PROFESSOR OSBORNE REYNOLDS ON ROLLING-FRICTION. 
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This becomes apparent when we consider that of the two parts of the belt which stretch 
from pulley to pulley the one is tighter and hence more stretched than the other, that 
is, when the belt is transmitting power. For that side which is most stretched, and 
consequently thinner, will have to move faster than the slacker side in order to prevent 
the belt accumulating at one pulley ; and the speed of the driving-pulley will be equal 
to that of the tight side of the belt, while the speed of the following pulley will be 
equal to that of the slack side. This difference of speed requires that the belt shall 
slip over the pulleys ; and this slipping takes place by the expansion and contraction of 
the belt on the pulleys as it passes from the tight side to the slack side, and vice versd. 
With leather belts this slipping is very small ; but with soft india-rubber it becomes so 
great as practically to bar the use of this material for driving-belts. 
The recognition of this slipping at once suggested to me that there must be an 
analogous slipping when a hard roller rolls on a soft surface, or when an india-rubber 
wheel rolls on a hard surface. A single experiment was sufficient to prove that such 
was the case — an iron roller rolled through something like three quarters of an inch 
less in a yard when rolling on india-rubber than when rolling on wood or iron. 
Having made this discovery, I proceeded to investigate the subject, and have obtained 
what I think to be satisfactory evidence that, whatever may be the material of which 
the plane and the roller are composed, the deformation at the point of contact always 
causes slipping, although, owing to the hardness of the materials, it may be far too small 
to be measured. 
In the following paper I shall first show that the deformation at the point of contact 
caused by the weight of the roller must affect the distance rolled through, that it must 
cause slipping, and that this slipping will be attended with friction. I shall then show 
that the friction will itself considerably modify the deformation which would otherwise 
take place, and endeavour to trace the exact nature of the actual deformation. The 
result of my experiments will then be given, together with the description of certain 
other causes of rolling-friction which appear under certain circumstances to exist. In 
conclusion, I shall indicate the direction in which I hope to continue the investigation, 
consider its bearing on the laws discovered by Coulomb, and discuss certain phenomena 
connected with the wear of railway-wheels which have been hitherto unexplained, and 
which serve to illustrate the importance of the subject. 
The Distance Boiled through. 
If a perfectly hard cylinder rolled on a perfectly hard plane and there were no slip- 
ping, then the distance which the cylinder would pass over in one revolution would be 
exactly equal to its circumference ; but if, from the weight of the cylinder or any cause, 
the length of the surface either of the cylinder or the plane underwent an alteration 
near the point of contact, then the distance traversed in one revolution would not be 
equal to the natural length of the circumference. For example, suppose that an iron 
cylinder is rolling on a surface of india-rubber across which lines have been drawn at 
T 2 
