On the Tides of Key West. 311 
The results are represented in Plate No. 3. 
The statement made above in relation to the high water ordi- 
nates is not true for those of low water, as the consideration of 
the formula y=C. cos 2t+D cos(t — E) will show, making E>9 
hours. The reverse is the case if E<9 hours, the statement 
applying then to the inequality of low water and not of high. 
At Key West, while the high water inequality in height is thus 
readily found from the maximum ordinate, the low water presents 
a less accordant result; while at Cedar Keys just the reverse 
occurs, as should be the case. 
It is plain, also, that changes in the coefficients C, D, and in E, 
will cause the inequalities in times and heights to vary, as well | 
as those of high and low water, losing all correspondence with 
each other, as is also well shown in the annexed diagram. Mr. 
Gordon suggests that in the value of (E) will be found the full 
explanation of the peculiarities of the Petropaulofsk tides described 
by the Rev. Mr. Whewell. 
In diagram No. 1, Plate No. 5, E is assumed 9 hours and 
S=D, and the inequality of high and low water in interval and 
height correspond to each other. The same is the case for E=15 
hours. In No. 2, E is 12 hours, and S=D. The inequality in 
interval of high water is Oh., of low water 4h., when that in 
height of high water is 2 feet, and of low water 0 feet. For E, 
18 hours and S=D, these inequalities would be reversed, that of 
interval of high water being 4h., and of low water Oh., while for 
ent the inequality of high water is 0 feet, and of low water - 
eet. 
_ Using the high water ordinates, determined as before stated, 
instead of the diurnal inequality in height, from which it has 
been shown not to differ sensibly, the numbers were compared 
With those of Mr. Lubbock’s formula : 
dh=B [(A) sin 2 cos (y —g)+sin 20 cos y]; 
Neglecting the variations of cos (yw — @), cos ¥, the coefficients B 
and (A) B were found by least squares for the separate six months 
aud for the year, agreeing sensibly in the partial and total deter- 
Minations. From two years’ results, B=0-56.and (A) B=0°16. 
The value of (A) thus obtained is, as it should be, the same as 
deduced from the half-monthly inequality. 
The sum of the squares of the difference of the numbers from 
the formula, and from the computed high water ordinates, 1s for 
ie year but 0-0087 foot; corrected for the moon’s parallax, but 
‘UU78 foot. | 
The individual results are given in the annexed table, in which 
the first column contains the moon’s age, the second the differ- 
nee between the computed high water ordinates and the corres- 
Ponding quantities from the formula for the variations of the 
