Introduction to the Science of Timekeeping .......................................... 8

Precise Timing Applications Pervade Our Society ................................ 10

Clocks and Timekeeping............................................................................ 14

The Definition of the Second and its General Importance .................. 19

Historical Perspective ................................................................................ 19

An Illustrative Timekeeping Example ..................................................... 22

UTC, Official Time for the World ............................................................. 26

GPS Time and UTC ..................................................................................... 30

Accuracy and Stability of UTC .................................................................. 31

Einsteins Relativity and Precise Timekeeping ...................................... 36

How to Access UTC .................................................................................... 39

Future Timing Techniques......................................................................... 44

Global Navigation Satellite System Developments ................................ 47

UTC and the Future .................................................................................... 52

Conclusions ................................................................................................. 53

Acknowledgments ...................................................................................... 54

Appendix A: Time and Frequency Measures Accuracy, Error,

Precision, Predictability, Stability, and Uncertainty ............................. 56

Appendix B: Stability Analysis of Harrison-like Chronometers ........... 66

Appendix C: Time and Frequency Transfer, Distribution

and Dissemination Systems ....................................................................... 72

Glossary and Definitions............................................................................ 82

Bibliography ................................................................................................ 85