HARMONIC ANALYSIS AND PREDICTION OF TIDES 79 
K(C) —K(A) = 
5 qle(B) —«(A)}] (323) 
or, 
«(C) =x(A) +5 —[e(B) —x(A)] (324) 
By formula (322) the amplitude of a constituent (B) may be inferred 
from the known amplitude of a constituent (A), and by formula (324) 
the epoch of a constituent (C) may be inferred from the known epochs 
of constituents (A) and (B). 
231. These formulas have, however, certain limitations. They 
are not applicable to shallow water and meteorological constituents, 
nor are they adapted to the determination of a diurnal constituent 
from a semidiurnal constituent: or of a semidiurnal constituent from 
a diurnal constituent. The results obtained by the application of 
the formulas to tides of similar type may be considered only as rough 
approximations to the truth. They may, however, be preferable to 
the values obtained for certain constituents when the series of obser- 
vations is short. 
232. By substituting the mean values of the coefficients and the 
speeds from table 2 the following special formulas may be derived 
from the general formulas (322) and (324) 
Diurnal constituents 
iG AO gaME (On ca) aK) 20.496 [x (KG)— «(,)) (325) 
H(OO)=0.043 H(O,); «(OO)=«(K,) +1.000 [«(K;) —«(O,)] (327) 
GE) =O.S31 IEG) e eB) =) OOS IC On) (328) 
A(Q,) =0.194 H(QO)); (Qi) =«(K,) —1.496 [«(K,) —«(O;)] (329) 
H(2Q) =0.026 H(O,); «(2Q) =«(K,) —1.992 [x(K,) —«(O;)] (330) 
F(p;) =0.038 H(O;); «(o:) =«(&i)—1.429 [«(Ky) —«(O;)] (331) 
Semidiurnal constituents 
=0.143 H(N,) ; =x(M2)+1.000 [e( Ma) —x(N) | (334) 
FI(N,) =0.194 H(M)); «(N2) =x(S.) —1.536 [xk(S.) —x(M.)] = (335) 
H(2N)=0.026 H(M.); «(2N)=«(S,) —2.072 [x(S)) —«(M,)] (336) 
=0.133 H(N;); = (Mz) —2.000 [x(M,) —«(N,)] (337) 
H(R2) =0.008 H(S2);  «(R2) =«x(S2) +0.040 [k(S.) —x«(M,)] (338) 
) =0.059 A(S,); «(T2) =«x(S.) —0.040 [x(S.) —«(M,)] (339) 
FAI(:) =0.007 H(M2); «(A2) =x«(S2) —0.536 [k(S.) —«(Mb2)] (340) 
Hu.) =0.024 H(M,); «(u2) =«(S:) —2.000 [«(S.) —«(M,)] (341) 
H(,) =0.038 H(M,); (v2) =«(So) —1.464 [x(S.) —«(M>)] (342) 
—0.194 H(N,); =«(M>»)—0.866 [«(M2) —x(N2)] = (343) 
233. In order to test the reliability of the results obtained by infer- 
ence as above, 60 stations representing various types of tide in different 
parts of the world where the harmonic constants had been determined 
from observations were selected and a comparison was made between 
the values for certain constants as obtained by inference and by 
observations. The tests were applied to the diurnal constituents 
