Tidal Wave on the Earth's Rotation. 287 



earth on the centre causes the water of the ocean to rise 34,950 

 feet at the point B, then a rotation on the centre 0' must also 

 cause the water to rise at the same point. The same mechanical 

 cause which produces the effect in the first case must operate in 

 the second. This is perfectly evident. As 0', the common 

 centre of gravity of the earth and moon, is situated in the inte- 

 rior of the earth, all parts of the earth must move round this 

 point once a month as truly as they do round the centre once 

 a day. The point B being further from the centre of rotation 

 than any other point on the surface of the globe, the waters of 

 the ocean will rise higher at this place than anywhere else. This 

 rise constitutes what is called the tidal wave. The wave of course 

 remains permanently situated at the point B, for this point never 

 changes either in relation to the moon or to the centre of rota- 

 tion. But as the earth revolves round the centre once a day, all 

 parts of the equator must within that period pass under this 

 point. The earth's surface at the equator must be moving under 

 the tidal wave at a rate of 1526 feet per second, and consequently 

 the waters of the ocean must be continually rising so as to main- 

 tain the wave continuously at B. At the point D, on the side 

 toward the moon, the centrifugal force will be but small, this 

 point being situated only 1261 miles from the centre of rotation. 

 But it will be observed that the attraction of the moon at this 

 place is not only stronger than at B, but is also acting in the 

 same direction as the centrifugal force. Consequently the waters 

 must rise at D also. At the points A and C the centrifugal 

 force acts in lines parallel to the earth's surface; hence the 

 waters at these places cannot rise, they will simply recede in the 

 direction of the point B. 



That the tidal wave must rise to the same height on both 

 sides of the earth will appear evident from the following con- 

 siderations. 



Let us suppose that our globe consists entirely of a fluid mass 

 revolving with a uniform velocity round the common centre of 

 gravity of the earth and moon once a month. TTe shall in the 

 mean time leave out of consideration the diurnal motion of rota- 

 tion. It can be easily demonstrated that such a fluid mass would, 

 under the specified conditions, assume the form of an oblong 

 spheroid with its greater axis pointing in the direction of the 

 moon. In other words, the waters on the side furthest from the 

 moon would, under the influence of centrifugal force, recede to 

 a certain extent; and the waters on the opposite side would, 

 under the influence of centripetal force, be drawn toward the 

 moon to the same extent. Here we have the rise constituting 

 the tidal wave on both sides of the earth. Suppose now that 

 the earth, instead of being a fluid mass, consists, as it really 



