56 V. S. COAST AND GEODETIC SURVEY. 



If we disregard for the present the slow variations in the value of 

 I, ^, and V, which for a series of observations of a year or less may be 

 considered as practically constant, each term in the above formula, 

 excepting (J.) 59, is an harmonic function of an angle which changes 

 uniformly with time. Each term represents an harmonic component 

 of the lunar tide, and, if the ideal conditions assumed under the 

 equilibrium theory (section 3) actually existed, each term including 

 tihe general coefficient would represent the approximate true height 

 of that component referred to mean sea level and the sum of all the 

 terms the approximate height of the entire lunar tide. , 



The notation following each term in the formula is the generally 

 recognized symbol for the component represented. The bracketed 

 symbols indicate that the terms only partially represent the compo- 

 nents designated. These will later be given special consideration. 

 The terms without symbols are of little practical importance and are 

 generally neglected. 



Terms with coefficients e and g^ represent the elliptic components, 

 since they depend directly upon the eccentricity of the moon's orbit. 

 Terms with coefficients me, and m? represent the evectional and 

 variational components, respectively, since they are derived from the 

 corresponding inequalities in the motion of the moon, (See formulas 

 for the true longitude and distance of the moon in Table 1.) 



10. EQUILIBRIUM ARGUMENT. 



Although the actual height of the tide and the time of occurrence 

 of the maxima and minima are greatly modified by conditions upon 

 the earth's surface, equation (100) fuiliishes us with important rep- 

 resentations of the elementary periodic forces which tend to produce 

 the lunar tide. These forces may be defined by their periods which 

 depend upon the varying angles of the several terms of the equation. 

 Disregarding for the time being the slow changes in the functions of 

 the angle /, the value of each term in general is the product of a con- 

 stant coefficient and the cosine of a var}dng angle. This angle is 

 called the equilibrium argument of the component represented. The 

 numerical value of the argument is constantly changing. The mean 

 rate of change is called the speed of the component, and the time 

 required for the argument to complete one cycle of 360° is the period 

 of the component. 



Examining equation (100) it will be noted that each argument is 

 composed of a combination of some of the following elements: 



T, hour angle of the mean sun at the place of observation; 



h, longitude of the mean sun ; 



s, longitude of the mean moon; 



p, longitude of the moon's perigee; 



Pi, longitude of sun's perigee (for solar tides only) ; 



I, longitude in moon's orbit of intersection (fig. 6) ; 



V, right ascension of intersection (fig. 6) . 



The hour angle T is zero at mean local noon at the place of obser- 

 vation and increases uniformly at the rate of 15° per solar hour. At 

 any given instant of time the value of T will be different for each 

 meridian of the earth, but will be identical for all places on the same 



