It is chiefly through the labors of Gibbs and Heaviside that an analysis has been perfected which not only does away with the unnecessary complexity and artificiality of other analyses but offers a strictly natural and therefore as direct and simple a substitute as possible, and, at the same time in no wise is at variance, but runs paralel to them. THIS NEW, yet old method is VECTOR ANALYSIS; it COMBINES within itself most of the advantages of both Quaternions and of Cartesian Analysis. The adoption of Vector Analysis is urged on the grounds of naturalness, simplicity and directness; with it...