An Elementary Treatise on Spherical Harmonics and Subjects Connected with ThemMacmillan and Company, 1877 - 160 páginas |
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Página 54
... volume , so that U = 4πb28b . Let CP , be the density of the sphere , P , being the zonal surface harmonic of the degree i , and C any con- stant . ૐ + d Draw two planes cutting the sphere perpendicular to the axis of z , at distances ...
... volume , so that U = 4πb28b . Let CP , be the density of the sphere , P , being the zonal surface harmonic of the degree i , and C any con- stant . ૐ + d Draw two planes cutting the sphere perpendicular to the axis of z , at distances ...
Página 56
... volume density , " i.e. the mass of an indefinitely small element of the attracting sphere , divided by the volume of the same element . The product of the volume density 56 APPLICATION OF ZONAL HARMONICS.
... volume density , " i.e. the mass of an indefinitely small element of the attracting sphere , divided by the volume of the same element . The product of the volume density 56 APPLICATION OF ZONAL HARMONICS.
Página 57
... volume density with an uniform thickness , as we have supposed , or by combining a variable thickness with a uniform volume density , or by varying both thickness and density . 8. We have seen , in Chap . II . , that any positive ...
... volume density with an uniform thickness , as we have supposed , or by combining a variable thickness with a uniform volume density , or by varying both thickness and density . 8. We have seen , in Chap . II . , that any positive ...
Página 67
... volume U , at any point on the axis of z , is Ur1 2 -1 ραλ ( c + 2-2λcz ) 2 which is equal to { pdx + pP , ( x ) dx + ... U 2c -1 for an internal point , + [ _pp , ( x ) dx + ... U ( 1 and to -1 + ... +1 + - _ P ( x ) dx + ... , -1 for ...
... volume U , at any point on the axis of z , is Ur1 2 -1 ραλ ( c + 2-2λcz ) 2 which is equal to { pdx + pP , ( x ) dx + ... U 2c -1 for an internal point , + [ _pp , ( x ) dx + ... U ( 1 and to -1 + ... +1 + - _ P ( x ) dx + ... , -1 for ...
Página 97
... volume of the solid will be a3 . For it is equal to 1 2π 1 2π 3 SS Str2 dr dμ do -1 = { } [ ' , [ ] , " ( a2 + 3a'a ( a , Y , + a , Y , + ... + a , X , + ... . ... .. ) ] du dø 4 { a3 2π = wa , since [ [ Y , dudp = 0 , 3 πα , for all ...
... volume of the solid will be a3 . For it is equal to 1 2π 1 2π 3 SS Str2 dr dμ do -1 = { } [ ' , [ ] , " ( a2 + 3a'a ( a , Y , + a , Y , + ... + a , X , + ... . ... .. ) ] du dø 4 { a3 2π = wa , since [ [ Y , dudp = 0 , 3 πα , for all ...
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An Elementary Treatise on Spherical Harmonics and Subjects Connected with Them N M (Norman MacLeod) 1829-19 Ferrers Sin vista previa disponible - 2015 |
Términos y frases comunes
A. S. WALPOLE A. W. VERRALL Assistant Master Assistant-Master axis BEGINNERS BOOK Cambridge centre Classical Clifton College coefficients cos² Crown 8vo degree denoted density Edited by E. S. Edited by Rev ELEMENTARY English Exercises expression external point Extra fcap Fcap Fellow of St Fellow of Trinity Globe 8vo GRAMMAR Hence Illustrations internal Introduction and Notes J. P. MAHAFFY JOHN BOND John's College late Fellow LATIN Lecturer Litt LL.D numerous obtain Owens College Oxford P₁ P₂ plane potential preparation PRIMER radius rational integral function revised and enlarged satisfies the equation School Second Edition sin² solid solid harmonic sphere spherical harmonic suppose surface harmonic Tesseral Translated TREATISE Trinity College University V₁ Vocabulary y+b² y+c² zonal harmonics αμ αμσ µ² µ³
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