IX.
QUATERNIONS AND THE ALGEBRA OF VECTORS.
[Nature, vol xlvii. pp. 463, 464, Mar. 16, 1893.]
In a recent number of Nature [voL xlvii, p. 151], Mr. McAulay puts certain questions to Mr. Heaviside and to me, relating to a subject of such importance as to justify an answer somewhat at length. I cannot of course speak for Mr. Heaviside, although I suppose that his views are not very different from mine on the most essential points, but even if he shall have already replied before this letter can appear, I shall be glad to add whatever of force may belong to independent testimony.
Mr. McAulay asks: "What is the first duty of the physical vector analyst quâ physical vector analyst?" The answer is not doubtful. It is to present the subject in such a form as to be most easily acquired, and most useful when acquired.
In regard to the slow progress of such methods towards recognition and use by physicists and others, which Mr. McAulay deplores, it does not seem possible to impute it to any want of uniformity of notation. I doubt whether there is any modern branch of mathematics which has been presented for so long a time with a greater uniformity of notation than quaternions.
What, then, is the cause of the fact which Mr. McAulay and all of us deplore? It is not far to seek. We need only a glance at the volumes in which Hamilton set forth his method. No wonder that physicists and others failed to perceive the possibilities of simplicity, perspicuity, and brevity which were contained in a system presented to them in ponderous volumes of 800 pages. Perhaps Hamilton may have intended these volumes as a sort of thesaurus, and we should look to his shorter papers for a compact account of his method. But if we turn to his earlier papers on Quaternions in the Philosophical Magazine, in which principally he introduced the subject to the notice of his contemporaries, we find them entitled "On Quaternions; or on a New System of Imaginaries in Algebra," and in them we find a great deal about imaginaries, and very little of a vector analysis. To show how slowly the system of vector analysis developed itself in the quaternionic nidus, we need only say that the symbols and do not appear until two or three years after the discovery of quaternions. In short, it seems to have been
