16 
b) Synchronisation of the mean Moon with the 
transit times of the true Moon 
Our experiences regarding the chronology of natural events and phenomena 
are oriented, within the rough framework of time zones, on the Sun's transit over 
the local meridian. The temporal allocation of natural phenomena is significantly 
disturbed by the change between summer and winter time as stipulated by law. 
It is urgently recommended to use UTC during the entire arithmetical operation 
a) to g) and to convert the data into legal times only for the purpose of creation 
of local products. 
The mean Moon is defined as a fictive celestial object orbiting Earth on the 
equatorial plane. Its transits over the upper and lower local meridian occur at 
intervals of 3607(28.9841042 7h) = 12.4206012 h [NB: in Muller-Navarra 
(2009), bottom of page 386, this number is Incorrect from the 6th decimal place 
onwards.]. This time, divided by 12, results In a Moon hour of 1.0350501 h. The 
given 7 decimal places are fully sufficient for calculating multiples of this Moon 
hour in order to define the time grid, which then Is superimposed on the water 
gauge time series. 
It Is advisable to number the Moon transits and to apply these numbers also to 
the following four vertices (Muller-Navarra, 2009). The transit of the true Moon 
over the prime meridian in upper culmination on 31 December 1949 at 
21:08 UTC (T 0 ) Is given the number zero. The preceding transits are given neg 
ative numbers, the subsequent transits are given positive numbers. For exam 
ple, the transit on 4 September 2006 carries the number 20,000. 
Finally, the time grid of the mean Moon has to be fixated to the time line, so that 
the high and low water intervals (Table 2) can be represented directly by the 
coefficients c kl0 , k = 1,..,4 . To this end, the grid of the mean Moon Is set In 
such a manner that t 0 =T 0 . If one now compares the true transits with the thus 
fixated mean transits, the former reveal significant Inequalities, which were In 
part known already In antiquity. These astronomical Inequalities with a standard 
deviation of approximately 21 minutes are reflected in the natural, meteorologi- 
cally disturbed tidal gauges as greater Inequalities in time. The mean value 
T —t for the time period 01 January 1801 to 30 December 2049 is approxi 
mately +24.23 min; In a final step, the time grid of the mean Moon Is moved by 
just this value, so that t = t +T-t . Within the procedure, all times t, t and T 
are calculated as a day number (Muller-Navarra, 2009). It is then a simple step 
to derive from these day numbers temporal differences with the onset of verti 
ces, e. g. high water or low water intervals (Table 6, Column 6).