Remarks on the "International Association for Promoting the Calculus of Quaternions" by Professor Eduardo L. Ortiz Senior Research Fellow, Imperial College London, England xxxxxxxxxxxxxxxxxxxxxxxxxxxx The project of an "International Association for Promoting the Calculus of Quaternions" originated from Dr. Molenbroeck, of The Hage, in 1895. He was seconded by the Japanese student Shunkichi Kimura, who was then doing research at Yale University. Quaternionists took advantage of the Toronto meeting of the British Association for the Advancement of Science, in 1897, to discuss the prospects of the new association. An "International Association for Promoting the Study of Quaternions and Allied Systems of Mathematics" was created in 1899. The new name reflected the member's desire to include Grassmann's Ausdehnugnslehere in their field of interest. The first president elected was Tait, but he declined on grounds of health. On the initiative of Professor Georges Francis FitzGerald, Prof. Sir Robert Stawell Ball, FRS, was elected its first president for the period 1899-1900. Molenbroek was elected Treasurer and Alexander Macfarlane, Secretary. In the meantime, Kimura was asked to return to Japan. As Molenbroek's health deteriorated, Macfarlane took over as Secretary-Treasurer. He soon became the main force behind the new association. Macfarlane was born in Scotland in 1851 and studied at Edinburgh; later he moved to the United States, as a university mathematics teacher, and by 1894 to Canada to take care of family business there. He was elected a fellow of the Royal Society of Edinburgh, and received an LL. D. The association attracted some well known names in the field, such as Laisant, Hathaway, Joly, Stockes, Tait, Peano, and also Hamilton's son. The initial membership of the association included some sixty mathematicians; it never reached much higher numbers. North America led the pack with twenty two members, eighteen of them in the United States. Great Britain followed with seventeen members, eight of which were in Ireland. >From a financial point of view, it relied on large donations (up to $ 50) from amateurs and smaller ones by mathematicians (Prof. Peirce, of Harvard, gave $ 5). The main contributing countries were the United States, with nearly $ 100, and Great Britain, with some $ 70. The society published and Annual Report from March 1900, and wished to publish its own journal; this is an objective that, as such, never materialized. It tried to acquire an international standing inviting persons interest on quaternions from several countries to join in the society and act as national representatives. In turn, these representatives were asked to attract more members in every country that had shown an interest in the subject. Besides the mathematically leading European countries of the time, and the emerging United States, such interest existed also in the periphery. In Argentina, for example, a treatise on quaternions had already been published, and quaternions was one of the topics in university courses on advanced mathematics. There was also an interest in, at least, Russia, Japan, Portugal, Spain, Tasmania, and Canada. In these countries, interest on quaternions is usually related to some scientific contacts with Great Britain. Around 1905, under the presidency of Joly, efforts were made to enter "on a new stage" and give the association a new and more vigorous life. It was clear to the association's leaders that even with the addition of Grassmann's ideas, the range of subjects it covered was rather limited to make it really attractive. For Joly the main aim of the association was defined to be to "further in every way possible the study of the calculus of vectors and related quantities." He indicated that the new Encyklopaedie der Mathematischen Wissenschaften was a further proof that vector methods were fully accepted as a part of mathematics. Joly suggested the association should create an international network of communication between those interested on vectors, quaternions and other similar topics. However, with a substantial part of their membership scattered over a very extensive geographical area, it was clear to him that the association may disintegrate unless a stronger bond, such as a journal, was created. The Annual Reports tried to fill that gap. When Joly became president, publication of Annual Reports was moved to Dublin. Macfarlane started compiling a Bibliography of Quaternions and Allied Systems of Mathematics, (the document you referred to) which was finished by the end of 1903 and published by the Dublin University Press, with the report of 1904. He added to his bibliography papers in which vector ideas were used. Macfarlane 86 pages bibliography, with some one thousand references, is still an important source on the literature on quaternions. Besides papers, it includes some important reviews on them. Macfarlane also attempted to go back in time in his bibliography, even before the times when Hamilton's quaternions were first presented. For example, he quoted Olinde Rodrigues's paper of 1840. [A meeting on Olinde Rodrigues and the history of quaternions, including the Association, will be held at Imperial College, London, next December to commemorate 150 years of his death.] The association also compiled information on the position of quaternions in university curricula through the world. Macfarlane coordinated this effort. By 1905, following the publication of Macfarlane's bibliography, the association's annual reports began to play the role of a journal. Updates of bibliography, and later abstracts and reviews of technical papers, began to appear in their pages. The range of topics covered by the association was increased further, including Matrices, Linear Substitutions, Quadratic forms, Complex numbers, Equipollences, Vector Analysis, Commutative algebras, Quaternions, Biquaternions, Linear associative algebras, General algebra and operations, as separate topics, in the annual updates to the Bibliography Some changes were introduced in 1905 to make the administration more agile; membership agreed to the proposal of extending periods in office to three, instead of two years. Also in 1905 a new national secretary was added, it cover South America; it was in charge of the Argentine mathematician Claro Cornelio Dasseen, a former student of Balb/in, the author of the Argentine quaternion's book mentioned before. The death of Macfarlane in 1913 was also the beginning of the final decline of the Association's difficult life. The outbreak of the First World War also dealt a heavy blow to the idea of internationalism in science.