A treatise on attractions, Laplace's functions, and the figure of the earth1860 |
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Page xvi
... Formula for correcting the observed latitudes to make them suit the general curve 115. Examples , taken from the Indian Arc • PAGE 113 • 115 116 116. The application of the Principle of Least Squares to find the general figure of the ...
... Formula for correcting the observed latitudes to make them suit the general curve 115. Examples , taken from the Indian Arc • PAGE 113 • 115 116 116. The application of the Principle of Least Squares to find the general figure of the ...
Page 14
... formula for the calculation of the attraction of a heterogeneous mass upon any particle . 18. Let p be the density of the body at the point ( xyz ) ; fgh the co - ordinates of the attracted particle ; and , as before , suppose that A ...
... formula for the calculation of the attraction of a heterogeneous mass upon any particle . 18. Let p be the density of the body at the point ( xyz ) ; fgh the co - ordinates of the attracted particle ; and , as before , suppose that A ...
Page 31
... formula A1 = == - ( i - n - 28 + 2 ) ( i − n −2s + 1 ) 2s 28 ( 2i - 28 + 1 ) A. - 1 . 2 By making s successively equal 1 , 2 , 3 ... we have 4,4 , ... in terms of A. Let these be substituted , and we have the coefficient of cos n ( w ...
... formula A1 = == - ( i - n - 28 + 2 ) ( i − n −2s + 1 ) 2s 28 ( 2i - 28 + 1 ) A. - 1 . 2 By making s successively equal 1 , 2 , 3 ... we have 4,4 , ... in terms of A. Let these be substituted , and we have the coefficient of cos n ( w ...
Page 31
... formula A1 = == - ( i − n − 2s + 2 ) ( i − n − 2s + 1 ) - 28 ( 2i - 28 + 1 ) - A. - 1 . 2 to By making s successively equal 1 , 2 , 3 ... we have 4,4 , ... in terms of A. Let these be substituted , and we have the coefficient of cos ...
... formula A1 = == - ( i − n − 2s + 2 ) ( i − n − 2s + 1 ) - 28 ( 2i - 28 + 1 ) - A. - 1 . 2 to By making s successively equal 1 , 2 , 3 ... we have 4,4 , ... in terms of A. Let these be substituted , and we have the coefficient of cos ...
Page 33
... formula 1 2π 2i + 1 F1 = 2 + 1 [ ' [ * F ( μ ' , ' ) P.dμ'do ' , proved in Art . 32 . 4π 0 Ex . 1. Arrange a + bu2 in terms of Laplace's Functions . Here Fu ' , w ' ) = a + bμ'2 . First put i = 0 , P = 1 ; 1 2π 1 : . F. = S " ( a + bμ ...
... formula 1 2π 2i + 1 F1 = 2 + 1 [ ' [ * F ( μ ' , ' ) P.dμ'do ' , proved in Art . 32 . 4π 0 Ex . 1. Arrange a + bu2 in terms of Laplace's Functions . Here Fu ' , w ' ) = a + bμ'2 . First put i = 0 , P = 1 ; 1 2π 1 : . F. = S " ( a + bμ ...
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Common terms and phrases
amplitudes angles angular velocity attraction axes axis of revolution calculated Cambridge Cape Comorin cause centre centrifugal force CHARLES KINGSLEY Clairaut's Theorem cloth co-ordinates coefficient coincidence CONIC SECTIONS const cos² Crown 8vo crust Damargida deduced distance Ea² Earth Earth's mass ellipticity equi error Fcap fluid mass formula geodetic Hence hypothesis integration Kaliana Laplace's Equation Laplace's Functions last Article latitude law of density librium M.A. Second Edition mean ellipticity measured Mechanical Philosophy meridian miles nearly spherical Ocean original fluidity particle pendulum plumb-line point xyz Precession pressure PROP quantities ratio result series of Laplace's shell sin² spheroid station strata stratum Substituting Suppose surfaces of equal term thickness ticity Treatise Trinity College vanish W₁ w²a Y₁ zero μ² µ³
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