CONTENTS. 



PART I.— DESCRIPTION. 



Page. 



Introduction 1 



1. Historical statement 1 



2. General explanation 2 



3. Equilibrium theorj^ 4 



4. Astronomical data 10 



5. Degree of approximation 15 



Tidal components 16 



6. Tide-producing force 16 



7. Tide-producing potential 21 



8. Surface of equilibrium 22 



9. Development of equilibrium tide 29 



10. Equilibrium argument 36 



1 1 . Coefficients 40 



12. Factors of reduction 46 



13. The L2 tide 47 



14. The Ml tide 49 



15. Tides depending upon the fourth power of moon's parallax i__ 53 



16. Solar tides 55 



17. Lunisolar Ki and K9 tides 56 



18. Overtides 59 



19. Compound tides 59 



20. Meteorological tides 60 



Analysis and prediction 61 



21. Harmonic constants 61 



22. Observations 61 



23. Summations 63 



24. Stencils . 66 



25. Secondary stencils 70 



26. Fourier series 75 



27. Augmenting factors 85 



28. Reduction of epochs and amplitudes to mean values 89 



29. Inference of constants 91 



30. Elimination 98 



31. Long-period components 101 



32. Analysis of high and low waters 114 



33. Harmonic prediction of tides 118 



34. U. S. Coast and Geodetic Survey tide-predicting machine No. 2_ 123 



35. Tidal currents 138 



36. Forms used for analysis and predictions 142 



PART II.— TABLES. 



Explanation of tables 161 



Tables: 



1. Astronomical constants and formulas frona original sources 172 



2. Astronomical quantities and relations derived from Table 1 173 



3. Principal harmonic components, with arguments, speeds, coeffi- 



cients, and reduction factors _^ 174 



4. Mean longitude of lunar and solar elements for beginning of each 



year 1800 to 2000 176 



5. Differences to adapt Table 4 to any month, day, and hour 178 



6. Values of /, v, ^, v' , and 2v" for each degree of N 179 



7. Values of log Ra. for amplitude of component L2 183 



8. Values of E for argument of component L2 184 



9. Values of log Q^ for amplitude of component Mi 185 



10. Values of Q for argument of component Mi 186 



m 



