HARMONIC ANALYSIS AND PREDICTION OF TIDES 89 
since in using the daily sums, the solar hour of the day to which each 
such sum applies will always be 11.5 hour. 
By substituting the speeds of the constituents from table 2 the 
a 
15p° 
Mf, 0.036,601,10; MSf, 0.033,863,19; Mm, 0.036,291,65; 
Sa and Ssa, 0.002,737,91. 
By using the appropriate coefficient and substituting successively 
the numerals corresponding to the day of series (d), the corresponding 
value of the constituent division to which each daily sum is to be 
assigned may be readily obtained. The value of such division as 
obtained directly from the formula will usually be a mixed number. 
For table 34 the nearest integral number, less any multiple of 24, is 
used. 
258. The distribution of the daily sums for the analysis of the long- 
period constituents may be conveniently accomplished by copying 
such sums in Form 142 (fig. 12), taking the constituent divisions as 
the equivalents of the constituent hours and using table 34 to deter- 
mine the division or hour to which each sum should be assigned. 
The total sum and mean for each division may then be readily ob- 
tained. These means can then be treated as the hourly means of the 
short-period tides according to the processes outlined in Form 194 
(fig. 16) with such modifications as will now be described. 
259. In using the daily means as ordinates of a long-period constitu- 
ent consideration must be given to the residual effects of any of the 
short-period constituents upon such means and steps taken to clear the 
means of these effects when necessary. Constituent S, with a period 
commensurate with the solar day, may be considered as being com- 
pletely eliminated from each daily mean. Constituents K, and K, 
are very nearly eliminated because the K day is very nearly equal 
to the solar day. Other short-period constituents may affect the 
daily means to a greater or less extent, dependmng largely upon their 
amplitudes. Of these the principal ones are constituents M2, No, and 
O,. In the distribution and grouping of the daily means for the 
analysis of the several long-period constituents the disturbing effects 
of the short-period constituents just enumerated, excepting the effects 
of M, upon MSf, will be greatly reduced, and in a series covering 
several years may be practically eliminated. Because the period of 
MSf is the same as the synodic period of M, and 8, there will always 
remain a residual effect of the constituent M, in the constituent MSf 
sums of the daily means, no matter how long the series, which must 
be removed by a special process. 
260. Let the equation of one of the short-period constituents be 
y=A cos (at+a) (396) 
Letting d=day of series, the values of ¢ for the hours 0 to 23 of d 
day will be 
following numerical values are obtained for the coefficient 
DGD), PAGS), (Ses on Ss PGS) = 2s. 
Substituting these values for ¢ in (396) and designating the corre- 
sponding values of the ordinate y as Yo, Yi, Yo. » - - Yo3 the following 
are obtained: 
