70 



coefficients" conventionally used, and shown in table IV at the end 

 of this paragraph, are the complete coefficients divided by 1.7527, 

 the numerical value of the general factor 3/2 {Ma^/Ec^)a, in equation 

 (68) ; but these afford an equally good measure of the relative magni- 

 tudes of the mean amplitudes of the equilibrium components in the 

 three classes. Thus the mean value of the coefficient of the M2 com- 

 ponent is (1/2 — 5/4 e^)M, in which M has the numerical value of 0.9154 

 derived in paragraph 125. The mean value of the coefficient of the 

 S2 component is 6^(1/2 — 5/4 e\) cos* jio), in wliich 6^ is the ratio of the 

 general factor in equation (69) to the general factor in equation (68), 

 this ratio beino- 0.46164. 



INFERENCE OF AMPLITUDES AND EPOCHS 



130. It has been found that the mean values of the amplitudes of 

 the semidiurnal components of the actual tides at any station are 

 generally proportional to the mean values of the amplitudes of their 

 corresponding equilibrium components, as are the amplitudes of the 

 diurnal components. The amplitudes of the minor components may 

 therefore be approximately determined from those of the larger com- 

 ponents of the same type by applying this proportion, without going 

 through the laborious process of determining them by harmonic 

 analysis. The ratio of the amplitudes of the equilibrium compo- 

 nents is given by the ratio of the "mean values of the coefficients" 

 listed in table IV. It has also been found that the difference in the 

 epochs of components of the same type is proportional to the differ- 

 ence in their speeds. Thus if ki, k2, K3 are the epochs of three com- 

 ponents, and a', a", and a" their speeds 



iKz-K{)KK2-K{) = {a^''-a')/{a''-a') 

 whence 



K,=K,-h{K2-K0 {a"'-a')l{ci"-a') (95) 



If then the epochs ki and K2 hav^e been determined by analysis, the 

 epoch K3 can be determined by inference. 



131. In the harmonic analysis of small components, accidental 

 variations in the tidal heights may conceal, to a relatively large meas- 



