**By Wilfried Schroeder**

**Extracts from papers by Hans Ertel
(1904-1971) relating to geophysics and cosmic physics are presented here as to
give an idea about his contribution to this subject during the years 1925 to
1971.
**

**Keywords**: cosmic physics; Ertel's
potential vorticity.

Hans Ertel (1904-1971) was appointed in 1946 Professor
of Geophysics at the University Berlin, as well as director of the Institute of
Meteorology and Geophysics there. He died suddenly and unexpectedly in 1971. He
held then lectures as visiting Professor at the University Uppsala (Sweden) and
met his old friend, theoretical meteorologist Hilding Koehler as well as Markus
Bath. Koehler was tutor of Bert Bolin and contributed significantly to the
scientific carrier of Carl-Gustaf Rossby. It is of historical interest that
Ertel and Rossby could met again after the war in Stockholm and Uppsala, as
Uppsala invited Ertel for some lectures. Else Rossby was the first foreign guest
who visited Ertel's institute in Berlin after the war. Rossby's lecture on the
waves later named after him have shown that this result was implicitely included
in Ertel's papers but they did not became know to the Anglo-American scientific
community. This is exactly the tragic point that many important papers by Hans
Ertel published in the forties in the "Meteorologische Zeitschrift"
did not get known for many researchers in the United States/England due to the
war.

A
later publication by Ertel co-authored by Rossby remained similarly unknown for
a certain time. This situation changed when C. Truesdall studied his papers and
presented a general survey on Ertel's results in his well-known paper in
"Handbuch der Physik" (1960).

With
the re-opening of the Institute of Meteorology, Ertel started most successful
activities both as a university professor and as a researcher. His activity
became even broader when in 1948 he was appointed director of the Institute of
Physical Hydrograpy of the German Academy of Sciences (DAW) in Berlin. In this
institute he continued his hydrodynamic research and together with it, he
started to tackle with his staff important geoecological issues; these
activities are considered today as pioneering works. The fields of research of
this institute, as e.g. theoretical hydrodynamics, special hydrography of
Northern German lakes and coasts (coast protection), hydraulic nomography,
hydrographic cartography, as well as weather history of Europe were successfully
elaborated with a small staff and led within a short time to a high
international reputation of the Institute. Many results were published in the
journal of the institute, "Acta Hydrophysica", and Curt Weikinn
succeeded in publishing a source-book on the weather history. The latter could
be published due to Ertel's proleptic wisdom and it gained international
recognition, too. In later years Ertel was increasingly engaged in problems of
coast protection,- in the framework of activities of the Academy and this
research resulted in new insights, as e.g. the theory of lake embankment, the
problem of "sea bears", i.e. of sudden increases of the sea level, as
well as many new results in connection with theoretical geomorphology. Ertel
published a considerable part of his papers in "Monatsberichte der
Deutschen Akademie der Wissenschaften" (Monthly Reports of the German
Academy of Sciences) being not very well known internationally, thus these
important papers became only later known, too (as e.g. in Scheidegger's "Theoretical
Geomorphology"). Else Ertel treated meteorological problems too, as shown
by his studies in the working group "Influence of the orography on the
development of weather" in the framework of the Conferences on Carpathian
Meteorology. The title of his last paper is 'A differential invariant of
inertial movements in the atmosphere and in the oceans" (Z. Meteorologie,
22, 1971, 329-331).

Ertel
was elected in 1949 an ordinary member of the German Academy of Sciences at
Berlin and became for ten years its vice president. During this time many new
institutes of the Academy were founded, the German-German co-operation, e.g. in
the framework of the International Geophysical Year promoted, and many other
projects were also supported. Ertel and Julius Bartels joined the forces for
these aims. Ertel participated intensively in other international projects, as
e.g. in the International Decade of Hydrology. He took part in the Carpathian Co-operation,
too, he visited many conferences and influenced strongly international
co-operation in this field.

Ertel influenced international
discussion as editor of the journals Gerlands Beitraege zur Geophysik,
Zeitschrift fuer Meteorologie, Forschungen und Fortschritte and Deutsche
Literaturzeitung publislied in cooperation of the German academies. He also influenced strongly the "Alexander-von-Humboldt-Forschung"
for which the DAW founded a special commission on his advice and published in
1959 a Humboldt memorial volume.

Ertel's
later interests were partly determined by his Institute, but he returned often
to meteorological problems and worked on an extension of the geophysically
oriented hydrodynamics with its wide range of applications.

Ertel
considered his field as theoretical mechanics (thus e.g. Theoretical Mechanics
was added In 1960 to his university institute) and mathematical physics and
devoted himself to the task to elaborate laws of physics in a form which is
applicable to the Earth and to the Universe.

Ertel's
vorticity theorems axe formulated in a form which is valid and directly
applicable in all systems of reference and with many complementary conditions.
They make it possible to discuss the dependence of the continuum on
non-mechanical parameters, first of all, on thermodynamic parameters (as on
temperature) and on physical-chemical ones (as on air humidity). Thus they
enable us to deduce mathematically the excitation and annihilation of vortices.
Ertel's theorem is, however, for all continua valid in which a vortex Potential
can be defined; thus they are also' valid in magnetohydrodynamics.

The
problems of the validity limits of the continuum physics and the possibility to
deduce them from atomistics have been repeatedly discussed by Hans Ertel and H J
Treder. Ertel supposed that this problem would never be solved "in a final
form". Ertel supposed the stochastic cause in atomistic variations as in
the "macroscopically random" swinging over of instable weather
situations, and generally the basis of the "randomness" both in space
and time of the transitions of instable situations into stable ones, as well as
cause of the randomness of the location and time of the transition of the
unstable into new, stable states (according to Poincaré's stability criteria).

Ertel
had been known in the thirties in certain circles as a cosmologist (his
corresponding works were supported among others by von Laue, Einstein and Schroedinger).
In the papers on relativistic universe models with a spherically closed
expanding space and with a value L > 0 of Einstein's cosmological constant, Ertel
treated the "great cosmic numbers" which according to A S Eddington
and H Weyl refer to relations between cosmos and elementary particles.

It
is valid according to the order of magnitude for Planck's quantum h, the gravity
constant s, the velocity of light c and the mass of the proton m:

Eddington
considered this connection as the result of a primary stationary, but instable
state of the cosmos with the mass density:

Ertel
remarked that this mass density determines in a very general class of
cosmological solutions of Einstein's gravity equations, namely in the Friedmann-
Lemaitre-models, a quasi-stationary state which can survive for a very long time
and that the connections between cosmological and atomistic quantities had to
develop in this quasi-stationary phase ("Previously there was the "big
bang").

According
to Einstein's self critical remark that in interest of an unambiguous putting of
the question it is better to use L = 0, the cosmological models
with L > 0 and together with them, the great cosmic
numbers lost significance for many years. Since a few years astrophysicists
reached again and again the conclusions that it has to be L > 0, and therefore Ertel's work became again
important.

Ertel's
last publication (1971) was a new about cosmology. Treder remarked to Ertel that
all universe models, both Newtonian and Einsteinian ones together with their
modifications set out from the fact that the Hamiltonian of the cosmos is
constant. Ertel as a Potential theorist suggested at once that this is identical
with the statement that the average variations of the Newtonian gravity
Potential disappear in cosmic dimensions (Ertel and Treder 1971).

Ertel
H 1942a: Meteorol. Z., 59, 277-281.

Ertel H 1942b: Meteorol. Z., 59,
385-387.

Ertel H 1955: Kanonischer
Algorithmus hydrodynamischer Wirbelgleichungen. Sitz.-Ber. Deutsche Akad. Wiss.,
Berlin, Akademie-Verlag, 1954/4.

Ertel H 1960: Gerlands Beitr.
Geophysik, 69, 357-361.

Ertel H 1962: Monatsber. Dt. Akad.
Wiss. Berlin, 4, 368-372.

Ertel H 1963. Monatsber. Dt. Akad.
Wiss. Berlin, 5, 362-365

Ertel H 1971: Z. f. Meteorol.,
22, 329-331.

Ertel H, Treder H J 1971: Ann. d.
Physik, 26, 23-28.

Schroeder
W 1991: Geophysical hydrodynamics and Ertel's Potential vorticity (including
english translations of Ertels hydrodynamical theorems). IAGA/Science, Bremen.

Schroeder
W 1993: Ertel´s Potential Vorticity. Science Edition Bremen..

Schroeder
W 1998: The Earth and the Cosmos. The Legacy of Hans Ertel. Science Edition
Bremen.