104 U. Ss. COAST AND GEODETIC SURVEY 
analysis of the hourly heights. Account should be taken of the num- 
ber of items entering into each sum and the mean for each constituent 
hour obtained. The 24 hourly means for each constituent are then to 
be analyzed in the usual manner. 
299. The results obtained by this process are, of course, not as 
dependable as those obtained from a continuous record of hourly 
heights. The approximate results first obtained can, however, be im- 
proved by the following treatment if a tide-computing machine is 
available. Using the approximate constants as determined above for 
the principal constituents and inferred values for smaller constituents, 
set the machine for the beginning of the period of observations and 
find the predicted heights corresponding to the observed times of the 
high and low waters. Tabulate the differences between the observed 
and predicted heights for these times, using the hourly height form 
and entering the values according to the nearest solar hour. These 
differences are then to be summed and analyzed the same as the 
original observed heights. In this analysis of the residuals the con- 
stituent M, should be included. The results from the analysis of the 
residuals are then combined with the constants used for the setting 
of the predicting machine. 
300. In making the combinations the following formulas may be 
used: 
Let A’ and x’ represent the first approximate values of the constants 
of any constituent. 
A”’ and x’’, the constants as obtained from the residuals. 
A and x, the resultant constants sought. 
Then 
A=+(A’ cos x’ A” cos x”)?+(A’ sin x’ +A” sin x”)? (444) 
and 
= A Sine sea Sn 
A’ cos x’ +A” cos x” 
c=tan (445) 
FORMS USED FOR ANALYSIS OCF TIDES 
301. Forms used by the Coast and Geodetic Survey for the harmonic 
analysis of tide observations are shown in figures 9 to 19. A series of 
tide observations at Morro, California, covering the period February 
13 to July 25, 1919, is taken as an example to illustrate the detail of 
the work. 
302. Form 362, Hourly heights (fig. 9)—The hourly heights of the 
tide are first tabulated in form 362. Although the zero of the tide 
staff is usually taken as the height datum, any other fixed plane will 
serve this purpose. For practical convenience it is desirable that the 
datum be low enough to avoid negative tabulations but not so low 
as to cause the readings to be inconveniently large for summing. 
303. The hours refer to mean solar time, which may be either local 
or standard, astronomical or civil, but standard civil time will generally 
be the most convenient to use. The series must commence with the 
zero (0) hour of the adopted time, and all vacancies in the record 
should be filled by interpolated values in order that each hour of the 
series may be represented by a tabulated height. It is the general 
practice to use brackets with interpolated values to distinguish them 
from the observed heights. The record for successive days of the 
series must be entered in successive columns of the form, and these 
