T I D 



VII. The height of the two tides, when the moon passes the meridian, 

 being (cos. D X cos. L -}- sin. D X sin. L) 2 X m> and ( cos. D X cos. 

 L -f sin. D X sin. L) 2 X m, the mean height is (cos.* D X cos. 2 L 4. 

 sin. 2 D X sin. 2 L) X m. Hence the same north and south declination of 

 the moon give the same mean altitude. 



VIII. Under the equator the mean height = cos. 2 D X m. 



The general phenomena of the tides agree very well with the conclu- 

 sions deduced from the theory of gravity, indeed much more accurately 

 than could have been expected, when we consider that the theory sup- 

 poses the whole surface of the earth to he covered with deep waters j 

 that there is no inertia of the waters ; that the major axis of the sphe- 

 roid is constantly directed to the moon ; and that there is an equilibrium 

 of aH the parts j none of which suppositions are strictly founded in fact. 



As a sequel to this Article we will subjoin a few of the principal phse. 

 nomena of the tides, as deduced from actual observation. ( Play fair. ) 



The time from one high water to the next, is, at a mean, 12 k. 2dm. 2k. 

 The instant of low w r ater is not exactly in the middle of this interval ; 

 the tide in general taking 9 or 10 minutes more in ebbing than inflowing. 



At new and full moon, or at the spring tides, the interval between the 

 consecutive tides is the least, viz. I2h. Win. 28*. At the quadratures, or 

 neap tides, the interval is greatest, viz. \2h. 30?/z. 7*. 



The gradual subsidence of the waters is such, that the diminution of 

 heights are nearly as the squares of the times from high water. 



The time of high water in the open sea is from 2 to 3 hours after the 

 moon has been on the meridian, either above or under the horizon ; but 

 on the shores of large continents, and where there are shallows and ob- 

 structions, there are great irregularities in this respect j but for any 

 given place the hour of high water is always nearly at the same distance 

 from that of the moon's passage over the meridian. 



The highest of the spring tides is not the tide that immediately follows 

 the syzygy, but is in general the third, and in some cases the fourth. 



At Brest, the spring tides rise to 19,317 feet ; and those of .the neap to 

 9,151. In the Pacific Ocean, the rise, in the first case, is 5 feet ; in the 

 second, 2 or 2,5. Indeed it may happen, that although the greatest ele- 

 vation produced by the joint action of the sun and moon, in the open 

 sea, does not exceed 8 or 9 feet, the tide in some singular situations may 

 amount considerably higher. For instance, in the harbour of Annapo- 

 lis-Royal, it sometimes rises 120 feet; the water accumulating to this 

 astonishing height in consequence of its being stopped in the Bay of 

 Fundy as in a hook. 

 306 



