*To Friends and Fellow Workers in Quaternions*in

*Nature*

**52**(1895), 545-546. We present below a version of their notice encouraging mathematicians to form a Quaternion Association:

**To Friends and Fellow Workers in Quaternions.**

Since the publication of Hamilton's *Elements of Quaternions*, in which the great mathematician developed his new calculus with admirable skill and clearness, more than thirty years have passed away, without it finding the adequate recognition which it so highly deserves. The circumstances is still the more deplorable as the calculus has since been further developed by Professor Tait and others.

There is, in truth, no question as to the importance of the use of vectorial quantities in physics, but on account of their apparently preponderating importance, various physicists have been led to invent new forms of vector-theory excluding the idea of quaternions. But, as far as we can see, they are founded on definitions which are established by quaternions, and are systems of notation rather than logical developments of a mathematical idea.

On the other hand, many who are prejudiced against the calculus of quaternions maintain the opinion that it is hard to understand, and that it contains a great deal which is useless in addition to things immediately applicable. To the latter charge there need be no answer, since all forms of mathematics are exactly alike in this respect, and since in the very combination of the pure and the applied lies the potentiality of further development. In regard to the former objection, quaternionists need only say that if the objectors approach the calculus of quaternions with proper care and meekness, they will ere long assuredly rejoice at having at their disposal an instrument of research mightier far than they had the slightest notion of so long as they were in the domain of cartesian coordinates. Certainly it would be a blessing to science if they could accept these assertions, and their endeavours would find a sure reward in its advancement wherever this method might be applied. So much for these objections.

New notations in the calculus of quaternions must need be invented from time to time. But since they are becoming complex (though far simpler than in cartesian coordinates) as the problems are getting more complicated, it is highly desirable already at this stage of development, to exchange opinions on the selection or adoption of new symbols.

By these and other considerations we have been led to believe that the time has come for those who are interested in vector analysis to come to the fore and join hands. In order to further this purpose, we venture to suggest the establishing of something like an *International Association for Promoting the Calculus of Quaternions*. The following would be among its principal objects:-

(2) That the members should be afforded the means of exchanging opinions on the introduction and adoption of new notations.

We earnestly hope that all friends will appreciate our endeavours and show us at once some token of approval. We would ask those who are in Europe to communicate with the first of the names below, and those in America with the second.

P Molenbroek, the Hague, Holland.

S Kimura, Yale University, U.S.A.

7 August 1895.

P.S. It has been suggested by friends interested in this matter to enlarge the scope of the proposed Association so as to include all systems allied to quaternions and to Grassmann's *Ausdehnulgslehre*. This suggestion we are in full sympathy with. The name of the Association might then be *The International Association for Promoting the Study of Quaternions and Allied Systems of Mathematics*.

P.M.

S.K.

17 September 1895