Théorie des Machines simples, en ayant égard au frottement de leurs parties et a la roideur des Corages. Piece qui remporté le Prix double de l'Academie des Sciences pour l'année 1781.

Paris: Moutard, 1782.

Extremely rare offprint, with imprint three years before publication in journal form, of this important memoir in which Coulomb created the science of friction. “Coulomb’s most celebrated study, one that brought him immediate acclaim, was “Théorie des machines simples,” his prize-winning friction study of 1781. He investigated both static and dynamic friction of sliding surfaces and friction in bending of cords and in rolling. From examination of many physical parameters, he developed a series of two-term equations, the first term a constant and the second term varying with time, normal force, velocity, or other parameters. In agreement with Amontons’s work of 1699, Coulomb showed that in general there is an approximately linear relationship between friction and normal force; but he extended the investigation considerably to show complex effects due to difference in load, materials, time of repose, lubrication, velocity, and other considerations. Coulomb’s work in friction remained a standard of theory and experiment for a century and a half, until the advent of molecular studies of friction in the twentieth century. To quote Kragelsky and Schedrov’s recent monograph ([Development of the Science of Friction - Dry Friction (1956)], p. 52) on the history of friction: “Coulomb’s contributions to the science of friction were exceptionally great. Without exaggeration, one can say that he created this science” (Gillmor in DSB III.442). The Théorie was delivered orally in 1781 and it won an important prize of the Academy of Sciences, a fact advertised on the title: ‘Piece qui a remporté le Prix double de l’Académie des Sciences pour l’Année 1781.’ It was published in 1785 in Tom. X of the Mémoires de Mathématique et de Physique Présentés à l’Académie Royale des Sciences, Par Divers Savans, pp. 161-332. The completely different pagination (and signatures) establish the present work as a separate publication, and it was almost certainly intended for limited distribution (Academy members, etc.). OCLC lists three copies of this offprint worldwide: Harvard, Université Louis Pasteur, Strasbourg (2 copies or a duplicate record?). No copies located in auction records.

“During the period 1720-1793 the Academy offered numerous prizes in essay contests. Capturing one of the handsome awards was not always a guarantee of entrance into the Academy, but those who did win found themselves among an impressive group which included Pierre Bouguer, three Bernoullis (Johann, Johann II and Daniel), Euler, Lagrange, Bossut and Bailly. The contests fell into two main categories, astronomy and maritime …

“The Academy had proposed for the prize for 1779 (and again for 1781), the solution of problems of friction for sliding and rolling surfaces, the resistance to bending in cords and the application of these solutions to simple machines used in the navy. There existed so many friction theories and experimentally determined constants that it was specifically indicated that the contestants must examine “the effects resulting from the stiffness of ropes, being determined after new experiments made on the full scale; it is required also, that the experiments be applicable to machines utilized in the Navy, such as the pulley, the capstan, and the inclined plane.” The solutions of some of these problems were of the highest priority. For example, the data on inclined planes would be used in constructing arrangements for ship launchings. Coulomb noted that often when ships were launched by sliding down ways they would stick halfway down, the ways would catch fire from the generated heat or the ship would fall over and possibly suffer major damage ….

“In the preface to “Theory of Simple Machines” Coulomb discussed the existing work on friction – the original hypothesis of Amontons and the experimental variances found by Musschenbroek, Camus and Desaguliers. He criticized the neglect of deformation considerations in previous work. Camus and Desaguliers had noted that friction varied with the time that the two static surfaces had remained together before motion, but neither had investigated this relationship. As in previous memoirs, Coulomb acknowledged his debt to Bossut.

“The “Theory of Simple Machines” was composed in two parts: 1) the friction of sliding surfaces and 2) the bending of cords and movements of rotation. In each of these sections Coulomb gave numerous figures depicting his apparatus. He carefully described his materials and the reasons for employing each particular piece. For instance he explained that in the investigations on sliding surfaces he disregarded the friction of a small pulley in his friction table apparatus. He did so because in separate experiments he examined the friction in the pulley and found it to be less than 1/150th of the total value in the experiments with the table. In other cases he noted the exact temperature of the air, and examined rope that had been weathered by sun, rain, or salt water. He found correction factors for these variables. In another case he considered the humidity of the air. He left this factor out of his published results only after it was found to have no differential effect on the various experiments. Thus it had been assumed that if a pulley or a plane surface were polished to a high sheen then it could be considered smooth and as frictionless as possible. Desaguliers had stated that such surfaces would produce higher friction values due to cohesive forces. Coulomb discovered that one cannot determine directly by any human sense whether a plane surface, for instance, is perfectly smooth. Nevertheless the friction coefficient can be decreased by “running-in” the object. For a plane surface this would entail passing a very heavy plane object back and forth over its surface. A pulley could be “run-in” by drawing a rope over it for a number of hours. In each case the friction coefficient would be reduced after a period of time, even if the surface had formerly appeared perfectly smooth.

“This patient, inquisitive, wide-ranging type of experimentation was unique in the history of friction studies. Coulomb’s method produced physical answers expressed in analytical terms that could never arise out of the purely rational approach of an Euler … And oppositely, Coulomb’s use of analysis to frame his experimental laws and to guide him in searching for patterns of development could bring a myriad of facts into account. This was never accomplished by the rambling experimentation of a Bélidor or a Desaguliers … Coulomb used analytical methods evolved by Parent, Euler, Daniel Bernoulli, and Bossut. He extended and codified the experiments of Amontons, Desaguliers, and others. It was just this fruitful combination of analysis and directed experiment that led him to his results.

“In nearly all of Coulomb’s formulas for calculating friction effects he employed two-term equations. These contained a constant term and a term varying with time, normal force, velocity, or some other parameter. These formulas accounted for the small effect due to cohesion or surface films and the larger effect due to mechanical interaction … In articles III and IV at the beginning of his memoir he noted the five most important parameters in static and dynamic friction:

  1. the nature of materials and their surface coatings
  2. the extent of surface area
  3. normal force
  4. the length of time that the surfaces remain in contact before motion begins (time of repose)
  5. the relative velocity of the contact surfaces.

Coulomb then proceeded immediately to discuss the two major hypotheses for the cause of friction phenomena: first, the engagement or enmeshing of surface asperities; and second, the cohesion of the surface molecules. Those, as Desaguliers, who held that friction depended on the area of surface contact, employed the cohesion theory to explain friction. Most others accounted for it by the use of Amontons’ mechanical surface-asperity theory … Coulomb said that Amontons’ Law held for most practical cases of friction phenomena. By this he meant that there was an approximately linear relationship between friction and normal forces but that this did not remain constant from one material to another …

“Coulomb became aware that Amontons’ Law did not accurately reflect the situation in friction problems. Abbé Bossut had been the first to indicate clearly the difference between static and dynamic friction but he had not sufficiently examined the problem. Camus and Desaguliers had noted that the friction of a body shocked or shaken was less than that of a body started from rest but they had not tried to determine the relation that exists between these two kinds of friction. Bossut had noted that the longer two surfaces remained in static contact the harder it was to start them in motion. Coulomb … advanced the suggestion that the contacting surfaces might be covered with a small surface layer or film.

“Of greater import than the small cohesion contributions was the factor of normal force. According to Amontons’ Law, the friction was approximately proportional only to the normal force exerted by the upper body. Amontons further added that the friction force was equal to about one-third of the normal force. Amontons had expressed both surface-asperity and surface-spring hypotheses to explain the behaviour of friction. However, he considered springs to deform instantaneously. Coulomb was faced with the following experimental facts: metals seemed to have approximately the same coefficient of friction for both static and dynamic conditions; friction in fibrous materials, on the other hand, varied depending upon the length of time the surfaces had remained in contact and upon the velocity of surface motion. Adapting the “brush bristle” analogy of Musschenbroek, Coulomb explained the variation of friction with the time of repose and with velocity in fibrous matter in the following way: if wood fibers are considered as little springs capable of deformation, then as two substances remained pressed together, their asperities would interlock or enmesh more and more with time of repose. There was a definite time needed for this deformation to occur. After increasing for a time the static friction seemed to reach a limit value. Coulomb assumed that this limit indicated the occurrence of full deformation. In dynamic friction, the surface asperities did not have time enough to enmesh, thus, the surface asperities could be regarded as almost rigid and the friction would be proportional to normal force alone.

“Under “enormous” pressures the surface asperities or cavities became bent, and with increasing velocity the asperities enmeshed less and less. This would explain the relative decrease of friction with increasing velocity at high pressures. Metals did not seem to share this property. There was no effect of time of repose, nor of lessening friction with velocity. This was easily explained by Coulomb. Wood was thought to be composed of flexible, elastic, elongated fibers. Metal, however, was composed of “angular, globular, hard and inflexible parts, so that no degree of pressure nor of tension can change the shape of the parts which cover the surface of metals” …

“In sum, Coulomb’s hybrid two-term formulas and his composite theory gave a very good account of known frictional behaviour” (Gillmor, pp. 127-136).

The present work presents a bibliographical puzzle. The leading American scholar of Coulomb, C.S. Gillmor of Wesleyan University, does not list this 1782 publication of the Théorie des Machines in the DSB article or his monograph, Coulomb and the evolution of Physics and Engineering in 18th-century France (1972). According to Gillmor, the first published version of the present work appeared in 1785 on pages 161-332 of vol. X of the Mémoires de Mathématique et de Physique Présentés à l’Académie Royale des Sciences, Par Divers Savans. The Norman catalogue also cites the 1785 journal appearance as being the first. The plates in the present edition (figures 1-27 on plates numbered II-VI) are integral with the text, and appear to be the same as those in the journal publication (the ‘missing’ plate I belongs to a different article in the journal). Each plate contains the printed title ‘Scavants Etrangers T.X. Pag. 332’ within the platemark. This links the plates to the journal, since the plates in such publications are generally bound at the end of the article and the page number is precisely the last numbered page of the work in the journal publication (332). But, the pagination in the present edition is completely different, pp. [1]–172, and the date of the imprint is three years earlier. This anomaly may be explained by the fact that the volumes of the Mémoires at this time were published about once every five years – the previous Tom. IX was published in 1780. The text and plates of each volume were probably printed over a period of years, so that the present work may have been printed in 1782 even though the complete volume of the Mémoires was not completed until three tears later.

Separate printings of Coulomb’s other Academy memoirs are known, for example his Mémoires sur l’Électricité et le Magnétism (Horblit 31b; Dibner 58; Norman 527). Those printings, however, were probably assembled after their appearance in journal form and issued by the printer as collections, with new title pages, from leftover sheets from the journal publication as they are not separately-paginated and retain the signatures of the journal issue. The offered item is thus a highly unusual case of a true offprint preceding the journal issue by several years.

The present work was first published in book form in 1809, and again in 1821.

Norman 526 (journal issue); Roberts & Trent, p. 82 (1821 book edition). Gillmor, Coulomb and the evolution of Physics and Engineering in 18th-century France, 1972.

4to (249 x 190 mm), [1-3] 4-172 pp., 5 plates numbered ii-vi (fully complete), contemporary half calf over marbled boards, front and rear boards with some surface wear and scratches, lower capital chipped, spine with moderate ware, very light spootting to a few leaves. A very nice and completley unrestored copy.

Item #4273

Price: $13,500.00