A treatise on attractions, Laplace's functions, and the figure of the earth1860 |
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Page xi
... a slender pyramid on a particle at its vertex ; also of a frustum . • 51. Attraction of an extensive plain of given depth or thickness on a point above it . • 43 · ib . 44 · 45 ART . 55. Attraction of a rectangular mass on a CONTENTS . xi.
... a slender pyramid on a particle at its vertex ; also of a frustum . • 51. Attraction of an extensive plain of given depth or thickness on a point above it . • 43 · ib . 44 · 45 ART . 55. Attraction of a rectangular mass on a CONTENTS . xi.
Page 45
... depth varies ; and let k be the linear depth of the transverse section of the base ; then aẞlk is the area of the base ; and the attraction of the whole pyramid on the vertex = pßk . Hence , all pyramids having the same angular width ...
... depth varies ; and let k be the linear depth of the transverse section of the base ; then aẞlk is the area of the base ; and the attraction of the whole pyramid on the vertex = pßk . Hence , all pyramids having the same angular width ...
Page 46
... depth of matter constituting the plain . PROP . To find the attraction of a rectangular mass , of small elevation compared with its length and breadth , upon a point lying in the plane of one of its larger sides . 55. Let the attracted ...
... depth of matter constituting the plain . PROP . To find the attraction of a rectangular mass , of small elevation compared with its length and breadth , upon a point lying in the plane of one of its larger sides . 55. Let the attracted ...
Page 48
... depth is not so great that its square may not be neglected in comparison with the square of the distance from the attracted point . In this case is the sum of the height and depth , above and below the plane of xy . - 56. Ex . 1. The co ...
... depth is not so great that its square may not be neglected in comparison with the square of the distance from the attracted point . In this case is the sum of the height and depth , above and below the plane of xy . - 56. Ex . 1. The co ...
Page 51
... 3 275 h 12 4π 566 9 = 0.000005523h sin + 8.g , a being expressed in parts of a mile . Since 0.000005523 = tan ( 1 ′′ . 1392 ) 4-2 LAW OF DISSECTION OF THE MASS . 51 Attraction of an extensive plain of given depth or thickness.
... 3 275 h 12 4π 566 9 = 0.000005523h sin + 8.g , a being expressed in parts of a mile . Since 0.000005523 = tan ( 1 ′′ . 1392 ) 4-2 LAW OF DISSECTION OF THE MASS . 51 Attraction of an extensive plain of given depth or thickness.
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Common terms and phrases
amount amplitudes angles assumed attraction axes axis becomes calculated Cambridge cause centre Chapter cloth co-ordinates coefficient coincidence College condition considered constant corrections Crown 8vo crust deduced density determine differential distance Earth effect element ellipticity English equal equation equilibrium error evidence Examples expanding expression Figure fluid force formula give given gravity greater Hence hypothesis increase integration interior Laplace's Functions late latitude length mass matter mean measured meridian miles nearly spherical observed obtained Ocean original particle passing Precession present pressure principal PROP putting quantities radius ratio regarding result Second Edition shell shown solid spheroid square station strata Substituting Suppose surface term thickness varies whole µ³
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