38 



The first of these speeds is one half of the speed of the hmisolar semi- 

 diurnal component K2. It is therefore designated as ki. The second 

 is conventionally designated as Oi. 



Since the amplitude of each of the lunar diurnal components just 

 developed also fluctuates during the anomalistic month because of the 

 varying distance between the earth and the moon, each should be 

 made up of a principal and two minor components, giving the six 

 components in the form 



2/=Ki cos (ki#+a)+K'i cos [(ki+c) t-\-a] + K'\ cos [(ki-c)^+a] 



+ 0i cos (0i^ + a) + 0'i COS [(oi + c)i + a] + 0"iCos[(oi-c)i+a] (41) 



where c is the speed of the anomalistic month, and the value of a in 

 the various terms is not generally the same. 



The speeds of the minor components then have the values: 



ki + c=15°.041, 068,6 + 0°. 544,374,7= 15°. 585,443, 3 



ki-c=15°.041,068,6-0°. 544,374,7= 14°.496,693,9 



Oi + c= 13°. 943,035,6 + 0°. 544,374,7= 14°.487,410,3 



Oi-c=13°.943,035,6-0°. 544,374, 7= 13°.398,660,9 



The component having the speed ki + c is designated as the Ji com- 

 ponent and that having the speed of Oj — c the Qi component. The 

 other two have speeds so close to that of the lunar day, besides being 

 intrinsically small, that they are replaced by a component designated 

 as Ml, with the speed of the lunar day. 



69. The components identified in the preceding paragraph are 

 named as follows: 



Ki, lunar portion oj the lunisolar diurnal, whose speed is the 

 sum of those of the lunar day and tropical month. 



Oi, lyrincipal lunar diurnal, whose speed is the difference 

 between those of the lunar day and tropical month. 



Ji, small lunar elliptic, whose speed is the sum of those of the 

 lunisolar diurnal and the anomalistic month. 



Qi, larger lunar elliptic, whose speed is the difference between 

 those of the principal lunar diurnal and of the anomal- 

 istic month. 

 Ml, smaller lunar elliptic, whose speed is that of the lunar day. 



70. The corresponding solar diurnal components are: 



Ki, solar portion oj the lunisolar diurnal, whose speed is the 

 sum of those of the solar day and the tropical year, or 

 15°. 041, 068, 6. This unites with the lunar tide of the 

 same speed to form the lunisolar diurnal component. 



