516 
MESSES. ELEEMING JENKIN AND J. A. EWING ON EEICTION 
A single numerical example will suffice to explain the method of calculation by 
which, in each experiment, the acceleration due to friction was deduced from the 
graphic record. The particular case chosen is that of steel rubbing against bearings 
of beech, without any unguent. The curve is a comparatively short one, extending 
over only three complete revolutions of the disk. Column I. Table I. gives the 
distance (measured in six-hundredths of a foot) from a point which corresponds in this 
example to the point P in fig. 5, to the successive points in which the curve crosses the 
central line. Column II. gives the differences between these successive values, or what 
we have called As — that is, the distance moved through by a point in the circumference 
of the disk in times equal to the half-period of the pendulum. 
Table I. 
I. 
II. 
I. 
II. 
I. 
II. 
s 
As 
s 
As 
s 
As 
. feet 
. feet 
. feet 
. feet 
. feet 
. feet 
m 600' 
ln 600’ 
111 600' 
m 600' 
m 600' 
m 600 ‘ 
8 
8 
1533 
163 
5692 
315 
24 
16 
1705 
172 
6021 
329 
49 
25 
1887 
182 
6357 
336 
85 
36 
2077 
190 
6703 
346 
128 
43 
2275 
198 
7054 
351 
183 
55 
2483 
208 
7419 
365 
244 
61 
2701 
218 
7787 
368 
317 
73 
2925 
224 
8173 
386 
397 
80 
3161 
236 
8561 
388 
487 
90 
3402 
241 
8964 
403 
586 
99 
3659 
257 
9368 
404 
694 
108 
3921 
262 
9788 
420 
809 
115 
4195 
274 
10211 
423 
937 
128 
4475 
280 
10648 
437 
1071 
134 
4768 
293 
11093 
445 
1217 
146 
5063 
295 
11542 
449 
1370 
153 
5377 
314 
feet 
s for one revolution = 371 8 
600' 
When the curve is drawn corresponding (in this example) to that shown in fig. 6, the 
irregularities in the successive values of As, which are due to the fact that the central 
line has not been exactly central, disappear, and the curve turns out to be exactly 
straight. Hence between the limits of velocity to which this experiment extends the 
friction is perfectly constant. The tangent of the inclination of the line is measured and 
found to be -01515, by (see fig. 6) being expressed in feet, and bx in terms of the unit 
At. 
To find 
d?s 
dt 25 
the acceleration in the direction of motion of a point in the circum- 
ference of the disk in feet and seconds, we must divide this quantity by (A t) 2 in seconds. 
Throughout all the experiments At was 0*3571 second. Hence for this example 
■ 
