A Treatise on Attractions, Laplace's Functions and the Figure of the EarthMacmillan, 1865 - 162 páginas |
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Página iv
... strata , whatever its former history may have been ; that , on the fluid hypothesis , the form of its surface and of all its internal layers must be oblate spheroids ; and that the plumb- line must be everywhere a normal to its surface ...
... strata , whatever its former history may have been ; that , on the fluid hypothesis , the form of its surface and of all its internal layers must be oblate spheroids ; and that the plumb- line must be everywhere a normal to its surface ...
Página x
... strata nearly spherical 75. The Equation of Equilibrium of a mass consisting of nearly spherical strata 77. The form of the strata is spheroidal " " · 78. Conditions resulting from the fluid theory . Meaning of " sphe- roid of ...
... strata nearly spherical 75. The Equation of Equilibrium of a mass consisting of nearly spherical strata 77. The form of the strata is spheroidal " " · 78. Conditions resulting from the fluid theory . Meaning of " sphe- roid of ...
Página 40
... pr3 √1— μ3 cos wdr dμdw √1 - μ cos wdμdw , pr VI · M. y = [ ' " [ " _ " [ " pr3 √1— μ3 sin wdr dμdw -10 1 = 1 SS . = 1 √ √ * 0 2π - — pr * √1 – μ3 sin wdμdw , BODY CONSISTING OF NEARLY SPHERICAL STRATA . M.Z = 1 40 ATTRACTIONS .
... pr3 √1— μ3 cos wdr dμdw √1 - μ cos wdμdw , pr VI · M. y = [ ' " [ " _ " [ " pr3 √1— μ3 sin wdr dμdw -10 1 = 1 SS . = 1 √ √ * 0 2π - — pr * √1 – μ3 sin wdμdw , BODY CONSISTING OF NEARLY SPHERICAL STRATA . M.Z = 1 40 ATTRACTIONS .
Página 41
... strata nearly spherical , homogeneous in themselves , but differing one from another in density . 45. Let a ' ( 1+ y ' ) be the radius of the external surface of any stratum , a ' being chosen so that y ' = Y + Y2 + ... + Y + ... ( Art ...
... strata nearly spherical , homogeneous in themselves , but differing one from another in density . 45. Let a ' ( 1+ y ' ) be the radius of the external surface of any stratum , a ' being chosen so that y ' = Y + Y2 + ... + Y + ... ( Art ...
Página 42
... strata within the surface of which the radius is a ( 1+ y ) , we have 4π α Ꮴ = 12 d la da ' 3r a li + 3 Y- 4 = [ ' { ( a + // ( ~ = x + - + ( 2 + 1 ) + i + ... ) } da ' . ρ 2 0 ... pi But for a stratum external to the particle we have ...
... strata within the surface of which the radius is a ( 1+ y ) , we have 4π α Ꮴ = 12 d la da ' 3r a li + 3 Y- 4 = [ ' { ( a + // ( ~ = x + - + ( 2 + 1 ) + i + ... ) } da ' . ρ 2 0 ... pi But for a stratum external to the particle we have ...
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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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