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 37
Page 7
... expression by diffe- rentiating it with respect to c , and is attraction of shell = 4πρε . δε a2 mass of shell a2 COR . 2. Therefore , the attraction of a heterogeneous sphere on an external particle will be the same as if the whole ...
... expression by diffe- rentiating it with respect to c , and is attraction of shell = 4πρε . δε a2 mass of shell a2 COR . 2. Therefore , the attraction of a heterogeneous sphere on an external particle will be the same as if the whole ...
Page 19
... EXPRESSIONS OF THE FORCES . E 19. The earth having been reduced to rest by the process described in Art . ( 9 ) , its centre may be taken as origin of coordinates , the fixed plane of reference as plane of xy and the line ET as axis of ...
... EXPRESSIONS OF THE FORCES . E 19. The earth having been reduced to rest by the process described in Art . ( 9 ) , its centre may be taken as origin of coordinates , the fixed plane of reference as plane of xy and the line ET as axis of ...
Page 25
... expressions of the accelerating forces on M are rigorous , and can be expressed in terms of the masses and coordinates of the bodies ; but since our investigations will be carried only to the second order , it will be sufficient if , in ...
... expressions of the accelerating forces on M are rigorous , and can be expressed in terms of the masses and coordinates of the bodies ; but since our investigations will be carried only to the second order , it will be sufficient if , in ...
Page 28
... expressions for the forces ( 23 ) , will either enter to the second power or else in combination with the disturbing force . When this is done the equations become integrable , and values of u and s may be obtained in terms of correct ...
... expressions for the forces ( 23 ) , will either enter to the second power or else in combination with the disturbing force . When this is done the equations become integrable , and values of u and s may be obtained in terms of correct ...
Page 29
... expressions for the forces , also express these as functions of 0 , and we can proceed to a higher approximation . The new approximate values of P , T , S are then made use of to reduce the second members of the differential equations ...
... expressions for the forces , also express these as functions of 0 , and we can proceed to a higher approximation . The new approximate values of P , T , S are then made use of to reduce the second members of the differential equations ...
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.