518 
MESSES. ELEEMING JENKIN AND J. A. EWING ON EEICTION 
The greatest and least values of the relative velocity of the sliding surfaces in this 
experiment are determined as follows : — The greatest value of As (Table I.) is 449 six- 
hundredths of a foot, and this distance was passed through by a point in the circum- 
ference of the disk in At, or 0-3571 second. The ratio of the radius of the disk to that 
of the axle is 238’4. Hence the greatest velocity of sliding between the circumference 
of the axle and the bearings is 0-0088 foot per second. The lowest limit of velocity of 
sliding down to which the observation can be said to extend depends, of course, upon 
how near to velocity =0 in the curve shown in fig. 6 the tangent can be drawn by which 
the acceleration is determined. In this case any change in the inclination of the curve 
could certainly be observed down to as low a velocity as that corresponding to As=10. 
This ordinate corresponds to a velocity of sliding of 0-0002 foot per second. Hence the 
above determination of p, extends from a velocity of 0-0088 foot per second, as the higher 
limit, down to 0-0002 foot per second, as the lower limit, and between these two limits 
the value of ^ remains perfectly constant. 
This limit of 0-0002, or one five-thousandth of a foot jper second, as the least relative 
velocity of the sliding surfaces for which the determination of the coefficient of friction 
is definite, is approximately the same for all the experiments that follow. In every case 
the determination of ^ is definite for as low a velocity as this. In some cases it is definite 
for even lower velocities. The higher limit of velocity to which the experiments extend 
varies in different cases, and is stated in each. 
This exceedingly low limit of velocity could only be secured by making the diameter 
of the axle very small. As a result of this, the state of balance of the disk was rarely 
perfect. Although the disk was turned with the greatest care, so as to be truly cylin- 
drical, it proved, when placed in its bearings, to be slightly heavier on one side than on 
the other. This irregularity was easily removed by applying a small counterpoise near 
the periphery ; but we found that the state of balance so produced was not permanent. 
This was, no doubt, due to an almost infinitesimal bending of the axle from time to 
time. Although this irregularity could not be observed by the eye when the disk was 
revolving, it became apparent when the curve corresponding to fig. 6 was drawn, its 
effect on the curve being to introduce an undulation whose period was that of one revo- 
lution of the disk. Of course, if the friction was uniform throughout the movement, 
tangents drawn to the curve at corresponding phases in the successive undulations should 
be parallel. In this way the irregularity due to a want of balance in the disk was 
eliminated, and the friction determined throughout the whole curve. The example 
which has been given above is one of the comparatively rare cases in which the disk 
was for the time being in a state of sensibly perfect balance. 
The cases examined were as follows : — Steel on steel, steel on brass, steel on polished 
agate, steel on greenheart, and steel on beech ; in each case under the three different 
conditions, dry, oiled, and wet with water. The oil made use of was the fine oil employed 
by watchmakers. In order that no trace of unguent might be present when dry or wet 
surfaces were being examined, the oil was removed from the metallic surfaces by washing 
