HARMONIC ANALYSIS AND PREDICTION OF TIDES 157 
formula from which a factor of approximately 1.5 was inadvertently 
omitted (see page 43). 
Table 14. Node factor f for middle of each year 1850 to 1999.—The 
factor f is the reciprocal of factor F. The values for the years 1850 to 
1950 were taken directly from the Manual of Tides, by R. A. Harris, 
and the values for 1951 to 1999 were derived from tables 12 and 13. 
Table 15. Equilibrium argument (V,+u) for beginning of each year 
1850 to 2000.—The equilibrium argument is discussed on page 22. 
The tabular values are computed by the formulas for the argument 
in table 2, the V, referring to the value of V on January 1, 0 hour 
Greenwich mean civil time, for each year, and the wu referring to the 
middle of the same calendar year; that is, Greenwich noon on July 
2 in common years and the preceding midnight in leap years. The 
value of the 7 of the formulas is 180° for each midnight, and the 
values of the other elements for the V may be obtained from table 
4. The wu of the argument may be obtained from tables 11 and 13 
after the value of NV has been determined for the middle of each year 
from tables 4 and 5. In constructing table 15 the values for the 
years 1850 to 1950 were taken directly from the Manual of Tides, by 
R. A. Harris, and the values for the years 1951 to 2000 were computed 
as indicated above. 
Tables 16, 17, and 18.—These tables give the differences to adapt 
table 15 to any month, day, and hour, and are computed from the 
hourly speeds of the constituents as given in table 2. The differ- 
ences refer to the uniformly varying portion V of the argument, it 
being assumed that for practical purposes the portion wu is constant 
for the entire year. 
The approximate Greenwich (V,-+w) for any desired Greenwich 
hour may be obtained by applying the appropriate differences from 
tables 16, 17, and 18 to the value for the first of January of the 
required year, as given in table 15. To refer this Greenwich (V,+ 4) 
to any local meridian, it is necessary to apply a further correction 
equal to the product of the longitude in degrees by the subscript of 
the constituent, which represents the number of periods in a con- 
stituent day. West longitude is to be considered as positive and 
east longitude as negative, and the subscripts of the long-period 
constituents are to be taken as zero. This correction is to be 
subtracted. 
The (V,+wu) obtained as above will, in general, differ by a small 
amount from the value as computed by Form 244, because in the 
former case the wu refers to the middle of the calendar year and in 
the latter case to the middle of the series of observations. 
Table 19. Products for Form 194.—This is a multiplication table 
especially adapted for use with Form 194, the multipliers being the 
sines of multiples of 15°. 
Table 20. Augmenting factors —A discussion of augmenting factors 
is given on page 71. The tabular values for the short-period constit- 
uents are obtained by formulas (308) and (309) on page 72, and those 
for the long-period constituents by formulas (403) and (404) on 
page 92. For constituents S,, S:, etc. the augmenting factor is unity. 
Tables 21 to 26.—These tables represent perturbations in K, and 
S. due to other constituents of nearly equal speeds. They are based 
upon formulas (359) to (864), inclusive, on page 83. 
