Genesis
Professor Gibbs produced an 85-page outline of his treatment of vectors for use by his students and had sent a copy to Oliver Heaviside in 1888. In 1892 Heaviside, who was formulating his own vectorial system in the Transactions of the Royal Society, praised Gibbs' "little book", saying it "deserves to be well known". However, he also noted that it was "much too condensed for a first introduction to the subject".
On the occasion of the bicentennial of Yale University, a series of publications were to be issued to showcase Yale's role in the advancement of knowledge. Gibbs was authoring Elementary Principles in Statistical Mechanics for that series. Mindful of the demand for innovative university textbooks, the editor of the series, Professor Morris, wished to include also a volume dedicated to Gibbs's lectures on vectors, but Gibbs's time and attention were entirely absorbed by the Statistical Mechanics.
E. B. Wilson was then a new graduate student in mathematics. He had learned about quaternions from James Mills Peirce at Harvard, but Dean A. W. Phillips persuaded him to take Gibbs's course on vectors, which treated similar problems from a rather different perspective. After Wilson had completed the course, Morris approached him about the project of producing a textbook. Wilson wrote the book by expanding his own class notes, providing exercises, and consulting with others (including his father).
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