60 



expression for cos d derived as explained in paragraph 107 and reducing, 

 by the general method pursued in determining the tides due to the third 

 power of the moon's parallax. All of the resulting terms are very 

 small, the only one recognized being: 



y=3/2(MayEc')a[5ll2 cos^Xcos-^ jilcos (3r+3/i,-3s + 3^-3v)]. MsCTO) 



112. Equilibrium argument.— E?ich term of equation (68) contains 

 the general factor 3/2 {Ma^jEc')a, which has a constant value of 1.7527 

 feet; a factor composed of a function of the latitude of the tidal sta- 

 tion, which is constant at a given station; a factor composed of a 

 function of /, which changes very slowly, a constant factor containing 

 e and m, and the cosine of an angle formed by the algebraic sum of 

 simple multiples of the angles T, h, s, p, |, and v. This angle is called 

 the equilibrium argument. The term in equation (70) is in the same 

 form but with a different general factor. 



Similarly each term of equation (69) contains the general factor 

 3/2 {Sa^/Eci^)a, which has the constant value of 0.8091 feet; a factor 

 composed of a function of the latitude of the tidal station; a factor 

 composed of a function of co, which does not change ; a constant factor 

 containing ei and the cosine of an equilibrium argument containing T, 

 h, and jpi only. 



113. Since Tis the hour angle of the mean sun at the tidal station, 

 it is zero at noon, mean local time, at the station, and increases at the 

 rate of 15° per mean solar hour. 



The values of the angles h, s, p, and pi, the longitudes of the mean 

 sun, moon, and lunar and solar perigee, respectively, at the beginning 

 of each calendar year at Greenwich are given in Manuals on Harmonic 

 Analysis of Tides. Their rates of change remain practically constant 

 for a century of time, and are as follows : 



That part of the equilibrium argument made up of the angles T, h, 

 s, p, and pi which change at a constant rate, together with any con- 

 stant term formed by the introduction of 90° or 180°, is convention- 

 aUy represented by the symbol V. This part then has the form; 



y=nir+7i2/t+7i3S+n4p+%^i+7i690° (71) 



where ni, n2, n^, etc., are small positive or negative integers, or zero. 



