A Treatise on Attractions, Laplace's Functions and the Figure of the EarthMacmillan, 1865 - 162 páginas |
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Página viii
... equals zero 28. Any function , which does not become infinite between the limits used , can be expanded in a series of ... equal mass as a standard , the general radius of the body is simplified 45. Attraction of a body consisting of ...
... equals zero 28. Any function , which does not become infinite between the limits used , can be expanded in a series of ... equal mass as a standard , the general radius of the body is simplified 45. Attraction of a body consisting of ...
Página 2
... equals rde . r sin Odp . dr ulti- mately , since its sides are ultimately at right angles to each other . Then , if the unit of attraction be so chosen , that it equals the attraction of the unit of mass at the unit of distance , the ...
... equals rde . r sin Odp . dr ulti- mately , since its sides are ultimately at right angles to each other . Then , if the unit of attraction be so chosen , that it equals the attraction of the unit of mass at the unit of distance , the ...
Página 3
... equal , and being in opposite directions will not affect the point . The whole shell may be thus divided into pairs of equal attracting elements and in opposite direc- tions , and therefore the whole shell has no effect in drawing the ...
... equal , and being in opposite directions will not affect the point . The whole shell may be thus divided into pairs of equal attracting elements and in opposite direc- tions , and therefore the whole shell has no effect in drawing the ...
Página 8
... equal the integrals of the attrac- tions of the element ; the limits of r being - r ' and r " , of being 0 and 7 , of 4 being 0 and π . Hence A الم Π - " " sin2 0 p sin2 e cos par do do , --CIT B = G Then A = 0 0 π π 0 π π - [ " SS " 0 ...
... equal the integrals of the attrac- tions of the element ; the limits of r being - r ' and r " , of being 0 and 7 , of 4 being 0 and π . Hence A الم Π - " " sin2 0 p sin2 e cos par do do , --CIT B = G Then A = 0 0 π π 0 π π - [ " SS " 0 ...
Página 15
... x ) 2 + ( g − y ) 2 + ( h − z ) * } § - When the attracted particle is not a portion of the attract- ing mass itself , then xyz will never equal fgh respectively , and consequently the expression under the signs of integration vanishes.
... x ) 2 + ( g − y ) 2 + ( h − z ) * } § - When the attracted particle is not a portion of the attract- ing mass itself , then xyz will never equal fgh respectively , and consequently the expression under the signs of integration vanishes.
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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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