Vector Analysis: an Introduction to Vector-methods and their Various Applications to Physics and Mathematics

Abstract

THIS “Introduction to Vector-methods and their Various Applications to Physics and Mathematics” is an exposition of the late Willard Gibbs' vector analysis. The author in his preface warns us that “no attempt at mathematical rigor is made” which perhaps explains the opening sentence of chapter i.: “A vector is any quantity having direction as well as magnitude.” What of finite rotations? Are they not to be considered quantities having direction and magnitude? In an appendix the author compares notations, not always quite accurately. He believes Willard Gibbs' notation to be the simplest and most symmetrical of any of the existing kinds. Burali-Forti and Marcolongo, who believe they have devised the perfect notation, object to Willard Gibbs's “dot” in the scalar product, using a “cross” instead. As regards the question of symmetry, the truth is that the vector product is not symmetrical, for in Gibbs's notation a × b=-b x a. As a matter of fact each vector analyst can always find sufficiently self-pleasing arguments in favour of his pet notation.

Vector Analysis: an Introduction to Vector-methods and their Various Applications to Physics and Mathematics.

By Dr. J. G. Coffin. Pp. xix + 248. (New York: John Wiley and Sons; London: Chapman and Hall, Ltd., 1909.) Price 10s. 6d. net.