Harmonie Representation of Inequalities (HRol) 
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3 Harmonic Representation of Inequalities (HRol) 
The harmonic representation of inequalities seizes the idea of the non-harmonic 
procedure, which has been used for a long time to create, based on observa 
tions of the Moon, serviceable tidal predictions for high and low water heights 
and times (Lubbock, 1831). Towards the end of the nineteenth century, the non 
harmonic procedure had become almost entirely displaced by the harmonic 
procedure, since the latter enabled the calculation of complete curves (for a 
detailed list of references see Cartwright, 1999). Up until 1953, the German tide 
tables were likewise calculated by this method; however, the results remained 
unsatisfactory In spite of the enormous effort (Pansch, 1989). Since shipping 
was content with the forecast of the vertices (HWH, LWH), Horn (1948) sug 
gested a more economic procedure and Introduced It Into practice (Horn, 
1960), which has been In use since 1954 to compile the German tide tables. 
Since as yet no In detail comprehensible documentation exists for the method 
of “Harmonic Representation of Inequalities” practised at the German Federal 
Maritime and Hydrographic Agency since 1953, this paper alms to fill this gap. 
To begin with, I shall introduce the acronym HRol for the method’s long name. 
The method’s name already conveys the important information that this Is not 
about the calculation of the overall signal of water level, but only about the 
mathematical description of the deviations from mean values of any kind. The 
word inequalities has been used for a long time In celestial mechanics; it Indi 
cates marked disturbances In the Moon’s only seemingly uniform movement, 
which had been observed already In antiquity (Smlts, 1910).