13 



This potential is evidently a maximum at Pi and P2, figure 5, 

 where d=0 and 180°, respectively, and a minimum on the great 

 circle P3P4, where 0=90°. The difference in the potential wiU 

 therefore tend to cause the water of the oceans to pile up toward Pi 

 and P2 as was shown from the analysis of the tide-producing forces 

 in paragraph 18. To an observer at any point on the great circle 



G- 



Figure 5. 



P3P4 the moon is on the horizon; at Pi directly overhead. The tide- 

 producing potential at any point is therefore a minimum when the 

 moon is on the horizon, and a maximum when it attains its greatest 

 altitude above (or below) the horizon. 



'^.^^^^=^'=^ 



THE SURFACE OF EQUILIBRIUM AND THE EQUILIBRIUM TIDE 



26. Lunar equilibrium tide. — If the earth, instead of rotating daily 

 about its axis, rotated once in a lunar month, so that the same side 

 of the earth was al- 

 ways presented to the 

 moon, the lunar tide- 

 producing force evi- 

 dently would create 

 two permanent bulges 

 or distortions in the 

 surface of the oceans, 

 which would be di- 

 rected toward the 

 moon on one side 

 of the .earth, and in 

 the opposite direction 

 on the other. The surface of the oceans would then conform 

 to the surface of equilibrium resulting from the joint action of 

 the force of gravity and the lunar tide-producing force. If 

 the oceans entirely covered the earth, this surface of equilibrium 

 evidently would take the form of a prolate spheroid of revolution, 

 with its axis pointing toward the moon, as shown in figure 6. The 

 displacement of this theoretical tidal surface of e(;iuilibnum from the 



Figure 6.— Tidal surface of equDihrium. 



