An Elementary Treatise on Spherical Harmonics and Subjects Connected with ThemMacmillan and Company, 1877 - 160 Seiten |
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Seite 5
... origin of co - ordinates , and radius unity , is called the Pole of the system . Any constant multiple of a zonal harmonic ( solid or surface ) is itself a zonal harmonic of the same order . 2. The zonal harmonic of the degree i , of ...
... origin of co - ordinates , and radius unity , is called the Pole of the system . Any constant multiple of a zonal harmonic ( solid or surface ) is itself a zonal harmonic of the same order . 2. The zonal harmonic of the degree i , of ...
Seite 8
... origin , and R be the distance between these points , we know that , and that Ra = x2 + y2 + ( z ' — 2 ) 3 , 2 = 0 . Now , transform these expressions to polar co - ordinates , by writing x = r sin 0 cos p , y = rsin @ sind , z = r cos ...
... origin , and R be the distance between these points , we know that , and that Ra = x2 + y2 + ( z ' — 2 ) 3 , 2 = 0 . Now , transform these expressions to polar co - ordinates , by writing x = r sin 0 cos p , y = rsin @ sind , z = r cos ...
Seite 44
... origin , its potential at any point of its axis , distant z from its centre , will be M ( c2 + z2 ) . Now , this expression may be developed into either of the following series : M ( 122 1.324 + c 2 c2 2.4 c * ¡ — ... + ( − 1 ) ' - 1.3 ...
... origin , its potential at any point of its axis , distant z from its centre , will be M ( c2 + z2 ) . Now , this expression may be developed into either of the following series : M ( 122 1.324 + c 2 c2 2.4 c * ¡ — ... + ( − 1 ) ' - 1.3 ...
Seite 46
... origin be taken within the interior bounding surface ; and suppose the potential , at any point of the axis within this surface , to be A ̧ + Â ̧≈ + Â ̧≈2 + ... + Â ̧1⁄23 + ... .. Then the potential at any point lying within the inner ...
... origin be taken within the interior bounding surface ; and suppose the potential , at any point of the axis within this surface , to be A ̧ + Â ̧≈ + Â ̧≈2 + ... + Â ̧1⁄23 + ... .. Then the potential at any point lying within the inner ...
Seite 54
... origin , and the axis of the system of zonal harmonics as the axis of z . Let b be the radius of the sphere , 8b its thickness , U its volume , so that U = 4b28b . Let CP , be the density of the sphere , P , being the zonal surface ...
... origin , and the axis of the system of zonal harmonics as the axis of z . Let b be the radius of the sphere , 8b its thickness , U its volume , so that U = 4b28b . Let CP , be the density of the sphere , P , being the zonal surface ...
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An Elementary Treatise on Spherical Harmonics and Subjects Connected with Them N M (Norman MacLeod) 1829-19 Ferrers Keine Leseprobe verfügbar - 2015 |
Häufige Begriffe und Wortgruppen
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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