NEWTON S PRINCIPIA. 287 



Let us imagine that a uniform channel is cut round the 

 earth at the equator and filled with water : let it be sup 

 posed that this fluid is disturbed by the action of the sun 

 or moon; supposed for simplicity also to move in the 

 equator. Newton endeavoured to discover in what man 

 ner the water would move in this imaginary channel, 

 Book I., Prop. LXVI., Cor. 19. In considering the motion 

 of a satellite supposed when undisturbed to describe a 

 circle round the earth, Newton has shown that the 

 disturbing force will in two different ways cause the orbit 

 to become slightly oval, the earth remaining in the centre 

 and the greater axis being perpendicular to the straight 

 line joining the sun and the centre of the earth. This is 

 somewhat parallel to the case in point. If each particle 

 of water were kept in its place by its centrifugal force 

 they would tend to rise at the quadratures and sink at the 

 syzygies, they would be swifter at the syzygies and slower 

 at the quadratures ; they would ebb and flow in its 

 channel after the manner of the sea. But the analogy is 

 not perfect, for the water is supported, not by its centri 

 fugal force, but by the channel in which it flows. We see, 

 however, that an ebbing and flowing of the sea will be 

 produced, though the points of greatest and least height of 

 water may be different. This reasoning applies whether 

 the disturbing body be the sun or moon. 



Though, therefore, by this reasoning we cannot deduce 

 a perfectly accurate theory of the tides, yet we are able to 

 perceive that the sea ought to rise and fall twice in each day. 

 The moon will form at any place two high tides and two 

 low tides in the interval between leaving the meridian of 

 that place and returning to it again, that is, in a lunar day. 

 The sun will also at the same place form two high tides 

 and two low tides in the interval between leaving the 

 meridian and returning to it again, that is, in a solar day. 



