NEWTON S PRINCIPIA. 289 



low tide formed by the moon. They tend to neutralise 

 each other. The high tides will be lower and the low 

 tides higher than at other times. These are called Neap 

 Tides. 



Thirdly, The effects of the luminaries depend on their 

 distance and vary inversely as the cubes of their distances. 

 Hence the respective tides of the sun or moon are greatest 

 when the luminary is in perigee and least when in apogee. 

 In winter the solar tides are therefore greater than in the 

 summer, and the lunar tides have like changes every fort 

 night. 



Fourthly. The effects of the disturbing bodies depend on 

 their declinations. If the moon were at the pole, it would 

 attract the water without any daily remissions of its action. 

 The water would assume a position of equilibrium, and 

 there would then be no daily tides. Thus as the luminaries 

 decline from the equator, their effects become less and less. 



Fifthly. The river tides are formed by the propagation 

 of the tidal disturbance from the seas where they were 

 formed. In these therefore the greatest tides occur later 

 than they should do according to the above statement. 



Sixthly. The effects of the disturbing bodies depend on 

 the latitude of the place. Suppose the attraction of the 

 moon to raise a tide, one of whose highest points is in la 

 titude , therefore the other is in the other hemisphere at 

 the same latitude. This state of tide in one day will travel 

 round the earth, the vertices always remaining at the same 

 latitude a. Then it is clear that the altitude of the tide at 

 any place will depend on its distance from a vertex of 

 this heap of waters. That place will have the highest 

 tide over which the vertex passes, and the height at any 

 other place will be less and less the greater the angular 

 distance from the vertex ; that is, the greater the difference 

 of latitude between the place and one vertex. The tide 

 will therefore be least at the equator and poles, and 



