A Treatise on Attractions, Laplace's Functions and the Figure of the EarthMacmillan, 1865 - 162 σελίδες |
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Σελίδα 2
... space described by P. Again , let OPM revolve about OC through a small angle do , then r sin edo is the space described by P. And the thickness of the shell is dr . Hence the volume of the elementary portion of the shell thus formed at ...
... space described by P. Again , let OPM revolve about OC through a small angle do , then r sin edo is the space described by P. And the thickness of the shell is dr . Hence the volume of the elementary portion of the shell thus formed at ...
Σελίδα 47
... space t . Then gravity at a station on the continent will be diminished from this cause by the amount 2t a 9 { 1- ( 1 + ) - 9 nearly . But the attraction of the underlying mass of thickness t must be taken into account . Hence the real ...
... space t . Then gravity at a station on the continent will be diminished from this cause by the amount 2t a 9 { 1- ( 1 + ) - 9 nearly . But the attraction of the underlying mass of thickness t must be taken into account . Hence the real ...
Σελίδα 51
... spaces , such that if the height of the attracting mass were the same in them all , they would all attract the given station exactly to the same amount , whether far or near . In this case it would be necessary only to calculate for one ...
... spaces , such that if the height of the attracting mass were the same in them all , they would all attract the given station exactly to the same amount , whether far or near . In this case it would be necessary only to calculate for one ...
Σελίδα 61
... space should attract the station as if it were collected into the middle point of p . The area of the space = = a2ß { cos ( 0 — 14 ) — cos ( 0 + 14 ) } = 2a2ß sin 10 sin 0 , = and the chord between the mid - point and the station being ...
... space should attract the station as if it were collected into the middle point of p . The area of the space = = a2ß { cos ( 0 — 14 ) — cos ( 0 + 14 ) } = 2a2ß sin 10 sin 0 , = and the chord between the mid - point and the station being ...
Σελίδα 62
... space may be as near as 400 miles to the station , and yet the whole mass be supposed to be col- lected into its centre . The area a2ßp sin 0 = 2a2ßp2 = ( ap ) 2 very nearly = ( 200 ) miles , or the space is equal to a square of 200 ...
... space may be as near as 400 miles to the station , and yet the whole mass be supposed to be col- lected into its centre . The area a2ßp sin 0 = 2a2ßp2 = ( ap ) 2 very nearly = ( 200 ) miles , or the space is equal to a square of 200 ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
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Σελίδα 4 - The design of this work has been to render the subject intelligible to beginners, and at the same time to afford the student the opportunity of obtaining all the information which he will require on this branch of Mathematics.
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