Quaternion Society (1899 - 1913)

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 related systems in linear algebra. The guiding light was Alexander MacFarlane (mathematician) who served as its secretary throughout the life of the society. The society, through MacFarlane, published a “Bulletin” (annual report) from 1900, and a Bibliography in 1904. By exercising mathematics and the imagination, the society helped prepare for the four-dimensional theory of space and time called relativity.

Genesis

In 1895, Professor P. Molenbroeck 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 (journal), Science (journal), and the Bulletin of the American Mathematical Society (see references). The idea was supported by discussions at the 1897 meeting of the British Association at Toronto. When organized in 1899, Peter Guthrie Tait was chosen as president, but he declined for reasons of poor health. Robert Stawell Ball then served for a year. Charles Jasper Joly, who published his "Manual of Quaternions" in 1905, took over the presidency that year.

A system of national secretaries was announced in the AMS Bulletin in 1899: Alexander MacAulay for Australasia, Paul Genty for France, Victor Schlegel for Germany, Joly for Great Britain and Ireland, Giuseppe Peano for Italy, Kimura for Japan, A.P. Kotelnikov for Russia, F. Kraft for Switzerland, and A.S. Hathaway for the USA.

Bulletin

The annual report included articles, reviews, and society notes. It did not serve as a professionally reviewed scholarly journal, so there has been little reference to this publication in later work. However, in historical work the bulletin is of great value. One instance can be viewed in A History of Vector Analysis by M.J. Crowe. Another case is the 1984 article “The Quaternion Group and Modern Physics” by P.R. Girard in the European Journal of Physics 5:25-32. Girard notes that MacFarlane supplemented his 1904 Bibliography with lists in the bulletin for 1905, 08, 09, 10, 12, and 1913. Ortiz (see external link) notes also that the bulletin kept tabs on the use of quaternions at various academic locales.

MacFarlane

As the society existed only with each individual, their writings and correspondence, the secretary was the motive force. By the time he steered the society MacFarlane had left the halls of learning at University of Texas and Lehigh University. From his home base at Chatham Ontario he ventured to campuses such as University of Michigan and Lehigh for research and lectures, and to the International Congresses of Mathematicians. Having been educated in Tait’s Lab in Edinburgh, he was grounded in physical science and, like many others at the time, thought quaternion methods could clarify physical theory. For instance, he initiated the idea of hyperbolic quaternions and began the exploitation of biquaternions that appealed also to some later theorists. When MacFarlane died, the society died too, showing how he had carried the bulk of the enterprise.

Bibliography

Published in 1904 at Dublin, cradle of quaternions, the 86 page bibliography of quaternions cited some one thousand references. The publication set a professional standard; for instance the "Manual" of Joly has no bibliography beyond citation of MacFarlane.

In 1967 when M.J. Crowe published A History of Vector Analysis, he wrote in the preface (page ix) ::"Concerning bibliography". No formal bibliographical section has been included with this book. … the need for a bibliography is greatly diminished by the existence of a book that lists nearly all relevant primary documents published to about 1912, this is Alexander Macfarlane’s "Bibliography" …

Now available on-line in the Cornell University Historical Mathematical Digital Library, Macfarlane's work continues to be an important tool in research.

Aftermath

In 1912 the International Congress of Mathematicians met in Cambridge England. MacFarlane attended, as did Ludwik Silberstein, who used biquaternions in his presentation to the congress and in his book Theory of Relativity. Silberstein made no reference to the society or MacFarlane, viewing them as the common background of the time. Silberstein’s flowing prose and concrete application of relativity to electromagnetic theory shifted the attention of the scientific public from the abstract algebra with which the society had been concerned to physical science.

References

* S. Kimura & P. Molenbroek (1895) "Friends and Fellow Workers in Quaternions" Nature 52:545-6.
* S. Kimura & P. Molenbroek (1895) "To those Interested in Quaternions and Allied Systems of Mathematics" Science 2nd Ser, 2:524-25.
* "Notes" Bulletin of the American Mathematical Society 2:53,182; 5:317.
*Eduardo L. Ortiz [http://www.ma.utexas.edu/users/villegas/F02/quaternions.txt International Association for Promoting the Calculus of Quaternions]