On the Energy expended in Propelling a Bicycle. 315 
lowest position. From twelve to twenty such dots were produced in each experi- 
ment. 
From the record so produced acurve was plotted down on millimetric paper, 
giving the relation between the times (in swings of the chronograph pendulum), 
at which each revolution was completed, and the distances (in circumferences of the 
wheel) traversed by the bicycle. 
A straight ruler being placed to touch this curve at any poimt enabled us to 
read off on the millimetric paper the tangent of its inclination, which was the 
velocity of the bicycle at the corresponding point of its journey. In this way the 
‘velocities at the end of each five revolutions of the wheel were determined, and 
plotted down in a second diagram which gave the relation between v the velocity, 
and s the distance traversed. This second diagram proved to be nearly a straight 
line, the deviations being within the limits of errors of observation; and the 
tangent of its inclination being read off on the millimetric paper furnished the value 
dv 
Oe ) 
twenty-one experiments each of which had to be reduced in this way. 
which is the basis of the calculation which has next to be made. We made 
: d 
The resulting values of = are as follows :— 
TABLE III. 
In Arbitrary In Kinetic 
Measure. Measure. a 
ae level path with light © _.06 —-045 Average of five experiments. 
; ds 
ae levell path’ against light & =| = 09 Average of three experiments. 
: ; dv s : 
C.—On level path without wind. = 018 ='059 | Average of seven experiments. 
ds 
D.—On an ordinary good level dv ; ; : 
ee ot aa 5 Ra 08 =:(064 Average of six experiments. 
We have to deduce from these the energy per mile which would maintain any 
of the several velocities which the bicycle passed through. This is effected by the 
formula 
in which we must use some systematic set of kinetic measures. The most con- 
TRANS, ROY, DUB. SOC., N.S., VOL. I. 3G 
