PROFESSOR OSBORNE REYNOLDS ON ROLLING-FRICTION. 
161 
each other, compressing the india-rubber, which will extend laterally. Now if there 
were no friction between the rubber and the plates, then the surfaces in contact with 
the plates would extend in the same proportion as the rest of the bar, and the section 
would preserve its rectilinear form, as shown in fig. 3. 
ee' ee' 
With friction, however, the case would be different. The friction would prevent the 
surface of the india-rubber expanding laterally to the same extent as the rest of the bar, 
and the section would lose its rectilinear form and bulge out in the middle, as shown in 
figs. 4 and 5. 
If we imagine the section of the bar to have been marked with a series of lines ( ee ') 
initially vertical and at equal intervals apart, these lines will when the bar is compressed 
assume the form shown in the figures. 
If there were no friction, then, as shown in fig. 3, the ends of these lines would still 
be equidistant after compression ; but with friction the intervals will not be all equal, 
but will vary according to their distance from P, the middle of the section. Up to a 
certain distance ( er ) the friction will be sufficient to prevent slipping ; and hence up to 
this point the ends of the lines will preserve their original distance. From this point 
(er), however, slipping will commence and will go on increasing to the edge of the 
surface. From this point, therefore, the distance between the ends of the lines will 
continually increase. 
With regard to the distribution of the pressure between the india-rubber and the 
plates : — Without friction this will obviously be uniform over the whole surface. 
Friction, however, will not only increase the mean intensity of the pressure, but will 
also alter its distribution, causing it to be greatest at P and gradually diminish towards 
the edge. 
The inclination of the ends of the lines e e' is caused by, and may be taken to repre- 
