An Elementary Treatise on Spherical Harmonics and Subjects Connected with Them |
From inside the book
Results 1-5 of 17
Page 10
... greater than 1 , this series becomes divergent . But we may write ( h2 — 2μh + 1 ) − = 1 1 - 2 1⁄2 + h2 ) 11-1 h P - ( P. + 2 + ... + + ... ) . = 0 h 1 since is less than 1 , + Bit + ... ++ .... P P. P = h h Hence P is also the ...
... greater than 1 , this series becomes divergent . But we may write ( h2 — 2μh + 1 ) − = 1 1 - 2 1⁄2 + h2 ) 11-1 h P - ( P. + 2 + ... + + ... ) . = 0 h 1 since is less than 1 , + Bit + ... ++ .... P P. P = h h Hence P is also the ...
Page 32
... expressions i may be any integer such that mi is even , i being not greater than m . Hence they will always be negative , except when i is equal to m . 20. We may apply these expressions to develop cos me 32 ZONAL HARMONICS .
... expressions i may be any integer such that mi is even , i being not greater than m . Hence they will always be negative , except when i is equal to m . 20. We may apply these expressions to develop cos me 32 ZONAL HARMONICS .
Page 39
... greater than a2 . For , if b2 be not greater than a2 , cos I cannot become α equal to while increases from 0 to π , and therefore the b expression under the integral sign cannot become infinite . Supposing then that we write z for a ...
... greater than a2 . For , if b2 be not greater than a2 , cos I cannot become α equal to while increases from 0 to π , and therefore the b expression under the integral sign cannot become infinite . Supposing then that we write z for a ...
Page 44
... lie within the sphere of which the ring is a great circle , and the series ( 2 ) if z be greater than c , or if the attracted point lie without this sphere . Now , take any point whose distance from the centre 122 CHAPTER V.
... lie within the sphere of which the ring is a great circle , and the series ( 2 ) if z be greater than c , or if the attracted point lie without this sphere . Now , take any point whose distance from the centre 122 CHAPTER V.
Page 45
... greater than C , while ( 1 ' ) becomes equal to ( 2 ' ) when r = c , and will therefore denote the required potential for all values of r less than c . These expressions may be reduced to other forms by means of the expressions ...
... greater than C , while ( 1 ' ) becomes equal to ( 2 ' ) when r = c , and will therefore denote the required potential for all values of r less than c . These expressions may be reduced to other forms by means of the expressions ...
Other editions - View all
Common terms and phrases
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
Popular passages
Page 72 - TAYLOR— WORDS AND PLACES; or, Etymological Illustrations of History, Ethnology, and Geography. By the Rev. ISAAC TAYLOR, MA Third and cheaper Edition, revised and compressed. With Maps. Globe 8vo. 6s.
Page 87 - Supernatural Religion." Crown 8vo. IOJ. 64. INTRODUCTION TO THE STUDY OF THE FOUR GOSPELS. Fifth Edition. Crown 8vo. los. 6d. THE BIBLE IN THE CHURCH." A Popular Account of the Collection and Reception of the Holy Scriptures in the Christian Churches. New Edition.
Page 68 - HALES— LONGER ENGLISH POEMS, with Notes, Philological and Explanatory, and an Introduction on the Teaching of English. Chiefly for Use in Schools. Edited by JW HALES, MA, Professor of English Literature at King's College, London.
Page 87 - A GENERAL SURVEY OF THE HISTORY OF THE CANON OF THE NEW TESTAMENT DURING THE fIRST FOUR CENTURIES. Fourth Edition. With Preface on "Supernatural Religion.
Page 44 - AN ELEMENTARY TREATISE ON THE LUNAR THEORY, with a Brief Sketch of the Problem up to the time of Newton. Second Edition, revised. Crown 8vo. $s. 6d. HEMMING— AN ELEMENTARY TREATISE ON THE DIFFERENTIAL AND INTEGRAL CALCULUS, for the Use of Colleges and Schools.
Page 27 - Prize Essay for 1877. 8vC. &r. 6d. SMITH— Works by the Rev. BARNARD SMITH, MA, Rector of Glaston, Rutland, late Fellow and Senior Bursar of St. Peter's College, Cambridge. ARITHMETIC AND ALGEBRA, in their Principles and Application ; with numerous systematically arranged Examples taken from the Cambridge Examination Papers, with especial reference to the Ordinary Examination for the BA Degree.
Page 78 - Whitney and Edgren. — A COMPENDIOUS GERMAN AND ENGLISH DICTIONARY, with Notation of Correspondences and Brief Etymologies. By Professor WD WHITNEY, assisted by AH EDGREN.
Page 64 - EUROPEAN HISTORY. Narrated in a Series of Historical Selections from the Best Authorities. Edited and arranged by EM SEWELL and CM YONGE. First Series, 1003 — 1154. Third Edition. Crown 8vo. 6s. Second Series, 1088—1228. Crown 8vo. 6s. Third Edition. " We know of scarcely anything which is so likely to raise to a higher level the average standard of English education.
Page 7 - Fcap. 8vo. Being select portions of Greek and Latin authors, edited with Introductions and Notes, for the use of Middle and Upper forms of Schools, or of candidates for Public Examinations at the Universities and elsewhere.
Page 18 - HODGSON -MYTHOLOGY FOR LATIN VERSIFICATION. A brief Sketch of the Fables of the Ancients, prepared to be rendered into Latin Verse for Schools. By F. HODGSON, BD, late Provost of Eton. New Edition, revised by FC HODGSON, MA i8mo. 3*.