182 A. S. Kimhall— Sliding Friction on an Inclined Plane, 



would trace iipon the smoked glass a waved line, which would 

 ■ er of the experiment. The time 

 point, the distance passed over 

 of time, could all be measured or counted directly 

 from the smoked glass. 



The graphical method of working up the experiment was 

 employed, as follows: The bottom of a sheet of section paper 

 was made a "time line" {^\^ of a sec.= a unit). At various 

 points on this line the corresponding velocities were erected as 

 ordinates. The equation of a line connecting the upper ex- 

 tremities of these ordinates would express the law of the motion 

 studied. 



It is evident that this line would have been straight if the 

 acceleration of the slide had been uniform, like that of a body 

 falling in vacuo. If, however, a variable resistance be opposed 

 to the motion of the slide, the acceleration will no longer be 

 uniform, and the line will become curved, concave toward the 

 axis of abscissas, if the resistance is increasing, convex if the 

 resistance diminishes. The acceleration of such a motion at any 

 time will be proportional to the tangent of the angle which the 

 direction of the curve at that point makes with the time line. It 

 is also evident that such acceleration may at once be measured 

 from the paper, since it is the difference between the velocities 

 for two successive units of time. The curve constructed as 

 above, from every experiment made, was decidedly convex 

 toward the time line, showing a constantly decreasing resistance 

 to the motion of the slide as the velocity increased. If we 

 assume that this increase in acceleration was due to a dimin- 

 ished coefficient of friction, the value of the coefficient for any 

 time may be found in the following manner : 

 Let a, h, and h= the altitude, base, and length of the inclined 

 plane. 

 W~ weight of the slide and contents. 

 'W'= normal pressure on the plane, = W.-j-. 

 g— acceleration of a body falling freely. 

 g'= theoretical acceleration of the slide =g-jr- 

 g"= the observed acceleration at any time. 

 Then the resistance of friction =F= —{g'-g")^ and the co- 

 efficient of friction. ^= Z, = /^' . i = (J_^)| = 



X j= tangent of inclination— — ^. 



^ gb ^ gb 



The following tables give the results obtained from a series 



