HARMONIC ANALYSIS AND PREDICTION OF TIDES 35 
veloped into numerous constituent terms by a method similar to that 
already described in the development of the principal lunar force 
(paragraphs 59-69). In the following development constituents of 
very small magnitude are omitted. Those given are numbered con- 
secutively with the constituent terms of the principal lunar force. 
Fy /g=15/4 (M/E) (a/c)! sin Y (cos? Y—2/5) X 
(Ags) [(sin J—5/4 sin? [){3(1+2e?) cos (s—90°—€é) 
(Ags) +9e cos (2s—p—90°—€) 
(Ags) +3¢ cos (p—90°—£)} 
(Ag. +sin? [{5/4(1—6e?) cos (8s—90°—3é) 
(Ags) +25/4 e cos (4s—p—90° — 38) }] (137) 
F4, /[g=45/8 (M/E) (a/c)* cos Y (cos? Y—4/5) x 
(Ago) [sin? I cos? 4/{ 5/4(1—6e?) cos (T—3s+h+3é—1) 
(Azo) +25/4 e cos (T—4s+h+p+3é—y) } 
+(1—10 sin? 4J+15 sin* 4/) cos? 42 
(An) ( (Cige2e2) CoS GI S0-Fitar ey) Seah et [M1] 
(Azo) +3e cos (7—2s+h+p+évp) 
(Azz) se cos (hp 6) 
+ (1—10 cos? 41+15 cos* 41) sin? 4] 
(Ars) {(1-+2e?) cos (T+s+h—£—») 
(Ajs) +3e cos (T-+2s+h—p—é—y) }] (138) 
Fy, /[g=45/8 (M/E) (a/c)* sin Y cos? Y X 
(Aze) [sin I cos‘ 47{ (1—6e?) cos (2T—3s+2h490°+3é—27) 
(Azz) +5e cos (27—4s+2h+p+90° +3£—27) 
(Azs) sé cos 27 —2s--2h—p—90° + 3£—2y) } 
+ (cos? 4/—2/3) sin I cos? 41 
(Azo) {3(1+2e?) cos 2T—s+2h—90°+ é—2v) 
(Ago) +9e cos (2T—2s+2h+ p—90°-+ ——2yp) } 
-+ (cos? 4/—1/3) sin I sin? 4] 
(Asy) {3(1+2e?) cos (27-+s+2h—90°—é—27)}] (189) 
F'y3 /g=15/8 (M/E) (a/c)* cos’ YX 
(Ago) [cos® 7 { (1—6e?) cos (83T7—3s+3h+3E—3p) _____ M; 
(Ags) +5e cos (3T—4s+3h+p+3t—37) 
(Ags) +e cos (3T—2s+3h—p-180°+3£—37) 
(Ags) +127/8 e cos 8T—5s+3h+2p+3£—3r) 
(Ags) +75/8 me cos (83T—4s+5h—p+3é—37) } 
+ cos* 4] sin? 41 
(Ag7) {3(1+2e?) cos (3T—s+3h+£—37) 
(Ags) +9e cos (3T—2s+3h-+ p+é—37) }] (140) 
106. All of the constituent terms in formulas (137) to (140) are 
relatively unimportant but they are listed in table 1 because of their 
theoretical interest. The only one of these terms now used in the 
prediction of tides is (Ag:.) representing the constituent M; which has 
a speed exactly three-halves that of the principal lunar constituent 
M;. Term (Az) is of interest in having a speed exactly one-half that 
of M, and is sometimes called the true M, to distinguish it from the 
composite M, which is used in the prediction of tides and which will 
be described later. 
