Now Joachim Étienne Esclangon, Ernest's half-brother, became a schoolmaster at the College in Manosque, the largest town in Alpes-de-Haute-Provence about 50 km south of Sisteron. This school is now known as the Lycée Félix Esclangon, named after Jules Félix Esclangon who was the son of Joachim Étienne Esclangon and born in 1905. Ernest was educated at this school in Manosque before going to the Lycée in Nice to prepare for entry into the Grand Écoles of Paris. It was during his time at the Lycée in Nice that his teachers realised that they had a pupil with outstanding abilities, particularly in mathematics.
He studied mathematics in Paris at the École Normale Supérieure, entering the École in 1895, and was awarded his licence in mathematical science and in physical science in 1897. In the following year he graduated with an agregé in mathematical science. He became an assistant astronomer in 1899 when, looking for a way to fund his doctoral studies in mathematics, he accepted a position offered to him at Bordeaux as assistant to Georges Antoine Pons Rayet (1839-1906). Rayet, the founder of the Bordeaux Observatory, was a leading expert in spectroscopy. It had been only three years earlier, in 1896, that Bordeaux was reconstituted as a university and given autonomy and state financing. Although Esclangon accepted a post at the university observatory, he continued to work on mathematical topics for his doctorate and also taught mathematics at the Faculty of Sciences at Bordeaux University. In 1902-03 he was in charge of the course on rational mechanics at the Faculty of Sciences. In 1904 he was appointed as Professor at the Colonial Institute of Bordeaux, a position he held for ten years. His doctoral thesis, Les fonctions quasi-périodiques , published in the Annales de l'Observatoire de Bordeaux in 1904 was on quasi-periodic functions. As was standard procedure at the time, candidates for a doctorate had to submit a second thesis and Esclangon's second thesis was Théorie des tourbillons ; it was not published. Lévy writes in :-
Quasi-periodic functions, newly introduced, constitute a remarkable class among the almost periodic functions. Esclangon elaborated a theory for these functions, studied their differentiation and integration, and examined the differential equations which allow them as coefficients. His doctoral thesis established a basis for their employment at a time when their role in mathematical physics was only beginning to be developed.In  Gaiduk shows how Esclangon anticipated many of Harald Bohr's results on almost periodic functions.
Inese Bula describes in  how Piers Bohl had contacted Esclangon while he was still working on his doctorate:-
Several years before the translation of his work into French, Piers Bohl made the acquaintance of the astronomer E Esclangon from Bordeaux. This happened in the following manner. In 1902 there appeared in Volume 135 of Comptes rendus of the Paris Academy of Sciences a note written by Esclangon (communicated by Paul Painlevé) entitled 'Sur une extension de la notion de périodicité' (On a generalization of the concept of periodicity). Bohl read this note and concluded that Esclangon's concept of "quasi-periodic function" agreed with the "periodic function in generalized sense" that he had defined in his master's dissertation. He shared this with Paul Painlevé and probably sent him a copy of his dissertation. In 1903 Bohl found a second note by Esclangon in the "Comptes rendus", in which he acknowledged Bohl's priority in the discovery of the new functional class. In the same note Esclangon announced that he had reached independently of Bohl many results, discussed the differences between the two works, and presented several new results. Bohl was very pleased with this response; in the subsequent correspondence between him and Esclangon he shared his ideas on various new research results and commented very favourably on Esclangon's scientific projects.In 1905 Esclangon was promoted to Deputy Astronomer at the Bordeaux Observatory. He was also appointed as Maître de conférences (assistant lecturer) in analysis and mechanics and adjoint professor in the Faculty of Sciences of Bordeaux. Among the papers he published over the following years are Étude sur l'orientation de la queue de la comète de Halley: sa rencontre avec la Terre en ma 1910 (1911), Étude sur la réfraction astronomique: réfractions différentielles, déformations absolues et relatives, déformations photographiques (1913), Sur un régulateur de température (1913), Sur l'entraînement du support dans les observations du pendule (1913), and L'Energie rayonnante et les bases physiques de l'Héliothérapie (1914).
He continued to hold the posts mentioned above until World War I broke out in July 1914. France began mobilising its troops by the beginning of August. It was in September that Esclangon presented his ideas to the Service Géographique de l'Armée on pinpointing the position of an enemy gun from the sound of it firing. The Service Géographique had, at this time, withdrawn to Bordeaux. Esclangon was conscripted into the 55th Infantry Regiment and was assigned to the commission for naval artillery, part of the ballistics and sound ranging service. Early in 1915 he was sent to Gâvres, Ille-et-Vilaine, where the naval artillery was stationed. His important mathematics paper, Sur les intégrales bornées d'une équation différentielle linéaire , was published in Comptes rendus in 1915.
There were many problems which had to be solved before Esclangon's idea of using triangulation to pinpoint gun positions could work in practice. To solve these he undertook experiments and constructed equipment. When a missile is fired there are two shock waves emitted, one being a spherical wave at the instant of firing which was centred at the position of the gun, while the other was a conical shock wave from the projectile. By 1916 he had devised a method to calculate the position from which the projectile was fired very accurately allowing enemy gun locations to be targeted. Esclangon's ideas are described in :-
The principle of the sound-ranging which was developed by Esclangon, and employed against hostile guns in the late War, will be familiar to most. The arrival of the sound was recorded at a number of stations (at least three) behind the front. The registration was made electrically on a common strip, so that the differences of the instants of arrival at the stations were known. From these times the position of the gun was located as the intersection of two lines on a map. The method, so simple in principle, was not made a practical success without several years of experimenting. The main obstacle to its perfection was that the sound actually made by the firing - the 'onde de bouche' - is an almost inaudible pulse consisting of a large movement of the air of small duration and low frequency, whereas the sound propagated from the projectile itself in its flight, which precedes the arrival of the 'onde de bouche' at a station in the line of fire, is of high frequency and easily picked up by a microphone. In order to make the recording apparatus ignore this high-frequency 'onde de choc', and make a large response to the sound propagated from the gun itself, it was necessary to use as recorder a vessel of large capacity and inertia, the air in which was set in motion by the wave of slow-period, but not by the rapid oscillations due to the 'onde de choc'. Since the method depends on an accurate knowledge of the velocity of sound in air under the conditions prevailing, it is open to error, the principal source of error being that the velocity increases with the amplitude of the disturbance, so that in the immediate neighbourhood of a gun of large calibre the sound is travelling faster than normal, until the amplitude of the wave is reduced by spreading-out and the normal velocity is reached.It is worth noting that General Erich Ludendorff, German Quartermaster General from 1916 to 1918, states in his memoirs Ludendorff's Own Story (1920) that Esclangon's device was one of the main reasons that the Allies defeated the Germans. The Paris Academy of Sciences awarded Esclangon their Baron de Joest prize in 1917:-
... for his researches on the sound phenomena produced by cannon and projectiles.He became professor of astronomy at the Faculty of Sciences at Strasbourg in 1919, having been appointed director of the Observatory there in the previous year. In  Hélène Gispert and Juliette Leloup quote from a notice that Esclangon wrote in 1929 about his move to Strasbourg:-
After the armistice, I was sent to Strasbourg as director of the Observatory and professor of astronomy. The reorganization of the observatory equipment was difficult at this time, firstly, because of industrial and economic disruption, and, secondly, because of very great staff recruitment difficulties .... At present this reorganization is completed.Although Esclangon had staff recruitment difficulties, he did have the help of André Danjon (1890-1967) in his reorganisation of the Strasbourg Observatory. Danjon had, like Esclangon, served in the military during World War I and was appointed as an astronomer at the Strasbourg Observatory in 1919. He would be appointed as its director after Esclangon left Strasbourg in 1929.
Of course, one of the major topics arousing attention in astronomy during his years in Strasbourg was attempts to verify Einstein's general theory of relativity by making observations of the deviation of light passing close to the sun. Eddington had made observations during an eclipse in 1919 and Freundlich was also much involved in arguments about whether Newton's theory had to be abandoned in favour of general relativity. In 1924 Esclangon published Sur la déviation einsteinienne des rayons lumineux par le soleil in which he stated his thoughts on the experimental evidence:-
The true conclusion to draw is that these observations are still powerless to elucidate the question. They neither confirm nor disprove Einstein's deflection law. They suggest only, if you can really rule out any hypothesis of systematic errors, the existence of deviations near the Sun without being able to fix the law, nor the exact size at the edge of the sun.However, despite being a leading astronomer, he did not give up his work on quasi-periodic functions and published a major work Nouvelles Recherches sur les Fonctions quasi-périodiques in 1921. Ideas in this paper are discussed by Edmund Landau in .
Then, from 1929 to 1946 he was director of the Observatory at Paris, again holding the position of professor of astronomy from 1930 to 1946.
The range of topics on which Esclangon worked during his career is quite remarkable. These include :-
... pure mathematics, applied celestial mechanics, relativity, observational astronomy, instrumental astronomy, astronomical chronometry, aerodynamics, interior and exterior ballistics, and aerial and underwater acoustic detection.In astronomy he worked on making observations more precise by improving astronomical instruments. He is particularly famous in this area for his brilliant ideas on improving the design of a transit instrument. One of the first projects he worked on after moving to Paris was the new idea that the solar system was moving through space :-
Esclangon found peculiarities in the location of stars that can be explained by a motion of the solar system. The French astronomer also found evidence for the motion in observations of stars passing behind the moon, earth tides and ocean tides. By studying the reflection of light from a mirror, Esclangon found strong evidence for an "optical dissymmetry of space" which can be explained by an ether drift.In 1933, using an astronomical calculation of time, he started the 'talking clock' telephone service in Paris. This work was carried out in his role as Director of the Bureau International de l'Heure which he held from 1929 to 1944 :-
At the Paris Observatory, Esclangon responded creatively to an increasing demand from citizens to obtain the proper time by telephone. He created the first "talking" (i.e., automatic self-announcing) clock. Esclangon broadcasts the time through a series of photoelectric cells, which activated 'pistes sonores' located on a rotating cylinder. The corresponding "blips" were issued from a synchronous clock, driven in turn by a fundamental clock at the observatory. The time service was inaugurated on 14 February 1933, and immediately the number of calls jumped to more than several thousand per day. The accuracy of the time provided on the telephone was better than 0.1 s.He published the paper L'horloge parlante de l'Observatoire de Paris in 1946.
The years of World War II were extremely difficult and he continued to hold his positions in Paris through the time of the German occupation. On 5 June 1940 Germany invaded France with Panzer divisions moving rapidly south and west bypassing the Maginot line. On that day Esclangon considered operating the speaking clock from Bordeaux to continue to give an accurate time to the radio if Paris fell to the advancing Germans. However, after further consideration, on 23 June the Observatory stated that:-
... the effort is on the maintenance and continuity of the time service .... The speaking clock of the Paris Observatory will be restarted and everyone can use the phone as before.This statement was made one day after France surrendered to Germany. We note that the Paris Observatory speaking clock continued to operate until 1966. Esclangon retired as Director of the Paris Observatory and as Professor of Astronomy at the Sorbonne in 1946. At this time, he was made Honorary Director of the Paris Observatory and Honorary Professor of Astronomy at the Sorbonne. He continued to write papers and his book Histoire de l'astronomie was published the year after he retired.
His last paper, La Vie serait-elle possible à bord de satellites artificiels de la terre ou de projectiles astronautiques? (1950), looked at the mechanics of the orbit of an artificial satellite of the earth. This was not his first paper on this topic having published works such as Sur la transformation en satellites permanents de la terre de projectiles auto-propulsés (1947) and Étude sur les satellites artificiels et éventuels de la Terre (1949) a few years earlier.
Esclangon was honoured with election to the Académie des Sciences in 1929 and the Bureau des Longitudes in 1932. He was elected president of the International Astronomical Union in 1935 and held this position until 1938.
Lévy writes in :-
He assumed his official functions with simplicity and amiability; he was affable and loved to joke, and did not deny himself leisure time. It would almost seem that he accomplished his body of important work without effort.This is even more remarkable when one realises that during his career he wrote 247 scientific papers.
Lévy ends his biography  as follows:-
Esclangon lived in the village Eyrenville, where he owned a house in which he installed a water mill to provide electricity. He rode an old bicycle, which made such a noise that the citizens were preinformed of his arrival. They much appreciated Esclangon's kindness, simplicity, and the accuracy of his weather forecasts.The binary asteroid 1509 Esclangona is named after him as is the lunar crater Esclangon. On 22 June 1965 the Paris street previously named Ornano, was named for Esclangon.
Article by: J J O'Connor and E F Robertson