40 U. S. COAST AND GEODETIC SURVEY 
(Bro) +9/8 e?, cos (2T+2,) 
(Bs1) +9/8 e, cos (2T+4h—2p))} 
(Bs) +sin* 4w{ (1—5/2 e?,) cos (27'+4h) 
(Bs7) +7/2 e, cos (2T+5h—p;) 
(Bs) +1/2 e, cos 27+38h+,4+ 180°) 
(Bso) +17/2 e; cos (2T+6h—2>p)) }] (187) 
118. The general coefficient for the solar tide-producing force 
differs from that of the lunar force in the basic factor. From the 
fundamental data in table 1, the ratio of U,/U is found to be 0.4602. 
This ratio, which will be designated as the solar factor with symbol 8’, 
represents the theoretical relation between the principal solar and 
lunar tide-producing forces. In computing the constituent coefficients 
of the solar terms for use in table 2, the solar factor was included in 
order that the same general coefficient may be applicable to both 
lunar and solar terms. All of the summarized formulas involving the 
coefficients and arguments of table 2 are therefore applicable to both 
lunar and solar constituents. For the solar constituents, however, 
the node factor (f) is always unity since w, the obliquity of the ecliptic, 
may be considered as a constant. 
119. By substituting solar elements in formulas (137) to (140) the 
corresponding solar constituents pertaining to the 4th power of the 
sun’s parallax are readily obtained. Since the theoretical magnitude 
of the lesser solar tide-producing force is less than 0.00002 part of the 
total tide-producing force of moon and sun, it is usually disregarded 
altogether. However, certain interest is attached to three of the 
constituents which are considered in connection with shallow water 
and meteorological tides (p. 46). These are constituents Sa, S$,, and 
S3, corresponding respectively to terms Ags, A7;, and Age of the lunar 
series. They are listed in table 2 with reference letter B and cor- 
responding subscripts. Sa has a speed one-half that of constituent 
Ssa represented by term B, of formula (185). Its theoretical argu- 
ment as derived from term A,, contains the constant 90°, but being 
considered as a meteorological rather than an astronomical consti- 
tuent, this constant is omitted from the argument. Constituents S, 
and S; have speeds respectively one-half and three-halves that of the 
principal solar constituent S. 
120. The arguments of a number of the solar constituents include 
the element p, which represents the longitude of the solar perigee. 
As this changes less than 2° in a century, it may be considered as 
practically constant for the entire century. Referring to table 4 it 
will be noted that p, changes from 281.22° in 1900 to 282.94° in 2000. 
The value of 282° may therefore be adopted without material error 
for all work relating to the present century. With p, taken as a 
constant, it will be found that a number of terms in table 2 have the 
same speeds and may therefore be expected to merge into single 
constituents. Thus, constituents receiving contributions from more 
than one term are as follows: Sa from terms B:, B;, and Begs; Ssa 
from terms B; and B;; P, from terms B,, and B,;; S; from terms Byjg, 
B.3, and Bz; ¥, from terms By, and B33; ¢, from terms B., and B3;; 
S. from terms By) and Bs; and Re from terms By and By. A few 
other solar terms also merge. 
