On the Form and Position of the Sea Level: With Special References to Its Dependence on Superficial Masses Symmetrically Disposed about a Normal to the Earth's Surface

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U.S. Government Printing Office, 1888 - Sea level - 88 pages
 

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Page 162 - ... of the solid. As an assumption leading to a simple calculation, let us suppose the solid earth to rise out of the water in a vast number of small flat-topped islands, each bounded by a perpendicular cliff, and let the proportion of water area to the whole be equal in all quarters.
Page 162 - Croll's directions, it is easily found that the change of sea level which this will produce will consist in a sinking in the first hemisphere and rising in the second, through heights varying according to the same law (that is, simple proportionality to sines of latitudes), and amounting at each pole to 1...
Page 162 - ... itself, expresses the essence of Laplace's celebrated demonstration of the stability of the ocean, and suggests the proper elementary solution of the problem to find the true alteration of sea-level produced by a given alteration of the solid. As an assumption leading to a simple calculation, let us suppose the solid earth to rise out of the water in a vast number of small...
Page 89 - On the form and position of the sea level, with special reference to its dependence on superficial masses symmetrically disposed about a normal to the earth's surface.
Page 162 - ... where t denotes the thickness of the ice-crust at the pole ; i the ratio of the density of ice, and w that of sea-water, to the earth's mean density ; and a> the ratio of the area of ocean to the whole surface. Thus, for instance, if we suppose...
Page 112 - ... neglected. The grounds of this assumption need to be examined with some care. For this purpose we shall derive the exact expressions, in form at least, for the potential of the disturbing mass at its center, at its border, and at 180° from its center. A comparison of these exact values with the approximate values given by (27), (29), and (31) will show the order of approximation of (20) and (21).
Page 105 - V=C>, a constant, (5) The difference of this and (4) to terms of the first order inclusive in v is whence, putting v=(V~V0fĢ.
Page 104 - The solution of the general problem outlined in the preceding section depends on the principle of hydrostatics that the potential of the forces producing a liquid surface in equilibrium has a constant value for all points of that surface. In the case of the earth, if the potential of all the attractive forces acting on a unit mass at any point of the sea surface be denoted by P, the distance of the point from the earth's axis of rotation by I, and the velocity of rotation by...
Page 107 - F of the attracting mass for any point of the disturbed surface, whether without or within the circle which we have assumed to define the boundary of the mass. Although the nature of the mass may be such as to prevent the water from permeating it freely, the surface the water would take if not so restricted is an essential part of the disturbed surface.
Page 162 - ... proportion to the [sine of the] latitude. Let this ice be removed from the first hemisphere and similarly distributed over the islands of the second. By working out according to Mr Croll's directions, it is easily found that the change of...

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