78 



At Pliiladelphia, the high-water interval is 1.49 hours, and the 

 low-water interval 8.97 hours. The epoch of the M2 component 

 from formula (105) then is 



14°.492(1.49 + 8.97)-90° = 62° 



Its value from harmonic analysis is 49°. 



Formula (105) gives evidently only an approximate value of the 

 epoch of the M2 component. 



143. The S2 component — spring and neap tides. — At stations having 

 a tide of the semidiurnal type, the amplitude of the S2 component is 

 generally from one-sixth to one-half of that of the M2 component. 

 Since the difference in the speeds of these two components is relatively 

 small, the resultant of the two fluctuates slowly from a maximum 

 of M2 + S2, when the generating radii of these components coincide, 

 to a minimum of M2— S2 when they are 180° apart (par. 54), the period 

 of the fluctuation, from maximum to minimum, being the synodic 

 period of the two components, or 360°/(s2—m2) = 354.367 hours. 

 This period is one-half of the lunar synodic month, the average 

 interval from full moon to full moon. 



Other tidal influences disregarded, the high and low waters occur- 

 ring nearest the time at which the resultant of the M2 and S2 com- 

 ponents is at a maximum are respectively higher and lower than at 

 other times, and the tidal range is the greatest. These are the spring 

 tides, and their range is the spring range (pars. 2 and 20). The tides 

 nearest the time at wliich the resultant is a minimum are similarly 

 the neap tides. The times at which the generating radii of the M2 

 and S2 components are in coincidence, and their resultant a maximum, 

 may be called the time of spring tides, although this time is not 

 generally the exact time of either spring high water or spring low water. 

 Similarly, the time at wliich these generating radii are opposed may 

 be called the time of neap tides. Because of the effect of the other 

 components, the average spring range somewhat exceeds 2 (M2+S2) 

 and the average neap range somewhat exceeds 2 (M2 — S2). 



144. Phase age. — The interval between the instant of full or new 

 moon, and the time of spring tides is called the phase age. At the 

 instant of full or new moon, the S2 and M2 components of the equilib- 

 rium tides quite evidently are in conjunction, and the difference in 

 their phases is zero. Since the phases of the corresponding com- 

 ponents of the actual tides differ from those of the equilibrium com- 

 ponents by their respective epochs, 82° and M2°, the difference in the 

 phases of these components of the actual tides at the instant of full 

 or new moon is 82° — M2°; and since the S2 component gains on the 

 M2 component at the rate of S2— m2° per hour, they are in conjunction 



