Theory of the Tides 



277 



ever, the observed tides are generally much greater than those derived from 

 the equilibrium theory. On the other hand, the daily inequality of the theory 

 agrees with the observations insofar as it will disappear when the tide-generat- 

 ing body is at the equator and will reach a maximum at the times of greatest 

 northerly and southerly declination. The magnitude of the daily inequality 

 does not agree with the theory, and in many localities the tide is largest when 

 it should be the smallest according to the theory and vice versa. Furthermore, 

 the theory requires that at the syzygies (full and new moon) high water occurs 



♦ 20 

 ♦10 





 Equator 



♦ 10 

 



I0°N . l0 



♦ 10 

 



30°S -io 





60° 



120° 60° 240° 300° 360° 



Longitude 



Fig. 120. Profile for three circles of latitude from Fig. 119. 



exactly at noon and at midnight; hence, that the lunar tidal interval is zero 

 for all localities. According to experience, this interval can have any value 

 between zero and 6 h, and it is apparent that we have here a downright contra- 

 diction between the observations and the theory. 



The equilibrium theory, therefore, is unfit to explain the actual tides of 

 the oceans. The main reason is, no doubt, that it attributes certain properties 

 to the water which it definitely lacks. The theory requires that, at any mo- 

 ment, there is equilibrium between the tide-producing forces and the gradient 

 forces of the zonal spheroid. Inasmuch as the tide-producing celestial bodies 

 change their position to the earth so -rapidly after all, tremendous displace- 

 ments of water-masses should take place within the ocean with great velocities 

 which never occur in nature, and the water-masses would go beyond their 

 position of equilibrium because of its inertia. Hence, the equilibrium theory 

 requires that the water be deprived of its inertia, whereas its gravitational 

 properties should be kept. Such an assumption, however, has no basis 

 and can only give approximate results, if the tidal forces vary very slowly. 

 This theory, therefore, can be applied at the most to the long-period partial 

 tides. 



Despite this bad agreement, it has frequently been attempted to improve 

 the noticeable difference between the time of occurrences of high water and 

 the time of maximum tide potential. The constant C in (IX. \a) is determined 



