88 U. S. COAST AND GEODETIC SURVEY 
meteorological conditions, often have an appreciable effect upon the 
mean daily level of the water. 
255. To obtain the long-period constituents, methods similar to 
those adopted for the short-period constituents with certain modifica- 
tions may be used. For the fortnightly and monthly constituents 
the constituent month may be divided into 24 equal parts, analogous 
to the 24 constituent hours of the day. Similarly, for the semiannual 
and annual constituents the constituent year may be divided into 
24 equal parts, although it will often be found more convenient to 
divide the year into 12 parts to correspond approximately with the 
12 calendar months. 
256. Instead of distributing the individual hourly heights, as for the 
short-period constituents, a considerable amount of labor can be 
saved by using the daily sums of these heights. The mean of each 
sum is to be considered as applying to the middle instant of the period 
from 0 hour to 23d hour; that is, at the 11.5 hour of the day. If the 
constituent month or year is divided into 24 equal parts, the in- 
stants separating the groups may be numbered consecutively, 
like the hours, from 0 to 23, with the 0 instant of the first group 
taken at the exact beginning of the series. A table may now be 
prepared (table 34) which will show to which division each daily 
sum, or mean, of the series must be assigned. 
257. Letting 
a=the hourly speed of any constituent, in degrees. 
p=1 when applied to a monthly or an annual constituent, and 
p=2 when applied to a fortnightly or a semiannual constituent. 
d=day of series. 
s=solar hour of day. 
Then 
1 constituent period= > solar hours (391) 
and 
1 constituent month="~2 solar hours (392) 
also 
1 constituent year= FP solar hours (393) 
Dividing the constituent month or year into 24 equal parts, the 
length of 
1 constituent division= "2? solar hours (394) 
Therefore, to express the time of any solar hour in units of the con- 
stituent divisions to which the solar hourly heights are to be assigned, 
the on hour should be multiplied by the factor a/15p. 
Thus, 
Constituent division=75- (solar hour of series) 
a 
Ayes dl 
a 
= 755 24(d—1) +115] (395) 
