CHAPTER 1 Introduction 1-3

CHAPTER 2 Some Geometry 4-11

Some Differences Between Plane and Spherical Geometry
4

General Definitions 5

Angles on a Sphere 7

Distances Between Points on the Surface of a Sphere 9

Definition of Polygons on a Sphere 9

Spherical Triangles 10

Construction of the Polar Stereographic Map 13

What is a Straight Line on the Polar Stereographic Map? 15

The Nature of Pattern Distortions Created by the Polar Stereographic Map
17

The Irregular Appearance of the Projection of the Centers of Circles 21

All Circles on the Earth's Surface Project as Circles on the Map 22

The Value of the Angle Between any two Arcs on the Surface of a Sphere
is

Exactly Reproduced on the Polar Stereographic Map 26

Space and Some of its Features 28

Space Filling Patterns on a Two-Dimensional Surface 34

Principles of Closest Packing of Spheres 41

Examples and Experiments in Closest Packing of Spheres 44

Angles of the Hexagon 48

General 50

The Principle of Similitude 50

Kepler's Laws 51

Wolf's Law 52

Rings and Spokes of Saturn 53

Roche's Law 53

Laws of the Atom 54

General 58

Equilibrium 59

Oscillations and Resonance 59

Harmonic Movement 60

Fourier Analysis 61

Wave Pulses 63

Interference 63

Definition of Symmetry 66

Classes of Symmetry 67

Types of Symmetry Operations 68

Symmetry Along a Straight Line 71

Dilation Symmetry 71

Symmetry in a Network of Points 71

Equivalent Symmetry Points 76

Symmetry of Averages 76

How Many Points Will be Crossed by anyStraight Line in a Regular Network?
77

Symmetry and Equilibrium 79

The Conic Sections 82

Surfaces of Revolution 84

Collapseof Cylindrical Structures 86

The Splash of a Drop 89

The Center of a Structure is Related to its Shape 89

Two Modes of Vibration 92

Some Differences Between the Hemispheric Cap of Air and Chladni Plates
94

VII

Everything is Packaged in Quantum Units 96

Some Factors Determining the Quantum Sized Vortex on a

Surface Weather Map 97

"Diffraction Grating" for Finding the Quantum Vortex and also

for Exposing Simple Geometric Configurations 99

Construction of theWeatherTool 102

Other Possible Weather Tools 103

Why December 7,1950 was Chosen for Analysis 107

Why June 6,1944 was Chosen 108

Some Rules Followed in the Drawing of the Charts 108

The Identification Chart 109

Some Unusual Aspects of the Charts 111

Some Simple Definitions of Simple Weather Terms 111

What is the Center of a Low or High and How is it to be Determined? 112

Two Types of Chart Analysis: Circumferential and Radial 114

Some Rules Followed in Drawing the Circumferential Charts
115

CHAPTER 14 June6,1944 320-322

CHAPTER 15 Some Firsts in Meteorology 323-325

CHAPTER 16 Problems Following Discoveries 326-330

About the Author 331

About the Assistant 331