HARMONIC ANALYSIS AND PREDICTION OF TIDES Ol 
1 2 
Heine a anvans 
coefficient. The speed a is a known constant and the values of A 
and a are presumed to have already been determined from the har- 
monic analysis of the short-period constituents. Similarly, the dis- 
turbing effects of other short-period constituents may be represented 
by 
constituent A, except that it includes the factor 
sin 126 
1 
Yo og B sin 26 cos (bt+ 8) 
1 _ sin 12¢ 
Yu 94 C sin 4¢ cos (ct+7) (401) 
cte. 
The combined disturbing effect of all the short-period constituents 
may, therefore, be represented by the equation 
sin 12a 
sin 4a 
Y=YatYotete.=s, 7A 
1 i 
On B a cos (b¢t+ B)-+ etc. (402) 
cos (at+ a) 
263. This formula is adapted to use on the tide-computing machine. 
With the constituent cranks set in accordance with the coefficients 
and initial epochs of the above formula, the machine will indicate 
the values of y corresponding to successive values of ¢. The values. 
of y desired for the clearances are those which correspond to ¢ at the 
11.5 hour on each day. Thus, the clearance for each successive day 
of series may be read directly from the dials of the machine. In 
practice, it may be found more convenient to use the daily sums 
rather than the daily means for the analysis. In this case the co- 
efficients of the terms of (402) should be multiplied by the factor 24 
before being used in the tide-computing machine. 
_ 264. Assuming that all the daily sums are used in the analysis, the 
augmenting facter represented by formula (308) which is used for 
the short-period constituent is also applicable to the long-period con- 
stituents, with p representing the number of constituent periods in a 
constituent month or year. Thus, for Mm and Sa, p equals 1, and 
for Mf, MSf, and Ssa, p equals 2. For the long- period constituents a 
further correction or augmenting factor is necessary, because the. 
mean or sum of the 24 hourly heights of the day is used to represent. 
the single ordinate at the 11.5 hour of the day. 
265. If we let formula (396) be the equation of the long-period 
constituent sought, formula (400) will give the mean value of the 24 
ordinates of the day which, in the grouping for the analysis, is taken. 
as representing the 11.5 hour of the day or the ¢a hour of the series. 
Since the true constituent ordinate for this hour should be A cos. 
sin 5a 
7124 ust be 
applied to the mean ordinates as derived from ie: sum of the 24 
hourly heights of the day in order to reduce the means to the 11.5 
hour of each day. 
(atat+ a), itis evident that.an augmenting, factor of 24 - 
