A 



l ^- J n b 

 kZ. / \c 



198 TIDAL AND LEVELLING OBSERVATIONS. 



process pursued. If the height attained at any tide be marked 

 upon a wharf wall, as at A in the annexed 

 diagram, and also the point of lowest 

 depression as at G-, and a circle drawn 

 through these two extreme points, then, 

 roughly, the heights at equal successive 

 times may be found by dividing the cir- 

 cumference of the circle into equal parts, 

 as at B, 0, D, &c, the fall and succeeding 

 rise of the water reaching the points thus 

 found in equal times. If now, for sim- 

 plicity, the tidal heights at each hour of the day be thus grouped 

 together for an entire year,* and the sums and means of the 365 

 groupings taken, the mean value of the effect clue to the sun will 

 be obtained. Similarly, another grouping according to mean lunar 

 hours will give the mean value due to the moon. These values 

 would represent the values supposing the sun and moon to be always 

 at the same distance from the earth, and also at the same inclina- 

 tion to the horizon. The lunar orbit, however, is far from circular, 

 and in practice it is found that it is necessary to include several 

 other groupings to correct the mean values obtained as above. 

 A smaller number suffices for the solar tide, the earth's orbit 

 approximating much nearer to a circle. Other groupings correct 

 the mean values for the varying inclinations of the sun and moon 

 due to the different declinations or distances from the equator of 

 these bodies. The effects due to rainfall and other meteorological 

 causes are similarly found. 



In practice about 25 groupings are made, and some 30 values 

 obtained. The quantities obtained give the value of each tidal 

 constituent in feet (or other measure) and the time at which such 

 constituent tide is at its maximum. For simplicity we may assume 

 that the tide traced on the wharf wall is due to only one body, and 

 that the water attains the successive positions indicated by the 

 points A. B, C at each succeeding hour from noon at A to midnight. 

 Then the value of the tide found from the groupings will be 

 radius of the circle A, and an angle such as A B 

 will give the time at which the tide was at its maximum or highest 

 point. The mean level of the water will be given by taking the 



* For special reasons a period of 369 days 3 hours is generally used, being 

 25 semilunations. 



