The Hill-Brown Theory of the Moon's Motion

Its Coming-to-be and Short-lived Ascendancy (1877-1984) Contents

Preface vii

Acknowledgments '. xi

Part I Hill Lays the Foundation (1877-1878)

1 George William Hill, Mathematician 3

2 Lunar Theory from the 1740s to the 1870s - A Sketch 9

3 Hill on the Motion of the Lunar Perigee 31

4 Hill's Variation Curve 55

5 Early Assessments of Hill's Lunar Theory 69

Part II Brown Completes the Theory (1892-1908), and Constructs Tables (1908-1919)

6 E. W. Brown, Celestial Mechanician 75

7 First Papers and a Book 79

8 Initiatives Inspired by John Couch Adams' Papers 109

9 Further Preliminaries to the Systematic Development 123

10 Brown's Lunar Treatise: Theory of the Motion of the Moon; Containing a New Calculation of the Expressions for the Coordinates of the Moon in Terms of the Time 137 xiv Contents

11 A Solution-Procedure Without Approximations 157

12 The "Main Problem" Solved 167 13 Correcting for the Idealizations: The Remaining Inequalities 171

14 Direct Planetary Perturbations of the Moon (The Adams Prize Paper) 181 15 Indirect Planetary Perturbations of the Moon 193 16 The Effect of the Figures of the Earth and Moon 201 17 Perturbations of Order (SR)2 207 18 The Tables 209 19 Determining the Values of the Arbitrary Constants 219 20 Ernest W. Brown as Theorist and Computer 225

Part III Revolutionary Developments in Time-Measurement, Computing, and Data-Collection

21 Introduction 237

22 Tidal Acceleration, Fluctuations, and the Earth's Variable Rotation, to 1939 239 23 The Quest for a Uniform Time: From Ephemeris Time to Atomic Time 285 24 1984: The Hill-Brown Theory is Replaced as the Basis of the Lunar Ephemerides 305

25 The Mathematical and Philosophical Interest in an Analytic Solution of the Lunar Problem 313 Appendix "Observations on the Desirability of New Tables of the Moon" (undated typescript of 3 pages, possibly intended for Newcomb; Naval Observatory Library, file of George William Hill) 319 Index 321