A TREATISE ON THE DIFFERENTIAL AND INTEGRAL CALCULUS AND THE CALCULUS OF VARIATIONS. BY THOMAS G. HALL, M.A. PROFESSOR OF MATHEMATICS IN KING'S COLLEGE, LONDON; PREBENDARY OF ST. PAUL'S; AND LATE FELLOW AND TUTOR OF MAGDALENE COLLEGE, CAMBRIDGE. THE SIXTH EDITION. LONDON: LONGMAN, GREEN, LONGMAN, ROBERTS, & GREEN. PREFACE. A KNOWLEDGE of this branch of the Pure Mathematics is absolutely necessary, before anyone can successfully undertake the perusal of works on Natural Philosophy, in which the effects of the observed laws that govern the material world are reduced to calculation. For Students deficient in this knowledge, yet anxious to obtain as much as may enable them to master the chief analytical difficulties incident to the study of Elementary Treatises on the Mixed Mathematics, this book has been written: and with the hope that by its means, a subject of high interest may be rendered accessible to an increased number of readers. The Table of Contents which accompanies the work will sufficiently exhibit its plan, as well as the subjects treated of in it: And if it be considered necessary to offer an inducement to any one to enter upon the study of a |