36 



Since the speed of the hour angle of the moon tends to become a 

 minimum at perigee, when the increase in the amphtude of the semi- 

 diurnal part of the lunar equilibrium tide because of the decreased 

 distance of the moon is a maximum, the component with the lesser 

 speed, N2 cos [(jn.2—c)t-\-a5], is the larger. Both of this pair of com- 

 ponents are found necessary, however, to represent the variations in 

 the tide because of the changing distance of the moon. 



65. Writing then equation (38) in the form: 



2/=M2 cos (m2/+Q!i)+K2 cos (1^2^ + 0:2) +L2 cos (l2#+«3)N2 cos (n2^+o!4) 



(39) 

 m2 = 28°. 984, 104,2 per mean solar hour. 

 k2=m2+6 = 30°. 082, 137,2 per mean solar hour. 

 I2=m2+c=29°.528,478,7 per mean solar hom\ 

 n2=m2—c=28°. 439, 729,5 per mean solar hour. 



The detailed mathematical analysis shows that components having 

 these speeds are sufficient to reproduce with substantial accuracy 

 the lunar semidiurnal part of the tide. Certain other small compo- 

 nents are developed by that analysis, principally to account for the 

 variations in the tides due to the irregularities in the movement of 

 the moon because of the sun's attraction, but these are of no sub- 

 stantial importance. 



66. Designation of components. — The capital letters designating the 

 amplitudes of the components whose speeds are identified in the pre- 

 ceding paragraphs are those conventionally assigned to these com- 

 ponents. The subscript 2 indicates that the component is a semi- 

 diurnal one; i. e., that its speed is in the vicinity of 30° per mean 

 solar hour. Diurnal components, with a speed not far from 15° per 

 hour, are given the subscript 1. The speed of the component is 

 conventionally designated by the corresponding small letter of the 

 alphabet, and is given the same subscript. Components are custom- 

 arily referred to by the letter and subscript designating the amplitude; 

 i. e., as the "M2 component," and "K2 component," etc. The com- 

 ponents previously identified are named as follows : 



M2, the principal lunar component, 



N2, the larger lunar elliptic, semidiurnal, 



L2, the smaller lunar elliptic, semidiurnal, 



K2, the discussion in paragraph 63 indicates that a solar com- 

 ponent of the same speed is to be anticipated. This 

 component is therefore called the lunar portion of the 

 lunisolar semidiurnal. 



67. Solar semidiurnal components. — ^The speeds of the solar semi- 

 diurnal components corresponding to the lunar semidiurnal compo- 

 nents already identified may be written at once by substituting the 



