McAulay A. Octonions. A development of Clifford's bi-quaternions

Cambridge: University Press, 1898. — 266 p.I have in the treatise itself tried to justify my deviation from Clifford's usage of vector and quaternion (replaced below by lator and axial), bnt I have given no reasons for the serious step of changing the name of the whole subject from Bi-quaternions to Octonions. The following reasons seemed to form sufficient justification. (1) I think it desirable to have a name for what Hamilton has called Bi-quaternions. For these there could scarcely be a better name. (2) I wish to imply that quaternions are not particular kinds of octonions but only very similar to such particular kinds. (3) Octonions like quaternions treat space impartially. By this I mean that they do not depend in any way on an arbitrarily chosen system of axes or arbitrary origin. But one of the two quaternions implied by Clifford's term does so depend on an arbitrary origin. This to me appears an absolute bar to the propriety of his term. If Clifford, in choosing his term, wished to emphasise his indebtedness to the inventor of Quaternions, this is scarcely a reason for one who merely follows Clifford to copy him in this respect, if there are intrinsic objections.
Most of the methods and some of the results which follow are to some extent, I believe, novel. But I fear that many references to the work of others which ought to occur are wanting. The treatise was written at a distance from all mathematical libraries. I believe I should have been able to improve it in many respects if I had been able to consult the many authorities cited by Sir Robert Ball in his Theory of Screws.