HARMONIC ANALYSIS AND PREDICTION OF TIDES 39 
from the lesser force are made comparable with the others in respect 
to the vertical component force rather than in respect to the equi- 
librium height. 
SOLAR TIDES 
116. Since the tide-producing force of the sun is similar in action 
to that of the moon, the formulas derived for the latter are applicable, 
with suitable substitutions, to the solar forces. Referring to formulas 
(62), (63), and (64), let U be replaced by U; representing the product 
(S/E )(a@/e1)? in which S is the mass of the sun and (a@/c;) its mean parallax. 
Also replace e by e, the eccentricity of the earth’s orbit; IJ by w, the 
obliquity of the ecliptic; s by h, the mean longitude of the sun : and 
p by pi, the longitude of the solar perigee. For the solar forces the 
arcs € and v become zero and all terms representing the evectional 
and variational inequalities are omitted. 
117. Making the changes indicated the solar constituents are now 
expressed in the following formulas. Each term is marked for iden- 
tification by the letter B with the same subscript used for the corre- 
sponding term in the lunar tide. The usual constituent symbol is 
also given for the more important terms. Using the same system of 
notation as before, 
Solar F',3) /g =3/2 U, (1/2—3/2 sin? Y)X 
(B;) [(2/3—sin? w){(1+3/2 e?,) -..-____- permanent term 
(B.) +3 e, cos (h—7p,) 
(Bs) +9/2 e?, cos (2h—2p,) } 
(Bs) STASI co (== 5)/2) Cry COSe2 Npt ates ben Ssa 
(Bz) +7/2 e, cos (3h—py) 
- (Bs) +1/2 e, cos (h+p:+180°) 
“(B)) +17/2 e, cos (4h—2>7,) }] (185) 
Solar F',3; /g=3/2 U, sin 2YX 
(By4) [sin w cos” 4w{ (1—5/2 e,;) cos (T—h+90°)____- P, 
(Bis) +7/2 e,cos (T—2h+ p,+90°)_______- TH 
(Bis) +1/2 e, cos (T—p;—90°) 
(B;7) +17/2 e, cos (T—3h+2p,+90°) } 
(Boo) +sin 2w{ (1/2+3/4 e,) cos (T+h—90°)______- [Ky] 
(Bos) -+3/4 e, cos (T-+p,—90°) 
(Bos) sro eeer Gos Gia woe OS eases V1 
(Bos) +9/8 e1 cos (T—h+2p,—90°) 
(Bos) ok e”, cos (T+3h—2p,—90°) } 
(B31) +sin w sin? tw{ (1—5/2 e”,) cos (T+3h—90°)_- 
(B32) Tp e, cos (T+4h— p,— 90°) 
(Bs3) +1/2 e, cos (T+2h+p,+90°) 
(Bzx) +17/2 e, cos (T+5h—2p,—90°) }] (186) 
Solar F,3, /g=3/2 U, cos? YX 
(Bsy) [cost ta" 5)/ 2862) cos Oe 2 2. bas aoe S, 
(Bao) +7/2e,cos (2T—h+p,)__----------- i 
(Bux) +1/2e,cos (27+h—p,+180°)____._- R, 
(Biz) +17/2 e, cos (2T—2h+2p,)} 
(Biz) +sin? w{ (1/2+3/4 e7,) cos (2T+2h)__.__--__- [K] 
(Bis) +3/4 e, cos (27+h+7p)) 
(Bis) +3/4 e, cos (27+3h—/p,) 
(Formula continued on next page) 
