WHEN I undertook to adapt the lectures of Professor Gibbson VECTOR ANALYSIS for publication in the Yale Bicentennial Series, Professor Gibbs himself was already so fullyengaged upon his work to appear in the same series, Elementary Principles in Statistical Mechanics, that it was understood no material assistance in the composition of this book could be expected from him. For this reason he wished me to feel entirely free to use my own discretion alike in the selection of the topics to be treated and in the mode of treatment. It has been my endeavor to use the freedom thus granted only in so far as was necessary for presenting his method in text-book form......