A Treatise on Attractions, Laplace's Functions and the Figure of the EarthMacmillan, 1865 - 162 páginas |
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Página viii
... distance of the attracted particle from any point of the body 23 , 24. Transformation of equations in R and V to polar co - ordi- nates 25. Method of expanding R 26. Laplace's Coefficients , Equation , and Functions defined 27 . PAGE ...
... distance of the attracted particle from any point of the body 23 , 24. Transformation of equations in R and V to polar co - ordi- nates 25. Method of expanding R 26. Laplace's Coefficients , Equation , and Functions defined 27 . PAGE ...
Página 1
... distance between the attracted and the attracting particles . Taking this law as our basis of calculation , we shall investigate the amount of attraction exerted by spherical , spheroidal , and irregular nearly - spherical masses upon a ...
... distance between the attracted and the attracting particles . Taking this law as our basis of calculation , we shall investigate the amount of attraction exerted by spherical , spheroidal , and irregular nearly - spherical masses upon a ...
Página 2
... distance , the attraction of the elementary mass at P on C in the direction CP pr2 sin 0 drd0dp y * , p the density of the shell ; .. attraction of P on C in COP sin drded = y2 -r cos 0 Y We shall eliminate O from this equation by means ...
... distance , the attraction of the elementary mass at P on C in the direction CP pr2 sin 0 drd0dp y * , p the density of the shell ; .. attraction of P on C in COP sin drded = y2 -r cos 0 Y We shall eliminate O from this equation by means ...
Página 3
... distance from the at- tracted point ; and therefore the masses of the two opposite elements of the shell will vary directly as the square of the distance from that point , and consequently their attractions will be exactly equal , and ...
... distance from the at- tracted point ; and therefore the masses of the two opposite elements of the shell will vary directly as the square of the distance from that point , and consequently their attractions will be exactly equal , and ...
Página 4
... distance . To determine this is the object of the four following Propositions . PROP . To find the attraction of a homogeneous spherical shell on a particle without it ; the law of attraction being repre- sented by ( y ) , y being the ...
... distance . To determine this is the object of the four following Propositions . PROP . To find the attraction of a homogeneous spherical shell on a particle without it ; the law of attraction being repre- sented by ( y ) , y being the ...
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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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