An Elementary Treatise on Spherical Harmonics and Subjects Connected with ThemMacmillan and Company, 1877 - 160 Seiten |
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Seite 5
... 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 which the line μ1 is the axis ...
... 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 which the line μ1 is the axis ...
Seite 41
... radius a , C any point within the circle , PCQ any chord drawn through C , and let OC = b , COP = I , COQ = y . Then CP3 = a + b2 - 2ab cos , CQ2 = a2 + b2 - 2ab cos . Hence ( a2 + b2 — 2ab cos F ) ( a2 + b2 − 2ab cos ¥ ) = ( a2 — b2 ) ...
... radius a , C any point within the circle , PCQ any chord drawn through C , and let OC = b , COP = I , COQ = y . Then CP3 = a + b2 - 2ab cos , CQ2 = a2 + b2 - 2ab cos . Hence ( a2 + b2 — 2ab cos F ) ( a2 + b2 − 2ab cos ¥ ) = ( a2 — b2 ) ...
Seite 44
... radius of such a wire , p its density , k its transverse section . Then its mass , M , will be equal to 2πрck , and if its centre be taken as the origin , its potential at any point of its axis , distant z from its centre , will be M ...
... radius of such a wire , p its density , k its transverse section . Then its mass , M , will be equal to 2πрck , and if its centre be taken as the origin , its potential at any point of its axis , distant z from its centre , will be M ...
Seite 48
... radius Q0 , describe a circle , cutting QE in L. From L draw LN , perpendicular to QO . Let OE = c , 0Q = z . Then EL = ( c2 + z2 ) 3 — 2 , ON = 2 ( c2 + z2 ) } { ( c2 + 2 ° ) 1 — z } 22 = 2 ( c2 + z2 ) 3 ° And the solid angle subtended ...
... radius Q0 , describe a circle , cutting QE in L. From L draw LN , perpendicular to QO . Let OE = c , 0Q = z . Then EL = ( c2 + z2 ) 3 — 2 , ON = 2 ( c2 + z2 ) } { ( c2 + 2 ° ) 1 — z } 22 = 2 ( c2 + z2 ) 3 ° And the solid angle subtended ...
Seite 51
... radius , let OP = r , POC 0. Also let CA = a , CO = c . = Let the density of the sphere at its centre be p , then its density at P will be p C5 2.5 · Hence C5 M = 2 e 25 sin dr do , the limits of equation of the being the two values 4-2 ...
... radius , let OP = r , POC 0. Also let CA = a , CO = c . = Let the density of the sphere at its centre be p , then its density at P will be p C5 2.5 · Hence C5 M = 2 e 25 sin dr do , the limits of equation of the being the two values 4-2 ...
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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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