Arithmetical Operation 
15 
day (Table 5); i counts the transits of the Moon and one only has to bear In mind 
that this numerator has the same zero point both In analysis and synthesis. 
The following paragraphs will put the reader In a position, If required, to 
develop his or her own computer programme for tidal analysis and synthesis. 
The problem can be roughly organised Into 7 steps a) to g): 
a) Calculation of passage times of the true Moon over the prime meridian In 
upper and lower culmination, 
b) Synchronisation of the mean Moon with the transit times of the true Moon, 
c) Processing of 19 years of gauge observations, 
d) Filtering of data (3 standard deviations), 
e) Determination of the relevant angular velocities, 
f) 8 or, respectively, 96 least square fits for calculating the coefficients and 
g) Synthesis. 
a) Calculation of passage times of the true Moon 
over the prime meridian in upper and lower 
culmination 
Here, the transit time shall be defined as the point In time of the Moon's transit 
(centre of mass) over the prime meridian (Greenwich Observatory). A proce 
dure exact to the minute can be programmed on the basis of the data given In 
Meeus (1998), chapters 7,10, 13, 22, 47. Alternatively, one may substitute 
tables obtained from astronomical service providers. Due to the uncertainty of 
gauge observations (see c)), It Is not necessary to observe a high degree of 
accuracy In transit calculations.