95 



We may, if we please, regard our theories as true of an ideal world, 

 and consider that we are comparing its circumstances with our own. 



Let us, then, with Newton, imagine the earth covered with 

 a deep ocean, of density equal to its own and of uniform depth, and 

 consider the tides produced in this ocean by the moon. Were every 

 particle of the earth and ocean attracted by the moon with equal and 

 parallel forces, it is evident that, all the particles yielding equally to 

 the influence of these forces, their relative positions would be 

 unaltered. There would, therefore, be no alteration of the form of the 

 ocean, and consequently no tides. 



The moon attracts each particle of the ocean directly towards 

 herself, with a force which decreases (according to a fixed law) as the 

 distance increases ; this force accordingly differs both in direction 

 and magnitude for each particle, but the solid earth is also attracted 

 by the moon with a certain force ; therefore the difference between the 

 moon's attraction on any particle of the ocean and her attraction on 

 the earth, represents her disturbing force on this particular particle, 

 this disturbing force being diflerent for dififerent particles. 



Again : every particle, of the ocean is also attracted by the earth 

 and the rest of the ocean, or, in other and more familiar words, it 

 gravitates or has weight. 



These two attractions are equivalent, by the first principles of 

 mechanics, to a single attraction, or resultant force, as it is termed. 

 Thus we see that every particle of the surface of the ocean is acted 

 on by what we may term a resultant force. But that the ocean maj- 

 be in equilibrium its surface must be everywhere perpendicular to the 

 directions of the various resultant forces. 



Analysis she\vs that the form of such a surface is a prolate 

 spheroid of small eccentricity (with its axis directed to the moon's 

 centre^. 



In general language, then, we may describe the form of our 

 theoretical ocean as a slightly elongated sphere. 



It is further supposed that at every instant the ocean assumes this 

 form of equilibrium under the action of the forces animating it at 

 that moment. 



We are now in a position to trace the variations in the depth of 

 the ocean at any spot in the course of a day. 



