CONTENTS 



PAGES 



The Former Rates of the Earth's Rotation and their Bearings on its 



Deformation 1-59 



The Astronomical Deductions 6-20 



Considerations Based on the Older Cosmogonies 6-8 



Considerations Based on the Planetesimal Theory 8-14 



Genesis of the Moon 14-20 



Evidences of a Present Change of Rotation 20 



Deductions from the Tides Themselves 21-46 



Tidal Phenomena of the Atmosphere 21-23 



Tides of the Lithosphere 23-25 



Pulsations of the Lithosphere 25-31 



Tides of the Hydrosphere 31-37 



More Radical Mode of Treatment 37-46 



Geological Evidences 46-59 



Evidences from the Lithosphere 46-54 



Evidence from the Hydrosphere 54-57 



Minor Evidences 58 



Accelerative Agencies 58-59 



Conclusion 59 



The Rotation Period of a Heterogeneous Spheroid 63-67 



The Loss of Energy by Friction of the Tides 71-75 



Certain Relations among the Possible Changes in the Motions of Mutu- 

 ally Attracting Spheres when Disturbed by Tidal Interactions. 79-133 



Introduction 79-83 



General Equations 84-86 



Laplacian Law of Density 87 



Moment of Inertia for the Laplacian Law of Density 88 



SpeciatCase i = t\ = 03 = e = <S = 89-94 



Application of Section V to the Earth-moon System 95-99 



Caset = ii = 1*2 = a^^O e=0 aS = 100-104 



Application of Section VII to the Earth-moon System 105 



Application to Binary Star Systems 106-1 10 



Casei = ii = t2=0 0^=0 e^O <S = 111-115 



Application of Case X to the Earth-moon system 116 



Case 1:4:0 ti = 02 = e = S = 117-118 



Application of Case XII to the Earth-moon System 119 



Case t = ti = e = a^^O S^O 120-125 



Secular Acceleration of the Moon's Mean Motion 125-126 



Summary 127-133 



Notes on the Possibility of Fission of a Contracting Rotating Fluid 



Mass 137-160 



Introduction 137-138 



Ellipsoidal Figures of EquiUbrium of Rotating Homogeneous Fluids 139-141 



Poincar^'s Theorems Respecting Forms of Bifurcation and Exchange of Sta- 

 bilities 142-144 



Figures of EquiUbrium of Rotating Heterogeneous Fluids 145-147 



Equations of EquiUbrium for Constant Moment of Momentum 148-149 



Application to the Solar System 150-152 



Application to the Binary Stars 153-157 



Summary 158-160 



iii 



