HARMONIC ANALYSIS AND PREDICTION OF TIDES 19 
61. Substituting the values of 7 and X from (46) and (47) m formu- 
las (43) to (45), these may be written 
F 39 /g==3/2 U(1/2—3/2 sin? Y) X 
[(c/d)?(2/3—sin? I) 
+ (c/d)® sin? I cos (2s—2&+2k)] (48) 
F331 /g=3/2 U sin Dix 
[(c/d)? sin I cos? 41 cos (T—2s+h+2&—v+90°—2k) 
+1/2 (c/d)? sin 2I cos (T+h—v—90°) 
+ (e/d)* sin I sin? 47 cos (T+2s+h—2é—v—90°+ 2k)] (49) 
F 32 /[g=3/2 U cos? YX 
[(c/d)* cos* 41 cos (2T—2s+2h+2&—2y—2k) 
+1/2 (c/d)® sin? I cos (2T-+2h—27) 
+ (e/d)? sin 42 cos (2T7+2s+2h—2é—27+ 2k) (50) 
Cc 
FIGURE 4. 
Disregarding at this time the slow change in the function of J, the 
variable part of each term of the above formulas may be expressed in 
one of the following forms—(e/d)3, (c/d)? cos A, (e/d)* cos (A+2k), or 
(c/d)? cos (A—2k), in which A includes all the elements of the variable 
angular function excepting the multiple of k. 
62. The following equations for the motion of the moon were 
adapted from Godtray’s Elementary Treatise on the Lunar Theory: 
s’=true longitude of moon (in radians) 
ee Ba Ray ay aly RR NY nn, ein (mean longitude) 
+2e sin (s—p)+5/4 e? sin 2(s—p)-_----- (elliptic inequality) 
+15/4 me sin(s—2h+p)___-------- (evectional inequality) 
+11/8 m? sin 2(s—h)_______-- (variational inequality) (51) 
