To those Interested in Quaternions and Allied Systems of Mathematics.
The mathematical ideas associated with the direct treatment of vectors and vector functions are daily becoming more familiar to the scientific mind. Half a century ago the broad principles of vector theory were laid down in the Quaternions of Hamilton and the Ausdehnungslehre of Grassmann. In his second monumental work Hamilton developed a vector calculus of great power and flexibility, peculiarly appropriate to geometry and physics; while both systems, in their richness of transformations, generality of treatment, simplicity of expression and interpretation, surpass any other known forms of mathematics. Nevertheless, these systems have not received the attention that is surely their due, and remain still in a comparatively undeveloped state.
Meanwhile, in connection chiefly with the remarkable advance in electrical theory, the growing necessity for a vector calculus, or at least for a compact vector notation, has induced more recent investigators to invent new systems, which have very much in common with those already established by Hamilton and Grassmann.
The time, therefore, seems to be ripe for a combination of forces, so that workers in these important lines may become known to one another, and the enthusiasm of students excited and sustained.
Led by these considerations we venture to suggest the organization of what we provisionally call The International Association for promoting the Study of Quaternions and allied systems of Mathematics. By such an organization vector analysis would receive a great impetus. A journal published from time to time would keep the members of the Association in touch with the various aspects of the subject, both pure and applied, and would facilitate interchange of opinions on the introduction and adoption of new notations.
In these few lines we have tried to point out the important task of the Association, but shall be obliged for any suggestion or improvement. It is almost needless to say that we are only preparing the way; and once the Association has been started we shall be ready to place it in the hands of persons much more competent than ourselves to further its best interests. We earnestly hope that all friends will appreciate our endeavours and show us at once some token of approval.
We remain, Dear Sirs,
Very respectfully yours,
P Molenbroek, the Hague, Holland.
S Kimura, Yale University, U.S.A.