BOUGUER, PIERRE

BOUGUER, 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 Croisic 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 Maupertius 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 geodetical operation, and the younger Jussieu 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 the Memoirs of the Academy of Sciences, 1744, and in a separate 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 $\backslash alpha$ of 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 $3^\{\backslash circ\}\; 7\text{'}$ of latitude. A star near the zenith was employed, that the observation might not be affected by refraction; $\backslash alpha$ of Orion passed the meridian in the zenith near the middle of the line measured, so that the distance of that star south of the zenith of the northern extremity of the line was $1^\{\backslash circ\}\; 25\text{'}\; 46\text{'}\text{'}$; and its distance north of the zenith of the southern extremity of the line was $1^\{\backslash circ\}\; 41\text{'}\; 13\text{'}\text{'}$, the sum of these two numbers making $3^\{\backslash circ\}\; 7\text{'}$. 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 situate 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 resulting was 55,767 toises; but this was the degree of a curve circumscribed 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 55,753 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 time of Bouguer, degrees have been measured 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 $\backslash frac\{1\}\{10\}$; Sir Isaac Newton made it $\backslash frac\{1\}\{15\}$; Laplace, calculating from the lunar motion, $\backslash frac\{1\}\{18\}$; Melanderhielm and Svanberg, from a degree measured anew in

Bouhours. Lapland in 1783, compared with the degree measured in the province of Quito, etc. Bouguer found the seconds pendulum $\backslash frac\{1\}\{2\}$ of a line shorter at the summit of Pichincha than at the level of the sea; that is, the force of gravity was less by a 1200th part at that elevation.

Bouguer also made 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 $23^\{\backslash circ\}\; 28\text{'}\; 25\text{'}\text{'}$. 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 Schihallen.

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 applied to the determination of the diameters 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 Mém. de l'Académie des Sciences, 1754. In the volume for 1739 and 1749 there are papers of his on the astronomical refraction in the torrid zone, particularly in cases where the star is seen at more than $90^\{\backslash circ\}$ from the zenith, in consequence of the observer 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, &c., 1740, 4to. La Figure de la Terre déterminée, &c., 1749, 4to. Nouveau Traité de Navigation, contenant la Théorie et la Pratique du Pilotage, 1753. Solution des Principaux Problèmes sur la Manœuvre des Vaisseaux, 1757. Opérations faites pour la Vérification du Degré du Méridien entre Paris et Amiens; par Mess. Bouguer, Camus, Cassini, et Plogré, 1757.

After his return from South America he was editor of the Journal des Savans. His Éloge is contained in the Memoirs of the Academy of Sciences for 1758. (W. A. C.)