## EULER, LEONHARD. - SOLVING FOR THE FIRST TIME THE CONTACT PROBLEM OF FRICTION.

# Sur l'atmosphere de la Lune prouvée par la derniere eclipse annulaire du Soleil. (On the atmosphere of the moon as proved by the last ringed eclipse of the sun) + Sur le frottement des corps solides. (On the friction of solid bodies) + Sur la diminution de la resistance du frottement. (On the reduction of the resistance of friction). 3 Memoires.Sur l'atmosphere de la Lune prouvée par la derniere eclipse annulaire du Soleil. (On the atmosphere of the moon as proved by the last ringed eclipse of the sun)

(Berlin, Haude et Spener, 1750). 4to. No wrappers, as issued in "Mémoires de l'Academie Royale des Sciences et Belles-Lettres", tome IV, pp. 103-121 + pp. 122-132 + pp. 133-148 and 6 engraved plates (on 5).

*Three first editions by Euler. Euler's goal in the first paper is to show that certain phenomena that resulted from the eclipse of July 25, 1748 are evidence that the moon has an atmosphere that is almost 200 times less dense than that of the earth. (The phenomena Euler observed are optical effects of light passing close to a sharp edge, and not the refraction of a lunar atmosphere).*

The other papers on the physics of rigid bodies are groundbreaking as Euler here set forth what is known as "Euler's dynamical equations of the motion of the mass-center of any solid", and thus STATING FOR THE FIRST TIME THE LAW OF DRY FRICTION, mathematically. Euler explains his experiments with the inclined plane and discovers the DIFFERENCE BETWEEN KINETIC AND STATIC FRICTION.

"Leonhard Euler occupied himself with the mathematical point of view of friction as well as the experimental. He introduced the differentiation between static frictional forces and kinetic frictional forces, and solved the problem of rope friction, probably the first contact problem to be analytically solved in history. (1750, the papers offered). He was the first to lay the foundations of the mathematically way of dealing with the law of dry friction and in this way promoted further development. We have to thank for the symbol as the coefficient of friction. Euler worked with the idea that friction originates from the interlocation, between small triangular irregularities.This understanding survived, in different variations,for a hundred years and is also used today as the "Tomlinson Model" in connection with friction on atomic scale."(L. Popov "History of the Contact Mechanics and the Physics of Function", p.3).

Eneström: E142, E143, E144.

Order-nr.: 45497