HARMONIC ANALYSIS AND PREDICTION OF TIDES if 
0.4, 0.2754, and 0.3849, respectively, if the sign of the function is 
disregarded. In formula (154), as in the corresponding formulas for 
the principal tide-producing force, the maximum value of this factor 
is unity. In comparing the relative importance of the various con- 
stituents of the tide-producing force the latitude factor should be in- 
cluded with the mean coefficient. Attention is also called to the fact 
that the relative importance of the constituents mvolving the 4th 
power of the moon’s parallax is greater in respect to the vertical com- 
ponent of the tide-producing force than in respect to the height of the 
equilibrium tide. In table 2 the mean coefficients are taken com- 
parable in respect to the vertical component of the tide-producing 
force and the constituent coefficients pertaining to the lesser force are 
therefore 50 percent greater than they would be if taken comparable 
in respect to the equilibrium tide. 
110. The south and west horizontal components of the lesser tide- 
producing force may be obtained by multiplying formula (26) by cos 
A and sin A, respectively. Using the same system of notation as 
before, we then have 
FP, /g=3/2 (M/E) (a/d)* sin 2 (5 cos? z—1) cos A (155) 
Fy, /g=3/2 (M/E) (a/d)* sin z (5 cos? z—1) sin A (156) 
111. By means of the relations expressed in formulas (31), (86), 
and (87), the above component forces may be separated into long- 
period, diurnal, semidiurnal, and terdiurnal terms as follows: 
South component, 
Fs49 [= —15/4 (M/E) (a/d)* cos Y (cos?¥ —4/5) sin D(5 cos2?D—2) (157) 
Ps, [g=45/8 (M/E) (a/d)* sin Y (cos? ¥ —4/15) cos D(5 cos? D—4) cos t 
(158) 
Paz [g= —45/4 (M/E) (a/d)* cos Y (cos? ¥—2/3) sin D cos?D cos 2t (159) 
Faz [g=15/8 (M/E) (a/d)* sin Y cos?Y cos*D cos 3t (160) 
West component, 
Fy /g=15/8 (M/E) (a/d)*(cos?Y —4/5) cos D(5 cos?D—4) sint (161) 
Pi /g=15/4 (M/E) (a/d)* sin 2Y sin D cos?D sin 2¢ (162) 
Fx3 |g=15/8 (M/E) (a/d)* cos?Y cos?D sin 3¢ (163) 
112. Comparing formulas (157) to (160) for the south component 
force with the corresponding terms of (132) for the vertical com- 
ponent, it will be noted that they differ only in the latitude factors 
and in sign for two of the terms. With adjustments for these dif- 
ferences the summarized formulas (151) to (154) are directly applicable 
ir expressing the corresponding terms in the south component. 
us 
Py) /g=3/2 U cos Y(cos*¥—4/5) 2 fC cos(H+180°) (164) 
Fy [g=3/2 U sin Y(cos?¥—4/15) = fC cos HE (165) 
F'42 [g=3/2 U cos Y(cos?¥ —2/3) = fC cos(H+180°) (166) 
F43 [g=3/2 U sin Y cos’Y 2 fC cos E (167) 
113. For the west component there is no long-period term. Com- 
paring (161) to (163) with the corresponding terms of (132), it will 
be noted that the ¢-functions are expressed as sines instead of cosines 
but they may be changed to the latter by subtracting 90° from each 
