A Treatise on Attractions, Laplace's Functions, and the Figure of the EarthMacmillan and Company, 1861 - 122 sider |
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Side vi
John Henry Pratt. · ART . 27. Any function , which does not become infinite between the limits used , can be expanded in a series of Laplace's Func- tions . Remarks on this Proposition · 34. A function can be arranged in only one series ...
John Henry Pratt. · ART . 27. Any function , which does not become infinite between the limits used , can be expanded in a series of Laplace's Func- tions . Remarks on this Proposition · 34. A function can be arranged in only one series ...
Side 7
... becomes ( f + r sin cos ) 2 + ( g + r sin 0 sin ) 2 , ( h + r cos 0 ) 2 + c2 = = 1 , fsin @ cos + g sin 0 sin p , h cos cos 2 a2 a2 or 22 / sin20 cos 0 + + 2r a2 c2 ( fsin = 1- - a2 c2 ; put + = = K , c2 ƒ2 + g2 h2 + sin2 0 cos2 0 fsin ...
... becomes ( f + r sin cos ) 2 + ( g + r sin 0 sin ) 2 , ( h + r cos 0 ) 2 + c2 = = 1 , fsin @ cos + g sin 0 sin p , h cos cos 2 a2 a2 or 22 / sin20 cos 0 + + 2r a2 c2 ( fsin = 1- - a2 c2 ; put + = = K , c2 ƒ2 + g2 h2 + sin2 0 cos2 0 fsin ...
Side 13
... becomes 2 x y + αα 2 + 2 2 = = 0 , an equation which can be satisfied only by x = 0 , y = 0 , z = 0 . But these do not satisfy the equations above ; and therefore the surfaces do not intersect in any point . To find the attraction of ...
... becomes 2 x y + αα 2 + 2 2 = = 0 , an equation which can be satisfied only by x = 0 , y = 0 , z = 0 . But these do not satisfy the equations above ; and therefore the surfaces do not intersect in any point . To find the attraction of ...
Side 16
... becomes , when x = f , y = g , z = h . d2 V d2 V d2 V df2 + dg2 + dh2 in that case , To determine the value of suppose a sphere described in the body , so that it shall include the attracted particle ; and let Ț = U + U ' , U referring ...
... becomes , when x = f , y = g , z = h . d2 V d2 V d2 V df2 + dg2 + dh2 in that case , To determine the value of suppose a sphere described in the body , so that it shall include the attracted particle ; and let Ț = U + U ' , U referring ...
Side 18
... d2r + + dr ̄ df2 * dg2 * dh2 dR d20 d20 д20 2 = " the coefficient of = do - df2 + + dg dh = dR d'o d2w d2w d2w cos ? sin 60 ? the coefficient of do + + df * dg2 dh2 - 0 . Hence the equation in R becomes d2R 2 dR + 18 ATTRACTIONS . dg2.
... d2r + + dr ̄ df2 * dg2 * dh2 dR d20 d20 д20 2 = " the coefficient of = do - df2 + + dg dh = dR d'o d2w d2w d2w cos ? sin 60 ? the coefficient of do + + df * dg2 dh2 - 0 . Hence the equation in R becomes d2R 2 dR + 18 ATTRACTIONS . dg2.
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A Treatise on Attractions: Laplace's Functions, and the Figure of the Earth John Henry Pratt Uten tilgangsbegrensning - 1860 |
A Treatise on Attractions: Laplace's Functions, and the Figure of the Earth John Henry Pratt Uten tilgangsbegrensning - 1860 |
A Treatise on Attractions, Laplace's Functions, and the Figure of the Earth John Henry Pratt Uten tilgangsbegrensning - 1861 |
Vanlige uttrykk og setninger
amplitudes angle attracted particle attracted point attracting mass axes axis calculation Cambridge Cape Comorin Cavendish experiment centre cloth co-ordinates coefficient College compartment cos² cos² a+10 Crown 8vo d²R Damargida deflection caused Deflexion depth df² dg² dh² distance dr² dw² Earth element ellipsoid equal equation expanded Fcap find the attraction fluid formula frustum gravity height Hence integration Kaliana Kalianpur Laplace's Equation Laplace's Functions last Article last Proposition law of attraction law of dissection length lune mean ellipse Mechanical Philosophy meridian mid-line miles mountains ocean Ordnance Survey plane plumb-line prism PROP quantities radius result Second Edition shell sin² sin³ sphere spherical spheroid square station strata Suppose surface thickness Trinity College vertical Y₁ αμ µ² µ³
Populære avsnitt
Side 115 - Christ and other Masters. A Historical Inquiry into some of the Chief Parallelisms and Contrasts between Christianity and the Religious Systems of the Ancient World.
Side 116 - HERVEY.— The Genealogies of our Lord and Saviour Jesus Christ, as contained in the Gospels of St. Matthew and St. Luke, reconciled with each other and with the Genealogy of the House of David, from Adam to the close of the Canon of the Old Testament, and shown to be in harmony with the true Chronology of the Times.
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Side 111 - BIRKS.— The Difficulties of Belief in connexion with the Creation and the Fall. By THOMAS RAWSON BIRKS, MA Rector of Kelshall, and Author of "The Life of the Rev. E. Bickersteth.
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