He now became acquainted with Pierre-Simon Laplace, and through his influence was commissioned, with Jean Baptiste Biot, to complete the meridianal measurements which had been begun by J. B. J. Delambre, and interrupted since the death of P. F. A. Méchain in 1804). Arago and Biot left Paris in 1806 and began operations along the mountains of Spain. Biot returned to Paris after they had determined the latitude of Formentera, the southernmost point to which they were to carry the survey. Arago continued the work until 1809, his purpose being to measure a meridian arc in order to determine the exact length of a metre.

After Biot's departure, the political ferment caused by the entrance of the French into Spain extended to the Balearic Islands, and the population suspected Arago's movements and his lighting of fires on the top of Mount Galatzo as the activities of a spy for the invading army. Their reaction was such that he was obliged to give himself up for imprisonment in the fortress of Bellver in June 1808. On July 28 he escaped from the island in a fishing-boat, and after adventurous voyage he reached Algiers on August 3.

From there he obtained a passage in a vessel bound for Marseille, but on August 16, just as the vessel was nearing Marseille, it fell into the hands of a Spanish corsair. With the rest the crew, Arago was taken to Roses, and imprisoned first in a windmill, and afterwards in a fortress, until the town fell into the hands of the French, when the prisoners were transferred to Palamos. After three months' imprisonment they were released on the demand of the dey of Algiers, and again set sail for Marseille on the November 28, but then within sight of their port they were driven back by a northerly wind to Bougie on the coast of Africa.

Transport to Algiers by sea from this place would have occasioned a weary delay of three months; Arago, therefore, set out over land, guided by a Moslem priest, and reached it on Christmas Day. After six months in Algiers he once again, on the June 21, 1809, set sail for Marseille, where he had to undergo a monotonous and inhospitable quarantine in the lazaretto, before his difficulties were over. The first letter he received, while in the lazaretto, was from Alexander von Humboldt; and this was the origin of a connection which, in Arago's words, lasted over forty years without a single cloud ever having troubled it.

Arago had succeeded in preserving the records of his survey; and his first act on his return home was to deposit them in the Bureau des Longitudes at Paris. As a reward for his adventurous conduct in the cause science, he was elected a member of the Academy of Sciences, at the remarkably early age of twenty-three, and before the close of 1809 he was chosen by the council of the polytechnic school to succeed Gaspard Monge in the chair of analytical geometry. At the same time he was named by the emperor one of the astronomers of the Royal Observatory, which was accordingly his residence till his death, and it was in this capacity that he delivered his remarkably successful series of popular lectures in astronomy, which were continued from 1812 to 1845.

In 1816, along with Joseph Louis Gay-Lussac, he started the Annales de chemie et de physique, and in 1818 or 1819 he proceeded along with Biot to execute geodetic operations on the coasts of France, England and Scotland. They measured the length of the seconds-pendulum at Leith, Scotland, and in the Shetland Islands, the results of the observations being published in 1821, along with those made in Spain. Arago was elected a member of the Bureau des Longitudes immediately afterwards, and contributed to each of its Annuals, for about twenty-two years, important scientific notices on astronomy and meteorology and occasionally on civil engineering, as well as interesting memoirs of members of the Academy.

Arago's earliest physical researches were on the pressure of steam at different temperatures, and the velocity of sound, 1818 to 1822. His magnetic observations mostly took place from 1823 to 1826. He discovered what has been called rotatory magnetism, and the fact that most bodies could be magnetized; these discoveries were completed and explained by Michael Faraday. He warmly supported Jean-Augustin Fresnel's optical theories, helping to confirm Fresnel's wave theory of light by observing what is now known as the spot of Arago.

The two philosophers conducted together those experiments on the polarization of light which led to the inference that the vibrations of the luminiferous ether were transverse to the direction of motion, and that polarization consisted in a resolution of rectilinear motion into components at right angles to each other. The subsequent invention of the polariscope and discovery of rotatory polarization are due to Arago. The general idea of the experimental determination of the velocity of light in the manner subsequently effected by Hippolyte Fizeau and Léon Foucault was suggested by him in 1838, but his failing eyesight prevented his arranging the details or making the experiments.

Nearly all the mathematical work of the "French school" was done before the year 1830. They are the direct successors of the French writers who flourished at the beginning of the nineteenth century, and seem to have been out of touch with the great German mathematicians of the early part of it, on whose researches much of the best work of that century is based; they are thus placed here, though their writings are in some cases of a later date than those of Gauss, Abel and Jacobi.

In 1830, Arago, who always professed liberal opinions of the breme republican type, was elected a member of the chamber of deputies for the Pyrénées-Orientales département, and he employed his talents of eloquence and scientific knowledge in all questions connected with public education, the rewards of inventors, and the encouragement of the mechanical and practical sciences. Many the most creditable national enterprises, dating from this period, are due to his advocacy - such as the reward to Louis-Jacques Daguerre for the invention of photography, the grant for the publication of the works of Fermat and Laplace, the acquisition of the museum of Cluny, the development of railways and electric telegraphs, the improvement of the reneile.

In 1830 also he was appointed director of the Observatory, and as a member of the chamber of deputies he was able to obtain grants of money for rebuilding it in part, and for the addition of magnificent instruments. In the same year, too, he was chosen perpetual secretary of the Academy of Sciences, the place of J. B. J. Fourier. Arago threw his whole soul into its service, and by his faculty of making friends he gained at once for it and for himself a world-wide reputation. As perpetual secretary it was his duty to pronounce historical éloges on deceased members; and for this duty his rapidity and facility of thought, and his happy piquancy of style, and his extensive knowledge peculiarly adapted him.

In 1834 he again visited Scotland, to attend the meeting of the British Association at Edinburgh. From this time till 1848 he led a life of comparative quiet - although he continued to work within the Academy and the Observatory to produce a multitude of contributions to all departments of physical science - but on the fall of Louis-Philippe he left his laboratory to join the Provisional Government (February 24, 1848). He was entrusted with two important functions, that had never before been given to one person, viz. the ministry of marine and colonies (February 24, 1848 - May 11, 1848) and ministry of war (April 5, 1848 - May 11, 1848); in the former capacity he improved of rations in the navy and abolished flogging. He also abolished political oaths of all kinds, and, against an array of moneyed interests, succeeded in procuring the abolition of negro slavery in the French colonies.

On May 10, 1848, he was elected a member of the Executive Power Commission, a governing body of the French Republic. He was made President of the Executive Power Commission (May 11, 1848) and served in this capacity as provisional head of state until June 24, 1848, when collective resignation of the Commission was submitted to the National Constituent Assembly. At the beginning of May 1852, when the government of Louis Napoleon required an oath of allegiance from all its functionaries, Arago peremptorily refused, and sent in his resignation of his post as astronomer at the Bureau des Longitudes. This, however, the prince president declined to accept, and made "an exception in favour of a savant whose works had thrown lustre on France, and whose existence the government would regret to embitter."

Arago's fame as an experimenter and discoverer rests mainly on his contributions to magnetism and still more to optics. He showed that a magnetic needle, made to oscillate over nonruginous surfaces, such as water, glass, copper, etc., falls more rapidly in the extent of its oscillations according as it is more or less approached to the surface. This discovery, which earned him the Copley Medal of the Royal Society in 1825, was followed by another, that a rotating plate of copper tends to communicate its motion to a magnetic needle suspended over it ("magnetism of rotation").

Arago is also fairly entitled to be regarded as having proved the long-suspected connexion between the aurora borealis and the variations of the magnetic pa ments. In optics we owe to him not only important optical discoveries of his own, but the credit of stimulating the genius of Jean-Augustin Fresnel, with whose history, as well as with that of Etienne-Louis Malus and of Thomas Young, this part of his life is closely interwoven. Shortly after the beginning of the 19th century the labours of at least three philosophers were shaping the doctrine of the undulatory, or wave, theory of light.

Fresnel's arguments in favour of that theory found little favour with Laplace, Poisson and Biot, the champions of the emission theory; but they were ardently espoused by Humboldt and by Arago, who had been appointed by the Academy to report on the paper. This was the foundation of an intimate friendship between Arago and Fresnel, and of a determination to carry on together further fundamental laws of the polarization of light known by their means. As a result of this work Arago constructed a polariscope, which he used for some interesting observations on the polarization of the light of the sky.

To him also due the discovery of the power of rotatory polarization exhibited by quartz, and last of all, among his many contributions to the support of the undulatory hypothesis, comes the experimentum crucis which he proposed to carry out for measuring directly the velocity of light in air and in water glass. On the emission theory the velocity should be accelerated by an increase of density in the medium; on the wave theory, it should be retarded. In 1838 he communicated to the Academy the details of his apparatus, which utilized the relaying mirrors employed by Charles Wheatstone in 1835 for measuring the velocity of the electric discharge; but owing to the great care required in the carrying out of the project, and to the interruption to his labours caused by the revolution of 1848, it was the spring of 1850 before he was ready to put his idea the test; and then his eyesight suddenly gave way.

Before his death, however, the retardation of light in denser media was demonstrated by the experiments of H. L. Fizeau and B. L. Foucault, which, with improvements in detail, were based on the plan proposed by him.

He remained a consistent republican to the end, and after the coup d'état of 1852, though suffering first from diabetes, then from Bright's disease, complicated by dropsy, he resigned his post as astronomer rather than take the oath of allegiance. Napoleon III gave directions that the old man should be in no way disturbed, and should be left free to say and do what he liked. In the summer of 1853 Arago was advised by his physicians to try the effect of his native air, and he accordingly set out to the eastern Pyrenees, but it was ineffective and he died in Paris.