162 U. S. COAST AS'D GEODETIC SUEVEY. 



the earth. In expressing this radius in feet the result is rounded off 

 to the nearest hundred, since a greater precision is not warranted by 

 the data from which it is obtained. 



The numerical values of several other important quantities that 

 appear in the text are also included in Table 2 for convenience of 

 reference. 



Table 3. Principal Tiarmonic components. — This table gives a hst 

 of the principal harmonic components used in the prediction of the 

 tides. The symbol by which each component is generally designated 

 and a brief description suggesting the derivation of the component are 

 given in the first and second columns, respectively. 



A general discussion of the argument (V+u) will be found in 

 section 10. The formulas for these arguments are derived from 

 formulas (100), (176), (190), (194), (208), (215), (228), and (230) in the 

 text. References to the overtides, compound tides, and meteorologi- 

 cal tides will be found in sections 18, 19, and 20. 



The speed, or average rate of change in the argument, in general, 

 depends entnely upon that part of the argument designated as V, 

 the u being an inequality that does not affect the average rate of 

 change. The speed formulas are readily derived from formulas for 

 V by substitutmg for the variable elements T, h, s, p, and p^ the 

 corresponding hourly rates of change in these elements, represented 

 hj d, T), a-, cs, andcji, respectively. The value for d is 15°, this being 

 the hourly rate of change in the hour angle of the mean sun. The 

 values for the other elements may be obtained from Table 2, and by 

 substituting in the formulas the corresponding numerical values for 

 the speeds of the components are readily obtained. An explanation 

 of the double expression for the argument for component M^ will be 

 found in section 14. 



The coefficients are discussed in section 11. The coefficient for- 

 mulas of Table 3 are derived from formulas (100), (176), (190), (194), 

 (208), (215), (228), and (230) of the text. In the coefficients of the 

 solar components the factor G has been introduced in order that the 



general lunar coefficient, o ^ ( ~ ) ^ ^ (function of X) may be used as 



a common coefficient factor for both the lunar and solar components. 

 The mean values of the coefficients are obtained by mutliplying the 

 constant factors by the mean values of the variable factors. The 

 numerical values of the constants are given in Table 2, and the mean 

 values of the variables, which depend upon some function of I, are 

 given in the formulas indicated by the references. The mean value 

 of the coefficient does not include the general coefficient. 



For the evectional and variational components ^2, X2> P^2> ^^^ Pit 

 two mean values are given for each coefficient. The first is that 

 derived from the given formula and the second is a value obtained by 

 Prof. J. C. Adams, who was associated with Sir George H. Darwin 

 in the investigation of the Harmonic Analysis of Tidal Observations, 

 and who in his computations carried the development of the lunar 

 theory to a higher order of precision than is provided for in this work. 

 (See pp. 60-61 of Report oi British Association for the Advancement 

 of Sciences for the year 1883.) The second value may therefore be 

 presumed to be a more precise determination of the mean coefficient 

 for each of these components. 



