316 On the Energy expended in Propelling a Bicycle. 
venient for such mechanical problems are the measures based on the second as 
unit of time, the metre as unit of length, and the kilogram as unit of mass. These 
give one metre per second as the unit of velocity, and a Hyper-hectogrammetre as 
the unit of energy. The Hyper-hectogrammetre means the work done in pushing 
against a force of one Hyper-hectogram through a metre, and a Hyper-hectogram, 
which is the unit of force, is the weight of a hectogram increased in the proportion 
of 10 : g (v.e., increased about 2 per cent.), g being gravity at the place of 
observation. 
The second column of Table III., gives the values of = using the swing of the 
pendulum of the chronograph as unit of time, and the next column gives the 
equivalent values when a second is used as unit of time, the swing of the pendulum 
having been determined by independent experiments to be equal to 1:32 seconds. 
It is these latter values that are to be used in formula (1); m, in the same formula 
= 207 pounds or 94 kilograms (see p. 314); v is the velocity in metres per second. 
2 yer-hectogri e : etres dv 
Atenas £2 de (., Hyper-hectogrammetres\ _ OA semn(t Sn — He 
ds per metre per second) ds 
(where for Swe are to use one of the values furnished by the third column of 
‘Table IIL.) 
Hyper-hectogrammetre _-74 of a foot-pound 
Now a a Sa 
—1609 x 4 of a foot-pound _ — 1191 foct-pounds, 
per metre per metre per mile per mile 
ametre 3600 miles 
And ene per second 1609 per hour 
(5 in foot- a a 1609 Shs a 
Hence ds per mule x 3600 © in :) <i, 
T191 per hour ds 
Or (# 5, foot- a) = RNR (Co oe miles \E meararh(o) 
ds per mile per hour ds 
Hence, introducing the values of 2 from Table III., we find— 
TABLE IV. 
32 to 26 =2252xv | On level footpath, in the direction of light wind. 
37 ae Lee | Pees. a. wind. at 4 
tes 46 = 2952 vee On the footpath, without wind. aoe 
47 to 52 ee xv ran good level road, without wind. ia 
the energy being measured in foot-pounds, and v, the velocity, in miles per hour. 
