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PROFESSOR OSBORNE REYNOLDS ON ROLLING-FRICTION. 
The turning of the plate A B, which has been supposed to be going on in figure 7, 
represents very closely the action of a roller in compressing the material beneath it ; and 
this case affords us an illustration of the way in which the lateral extension of the 
material under the roller, or of the roller itself, will by causing slipping alter the distance 
travelled by the roller. If the roller be hard and the surface on which it rolls soft, 
then the top plate A B may be taken to represent the roller, and, as has just been 
explained, this slips hack ; whereas if the roller be soft and the surface hard, then we 
may take the india-rubber to represent the roller, and this slips forward. 
A Continuous Surface. 
It is clear that in the case of the bar shown in fig. 7 the slipping will diminish as 
the coefficient of friction increases. There is, however, an important difference between 
this case and that of a roller in which it is not the entire breadth of a bar that is 
compressed, but a portion of a continuous surface ; for whatever lateral extension there 
may be immediately under the roller must be compensated by a lateral compression 
immediately in front and behind it. The greater the lateral extension under the roller 
the greater will be the lateral compression ; and since the action of the roller is 
continually to change the one for the other, the one effect will to a certain extent 
counteract the other ; so that in this case we need not expect to find the diminution 
attended with a corresponding increase in the ostensible slipping. This will be rendered 
clearer by examining these circumstances as they affect rolling. 
The Deformation caused by a Boiler. 
Fig. 8 may be taken to represent a section of an iron cylinder on an india-rubber 
plane. The lines on the plane are supposed to represent lines initially vertical and at 
equal distances apart. The motion of the roller is towards B. P is the point of greatest 
compression directly below the centre of the roller ; e r and fr limit the surfaces over 
which there is no slipping ; D is the point at which contact commences, and C that at 
which it ceases. 
Fig. 8. 
The portions of the india-rubber immediately without C and D are laterally compressed ; 
