T I B 



rompared with the passage of the sun and moon over the meridian ; and 

 thus from these we might construct a table, shewing the theoretical 

 times of high tide during the month. 



Hitherto \ve hare supposed the luminary to be in the equator : we 

 come in the next place to consider the effect arising from the declination 

 of the moon. 



5. Let D moon's declination, L = latitude of the place, 8 = hour 

 / from high water j then the height of tha water from the lowest point 



is 



(cos. D X cos. L X cos. -f sin. D X sin. L)s X m. 



Hence we may consider the following cases : 



I. To find the interval from high to low tide, put cos. D X cos. L X 



sin D X sin. L 



cos. 4. sin. D X sin. L ; .'. cos. 6 = i=i - x ^-. 



cos. D X cos. L 



II. When the latitude of the place comp. of moon's declination, cos. 

 1 ; .*. 180, i.e. the interval between high and low tide -=i 12 

 hours, i.e there is only one high and one low tide in 24 hours. 



III. When the distance of the place from the pole is less than the 

 moon's declination, the expression in Art. 5 never can become with- 

 in the limits of cos. I); .*. there is only om; high jind one low tide in 24 

 lunar hours. And if \ve make cos. & I , and cos. = 1 , we have the 

 difference of the altitudes of the two tides 4 cos. D X cos. L X sin. D 

 X sin. L X m. 



IV. When D = L, make cos. 6=1, r.nd we have the greatest altitude 

 =. m ; also cos. - : = interval from high to low water. 



V. When the moon is in the equator, the altitude of the tide = cos.* 

 LX m. 



VI. The height of the tide, when the moon passes the meridian, = 

 (cos. D X cos. L 4- sin. D X sin. L) 2 X m ; and when the moon is at the 

 opposite meridian, the height is ( cos. D X cos. L 4. sin. D X sin. L) 

 X m. Hence when the moon is in the equator, sin. D o, and the 

 height of both tides is equal. To a place on the north of the equator, 

 when the moon has south declination, sin. D becomes negative, and the 

 latter tides are the greatest ; but when the moon has north declination, 

 sin. D is positive, and the former is the greatest. Hence, to us in this 

 case, the high tide is greater when the moon is above the horizon than. 

 when below. The difference of the two tides is always what is given in 

 Case III. 



305 R i 



