288 NEWTON S PRINCIPIA. 



These two will not appear separately, but a mixed tide 

 will result from the two. Since both are small, we may 

 consider the actual tide as being the sum of the two tides 

 that would have been formed had the disturbing bodies 

 acted alone. The force of the moon to raise the tides is 

 much greater than that of the sun, as we shall presently 

 see, so that for most purposes we may altogether neglect 

 the solar tide, or rather regard it as a small correction to 

 be applied to results calculated on the supposition that the 

 moon alone acted to raise the tide. 



First. The lunar tide follows the moon at a given in 

 terval, called the &quot; establishment.&quot; Hence as the moon by 

 her proper motion rises every day about forty minutes later 

 than on the preceding day, the high tide will be as much 

 later every successive day. But more minute investigation 

 shows that the high tide does not follow the moon s passage 

 over the meridian by any constant interval. We must 

 make a small correction for the effect of the solar tide. If 

 the sun follow the moon across the meridian, the solar high 

 tide will follow the lunar high tide, and the actual high 

 water formed by the union of the two will lie between 

 these two tides, and will therefore follow the moon s passage 

 across the meridian at an interval slightly greater than the 

 &quot; establishment&quot; So if the sun precede the moon the 

 interval will be less. Therefore, when the moon is in the 

 first and third quarters, the high water is a little later, when 

 in the second and fourth a little earlier, than the establish 

 ment would indicate. 



Secondly. At or about new and full moon, the high tide 

 formed by the sun coincides with that formed by the moon, 

 hence the high tides will be higher and the low tides lower 

 than when the moon is in any other position relative to the 

 sun. These are called Spring Tides. At or about the half 

 moon, the high tide formed by the sun coincides with the 



