Recent Innovations in Vector Theory ¹

OF late years there has arisen a clique of vector analysts who refuse to admit the quaternion to the glorious company of vectors. Their high priest is Prof. Willard Gibbs. His reasons for developing a vector, analysis devoid of the quaternion are given with tolerable fullness in NATURE, vol. xliii. p. 511. His own vector analysis is presented in a pamphlet, “Elements of Vector Analysis, arranged for the Use of Students in Physics, not Published” (1881-84). Mr. Oliver Heaviside, in a series oh papers published recently in the Electrieian and in an elaborate memoir in the Philosophical Transactions, supports some of Gibbs' contentions and cannot say hard enough things about the quaternion as a quantity which no physicist wants. Prof. Macfarlane, of Texas University, has added to the lilerature of the subject, and without altogether agreilng with Gibbs takes umbrage at a most fundamental principle of quaternions and developes a pseudo-quaternionic system of vector algebra which is non-associative in its products!