Pierre, an eminent French mathematician, was born in 1698. His father, one of the best hydrographers of his time, was regius professor of hydrography at Croix in Lower Brittany, and author of an excellent treatise on navigation. Young Bouguer was bred to mathematics from his infancy, and at an early age was appointed to succeed his father as professor of hydrography. In 1727 he gained the prize given by the Academy of Sciences for his paper "On the best manner of forming and distributing the Masts of Ships;" and two other prizes, one for his dissertation "On the best method of observing the Altitude of Stars at Sea;" the other for his paper "On the best method of observing the Variation of the Compass at Sea." These are published in the Prix de l'Académie des Sciences. In 1729 he published Essai d'Optique sur la Gradation de la Lumière, the object of which is to define the quantity of light lost by passing through a given extent of the atmosphere. He found the light of the sun to be 300 times more intense than that of the moon. He was soon after made professor of hydrography at Havre; and succeeded Maupertuis as associate geometer of the Academy of Sciences. He was afterwards promoted in the academy to the place of pensioned astronomer, and went to reside in Paris.

It was resolved to send an expedition to South America for the purpose of measuring a degree of the meridian near the equator. From that measurement, compared with the length of a degree of the meridian in other latitudes, the deviation from sphericity in the figure of the earth might be known. The academy made choice of four of its members to proceed on this voyage. These were Godin, Bouguer, and De la Condamine, for the geodetic operations, and the younger Jessieu as naturalist. They sailed from La Rochelle in 1735, and it was ten years before Bouguer returned to France. The account of his operations during the expedition is given by him in his Memoir, entitled Nouvelles Observations sur les Variétés de la Terre, et sur les Variétés de la Lumière. He also published a work entitled La Figure de la Terre déterminée par les Observations de MM. Bouguer et De la Condamine. There is likewise an account of this expedition published by Don George Juan and Don Antonio de Ulloa, two scientific officers of the Spanish navy, who accompanied the expedition. The length of a portion of the meridian was measured on the ground by means of a base and a set of triangles. Then, by observing the altitude of the star Orion which passed near the zenith simultaneously at the two ends of the meridian line that had been measured, that line was found to contain 3° 7' of latitude. A star near the zenith was employed, that the observation might not be affected by refraction; i.e., Orion was seen from the middle of the arc being measured, so that the distance of that star south of the zenith of the northern extremity of the line was 1° 25' 46"; and its distance north of the zenith of the southern extremity of the line was 1° 41' 13", the sum of these two numbers making 3° 7'. The altitude was taken by zenith sectors of a long radius. The ground on which these operations were performed was 12,000 feet above the level of the sea, and 4200 feet above the neighbouring city of Quito, and situated in a plain extending from north to south, between the two ridges of the Cordillera. The northern extremity of the arc was on the equator; the length of the degree, reckoning from 56° 7' 67" north, but this was the elongated form of the circumference round the earth at the height of 12,000 feet above the level of the sea; and the length of the degree at the level of the sea deduced from this, with some other corrections, is 56,763 toises. This length of the degree of the meridian at the equator was compared with the degree of the meridian measured in France, with the degree measured in Lapland, and with the degree of longitude deduced in the south of France. From this comparison it was concluded that the equatorial diameter of the earth is to the polar diameter as 179 to 178, and that the equatorial radius of the earth was about eight leagues longer than the polar. Since the work of Bouguer, doubt has been expressed in different climates with more accurate instruments than he possessed; but the precise proportion of the equatorial and polar diameters of the earth is not yet finally ascertained. Bouguer makes the excess of the equatorial diameter above the polar to be \( \frac{1}{19} \); Sir Isaac Newton made it \( \frac{1}{19} \); Laplace, calculating from the lunar motion, \( \frac{1}{19} \); Melanderhielm and Svanberg, from a degree measured anew in Lapland in 1783, compared with the degree measured in the province of Quito, y. Bouguer found the seconds pendulum of a line shorter at the summit of Michelin than at the level of the sea; that is, the force of gravity was less by 1200th part at that place.

Bouguer made some observations on the limit of perpetual snow, a subject which has been elucidated since his time by the researches of Humboldt, Von Buch, Wahlenberg, and others. Whilst at the equator, he made observations to ascertain the obliquity of the ecliptic, which he found to be 23° 26' 28". He also made some experiments on the deviation of the plumb-line from the vertical, occasioned by the attraction of a neighbouring mountain—a phenomenon afterwards investigated by Dr Maskelyne on the mountain Schiahallen.

The number of Bouguer's papers contained in the printed Memoirs of the Academy of Sciences, is a sufficient proof of his great assiduity. One of his most valuable inventions, the Heliometer, an instrument for calculating very acute angles with extreme precision and facility to the observation of the diameter of stars and their distances from the earth, is described in the Memoirs for 1748. See HELIOMETER. Some experimenters maintained that the plumb-line had a diurnal oscillation; Bouguer showed that it remains at rest. He employed for this purpose a telescope, attached to the end of a chain 187 feet long, suspended within the dome of the Invalides at Paris; the telescope was directed to a distant mark, so that any motion in this long pendulous system might be seen by the deviation of the wires of the telescope from the mark. The particulars of this experiment are to be found in the Mem. de l'Académie des Sciences, 1754. In the volume for 1739 and 1749 there are papers of his on the astronomical refraction in the horizon zone particularly in cases where the star can be seen more than 90° from the zenith, and on the use of the quadrant in being in a high situation. In the volume for 1747, he proposed a log of a new construction for measuring a ship's way. In the same collection there are papers of his on the length of the pendulum, on the form of the prow which suffers least resistance in passing through the water, and on a variety of other subjects. Bouguer died in 1758, aged sixty. His disposition was naturally mild, and the dissensions that arose between him and his fellow traveller De la Condamine caused him great vexation. By economy he had acquired a moderate fortune, a part of which he bequeathed to the poor.

The following is a list of his principal works:—Traité d'Optique sur la Gradation de la Lumière, 1729 and 1760; Entretiens sur la Cause d'Inclinaison des Orbites des Planètes, 1734; Traité de Navigation, 1736, 4th ed.; Nouveaux Entretiens, 1749; Nouveau Traité de Navigation, contenant sa Théorie et sa Pratique du Pilotage, 1753; Solution des Principaux Problèmes sur la Manœuvre des Vaisseaux, 1757; Opérations faites pour la Verification du Dégré du Méridien entre Paris et Amiens; par Mess. Bouguer, Camus, Cassini, et Picquet, 1757.

After his return from South America he was editor of the Journal des Sçavans. His obituary is contained in the Memoirs of the Academy of Sciences for 1758.