An Elementary Treatise on Spherical Harmonics and Subjects Connected with ThemMacmillan and Company, 1877 - 160 Seiten |
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Seite viii
... angle subtended by a circle at any point 4 . 47 Potential of an uniform circular lamina 5. Potential of a sphere whose density varies as R - 5 49 51 6 , 9. Relation between density and potential for a spherical surface 54 10 . Potential ...
... angle subtended by a circle at any point 4 . 47 Potential of an uniform circular lamina 5. Potential of a sphere whose density varies as R - 5 49 51 6 , 9. Relation between density and potential for a spherical surface 54 10 . Potential ...
Seite 30
... angles of the form { i - 2n + ( m + 1 ) } 0 , that is of even or odd multiples of 0 , as i + m is odd or even . Therefore , when integrated between the limits 0 and π it will vanish , if i + m be odd . We may therefore limit our- selves ...
... angles of the form { i - 2n + ( m + 1 ) } 0 , that is of even or odd multiples of 0 , as i + m is odd or even . Therefore , when integrated between the limits 0 and π it will vanish , if i + m be odd . We may therefore limit our- selves ...
Seite 41
... b2 2ab cos . Hence — ( a2 + b2 — 2ab cos D ) ( a2 + b2 — 2ab cos y ) = ( a2 — b2 ) 2 ; - sind de a2 + b2 — 2ab cos + - sin dy = 0 . a2 + b2 - 2ab cos y Again , since the angles OPC , OQC are equal ZONAL HARMONICS . 41.
... b2 2ab cos . Hence — ( a2 + b2 — 2ab cos D ) ( a2 + b2 — 2ab cos y ) = ( a2 — b2 ) 2 ; - sind de a2 + b2 — 2ab cos + - sin dy = 0 . a2 + b2 - 2ab cos y Again , since the angles OPC , OQC are equal ZONAL HARMONICS . 41.
Seite 42
Norman Macleod Ferrers. Again , since the angles OPC , OQC are equal to one another , sin sin OPC sin OQC sin whence And = = CP ου ; ос CQ sin y ) ' sin ( a2 + b2 - 2ab cos ) = ( a + b2 - 2ab cos ) do d ( a2 + b2 — 2ab cos 9 ) + ( a + b2 ...
Norman Macleod Ferrers. Again , since the angles OPC , OQC are equal to one another , sin sin OPC sin OQC sin whence And = = CP ου ; ос CQ sin y ) ' sin ( a2 + b2 - 2ab cos ) = ( a + b2 - 2ab cos ) do d ( a2 + b2 — 2ab cos 9 ) + ( a + b2 ...
Seite 47
... angle subtended by a circle at any point . We must first prove the following theorem . The solid angle , subtended by a closed plane curve at any point , is proportional to the component attraction perpendicular to the plane of the ...
... angle subtended by a circle at any point . We must first prove the following theorem . The solid angle , subtended by a closed plane curve at any point , is proportional to the component attraction perpendicular to the plane of the ...
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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 |
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ALGEBRA ARITHMETIC Assistant Assistant-Master attraction Author axis becomes BEGINNERS BOOK Cambridge centre CHEMISTRY Classical consider corresponding Course Crown 8vo density determine ELEMENTARY ellipsoid English equal equation Examination Examples Exercises expression external point Extra fcap factor Fellow of St Fellow of Trinity formerly function GEOMETRY Globe 8vo GRAMMAR Greek Hence HISTORY homogeneous function Illustrations integral internal JOHN John's College late Fellow LATIN Lecturer LL.D London Maps Master Mathematics Nature Notes numerous obtain Oxford P₁ P₂ Physics plane potential preparation PRIMER Principal Professor prove putting respectively revised Royal satisfied School Science Second Edition Selected shell solid solutions sphere suppose surface Text Translated TREATISE Trinity College University Vocabulary volume writing zonal harmonics αμ µ³
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