50 U. S. COAST AND GEODETIC SURVEY 
physical changes in the region that might affect the tidal conditions. 
145. If we let y,; equal the height of one of the tidal constituents as 
referred to mean sea level, it may be represented by the following 
formula: 
y¥i=fH cos (HE—«)=fH cos (V+u—x) (236) 
The combination symbol V+ is the equivalent of / and represents 
the argument or phase of the equilibrium constituent. 
146. Formula (236) is illustrated graphically in figure 7 by a 
cosine curve with amplitude fH. The horizontal line represents 
mean sea level and the vertical line through 7 may be taken to indi- 
cate any instant of time under consideration. If the point M/ repre- 
sents the time when the constituent argument equals zero, the interval 
from M to the following high water of the constituent will be the 
epoch «x. The interval from the preceding high water to M is 
measured by the explement of x which may be expressed as —x. 
The phase of the constituent argument at time TJ is reckoned from M 
and is expressed by the symbol (V+w). The phase of the constit- 
mM HW 
(-K)i 
FIGURE 7. 
uent itself at this time is reckoned from the preceding high water 
and therefore equals (V-+u—xk). 
OBSERVATIONAL DATA 
147. The most satisfactory observational data for the harmonic 
analysis are from the record of an automatic tide gage that traces a 
continuous curve from which the height of the tide may be scaled at 
any desired interval of time. This record is usually tabulated to give 
the height of the tide at each solar hour of the series in the kind of 
time normally used at the place. It is important, however, that the 
time should be accurate and that the same system be used for the 
entire series of observations regardless of the fact that daylight saving 
tume may have been adopted temporarily for other purposes during a 
portion of the year. When the continuous record from an automatic 
gage is not available, hourly heights of the tide as observed by other 
methods may be used. The record should be complete with each 
hour of the series represented. If a part of the record has been lost, 
the hiatus may be filled by interpolated values; or, if the gap 1s very 
extensive, the record may be broken up into shorter series which do 
not include the defective portion. 
