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PROFESSOR OSBORNE REYNOLDS ON ROLLIN G-ERICTION. 
notliing at the edges. Thus deformation is allowed to go on between the surfaces after 
they have come in contact, and is performed by the slipping of the one over the other. 
The Friction. 
The slipping is performed against friction, and therefore gives rise to resistance to 
the motion of the roller. 
This resistance will obviously be proportional to the work spent in overcoming the 
friction between the surfaces during a certain extent of motion ; and at first sight it 
appears as if this would be proportional to the coefficient of friction between these 
surfaces. When I first commenced this investigation I was under the impression that 
such would be the case, and that by oiling the surfaces the resistance to rolling might 
be considerably reduced. Finding by experiment, however, that this was not the case, 
that although in certain cases the effect of oiling or blackleading the surfaces does 
reduce the resistance to rolling, yet this reduction is never great, and in some cases 
the effect appears to be reversed, it occurred to me that the friction would itself 
modify the deformation which would otherwise take place after contact had commenced, 
and by preventing slipping might diminish the work that would otherwise have been 
spent. 
The Deformation. 
The action of friction to prevent the deformation at any point of the surfaces in 
contact will obviously depend on two things — the magnitude of the friction, and the 
force tending to slide the one surface over the other. Now if P (fig. 1) be the point of 
greatest pressure, the possible friction will gradually diminish with the pressure as the 
distance from P increases ; whereas we may assume that the tendency of the one surface 
to slip over the other will be nothing at P, and will gradually increase with the distance ; 
so that for a certain distance the Trie tion may be sufficient to prevent slipping altogether, 
but beyond this distance slipping will go on in an increasing ratio. 
The effect of oiling the surface would therefore be to diminish the region of no 
slipping, and increase the area over which slipping goes on as well as the extent of 
slipping at each point. These effects would to a certain extent counteract the advan- 
tage gained by the reduced coefficient of friction ; and it may well be conceived that 
under certain circumstances they would overbalance it, and that the oil would actually 
increase the resistance. 
The effect which friction has upon the deformation beneath the roller, as well as the 
general nature of this deformation, will be rendered clearer by examining the effect of 
friction under circumstances of a less complicated nature than those of rolling. 
A Soft Bar between Hard Plates. 
Let fig. 2 represent the end or a section of a long rectangular bar of india-rubber, or 
any elastic material, placed between two flat plates. Suppose these plates to approach 
