(*> 
5. Neither of the two methods, which can be used when we 
calculate watertides, is applicable to the case under discussion; as 
evidently the tide S, is great we may not assume that the annual 
variation of S t will be small with respect to the quantities to be 
found. Neither is there a reason to assume that in winter or in 
summer, regarded separately, S, will be fairly constant, as we are 
still quite uncertain about the nature and the origin of it. 
Another favourable circumstance however, not appearing for 
watertides, makes in this case an approximative solution possible. 
For when X 1 appears in the monthly means with a certain value 
K and an argument Xi> then we can say almost with certainty that 
the tide P will make its appearance with an amplitude: 
P = aK , 
in which a is the theoretic proportion of P to K x : 
a = 0.371. 
Furthermore we can state with equal probability 
X 2 = ..(6) 
Thus out of the equations (4) two unknown quantities disappear 
and they can be replaced by two others characterizing S x more 
closely. 
We represent this tide by the form : 
\S + Loo 8{90.* -m)}cos(lht - C x ) 
and so we assume that the amplitude is submitted to an annual 
variation, but that C x remains constant, which, if this phenomenon 
finds its origin in the radiation of the sun, cannot be far from the 
truth. 
Furthermore follows from (6) : 
V* = + V 0 - V' 0 — ^ 4- « = + 49°.55. 
Instead of the formulae (5) we get the four equations 
L cos C cosm + K cos + Ka cos + «) — R j 
L cos C sin m -f K sin — Ka sin (ty 1 a) = Q 
LsinCcosm + Ksin ^ + Ka sin + a) = S 
L sin C sin m — K cos ip, -j- Ka cos (qjj -f a)=Q' j 
With 
R— 42.22 
Q— 34.98 
C = 245°.5 
we find from this: 
K x = 51.2 
if?, = 44°.5 
R\ = 69.94 
Q'= 0.96 
L ~ 46.3 
m — 248°.7 
• (7) 
