36 U. §. COAST AND GEODETIC SURVEY 
107. For simplicity and the purposes of this publication, the mean 
values of the obliquity factors in the terms of the lesser tide-producing 
force will be taken as the values pertnining to the time when J equals 
w or 23.452°, excepting that for constituent M; and associated terms 
the mean has been obtained in accord with the system described in 
paragraph 75. The corresponding node factors (paragraph 77) may 
then be expressed by the following formulas in which the denominators 
are the accepted means of the obliquity factors: 
F(Ags) to f(Acs) = (sin J—5/4 sin?J)/0.3192 (141) 
F(Agz) to f( Ags) =sin®//0.0630 (142) 
F (Ass) to f(Ayo) =sin?l cos*41/0.1518 (143) 
F(An) to f(Az3) = (1—10 sin?37+15 sin*4/) cos’3I/0.5873 (144) 
f(A) to f(Azs) = (1—10 cos’4I+15 cos*4J) sin?47/0.2147 (145) 
Ff (Are) to f(Ars) =sin I cos*31/0.3658 (146) 
F(Ar) to f(Aso) = (cos?3/—2/3) sin I cos?37/0.1114 (147) 
Ft (Asi) = (cos’37—1/3) sin I sin?4//0.0103 (148) 
F(Age) to f(Ase) =f(M3) = cos®3I/0.8758 (149) 
f(As;) to f(Asg) =cos*3l sin?47/0.0380 (150) 
Comparing formulas (149) and (78), it will be noted that the node 
factor for M; is equal to the node factor for M, raised to the 3/2 
power. Computed values applicable to terms Ag. to Ass are included 
in table 14 for years 1850 to 1999, inclusive. 
108. For the tabulated constituent coefficients of the terms in 
formulas (137) to (140) there are included not only the elliptic and 
mean obliquity factors but also such other factors as may be necessary 
to permit the use of the general coefficient (8/2 U) of formulas (81) 
to (83) for the vertical component of the principal tide-producing 
force. The common coefficient ((4/E) (a/e)* of formulas (137) to 
(140) is equal to U multiplied by the parallax a/c, and the latter 
together with the necessary numerical factors is included in the 
constituent coefficients in table 2. Formulas (137) to (140) may 
then be summarized as follows: 
Fay [g=3/2 U sin Y(cos?-Y—2/5) 2 fC cos E (151) 
Fy. /g=3/2 U cos Y(cos*¥—4/5) 2 fC cos E (152) 
Fy, /g=3/2 Usin Y cos?¥ 2 fC cos E (153) 
Fa. (G3) 2. ico Ya C. cose Es, (154) 
109. It is to be noted that in formulas (151), (152), and (153), the 
maximum value of the latitude factor in each is less than unity, being 
