A Treatise on Attractions, Laplace's Functions and the Figure of the EarthMacmillan, 1865 - 162 páginas |
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Página 2
... obtain the attraction of all the particles of the shell we integrate this with respect to p and y , the limits of 0 and 2π , those of y being c - r and c + r ; ... attraction of shell on C = = Tordr ctr #prar fer ( 1 c2 c - r 1+ - y ...
... obtain the attraction of all the particles of the shell we integrate this with respect to p and y , the limits of 0 and 2π , those of y being c - r and c + r ; ... attraction of shell on C = = Tordr ctr #prar fer ( 1 c2 c - r 1+ - y ...
Página 10
... obtain the attraction of a spheroid on an external particle . Mr Ivory has , however , devised an indirect method of obtaining it , which we shall now proceed to develop . He has discovered a theorem by which the attraction of an ellip ...
... obtain the attraction of a spheroid on an external particle . Mr Ivory has , however , devised an indirect method of obtaining it , which we shall now proceed to develop . He has discovered a theorem by which the attraction of an ellip ...
Página 14
... obtain formula for the calculation of the attrac- tion of a heterogeneous mass upon any particle . 18. Let p be the density of the body at the point ( xyz ) ; fgh the co - ordinates of the attracted particle ; and , as before , suppose ...
... obtain formula for the calculation of the attrac- tion of a heterogeneous mass upon any particle . 18. Let p be the density of the body at the point ( xyz ) ; fgh the co - ordinates of the attracted particle ; and , as before , suppose ...
Página 20
... obtain equations for calculating the coefficients P , P1 , P ... substitute either of the series ( 1 ) in the differential equation in R in the last article , and equate the coefficients of the several powers of r to zero . The general ...
... obtain equations for calculating the coefficients P , P1 , P ... substitute either of the series ( 1 ) in the differential equation in R in the last article , and equate the coefficients of the several powers of r to zero . The general ...
Página 25
... ( 1 + 1 = 0 ) 2π = 4π . C с It is remarkable that this result is altogether independent of c * . * This result can be obtained more shortly as follows ; but the proof given 31. By analysing the integral in the last Article and.
... ( 1 + 1 = 0 ) 2π = 4π . C с It is remarkable that this result is altogether independent of c * . * This result can be obtained more shortly as follows ; but the proof given 31. By analysing the integral in the last Article and.
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Otras ediciones - Ver todo
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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