Observatorium Hoher List, Institute of Astronomy, University of Bonn, Daun, Germany

E-mail : pbrosche@astro.uni-bonn.de

For a long time, two separate lines of thought governed our perceptions of tidal friction. Empirical evidence from observations of solar eclipses made as early as in Antiquity pointed to a secular acceleration of the mean angular motion of the Moon amongst the stars which was first noted by Edmund Halley in 1695. However, according to the solitary theoretical speculations of the philosopher Immanuel Kant (1754), oceanic tides retarded the rotation of the earth. When did these two lines of thought converge?

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Science rarely evolves linearly. The path taken by evolution is far from a straight line and, to learn about science, we should focus on its detours! For instance, if we were to take a look at the genealogical tree describing our perceptions of tidal friction (a) over time, we could build the following series of aphorisms:

In 1754, however, the young philosopher Immanuel Kant, who took great interest in scientific issues, reasoned on the basis of pure theory that the action of oceanic tides must slow down the earth's rotation (4) (5). His article appeared in a newspaper devoted in large part to advertisements and warrants amidst a windmill sales-ad and a want-ad for peacocks! Kant apparently did not take his ideas on tides very seriously as they have no mention in his "

Julius Robert Mayer (11) was the first to describe both aspects of the earth-moon interaction in his book "

Mayer was an outsider who was finally accepted by the scientific community not for his work on tidal friction but for the theorem of energy conservation. His theorem's application to the earth-moon-system was neglected because,

Unfortunately, Darwin's analytical treatment does not really further our understanding. The tidal force field of an external body such as the moon on the Earth diminishes the Earth's gravity along the line connecting the centres of these planets and strengthens it at the girdle perpendicular to the first. Darwin painted a picture of a deformable earth with two tidal bulges in the sea surface, one immediately underneath the moon and the other on the opposite side of the globe. This nice phenomenological description can be woven into a consistent theory but its core, i.e. the strength of the interaction between the earth's oceans and the moon (given by the amplitude and phase lag of the tidal bulges), remains a free parameter!

It is only with current scientific and technological means that oceanic tides, which are geometricallv much more complex than solid earth tides and which are the effects of choice to explain tidal interaction since Kant's day, can be treated in any detail. The average torques between the oceans and the moon for the main partial tides (j) calculated with available mathematical models agree with observed values. It thus seems that we have now moved one step up the

(a) Tidal friction is the time-averaged global transfer of rotational energy and angular momentum by tides. It is caused by tidal forces and the instantaneous local effects of these forces are currents and heights.

(b) The place where solar eclipses are observed contains information on the rotational position of the earth.

(c) Secular: Lasting or going on for ages, occurring over an indefinitely long time.

(d) Rome has spoken, the issue is settled.

(e) Conservative celestial mechanics means that forces are derived from a potential, in this instance, the potential of mutual gravitational attraction. As soon as friction is implied, this assumption no longer holds and energy is no longer conserved.

(f) I am grateful to François Mignard (CERGA, Grasse) for this information.

(g) The observed phase lag is small and theorists today consider that the real value is even smaller, in other words, that earth tides are not important.

(h) A dynamic time-scale is a physical time-scale based on the laws of celestial mechanics (e). A time t enters into these laws, and motions and positions x(t) are predicted in dependence of t. It is thus possible to reverse the process and to deduce the corresponding t from an observed x.

(i) Synodical (or synodial) : pertaining to the conjunction of the planets.

(j) Total tides are decomposed mathematically into a sum of simple sine waves with special periods. The main partial tide is the lunar semi-diurnal one with a period of 12 hours and 25 minutes.

(k) Step to Parnassus: Title of a dictionary of Latin prosody used in schools to help in writing Latin verse. Parnassus is a mountain in Greece anciently sacred to the Muses.

2. Halley E. Some account of the ancient state of the city of Palmyra, with short remarks upon the inscriptions found there.

3. Dunthorne J. XIV. A Letter from the Rev. Mr. Richard Dunthorne to the Reverend Mr. Richard Mason F. R. S. and Keeper of the Woodwardian Museum at Cambridge concerning the Acceleration of the Moon.

4. Kant I. Untersuchung der Frage, ob die Erde in ihrer Umdrehung um die Achse, wodurch sie die Abwechselung des Tages und der Nacht hervorbringt, einige Veränderung seit den ersten Zeiten ihres Ursprungs erlitten habe und woraus man sich ihrer versichern könne, welche von der Konigl. Akademie der Wissenschaften zu Berlin zum Preise fur das jetzt laufende Jahr aufgegeben worden. Kants Werke, Bd. I, Vorkritische Schriften I, 1747-1756, S. 185, 1754.

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