Sir Isaac Newton. 



Moon and Sun, but it was not until Newton's time that we were 

 given a rational explanation of the link. In his Principia, published 

 in 1687, Newton showed that the tides are one of the consequences 

 of the laws of gravitation. Every particle of matter on the Earth 

 is attracted by the Moon, and the force of attraction is directed 

 toward the Moon's center; also, the farther away from the Moon's 

 center the particle is, the weaker the attracting force. So the force 

 varies slightly in both direction and in strength, depending on the 

 position of the particle on the Earth. It is this variation in the 

 attracting force that causes the ocean waters to move to and fro 

 over the Earth's crust and so produce the tides. As we might expect, 

 the tidal forces tend to cause the water on the side of the Earth 

 facing the Moon to be heaped up, but a similar bulge also forms 

 on the opposite side of the Earth. 



Because the ocean waters on the far side of the Earth (most 

 distant from the Moon) are the least affected by the Moon's gravita- 

 tional attraction, they tend, in a sense, to be left behind and so form 

 a far-side bulge. 



We know that the Sun also exerts a tide-generating force on the 

 Earth's waters. It may seem surprising that the Sun, nearly twenty- 

 five million times more massive than the Moon, does not have a 

 greater effect. But mass is not the only key to the explanation. 

 Although tidal force is directly proportional to the mass of the 

 heavenly body concerned, it is also inversely proportional to the 

 cube of its distance. The Sun's greater distance from us, then, is 

 the dominating fact, with the result that its ability to raise tides 

 on Earth is less than half that of the Moon. 



Although we can calculate exactly the tide-generating forces at 

 every point on the Earth's surface, we have yet to reach a complete 

 understanding of the movements of the waters of the oceans and 

 seas in response to these forces. Newton himself found a solution 

 of sorts : he imagined an ideal ocean that covered the whole earth 

 and he assumed that its water could respond instantly to the 

 changing tidal forces. According to this solution, known as the 

 equilibrium tide, the surface of the world ocean would rise in a 

 bulge reaching its maximum height at the point directly below the 

 Moon. At the same time a similar bulge would form on the oppo- 

 site side of the Earth. As the Earth rotated on its axis, each point 

 on the surface would have two high waters and two low waters 

 each lunar day. 



With the same hypothetical ocean, the Sun would tend to pro- 

 duce its own equilibrium tide. Now if we consider the combined 

 action of both Moon and Sun, we can see how the alternation of 

 spring and neap tides occurs. When the Earth, Moon, and Sun are 

 in Hne (at either new or full Moon) the high waters produced 

 individually by solar and lunar attraction reinforce one another, so 

 a tide of maximum range occurs. When the Sun and Moon form 

 a right angle with the Earth (at the first or third quarter of the 

 Moon), the solar and lunar tides oppose one another, resulting in 

 a tide of minimum range. 



Newton's imaginary world ocean with its equilibrium dde, 

 although greatly oversimplified, explains many of the features of 

 the tides. But there are other influences at work. In 1775 the French 

 mathematician Laplace showed that the tidal picture is made much 

 more complex because of the inertia of the ocean waters and the 



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