11 



units of mass at one unit of distance. The ratio of the vertical com- 

 ponent of the lunar tide-producing force to the force of gravity is^ 

 from equation (7) : 



{Mu.a]m){?> cos- e-l)!(E(x/a') = {M/E)(a'/R'){S cos^ d-1) 



This ratio reaches a maximum of 2{M/E)(a^/R^) when d=0. 



Since the mass of the earth is approximately 80 times the mass of 

 the moon, and its distance from the moon approximately 60 times the 

 earth's radius : 



M/E= 1/80 a/R=l/QO 



W" 

 » 



Qy ^'c> 3 (J 



U" 



\ Earth / 

 \ / 



Figure 3. — -Phases of moon. 



The substitution of these values shows that the maximum value of 

 the vertical component of the lunar tide-producing force is about 

 1/8,640,000 of the force of gravity. The maximum value of the hori- 

 zontal component is similarly found to be about 1/17,280,000 of the 

 force of gravity. The maximum values of the components of the 

 solar tide-producing force are less than half of those of the lunar com- 

 ponents. Such small forces evidently are not directly measurable 

 by the most delicate instruments, nor can they sensibly affect the 

 levels of limited bodies of water even as large as the Great Lakes. 

 The accumulated effect of these small forces over the vast areas of 

 the oceans is however sufficient to produce the tides. 



THE TIDE-PRODUCING POTENTIAL 



22. The effect of the tide-producing forces upon the waters of the 

 oceans is indicated by the ])otentials of these forces. The potential 

 of a force at any point is defined as the work required to move a 

 unit of mass against the force to a position where the force is zero. 

 Since the tide producing force is zero at the earth's center, the tide- 

 producing potential at P, distant r from the center C (fig. 4) is the 



192750—40 2 



