77 



Similarly, at each high water of the equilibrium tide 



t=-{y^-{-u)jm2 (101) 



The nature of the equilibrium tide is such that the high waters of 

 its M2 component must occur at the moon's transits across the meri- 

 dian of the tidal station. When the origin of time is taken at a lunar 

 transit, equation (101) shows that V^-^rU must be zero. The time of 

 high water of the M2 component of the actual tide is then, from equa- 

 tion (100), M2°/m2 hours after a lunar transit. 



The M2 component is the dominant one when the tide is of the semi- 

 diurnal type, and largely determines the time of high water of the 

 entire tide. The other semidiurnal components, alternately advance 

 and retard the time of high water. The diurnal components and lunar 

 overtides may produce a systematic difference in the time of high 

 water. Denoting this systematic difference by M, the average inter- 

 val between a lunar transit and the time of high water at a station is 

 then (M2°/m2) + M. This average interval is the high-water interval at 

 the station (paragraph 8) and is designated as HWI. It follows 

 therefore that: 



M2°=m2(HWI-A0 (102) 



The low water of the Mo component similarly occurs when: 



m2#-M2°=±180° 

 or when 



«=(M2°±180°)/m2 (103) 



Since the diurnal components and lunar overtides retard (or 

 advance) the time of low water by the same amount that they advance 

 (or retard) the time of high water 



M2°=m2(LWI+A0T180° (104) 



where LWI is the low-water interval at the station. 



Combining equations (102) and (104) to eliminate M, and sub- 

 stituting for m2 its numerical value: 



M2° = 14°.492(HWI+LWI)T90° (105) 



The negative sign is applied to the last term when the HWI is less 

 than the LWI. 



For example, at Fort Hamilton, New York Harbor, the high-water 

 interval is 7.67 hours and the low-water interval is 1.64 hours. The 

 epoch of the M2 component, from formula (105), then is: 



14°.492 (7.67 + 1.64) +90°=225° 



Its values from harmonic analysis is 221°. 



