An Elementary Treatise on Spherical Harmonics and Subjects Connected with Them |
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Page 47
... element of such a lamina , r its distance from the attracted point , the inclination of r to the line perpendicular to the plane of the lamina , the elementary solid angle subtended by dS at the point will be dS cos 0 p2 And the ...
... element of such a lamina , r its distance from the attracted point , the inclination of r to the line perpendicular to the plane of the lamina , the elementary solid angle subtended by dS at the point will be dS cos 0 p2 And the ...
Page 48
... element , the component attraction is to the solid angle as pk to 1 , and the same relation holding for every element of the lamina , we see that the component attraction of the whole lamina is to the solid angle subtended by the whole ...
... element , the component attraction is to the solid angle as pk to 1 , and the same relation holding for every element of the lamina , we see that the component attraction of the whole lamina is to the solid angle subtended by the whole ...
Page 56
... element of the attracting sphere , divided by the volume of the same element . The product of the volume density 56 APPLICATION OF ZONAL HARMONICS.
... element of the attracting sphere , divided by the volume of the same element . The product of the volume density 56 APPLICATION OF ZONAL HARMONICS.
Page 57
... element of the shell , into the thickness of the shell in the neighbourhood of that element , is called " surface den- sity . " We see from the above that , if the surface density be expressed by the series σP12 + σ12 + σ2P2 + ... + σ ...
... element of the shell , into the thickness of the shell in the neighbourhood of that element , is called " surface den- sity . " We see from the above that , if the surface density be expressed by the series σP12 + σ12 + σ2P2 + ... + σ ...
Page 70
... element of the shell in the im- mediate neighbourhood of Q , its potential at P is to its potential at P as QP is to QP , that is , as c to r , or ( which is the same thing ) as r ' to c , which ratio , being independent of the position ...
... element of the shell in the im- mediate neighbourhood of Q , its potential at P is to its potential at P as QP is to QP , that is , as c to r , or ( which is the same thing ) as r ' to c , which ratio , being independent of the position ...
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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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