An Elementary Treatise on the Lunar Theory: With a Brief Sketch of the History of the Problem Up to the Time of Newton |
From inside the book
Results 1-5 of 17
Page 31
... argument * is nearly equal to 1 or 0 ; and terms in which the coefficient of the argument is nearly equal to 0 , must be retained TWO ORDERS beyond the proposed approximation when they occur in T h2u3 . * The angle of a periodical term ...
... argument * is nearly equal to 1 or 0 ; and terms in which the coefficient of the argument is nearly equal to 0 , must be retained TWO ORDERS beyond the proposed approximation when they occur in T h2u3 . * The angle of a periodical term ...
Page 43
... in finding t , when it will become of the second order . The other terms of the third order , which arise in the development of the expression , are neglected , as the coefficients of in their arguments are neither small.
... in finding t , when it will become of the second order . The other terms of the third order , which arise in the development of the expression , are neglected , as the coefficients of in their arguments are neither small.
Page 44
... arguments are neither small nor near unity . T 3m'u'3 h2u 2hu sin 2 ( 0 – 0 ' ) - == = - 3m'a ( 1 + e ' cos ( m0 + B − ( ) } 3 2h * a * { 1+ e cos ( c✪ — a ) } * - 3m2 ( 1 + 3e ' cos ( m0 + B− } ) } sin { ( 2 — 2m ) 0 — 2B ) [ 1-4e ...
... arguments are neither small nor near unity . T 3m'u'3 h2u 2hu sin 2 ( 0 – 0 ' ) - == = - 3m'a ( 1 + e ' cos ( m0 + B − ( ) } 3 2h * a * { 1+ e cos ( c✪ — a ) } * - 3m2 ( 1 + 3e ' cos ( m0 + B− } ) } sin { ( 2 — 2m ) 0 — 2B ) [ 1-4e ...
Page 46
... arguments are cơ – a and go - y . - 47. Since the form of the solution is known , the actual expressions for u and s ... argument is near unity , the term becomes important in the radius vector , and when near zero , in the longitude ...
... arguments are cơ – a and go - y . - 47. Since the form of the solution is known , the actual expressions for u and s ... argument is near unity , the term becomes important in the radius vector , and when near zero , in the longitude ...
Page 50
... argument not being small . We have now to multiply these results together , and we see that the term having for argument ( 2—2m - 2c ) 0−2B + 2a will disappear in the product . If we trace this term , we shall de , from retaining ...
... argument not being small . We have now to multiply these results together , and we see that the term having for argument ( 2—2m - 2c ) 0−2B + 2a will disappear in the product . If we trace this term , we shall de , from retaining ...
Other editions - View all
Common terms and phrases
3m²e accelerating forces Algebra angle angular velocity annual equation anomaly apogee apse line astronomers attraction bodies BROOKE FOSS WESTCOTT calculated Cambridge centre cloth coefficient considered correct cos2 Crown 8vo determined differential equations distance disturbing force E-Ma E+Ma earth eccentricity ecliptic ELEMENTARY TREATISE elliptic inequality epicycle equal evection expression Fcap fixed plane fourth order h²u³ higher order Hipparchus hu³ integration John's College Lunar Theory MACMILLAN AND CO'S Mathematical mean anomaly mean longitude mean motion mean value method moon moon's mean moon's motion moon's orbit nearly neglected Newton node numerous observations obtained order of approximation parallax particle perigee periodical terms position Ps-S Ptolemy quadrature quantity radius vector revolution Schools Second Edition second order shew sidereal month sin2 solution sphere student substituted syzygy third order true anomaly true longitude Tycho variation že²
Popular passages
Page 10 - MORGAN — A COLLECTION OF PROBLEMS AND EXAMPLES IN MATHEMATICS. With Answers. By HA Morgan, MA, Sadlerian and Mathematical Lecturer of Jesus College, Cambridge.
Page 5 - THE SEVEN KINGS OF ROME. An Easy Narrative, abridged from the First Book of Livy by the omission of Difficult Passages; being a First Latin Reading Book, with Grammatical Notes and Vocabulary.
Page 9 - THE FIRST THREE SECTIONS of NEWTON'S PRINCIPIA. With Notes and Illustrations. Also a Collection of Problems, principally intended as Examples of Newton's Methods. By PERCIVAL FROST, MA, late Fellow of St. John's College, Mathematical Lecturer of King's College, Cambridge.
Page 22 - WILSON — THE BIBLE STUDENT'S GUIDE to the more Correct Understanding of the English Translation of the Old Testament, by reference to the original Hebrew. By WILLIAM WILSON, DD, Canon of Winchester, late Fellow of Queen's College, Oxford. Second Edition, carefully revised. 410. cloth. 25*. YONGE (CHARLOTTE M.)— SCRIPTURE READINGS FOR SCHOOLS AND FAMILIES. By CHARLOTTE M. YONGE, Author of "The Heir of Redclyffe.
Page 2 - CICERO— THE SECOND PHILIPPIC ORATION. From the German of Karl Halm. Edited, with Corrections and Additions, by JOHN EB MAYOR, Professor of Latin in the University of Cambridge, and Fellow of St.
Page 21 - 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 19 - THE ELEMENTS OF GRAMMAR TAUGHT IN ENGLISH, With Questions. Fourth Edition. i8mo. 2s. THE CHILD'S GRAMMAR. Being the Substance of "The Elements of Grammar taught in English," adapted for the Use of Junior Classes.
Page 4 - Thucydides. — THE SICILIAN EXPEDITION. Being Books VI. and VII. of Thucydides, with Notes. A New Edition, revised and enlarged, with a Map. By the Rev. PERCIVAL FROST, MA. late Fellow of St. John's College, Cambridge. Fcap. 8vo.
Page 5 - HELLENICA; OR, A HISTORY OF GREECE IN GREEK, as related by Diodorus and Thucydides ; being a First Greek Reading Book, with explanatory Notes, Critical and Historical.
Page 20 - PROCTER— A HISTORY OF THE BOOK OF COMMON PRAYER, with a Rationale of its Offices. By FRANCIS PROCTER, MA Thirteenth Edition, revised and enlarged. Crown 8vo. loг. 6d. PROCTER AND MACLEAR— AN ELEMENTARY INTRODUCTION TO THE BOOK OF COMMON PRAYER.