1905) of Joly has no bibliography beyond citation of Macfarlane. Furthermore, in 1967 when M.J. Crowe published A History of Vector Analysis , he wrote in the preface (page ix)
Every year more papers and books appeared that were of interest to Association members so it was necessary to update the Bibliography with supplements in the Bulletin. The categories used to group the items in the supplements give a sense of the changing focus of the Association:
In 1913 Macfarlane died, and as related by Dirk Struik, the Society "became a victim of the first World War".
James Byrnie Shaw, the surviving officer, wrote 50 book notices for American mathematical publications.The final article review in the Bulletin was The Wilson and Lewis Algebra of Four-Dimensional Space written by J. B. Shaw. He summarizes,
The article reviewed was "The space-time manifold of relativity, the non-Euclidean geometry of mechanics, and electromagnetics".However, when the textbook The Theory of Relativity by Ludwik Silberstein in 1914 was made available as an English understanding of Minkowski space, the algebra of biquaternions was applied, but without references to the British background or Macfarlane or other quaternionists of the Society. The language of quaternions had become international, providing content to set theory and expanded mathematical notation, and expressing mathematical physics.
Linear algebra is the branch of mathematics concerning linear equations such as:
In mathematics, hypercomplex number is a traditional term for an element of a finite-dimensional unital algebra over the field of real numbers. The study of hypercomplex numbers in the late 19th century forms the basis of modern group representation theory.
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 quaternion as the quotient of two directed lines in a three-dimensional space, or, equivalently, as the quotient of two vectors. Multiplication of quaternions is noncommutative.
Hermann Günther Grassmann was a German polymath, known in his day as a linguist and now also as a mathematician. He was also a physicist, general scholar, and publisher. His mathematical work was little noted until he was in his sixties.
Multilinear algebra is a subfield of mathematics that extends the methods of linear algebra. Just as linear algebra is built on the concept of a vector and develops the theory of vector spaces, multilinear algebra builds on the concepts of p-vectors and multivectors with Grassmann algebras.
Eduard Study, more properly Christian Hugo Eduard Study, was a German mathematician known for work on invariant theory of ternary forms (1889) and for the study of spherical trigonometry. He is also known for contributions to space geometry, hypercomplex numbers, and criticism of early physical chemistry.
Alexander Macfarlane FRSE LLD was a Scottish logician, physicist, and mathematician.
In abstract algebra, the algebra of hyperbolic quaternions is a nonassociative algebra over the real numbers with elements of the form
Alexander McAulay was the first professor of mathematics and physics at the University of Tasmania, Hobart, Tasmania. He was also a proponent of dual quaternions, which he termed "octonions" or "Clifford biquaternions".
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.
In mathematics, a versor is a quaternion of norm one. The word is derived from Latin versare = "to turn" with the suffix -or forming a noun from the verb. It was introduced by William Rowan Hamilton in the context of his quaternion theory.
Cargill Gilston Knott FRS, FRSE LLD 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.
In mathematics and physics, vector notation is a commonly used notation for representing vectors, which may be Euclidean vectors, or more generally, members of a vector space.
In mathematics, quaternions are a non-commutative number system that extends the complex numbers. Quaternions and their applications to rotations were first described in print by Olinde Rodrigues in all but name in 1840, but independently discovered by Irish mathematician Sir William Rowan Hamilton in 1843 and applied to mechanics in three-dimensional space. They find uses in both theoretical and applied mathematics, in particular for calculations involving three-dimensional rotations.
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 is a contribution to the history of science. In 2002, Crowe gave a talk summarizing the book, including an entertaining introduction in which he covered its publication history and related the award of a Jean Scott prize of $4000. Crowe had entered the book in a competition for "a study on the history of complex and hypercomplex numbers" twenty-five years after his book was first published.
Charles Jasper Joly was an Irish mathematician and astronomer who became Royal Astronomer of Ireland.
In mathematics and physics, vector is a term that refers colloquially to some quantities that cannot be expressed by a single number, or to elements of some vector spaces.
In mathematics, hypercomplex analysis is the basic extension of real analysis and complex analysis to the study of functions where the argument is a hypercomplex number. The first instance is functions of a quaternion variable, where the argument is a quaternion. A second instance involves functions of a motor variable where arguments are split-complex numbers.
The subject of physical mathematics is concerned with physically motivated mathematics and is considered by some as a subfield of mathematical physics.
Hüseyin Tevfik Pasha was a military adjutant representing Turkey in the purchase of foreign rifles. He is remembered for his Linear Algebra which outlined some vector algebra including a "special perpendicular" and properties of curves. The book title was precocious since the early vector algebra was generalized in vector space, and this concept later produced linear algebra. He is known as Tawfiq Pasha of Vidin or as Vidinli Huseyin, Tawfiq Pasha in Turkish literature. He served as Envoy of the Ottoman Empire to the United States.