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\noindent{\bf Anton MEYER}\\
b. 31 May 1801 - 29 April 1857
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{\bf Summary.} Meyer, a Belgian professor of Luxemburg origin, was the author
of one of the few treatises of probability theory in the 19th century. He
propagated the methods of Gauss, Bessel and Baeyer among geodesists of the
French tradition.
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Anton Meyer was born in Luxemburg, but became a naturalised Belgian
on 2 April 1839.
Although from a family of modest means (his father was a shoemaker),
he completed his secondary schooling in the humanities in 1818, and
then pursued his scientific studies with brilliance at Li\`ege
University.  During this period, in order to earn a living, he
taught and also catalogued the scientific books at the University's
academic library.  He worked towards a doctor's degree in the
Mathematical and Physical Sciences, completing his thesis on
``Maxima and minima" on 29 November 1823, though his defence only
took place on 16 June 1832.  In 1824-25, Meyer travelled to Paris
to listen to the eminent scientists of the day. On his return to
Belgium, he taught at the Echternach College and later at the
Military School of Br\'eda.   In 1827, he published a paper in
Quetelet's (q.v.) {\it La correspondance math\'ematique et physique},
about an instrument he had invented for drawing in perspective.  In
1831 he taught at the Louvain College, and later from 1832 to 1837
at the Institut Gaggia in Brussels, where he prepared students for
the Military School.

In 1834, he also became Professor of Analysis and Mechanics at the
Brussels Military School, which had just opened, but he resigned
from this position in 1836.  In 1838, he was appointed to the Chair
of Mathematical Analysis at the Universit\'e Libre de Bruxelles,
and later he replaced Lemaire in the Chair of Differential and
Integral Calculus, Higher Analysis and Calculus of Probabilities at
Li\`ege University from 1849 until his death. Under Meyer, two
distinct subjects were taught, analysis, and 
probability theory and political arithmetic.

Meyer was clearly a dedicated teacher: his lessons, according to
the reports of his pupils, were very appealing. After 1838, having
achieved a stable position, he wrote a dozen text books. These were
original, and written in simple and precise language; furthermore,
Meyer was quick and accurate in his calculations, which were
carried out with great ability. His lectures on
probability were  published only many years after his death, in 1874 by F.
Folie, based on the author's manuscripts, as the {\it Cours de
Calcul des Probabilit\'es fait \`a l'Universit\'e de Li\`ege de
1849 \`a 1857} (F. Hayez, Bruxelles). This work, given the relative dearth of
treatises on probability at the time, created something of a stir,
and was translated into German in 1879 by E. Czuber under the title
{\it Vorlesungen \"uber Wahrscheinlichkeitsrechnung}.  It contains
a thoroughly researched account of the theory of errors. In the
preface, F. Folie points out:  ``This book by Meyer is a very
complete summary of the most important works of Bernoulli (q.v), 
de Moivre (q.v.), Laplace (q.v.), Poisson (q.v.), Gauss (q.v.),
Encke, Bienaym\'e (q.v.)... on the calculus of
probabilities.  One might well suggest that there does not exist a
broader treatise on the subject, except for Laplace's {\it Th\'eorie
analytique des probabilit\'es} ...".

The treatise is very theoretical, even in his chapters concerned with
the theory of errors, concentrating essentially on his proofs. This
is in contrast to J.B.J. Liagre (1815-1891), who, in his {\it Calcul des
probabilit\'es et th\'eorie des erreurs} published in 1852, gave a
large number of applications of the theory of errors, particularly
in geodesy.

Meyer was nevertheless interested in applications of mathematics,
most particularly to geodesy.  In 1835, while he was  at the Military School
in Brussels, Meyer's colleagues
were Quetelet, Professor of Geodesy and Astronomy and
Nerenburger, Professor of Descriptive Geometry.   He collaborated with
cartographic
officers, and with the astronomer Houzeau, Quetelet's assistant.
From the 1830's, he personally carried out triangulations, working
out the calculations which were involved in them.   Traces of his
notes are to be found in the {\it Le\c{c}ons de trigonom\'etrie
rectiligne} and the {\it Le\c{c}ons de trigonom\'etrie sph\'erique}
published in 1844, as well as his {\it Cours de g\'eod\'esie} dated
1845, which faithfully followed the French mathematical tradition.
It is well known that since
the 17th Century, particularly with the measurement of the metre
during the French Revolution, France had played a leading role in
the area of geodesy.  But, from around 1820-1830, leadership passed
fairly rapidly to Germany with the works of Gauss, Bessel and
Baeyer who made systematic and relevant use of the method of least
squares. Belgian scholars like Quetelet, Liagre, Nerenburger and
Meyer, trained by the French, but open to other traditions,
fostered the spread of German methods in Europe.  A direct
consequence of Meyer's travel to Germany in 1846 was the modification of
his lectures on geodesy, and then of lecture material by other geodesists
formerly written in the French tradition.
Among these modifications are a section concerning the theory of errors, some
lines on the personal equation, the use of the theory of least
squares to obtain most probable values, an iteration method for the
observation of angles, the use of the method of least squares as it
arises in the calculation of most probable directions, and in the
compensation theory for a network of triangles.  The notation used
for the solution by the method of indeterminate coefficients was
that introduced by Gauss, and the weight equations correspond to
those of Baeyer, as does also the study of their influence on the
initial direction.

On February 6, 1847, Meyer presented a report on the application of
the calculus of probabilities in operations of topographic
surveying, to the science Section (``Classe") of the Royal Academy of Belgium.
In this, he discussed an example of the use of the method of least
squares. It was rejected by the Academy and never published. 
The bibliography of a thesis by L. Bouvier entitled {\it Dissertation 
sur la th\'eorie
des moindres carr\'es} which appeared in 1848 is identical with that
of Meyer's report.  Thus Meyer attempted to spread the information he had
gathered in Germany on the method of least squares and its
application to geodesy by channels other than those of Academic
recognition. Bouvier remarked that there existed no special text describing the
method of least squares, and that he hoped to fill this gap by
giving an exposition  from a
practical viewpoint.  Liagre's later work in 1852 would accomplish this
on a larger scale.  Bouvier does not
discuss the foundations of the method.  He concentrates
essentially on the ``method of  equations" which are to be satisified. 
The author
describes Gauss' two methods: he gives as an example the content of 
Meyer's note
rejected by the Academy, and compares the formulae used by Gauss
and Laplace to estimate the precision of arithmetic means.  Both
the importance of Meyer's contribution to geodesy and the obstacles
which he encountered, as well as the militant devices he had to use  to put
his views, are evident.

Meyer's scientific opus consists of 30 papers and 12 textbooks. His
publications on the calculus of probabilities were written in the
latter part of his life, some of them appearing posthumously.  In
particular, we note his {\it Essai sur une exposition nouvelle de
la th\'eorie des probabilit\'es a posteriori}, 1857.  This work was
at the printer's when Meyer died. The author goes over the enunciations
and proofs of Bayes' theorem in the continuous case, Laplace's
theorem and the inverse theorem to J. Bernoulli's; but one cannot
honestly claim that he brings much that is new to
probabilistic thinking. 

Also in 1857, Meyer published his reaction ``Examen critique de la notice 
de M. Liagre"
to a memoir entitled ``Sur la probabilit\'e de
l'existence d'une cause d'erreur r\'eguli\`ere", which Liagre had
presented to the Royal Academy of Belgium in 1855.  The topic is
the use of the calculus of probabilities to detect systematic
errors, and is  the precursor of a statistical test for the
random nature of observations (the turning-point test).  Liagre's
article, which discusses the combinatorial aspects of the topic, is
certainly subject to criticism, but so also is Meyer's reponse.
This note, as well as another in 1856, was published at the
author's expense; and provides further  evidence of Meyer's
disagreements with the science Section of the Royal Academy of
Belgium, to which he had been elected a corresponding member on 16
December 1846. An account of this conflict, in which Meyer invoked the
support of the leading authority of the day on statistical matters,
I.J.Bienaym\'e (q.v.), is given by Breny, Jongmans and Seneta (1992). 
Bienaym\'e,
himself no stranger to controversies, recalled it in a paper of 1875, which
linked his name with the turning-points test.

Meyer was
not a  creator of originality in probability and statistics; but rather an
interpreter, able to clarify, simplify and make rigorous in an age not
noted for mathematical lucidity. He is better known in Luxemburg as the 
first poet of the
Luxemburg language, and a man who fostered the development of
national culture.
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\begin{thebibliography}{3}
\bibitem{1}  Bergmans, C. (1897). Notice sur A. Meyer. In {\it Biographie
Nationale de Belgique}, Vol. XIV, columns 765-773.

\bibitem{2}  Blum, M. (1902-1908). {\it Biographie Luxembourgeoise}, Vol. 2.
(Chez l'auteur, Luxembourg)

\bibitem{3}  Breny, H., Jongmans, F. and Seneta, E. (1992). Annexe: A. Meyer et
l'Acad\'emie. In {\it Regards sur 175 ans de science \`a l'Universit\'e de
Li\`ege, 1817-1992.} Anne-Marie Bern\`es (Ed.). Centre d'Histoire des
Sciences et des Techniques, Universit\'e de Li\`ege. pp. 13-22bis.

\bibitem{4}  Gloden, A. (1949). La vie et l'oevre scientifique de neuf
math\'ematiciens
belges d'origine luxembourgeoise. In {\it Themecht Zeischrift
f\"ur Luxemburger Geschichte}, {\bf 1}, 13-16. 

\bibitem{5}  Godeaux, L. (1956). Notice sur Antoine Meyer, membre de l'Acad\'emie.
{\it Annuaire pour 1956.} Acad\'emie Royale de Belgique, Brussels. [In
"Notices biographiques", pp.2-15.]
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\hfill{M.F. Jozeau}


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