HARMONIC ANALYSIS AND PREDICTION OF TIDES 5 23 
ment of the equilibrium tide. By analogy, the argument of the per- 
manent term may be considered as zero, the cosine of zero being unity. 
71. The argument serves to identify the constituent by determining 
its speed and period and fixing the times of the maxima and minima 
of the corresponding tidal force. It usually consists of two parts 
represented by the symbols V and wu. When referring to a particular 
instant of time such as the beginning of a series of observations, the V 
is written with a subscript as Vj). The first part of the argument in- 
cludes any constant and multiples of one or more of the following 
astronomical elements—T, the hour angle of the mean sun at the 
place of observation; s, the mean longitude of the moon; h the mean 
longitude of the sun; and 7, the longitude of the lunar perigee. The 
second part wu includes multiples of one or both of the elements é and », 
which are functions of the longitude of the moon’s node and vary 
slowly between small positive and negative limits throughout a 19-year _ 
cycle. In a series of observations covering a year or less they are 
treated as constants with values pertaining to the middle of the series. 
They do not affect the average speed or period of the constituent. 
Their values corresponding to each degree of N, the longitude of the 
moon’s node, are included in table 6, formulas for their computation 
being given on p. 156. 
72. The hourly speed of a constituent may be obtained by adding 
the hourly speeds of the elements included in the V of the argument. 
These elementary speeds will be found in table 1. The period of a 
constituent is obtained by dividing 360° by its speed. The approxi- 
mate period is determined by the element of greatest speed contained 
in the argument. Thus, the hour angle T has a speed of 15° per 
mean solar hour and all constituents with a single 7 in their argu- 
ments have periods approximating one day, while constituents with 
arguments containing the multiple 27 have periods approximating 
the half day. Next to J, the element of greatest speed is s the 
mean longitude of the moon, and long-period constituents with a 
single s in their arguments will have periods approximating the 
month and with any multiple of s the corresponding fraction of a 
month. The arguments and speeds of the constituents are listed in 
table 2. Numerical values of the arguments for the beginning of 
each calendar year from 1850 to 2000 are given in table 15 for con- | 
stituents used in the Coast and Geodetic Survey tide-predicting | 
machine. Tables 16 to 18 provide differences for referring these 
arguments to any day and hour of the year. 
73. In order to visualize the arguments of the constituents depend- 
ing primarily upon the rotation of the earth, some have found it 
convenient to conceive of a system of fictitious stars, or ‘‘astres fictifs”’ 
as they are sometimes called, which move at a uniform rate in the 
celestial equator, each constituent being represented by a separate star. 
Thus, for the principal lunar constituent we have the mean moon and 
for the principal solar constituent the mean sun, while the various 
inequalities in the motions of these bodies are served by imaginary 
stars which reach the meridian of the place of observation at times 
corresponding to the zero value of the constituent argument. For 
the diurnal constituents the argument equals the hour angle of the 
star but for the semidiurnal constituents the argument is double the 
hour angle of the star. 
