MECHANICS. 



Fig. 3. 

 A, 



cylinder, having dishes of exactly equal 

 weight suspended at its extremities. By 

 placing equal weights in these dishes, 

 any required pressure may be produced 

 upon the table. If, then, fine sand be 

 poured into either scale until its pre- 

 ponderance just gives motion to the 

 cylinder, this additional weight will be 

 equal to the friction. 



In this way the diameter and material 

 of the cylinder, as well as the pressure 

 it exerts against the plane, may be 

 varied at pleasure. In making experi- 

 ments, it would be useful, in each trial, 

 to pour the sand successively in each 

 scale, so as just to make the cylinder 

 move in each direction. If the weights 

 which produce the motion differ by a 

 small quantity, a mean between may be 

 taken to represent the friction. 



(18.) The results of numerous expe- 

 riments instituted in this way by Cou- 

 lomb were as follow : 



1. With the same cylinder the fric- 

 tion is proportional to the pressure. 



2. With cylinders of the same sub- 

 stance, having different diameters, but 

 equal pressures, the friction is inversely 

 as the diameters. 



3. With cylinders of the same sub- 

 stance, differing both in diameter and 

 pressure, the friction is directly as the 

 pressures, and inversely as the diame- 

 ters ; or in a ratio compounded of the 

 direct ratio of the pressures and the in- 

 verse ratio of the diameters. 



To explain the last two results to 

 those who are not conversant with ma- 

 thematical phraseology : Suppose that 

 two cylinders, one of two and the other 

 of five inches diameter, exerted equal 

 pressures on the tables, it would be 

 found that the friction of the two-inch 

 cylinder would be greater than that of 

 the five-inch cylinder, in the proportion 

 of five to two. 



Again, suppose that the twp-inch 



cylinder exerts a pressure of three 

 pounds, and the five-inch cylinder a 

 pressure of seven pounds, it will be 

 found that the friction of the two- inch 

 cylinder will be to that of the five-inch 

 cylinder in the proportion of the pro- 

 duce of five and three to the product of 

 two and seven, or as fifteen to fourteen. 



It was found that greasing the sur- 

 faces does not at all diminish this spe- 

 cies of friction. 



When a cylinder of mahogany, whose 

 diameter was about three inches, was 

 rolled upon a plane of oak, the friction 

 was about one-sixteenth of the pres- 

 sure ; and when it rolled upon a plane 

 of elm, the friction was only one hun- 

 dredth of the pressure. 



It is evident, therefore, that between 

 the same substances this species of 

 friction is much less than that of sliding. 



The string used in these experiments 

 should be so flexible, that its rigidity or 

 stiffness shall produce no sensible effect 

 upon the results. 



CHAPTER IV. On the Friction of one 

 Surface revolving in contact with an- 

 other) without rolling. 



(19.) IF a body, having any round 

 figure, be made to revolve while it is 

 pressed with any force against any sur- 

 face, and at the same time is prevented 

 from rolling along that surface, a spe- 

 cies of friction will be produced differ- 

 ent from any which we have yet con- 

 sidered. This species of friction seems 

 to partake of the nature of each of 

 those which we have considered in the 

 last two Chapters. As in the former, 

 the surfaces slide one over the other, 

 and as in the latter, the surface of con- 

 tact is reduced to a line ; we accord- 

 ingly find the degree of this friction, 

 under similar circumstances, holding an 



