A Treatise on Attractions, Laplace's Functions and the Figure of the EarthMacmillan, 1865 - 162 páginas |
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Página 10
... ellipsoid of revolution ) determinable by the last Proposition . PROP . To enunciate and prove Ivory's Theorem . x2 16. Let ++ = 1 , and + -1 , and x2 a2 ++ = 1 , SPHEROID ON EXTERNAL POINT . IVORY'S THEOREM . 11 be 10 ATTRACTIONS .
... ellipsoid of revolution ) determinable by the last Proposition . PROP . To enunciate and prove Ivory's Theorem . x2 16. Let ++ = 1 , and + -1 , and x2 a2 ++ = 1 , SPHEROID ON EXTERNAL POINT . IVORY'S THEOREM . 11 be 10 ATTRACTIONS .
Página 13
... proved for the attractions parallel to the other axes : and consequently the Theorem , as enunciated , is true . We may observe that one of these ellipsoids must neces- sarily be wholly within the other . For if not , the points in ...
... proved for the attractions parallel to the other axes : and consequently the Theorem , as enunciated , is true . We may observe that one of these ellipsoids must neces- sarily be wholly within the other . For if not , the points in ...
Página 15
... prove that d2 17 d2 V d2 V + + = df2 dg2 dh = 0 , or — 4πр ' , αc- cording as the attracted particle is not or is part of the mass itself ; p ' being the density of the attracted particle in the latter case . 21. By differentiating V ...
... prove that d2 17 d2 V d2 V + + = df2 dg2 dh = 0 , or — 4πр ' , αc- cording as the attracted particle is not or is part of the mass itself ; p ' being the density of the attracted particle in the latter case . 21. By differentiating V ...
Página 16
... proved , d'U ' d2U ' d2 U ' dfs + + - dg dh 0 ; d2 V d2 V d2 V d2 U d2 U d'U + + = + df * dg df2 + dg2 dh2 dh2 The centre of the sphere may be chosen as near the attracted particle as we please ; and therefore the radius of the sphere ...
... proved , d'U ' d2U ' d2 U ' dfs + + - dg dh 0 ; d2 V d2 V d2 V d2 U d2 U d'U + + = + df * dg df2 + dg2 dh2 dh2 The centre of the sphere may be chosen as near the attracted particle as we please ; and therefore the radius of the sphere ...
Página 21
... prove that if Qi and R , be two Laplace's Co- 1 2π efficients or Functions , then [ * [ ** QR , dμ dw = 0 , when i and i ' are different integers . 27. By Laplace's Equation in the last Article i ( i + 1 ) Qi = - - d άμ 1 ( 1 − μ3 ) ...
... prove that if Qi and R , be two Laplace's Co- 1 2π efficients or Functions , then [ * [ ** QR , dμ dw = 0 , when i and i ' are different integers . 27. By Laplace's Equation in the last Article i ( i + 1 ) Qi = - - d άμ 1 ( 1 − μ3 ) ...
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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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