By substitution from equation (4) for G into equation (3), letting M equal M2 be tlie 

 mass of the Moon or Sun, and d the distance between tlieir centers, the law which governs 

 the gravitational force between them may be stated as 



- <J) (") 



(5) 



where F is the tide-generating force per unit mass. 



The forces responsible for tide generation can be visualized in Figure 8: let C be the 

 center of the attracting body, Sun or Moon, tlie center of the Earth, and P an arbitrary 

 point at a distance r from the center of the Earth, and z the angle COP. The force along 

 Une OC attracting a unit mass at the center of the Earth to the other body is given by 



Foe = Pg (I)' f W 



The force along line PC attracting a unit mass at P to the other body is given by 



»c=Pg(iyf O 



Figure 8. Force diagram for the generation of astronomical 

 tides (after Schureman, 1941). 



The vector difference between the forces described by equations (6) and (7) is tlie 

 tide-generating force. To compute this difference, it is necessary to resolve the forces into 

 components along a common set of axes. The most useful axes are defined by 

 Une OP, directed toward the center of the Earth, a line directed north-south and a line 

 directed east-west in the plane, orthogonal to OP which passes tlirough point P. The 

 component of the tide-generating force, directed along a line normal to the surface of the 

 Earth, acts only to cause a slight change in the effective value of g by about ±0.0002 of the 

 mean value. This perturbation in the effective gravitational attraction is too small to have 

 any practical effect. The component of the tide-generating force normal to the Earth's 



27 



