Arithmetical Operation 
19 
Table 4: Numeric values for the four variables In the coordinates of Moon and 
Sun In °/Moon day and related periods (cf. Table 5) 
Designation 
[°/Moon day] 
Period [a] 
13,638230516 
27,321583 days=tropical Month 
h 
1,020194382 
365,242196 days=tropical year 
P 
0,115308512 
8,84752 years=orbital period of mean perigee 
N‘ 
0,054809904 
18,6133 years=orbital period of the mean node 
f) 8 or, respectively, 96 least square fits for calcula 
ting the coefficients 
The coefficients c In equation (1) with j = 0...2/7- at respectively retained k 
and / - are determined on the basis of a sufficient number of (filtered) observa 
tions by k*I=8 least square fits In such a manner that 
||Ac — bll —» Minimum\ A e R'"’", b e R" with m > n . (4) 
In the event of 1=1, the vector b consists of observed time differences 
HWI = HWT° bs - t t or LWI = LWT° bs - t t and in the event of 1=2, it consists 
of HWH or LWH. Due to filtering m < N start - N end +1. Thus, a solution c e R" Is 
required for the linear root mean square problem (4) and hence a vector c, 
which minimises the residuum r(c) := b - Ac of the overdetermined system In 
the Euclidean norm. For calculating the vector c a method with singular value 
decomposition after Golub and Relnsch (1970) was used. 
In the case of 2 with k=96 least square fits for calculating the coefficients c of 
the hydrograph (tidal curve), the method Is analogous to case 1, with the differ 
ence that the points In time are already predetermined by fixed Intervals of 1/4 
Moon hour.