62 



constituents of V given in paragraph 113. Thus the speed of the 

 component represented by the first term of equation (68), viz, 



3/2{Ma^/Ec^)a cos^ X cos'' }a(l/2-5/4 e') cos (2T+2h-2s+2^+2v) 



is 



a=2e + 27?-2(7=30° + 0°.082, 137,28- 1°.098,035,06 = 28°.984, 104,22 



This is then the M2 component of the equihbrium tide, its speed 

 being identical with that previously identified for that component 

 (par. 75). All of the other terms in equations (68), (69), and 

 (70) may be similarly identified as the equilibrium components corre- 

 sponding to the components listed in paragraphs 75 and 76. Their 

 conventional symbols, conforming to those previously listed, are shown 

 opposite each term. It will be noted that the semidiurnal components 

 are those whose arguments contain the term 2T; the diurnal compo- 

 nents are those whose arguments contain the term T, and the long- 

 period components are those in whose arguments T does not enter. 

 The lunar and solar components designated as K2 and Ki, each have 

 the speed of 2d-\-2'>] and 6-\-7], respectively. As previously pointed 

 out, these pairs each unite into a single component. Their symbols 

 are therefore enclosed in brackets to indicate that they are parts of a 

 combined component. Two other lunar components, L2 and M2, 

 appear twice in the list in brackets. The speed of the L2 component 

 represented by the third term in equation (68) is 2d-\-2r]—a—u = 

 29°. 528,478,92 and that of the ninth term is 20+27?— (t + w = 

 29°.537,762,58. The difference in these speeds is evidently 2w =0.00928366 

 and the synodic period of the two components (par. 90) is 

 1 5/0.009,283,66 days = 1 ,720 days. They therefore cannot be separated 

 by analysing observations over a period of even a year, and conse- 

 quently are treated as a single component. The evaluation of the 

 coefficients of the two terms shows that the first is the larger, and its 

 speed is therefore assigned to both. The speed of the Mi component 

 represented by the twelfth term is similarly + 77— cr—w while that of 

 the eighteenth term is 0+77-0-+ w. Since the difference in these 

 speeds is also 2<5 they also cannot be separated by a year's observa- 

 tions. For convenience they are treated as a single component having 

 a speed of 14°.492, 052,1 whose component hour is the same as that 

 of the principal lunar diurnal component Mi. The speed of the lunar 

 fortnightly component MSf is exactly the same as that of a compound 

 tide whose speed is the difference of the speeds of the M2 and S2 

 components, and this component is therefore also bracketed. 



117. Determination of the epoch of a com'ponent of the actual tide.— 

 As shown in paragraph 103, the phase of a component of the actual 



