TIDAL OBSERVATIONS. 



157 



(£_'s declination zero. 





1860. Nov. 22^ O'' A. 



M. 



Dec. 5, 11 P. 



M. 



1861. June 1, A. 



M. 



" 15, T A. 



M. 



28, 1 A. M. 



Interval. 

 9'* IS*" 



10 

 10 



1 



4 



8 n 



10 u 



The apparent retard of the low water epoch is as follows : — 



Inequality vanishes. 



Dec. 1" 6 P. M. 



" 16 A.M. 



June 11 4 A. M. 



" 24 A. M. 



(July 7 A.M.] 



I " 10 6P. M.j 



On the .average, therefore, the diurnal inequality in the height of low water 

 disappears 9.8 days after the moon's passage over the equator. 



This difference in the epoch of the inequality in the height of high and low water, 

 amoimting to 7.9 days, is significant. With respect to the retard we remark, gene- 

 rally, for tidal waves that their oscillations are augmented by the continued action, 

 in the same direction, of the force having the same intervals as those oscUlations ; they 

 will, therefore, go on increasing for a considerable time after the forces have gone 

 on diminishing ; here the retard is due to an accumulated effect. It is plain that this 

 explanation cannot apply to the epoch of the diurnal wave which shows an epochal 

 difference of nearly eight days for high and low water, but must be the effect of 

 intei-ference of the diurnal and semi-diurnal wave. The subject of separation of 

 these two waves wiU be taken up and analyzed further on. 



By means of the . diagrams on Plate I we find the maximum range of the diurnal 

 inequality in height for high water to be 3.8 feet, determined from five cases, each 

 giving the same amount. For the low water diurnal inequality range the values 

 are more variable; they are 2.0, 3.7, 2.3, 2.2, and 2.0 feet, on the average 2.4 feet. 

 The last three values belong to the summer series, and are probably affected by the 

 solar action. The variations in the moon's parallax also affect the diurnal inequality, 

 and there are indications of an increase for a larger parallax ; our series, however, 

 are too short to pursue this subject any further. 



According to Sir J. Lubbock (Phil. Trans. 1837) the lunar portion of the diurnal 

 inequality can be represented by 



dJi = C sin 2h' for the heights, and dii = for the times. 



'^ 1 + ^ cos 2^ 



In these expressions the value of h' must be taken for an anterior date, which for 



the high water height inequality in our case is two days. Dividing the intervals 



between the moon's zero declination in six equal parts, and measuring for each the 



ordinate of the inequality and tabulating the corresponding declinations, without 



regard to sign, we obtain the following results for the inequality in height of high 



water from the two series. Each value is the restdt of five separate measures, and 



the computed value is derived from the expression dh = 4.6 sin 25'. 



S' 



Observed dh 



Computed dh 



0° 



0^0 



0".0 



12 



1.8 



1.9 



22 



3.2 



3.2 



25 . 



3.5 



3.5 



22 



3.1 



3.2 



12 



1.8 



1.9 







0.0 



0.0 



The inequality in the heights of low water cannot be expressed in this manner, 

 as the more complex figure on Plate I sufficiently indicates. 



