A Treatise on Attractions, Laplace's Functions, and the Figure of the Earth

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Macmillan, 1871 - Earth - 245 pages
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Page 201 - ... de niveau of the fluid should remain the same. At the time that the crust first became sufficiently thick to resist fracture under the strain produced by a change in its density — that is, when it first ceased to depend for the elevation or depression of its several parts upon the principles of floatation, the total amount of matter in any vertical prism, drawn down into the fluid below to a given distance from the earth's centre, had been the same through all the previous changes. After this,...
Page 1 - Newton generalized the law of attraction into a statement that every particle of matter in the universe attracts every other particle with a force which varies directly as the product of their masses and inversely as the square of the distance between them; and he thence deduced the law of attraction for spherical shells of constant density.
Page 235 - There must, .therefore, be some excess of matter in the solid parts of the earth between the Pacific Ocean and the earth's centre which retains the water in its place. This effect may be produced in an infinite variety of ways ; and therefore, without data, it is useless to speculate regarding the arrangement of matter which actually exists in the solid parts below.
Page 202 - This theory, that the wide ocean has been collected on parts of the earth's surface where hollows have been made by the contraction and therefore increased density of the crust below, is well illustrated by the existence of a whole hemisphere of water, of which New Zealand is the pole, in stable equilibrium. Were the crust beneath only of the same density as that beneath the surrounding continents, the water would be drawn off by attraction and not allowed to stand in the undisturbed position it...
Page 206 - In fact the testimony of these coast-stations is rather in favour of the theory, as they seem to indicate, by excess of attraction towards the sea, that the contraction of the crust beneath the ocean has gone on increasing in some instances still further since the crust became too thick to be influenced by the principles of floatation, and that an additional flow of water into the increasing hollow has increased the amount of attraction upon stations on its shores.
Page 201 - If solidification from a fluid state commenced at the surface, the amount of radial contraction in the solid parts beneath the surface of the mountain-region has been less than in the parts beneath the sea-bed. In fact it is this unequal contraction which appears to have caused the hollows in the external surface, which have become the basins into which the waters have flowed to form the Ocean.
Page 206 - ... suggested by the facts brought to light in India, viz. that mountain-regions and oceans on a large scale have been produced by the contraction of the materials, as the surface of the earth has passed from a fluid state to a condition of solidity — the amount of contraction beneath the mountain-region having been less than that beneath the ordinary surface, and still less than that beneath the ocean-bed, by which process the hollows have been produced into which the ocean has flowed. In fact...
Page 140 - ... perfectly rigid. It seems, therefore, nearly certain, " with no other evidence than is afforded by the tides, that the tidal " effective rigidity of the earth must be greater than that of glass.
Page 6 - It will be convenient to commence with the demonstration of a few known theorems relating to attractions, the law of attraction being that of the inverse square of the distance.* Preliminary Propositions respecting Attraction*. PROP. i. To express the components of the attraction of any mass in three rectangular directions by means of a single function. Let m...

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