306 On the Tides of Key West. 
Island (Louisiana), and Fort Morgan (Alabama.) The reductions 
by the ordinary methods thus become the tests of those by the 
other mode. ‘The former were made under my immediate direc-' 
tion by Lieut. Richard Wainwright, U.S.N., and Mr. M. H. Ober, 
U. S. Coast Survey, and the latter by Mr. W. W. Gordon, assisted 
by Messrs. Mitchell, Homans, and others, of the Coast Survey. 
The half-monthly inequality in time and height as deduced by 
the usual method is shown in the following Table No. 1, in which 
the first column contains the moon’s age, the second the mean 
lunitidal interval corresponding, and the fifth the height. 
TABLE No. 1. 
Half-monthly inequality of tides at Key West from one year’s observations. 







= { Interval. eee Height. ag 
Moon’s age. 0. wo ot 0. | RIT ER 2 
i 2: 3. 4. 5. 6. , 
H. M. H. M, H. M. M. feet, feet feet. 
0 30 9 21 9 21 00 6°34 6°34 00 
1 30 9 05 9 07 02 631 6°32 
2 30 8 51 8 54 03 625 6:26 01 
8 30 8 47 8 46 01 617 6°16 01 
4 30 8 50 8 55 05 6°08 6:06 02 
5 30 8 54 8 58 04 6:00 5-97 08 
6 30 9 22 9 25 08 5°94 5-94 00 
q 30 9 52 9 49 03 6-00 598 02 
& 30 9 59 10 00 Ol 6-02 6:08 06 
9 30 9 59 9 58 Ol 612 618 06 
10 30 9 58 9 58 05 6°22 627 05 
11 30 9 35 9 35 00 6:30 6°33 03 
9 22 









the epoch of the moon’s age of 24 minutes, showing tha 
transit E (of Mr. Lubbock’s notation) and not F should be used 
in the reduction for theoretical purposes. 
The comparison between the results of observation and those 
from the formula for the half-monthly inequality is shown in the 
fourth and seventh columns, the fourth referring to the interval 
and the seventh to the height. The difference in the mean is 
.inappreciable, and, at a maximum, is but five minutes of interval, 
and six hundredths of a foot of height. 
A graphic comparison is made on Plate 2, The value of the 
in 2p 
1+-(A) cos 2p 
is 0-325, and of E in the formula for the height h=D+E[(A) €98 
(2u —29)+ cos 2y] is 0-620. 
The values of the diurnal inequality of high and low water, 
both in time and height, were obtained by comparing the mean 
value of the interval and height for the first and second six 
months, with the individual values; they followed closely the 
law of change with the moon’s declination. The inequality 1n 
height of high water at a mean is to that of low water as 79 to 61. 
The mean interval for this table is 9h. 22m., corresponding tA 
the 
constant (A) of the formula for the interval, tang 2y= 

