Pep, 
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6 On the Tides of the Western Coast of the United States. 
up this branch of the subject again. In the mean time, it appears 
\ to me, the results now obtained are of sufficient interest to be 
presented to the Association. 
I have taken, as an example of the decomposition, the curve 
from the observations of January 21, 1852, the results correspon- 
ding nearly tothe maximum of the moon’s declination and to full 
moon. 
The diurnal curve, the interference of which with the semi- 
diurnal produces the form shown in diagram A, and also ona 
larger scale in diagram D, is given on the diagram. Its maximum 
ordinate, as found by summing the two series of heights from the 
hourly observations in which the same values of the ordinate of 
the diurnal curve occur with opposite signs, and referring to the 
curve of sines for their relation to the maximum ordinate, is 2°20 
eet. 
The sum of the squares of the differences between observation 
and computation is the least when the interference takes place, 
as shown in diagram D, the maximum ordinate of the diurnal 
curve being seven hours and a half from the maximum ordinate 
of the semi-diurnal curve. Subtracting the ordinates of the diur- 
nal curve, assumed as a curve of sines, from the heights given by 
the hourly observations, we have a residual curve, which is traced 
on the diagram. The average of the four loops of this curve is 
almost precisely a curve of sines, of which the maximum ordi- 
nate is 2°30 feet. ; 
The tidal curves near the maximum of declination, and for 
several days each side of it, result from the interference of a 
semi-diurnal and diurnal wave, which at the maximum of each 
are nearly equal in magnitude, the crest of the diurnal wave 
being at that period about eight hours in advance of that of the 
semi-diurnal wave. 
The following table gives the comparison made in the diagram. 
The first column contains the ordinates of the curve of observa- 
pets from the semi-diurnal, and its maximum ordinate is 22 
eet. 
For equal maximum ordinates of the diurnal curve and semi- 
diurnal curve, 2:1 feet, we have for E=8 hours the diurnal 
inequality in height of high water 2-03 feet, or -18 foot greater 
than the mean found by the curve of diurnal inequality, and 0 
low water, 3:57, or 0:3 foot less than the value given by the curve.. 
So, also, for the inequality in the intervals of high and low 
water, we have, respectively, 105 and 61 minutes, instead or 113 
~~ 3 
