An Elementary Treatise on Spherical Harmonics and Subjects Connected with ThemMacmillan and Company, 1877 - 160 sider |
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Resultat 1-5 av 15
Side 1
... mass , at any point x , y , z , not forming a part of the mass itself , it is known that V must satisfy the differential equation d'V d'V dev d2 V + + = 0 . dx2 + dy2 + dz2 or , as we shall write it for shortness , VV = 0 . . ( 1 ) ...
... mass , at any point x , y , z , not forming a part of the mass itself , it is known that V must satisfy the differential equation d'V d'V dev d2 V + + = 0 . dx2 + dy2 + dz2 or , as we shall write it for shortness , VV = 0 . . ( 1 ) ...
Side 44
... mass . The simplest case of this kind is that in which the attracting mass is an uniform circular wire , of indefinitely small transverse section . Let c be the radius of such a wire , p its density , k its transverse section . Then its ...
... mass . The simplest case of this kind is that in which the attracting mass is an uniform circular wire , of indefinitely small transverse section . Let c be the radius of such a wire , p its density , k its transverse section . Then its ...
Side 46
... mass is a hollow shell of uniform density , whose exterior and interior bounding surfaces are both surfaces of revolution , their common axis being the axis of z . Let the origin be taken within the interior bounding surface ; and ...
... mass is a hollow shell of uniform density , whose exterior and interior bounding surfaces are both surfaces of revolution , their common axis being the axis of z . Let the origin be taken within the interior bounding surface ; and ...
Side 47
... mass , will be 1 - π 0 - 3. We may next shew how to obtain , in terms of a series of zonal harmonics , an expression for the solid angle subtended by a circle at any point . We must first prove the following theorem . The solid angle ...
... mass , will be 1 - π 0 - 3. We may next shew how to obtain , in terms of a series of zonal harmonics , an expression for the solid angle subtended by a circle at any point . We must first prove the following theorem . The solid angle ...
Side 50
... mass of the lamina . Expanding this in a converging series , we get 1 22 M V = 1 -2+ 2 c - if z be less than c , and M ( 1c2 1.1c V = = c2 2z - 2.4z 3 4 1.1 1.1.3z 2.4 c3 + 6 2.4.6c5 - ( - 1 ) 1 − ( − 1 ) * . 2i 1.1.3 ... ( 2-3 ) 22 ...
... mass of the lamina . Expanding this in a converging series , we get 1 22 M V = 1 -2+ 2 c - if z be less than c , and M ( 1c2 1.1c V = = c2 2z - 2.4z 3 4 1.1 1.1.3z 2.4 c3 + 6 2.4.6c5 - ( - 1 ) 1 − ( − 1 ) * . 2i 1.1.3 ... ( 2-3 ) 22 ...
Andre utgaver - Vis alle
An Elementary Treatise on Spherical Harmonics and Subjects Connected with Them Norman Macleod Ferrers Uten tilgangsbegrensning - 1877 |
An Elementary Treatise on Spherical Harmonics, and Subjects Connected with Them Norman M. Ferrers Uten tilgangsbegrensning - 1877 |
An Elementary Treatise on Spherical Harmonics and Subjects Connected with Them N M (Norman MacLeod) 1829-19 Ferrers Ingen forhåndsvisning tilgjengelig - 2015 |
Vanlige uttrykk og setninger
Assistant-Master axis b²+w become infinite bounding surface C₁ Cambridge centre Chap co-ordinates coefficients component attraction confocal ellipsoid corresponding cos² Crown 8vo degree denoted distance dV dV dy dz Edited by Rev ellipsoidal harmonics equal Eton College expression external point Extra fcap factor fcap Fellow of St follows Greek Hence homogeneous function internal John's College lamina late Fellow LATIN monics multiplying numerous obtain Oxford P₁ P₂ plane positive integer potential Professor radius rational integral function satisfies the equation series of zonal shewn sin² solid angle solid harmonic solutions sphere spherical harmonic spherical shell suppose surface harmonic Tesseral thickness Trinity College V₁ writing y+b² y+c² zonal harmonics αμ αμσ µ² µ³ µ³)³ προ
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