An Elementary Treatise on Spherical Harmonics and Subjects Connected with Them |
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Page 6
... attraction of a sphe- roid on an external point . We shall discuss their properties more fully hereafter . 3. We have thus shewn that the most general solution of equation ( 2 ) of the form of a rational integral function of u involves ...
... attraction of a sphe- roid on an external point . We shall discuss their properties more fully hereafter . 3. We have thus shewn that the most general solution of equation ( 2 ) of the form of a rational integral function of u involves ...
Page 44
... ATTRACTION . FUNCTIONS BY SERIES OF ZONAL HARMONICS , 1. WE shall , in this chapter , give some applications of ... attracted point lie within the sphere of which the ring is a great circle , and the series ( 2 ) if z be greater than c ...
... ATTRACTION . FUNCTIONS BY SERIES OF ZONAL HARMONICS , 1. WE shall , in this chapter , give some applications of ... attracted point lie within the sphere of which the ring is a great circle , and the series ( 2 ) if z be greater than c ...
Page 47
... attraction perpendicular to the plane of the curve , exercised upon the point by a lamina , of uniform density and thickness , bounded by the closed plane curve . For , if ds be any element of such a lamina , r its distance from the ...
... attraction perpendicular to the plane of the curve , exercised upon the point by a lamina , of uniform density and thickness , bounded by the closed plane curve . For , if ds be any element of such a lamina , r its distance from the ...
Page 48
... 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 curve as pk to 1 . Now ...
... 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 curve as pk to 1 . Now ...
Page 49
... V be the potential of such a lamina , k its thickness , and p its density , we have for a point on the axis , dV -dr - pk . 2 = { 1- ( 4-273 } , dz F. H. = ( c2 + 22 ) 4 whence V = 2πpk { ( c2 + z2 ) TO THE THEORY OF ATTRACTION . 49.
... V be the potential of such a lamina , k its thickness , and p its density , we have for a point on the axis , dV -dr - pk . 2 = { 1- ( 4-273 } , dz F. H. = ( c2 + 22 ) 4 whence V = 2πpk { ( c2 + z2 ) TO THE THEORY OF ATTRACTION . 49.
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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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