A Treatise on Attractions, Laplace's Functions and the Figure of the EarthMacmillan, 1865 - 162 páginas |
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Página vii
... COEFFICIENTS AND FUNCTIONS . 18. Formulæ for the attraction of a homogeneous mass d2V d2V d2 V 21. Proof that + df2 + dg2 + dh • = 0 , or 4πp ' , according as the - attracted particle is not or is part of the attracting mass , V being ...
... COEFFICIENTS AND FUNCTIONS . 18. Formulæ for the attraction of a homogeneous mass d2V d2V d2 V 21. Proof that + df2 + dg2 + dh • = 0 , or 4πp ' , according as the - attracted particle is not or is part of the attracting mass , V being ...
Página viii
... Coefficients , Equation , and Functions defined 27 . PAGE · • 17 ib . 19 21 ib . The definite integral of the product of ... coefficient of the ¿ th order 39. Examples of arrangement in Laplace's Functions 22 30 31 • 33 38 CHAPTER III ...
... Coefficients , Equation , and Functions defined 27 . PAGE · • 17 ib . 19 21 ib . The definite integral of the product of ... coefficient of the ¿ th order 39. Examples of arrangement in Laplace's Functions 22 30 31 • 33 38 CHAPTER III ...
Página 13
... ( 3 ) , on an internal point ( fgh ) , f , g and h being given by equations ( 2 ) . And then the attractions required will be those multiplied by ab bc ac By ' ar " αβι respectively . " CHAPTER II . LAPLACE'S COEFFICIENTS AND FUNCTIONS . 17.
... ( 3 ) , on an internal point ( fgh ) , f , g and h being given by equations ( 2 ) . And then the attractions required will be those multiplied by ab bc ac By ' ar " αβι respectively . " CHAPTER II . LAPLACE'S COEFFICIENTS AND FUNCTIONS . 17.
Página 14
... COEFFICIENTS AND FUNCTIONS . To do this it will be neces- sary to anticipate the subject of the following Chapter , and to bring in here a Proposition which should properly stand at the head of that division of this treatise . PROP . To ...
... COEFFICIENTS AND FUNCTIONS . To do this it will be neces- sary to anticipate the subject of the following Chapter , and to bring in here a Proposition which should properly stand at the head of that division of this treatise . PROP . To ...
Página 18
... coefficient of dr d2R the coefficient of = de the coefficient of dr2 dr2 dr2 == + df2 + dg2 + dh2 = 1 , do 2 do2 do2 1 + + + = df2 + dg3 dh2 = gs d2R do dw2 dw2 d Ꭱ = + + 1 dw * = df * dg2 * dh2 — r2sin20 ' the coefficient of d'R dr de ...
... coefficient of dr d2R the coefficient of = de the coefficient of dr2 dr2 dr2 == + df2 + dg2 + dh2 = 1 , do 2 do2 do2 1 + + + = df2 + dg3 dh2 = gs d2R do dw2 dw2 d Ꭱ = + + 1 dw * = df * dg2 * dh2 — r2sin20 ' the coefficient of d'R dr de ...
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Términos y frases comunes
amplitude angle attracted particle axes axis calculation Cape Comorin centre Clairaut's Theorem co-ordinates coefficient compartments cos 2m cos² crust Damargida deduced deflection difference distance earth earth's mass effect ellipticity equal equation equilibrium expansion find the attraction fluid mass fluid theory formula geodesy gravity height Hence Himmalayas hypothesis Indian Arc integration Kaliana Kalianpur Laplace's Equation Laplace's Functions last Article latitude law of attraction length longitude mean arc mean ellipse mean figure measured Mechanical Philosophy meniscus meridian miles nearly spherical ocean Ordnance Survey pendulum experiments plumb-line pole precession prism PROP quantities radius result rigid sea-level semi-axes series of Laplace's shell sin² solid sphere spheroid square station strata suppose T₂ thickness tion δα µ² µ³
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