262 



The Tide-generating Forces 



It is quite apparent that the horizontal component vanishes in the zenith 

 and the nadir point, as well as on the great circle 90° distant therefrom and 

 attains a maximum value on circles 45° distant from these points. On the 

 hemisphere facing the moon, this horizontal force is directed concentrically 

 towards the zenith point; on the other hemisphere it is directed towards 

 the nadir point. This system of forces has a fixed position in regard to the 

 tide-producing body; if the latter shifts, the system of forces follows this 

 movement. Figure 1 1 1 shows, at the left, the distribution of the horizontal 



Fig. 111. Left: distribution of the horizontal component of the tide generating force when 

 the moon is in the equator. Right: same when the moon has a positive declination of 28° N. 



components when the disturbing body is located in the equatorial plane 

 of the earth; at the right when it stands 28° above same on the northern 

 hemisphere. 



This system of forces is fixed in relation to the direction of the moon, 

 meanwhile the earth rotates once a day around its axis, and these cause the en- 

 tire system of tide-producing forces to become periodical for a given point of the 

 earth's surface. If, for example, the moon's orbit is in the plane of the equator 

 (see Fig. 112), it will appear to somebody who looks at the earth from the 

 outside as if the observer is first in A x . The rotation of the earth moves him 

 to A 2 . The tide-producing force is directed towards the south just before 

 reaching A 2 and reaches its maximum value after three lunar hours in 

 a point A 3 . Then the force decreases to zero at a point A A , where the moon 

 sets. The force then changes its direction, reaches' a maximum after 3 lunar 

 hours, etc. The tidal force, therefore, changes its direction and force, with 

 a period equivalent to a half lunar day. Both components have obviously 

 the same period, but we can derive from the relations (VIII. 9 and 10) that 

 the phase of the horizontal component lags one-quarter period (3 h) behind 

 the vertical component. 



