PROFESSOR OSBORNE REYNOLDS ON ROLLING-FRICTION. 
163 
compression; but since that portion of the surface which lies beyond er has been 
extended by the compression, it will have to 
contract as the surfaces recede, and the friction 
of the surface will oppose such contraction. 
Hence the lines which during compression were 
curved outwards will gradually straighten and 
curve inwards, as shown in fig. 6. Those at the 
edges will take the form first, and then those 
nearer to er, until the expansion has become complete. 
The extent to which friction will deform the india-rubber during this operation will 
obviously depend on the extent to which friction has allowed the surfaces to expand 
during compression. The smaller the friction the greater will be this expansion, and 
consequently the further they will have to contract, and the greater will be the pressure 
under which contraction must take place. It is obvious, therefore, that the work spent 
in friction during the recoil will increase up to a certain point as the coefficient of friction 
diminishes ; and it would appear to be this increase which mainly balances the advantage 
which is gained during compression by reducing the coefficient. 
It is evident that the action of friction to prevent contraction during restitution will 
tend to reduce not only the mean pressure but also the whole pressure, for exactly the 
same reason as by preventing expansion the friction increases these pressures during 
compression. Therefore, for every distance between the plates, after the curves become 
inclined inwards the pressure on the surface would be less than at the same distance 
with no friction, and in a still greater degree than during compression with friction. 
We can see at once, therefore, that of the work spent in compressing the material only 
a part would be returned during restitution. The difference is what is spent in 
overcoming the friction. 
If 
Fig. 7. 
The Direction of the Friction. 
In figures 5 and 6 the direction of slipping is opposite on opposite sides of P. 
however, we conceive one half of the bar, that 
towards A, to have been compressed and to be ex- 
panding again, while the other half, that towards B, 
is being compressed and the distance between the 
plates which hold both parts to be the same, we 
may imagine the plate A B to have been first inclined 
towards A and then towards B so as to raise the 
end A. Then the lines would assume the form shown in fig. 7. 
In this case we see that the slipping takes place in the same direction on both sides 
of P, so that the top plate A B would slip backwards in direction A over the india-rubber, 
while, on the other hand, the india-rubber would slip forwards in the direction D over 
the lower plate. 
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