HARMONIC ANALYSIS AND PREDICTION OF TIDES Sl 
epochs of constituents S, and K, because of the disturbing effects of 
K, and T, on the former and P, on the latter. In a short series of 
observations these effects may be considerable because of the small 
differences in the periods of the constituents involved. 
237. Let 
yi=A cos (at+ a) (344) 
Y2=B cos (bt+ 8) (345) 
represent two constituents, the first being the principal or predomi- 
nating constituent and the latter a secondary constituent whose effect 
is to modify the amplitude and epoch of the principal constituent. 
The resultant tide will then be represented by 
y=yity=A cos (at+a)+B cos (bt+ 8) (346) 
Values of ¢ which will render (344) a maximum must satisfy the 
derived equation 
and 
Aa sin (at-+a)=0 (347) 
and the values of ¢ which will render (346) a maximum must satisfy 
the equation 
Aa sin (at+a)+ Bb sin (b¢+ 8) =0 (348) 
For a maximum of (344) 
jt te (349) 
in which n is any integer. 
238. Let “=the acceleration in the principal constituent A due to 
the disturbing constituent B. Then for a maximum of (346) 
;— 2h mat (350) 
This value of ¢t must satisfy equation (348), therefore we have 
Valein@nt 6) 48h ain | Fen 70-2) +6 | 
=— Aa sin 06+ Bb sin (2n 70-2) +p—a-0 =0 (3851) 
At the time of this maximum, when 
_2n z™—a—@ 
a 
the phase of constituent A will equal 
(2n r—a—0)+a 
and the phase of constituent B will equal 
- (2n r—a—O)+ 8B 
Let ¢=phase of constituent B—phase of constituent A at this time. 
Then 
t 
b] 
gt (2n r—a—O)+B—«a (352) 
