A scientific society, the Quaternion Society was 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 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 from 1900 to 1913. The Bulletin became a review journal for topics in vector analysis and abstract algebra such as the theory ofequipollence. The mathematical work reviewed pertained largely to matrices and linear algebra as the methods were in rapid development at the time.
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.
Bulletin
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 Toronto by Roswell-Hutchinson Press.
Published in Dublin at the University Press. President Charles J. Joly address.
, Lancaster. President Macfarlane address on notation.
, Lancaster. J.B. Shaw challenged by "inclusion or exclusion of certain papers which are only remotely connected with the theory of operations in the abstract."
, Lancaster. Obituary: Ferdinand Ferber. "Comparative Notation for Vector Expressions" by J.B. Shaw. President Macfarlane address citing Duncan Sommerville's comments.
, Lancaster. Secretary Shaw reports the death of A. Macfarlane and G. Combebiac.
Aftermath
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 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.
