HARMONIC ANALYSIS AND PREDICTION OF TIDES. 35 



With other notations as before, we then have 



<r = s-^ (98) 



X=T+Ji-v (99) 



Substituting (98) and (99) in (97), making all coefficients positive 

 by adding or substracting t from the angle, since — cos x = + cos (x ± tt) ^ 

 and neglecting all the smaller terms whose numerical maximum val- 

 ues as indicated are less than 0.003, we obtain the following: 



y = 3/2~('~J acos'X X 



(A), [(1/2 -5/4 e2) COS* K cos {2T+2h-2s+2^-2p) _.Ma 



(A)2 +7/4:ecos* ^ I QOs(2T+2h-Ss+p+2^-2v) Nj 



(^)s +1/4 e cos* ^ /cos i2T+2h-s-p+2^-2y+w).... [L2I 



(A)i +17/4 e2 cos" K cos (2r+2/i-4s+2p+2|-2j') . 2N 



(A)i +105/32 me cos* § / cos i2T+4:h-3s-p+2i-2p) fj 



(A)i +15/32 me cos* i / cos i2T -s+p +2^ -2v+Tr) X2 



(A)7 +23/16 m2 cos* ^ I cos {2T+4h-4:S+2^-2p) M2 



(A)i7 +(1/4+3/8 e2) sin^Z cos i2T+2h-2i') [K2] 



(A)i8 +3/8 e sin2 / cos {2T+2h+s-p-2v) 



(A)io +3/8 e sin2 / cos (2T+2h-s+p-2p)] [L2P 



+3/2 J (~y a sin 2X X 



(A)o6 [(1/2-5/4 e2) sin I cos* § I cos (T+h-2s+2i-v+w/2) O, 



{A)27 +7/4 e sin I cos* ^ / cos (T+h-3s+p+2i-v+ir/2)... Qi 



(A)28 +1/4 e sin / cos* ^ / cos iT+h-s-p+2^-v-irl2) [Mi^ 



{A)29 +17/4 e* sin I cos* | / cos (r+/i-4s+2p+2{-y+ir/2) 2Q 



(A)3o +105/32 me sin 7 cos* i I cos (r+3/i-3s-p+2|-v+ir/2)--Pi 



(A)32 +23/16 m* sin /cos* i /cos (r+3;i-4s+2$-;'+W2) 



iA)u +(1/2-5/4 6*) sin / sin* i I cos (!r+;i+2s-2^-i'-7r/2) — -OO 



(A)42 +(1/4+3/8 e*) sin 2 / cos {T+h-v—irf2) [KJ 



(A)« +3/8 e sin 2 / cos (r+/i+s-p-j'-x/2) Ji 



iA)u +3/8 e sin 2 / cos {T+h-s+p-v-Tr/2) [Mi] 



(A)47 +45/64 me sin 2 / cos (T -h+s+p-v-Tr/2) 



{A)ts +45/64 mesin2 /cos (r+3A-s-p-«'-7r/2)] 



+3/2 ^ (^)' a (1/2-3/2 sin* X) X 



(A)5i [(1/2-5/4 e*) sin* / cos (2s-20 - Mf 



(A) 52 + 7/4 e sin* / cos (3s - p - 2|) 



(A) 53 +1/4 e sin* / cos (s+p-2^+ir) 



{A)n +17/4e2sin2 / cos (4s-2p-2f) 



(A)6B +105/32 me sin* / cos (3s-2;i+p -2^) 



(A) 69 + (1/3 + 1/2 e*) (1 - 3/2 sin* /) 



(A)to +e (1-3/2 sin* /) cos (s-p) Mm 



(^)6i +3/2 e* (1 -3/2 sin3 /) cos (2s -2p) 



(A) 62 +15/8 me (1-3/2 sin* /) cos (s-2/i+p) 



(A)63 +w* (1-3/2 sin* /) cos (2s-2;i) [MSf] (100) 



