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VI. On Rolling-Friction. By Professor Osborne Reynolds, of Owens College , 
Manchester. Communicated by Professor B. Stewart, F.R.S. 
Beceived May 24, — Bead June 17, 1875. 
Introduction. 
Although the motion of wheels and rollers over a smooth plane is attended with much 
less resistance or friction than the sliding of one flat surface over another, however 
smooth, yet practically it has been found impossible to get rid of resistance altogether. 
Coulomb made some experiments on the resistance which wooden rollers meet with 
when rolling on a wooden plane, from which experiments he deduced certain laws 
connecting this resistance with the size of the rollers and the force with which they are 
pressed on to the plane. These laws have been verified and extended to other materials 
by Navier and Morin, and are now set forth in many mechanical treatises as “ the laws 
of resistance to rolling .” It does not appear, however, that any systematic investigation 
of this resistance has ever been undertaken or any attempts made to explain its nature. 
When hard surfaces are used it is very small, and it has doubtless been attributed to 
the inaccuracies of the surfaces and to a certain amount of crushing which takes place 
under the roller. On closer examination, however, it appears that these causes, although 
they doubtless explain a great part of the resistance which occurs in ordinary practice, 
are not sufficient to explain the resistance altogether ; and that, if they could be removed, 
there would still be a definite resistance depending on the size and weight of the roller 
and on the nature of the material of which it and the plane are composed. If it were 
not so, a perfectly true roller when rolling on a perfectly true surface ought to experi- 
ence no resistance, however soft the roller and the plane might be, provided both were 
made of perfectly elastic material so that the one did not crush the other ; and we 
might expect, although these conditions are not absolutely fulfilled, that a roller of iron 
would roll as easily on a surface of india-rubber as on one of iron, or that an india-rubber 
roller would experience no more resistance than one of iron when rolling on a true 
plane. Such, however, is not the case. The resistance with india-rubber is very con- 
siderable ; my experiments show it to be ten times as great as with iron. I am not 
aware that this fact has been previously recognized ; and that it has often been over- 
looked is proved by the numerous attempts which have been made to use india-rubber 
tires for wheels, the invariable failure of which may, I think, in the absence of any 
other assigned cause, be fairly attributed to the excessive resistance which attends their 
use. Another fact which I do not think has been hitherto noticed, but of which I have 
had ample evidence, and which clearly shows the existence of some hitherto unexplained 
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