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A TREATISE

ON

HYDROSTATICS AND HYDRODYNAMICS.

BY

W. H. BESANT, M.A.

FELLOW AND ASSISTANT TUTOR OF ST JOHN'S COLLEGE, CAMBRIDGE.

CAMBRIDGE:

DEIGHTON, BELL, AND CO.

LONDON: BELL AND DALDY.

1859.

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PREFACE.

In compiling the present treatise, I have endeavoured to place before the reader the course of study, in theoretical Hydrostatics and Hydrodynamics, which is usually required in the Examination for the Mathematical Tripos.

For the main portions of the subject, I have consulted chiefly Poisson's Mécanique and Duhamel's Cours de Mécanique, but I have occasionally found it necessary to refer to the larger and more important works of Laplace and Lagrange, the Mécanique Céleste and the Mécanique Analytique. The problem discussed in Chapter VII., for instance, is given with greater clearness and fulness by Laplace, than by any subsequent writer whose works I have been able to consult.

By the kindness of Professor Stokės I have been permitted to make some extracts, on a difficult part of the subject, from a very valuable paper by him in the Cambridge Philosophical Transactions.

The Examples by which the various Chapters are illustrated, and which it is hoped will form a sufficient and useful set of exercises for the student, have been chosen almost entirely from the Senate-House papers of the last few years, and from the Examination papers of St John's College and Caius College.

The investigations, relating to the vibrations of rods and strings, which have been introduced in Chapter XIII., can hardly be said to belong to the province of Hydrodynamics; they are however so closely connected with the theory of sound, and especially of musical sounds, that a chapter on the subject is not complete without them, and I have therefore ventured to devote a few articles to their discussion.

I have to offer my best thanks to several friends who have kindly assisted me by their advice, and in particular to Mr G. D. Liveing, of St John's College, and also to the Rev. J. R. Lunn, of St John's College, to whom I am indebted for important hints and corrections in the chapter on musical sounds.

W. H. BESANT.

ST JOHN'S COLLEGE,

June 7, 1859.

CONTENTS.

any given forces.

CHAPTER IV.

48-52. The equilibrium of a floating body.

53-58. On stable and unstable equilibrium.

59—60. Finite displacements.

61–64. Floating vessels containing fluid.

65–66. The oscillations of floating bodies.

CHAPTER V.

67–71. Pressure of the atmosphere. Marriotte's

72–77. Mixture of gases. The formation of dew.

78–81. The earth's atmosphere. The siphon.

82–87. Determination of weights by the barometer. Examples.

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