MECHANICS. 



" But, because in the three preceding 

 trials, the same bell was employed, the 



/*" > 



quantity f ' is the same : must 

 " J a x 



therefore be a constant quantity if A be 

 constant, and reciprocally. But in each 

 trial there was reckoned the time em- 

 ployed by the apparatus in performing 

 an entire'revolution. The mean velocity, 



or the velocity due to the half of each first 

 revolution, will, therefore, be measured 

 by the circumference run over. The 

 space described up to the end of the 

 motion, will be measured by the num- 

 ber of turns run through from the in- 

 stant where the mean velocity was de- 

 termined until the end of the motion. 

 Thus by computing from the data fur- 

 nished by the three trials, we may form 

 the following table : 



1st Trial. 



: 2d Trial. 

 3d Trial. 



1 turn in 4", stops at 34^ turns, whence results = : 



" This experiment, then, shows une- 

 quivocally that the quantity , and 



consequently the quantity A which ex- 

 presses the momentum of friction, are 

 constant quantities, whatever be the 

 primitive degree of velocity ; and that, 

 consequently, the velocity has not any 

 influence upon the resistance due to the 

 friction of pivots, which from this expe- 

 riment is necessarily proportional to a 

 function of the pressure. 



" When this experiment is made in a 

 vacuum, a much less heavy body may 

 be employed, and of any form whatever, 

 and the same result will be obtained. 



" In other experiments,Coulomb bent 

 a brass wire of 9 inches in length ; the 

 parallel branches were 24 lines distant 

 from one another : the part of the wire 

 curved in the form of a semicircle which 

 joined the two branches was about 3 

 inches long ; and the two vertical and 

 parallel branches were also each 3 

 inches long. To the extremity of each 

 vertical branch was attached by means 

 of wax a piece of metal, and there was 

 fixed, in like manner, in the middle of 

 the concave part of the wire, to serve 

 for the cheek or bush, a small well- 

 polished plane of different substances 

 on which the friction of the point of the 

 pivot was to be determined: finally, 

 there was fixed to the summit of a sup- 

 port a little needle of tempered steel, 

 and whose point it was necessary to 

 render more or less fine, rounded, or 

 obtuse, according to the nature of the 

 cheeks, and to the pressure which they 

 were to experience. The extremity of 

 the needle first used by Coulomb, ap- 

 peared, when examined by a micro- 

 scope, to form a conic angle'of 18 or 20 

 degrees. The friction of this needle 

 against well-polished planes of granite, 



agate, rock crystal, glass, and tempered 

 steel respectively, was tried ; and the 

 result, taking in each experiment the 



mean quantity represented by (a 



quantity which was always found to 

 vary between very narrow limits), gave 

 the momentum of friction of the point 

 of the needle against the planes of gra- 

 nite, agate, &c. respectively, in the 

 ratio of the fractions -5^5, sir, T^, ^, 

 so that the momentum of friction 

 of the plane of granite being represented 

 by unity, we shall have for the momen- 

 tum of "the friction of rotation relative 

 to the other substances as below : fric- 

 tion of granite, 1 : of agate, T214 ; of 

 rock crystal, T313; of glass, 1T77 ; of 

 steel, 2 : -J.37. 



" Coulomb likewise employed himself 

 during these experiments, in determin- 

 ing the more or less acute form which 

 should be given to the points of the 

 pivots. To this end he caused to be 

 successively rounded into cones of 

 greater or less acuteness, the extremity 

 of a steel needle, that it might thence 

 appear whether the change of figure 

 had any influence upon the friction. 

 Thus he found that, under a certain 

 charge, the point of the pivot being 

 shaped to 45 degrees, the quantity 



was, for granite, 5 & 5 ; agate, ^iW ; 



glass, TJ'OO ; tempered steel, ^ v . 



" Coulomb then gave to the point a 

 more acute form, so that the angle of 

 the cone which terminated it could not 

 be more than 6 or 7 degrees ; and he 

 found, still retaining the same charge 

 or pressure as before, that the quantity 



was, for agate, s <j; glass, 5 b ; tem- 

 pered steel, s fo, 



