156 
PEOFESSOE OSBOENE EEYNOLDS ON EO LLIN Gr-FEICTION . 
cause of resistance to rolling, is the tendency which a roller has to oscillate about any 
position in which it may be placed on a flat surface. 
However true and hard the roller and the surface may he, if the roller is but slightly 
disturbed it will not move continuously in one direction until it gradually comes to rest, 
but it will oscillate backwards and forwards through a greater or less angle, depending 
on the softness of the material. These oscillations are not due to the roller having 
settled into a hollow. This is strongly implied by the fact that the more care is taken 
to make the surfaces true and smooth the more regular and apparent do the oscillations 
become. But even if this is not a sufficient proof — if it is impossible to suppose that 
an iron roller on an iron plane can be made so true that when the one is resting on the 
other it will not be able to find some minute irregularities or hollows in which to 
settle — still we must he convinced when we find the same phenomenon existing when 
india-rubber is substituted for iron, and in such a marked degree that no irregularities 
there may be in the surface produce any effect upon it, much less serve to account 
for it. 
These phenomena, with others, have led me to conclude that there is a definite cause 
for the resistance to rolling besides the mere crushing of the surface or accidental 
irregularities of shape, a cause which is connected with the softness of the material as 
well as with the size and weight of the roller. 
Such a force, if its existence be admitted, must either be considered as exhibiting 
some hitherto unrecognized action of matter on matter, or must be supposed to arise 
in some intelligible manner from the known actions. The latter is the most natural 
supposition ; and it is my object in this paper to show that this force arises from what is 
ordinarily known as friction. It is to imply this connexion that I have gone back to 
the name Rolling -Friction in place of the more general title resistance to rolling 
(“resistance au roulement”), which Coulomb and subsequent writers have chosen 
avowedly because they did not wish to imply such a connexion. . 
The assumption that this force is due to friction necessarily implies that there is 
slipping between the roller and the plane at the point of contact ; and on the other 
hand, if it can be shown that there is slipping, it follows as a natural consequence that 
there must be friction or resistance to rolling. Therefore the question as to whether 
the resistance to rolling is due to friction reduces itself into a question as to whether 
there is any evidence of slipping between the roller and the surface on which it 
rolls. 
My attention was first called * to the possibility of such slipping while considering a 
phenomenon in the action of endless belts when used to transmit rotary motion from 
one pulley to another, namely that it is impossible to make the belt tight enough 
entirely to prevent slipping and cause the surfaces of the two pulleys to move with 
identically the same velocity. It appears that this slipping is due to the elasticity of 
the belt, and, since all material is more or less elastic, cannot altogether be prevented. 
* The Engineer, November 27, 1874. 
