33 



58. If the amplitudes of two components are equal, Aj — A = 

 and if their speeds are nearly equal, the curve of the resultant takes 

 the form shown in figure 22. 



Figure 22. — Tide curve of two components of equal amplitudes. 



Since the speed of the resultant in this case is the average of the 

 speeds of the two components, the equation of the resultant con- 

 veniently may be written: 



y=A cos [(a+/2&)^+«i]+^ cos [(a-K6)«+a2] (37) 



where a is the speed of the resultant and 6 the difference in the 

 speeds of the two components. 



59. The form of the curves shown in figures 21 and 22 indicates the 

 manner by which the periodical variations in the semidiurnal and 

 diurnal parts of the tidal fluctuations at any station, due to the 

 changing declinations and distances of the moon and sun (pars. 

 40-44), may be represented by a combination of components of prop- 

 erly chosen speeds, fixed by the accurately established periods and 

 speeds of the movements of the moon and sun. 



ASTRONOMICAL PERIODS DETERMINING THE SPEEDS OF 

 TIDAL COMPONENTS 



60. Mean solar and lunar days.^The intervals between the suc- 

 cessive transits of the true sun across the meridian of a place vary 

 slightly with its declination and distance, increasing as its declination 

 increases either north or south of the equator, and increasing also as 

 its distance decreases. The mean interval is the mean solar day of 24 

 mean solar hours. The speed at which the hour angle of the true sun 

 increases obviously must be the least when the interval between its 

 transits is the greatest. The speed of the hour angle of the true sun, 

 in degrees per mean solar hour, as influenced by the declination, is 

 therefore a maximum when the declination is zero, and a minimum 

 when the declination is at its maximum. As uifluenced by the 

 distance, the speed is a minimum at perihelion, when the distance to 

 the sun is the least, and a maximum at aphelion, when the distance 

 is the greatest. The angular speed of the hour angle of the moon goes 

 through simflar but more rapid changes, with further disturbances 

 because of the attraction exerted by the sun on the moon. The mean 



