118 LECTURE XIII. 



especially where the surfaces are large and the substances but moderately 

 hard. 



The truth of the assertion, that friction is a uniformly retarding force, 

 may be shown very conveniently by means of Atwood's machine for ex- 

 periments on accelerated motion. By suffering the axis of the pulley to 

 rest on the surface of any fixed substance, we may subject it to a friction 

 of which the magnitude may be varied by different methods ; and we shall 

 find that the motions of the boxes still indicate the action of a uniformly 

 accelerating force, the spaces described being always proportional to the 

 squares of the times of descent ; it follows therefore, that since the ope- 

 ration of gravity is uniform, that of friction which is deducted from it at 

 each instant, must also be uniform, in order that the remaining acceleration 

 may follow the same law. 



The uniformity of the force of friction may also be shown by the descent 

 of a flat substance on an inclined plane : if the body be caused to begin its 

 descent with a certain velocity, it will be retarded when the resistance is 

 greater than the relative force of gravity : in this case the retardation will 

 continue until it is wholly stopped, the resistance not diminishing with the 

 velocity. If, on the contrary, the relative weight overpowers the resistance 

 at first, the motion will be continually accelerated, the resistance not being 

 increased by the increase of the velocity. But since every experiment of 

 this kind must be performed in the presence of the air, the resistance of 

 this fluid, which follows another law, will in the end prevent the ac- 

 celeration. 



It may in general be asserted, with some exceptions, that the force of 

 friction is simply proportional to the weight or pressure that brings the 

 substances concerned into contact, independently of the magnitude of their 

 surfaces : but Mr. Coulomb has observed that in many cases there is, 

 besides this force, another resistance, amounting to several pounds for each 

 square foot of the surface, which is independent of the pressure ; and by 

 calculating these forces separately, we may probably always ascertain the 

 whole resistance with sufficient accuracy. This constant portion is usually 

 much smaller than that which varies with the weight, and in all common 

 cases it may be safely neglected, and the friction of stone on stone may be 

 called equal to one half of the pressure, that of wood on wood one third, 

 and that of metal on metal one fourth ; and this may serve as an estimate 

 sufficiently accurate for calculating the effects of machines ; although, if 

 their parts were perfectly adjusted to each other, and all the surfaces well 

 polished, the friction would not in general exceed one eighth of the 

 pressure, whatever might be the nature of the materials. The application 

 of unctuous substances lessens the friction in the first instance ; but unless 

 they are frequently renewed, they sometimes tend rather to increase it. 



The simplest mode of ascertaining the magnitude of the friction of two 

 bodies, is to incline their common surface to the horizon until the one 

 begins to slide on the other : this point determines the magnitude of their 

 adhesion ; but in order to find that of their friction when they are in mo- 

 tion, they must be first separated, and then allowed to move on each other, 

 while the whole apparatus is gently agitated. The friction will then be to 



