97 



spheroid. Let Q denote the same fixed point (of observation) on the 

 earth. Then we see from the figure that the high water, Q F, is greater 

 than in the previous case. The height of low water will be the same 

 as before, for it may be shewn to be equal to B C ; it will occur when 

 the moon sets, which in this case will be more than six hours after 

 high water ; the depth will then again increase, till twelve hours 

 after the first high water there will be a second high water, but, in 

 this case, much less in height than the first. Similarly the heights of 

 the tide at intervals of twelve hours will no longer be equal. 



There are thus two high waters of difterent heights in the course 

 of 24 hours, together with two low waters whose heights are equal. 



Analysis shews that we are to consider the height of the water at 

 any time as due to the combined action of two tides, viz., the semi- 

 diurnal tide, whose variations we have already traced, and a diurnal 

 tide, Avhich vanishes when the moon is in the equator (and thus enables 

 us to investigate the semi-diurnal tide separately). The height of this 

 diurnal tide is at its maximum when the moon is on the meridian ; it 

 then increases the high water of the semi-diurnal tide. Six hours 

 after it sinks to zero and then does not affect the semi-diurnal tide ; 

 continuing to decrease, its effect is to diminish the height of the semi- 

 diurnal tide ; a minimum high water being thus produced tAvelve 

 hours after the first or maximum high water. 



Besides these tides, there is a third variation in the height of 

 the water, known as the Tide of Long Period, going through all its 

 changes in 14 days, and caused by the varying distance of the moon 

 from the equator. 



For the sake of geometrical simplicity, we have spoken of the 

 earth as though revolving within a fixed fluid shell and of the \arying 

 height of the tide as due to the varying thickness of this shell, as any 

 particular place is successively brought under different portions of it. 



But we must now conceive that as the earth rotates the moon is 

 continually raising the waters of the ocean in a spheroidal shape. 

 This spheroid travels round the earth in one day, thus producinf^ a 

 great wave or undulation in the surface, and therefore a perpetual 

 oscillation in the height of the water at any particular place. 



Again, the moon, we know, is not stationary in the heavens, but 

 has a motion of its own round the earth from W. to L. in the same 



