398 NEWTON S PRINCIPIA. 



and the water on the earth. But she attracts the water 

 immediately under her with greater force than she attracts 

 the centre of the earth, and she attracts the centre of the 

 earth with greater force than the water on the opposite 

 side of the earth. But the tides are formed by the position 

 the water assumes relative to the earth. We must there 

 fore consider this as reduced to rest by a force supposed to 

 be applied to every particle of the earth and water equal 

 and opposite to the force with which the moon attracts the 

 centre of the earth. The particles of water immediately 

 under the moon will therefore be drawn towards the moon ; 

 those immediately opposite will appear to be drawn from 

 the moon. Thus the water will rise and form a high tide 

 both on that side next the moon and also on the other. 

 Let us now suppose the whole earth covered with water. 

 Each particle of the fluid is under the action of, first, the 

 attraction of the earth, and, secondly, the attraction of the 

 stratum of liquid surrounding the earth : this will depend 

 on the form its surface will assume under the action of all 

 the forces ; thirdly, the disturbing force of the luminary. 

 The form of the water must be determined by means of 

 the equations of fluid equilibrium. The result obtained is 

 that the form will be very nearly a spheroid whose longer 

 axis points to the luminary. If be the zenith distance of 

 the moon at any place and any instant, c her distance, a 

 the mean radius of the earth, a the radius of the solid 

 nucleus of the earth, E and M the masses of the earth and 

 moon, p, p the mean density of the earth and the density 

 of the sea; then the height of the tide at the given place 

 and at the given time will be 



5 M 



7 

 4 



(3 cos 2 0-1). 



The greater the depth of the ocean, or the less of is, the 

 greater is the height of the tide. 



