228 Wisconsin Academy of Sciences, Arts, and Letters. 



lating course about the sun and the common center or point of 

 revolution between the earth and moon describes the otbit. 



The ultimate result of these antagonistic efforts is, tTiat the 

 point of revolution between the earth and moon fluctuates be- 

 tween the earth's center and the common center of gravity of the 

 two bodies. 



The earth revolves about the common center of revolution, 

 which lies within its own volume, with the same regular velocity 

 that the moon revolves in her orbit, Th's motion produces a 

 centrifugal force, which, owing to eccentricity, is tangen!; to the 

 earth only in the plane of the moon and the axis of rotation ; the 

 constant change of the axis causes this force to fl.u'jtuate between 

 T^il and maximum twice in a lunation, that is, ml at quadratures 

 and maximum at syzygies. 



The force thus produced, which I will call centrifugal prepon- 

 derance, varies between the 1-900 and 1-500 of the centrifugal 

 force due to the earth's rotary motion. The effest of the earth's 

 rotation was to produce the spheroidal form of the eanh and its 

 present oflEiee is to maintain it with a flattening at the poles of 

 nearly 26 miles ; if this force were to cease, the oceans would 

 retire to the poles. 



Now a force equal to 1-900 part of this, acting uniformly and 

 constantly, would, if we simply consider the result proportionate 

 to the force, cause a flattenirg of 150 feet, but as we shall see, this 

 force does not act uniformly or constantly, neither have we a 

 continuous mobile surface to consider acted upon, so that this 

 change of form is impossible. Should we however assume a uni- 

 form surface of water and taking this force as acting in the mean 

 one half the time on one-tenth of the surface on opposite sides, 

 we would have a tide of seven feet which agrees with the pro- 

 tuberances of the Elipsoid of water produced by some highly 

 scientific investigations. 



The eccentricity of the force causes the same to deviate from 

 .the centrifugal force due to the earth's rotation everywhere on the 

 surface excptrng at two points ; these are, the p »int directly 

 under the moon and the point opposite. At other points in the 

 plane of the moon's orbit it has a tendency of only slightly de- 



