The Tide-generating Forces 



261 



attractive and centrifugal forces. The numbers indicated give the intensity, 

 with the assumption that m — \. Over the entire hemisphere of the earth 

 which faces the moon, the forces of attraction are greater than the centrifugal 



Fig. 110. Distribution of the total tide generating force of a celestial body in a meridional 



section of the earth. 



forces; on the other hemisphere, the predominance is reversed. It has been 

 found easier to consider separately the distribution of the two components 

 given in equation (VIII. 3). 



The radial component has the same direction as gravity and its intensity 

 is increased and decreased respectively, by very small amounts. It can, there- 

 fore, be considered as a tidal disturbance of the gravity, and it is then 

 advisable to count it positively downwards (same as the force of gravity). 

 From the second part of (VIII. 3) then follows: 



bg = — ^w(cos 2 # + £) . 



(VIII. 10) 



Its largest negative value is found in the zenith and nadir point, the largest 

 positive value on a great circle 90° distant from the zenith point, and the 

 ratio of these values is 2:1. The force disappears on the circles which are 

 at a distance of 54° 43' from the zenith, and the nadir point (nodal lines), 

 respectively. This vertical component of the tidal force causes also an 

 extraordinarily small periodical change in the density of the water-masses; 

 however, this change contributes so little to the motion of the water that 

 it can generally be completely disregarded. 



Whereas the radial component can only influence the magnitude of the 

 gravity very slightly, the horizontal component causes a slight change in its 

 direction. Its main significance for the motions of the water-masses on the 

 earth lies in the fact that its intensity equals the order of magnitude of other 

 forces acting in the horizontal direction, which are mainly gradient forces. 

 Its distribution, according to the first term of (VIII. 3), is expressed by 



K h = msinld 



(VIII. 11) 



