CONTENTS.

XXV

CHAPTER III.

FORM OF EQUILIBRIUM OF THE OCEAN UNDER THE MOOu’s ATTRACTION,AND THE FORM OF THE ATMOSPHERE.

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557, 558. The form of the Ocean a prolate spheroid of small ellipticity;

if we neglect the Earth 's motion and ellipticity: remarks. 567

559. Form of the atmosphere: only one form of equilibrium. Zodiacal Light

does not arise from the Sun's atmosphere. 570

HYDRODYNAMICS.

CHAPTER I.

EQUATIONS OF MOTION.

561. The transmission of pressure through a fluid in motion. 573

562—565. Equations of motion: fluid incompressible : fluid compressible 574566—568. The pressure at any point of a homogeneous incompressiblefluid mass in motion when udx + vdy + wdz is a perfect differen-tial : if this be a perfect differential at any instant it is at every

instant of the motion. 578

569, 570. Equations for calculating the motion of an elastic fluid, the

excursions of the molecules being very small, and no forces acting 579

CHAPTER II,

TIDES AND STABILITY OF THE OCEAN.

572. The difficulty of the subject of the Tides requires some hypothesisto be made in addition to that of gravitation. Laplace's and

Daniel Bernoulli ’s Theories. 581

573—576. Calculation of the height of the tide on Bernoulli ’s hypothesis.

Time of high tide at a given place. Establishment of the port.Comparison with observations. Tide at a port where the tidal

wave arrives by two distinct routs: Interference of tides. 583

577, 578. Transformation of the equations to polar co-ordinates. 589

579, 580. Stability of the Ocean. 595 •

CHAPTER III.

MOTION OF THE HEAVENLY BODIES IN A RESISTING MEDIUM.

581. Law of resistance .. 597