288 Mr. James Croll on the Influence of the 



does, of a solid body or nucleus surrounded by a fluid mass. It 

 is evident that the fluid mass surrounding the solid earth would 

 assume identically the same shape as it would do supposing there 

 were no solid matter. Now in order to know whether the tidal 

 wave rises to the same height on both sides of the globe or not, 

 we have merely to determine whether or not the centre of gravity 

 of the surrounding fluid mass coincides with the centre of gra- 

 vity of the enclosed solid mass. That the two centres must 

 coincide is evident from the fact that the centre of gravity of any 

 mass moving uniformly round a distant centre must remain 

 always at the same distance from that centre, whatever form the 

 mass may assume. The distance of the centre of gravity of the 

 mass from the centre of rotation is determined by the velocity of 

 the motion of the former centre round the latter. Now the centre 

 of gravity of the surrounding fluid, and the centre of gravity of 

 the solid mass, are in the present case moving with the same 

 velocity. Hence both centres must be at the same distance from 

 the centre of rotation, and consequently the solid mass must be 

 exactly in the centre of the surrounding fluid mass. It follows 

 that the depth of the waters, or, which is the same thing, the 

 height of the tidal wave on the opposite sides must be the same. 

 The following is a very simple mode of calculating the height 

 to which the tidal wave will rise at the point B. The distance 

 of the point B from the centre 0' is 6665 miles, and it performs 

 one revolution in 27 days 7 hours 43 minutes and 11 seconds. 

 This point therefore moves round the common centre of gravity 

 0', of the earth and moon, at the rate of 93*6 feet per second. 

 The same point in its diurnal motion round the earth's axis 

 moves at the rate of 1526 feet per second, this being the velo- 

 city of the earth's diurnal rotation at the equator. The height 

 to which the tidal wave will rise at the point B will of course be 

 proportional to the centrifugal force at that point. Now the 

 centrifugal force is as the square of the velocity. And as 34,950 

 feet is the height corresponding to a velocity of 1526 feet per 

 second, 130*7 feet must be the height corresponding to a velocity 

 of 93*6 feet per second; for 



(1526) 2 : (93-6) 2 : : 34950 : 130*7. 



But B is much further from the centre 0' than from the centre 

 ; and as the centrifugal force is in the inverse ratio of the dis- 

 tance from the centre of rotation, we have then 



6665: 3956:: 130-7: 77 feet. 



This is the height to which the tidal wave would rise at the 



point B did the moon move in the plane of the earth's equator, 



and were the entire globe covered with water to the mean depth 



of the ocean, and none of the centrifugal force wasted in friction 



