The Tide-generating Forces 



257 



The tide-generating force can easily be computed for the zenith and nadir point. The forces 

 of attraction and the centrifugal forces act in this case in the same direction and their resultants 

 can be simply obtained by adding and subtracting their magnitudes respectively. The direction 

 of the force towards the moon shall be positive. If R is the radius of the earth and a the distance 

 between the centre of the earth the centre of the moon, M is the mass of the moon, ft an element of 

 mass of the earth at the point under consideration, we obtain for the points 



Centre of 



It is easy to see that these values are the maxima tide-producing forces which can be found on 

 the earth's surface. Consequently, the tide-producing forces is proportional to the mass of the 

 disturbing body and inversely proportional to the cube of the distance of the earth to the disturbing 

 body. In the hemisphere facing the moon, the forces act in the direction towards the disturbing 

 body, in the other hemisphere they act in the opposite direction, i.e. away from the moon. 



It is easy to compare the tide-producing forces of the moon with those 

 of the sun. For a point of the earth, the tide-producing force of the sun, 

 according to (VIII. 2), is given by x/LtS(2R/s 3 ), in which S is the mass of the 

 sun and s the distance sun-earth. When E is mass of the earth, the ratio of 

 this force to that of the moon is then 



5 a s 333,200£ (60Rf 



M s 3 1/81-5JE7 (23,360/?) 3 



= 0460 



4 1 

 9<2 



The mass of the sun being 27 million times that of the moon, the tide- 

 producing force of the sun should be 27 million times that of the moon. 

 However, the sun's distance from the earth is 389 times the moon's distance. 

 Consequently, the sun's tide-generating force is to that of the moon in the 

 ratio of 27 x 10 6 to 390 3 or 1:217, less than half that of the moon. This 

 definitely explains why the influence of the moon is preponderant in 

 ocean tides. 



* The centrifugal force, according to (VIII. 1), has been equalized in the centre of the earth 

 with the negative attractive force. 



t If R 2 la 2 is neglected against 2R\a then 



1 1 / 2R 



= - ldz — 



(aTR) 2 a 2 \ a 



Rja being equal to 1/60, this means neglecting 1/3600 against 1/30. 



17 



