It seems to be desirable that your President should take this opportunity of making a few remarks on the inception and prospects of this Association. It is felt that some explanation is due to our Members, as well as to the wider circle of those interested in our subjects into whose hands this report may fall. I shall therefore sketch the history of the movement which led to the foundation of our Association, and shall briefly review the resources at our disposal for the advancement of those objects which have united us. Whether this Association shall be successful or not we cannot predict. It has been said that the range of our subjects is too limited to warrant our success. We should not be despondent on that account, for, in all probability, objections of a kindred nature have been urged against every similar society in its initial stages; yet it is the express purpose of societies such as ours to extend the somewhat limited range of the subjects they were designed to foster, and had the objections been received with the acquiescence their authors desired, few will refuse to admit that the growth of Science would have been stunted. It is now possible for us to look forward to a modest commencement in publication, and we are beginning to feel that many of our preliminary difficulties are being overcome. That these difficulties were quite exceptional will, I think, be allowed by all who read this report. We are now entering on a new stage, and our Association will be put to the test. I am fully convinced that this society is capable of doing good and useful work, and I believe means will not be lacking for its increased usefulness should it prove itself worthy of support.
The "International Association for Promoting the Calculus of Quaternions" was projected in the year 1895 by Dr P Molenbroek of the Hague, and by Mr Shunkichi Kimura of Japan, at that time a Graduate Student of Yale University. Almost immediately the name of the Association was changed, so as to include within its scope all systems allied to Quaternions and to Grassmann's "Ausdehnungslehre," and the name now in use was adopted. A fair number of mathematicians signified their appreciation of the movement by promising to join the society, and for the time Dr Molenbroek acted as Secretary and Treasurer for Europe, and Mr Kimura for America. Mr Kimura issued papers for the first election of Officers, but unfortunately for the immediate success of the Association the election proved a failure. Professor Tait received a majority of votes for the office of President. He declined to act on the ground of failing health, and suggested that a younger man should be appointed. Mr Kimura was elected secretary, but in the meantime he was obliged to return to his native country, where he felt it was impracticable to carry on the work of organization owing to the distance of his abode from the majority of the members, and the long delays involved in postal communication. Dr Molenbroek, the newly elected Treasurer, lost his health, and he became quite unable to transact the laborious duties of organization. Under these circumstances, Molenbroek and Kimura requested Professor Hathaway "to endeavour to bring the society into more active existence." Accordingly, on the occasion of the meeting of the British Association at Toronto in 1897, Professor Hathaway issued a circular suggesting that a meeting should be held for the election of permanent officers, and for the transaction of general business. On the motion of the late Professor FitzGerald - a warm friend of the Association, and a firm believer in its utility - it was resolved that Sir Robert Stawell Ball be requested to act as the first President. At the same time Dr Alexander Macfarlane was elected General Secretary in place of Mr Kimura, who wished to resign for the reasons I have mentioned. Dr Molenbroek remained Treasurer, as it was hoped his health would improve, and that he would soon be able to resume his duties. Unfortunately this hope was not fulfilled, and Dr Macfarlane was ultimately obliged to assume the office of Treasurer. Indeed, it was only last year that Dr Molenbroek was able to make up his accounts, and to forward the sums he had received to the new Treasurer.
The early misfortunes of the society had left their mark. The scheme had hung fire so long that much of the original enthusiasm was lost, and even its most ardent supporters began to question the possibility of carrying out the object of the Association in any useful way. There seemed to be no likelihood of a substantial increase in the number of members; the funds of the Association would not allow of the extensive publications originally contemplated, and the society appeared to languish in fruitless inactivity. Although many of the members recognised the advantages already gained by the publication of the names of workers in the subjects in which they were interested, but few were aware of the quiet labours of our zealous General Secretary, and the numerous difficulties he had to contend with in the slow process of organization. It is to be hoped that most of these preliminary difficulties are now at an end. To render the Association a success, it only remains for every individual member to do his best in furthering its aims. The Association at present consists of sixty or seventy mathematicians scattered over the whole world. We have no domicile, no place of meeting - and herein lies at once our weakness and our strength. A local society may often be made successful by the labours of a few earnest members, but in a society like ours success can only be attained by the co-operation of all. We are weak inasmuch as we necessarily lack the inspiration due to personal intercourse; we are strong because our members represent many different phases of thought modified by the National characteristics of the various countries to which we belong.
The results of our Association up the present are not to be despised. Those interested in the study of our subjects have been made known to one another; we have been enabled to interchange our papers in a really useful way. But this does not justify the continuation of our Association. It is necessary that we should undertake some publication, however unpretentious, and unite in our endeavours to extend the general interest in those branches of mathematics which it is the object of our Association to promote. Recently the General Secretary issued a circular asking each member to assist him in the preparation of a Bibliography. This project has my heartiest approval, as the Bibliography will not only be extremely useful, but its preparation will be the means of uniting us in one common labour. Every one of us can do something towards making the Bibliography more complete. It is intended that this work shall form the first publication of the Association.
I have also thought it desirable that we should draw up a report on the position of Quaternions and Allied Branches of Mathematics in the curricula of the various Universities and Colleges throughout the world. The members of our Association are so widely distributed that it should be possible to render this report full and valuable. There is scarcely any greater incentive to work than the discovery that others are doing more than we are. If we find that the institutions with which we are specially connected are lagging behind others in the facilities provided for the study of our subjects, our influence towards effecting an improvement is increased, as well as our desire to do more than we have done in the past. I hope therefore that every member will assist in this work by furnishing me or the General Secretary with full particulars of the instruction and encouragement given to students in these important branches of mathematics. We intend to publish the results of this inquiry at an early date.
Since the publication of our last Report, our Association has lost by death two of the most distinguished of its members, George Francis FitzGerald and Thomas Preston. Though neither had written specially on our subjects, both fully recognised their importance and their great educational value, and both were staunch friends of our Association. I need not here speak of the loss science has sustained; I must however express my conviction that the loss to our Association has been very serious, and those who had the good fortune to have been personally acquainted with either of my friends will pardon me for stating that the loss to myself is simply irreparable.
CHARLES J JOLY.