40 



the fourth power of the moon's parallax is very small, and that it goes 

 through three maxima and minima as the zenith distance of the moon 

 makes a cycle from 0° to 360°; wliile the principal part of the tide, 

 due to the third power of the moon's parallax, goes through two 

 maxima and minima during this cycle. It is not difficult to see, 

 therefore, that the fluctuations of both the equilibrium and the actual 

 tides due to the fourth power of the moon's parallax go through three 

 fluctuations each lunar day. This tide is therefore approximated by 

 the component: 



y=Ms cos (ms^+a) (42) 



where nis is three times the speed of the lunar day, or 43°.476, 156,3 per 

 mean solar hour. Additional components to account for the variations 

 in this part of the tide due to the changing declination and distance of 

 the moon, and other variations from this primary component, are too 

 small to be recognized. 



75. Resume of components identified. — For the purpose of harmonic 

 analysis, it is convenient to group together the components whose 

 speeds are multiples of another. The components identified in the 

 preceding paragraphs fall into groups and individual components as 

 follows : 



Table II 



Symbol 



Mi 



M2 



Ms 

 M4 

 Me 

 Ms 





O, 

 Pi 

 Qi 



Ji 



N2 

 L2 

 T2 

 E2 



Name 



Smaller lunar elliptic, diurnaL 



Principal lunar semidiurnal 



From 4th power moon's parallax. 



Lunar overtide 



.-._do._ 



do 



M Group 



Meteorolog'ica] 



Principal solar semidiurnal. 



Solar overtide 



do 



S Group 



Lunisolar diurnal 



Lunisolar semidiurnal. 



K Group 



Individual Diurnal Components 



Principal lunar diurnal 



Principal solar diurnal 



Larger lunar elliptic diurnal- 

 Small lunar elliptic diurnal.. 



Individual Semidiurnal Components 



Larger lunar elliptic semidiurnal. - 

 Smaller lunar elliptic semidiurnal. 

 Larger solar elliptic semidiurnal... 

 Smaller solar elliptic semidiurnal- , 



Speed in 



degrees per 



mean solar 



hour 



14. 492, 052, 1 

 28.984,104,2 

 43.476,156,3 

 57. 968, 208, 4 

 86. 952, 312, 6 

 115.936,416,8 



15.000,000,0 

 30.000,000,0 

 60.000,000,0 

 90.000,000,0 



15.041,068,6 

 30. 082, 137, 2 



13. 943, 035, 6 

 14.958,931,4 

 13. 398, 660, 9 

 15.585,443,3 



28. 439, 729, 5 

 29. 528, 478, 7 

 29. 958, 933, 3 

 30.041,066.7 



