(Charles Augustin), a profound and ingenious theoretical mechanic and natural philosopher, descended from a distinguished family of Montpelier, was born at Angoulême, the 14th of June 1736. He felt, at an early period of his life, a strong preference for mathematical studies, and would gladly have devoted his whole attention to the pursuit of science; but he found it more convenient to enter the military profession as an engineer. This department, however, afforded him ample scope for the exercise of his powers of observation and calculation: and after having been ordered on service to America, and remaining abroad nine years, with some injury to his health, he presented to the Academy of Sciences, in 1773, a memoir on cohesion, and on the resistance of various works of masonry, which, for the accuracy and originality of the views that it exhibits, for the clearness and neatness of the demonstrations, and for the practical utility of the results, is fully equal to any of his later productions, and shows a mind still in the vigour of youth, and yet matured by the approach of middle age. The Academy paid him the compliment of making him one of its correspondents, and in 1779 he had the satisfaction of sharing, with the laborious Van Swinden, the prize proposed for improvements in the construction of compasses. He resided for some time at Rochfort, where he had abundant opportunity of prosecuting, in the naval arsenal, his experimental researches on friction, which obtained him in 1781 the double prize for the theory of the effects of simple machines: in the same year he had the good fortune to be stationed permanently at Paris, and becoming a member of the Academy, devoted himself entirely to the investigation of the laws of electricity and magnetism, and of the force of frictions and resistances of various kinds. He is generally supposed to have been the first that provoked, by direct experiments, the law of the decrease of electrical and magnetic forces in the proportion of the squares of the distances: but it must not be forgotten that the late Lord Stanhope had published an experiment, five years before the date of Mr Coulomb's researches, which sufficiently established this law with respect to electricity; although the extension of the same law to the operation of magnetism appears to belong exclusively to Mr Coulomb. He continued to occupy himself in these researches till the time of the revolution, when he was expelled from Paris by the decree that banished all the nobility: having before given up the appointment of Intendant general of fountains, and having otherwise very materially suffered in his property. He retired with his friend Borda to a small estate which he possessed at Blois; and during his residence there, made some observations on vegetable physiology, which he afterwards presented to the Institute.

He was recalled to Paris in order to take a part in the new determination of weights and measures, which had been decreed by the revolutionary government. He returned, soon after, into the country, wishing to devote himself to the care of his family, and of the remains of his little fortune. But upon the establishment of the National Institute, he again became an inhabitant of the metropolis. He had, however, occasion to undertake a tour of considerable extent, in discharging the duty of an inspector of public instruction; and he was remarked, in his examinations of the young students, for the singular good nature and paternal tenderness of his manners. He still continued his application to his favourite pursuits, and in particular to the investigation of the magnitude of forces of various kinds, by means of the principles of torsion. And his last study was an inquiry respecting the universal diffusion of the magnetic power through nature, which he at first supposed to be almost unlimited; although he afterwards found reason to conclude, that its general cause was the presence of a minute quantity of iron. A short summary of his numerous and elaborate memoirs will best illustrate the extent and accuracy of his researches.

1. Statical Problems relating to Architecture. Mem. Sav. Etr. VII. 1773. p. 343. The fluxional modes of ascertaining maxima and minima are applied, in this admirable memoir, to the determina- tion of the strength of blocks of stone, and of pillars of masonry, and to that of the resistance of semi-fluids, and the thrust of earth. The author's manner of considering the subject was at that time new; it has been still further extended by some late researches in this country (Hutton's Mathematical Dictionary, Art. Pressure); and many of the calculations, contained in the articles Bridge and Carpentery of this Supplement, are principally founded on the same basis. Mr Coulomb very properly objects to Musschenbroek's mode of representing columns as exerting their passive strength like bars resisting flexure; and it is surprising that Mr Lagrange did not profit by his remarks, in abridging his laborious investigations of their elastic force. Mr Coulomb appreciates the friction of soft materials by the angle at which they will stand unsupported: an angle which has been termed in this country the angle of repose, by an author who perhaps imagined there was more novelty in the idea, than he would have done, if this memoir had been fresh in his mind.

For the thickness of the walls of an embankment, one-seventh of the height is recommended as a good proportion in common cases, with an increase of one-sixth towards the bottom: But the calculation is left in some measure incomplete, although it may be sufficiently accurate for the cases which most commonly occur in practice. In the last place, the proper direction of the joints of flat arches is determined; and the point of easiest fracture of arches in general is investigated, by an approximatory method, applied successively to each joint.

2. On the improvement of the construction of the Compass. Mém. Sav. Etr. IX. p. 165. This memoir contains a laborious and accurate investigation both of the operation of the force of magnetism, and of the resistances exhibited to the motion of a needle by friction or by other causes. The author lays down, as a fundamental principle, the equality of the accelerative force acting on a given needle, in all positions, when referred to the direction of the meridian; so that the properties of its vibrations become precisely similar to those of a pendulum actuated by the force of gravity. From the existence of an attractive and a repulsive force at the same time in each particle of the body, with respect to the opposite magnetic poles of the earth, he concludes the total impossibility of explaining the effects by means of any ethereal currents or vortices, which had been admitted by some of the best mathematicians of the century, then still surviving. He examines the comparative force of needles of different dimensions, and proves the extreme delicacy of the suspension afforded by a long fibre, whether of hair or silk; and he describes a compass in which the reading is performed by means of a microscope fixed to a graduated arm, serving as a vernier. In order to find the true direction of the magnetic action of a needle, he turns it upside down, and takes the mean of the observations. He ascertains the magnitude of the friction of steel on glass, by measuring the angle of repose; and he finds that it is equal to $\frac{1}{\sqrt{3}}$ of the pressure. He then proceeds to calculate the friction of a pivot, supposing it to be compressed most at the centre, but concludes, from a hasty experiment, that the magnitude of the surface is not much changed by a change of pressure. He infers, however, that a light needle has an advantage over a heavy one. A perforation in the middle of a needle appears to interfere but little with its magnetic force. He proposes to ascertain the position of the dipping needle, by measuring the frequency of the horizontal vibrations, and the force required to keep it level; and he concludes his memoir with an account of the diurnal variations of the needle, and a conjecture respecting the operation of the sun and his atmosphere, which he compares to a large aurora borealis; referring the secular change of the variation to the slow motion of the sun's apogee.

3. Recherches sur les moyens d'exécuter sans l'eau toutes sortes de travaux hydrauliques. 8. Par. 1779. Rozier XIV. P. 393. Addition. Rozier XVII. P. 301. Ed. 2. 8. Par. 1797. The Academy of Rouen had proposed a prize for an essay on the best mode of lowering a rock in the Seine, at Quillebeuf, which was about a foot below low water mark: this essay was originally written for the prize, but it was published without waiting for the competition, at the request of some engineers, who wished to have it made known without loss of time. The method recommended consists in employing a floating air chest in the manner of a diving bell, forcing out the water from its lower part by means of bellows, after shutting up the workmen in the upper part. In the additional paper, printed in the Journal de Physique, a stronger pneumatic apparatus is described, somewhat resembling the air vessel of a fire engine, which discharges its air into the chest, and is then filled again by letting out the water: it is also proposed to employ mercury, in a similar manner, in the construction of an air pump. The proposed apparatus does not appear to have been tried; but there can be no doubt that it might often be of advantage, when the inequalities of the rock, or any other causes, prevented the construction of a cofferdam.

4. Theory of Simple Machines, comprehending the effects of friction and of the stiffness of ropes. Mém. Sav. Etr. X. P. 161. This essay gained the double prize proposed by the Academy for 1781; the difficulty of performing experiments on a large scale having probably prevented the presentation of any memoir sufficiently comprehensive the preceding year, when the subject was first proposed. The author's principal merit consists in the determination of the different magnitude of the initial adhesion, according to the time that the substances had continued in contact with each other, and had been pressed together, and of the effect of the magnitude of the surface of contact of particular substances, as well as of the causes of the occasional difference of friction, with different velocities, especially when the unctuous substances employed are rendered too soft by the heat, which is produced by the motion. He compared the effect of the mutual contact of a great variety of substances; and for the purpose of launching ships, he recommends the use of oak, sliding on elm, previously well rubbed with hard tallow; but in some other cases he found tallow, if not frequently renewed, rather injurious than serviceable. He observed, that the rigidity of ropes increased more rapidly than their diameter, but somewhat less rapidly than their strength; and that in order to overcome this rigidity, besides a constant force, an additional force was required, proportional to the weight employed. With every allowance for resistance of all kinds, he calculates, that a well constructed machine, for instance a simple capstan, raising a large weight, will produce an effect equivalent to nine-tenths of the force employed. But, in many of the simple machines in common use, for instance in ships' blocks of the ordinary construction, it appears, from the reports of other authors, that the loss frequently amounts to more than half of the power.

5. Observations on the force of Windmills, and on the form of their sails. Mém. Ac. Par. 1781. P. 65. The inclination of the sails, found to succeed best in practice, varied from 60° to 80° in their different parts. The force was estimated by the weight of the stampers, raised in the process of extracting rape oil, and it appeared that only about one seventh of the power of the wind was lost. On an average the wind was observed to blow eight hours a day, with a velocity of fifteen English miles an hour; and the work of the mill was generally so arranged, that the velocity of the sails was in a certain proportion to that of the wind, experience having shown, that the effect thus obtained was the greatest possible. Mr Coulomb attempted to become a tenant of one of the mills for a few months, in order to make experiments on it with the greater convenience: but the proprietors suspected that he wished to discover some of their secrets, and refused to comply with his proposal.

6. Theoretical and experimental researches on the force of Torsion. Mém. Ac. Par. 1784. P. 229. The force of torsion is here very accurately and elegantly determined for substances of different diameters; and it may be inferred from Mr Coulomb's experiments, that the resistance of a steel wire, to a force tending to twist it, is always equal to that of a fixed axis, supposed to be \(\frac{1}{10}\) as great in diameter, having the same wire coiled round it, or rather simply attached to a point of its circumference: for brass wire the proportion must be \(\frac{3}{10}\); and according to Mr Cavendish's experiments, it must be \(\frac{1}{10}\) for copper; not \(\frac{1}{100}\), as has been stated by an accidental error, either of the printer's or of the calculator, in the article Carpentery of this Supplement, p. 622. The reaction of brass, notwithstanding its greater flexibility, is more perfect and durable than that of steel, and it is therefore preferred for the construction of balances for the measurement of minute forces by the effect of torsion, several varieties of which are here described: And as an instance of their utility, the author has ascertained, that the resistance of liquids depends almost entirely on two forces, the one varying as the velocity, the other as its square, the constant portion of the resistance being scarcely perceptible in any case. He proves, that tempering a bar or wire, of any metal, has no effect in the immediate force of its resistance at a given flexure, although it very materially modifies the extent of its action. Continued twisting of a soft wire seems to produce a very equable degree of hardness, which enables it to retain nine times as much magnetic power as in its original state: and on account of this increase of hardness only, a soft wire appears to exhibit a greater extent of elastic recoil when it is twisted round several times, than when only once or twice.

7. Description of a Compass. Mém. Ac. Par. 1785. P. 560. The needle is suspended by a number of single threads of silk, made to adhere by dipping them in hot water, or by means of a little gum, each thread being capable of bearing a weight of about 50 grams. The needle is to be so suspended, that the thread may have no tendency to cause it to deviate from the magnetic meridian; and this is to be ascertained by substituting a copper wire in its place. Cassini was in the habit of employing a compass of this construction, for making accurate observations on the diurnal variation.

8. Three Memoirs on Electricity and Magnetism. Mém. Ac. Par. 1785. P. 569, 578, 612. The first memoir is devoted to the description of an electrical balance, founded on the force of torsion, and to the demonstration of the law, according to which small bodies similarly electrified repel each other, with a force decreasing as the squares of the distances increase. One of the instruments employed was so delicate, that each degree of the circle of torsion expressed a force of only one hundred thousandth of an English grain; another, suspended by a single fibre of silk four inches long, made a complete revolution with a force of one seventy thousandth of a grain, and turned to the extent of a right angle, when a stick of sealing wax, which had been rubbed, was presented to it at the distance of a yard. The second memoir relates to the laws of electric attraction, and of the magnetic forces, which are all found to vary in the same proportion as the electric repulsion. The direct experiments, on the attraction of balls contrarily electrified, presented some difficulties, and the vibration of a small needle, at different distances from an electrified body, was employed for a collateral experiment. The poles, in which the magnetic forces appear to be concentrated, are at some little distance from the respective ends of a magnetic bar, and not exactly at the extremities. In the third memoir, Mr Coulomb investigates the laws of the gradual loss of the electricity of an insulated body, which seems to be always proportional to the intensity of the charge, and independent both of the form and of the conducting power, except in the case of sharp points or edges: it appears also to vary nearly as the cube of the quantity of water contained in the air, though probably somewhat diminished by an increase of temperature. It is however remarkable, that changes of moisture, indicated by the hygrometer, are not discoverable in the conducting power, for a considerable time afterwards. The quantity of electricity carried off by the air being ascertained, that which is lost by the imperfection of the insulating support remained to be determined: and it was found, that a certain length of a fibre of silk, varying as the square of the intensity, produced complete insulation with respect to all weaker charges.

9. Fourth Memoir on Electricity. Mém. Ac. Par. 1786, P. 67. It is here shown that the capacity for receiving electricity is totally independent of any chemical attraction of the body for the supposed fluid; since balls of copper and of pith, or plates of iron and of paper, when brought into contact with each other, divide the electricity in equal proportions. It is also experimentally proved, by boring cylindrical holes in a large piece of wood, and touching the bottom of the holes with a small circle of gilt paper, that the interior parts of an electrified body remain in a state of indifference.

10. Fifth Memoir on Electricity. Mém. Ac. Par. 1787, P. 421. When a large globe touches a smaller, the smaller receives a charge, which is stronger than that of the larger, but never twice as strong. It is proved by measuring the intensity of the electricity of a varnished wire or cylinder, that bodies are not surrounded by an electric atmosphere, but receive the charge within their substance; for the varnish, which is impermeable to the fluid, does not sensibly affect the capacity of the cylinder.

11. Sixth Memoir on Electricity. Mém. Ac. Par. 1788, P. 617. This interesting investigation relates to the distribution of electricity between a number of equal globes; in the different parts of a long cylinder; between a large globe and a number of small ones; and between a globe and a cylinder. In showing the agreement of the theory with experiments, Mr Coulomb's industry and ingenuity are very successfully exerted in order to overcome the difficulties of the approximatory calculation, although it might perhaps have been not much more laborious, and yet far more satisfactory, to have proceeded to a more correct and conclusive analysis. In a series of twenty-four globes, the charge of the first was to that of the second as three to two, and to that of the twelfth as seven to four; in a cylinder fifteen diameters long, the intensity at the end was to the intensity at the middle as twenty-three to ten. Of twenty-four small globes in contact with a larger, the last exhibited an intensity about four times as great as the first. The experiments on globes and cylinders combined are still more interesting, as affording an immediate application to the effects of conductors in carrying off electricity. At the remote end of a long cylinder equal in diameter to one-twelfth of that of the globe, the intensity was nearly twenty times as great as that of the globe; and it increased almost in the same proportion as the diameter of the cylinder or wire was diminished; but a short wire received a much weaker charge. From the formulae founded on these experiments, Mr Coulomb calculates, that a cloud, a thousand feet in diameter, will cause a wire a line in diameter, raised by a kite, to receive an electricity at the lower end more than sixty thousand times as great as its own. He also observes, that a point projecting but little from a large surface discharges electricity but slowly; a plane touching a globe received an electricity, equally intense with that of the globe, on both its surfaces. Mr Coulomb considers the hypothesis of the existence of two electric fluids as less objectionable than the theory of Franklin, Aepinus, and Cavendish, though he does not attempt to give any direct proof that he can decide the question; but he finds it difficult to believe, that matter can repel matter, and attract the electric fluid, with forces precisely equal, at the same time that matter is known to attract matter with a force of gravitation, varying according to the same law, but incomparably less active. It does not, however, appear that this difficulty is by any means a very important one, since we may avoid it altogether, by supposing that matter only repels matter, and that it attracts the electric fluid, with which matter is commonly saturated, with a force somewhat greater, so that the difference of these forces constitutes gravitation; which thus, like the newly discovered chemical attractions depending on electricity, may be reduced to a modification of the power of this wonderfully universal agent; an agent which appears almost to combine the subtilty of spirit with the energetic qualities of matter. It must, however, be remembered, that we have no evidence of the separate existence of electricity, independently of matter; it does not pass, like light and heat, through the vacuum of the barometer; nor, in all probability, through the empty spaces interposed between the different parts of the solar system; although the accelerative force, depending on it, is not confined by these or by any other limits; and it will probably long remain a question, whether electricity may not rather be a modification of matter or motion in the bodies concerned, than a semimaterial substance pervading them; especially among those who even doubt of the materiality of light and heat as separate substances.

12. Seventh Memoir, relating to Magnetism. Mém. Ac. Par. 1789, P. 455. In order to check the irregular oscillations of needles very delicately suspended, Mr Coulomb finds it convenient to attach to them a horizontal plate, immersed in a vessel of water. The directive power of a needle of given thickness appears to be nearly proportional to its length, the quantity of magnetism accumulated near the ends being constant, except that it extends to the distance of about twenty-five diameters, and if the needle is too short to allow space for this accumulation, the directive power decreases as the square of the length. The directive forces of similar needles, composed of pieces of the same twisted wire, are nearly as their weights. Mr Coulomb observes the difficulty of accounting for the well known fact, that neither half of a needle, when it has been divided, appears to be attracted either northwards or southwards, and he thinks that whether we admit the existence of one magnetic fluid or of two, it will still be necessary to consider every magnet as made up of minute parts, each possessing a north and a south pole, of intensities varying according to their situation; and he remarks that the high charges of electricity, supported by very thin plates, afford an analogy favourable to the existence of this kind of partial charge of magnetism; he might also have added, after the happy combinations of Volta, that the electrochemical battery exhibits an arrangement almost identical with that which he attributes to a magnet. With respect to the forms of needles, the rhomboid appeared to have some advantage over the rectangle: the temper required to be neither very hard nor very soft, and it was found best to anneal the needles to a dark red, or to employ plates of a spring temper, when they required to be larger. A number of needles combined into a mass lost more than half their strength, so that it is of advantage to attach several parallel needles, at a distance from each other, to the card of a compass. Mr Coulomb's mode of communicating magnetism is to lay the ends of the bar on those of two strong magnets, placed opposite to each other, and to draw two other magnets repeatedly along it, in an inclined position, from the middle to the respective ends, in opposite directions at the same time. His large battery consisted of a number of plates surrounding two pairs of pieces of soft iron, which formed the ends of each compound magnet, while the middle was left hollow; the whole weighed 30 or 40 pounds, and would lift 80 or 100; and it communicated to common needles as much magnetism as they were capable of retaining, when their ends were merely placed on it, without any farther operation.

13. Examination of the friction of pivots. Mém. Ac. Par. 1790, P. 448. Mr Coulomb tacitly acknowledges, in this paper, a slight inaccuracy in his former experiments on the friction of pivots, the result of which seemed to indicate that the rotatory resistance of the friction was simply as the pressure, independently of any change of the magnitude of the minute surface of contact; he now finds that this is only true of smaller weights, when the pivot has already supported a larger, and its surface has probably been a little flattened; otherwise, the observation agrees more nearly with the theory; and perfectly so on the supposition of a conical point affording a resistance proportional to the displacement of the surface. The friction of steel on garnet is a little less than half as much as on steel; on agate, a little more than half; and on glass, four-fifths. Light needles, with a pivot tapering in an angle of about 20°, seem to be the most advantageous for common purposes; but if the needle is heavy, the point must be more obtuse. The conoidal caps, commonly used for suspending needles, had always an irregularity at the centre, which made the friction many times greater than that of a well finished surface, uniformly concave.

14. Experiments on the Circulation of Sap. Mém. Inst. Sc. II. P. 246. Mr Coulomb seems to have sufficiently ascertained that the sap appears to rise, in the poplar, near the centre of the tree, mixed with a considerably larger portion of air, which is extricated with a hissing noise, when the tree is cut or bored; it is not, however, certain that this air is in an elastic state while the vessels remain closed. The phenomena was first observed in April, and continued throughout the summer, being most distinct in the hottest sunshine.

15. Observations on the daily Labour of Men. Mém. Inst. Sc. II. P. 380. This memoir was read to the Academy of Sciences in 1775, but was not then published. Mr Coulomb's general conclusion is in favour of the employment of strength in ascending stairs; but he observes, that former authors have very frequently exaggerated the whole amount of a man's daily labour. In fact, the day's work, which he assigns to a man of ordinary strength, thus employed, is less than half of that which Desaguliers attributes to a labourer turning a winch: and Professor Robison has recorded, in this Encyclopaedia, more than one instance of a much larger result of the labour of a man ascending an inclined plane, even besides the force lost in the machinery employed: so that we must suppose the labourers in France to be commonly less vigorous than in Great Britain; almost in the same proportion, as Mr Coulomb has observed the work of the same man in Martinique to be less than in France.

16. Comparison of the Magnetic Powers of different Needles. Mém. Inst. Sc. III. P. 176. A number of accurate experiments are here adduced in confirmation of this theoretical conclusion, that needles of a similar form, and composed of portions of the same wire, possess directive powers which are very nearly proportional to their weights.

17. On the Cohesion of Fluids, and their Resistance to Slow Motions. Mém. Inst. Sc. III. p. 246. The interesting experiments here related, demonstrate that the constant part of the resistance of fluids is insensible; that the portion varying simply as the velocity is more than seventeen times as great in oil as in water, while the portion, which varies as the square of the velocity, is nearly equal in both these fluids. The resistance did not increase with the depth of immersion; on the contrary, it was a little greater when the body was partly above the surface. It was observed, that very slow oscillations were somewhat accelerated even by the motion of a carriage passing along the street. Greasing the surface of the solid did not sensibly lessen the resistance to its motion, nor was it materially increased by sprinkling sand on the grease; so that the particles of the liquid seemed to slide rather on each other than on the solid. But it is probable that these differences would have been more perceptible in greater velocities; for it seems reasonable to expect, that the friction between a fluid and a solid should partake, in a slight degree, of the nature of the friction between two solids, so as to increase less rapidly, with an increase of velocity, than the friction of the particles of fluids among themselves.

18. A new method of determining the Position of the Dipping Needle. Mém. Inst. Sc. IV. P. 565. The method, suggested in a former memoir, is compared, in this short essay, with the mean of four observations made in the common way, the magnetism of the needle being reversed during the experiment; and it appears that the error of either method is not likely to exceed ten or twelve minutes.

19. On Universal Magnetism. Bullet. Soc. Philom. N. 61. 63. Journ. Phys. LIV. P. 240. 267. 454. Journ. R. Inst. I. P. 134. The experiments mentioned in the first of these papers were immediately repeated in this country, with results less satisfactory than those which Mr Coulomb had obtained; and he soon found reason, upon a further examination, to change the opinion which he had at first inferred from them, observing that a grain of iron was sufficient to communicate sensible magnetism to twenty pound weight of another substance. There still remain, however, some difficulties respecting the magnetism of brass, which have not Mr Coulomb's moral character is said to have been as correct as his mathematical investigations. At an early period of his life he gained the grateful acknowledgments of the inhabitants of Britainy, for his disinterested exertions in preventing the execution of some public works which threatened to be ruinous to the province. His manners were serious, but gentle, and sometimes diversified by a mild gaiety, which made him very amiable in society. His disposition was generous and benevolent; but, notwithstanding all his modesty, he could exhibit sufficient spirit, when he was called upon to repel an unjust attack. Such occurrences were, however, far from being frequent, for his merits and his success were universally acknowledged, and he was extremely popular, without ever having excited envy. In the particular department of science which he cultivated, he may fairly be ranked in the same class with Franklin, Æpinus, and Cavendish. He was less original than Franklin, but much more profound. He gave to the speculations of Æpinus both a more defined application, and a more satisfactory demonstration; and he was equally accurate with Cavendish, but much more persevering with respect to the more limited objects of his researches; and his improvements in the theory of electricity, may be considered as having immediately prepared the way for the elegant inventions of Volta, and the still more marvellous discoveries of Davy. In short, among all the men of science who have done honour to France, it would be difficult to point out a single individual who, with regard to the cultivation of terrestrial physics, could at all be put in competition with Mr Coulomb. His health had long been extremely feeble, and in addition to his more chronic complaints, he was at last attacked by a slow fever, to which he fell a victim on the 23rd of August 1806. He had been a Lieutenant-Colonel of Engineers, a Chevalier of the Order of St Louis, and a Member of the Legion of Honour; but he had acquired little property; and he left to his two sons scarcely any other patrimony than the public gratitude and esteem, for his merits and his virtues. (Delambre, Mém. Inst. Sc. 1806, ii. Hist. P. 206.)