MECHANICS. 



11 



(14.) From the circumstance of fric- 

 tion being; an uniformly retarding force, 

 it follows that it is independent of the 

 velocity, for it is found to continue the 

 same while the velocity is continually 

 increased. In this result all the expe- 

 riments agree very nearly. 



(15.) From all that we have stated, 

 the reader will easilv perceive that much 

 still remains to be discovered respecting 

 the nature and properties of friction. 

 The experiments of Coulomb and Vince 

 seem to be executed with equal preci- 

 sion, and governed by scientific prin- 

 ciples equally just, and yet we find them 

 differ considerably concerning the lead- 

 ins: and important principle of the pro- 

 portionality of the friction to the pres- 

 sure. Coulomb is, however, uniformly 

 supported in his results by the experi- 

 ments of Ximenes and various others ; 

 and Vince, we believe, stands alone in 

 his conclusions, at variance with these. 

 The experiments of Ximenes are subject 

 to some little discordance with each 

 other, and those of Coulomb, owing to 

 his not having noticed the circumstance 

 of the friction at rest depending on the 

 time of contact, and having put the 

 bodies in motion without having waited 

 for the friction to reach its maximum. 



(16.) Besides the results which we 

 have mentioned, there are other parti- 

 culars which were developed in the ex- 

 periments of Coulomb, which it may not 

 be useless to state. 



Friction varies in general with the 

 quality of the surfaces : in new wood 

 planed, it amounts to half the pressure ; 

 in metals, to one-fourth ; and in wood 

 and metals, to one-fifth. 



As the surfaces are worn by attrition, 

 the friction is generally diminished ; but 

 this has a limit, and the friction soon 

 reaches its minimum. In woods, from 

 being half the pressure, it is reduced 

 by attrition to a third. 



Between woods the friction is less 

 when the grains cross each other than 

 when they are placed in the same direc- 

 tion. It is, in the former case, one- 

 fourth of the pressure ; and, in the lat- 

 ter, half the pressure. 



In general, friction is greater between 

 surfaces of the same kind than between 

 surfaces of different kinds. 



While the attrition continues to dimi- 

 nish the friction it is not an uniformly 

 retarding force, and, therefore, until 

 this effect ceases it will not be found 

 to be independent of the velocity. 



Friction diminishes as the smoothness 



of the surfaces of contact is increased. 

 However, by carrying the polish of 

 the surface too far, we shall produce a 

 considerable resistance from cohesion. 



Friction is diminished by anointing 

 the surfaces of contact with some unc- 

 tuous substances, as tallow, oil, grease, 

 $c. Coulomb considers that the greater 

 the consistency of the ointment, the 

 greater will be the advantage. Fresh tal- 

 low diminishes the friction by one-half. 



According to Vince 's results, it would 

 appear that friction is diminished by 

 diminishing the surface of contact. But 

 even admitting this as a general prin- 

 ciple, it has an obvious limit in practice, 

 for if the one surface be small and the 

 other soft, a groove will be ploughed by 

 one surface ^in the other, and thus the 

 friction will be produced. 



CHAPTER III. Of the Friction of one 

 Body rolling over the Surface of an- 

 other. 



(17.) WHEX one body rolls upon an- 

 other; it is very obvious that friction pro- 

 duces much less resistance to the mo- 

 tion than when it slides, as described 

 in the last Chapter. In this case the 

 parts of the one surface are, in some 

 degree, successively lifted from off the 

 other, and the asperities act in a man- 

 ner totally different from the case of 

 sliding, already considered. One, at 

 least^of the bodies must, in this case, 

 be bounded by a curved surface, and 

 therefore the surface of contact must 

 necessarily be very small, which is an- 

 other cause of the diminution of the 

 friction. If the rolling body be cylin- 

 drical, the points of contact of the sur- 

 faces will form a straight line upon the 

 surface of the cylinder, the surface on 

 which the cylinder rolls being either 

 that of another cylinder having its axis 

 parallel to that of the former, or a plane. 

 But if the rolling body be a sphere, a 

 spheroid, or any similar shape, the sur- 

 face of contact will be reduced to a 

 single point. 



To explain the manner of inves- 

 tigating experimentally the properties 

 of this species of friction, let us sup- 

 pose two perfectly plane tables, AB, 

 C D, (Jig. 3,) placed exactly in the same 

 horizontal plane. On these let a cylin- 

 der, E F, be placed with its axis at right 

 angles to their length. At the middle 

 of the interval between the tables, let a 

 flexible string be passed across^ the 



