An Elementary Treatise on Spherical Harmonics and Subjects Connected with Them |
From inside the book
Results 1-5 of 20
Page vii
... solution of this equation 3. Proof that P , is the coefficient of h in a certain series PAGE 6 5. Other expressions for P1 11 · • 6. Investigation of expression for P , in terms of u , by Lagrange's Theorem 12 7. The roots of the ...
... solution of this equation 3. Proof that P , is the coefficient of h in a certain series PAGE 6 5. Other expressions for P1 11 · • 6. Investigation of expression for P , in terms of u , by Lagrange's Theorem 12 7. The roots of the ...
Page 1
... solution of this equation cannot be obtained in finite terms . We can , however , determine an expression which we shall call V , an homogeneous function of x , y , z of the degree i , i being any positive integer , which will satisfy ...
... solution of this equation cannot be obtained in finite terms . We can , however , determine an expression which we shall call V , an homogeneous function of x , y , z of the degree i , i being any positive integer , which will satisfy ...
Page 6
... solution of equation ( 2 ) of the form of a rational integral function of u involves but one arbitrary constant , and that as a 6 ZONAL HARMONICS . Investigation of expression for P, in terms of u, by Lagrange's Theorem.
... solution of equation ( 2 ) of the form of a rational integral function of u involves but one arbitrary constant , and that as a 6 ZONAL HARMONICS . Investigation of expression for P, in terms of u, by Lagrange's Theorem.
Page 53
... solution of the equation , 2 προ V = − 3 mpc2 + ( 4 , + B. ) P. + ( 4 , r + B ) P , + . 3 p + Ar2 + - ( 4,02 + B ) P ; + · It remains to determine the coefficients A , A , ... A .... B1 , B ... B , so that this expression may not ...
... solution of the equation , 2 προ V = − 3 mpc2 + ( 4 , + B. ) P. + ( 4 , r + B ) P , + . 3 p + Ar2 + - ( 4,02 + B ) P ; + · It remains to determine the coefficients A , A , ... A .... B1 , B ... B , so that this expression may not ...
Page 69
... solutions of the equation V2V = 0 which are symmetrical about the axis of z , or in other words , those solutions of the equivalent equation in polar co - ordinates which are independent of p . We propose , in the present Chapter , to ...
... solutions of the equation V2V = 0 which are symmetrical about the axis of z , or in other words , those solutions of the equivalent equation in polar co - ordinates which are independent of p . We propose , in the present Chapter , to ...
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*.