92 TJ. S, COAST AND GEODETIC SURVEY. 



observations, and the phases would correspond with the equilibrium 

 arguments of the components. Under the conditions that actually 

 exist it has been found from observations that the amplitudes of the 

 components of a similar type at any place, although differing greatly 

 from their theoretical values, have a relation that, in general, agrees 

 fairly closely with the relations of their theoretical coefficients. It 

 has also been ascertained from the results obtained from observations 

 that the difference in the epochs or lags of the components have a 

 relation conforming, in general, with the relation of the differences 

 in the speeds of the components. This last relation is based upon 

 an assumption that the ages of the inequalities in any component 

 due to the disturbing influence of other components of a similar type 

 are equal when expressed in time. 



If the mean amplitudes, epochs, and speeds of several compo- 

 nents A, B, C, are represented by E{A), H{B), H{C), k{A),k{B), 

 k{C), and a, h, c, respectively, the above relations may be expressed 

 by the following formulas : 



■rr.^v mean coefficient component 5 „, .. /o^r.N 



S(B) = TfT- — ; 7-A S{A) (342) 



mean coefficient component A 



k{C)-k(A)=^ [k(B)-k{A)] (343) 



or, 



k{C)=k{A)+^ [k{B)-k{A)] (344) 



By formula (342) the amplitude of a component (B) may be 

 inferred from the known amplitude of a component (A), and by 

 formula (344) the epoch of a component (C) may be inferred from the 

 known epochs of components (A) and (B) . 



These formulas have, however, certain limitations. They are not 

 applicable to shallow water and meteorological components, nor are 

 they adapted to the determination of a diurnal component from a 

 semidurnal component or of a semidiurnal component from a diurnal 

 Component. The results obtained by the application of the formulas 

 to tides of similar type may be considered only as rough approxima- 

 tions to the truth. They may, however, be preferable to the values 

 obtained for certain components when the series of observations is 

 short. 



By substituting the mean values of the coefficients and the speeds 

 from Table 3 the following special formulas may be derived from the 

 general formulas (342) and (344) 



Diurnal components. 



H (Ji) = 0.079 H (Oi) ; k (JJ = k (Kj) + 0.496 \k (K J - k (O^)] (345) 



E (Ml) =0.071 H {0,);k (M^) =« (KJ -0.500 [k (K^) -« (O^)] (346) 



H (00) = 0.043 E (Oi) : k (OO) = k (KJ + 1.000 [k (K^) - k (O J] (347) 



E{V,) =0.331 ^(K,);« (PJ =/c (Kj) -0.075 [/c (K^) -/c (O,)] (348) 



E{q,) =0.194 iJ (0,);/c (Q,) =/c (K,) - 1.496 [/c (K,) -/c (0,)] (349) 



F(2Q) =0.026 ff(0,);/c (2Q) = ac (K,) - 1.992 [/.- (K,) -« (O,)] (350) 



E (p,) =0.038 E {0,);k (pj =/c (K,) -1.429 [k (KJ -/c (O,)] (351) 



