44 U. S. GOAST AND GEODETIC SURVEY 
term will therefore predominate and determine the speed of the 
composite constituent. 
129. With other symbols as before, let A and B represent the 
respective coefficients of the two terms and @ the argument of the 
first term. We then have 
Ay=A cos 6 (210) 
Aw=B cos (6+2P—180°)=—B cos (0+2P) (211) 
L,=Ay-+ A= (A—B cos 2P) cos 6+ B sin 2P sin 6 
B sin 2P 
lg Abies 2) 4 = fan 
= (A?—2AB cos 2P+B’)? cos E tan Teas OP 
=1/2e = 2Teos (2T—s+2h—p+180°+2t—2»—R) (212) 
in which i 
1/R,=(1—12 tan? 47 cos 2P+36 tan‘ 4)? (213) 
se St sin 2P (214) 
1/6 cot? 4J—cos 2P 
Values of log R, and R computed from the above formulas are given 
in tables 7 and 8, respectively. 
130. The obliquity factor for the composite L, constituent may be 
expressed by the formula cost $/1/R,. The mean value of 1/R, is 
approximately unity, and in accord with the Darwinian system the 
mean for the entire obliquity factor is taken as the product cos* 
1 cost 4i, which equals 0.9154 and is the same as the mean value of 
the obliquity factor for the principal constituent M;. Multiplying 
this by the elliptic factor 4e gives 0.0251 as the mean constituent 
coefficient. 
131. The node factor formula for constituent L, based upon the 
above mean for the obliquity factor is as follows: 
cost 4] 
fl) = Fes X VR. =f(Me) X UR, (215) 
Node factors for constituent L. based upon the above formula are 
included in table 14 for the middle of each year from 1850 to 1999, 
inclusive. The logarithms of the reciprocal reduction factors covering 
the period 1900 to 2000 are contained in table 13. 
LUNISOLAR Ki AND K2 TIDES 
132. Lunar diurnal term A, of formula (63) and solar diurnal 
term B,, of formula (186) have the same speed. Together they form 
the lunisolar K, constituent. Also, lunar semidiurnal term Ay, of 
formula (64) and solar semidiurnal term By; of formula (187) have 
speeds exactly twice that of constituent K, and together form the 
lunisolar K, constituent. In order that the solar terms may have 
the same general coefficient as the lunar terms, the solar factor 
U,/U, which will be designated by the symbol S’, will be transferred 
from the general coefficient of the solar terms and included in the 
constituent coefficients. Then, neglecting the general coefficient and 
