**Henri Andoyer**was an astronomer and mathematician, fondly remembered for his strong work ethic, enthusiasm toward his subject, and dedication to teaching his students. His father, Louis Jules Andoyer, was a chief clerk at the Bank of France. His mother was Marie Antionette Doubliez. Armand Lambert writes in [12]:-

Andoyer's secondary education came at first at Harcourt College and then at the lycée St Louis, a secondary school located in the Latin Quarter of Paris, which he entered in 1872. His teacher in the special mathematics class was Nicolas Dominique Piéron (1847-1906) to whom he retained an affectionate gratitude and with whom he remained friends. Piéron had studied at the École Normale Supérieure and taught mathematics in Caen, Besançon and the Lycée Charlemagne in Paris before being appointed to the Lycée St Louis in 1877. Andoyer went on in 1881 to attend the École Normale Supérieure, one of the most highly regarded and prestigious higher education establishments outside of the public university system framework, having come top of the list in the entrance examination for the Grandes Écoles. He graduated at the top of his class in 1884. At the École Normale Supérieure he initially specialised in pure mathematics which was the subject of his first degree, later turning to celestial mechanics, the subject in which he would achieve his doctor's degree.Even as a child he already showed his inclination for calculation. On a rainy day, which stopped him from going to play in the gardens of Luxembourg, where his mother used to take him, and as she was about to console him, he clapped his hands with satisfaction: "I will be able to have fun calculating;" and all afternoon he carried out divisions, to his delight. He was barely old enough to understand things when the war of1870broke out. His father took up arms and the young Henri was left with his mother to take refuge in Cherbourg. And shouldn't one see in his vivid memories from childhood the deep roots of the ardent patriotism which will animate him all his life?

He spent time from September 1884 in Toulouse filling both roles of teacher at the Faculty of Sciences and assistant at the observatory, having been employed by Benjamin Baillaud. He had been highly recommended by Jules Tannery who had taught him at the École Normale Supérieure, and he served in Toulouse for eight years. The observatory is best known for its contribution to the *Carte du Ciel* Ⓣ project, a component of an international astronomical project, working to catalogue and map the positions of millions of stars as faint as 11th or 12th magnitude. Among other interests, he worked on the inequalities in the motion of the moon. He also made observations of the eclipses of the satellites of Jupiter and Saturn. It was at the observatory that he lived, until his marriage, in a room allotted to him.

He obtained his doctor's degree in 1886, with a dissertation title (published the following year) of *Contribution à la théorie des orbites intermédiaires* Ⓣ which was a study of the three-body problem. Among his publications at this time we mention *Sur un problème de géométrie* Ⓣ (1889), *Sur les formules générales de la mécanique céleste * Ⓣ (1890) and *Sur quelques inégalités de la longitude de la lune* Ⓣ (1892). On 27 May 1889, he married Céleste Antoinette Marguerite Perissé (born 29 June 1866 in Saint-Gaudens) in Toulouse. She was the daughter of Sermin Laurent Bertrand Firmin Perissé, general secretary of a commercial and industrial syndicate in Toulouse, and Marie Joséphine Crouzet.

In November 1892, he returned to Paris upon his appointment at the Faculty of Science in Paris in the mathematics department. Ten years later, in 1902, he was appointed assistant professor on 25 January and as Professor of Astronomy on 28 July. In 1912 he succeeded Henri Poincaré as Professor of General Astronomy and Celestial Mechanics following Poincaré's death.

We can see something of Andoyer's mathematics teaching through the publications of his lecture notes, for example: *Cours de géométrie: à l'usage des élèves de l'enseignement primaire supérieur: ouvrage rédigé conformément au programme officiel de 1893* Ⓣ (1st edition 1894), (2nd edition 1895), (3rd edition 1896); *Cours d'algèbre à l'usage des élèves de l'enseignement primaire supérieur* Ⓣ (1896); *Cours d'arithmétique à l'usage des élèves de l'enseignement primaire supérieur* Ⓣ (2nd edition 1898); *Leçons élémentaires sur la théorie des formes et ses applications géométrique, à l'usage des candidats à l'agrégation des sciences mathématiques* Ⓣ (1898); and *Leçons sur la théorie des formes et la géométrie analytique supérieure, à l'usage des étudiants des Facultés des Sciences.* Ⓣ Volume 1 (1900). E B Elliot, in the review [8] of this 1900 publication writes:-

He published the first part of his two volume workAndoyer's aim is to present didactically the theory of Forms, and develop its application to a perfectly general geometry; and he is singularly successful. His plan is marked by great breadth of view. Possibly he is too chary of space when general lessons could be enforced and illustrated by particularisation. To be at once precise and general is throughout his effort. His expression is both forcible and abbreviated, and his notation is condensed. Considering the extreme compression it is truly remarkable how clearly his arguments are stated. The volume has had to be a bulky one, and it has evidently been always in the author's mind to allow no diffuseness or repetition to further enlarge it. Constant and painstaking collaboration is demanded from the reader by "il est clair," "facile de démontrer," "un calcul direct donne," and similar shortenings of demonstration. At times there is a suggestion of humour in the strife after brevity; as for instance when a short argument ends with a formula and the words "d'où une proposition facile à énoncer." We commend to our problem makers the original idea of sketching a solution and asking for the question.

*Cours d'Astronomie*Ⓣ in 1906. This first part on theoretical astronomy is reviewed in [14] where Kurt Laves writes that Andoyer's book serves the:-

The second part, on practical astronomy, was published in 1909.W R Longley writes [15]:-... needs of a mathematician who tries to inform himself about the application made in astronomy of a certain mathematical theorem he is interested in. ... After an introductory chapter concerning spherical trigonometry and a short deviation into spheroidal trigonometry to the extent to which this is needed for elementary geodesic questions, the author gives in the next seven chapters a rather condensed account of refraction, parallax and aberration. Before the theory of precession and nutation is taken up, the reader is initiated in Chapter9into the more elementary notions of celestial mechanics. ... In the ninth chapter a short discussion is found concerning the convergence of series used in astronomy. It is the only place in the book where a knowledge beyond the differential and integral calculus is needed. Chapter10is devoted to precession and nutation and formulas are derived for the equatorial and elliptic coordinates to correct the position of an object for the secular and periodic changes in the position of the planes of reference. ... The last chapters of the book deal with the geocentric motions of the sun, moon, planets and their satellites. Here the eccentricities and inclinations are assumed to be zero to simplify the deductions. An elementary exposition of the theory of eclipses of moon and sun and of the occultation of stars by the moon finally ends this first part of Professor Andoyer's treatise.

Besides teaching, Andoyer's work involved a lot of observational study. He travelled to El Arrouch, Algeria, in order to observe the total solar eclipse of 30 August 1905. He also devoted much attention to the moon, working to revise the lunar theory set out by fellow French astronomer and mathematician, Charles-Eugène Delaunay. Andoyer claimed that though Delaunay's terms were accurate up to the 7th order, beyond that they were very inaccurate. He continued publication on this topic for the rest of his life, with his final paper on it published in 1928. Andoyer also studied theThis volume completes the course, of which the first part deals with theoretical astronomy. As a text-book for a first course in practical astronomy, the subject matter of the second part is well chosen. Only the common instruments, namely, the theodolite, the equatorial, and the meridian transit are treated in detail ... In addition to the subject matter of observational astronomy the book contains an introductory chapter on numerical calculation, including the theory of interpolation and the method of least squares. The last chapter is an exposition of Gauss's method for determining the elements of an elliptic or parabolic orbit from three complete observations.

*n*-body problem, the problem of predicting the individual motions of a group of celestial bodies gravitationally interacting with each other, expanding the results of Joseph Lagrange concerning the equilibrium solutions for three bodies.

Following the death of Jean Charles Rodolphe Radau (1835-1911) on 21 December 1911, Andoyer succeeded him in the role of writing the *Connaissance des temps* Ⓣ, an annual publication of astronomical ephemerides in France. It also contained articles on various topics, giving a more in-depth insight, by famous astronomers.

Andoyer was very dedicated to his teaching and to his pupils, publishing many of his lectures for their benefit, several of which we listed above. His small publication, *Théorie de la Lune* Ⓣ would be recommended to anyone who wished to introduce themselves to the complexities of the moon's motion. Moreover, between 1911 and 1918, he was responsible for 4 large volumes of mathematical tables: *Tables of logarithms of Trigonometric Functions to *14* decimals* (1911) and 3 volumes of *Tables of the natural Trigonometric Functions to *15* decimals* (1915, 1916, 1918). He further did the computation for tables of addition and subtraction of logarithms, and also the computation for those of logarithms of numbers to a large number of decimal places. It was claimed that, for several years, he had dedicated three hours per day to this work. He published *Tables Logarithmiques á treize décimales* Ⓣ in 1923 which was reviewed in [2]:-

Several of his important works on the history of mathematical astronomy should be mentioned. For example there isProf Andoyer's13-place logarithm tables are based on the fact that any number may be expressed as the product of its first three figures and a number of which the first three figures are100. He thus reduces his tables to(1)

a13-place table of three-figure numbers and(2)

a13-place table of the numbers from100,000to101,000.00000

In the second table the first differences of the logarithms are tabulated and on a supplementary page are given the proportional parts of the second difference ... . A third table is also given containing the antilogs ofto00432(covering the range from log100to log101)with first differences and a page of proportional parts of second differences as in the second table. The use and application of the tables will be obvious.

*A propos de l'Almageste de Ptolémée*Ⓣ (1928),

*A propos des oeuvres de Copernic*Ⓣ (1928), (with Pierre Humbert)

*Histoire des Sciences en France, Mathématique, Méchanique, Astronomie*Ⓣ, and

*L'Oeuvre scientifique de Laplace*Ⓣ (1922). Florian Cajori writes in a review about this last mentioned work [5]:-

In 1923 Andoyer published the first volume of his two volume workAfter a brief sketch of the life of Laplace, Andoyer sets forth the characteristics of the works of this great French scientist. Andoyer cites the problems in celestial mechanics, which the eighteenth century mathematicians encountered, and reminds the reader how, through insufficient approximation, doubt was cast for a time upon the validity of Newton's law of inverse squares, and how a closer numerical approximation dispelled those doubts. Andoyer presents evidence showing the excessive harshness of the judgment passed upon Laplace by certain writers, to the effect that Laplace, in his writings, often failed to give due credit to his predecessors and contemporaries. Laplace's relations to D'Alembert, Biot and Poisson are described. Andoyer explains how Laplace again and again returned to certain topics in order that he might improve his exposition and perhaps free the subject from metaphysical entanglements. Not altogether surprising is Laplace's lack of interest in certain abstract fields of mathematics, like the theory of numbers. But strange is Laplace's adherence to Newton's corpuscular theory of light a quarter of a century after Thomas Young had advocated the undulatory theory and a decennium after Fresnel had won Arago over to the latter theory. Andoyer's masterly account of Laplace's researches on celestial mechanics, on the figure of the earth, on the tides, on the système du monde, on the analytical theory of probability, and of researches on physics contains numerous quotations from the works of Laplace, bearing on points of scientific and philosophical interest. Andoyer's booklet will be enjoyed by students interested in the evolution of the mathematical sciences.

*Cours de Mécanique Céleste*Ⓣ, the second volume being published in 1926. The review of the first volume [3] states:-

Andoyer was recognised for his work by receiving many honours. He became a member of the French Mathematical Society in 1896. He was awarded the Pontécoulant Prize by the Academy of Sciences in 1903. In 1910, he became a member of the Bureau des Longitudes, he was elected to membership of the Royal Astronomical Society on 13 November 1913 and of the Academy of Sciences on 30 June 1919. He was also offered the directorship of the Paris Observatory, a role which he declined. He was also an Officer of the Legion of Honour (the second of 5 orders of distinction, which required 8 years of service as Knight, which required 25 years of professional activity with "eminent merits").For twenty years it has fallen to the lot of Prof Andoyer to give an annual course, each lasting some six months and covering the ground that must be traversed by all who hope to embark with success upon the work of astronomical computations - a field in which the author of the book before us has won for himself the highest reputation. His aim is to give as simply and fully as possible to computers and practical astronomers the practical solutions afforded by Astronomy to the real problems of Celestial Mechanics. As he tells us in his Preface, to facilitate his task he confines himself almost exclusively to a development in all necessary detail of the methods which lead to the simplest and most trustworthy calculations. In the new and revised edition of his great 'Cours d'Astronomie', he has made a special point of utilising problems borrowed from reality to illustrate the numerical application of the formulae he establishes - e.g. the lunar eclipse of Feb.8,1925, the transit of Mercury of May7,1924, the solar eclipse of January24,1925. This excellent practice he has followed in the present treatise, and the resulting impression made upon the student by this contact with actualities cannot fail to be effective and lasting.

Henri and Céleste Andoyer had three children of which two were sons, one a daughter. The eldest of the sons, Firmin Marie Raphäel Andoyer, born in Toulouse on 13 February 1890, was killed at Brabant-sur-Meuse on 11 January 1915 during the First World War. The second son, Georges Leeon Andoyer was born in Toulouse on 8 December 1890. He became an engineer and worked for the North Railway Company as the head of the laboratory. Their daughter, Henriette Juliette Andoyer (born in 1892), married the mathematician Pierre Humbert on 28 April 1914. This connection to Andoyer supposedly increased Humbert's interest in the history of astronomy.

Andoyer died in Paris on 12 June 1929. The announcement in *Nature* states [9]:-

By the death on June12of Marie Henri Andoyer at the age of sixty-six years, French science has lost a distinguished member of the characteristic school of mathematical astronomers of which such men as Tisserand and Radau were eminent examples and Henri Poincaré the most brilliant ornament. In Andoyer a rare combination of qualities were united. To his knowledge and ability as a mathematician and his acquaintance with the technical side of practical astronomy he joined a skill and a passion for numerical calculation which recalls the kindred taste of J C Adams in England. He was at the same time a gifted teacher. with an enthusiasm and critical sense which made his exposition equally attractive in the shape of lectures or in published form.

**Article by:** I J Falconer, J G Mena, J J O'Connor, T S C Peres, E F Robertson, University of St Andrews.