Since the printing of a short pamphlet on the Elements of Vector Analysis in the years 1881-84, never published, but somewhat widely circulated among those who were known to be interested in the subject, the desire has been expressed in more than one quarter, that the substance of that trea tise, perhaps in fuller form, should be made accessible to the public. As, however, the years passed without my finding the leisure to meet this want, which seemed a real one, I was very glad to have one of the hearers of my course on Vector Analysis in the year 1899 — 1900 undertake the preparation of a text-book on the subject. I have not desired that Dr. Wilson should aim simply at the reproduction of my lectures, but rather that he should use his own judgment in all respects for the production of a text-book in which the subject should be so illustrated by an adequate number of examples as to meet the wants of stu dents oi geometry and physics.