An Elementary Treatise on Spherical Harmonics and Subjects Connected with Them |
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Page viii
... thickness . 12. Expression of certain discontinuous functions by an infinite series of zonal harmonics 54 58 . 61 • 14. Expression of a function of μ , infinite for a particular value of μ , and zero for all other values 65 15 ...
... thickness . 12. Expression of certain discontinuous functions by an infinite series of zonal harmonics 54 58 . 61 • 14. Expression of a function of μ , infinite for a particular value of μ , and zero for all other values 65 15 ...
Page 47
... thickness , bounded by the closed plane curve . For , if ds be any 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 ...
... thickness , bounded by the closed plane curve . For , if ds be any 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 ...
Page 48
Norman Macleod Ferrers. p being the density of the lamina , k its thickness . Hence , for this 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 ...
Norman Macleod Ferrers. p being the density of the lamina , k its thickness . Hence , for this 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 ...
Page 49
... thickness and density , at an external point . For we see that , if V be the potential of such a lamina , k its thickness , and p its density , we have for a point on the axis , F. H. - d = pk . 2 = { 1- ( ~ 4 ~ 5 ) ) } , dz ( c2 + 2 ) ...
... thickness and density , at an external point . For we see that , if V be the potential of such a lamina , k its thickness , and p its density , we have for a point on the axis , F. H. - d = pk . 2 = { 1- ( ~ 4 ~ 5 ) ) } , dz ( c2 + 2 ) ...
Page 54
... thickness , U its volume , so that U = 4b28b . Let CP , be the density of the sphere , P , being the zonal surface harmonic of the degree i , and C any con- stant . + d Draw two planes cutting the sphere perpendicular to the axis of z ...
... thickness , U its volume , so that U = 4b28b . Let CP , be the density of the sphere , P , being the zonal surface harmonic of the degree i , and C any con- stant . + d Draw two planes cutting the sphere perpendicular to the axis of z ...
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Common terms and phrases
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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