NEWTON S PRINCIPIA. 403 



tions as if the fluid at each moment put itself in equili 

 brium under the action of the luminary which attracts it* 

 And the error is less, the slower the motion of the luminary ; 

 it is therefore insensible for the sun, and we may even 

 assume it true for the moon. This is calculated on the 

 supposition that the resistance varies as the velocity, but 

 it will be, clearly, also true whatever be the law of the 

 resistance. 



Des oscillations de la seconde espece. These are oscilla 

 tions which go through their period in about a day, and 

 constitute therefore properly a diurnal tide. It is found 

 that this tide does not exist either at the equator or the 

 poles, and it is greatest about latitude 45. It will dis 

 appear in every latitude if the depth of the sea be uniform, 

 a result as remarkable as it was unexpected. But this 

 only refers to the elevation of the water. The diurnal 

 variations of the horizontal motions caused by these terms 

 would still remain. The expression for the elevation of 

 the water is found to change sign with q ; so that if the 

 water be shallower at the poles than at the equator, and 

 its depth be less than seven miles, low water occurs at the 

 transit of the luminary, if deeper at the poles, high water ; 

 provided the transit of the luminary takes place on the 

 same side of the equator as the place of observation; and 

 the reverse occurs if the transit takes place on the opposite 

 side. 



Des oscillations de la troisieme espece. These oscillations 

 go through their period in about half a day. They con 

 stitute a semi-diurnal tide, having two high waters and two 

 low waters every day. If the depth vary as the square of 

 the cosine of the latitude, the expression for the elevation 

 of the tide shows that there will be low or high water at 

 any place at the moment when the luminary crosses the 

 meridian, according as the depth of the sea is less or greater 

 than about seven miles. Laplace has also investigated the 

 nature of these tides in a sea of uniform depth, but the 

 Astronomer Royal has pointed out an error in his process, 



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