HARMONIC ANALYSIS! AND PREDICTION OF TIDES Pit 
(c/d)? cos A=(1+3/2 e?) cos A 
+3/2 € cos (A—s+p)+3/2 e cos (A+s—p) 
+9/4 e? cos (A—2s+2p)+9/4 e cos (A+2s—2p) 
145/16 | me cos (A—s+2h— p)+45/16 me cos (A+s—2h-+>p) 
+3/2 m? cos (A—2s+2h)+3/2 m? cos (A+2s—2h) (60): 
(c/d)® cos (A+2k) = (c/d)’ cos 2k cos A— (e/d)* sin 2k sin A 
=(1—5/2 e?) cos A 
+7/2 € cos (A+s—p)+1/2 e cos (A—s+p+180°) 
+17/2 e? cos (A+2s—2>p) 
+105/16 sme cos (At+s—2h+p) + 15/16 me cos (A—s+2h— py Ae 
+23/8 m? cos (A+2s—2h)+1/8 m? cos (A—2s+2h) (61) 
66. After suitable substitutions for A have been made in the three 
preceding equations they are immediately applicable to the final 
expansion of the several terms in formulas (48) to (50), excepting the 
first term of (48) for which formula (56) may be used directly. Hach 
term in the expanded formulas given below represents a constituent 
of the lunar tide-producing force and for convenience of reference is 
designated by the letter A with a subscript. There are also given the 
generally recognized symbols for the principal constituents, and when 
such a symbol is enclosed in brackets it signifies that the term given 
only partially represents the constituent so named. 
7. Formula for long-period constituents of vertical component of 
principal lunar tide-producing force: 
F439 /[g=3/2 U(/2—3/2 sin? Y) X 
Can) H(2/3 sincere 3/2 eae be WEY on ee Td permanent term 
Ay) ae ORCL COS (Shp) eae hee 7). Cus tues 4.1 Wine ain Mm 
(A3) +9/2 e? cos (2s—2p) 
(A,) +45/8 me cos (s—2h+ 7) 
(As) aS? COS, 28a Oh RRL e ey cima) vrei in MSf 
(An) =|-1sin el 5/202") teos Qs = 2 )e EP os Web Mf 
(A,) +7/2 € cos (8s—p—2é) 
(As) +1/2 e cos (s+p+180°—2é) 
(Ay) +17/2 e? cos (4s—2p—2é) 
(Ajo) +105/16 me cos (8s—2h-+ p—2é) 
(Aj;) +15/16 me cos (s+2h—p+180°—28) 
(Aj) +23/8 m? cos (4s—2h—28) 
(Aj) +1/8 m? cos (2h—2€)}] (62) 
68. Formula for diurnal constituents of vertical component of 
principal lunar tide-producing force: 
Tan (9 —3)/ 2 Oesime2 vax 
(Ay) [sin I cos? 1/2T 
{(1—5/2 e?) cos (T—2s+h+90°+2¢—v)____ O, 
(A,5) +7/2 e cos (T—38s+h+p+90°+2é—»)____ Q, 
(Ajg) +1/2 e cos (T—s+th—p—90°+2é—»y)_____ [M,| 
(Aj7) +17/2 e cos (T—4s+h+2p4+90°+2é—y)__ 2Q, 
(Ajs) +105/16 me cos(T-—3s+3h—p+90°+2é—»p)_ pi 
(Aj) +15/16 me cos (T—s—h+p—90° + 2é— 1) 
(Ago) +23/8 m? cos (T—4s+3h+90°+2&— 1) ____ O71 
(Aoi) +1/8 m? cos (T—h+90°+2¢—») } 
(Formula continued next page) 
